LMFDB - Embedded newform 403.2.a.e.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(1,403)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("403.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 10x^{5} + 37x^{4} - 33x^{3} - 36x^{2} + 33x - 4 $ x^8 - x^7 - 11x^6 + 10x^5 + 37x^4 - 33x^3 - 36x^2 + 33x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.06827$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.06827 q^{2} +2.49221 q^{3} +2.27774 q^{4} +1.40222 q^{5} +5.15456 q^{6} -5.08294 q^{7} +0.574435 q^{8} +3.21112 q^{9} +2.90017 q^{10} -1.23412 q^{11} +5.67660 q^{12} +1.00000 q^{13} -10.5129 q^{14} +3.49463 q^{15} -3.36739 q^{16} -3.10657 q^{17} +6.64146 q^{18} +4.61601 q^{19} +3.19389 q^{20} -12.6678 q^{21} -2.55250 q^{22} +4.95939 q^{23} +1.43161 q^{24} -3.03378 q^{25} +2.06827 q^{26} +0.526154 q^{27} -11.5776 q^{28} +3.91084 q^{29} +7.22784 q^{30} -1.00000 q^{31} -8.11353 q^{32} -3.07570 q^{33} -6.42521 q^{34} -7.12741 q^{35} +7.31409 q^{36} +5.29904 q^{37} +9.54714 q^{38} +2.49221 q^{39} +0.805485 q^{40} -2.16477 q^{41} -26.2003 q^{42} -5.10691 q^{43} -2.81101 q^{44} +4.50270 q^{45} +10.2574 q^{46} +0.580919 q^{47} -8.39224 q^{48} +18.8363 q^{49} -6.27466 q^{50} -7.74222 q^{51} +2.27774 q^{52} +8.35405 q^{53} +1.08823 q^{54} -1.73051 q^{55} -2.91982 q^{56} +11.5041 q^{57} +8.08866 q^{58} -2.72857 q^{59} +7.95985 q^{60} +11.3881 q^{61} -2.06827 q^{62} -16.3219 q^{63} -10.0462 q^{64} +1.40222 q^{65} -6.36137 q^{66} +10.4734 q^{67} -7.07594 q^{68} +12.3599 q^{69} -14.7414 q^{70} -13.2367 q^{71} +1.84458 q^{72} -2.41248 q^{73} +10.9598 q^{74} -7.56081 q^{75} +10.5140 q^{76} +6.27297 q^{77} +5.15456 q^{78} +8.85793 q^{79} -4.72182 q^{80} -8.32207 q^{81} -4.47733 q^{82} -13.2167 q^{83} -28.8538 q^{84} -4.35609 q^{85} -10.5625 q^{86} +9.74663 q^{87} -0.708924 q^{88} -9.57294 q^{89} +9.31280 q^{90} -5.08294 q^{91} +11.2962 q^{92} -2.49221 q^{93} +1.20150 q^{94} +6.47266 q^{95} -20.2206 q^{96} -3.93065 q^{97} +38.9585 q^{98} -3.96292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9} - 2 q^{10} - 2 q^{11} + 19 q^{12} + 8 q^{13} + 3 q^{14} + 6 q^{15} - 7 q^{16} + 7 q^{17} - 12 q^{18} - 5 q^{19} + 6 q^{20} + 8 q^{21} - 4 q^{22}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9 - 2 * q^10 - 2 * q^11 + 19 * q^12 + 8 * q^13 + 3 * q^14 + 6 * q^15 - 7 * q^16 + 7 * q^17 - 12 * q^18 - 5 * q^19 + 6 * q^20 + 8 * q^21 - 4 * q^22 + 14 * q^23 - 17 * q^24 + 17 * q^25 - q^26 + 7 * q^27 - 9 * q^28 + 12 * q^29 - 9 * q^30 - 8 * q^31 - 21 * q^32 + 10 * q^33 - 12 * q^34 - q^35 + 11 * q^36 + 2 * q^37 + 24 * q^38 + 7 * q^39 - 19 * q^40 + 13 * q^41 - 27 * q^42 - 5 * q^43 + 22 * q^44 + 19 * q^45 + 17 * q^46 + 23 * q^47 + 3 * q^48 + 26 * q^49 - 26 * q^50 + 18 * q^51 + 7 * q^52 + 25 * q^53 - 36 * q^54 - 17 * q^55 + 8 * q^56 - 35 * q^57 - 29 * q^58 - 5 * q^59 + 71 * q^60 - 9 * q^61 + q^62 - 37 * q^63 - 14 * q^64 + 11 * q^65 - 41 * q^66 + 22 * q^67 - 6 * q^68 - 7 * q^69 - 29 * q^70 - 17 * q^71 - 34 * q^72 - 27 * q^73 + 14 * q^74 - 33 * q^75 - 36 * q^76 + 31 * q^77 - 23 * q^79 + 9 * q^80 - 12 * q^81 + 18 * q^82 - 25 * q^83 - 62 * q^84 + 13 * q^85 + 11 * q^86 + 26 * q^87 + 5 * q^88 + 2 * q^89 - 14 * q^90 - 2 * q^91 - 20 * q^92 - 7 * q^93 - 38 * q^94 + 3 * q^95 - 52 * q^96 - 15 * q^97 + 39 * q^98 - 8 * 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 $

$2$	2.06827	1.46249	0.731244	−	0.682116i	$-0.238940\pi$
$2$	2.06827	1.46249	0.731244	+	0.682116i	$0.238940\pi$
$3$	2.49221	1.43888	0.719440	−	0.694555i	$-0.244399\pi$
$3$	2.49221	1.43888	0.719440	+	0.694555i	$0.244399\pi$
$4$	2.27774	1.13887
$5$	1.40222	0.627092	0.313546	−	0.949573i	$-0.398483\pi$
$5$	1.40222	0.627092	0.313546	+	0.949573i	$0.398483\pi$
$6$	5.15456	2.10434
$7$	−5.08294	−1.92117	−0.960585	−	0.277985i	$-0.910333\pi$
$7$	−5.08294	−1.92117	−0.960585	+	0.277985i	$0.910333\pi$
$8$	0.574435	0.203093
$9$	3.21112	1.07037
$10$	2.90017	0.917115
$11$	−1.23412	−0.372102	−0.186051	−	0.982540i	$-0.559569\pi$
$11$	−1.23412	−0.372102	−0.186051	+	0.982540i	$0.559569\pi$
$12$	5.67660	1.63869
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−10.5129	−2.80969
$15$	3.49463	0.902310
$16$	−3.36739	−0.841847
$17$	−3.10657	−0.753453	−0.376726	−	0.926325i	$-0.622950\pi$
$17$	−3.10657	−0.753453	−0.376726	+	0.926325i	$0.622950\pi$
$18$	6.64146	1.56541
$19$	4.61601	1.05898	0.529492	−	0.848315i	$-0.322383\pi$
$19$	4.61601	1.05898	0.529492	+	0.848315i	$0.322383\pi$
$20$	3.19389	0.714176
$21$	−12.6678	−2.76433
$22$	−2.55250	−0.544195
$23$	4.95939	1.03410	0.517052	−	0.855954i	$-0.327029\pi$
$23$	4.95939	1.03410	0.517052	+	0.855954i	$0.327029\pi$
$24$	1.43161	0.292227
$25$	−3.03378	−0.606755
$26$	2.06827	0.405621
$27$	0.526154	0.101258
$28$	−11.5776	−2.18796
$29$	3.91084	0.726224	0.363112	−	0.931745i	$-0.381714\pi$
$29$	3.91084	0.726224	0.363112	+	0.931745i	$0.381714\pi$
$30$	7.22784	1.31962
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−8.11353	−1.43428
$33$	−3.07570	−0.535410
$34$	−6.42521	−1.10192
$35$	−7.12741	−1.20475
$36$	7.31409	1.21901
$37$	5.29904	0.871156	0.435578	−	0.900151i	$-0.356544\pi$
$37$	5.29904	0.871156	0.435578	+	0.900151i	$0.356544\pi$
$38$	9.54714	1.54875
$39$	2.49221	0.399073
$40$	0.805485	0.127358
$41$	−2.16477	−0.338081	−0.169040	−	0.985609i	$-0.554067\pi$
$41$	−2.16477	−0.338081	−0.169040	+	0.985609i	$0.554067\pi$
$42$	−26.2003	−4.04280
$43$	−5.10691	−0.778796	−0.389398	−	0.921070i	$-0.627317\pi$
$43$	−5.10691	−0.778796	−0.389398	+	0.921070i	$0.627317\pi$
$44$	−2.81101	−0.423775
$45$	4.50270	0.671223
$46$	10.2574	1.51236
$47$	0.580919	0.0847357	0.0423678	−	0.999102i	$-0.486510\pi$
$47$	0.580919	0.0847357	0.0423678	+	0.999102i	$0.486510\pi$
$48$	−8.39224	−1.21132
$49$	18.8363	2.69090
$50$	−6.27466	−0.887371
$51$	−7.74222	−1.08413
$52$	2.27774	0.315865
$53$	8.35405	1.14752	0.573758	−	0.819025i	$-0.305485\pi$
$53$	8.35405	1.14752	0.573758	+	0.819025i	$0.305485\pi$
$54$	1.08823	0.148089
$55$	−1.73051	−0.233342
$56$	−2.91982	−0.390177
$57$	11.5041	1.52375
$58$	8.08866	1.06209
$59$	−2.72857	−0.355230	−0.177615	−	0.984100i	$-0.556838\pi$
$59$	−2.72857	−0.355230	−0.177615	+	0.984100i	$0.556838\pi$
$60$	7.95985	1.02761
$61$	11.3881	1.45810	0.729050	−	0.684461i	$-0.239962\pi$
$61$	11.3881	1.45810	0.729050	+	0.684461i	$0.239962\pi$
$62$	−2.06827	−0.262670
$63$	−16.3219	−2.05637
$64$	−10.0462	−1.25577
$65$	1.40222	0.173924
$66$	−6.36137	−0.783030
$67$	10.4734	1.27953	0.639764	−	0.768572i	$-0.279032\pi$
$67$	10.4734	1.27953	0.639764	+	0.768572i	$0.279032\pi$
$68$	−7.07594	−0.858084
$69$	12.3599	1.48795
$70$	−14.7414	−1.76193
$71$	−13.2367	−1.57091	−0.785453	−	0.618922i	$-0.787570\pi$
$71$	−13.2367	−1.57091	−0.785453	+	0.618922i	$0.787570\pi$
$72$	1.84458	0.217386
$73$	−2.41248	−0.282359	−0.141180	−	0.989984i	$-0.545089\pi$
$73$	−2.41248	−0.282359	−0.141180	+	0.989984i	$0.545089\pi$
$74$	10.9598	1.27405
$75$	−7.56081	−0.873047
$76$	10.5140	1.20604
$77$	6.27297	0.714872
$78$	5.15456	0.583640
$79$	8.85793	0.996594	0.498297	−	0.867006i	$-0.333959\pi$
$79$	8.85793	0.996594	0.498297	+	0.867006i	$0.333959\pi$
$80$	−4.72182	−0.527916
$81$	−8.32207	−0.924674
$82$	−4.47733	−0.494439
$83$	−13.2167	−1.45072	−0.725359	−	0.688371i	$-0.758326\pi$
$83$	−13.2167	−1.45072	−0.725359	+	0.688371i	$0.758326\pi$
$84$	−28.8538	−3.14821
$85$	−4.35609	−0.472485
$86$	−10.5625	−1.13898
$87$	9.74663	1.04495
$88$	−0.708924	−0.0755715
$89$	−9.57294	−1.01473	−0.507365	−	0.861731i	$-0.669380\pi$
$89$	−9.57294	−1.01473	−0.507365	+	0.861731i	$0.669380\pi$
$90$	9.31280	0.981655
$91$	−5.08294	−0.532837
$92$	11.2962	1.17771
$93$	−2.49221	−0.258430
$94$	1.20150	0.123925
$95$	6.47266	0.664081
$96$	−20.2206	−2.06376
$97$	−3.93065	−0.399097	−0.199549	−	0.979888i	$-0.563948\pi$
$97$	−3.93065	−0.399097	−0.199549	+	0.979888i	$0.563948\pi$
$98$	38.9585	3.93540
$99$	−3.96292	−0.398288
$100$	−6.91014	−0.691014
$101$	6.42153	0.638966	0.319483	−	0.947592i	$-0.396491\pi$
$101$	6.42153	0.638966	0.319483	+	0.947592i	$0.396491\pi$
$102$	−16.0130	−1.58552
$103$	10.0334	0.988616	0.494308	−	0.869287i	$-0.335422\pi$
$103$	10.0334	0.988616	0.494308	+	0.869287i	$0.335422\pi$
$104$	0.574435	0.0563280
$105$	−17.7630	−1.73349
$106$	17.2784	1.67823
$107$	4.36141	0.421633	0.210816	−	0.977526i	$-0.432388\pi$
$107$	4.36141	0.421633	0.210816	+	0.977526i	$0.432388\pi$
$108$	1.19844	0.115320
$109$	−18.1734	−1.74069	−0.870346	−	0.492441i	$-0.836105\pi$
$109$	−18.1734	−1.74069	−0.870346	+	0.492441i	$0.836105\pi$
$110$	−3.57917	−0.341260
$111$	13.2063	1.25349
$112$	17.1162	1.61733
$113$	17.8202	1.67638	0.838191	−	0.545377i	$-0.183613\pi$
$113$	17.8202	1.67638	0.838191	+	0.545377i	$0.183613\pi$
$114$	23.7935	2.22847
$115$	6.95416	0.648479
$116$	8.90786	0.827074
$117$	3.21112	0.296868
$118$	−5.64342	−0.519519
$119$	15.7905	1.44751
$120$	2.00744	0.183253
$121$	−9.47694	−0.861540
$122$	23.5537	2.13245
$123$	−5.39507	−0.486457
$124$	−2.27774	−0.204547
$125$	−11.2651	−1.00758
$126$	−33.7581	−3.00741
$127$	−8.98356	−0.797162	−0.398581	−	0.917133i	$-0.630497\pi$
$127$	−8.98356	−0.797162	−0.398581	+	0.917133i	$0.630497\pi$
$128$	−4.55117	−0.402270
$129$	−12.7275	−1.12059
$130$	2.90017	0.254362
$131$	−15.1691	−1.32533	−0.662663	−	0.748917i	$-0.730574\pi$
$131$	−15.1691	−1.32533	−0.662663	+	0.748917i	$0.730574\pi$
$132$	−7.00563	−0.609762
$133$	−23.4629	−2.03449
$134$	21.6618	1.87129
$135$	0.737785	0.0634984
$136$	−1.78452	−0.153021
$137$	11.8785	1.01485	0.507423	−	0.861697i	$-0.330598\pi$
$137$	11.8785	1.01485	0.507423	+	0.861697i	$0.330598\pi$
$138$	25.5635	2.17611
$139$	−17.3262	−1.46959	−0.734794	−	0.678291i	$-0.762721\pi$
$139$	−17.3262	−1.46959	−0.734794	+	0.678291i	$0.762721\pi$
$140$	−16.2344	−1.37205
$141$	1.44777	0.121924
$142$	−27.3770	−2.29743
$143$	−1.23412	−0.103203
$144$	−10.8131	−0.901090
$145$	5.48386	0.455410
$146$	−4.98965	−0.412947
$147$	46.9440	3.87188
$148$	12.0698	0.992133
$149$	1.96247	0.160772	0.0803860	−	0.996764i	$-0.474385\pi$
$149$	1.96247	0.160772	0.0803860	+	0.996764i	$0.474385\pi$
$150$	−15.6378	−1.27682
$151$	−12.9291	−1.05216	−0.526079	−	0.850436i	$-0.676338\pi$
$151$	−12.9291	−1.05216	−0.526079	+	0.850436i	$0.676338\pi$
$152$	2.65160	0.215073
$153$	−9.97555	−0.806476
$154$	12.9742	1.04549
$155$	−1.40222	−0.112629
$156$	5.67660	0.454492
$157$	13.8724	1.10714	0.553571	−	0.832802i	$-0.313265\pi$
$157$	13.8724	1.10714	0.553571	+	0.832802i	$0.313265\pi$
$158$	18.3206	1.45751
$159$	20.8201	1.65114
$160$	−11.3770	−0.899429
$161$	−25.2083	−1.98669
$162$	−17.2123	−1.35232
$163$	4.46728	0.349904	0.174952	−	0.984577i	$-0.444023\pi$
$163$	4.46728	0.349904	0.174952	+	0.984577i	$0.444023\pi$
$164$	−4.93078	−0.385029
$165$	−4.31281	−0.335752
$166$	−27.3356	−2.12166
$167$	−1.28629	−0.0995358	−0.0497679	−	0.998761i	$-0.515848\pi$
$167$	−1.28629	−0.0995358	−0.0497679	+	0.998761i	$0.515848\pi$
$168$	−7.27681	−0.561418
$169$	1.00000	0.0769231
$170$	−9.00957	−0.691003
$171$	14.8225	1.13351
$172$	−11.6322	−0.886946
$173$	13.5961	1.03370	0.516848	−	0.856077i	$-0.327105\pi$
$173$	13.5961	1.03370	0.516848	+	0.856077i	$0.327105\pi$
$174$	20.1587	1.52822
$175$	15.4205	1.16568
$176$	4.15577	0.313253
$177$	−6.80018	−0.511133
$178$	−19.7994	−1.48403
$179$	−21.5303	−1.60925	−0.804626	−	0.593782i	$-0.797634\pi$
$179$	−21.5303	−1.60925	−0.804626	+	0.593782i	$0.797634\pi$
$180$	10.2560	0.764435
$181$	10.5515	0.784287	0.392144	−	0.919904i	$-0.371734\pi$
$181$	10.5515	0.784287	0.392144	+	0.919904i	$0.371734\pi$
$182$	−10.5129	−0.779267
$183$	28.3816	2.09803
$184$	2.84885	0.210020
$185$	7.43042	0.546296
$186$	−5.15456	−0.377951
$187$	3.83389	0.280361
$188$	1.32318	0.0965028
$189$	−2.67441	−0.194535
$190$	13.3872	0.971210
$191$	23.8427	1.72520	0.862600	−	0.505886i	$-0.168834\pi$
$191$	23.8427	1.72520	0.862600	+	0.505886i	$0.168834\pi$
$192$	−25.0373	−1.80691
$193$	−9.50125	−0.683915	−0.341957	−	0.939715i	$-0.611090\pi$
$193$	−9.50125	−0.683915	−0.341957	+	0.939715i	$0.611090\pi$
$194$	−8.12965	−0.583675
$195$	3.49463	0.250256
$196$	42.9041	3.06458
$197$	−4.01663	−0.286173	−0.143086	−	0.989710i	$-0.545703\pi$
$197$	−4.01663	−0.286173	−0.143086	+	0.989710i	$0.545703\pi$
$198$	−8.19638	−0.582491
$199$	−8.66785	−0.614448	−0.307224	−	0.951637i	$-0.599400\pi$
$199$	−8.66785	−0.614448	−0.307224	+	0.951637i	$0.599400\pi$
$200$	−1.74271	−0.123228
$201$	26.1019	1.84109
$202$	13.2814	0.934479
$203$	−19.8786	−1.39520
$204$	−17.6347	−1.23468
$205$	−3.03549	−0.212008
$206$	20.7517	1.44584
$207$	15.9252	1.10688
$208$	−3.36739	−0.233486
$209$	−5.69672	−0.394050
$210$	−36.7387	−2.53521
$211$	−11.0894	−0.763428	−0.381714	−	0.924281i	$-0.624666\pi$
$211$	−11.0894	−0.763428	−0.381714	+	0.924281i	$0.624666\pi$
$212$	19.0283	1.30687
$213$	−32.9886	−2.26034
$214$	9.02056	0.616633
$215$	−7.16101	−0.488377
$216$	0.302242	0.0205649
$217$	5.08294	0.345052
$218$	−37.5874	−2.54574
$219$	−6.01241	−0.406281
$220$	−3.94166	−0.265746
$221$	−3.10657	−0.208970
$222$	27.3142	1.83321
$223$	15.0820	1.00996	0.504982	−	0.863130i	$-0.331499\pi$
$223$	15.0820	1.00996	0.504982	+	0.863130i	$0.331499\pi$
$224$	41.2406	2.75550
$225$	−9.74182	−0.649454
$226$	36.8569	2.45169
$227$	10.1692	0.674955	0.337478	−	0.941334i	$-0.390426\pi$
$227$	10.1692	0.674955	0.337478	+	0.941334i	$0.390426\pi$
$228$	26.2032	1.73535
$229$	−17.4637	−1.15403	−0.577016	−	0.816733i	$-0.695783\pi$
$229$	−17.4637	−1.15403	−0.577016	+	0.816733i	$0.695783\pi$
$230$	14.3831	0.948392
$231$	15.6336	1.02861
$232$	2.24652	0.147491
$233$	17.7783	1.16470	0.582348	−	0.812939i	$-0.302134\pi$
$233$	17.7783	1.16470	0.582348	+	0.812939i	$0.302134\pi$
$234$	6.64146	0.434166
$235$	0.814576	0.0531371
$236$	−6.21497	−0.404560
$237$	22.0758	1.43398
$238$	32.6590	2.11697
$239$	22.3470	1.44551	0.722754	−	0.691106i	$-0.242876\pi$
$239$	22.3470	1.44551	0.722754	+	0.691106i	$0.242876\pi$
$240$	−11.7678	−0.759607
$241$	28.1284	1.81191	0.905956	−	0.423372i	$-0.139154\pi$
$241$	28.1284	1.81191	0.905956	+	0.423372i	$0.139154\pi$
$242$	−19.6009	−1.25999
$243$	−22.3188	−1.43175
$244$	25.9391	1.66058
$245$	26.4126	1.68744
$246$	−11.1585	−0.711437
$247$	4.61601	0.293709
$248$	−0.574435	−0.0364767
$249$	−32.9388	−2.08741
$250$	−23.2993	−1.47358
$251$	−8.68486	−0.548184	−0.274092	−	0.961704i	$-0.588377\pi$
$251$	−8.68486	−0.548184	−0.274092	+	0.961704i	$0.588377\pi$
$252$	−37.1771	−2.34193
$253$	−6.12050	−0.384792
$254$	−18.5804	−1.16584
$255$	−10.8563	−0.679848
$256$	10.6793	0.667459
$257$	19.3837	1.20912	0.604560	−	0.796560i	$-0.293349\pi$
$257$	19.3837	1.20912	0.604560	+	0.796560i	$0.293349\pi$
$258$	−26.3239	−1.63885
$259$	−26.9347	−1.67364
$260$	3.19389	0.198077
$261$	12.5582	0.777331
$262$	−31.3737	−1.93827
$263$	−23.4756	−1.44757	−0.723785	−	0.690026i	$-0.757599\pi$
$263$	−23.4756	−1.44757	−0.723785	+	0.690026i	$0.757599\pi$
$264$	−1.76679	−0.108738
$265$	11.7142	0.719599
$266$	−48.5276	−2.97542
$267$	−23.8578	−1.46007
$268$	23.8556	1.45721
$269$	13.8442	0.844094	0.422047	−	0.906574i	$-0.361312\pi$
$269$	13.8442	0.844094	0.422047	+	0.906574i	$0.361312\pi$
$270$	1.52594	0.0928656
$271$	−4.53604	−0.275545	−0.137772	−	0.990464i	$-0.543994\pi$
$271$	−4.53604	−0.275545	−0.137772	+	0.990464i	$0.543994\pi$
$272$	10.4610	0.634292
$273$	−12.6678	−0.766688
$274$	24.5679	1.48420
$275$	3.74405	0.225775
$276$	28.1525	1.69458
$277$	−22.4922	−1.35142	−0.675711	−	0.737166i	$-0.736163\pi$
$277$	−22.4922	−1.35142	−0.675711	+	0.737166i	$0.736163\pi$
$278$	−35.8352	−2.14925
$279$	−3.21112	−0.192245
$280$	−4.09423	−0.244677
$281$	2.89001	0.172404	0.0862019	−	0.996278i	$-0.472527\pi$
$281$	2.89001	0.172404	0.0862019	+	0.996278i	$0.472527\pi$
$282$	2.99438	0.178313
$283$	14.5126	0.862686	0.431343	−	0.902188i	$-0.358040\pi$
$283$	14.5126	0.862686	0.431343	+	0.902188i	$0.358040\pi$
$284$	−30.1497	−1.78905
$285$	16.1312	0.955532
$286$	−2.55250	−0.150932
$287$	11.0034	0.649511
$288$	−26.0535	−1.53522
$289$	−7.34925	−0.432309
$290$	11.3421	0.666031
$291$	−9.79602	−0.574253
$292$	−5.49499	−0.321570
$293$	−2.22962	−0.130256	−0.0651279	−	0.997877i	$-0.520746\pi$
$293$	−2.22962	−0.130256	−0.0651279	+	0.997877i	$0.520746\pi$
$294$	97.0928	5.66257
$295$	−3.82606	−0.222762
$296$	3.04395	0.176926
$297$	−0.649339	−0.0376785
$298$	4.05892	0.235127
$299$	4.95939	0.286809
$300$	−17.2215	−0.994286
$301$	25.9581	1.49620
$302$	−26.7409	−1.53877
$303$	16.0038	0.919394
$304$	−15.5439	−0.891503
$305$	15.9687	0.914363
$306$	−20.6321	−1.17946
$307$	−9.02308	−0.514974	−0.257487	−	0.966282i	$-0.582895\pi$
$307$	−9.02308	−0.514974	−0.257487	+	0.966282i	$0.582895\pi$
$308$	14.2882	0.814145
$309$	25.0052	1.42250
$310$	−2.90017	−0.164719
$311$	16.4063	0.930314	0.465157	−	0.885228i	$-0.345998\pi$
$311$	16.4063	0.930314	0.465157	+	0.885228i	$0.345998\pi$
$312$	1.43161	0.0810492
$313$	−16.5955	−0.938033	−0.469016	−	0.883190i	$-0.655391\pi$
$313$	−16.5955	−0.938033	−0.469016	+	0.883190i	$0.655391\pi$
$314$	28.6919	1.61918
$315$	−22.8870	−1.28953
$316$	20.1760	1.13499
$317$	10.7896	0.606006	0.303003	−	0.952990i	$-0.402011\pi$
$317$	10.7896	0.606006	0.303003	+	0.952990i	$0.402011\pi$
$318$	43.0615	2.41477
$319$	−4.82646	−0.270230
$320$	−14.0870	−0.787487
$321$	10.8695	0.606679
$322$	−52.1375	−2.90551
$323$	−14.3399	−0.797895
$324$	−18.9555	−1.05308
$325$	−3.03378	−0.168284
$326$	9.23954	0.511731
$327$	−45.2918	−2.50464
$328$	−1.24352	−0.0686620
$329$	−2.95277	−0.162792
$330$	−8.92005	−0.491032
$331$	−30.0641	−1.65247	−0.826237	−	0.563323i	$-0.809523\pi$
$331$	−30.0641	−1.65247	−0.826237	+	0.563323i	$0.809523\pi$
$332$	−30.1041	−1.65218
$333$	17.0158	0.932462
$334$	−2.66039	−0.145570
$335$	14.6860	0.802382
$336$	42.6573	2.32715
$337$	12.6264	0.687803	0.343901	−	0.939006i	$-0.388251\pi$
$337$	12.6264	0.687803	0.343901	+	0.939006i	$0.388251\pi$
$338$	2.06827	0.112499
$339$	44.4117	2.41211
$340$	−9.92203	−0.538098
$341$	1.23412	0.0668315
$342$	30.6570	1.65774
$343$	−60.1631	−3.24850
$344$	−2.93359	−0.158168
$345$	17.3312	0.933083
$346$	28.1205	1.51177
$347$	21.0200	1.12841	0.564205	−	0.825634i	$-0.309183\pi$
$347$	21.0200	1.12841	0.564205	+	0.825634i	$0.309183\pi$
$348$	22.2003	1.19006
$349$	36.0315	1.92872	0.964360	−	0.264595i	$-0.0852381\pi$
$349$	36.0315	1.92872	0.964360	+	0.264595i	$0.0852381\pi$
$350$	31.8937	1.70479
$351$	0.526154	0.0280840
$352$	10.0131	0.533700
$353$	4.15309	0.221047	0.110523	−	0.993874i	$-0.464747\pi$
$353$	4.15309	0.221047	0.110523	+	0.993874i	$0.464747\pi$
$354$	−14.0646	−0.747525
$355$	−18.5608	−0.985103
$356$	−21.8047	−1.15564
$357$	39.3532	2.08279
$358$	−44.5305	−2.35351
$359$	14.4341	0.761803	0.380902	−	0.924616i	$-0.375614\pi$
$359$	14.4341	0.761803	0.380902	+	0.924616i	$0.375614\pi$
$360$	2.58651	0.136321
$361$	2.30751	0.121448
$362$	21.8234	1.14701
$363$	−23.6185	−1.23965
$364$	−11.5776	−0.606831
$365$	−3.38283	−0.177065
$366$	58.7008	3.06834
$367$	−25.5117	−1.33170	−0.665851	−	0.746085i	$-0.731931\pi$
$367$	−25.5117	−1.33170	−0.665851	+	0.746085i	$0.731931\pi$
$368$	−16.7002	−0.870558
$369$	−6.95134	−0.361872
$370$	15.3681	0.798950
$371$	−42.4631	−2.20458
$372$	−5.67660	−0.294318
$373$	−32.3294	−1.67395	−0.836977	−	0.547237i	$-0.815679\pi$
$373$	−32.3294	−1.67395	−0.836977	+	0.547237i	$0.815679\pi$
$374$	7.92951	0.410025
$375$	−28.0751	−1.44979
$376$	0.333700	0.0172093
$377$	3.91084	0.201418
$378$	−5.53140	−0.284505
$379$	33.0364	1.69696	0.848482	−	0.529224i	$-0.177517\pi$
$379$	33.0364	1.69696	0.848482	+	0.529224i	$0.177517\pi$
$380$	14.7430	0.756301
$381$	−22.3889	−1.14702
$382$	49.3132	2.52308
$383$	2.91525	0.148962	0.0744811	−	0.997222i	$-0.476270\pi$
$383$	2.91525	0.148962	0.0744811	+	0.997222i	$0.476270\pi$
$384$	−11.3425	−0.578819
$385$	8.79610	0.448291
$386$	−19.6511	−1.00022
$387$	−16.3989	−0.833602
$388$	−8.95300	−0.454520
$389$	−37.0538	−1.87870	−0.939350	−	0.342959i	$-0.888571\pi$
$389$	−37.0538	−1.87870	−0.939350	+	0.342959i	$0.888571\pi$
$390$	7.22784	0.365996
$391$	−15.4067	−0.779149
$392$	10.8202	0.546504
$393$	−37.8045	−1.90698
$394$	−8.30747	−0.418524
$395$	12.4208	0.624957
$396$	−9.02648	−0.453598
$397$	−17.7693	−0.891815	−0.445908	−	0.895079i	$-0.647119\pi$
$397$	−17.7693	−0.891815	−0.445908	+	0.895079i	$0.647119\pi$
$398$	−17.9274	−0.898622
$399$	−58.4745	−2.92738
$400$	10.2159	0.510795
$401$	0.00964957	0.000481877 0	0.000240938	−	1.00000i	$-0.499923\pi$
$401$	0.00964957	0.000481877 0	0.000240938		1.00000i	$0.499923\pi$
$402$	53.9857	2.69256
$403$	−1.00000	−0.0498135
$404$	14.6265	0.727698
$405$	−11.6694	−0.579856
$406$	−41.1142	−2.04046
$407$	−6.53966	−0.324159
$408$	−4.44740	−0.220179
$409$	−14.2434	−0.704292	−0.352146	−	0.935945i	$-0.614548\pi$
$409$	−14.2434	−0.704292	−0.352146	+	0.935945i	$0.614548\pi$
$410$	−6.27821	−0.310059
$411$	29.6036	1.46024
$412$	22.8533	1.12590
$413$	13.8692	0.682457
$414$	32.9376	1.61879
$415$	−18.5327	−0.909735
$416$	−8.11353	−0.397799
$417$	−43.1805	−2.11456
$418$	−11.7823	−0.576294
$419$	−24.9388	−1.21834	−0.609170	−	0.793040i	$-0.708497\pi$
$419$	−24.9388	−1.21834	−0.609170	+	0.793040i	$0.708497\pi$
$420$	−40.4595	−1.97422
$421$	−24.6283	−1.20031	−0.600156	−	0.799883i	$-0.704895\pi$
$421$	−24.6283	−1.20031	−0.600156	+	0.799883i	$0.704895\pi$
$422$	−22.9359	−1.11650
$423$	1.86540	0.0906988
$424$	4.79886	0.233053
$425$	9.42462	0.457161
$426$	−68.2293	−3.30572
$427$	−57.8851	−2.80126
$428$	9.93413	0.480185
$429$	−3.07570	−0.148496
$430$	−14.8109	−0.714245
$431$	−25.2766	−1.21753	−0.608765	−	0.793350i	$-0.708335\pi$
$431$	−25.2766	−1.21753	−0.608765	+	0.793350i	$0.708335\pi$
$432$	−1.77177	−0.0852441
$433$	−1.41387	−0.0679462	−0.0339731	−	0.999423i	$-0.510816\pi$
$433$	−1.41387	−0.0679462	−0.0339731	+	0.999423i	$0.510816\pi$
$434$	10.5129	0.504635
$435$	13.6669	0.655280
$436$	−41.3941	−1.98242
$437$	22.8926	1.09510
$438$	−12.4353	−0.594180
$439$	17.0469	0.813603	0.406801	−	0.913517i	$-0.366644\pi$
$439$	17.0469	0.813603	0.406801	+	0.913517i	$0.366644\pi$
$440$	−0.994068	−0.0473903
$441$	60.4856	2.88026
$442$	−6.42521	−0.305616
$443$	−19.8664	−0.943881	−0.471941	−	0.881630i	$-0.656446\pi$
$443$	−19.8664	−0.943881	−0.471941	+	0.881630i	$0.656446\pi$
$444$	30.0805	1.42756
$445$	−13.4234	−0.636330
$446$	31.1936	1.47706
$447$	4.89090	0.231332
$448$	51.0642	2.41256
$449$	1.43495	0.0677194	0.0338597	−	0.999427i	$-0.489220\pi$
$449$	1.43495	0.0677194	0.0338597	+	0.999427i	$0.489220\pi$
$450$	−20.1487	−0.949819
$451$	2.67160	0.125801
$452$	40.5897	1.90918
$453$	−32.2221	−1.51393
$454$	21.0327	0.987114
$455$	−7.12741	−0.334138
$456$	6.60834	0.309464
$457$	−11.6862	−0.546658	−0.273329	−	0.961921i	$-0.588125\pi$
$457$	−11.6862	−0.546658	−0.273329	+	0.961921i	$0.588125\pi$
$458$	−36.1196	−1.68776
$459$	−1.63453	−0.0762935
$460$	15.8398	0.738532
$461$	2.54808	0.118676	0.0593379	−	0.998238i	$-0.481101\pi$
$461$	2.54808	0.118676	0.0593379	+	0.998238i	$0.481101\pi$
$462$	32.3345	1.50433
$463$	0.705973	0.0328093	0.0164047	−	0.999865i	$-0.494778\pi$
$463$	0.705973	0.0328093	0.0164047	+	0.999865i	$0.494778\pi$
$464$	−13.1693	−0.611370
$465$	−3.49463	−0.162060
$466$	36.7703	1.70335
$467$	29.4937	1.36481	0.682404	−	0.730976i	$-0.260935\pi$
$467$	29.4937	1.36481	0.682404	+	0.730976i	$0.260935\pi$
$468$	7.31409	0.338094
$469$	−53.2356	−2.45819
$470$	1.68476	0.0777123
$471$	34.5731	1.59304
$472$	−1.56739	−0.0721449
$473$	6.30255	0.289792
$474$	45.6587	2.09718
$475$	−14.0039	−0.642544
$476$	35.9666	1.64853
$477$	26.8258	1.22827
$478$	46.2196	2.11404
$479$	8.27756	0.378211	0.189106	−	0.981957i	$-0.439441\pi$
$479$	8.27756	0.378211	0.189106	+	0.981957i	$0.439441\pi$
$480$	−28.3538	−1.29417
$481$	5.29904	0.241615
$482$	58.1772	2.64990
$483$	−62.8244	−2.85861
$484$	−21.5860	−0.981181
$485$	−5.51165	−0.250271
$486$	−46.1613	−2.09392
$487$	−4.17136	−0.189022	−0.0945112	−	0.995524i	$-0.530129\pi$
$487$	−4.17136	−0.189022	−0.0945112	+	0.995524i	$0.530129\pi$
$488$	6.54174	0.296131
$489$	11.1334	0.503470
$490$	54.6284	2.46786
$491$	−20.2384	−0.913344	−0.456672	−	0.889635i	$-0.650959\pi$
$491$	−20.2384	−0.913344	−0.456672	+	0.889635i	$0.650959\pi$
$492$	−12.2886	−0.554011
$493$	−12.1493	−0.547176
$494$	9.54714	0.429546
$495$	−5.55689	−0.249763
$496$	3.36739	0.151200
$497$	67.2813	3.01798
$498$	−68.1262	−3.05281
$499$	18.9530	0.848451	0.424226	−	0.905557i	$-0.360546\pi$
$499$	18.9530	0.848451	0.424226	+	0.905557i	$0.360546\pi$
$500$	−25.6590	−1.14751
$501$	−3.20570	−0.143220
$502$	−17.9626	−0.801712
$503$	8.31233	0.370628	0.185314	−	0.982679i	$-0.440670\pi$
$503$	8.31233	0.370628	0.185314	+	0.982679i	$0.440670\pi$
$504$	−9.37589	−0.417635
$505$	9.00440	0.400691
$506$	−12.6588	−0.562754
$507$	2.49221	0.110683
$508$	−20.4622	−0.907863
$509$	6.31125	0.279741	0.139871	−	0.990170i	$-0.455331\pi$
$509$	6.31125	0.279741	0.139871	+	0.990170i	$0.455331\pi$
$510$	−22.4538	−0.994269
$511$	12.2625	0.542460
$512$	31.1901	1.37842
$513$	2.42873	0.107231
$514$	40.0906	1.76832
$515$	14.0690	0.619953
$516$	−28.9899	−1.27621
$517$	−0.716925	−0.0315303
$518$	−55.7082	−2.44768
$519$	33.8845	1.48736
$520$	0.805485	0.0353229
$521$	28.2621	1.23818	0.619092	−	0.785319i	$-0.287501\pi$
$521$	28.2621	1.23818	0.619092	+	0.785319i	$0.287501\pi$
$522$	25.9737	1.13684
$523$	17.9657	0.785586	0.392793	−	0.919627i	$-0.371509\pi$
$523$	17.9657	0.785586	0.392793	+	0.919627i	$0.371509\pi$
$524$	−34.5511	−1.50937
$525$	38.4312	1.67727
$526$	−48.5539	−2.11705
$527$	3.10657	0.135324
$528$	10.3571	0.450733
$529$	1.59556	0.0693720
$530$	24.2282	1.05240
$531$	−8.76177	−0.380229
$532$	−53.4423	−2.31702
$533$	−2.16477	−0.0937667
$534$	−49.3444	−2.13534
$535$	6.11566	0.264403
$536$	6.01628	0.259864
$537$	−53.6581	−2.31552
$538$	28.6335	1.23448
$539$	−23.2463	−1.00129
$540$	1.68048	0.0723164
$541$	−3.38963	−0.145731	−0.0728657	−	0.997342i	$-0.523214\pi$
$541$	−3.38963	−0.145731	−0.0728657	+	0.997342i	$0.523214\pi$
$542$	−9.38175	−0.402980
$543$	26.2966	1.12849
$544$	25.2052	1.08067
$545$	−25.4831	−1.09157
$546$	−26.2003	−1.12127
$547$	7.25141	0.310048	0.155024	−	0.987911i	$-0.450455\pi$
$547$	7.25141	0.310048	0.155024	+	0.987911i	$0.450455\pi$
$548$	27.0560	1.15578
$549$	36.5686	1.56071
$550$	7.74371	0.330193
$551$	18.0524	0.769060
$552$	7.09993	0.302193
$553$	−45.0243	−1.91463
$554$	−46.5198	−1.97644
$555$	18.5182	0.786053
$556$	−39.4645	−1.67367
$557$	36.4362	1.54385	0.771926	−	0.635713i	$-0.219294\pi$
$557$	36.4362	1.54385	0.771926	+	0.635713i	$0.219294\pi$
$558$	−6.64146	−0.281155
$559$	−5.10691	−0.215999
$560$	24.0007	1.01422
$561$	9.55485	0.403406
$562$	5.97733	0.252138
$563$	−37.0802	−1.56274	−0.781371	−	0.624066i	$-0.785479\pi$
$563$	−37.0802	−1.56274	−0.781371	+	0.624066i	$0.785479\pi$
$564$	3.29764	0.138856
$565$	24.9878	1.05125
$566$	30.0160	1.26167
$567$	42.3006	1.77646
$568$	−7.60361	−0.319041
$569$	18.5586	0.778016	0.389008	−	0.921234i	$-0.372818\pi$
$569$	18.5586	0.778016	0.389008	+	0.921234i	$0.372818\pi$
$570$	33.3638	1.39745
$571$	−26.3452	−1.10251	−0.551256	−	0.834336i	$-0.685851\pi$
$571$	−26.3452	−1.10251	−0.551256	+	0.834336i	$0.685851\pi$
$572$	−2.81101	−0.117534
$573$	59.4212	2.48235
$574$	22.7580	0.949901
$575$	−15.0457	−0.627448
$576$	−32.2595	−1.34415
$577$	18.5901	0.773917	0.386958	−	0.922097i	$-0.373526\pi$
$577$	18.5901	0.773917	0.386958	+	0.922097i	$0.373526\pi$
$578$	−15.2002	−0.632246
$579$	−23.6791	−0.984071
$580$	12.4908	0.518652
$581$	67.1796	2.78708
$582$	−20.2608	−0.839838
$583$	−10.3099	−0.426993
$584$	−1.38581	−0.0573453
$585$	4.50270	0.186164
$586$	−4.61145	−0.190497
$587$	6.48087	0.267494	0.133747	−	0.991016i	$-0.457299\pi$
$587$	6.48087	0.267494	0.133747	+	0.991016i	$0.457299\pi$
$588$	106.926	4.40956
$589$	−4.61601	−0.190199
$590$	−7.91333	−0.325786
$591$	−10.0103	−0.411768
$592$	−17.8439	−0.733380
$593$	−14.0976	−0.578919	−0.289459	−	0.957190i	$-0.593476\pi$
$593$	−14.0976	−0.578919	−0.289459	+	0.957190i	$0.593476\pi$
$594$	−1.34301	−0.0551043
$595$	22.1418	0.907724
$596$	4.47000	0.183098
$597$	−21.6021	−0.884116
$598$	10.2574	0.419454
$599$	7.19207	0.293860	0.146930	−	0.989147i	$-0.453061\pi$
$599$	7.19207	0.293860	0.146930	+	0.989147i	$0.453061\pi$
$600$	−4.34320	−0.177310
$601$	15.6706	0.639218	0.319609	−	0.947550i	$-0.396448\pi$
$601$	15.6706	0.639218	0.319609	+	0.947550i	$0.396448\pi$
$602$	53.6883	2.18817
$603$	33.6313	1.36957
$604$	−29.4492	−1.19827
$605$	−13.2888	−0.540265
$606$	33.1002	1.34460
$607$	−9.22389	−0.374386	−0.187193	−	0.982323i	$-0.559939\pi$
$607$	−9.22389	−0.374386	−0.187193	+	0.982323i	$0.559939\pi$
$608$	−37.4521	−1.51888
$609$	−49.5416	−2.00753
$610$	33.0275	1.33724
$611$	0.580919	0.0235014
$612$	−22.7217	−0.918470
$613$	−16.1636	−0.652840	−0.326420	−	0.945225i	$-0.605842\pi$
$613$	−16.1636	−0.652840	−0.326420	+	0.945225i	$0.605842\pi$
$614$	−18.6622	−0.753144
$615$	−7.56508	−0.305054
$616$	3.60342	0.145186
$617$	35.7302	1.43844	0.719221	−	0.694781i	$-0.244499\pi$
$617$	35.7302	1.43844	0.719221	+	0.694781i	$0.244499\pi$
$618$	51.7176	2.08039
$619$	−27.9621	−1.12389	−0.561945	−	0.827175i	$-0.689947\pi$
$619$	−27.9621	−1.12389	−0.561945	+	0.827175i	$0.689947\pi$
$620$	−3.19389	−0.128270
$621$	2.60941	0.104712
$622$	33.9326	1.36057
$623$	48.6587	1.94947
$624$	−8.39224	−0.335959
$625$	−0.627330	−0.0250932
$626$	−34.3239	−1.37186
$627$	−14.1974	−0.566991
$628$	31.5978	1.26089
$629$	−16.4618	−0.656375
$630$	−47.3364	−1.88593
$631$	−6.54015	−0.260359	−0.130180	−	0.991490i	$-0.541555\pi$
$631$	−6.54015	−0.260359	−0.130180	+	0.991490i	$0.541555\pi$
$632$	5.08830	0.202402
$633$	−27.6372	−1.09848
$634$	22.3159	0.886276
$635$	−12.5969	−0.499894
$636$	47.4226	1.88043
$637$	18.8363	0.746321
$638$	−9.98241	−0.395207
$639$	−42.5046	−1.68145
$640$	−6.38175	−0.252261
$641$	−13.0835	−0.516767	−0.258383	−	0.966042i	$-0.583190\pi$
$641$	−13.0835	−0.516767	−0.258383	+	0.966042i	$0.583190\pi$
$642$	22.4811	0.887260
$643$	35.0881	1.38374	0.691869	−	0.722023i	$-0.256788\pi$
$643$	35.0881	1.38374	0.691869	+	0.722023i	$0.256788\pi$
$644$	−57.4179	−2.26258
$645$	−17.8468	−0.702715
$646$	−29.6588	−1.16691
$647$	11.1234	0.437307	0.218653	−	0.975803i	$-0.429834\pi$
$647$	11.1234	0.437307	0.218653	+	0.975803i	$0.429834\pi$
$648$	−4.78049	−0.187795
$649$	3.36739	0.132182
$650$	−6.27466	−0.246113
$651$	12.6678	0.496489
$652$	10.1753	0.398495
$653$	42.4232	1.66015	0.830075	−	0.557652i	$-0.188298\pi$
$653$	42.4232	1.66015	0.830075	+	0.557652i	$0.188298\pi$
$654$	−93.6757	−3.66301
$655$	−21.2704	−0.831102
$656$	7.28963	0.284612
$657$	−7.74675	−0.302230
$658$	−6.10713	−0.238081
$659$	−42.6807	−1.66261	−0.831303	−	0.555820i	$-0.812404\pi$
$659$	−42.6807	−1.66261	−0.831303	+	0.555820i	$0.812404\pi$
$660$	−9.82344	−0.382377
$661$	23.2735	0.905234	0.452617	−	0.891705i	$-0.350490\pi$
$661$	23.2735	0.905234	0.452617	+	0.891705i	$0.350490\pi$
$662$	−62.1807	−2.41672
$663$	−7.74222	−0.300683
$664$	−7.59212	−0.294631
$665$	−32.9002	−1.27581
$666$	35.1933	1.36371
$667$	19.3954	0.750992
$668$	−2.92982	−0.113358
$669$	37.5875	1.45322
$670$	30.3746	1.17347
$671$	−14.0543	−0.542562
$672$	102.780	3.96484
$673$	26.1090	1.00643	0.503213	−	0.864162i	$-0.332151\pi$
$673$	26.1090	1.00643	0.503213	+	0.864162i	$0.332151\pi$
$674$	26.1148	1.00590
$675$	−1.59623	−0.0614391
$676$	2.27774	0.0876053
$677$	22.9892	0.883549	0.441774	−	0.897126i	$-0.354349\pi$
$677$	22.9892	0.883549	0.441774	+	0.897126i	$0.354349\pi$
$678$	91.8553	3.52768
$679$	19.9793	0.766734
$680$	−2.50229	−0.0959586
$681$	25.3439	0.971179
$682$	2.55250	0.0977402
$683$	−14.5488	−0.556693	−0.278346	−	0.960481i	$-0.589786\pi$
$683$	−14.5488	−0.556693	−0.278346	+	0.960481i	$0.589786\pi$
$684$	33.7619	1.29092
$685$	16.6562	0.636402
$686$	−124.434	−4.75089
$687$	−43.5232	−1.66051
$688$	17.1969	0.655627
$689$	8.35405	0.318264
$690$	35.8457	1.36462
$691$	−5.62509	−0.213989	−0.106994	−	0.994260i	$-0.534123\pi$
$691$	−5.62509	−0.213989	−0.106994	+	0.994260i	$0.534123\pi$
$692$	30.9684	1.17724
$693$	20.1433	0.765180
$694$	43.4749	1.65029
$695$	−24.2951	−0.921567
$696$	5.59881	0.212222
$697$	6.72501	0.254728
$698$	74.5227	2.82073
$699$	44.3073	1.67586
$700$	35.1238	1.32756
$701$	−36.3247	−1.37196	−0.685982	−	0.727619i	$-0.740627\pi$
$701$	−36.3247	−1.37196	−0.685982	+	0.727619i	$0.740627\pi$
$702$	1.08823	0.0410726
$703$	24.4604	0.922541
$704$	12.3982	0.467276
$705$	2.03010	0.0764579
$706$	8.58972	0.323278
$707$	−32.6402	−1.22756
$708$	−15.4890	−0.582113
$709$	−9.63978	−0.362030	−0.181015	−	0.983480i	$-0.557938\pi$
$709$	−9.63978	−0.362030	−0.181015	+	0.983480i	$0.557938\pi$
$710$	−38.3886	−1.44070
$711$	28.4439	1.06673
$712$	−5.49904	−0.206085
$713$	−4.95939	−0.185731
$714$	81.3931	3.04606
$715$	−1.73051	−0.0647175
$716$	−49.0404	−1.83273
$717$	55.6935	2.07991
$718$	29.8536	1.11413
$719$	29.9288	1.11616	0.558078	−	0.829789i	$-0.311539\pi$
$719$	29.9288	1.11616	0.558078	+	0.829789i	$0.311539\pi$
$720$	−15.1623	−0.565067
$721$	−50.9989	−1.89930
$722$	4.77255	0.177616
$723$	70.1020	2.60712
$724$	24.0336	0.893200
$725$	−11.8646	−0.440640
$726$	−48.8495	−1.81297
$727$	−11.8942	−0.441133	−0.220567	−	0.975372i	$-0.570791\pi$
$727$	−11.8942	−0.441133	−0.220567	+	0.975372i	$0.570791\pi$
$728$	−2.91982	−0.108216
$729$	−30.6570	−1.13545
$730$	−6.99660	−0.258956
$731$	15.8649	0.586786
$732$	64.6459	2.38938
$733$	−4.28020	−0.158093	−0.0790464	−	0.996871i	$-0.525188\pi$
$733$	−4.28020	−0.158093	−0.0790464	+	0.996871i	$0.525188\pi$
$734$	−52.7652	−1.94760
$735$	65.8259	2.42802
$736$	−40.2382	−1.48320
$737$	−12.9254	−0.476115
$738$	−14.3772	−0.529234
$739$	−16.6732	−0.613332	−0.306666	−	0.951817i	$-0.599213\pi$
$739$	−16.6732	−0.613332	−0.306666	+	0.951817i	$0.599213\pi$
$740$	16.9246	0.622159
$741$	11.5041	0.422612
$742$	−87.8252	−3.22416
$743$	−17.8586	−0.655169	−0.327584	−	0.944822i	$-0.606235\pi$
$743$	−17.8586	−0.655169	−0.327584	+	0.944822i	$0.606235\pi$
$744$	−1.43161	−0.0524855
$745$	2.75182	0.100819
$746$	−66.8660	−2.44814
$747$	−42.4403	−1.55281
$748$	8.73258	0.319295
$749$	−22.1688	−0.810029
$750$	−58.0668	−2.12030
$751$	−20.0319	−0.730973	−0.365486	−	0.930817i	$-0.619097\pi$
$751$	−20.0319	−0.730973	−0.365486	+	0.930817i	$0.619097\pi$
$752$	−1.95618	−0.0713345
$753$	−21.6445	−0.788770
$754$	8.08866	0.294572
$755$	−18.1295	−0.659800
$756$	−6.09161	−0.221550
$757$	−12.0897	−0.439406	−0.219703	−	0.975567i	$-0.570509\pi$
$757$	−12.0897	−0.439406	−0.219703	+	0.975567i	$0.570509\pi$
$758$	68.3281	2.48179
$759$	−15.2536	−0.553670
$760$	3.71812	0.134871
$761$	1.15442	0.0418476	0.0209238	−	0.999781i	$-0.493339\pi$
$761$	1.15442	0.0418476	0.0209238	+	0.999781i	$0.493339\pi$
$762$	−46.3063	−1.67750
$763$	92.3741	3.34417
$764$	54.3075	1.96478
$765$	−13.9879	−0.505735
$766$	6.02951	0.217855
$767$	−2.72857	−0.0985230
$768$	26.6152	0.960393
$769$	18.1243	0.653580	0.326790	−	0.945097i	$-0.394033\pi$
$769$	18.1243	0.653580	0.326790	+	0.945097i	$0.394033\pi$
$770$	18.1927	0.655619
$771$	48.3082	1.73978
$772$	−21.6414	−0.778889
$773$	33.2167	1.19472	0.597361	−	0.801972i	$-0.296216\pi$
$773$	33.2167	1.19472	0.597361	+	0.801972i	$0.296216\pi$
$774$	−33.9173	−1.21913
$775$	3.03378	0.108976
$776$	−2.25791	−0.0810541
$777$	−67.1270	−2.40817
$778$	−76.6372	−2.74758
$779$	−9.99260	−0.358022
$780$	7.95985	0.285008
$781$	16.3357	0.584537
$782$	−31.8651	−1.13950
$783$	2.05770	0.0735364
$784$	−63.4291	−2.26532
$785$	19.4522	0.694280
$786$	−78.1899	−2.78894
$787$	−22.8485	−0.814461	−0.407230	−	0.913326i	$-0.633505\pi$
$787$	−22.8485	−0.814461	−0.407230	+	0.913326i	$0.633505\pi$
$788$	−9.14882	−0.325913
$789$	−58.5062	−2.08288
$790$	25.6895	0.913991
$791$	−90.5789	−3.22062
$792$	−2.27644	−0.0808897
$793$	11.3881	0.404404
$794$	−36.7517	−1.30427
$795$	29.1943	1.03542
$796$	−19.7431	−0.699775
$797$	−25.9204	−0.918147	−0.459073	−	0.888398i	$-0.651818\pi$
$797$	−25.9204	−0.918147	−0.459073	+	0.888398i	$0.651818\pi$
$798$	−120.941	−4.28126
$799$	−1.80466	−0.0638443
$800$	24.6146	0.870259
$801$	−30.7399	−1.08614
$802$	0.0199579	0.000704738 0
$803$	2.97730	0.105066
$804$	59.4532	2.09675
$805$	−35.3476	−1.24584
$806$	−2.06827	−0.0728517
$807$	34.5026	1.21455
$808$	3.68875	0.129770
$809$	46.0300	1.61833	0.809165	−	0.587582i	$-0.199920\pi$
$809$	46.0300	1.61833	0.809165	+	0.587582i	$0.199920\pi$
$810$	−24.1354	−0.848032
$811$	26.2086	0.920308	0.460154	−	0.887839i	$-0.347794\pi$
$811$	26.2086	0.920308	0.460154	+	0.887839i	$0.347794\pi$
$812$	−45.2781	−1.58895
$813$	−11.3048	−0.396475
$814$	−13.5258	−0.474079
$815$	6.26412	0.219422
$816$	26.0711	0.912670
$817$	−23.5735	−0.824733
$818$	−29.4592	−1.03002
$819$	−16.3219	−0.570334
$820$	−6.91405	−0.241449
$821$	−47.0599	−1.64240	−0.821201	−	0.570638i	$-0.806696\pi$
$821$	−47.0599	−1.64240	−0.821201	+	0.570638i	$0.806696\pi$
$822$	61.2283	2.13558
$823$	−15.0667	−0.525192	−0.262596	−	0.964906i	$-0.584579\pi$
$823$	−15.0667	−0.525192	−0.262596	+	0.964906i	$0.584579\pi$
$824$	5.76351	0.200781
$825$	9.33097	0.324863
$826$	28.6852	0.998085
$827$	16.2797	0.566100	0.283050	−	0.959105i	$-0.408654\pi$
$827$	16.2797	0.566100	0.283050	+	0.959105i	$0.408654\pi$
$828$	36.2734	1.26059
$829$	56.2123	1.95233	0.976166	−	0.217024i	$-0.0696351\pi$
$829$	56.2123	1.95233	0.976166	+	0.217024i	$0.0696351\pi$
$830$	−38.3306	−1.33048
$831$	−56.0552	−1.94453
$832$	−10.0462	−0.348289
$833$	−58.5162	−2.02746
$834$	−89.3089	−3.09251
$835$	−1.80366	−0.0624181
$836$	−12.9756	−0.448772
$837$	−0.526154	−0.0181866
$838$	−51.5802	−1.78181
$839$	43.2895	1.49452	0.747260	−	0.664532i	$-0.231369\pi$
$839$	43.2895	1.49452	0.747260	+	0.664532i	$0.231369\pi$
$840$	−10.2037	−0.352061
$841$	−13.7054	−0.472598
$842$	−50.9380	−1.75544
$843$	7.20252	0.248068
$844$	−25.2588	−0.869444
$845$	1.40222	0.0482379
$846$	3.85815	0.132646
$847$	48.1707	1.65517
$848$	−28.1313	−0.966034
$849$	36.1685	1.24130
$850$	19.4927	0.668593
$851$	26.2800	0.900867
$852$	−75.1394	−2.57423
$853$	20.8408	0.713574	0.356787	−	0.934186i	$-0.383872\pi$
$853$	20.8408	0.713574	0.356787	+	0.934186i	$0.383872\pi$
$854$	−119.722	−4.09680
$855$	20.7845	0.710815
$856$	2.50534	0.0856309
$857$	5.18774	0.177210	0.0886049	−	0.996067i	$-0.471759\pi$
$857$	5.18774	0.177210	0.0886049	+	0.996067i	$0.471759\pi$
$858$	−6.36137	−0.217174
$859$	46.0284	1.57047	0.785234	−	0.619199i	$-0.212542\pi$
$859$	46.0284	1.57047	0.785234	+	0.619199i	$0.212542\pi$
$860$	−16.3109	−0.556197
$861$	27.4228	0.934567
$862$	−52.2788	−1.78062
$863$	−13.8486	−0.471413	−0.235706	−	0.971824i	$-0.575740\pi$
$863$	−13.8486	−0.471413	−0.235706	+	0.971824i	$0.575740\pi$
$864$	−4.26897	−0.145233
$865$	19.0648	0.648222
$866$	−2.92426	−0.0993704
$867$	−18.3159	−0.622040
$868$	11.5776	0.392969
$869$	−10.9318	−0.370835
$870$	28.2669	0.958338
$871$	10.4734	0.354877
$872$	−10.4394	−0.353523
$873$	−12.6218	−0.427183
$874$	47.3480	1.60157
$875$	57.2600	1.93574
$876$	−13.6947	−0.462700
$877$	12.8560	0.434115	0.217057	−	0.976159i	$-0.430354\pi$
$877$	12.8560	0.434115	0.217057	+	0.976159i	$0.430354\pi$
$878$	35.2575	1.18988
$879$	−5.55668	−0.187422
$880$	5.82731	0.196439
$881$	−49.0894	−1.65386	−0.826932	−	0.562302i	$-0.809916\pi$
$881$	−49.0894	−1.65386	−0.826932	+	0.562302i	$0.809916\pi$
$882$	125.100	4.21235
$883$	−3.28403	−0.110516	−0.0552582	−	0.998472i	$-0.517598\pi$
$883$	−3.28403	−0.110516	−0.0552582	+	0.998472i	$0.517598\pi$
$884$	−7.07594	−0.237990
$885$	−9.53536	−0.320528
$886$	−41.0891	−1.38041
$887$	−26.4720	−0.888841	−0.444421	−	0.895818i	$-0.646590\pi$
$887$	−26.4720	−0.888841	−0.444421	+	0.895818i	$0.646590\pi$
$888$	7.58618	0.254575
$889$	45.6629	1.53148
$890$	−27.7632	−0.930624
$891$	10.2705	0.344073
$892$	34.3528	1.15022
$893$	2.68152	0.0897338
$894$	10.1157	0.338319
$895$	−30.1903	−1.00915
$896$	23.1333	0.772830
$897$	12.3599	0.412683
$898$	2.96786	0.0990388
$899$	−3.91084	−0.130434
$900$	−22.1893	−0.739643
$901$	−25.9524	−0.864600
$902$	5.52558	0.183982
$903$	64.6931	2.15285
$904$	10.2365	0.340462
$905$	14.7955	0.491821
$906$	−66.6440	−2.21410
$907$	45.0636	1.49631	0.748156	−	0.663523i	$-0.230939\pi$
$907$	45.0636	1.49631	0.748156	+	0.663523i	$0.230939\pi$
$908$	23.1628	0.768685
$909$	20.6203	0.683932
$910$	−14.7414	−0.488673
$911$	33.8799	1.12249	0.561246	−	0.827649i	$-0.310322\pi$
$911$	33.8799	1.12249	0.561246	+	0.827649i	$0.310322\pi$
$912$	−38.7386	−1.28276
$913$	16.3110	0.539815
$914$	−24.1702	−0.799480
$915$	39.7973	1.31566
$916$	−39.7777	−1.31429
$917$	77.1034	2.54618
$918$	−3.38065	−0.111578
$919$	16.0295	0.528764	0.264382	−	0.964418i	$-0.414832\pi$
$919$	16.0295	0.528764	0.264382	+	0.964418i	$0.414832\pi$
$920$	3.99472	0.131702
$921$	−22.4874	−0.740986
$922$	5.27011	0.173562
$923$	−13.2367	−0.435691
$924$	35.6092	1.17146
$925$	−16.0761	−0.528579
$926$	1.46014	0.0479832
$927$	32.2183	1.05819
$928$	−31.7307	−1.04161
$929$	−12.4309	−0.407845	−0.203923	−	0.978987i	$-0.565369\pi$
$929$	−12.4309	−0.407845	−0.203923	+	0.978987i	$0.565369\pi$
$930$	−7.22784	−0.237010
$931$	86.9484	2.84962
$932$	40.4943	1.32644
$933$	40.8879	1.33861
$934$	61.0010	1.99601
$935$	5.37596	0.175813
$936$	1.84458	0.0602920
$937$	−40.8117	−1.33326	−0.666630	−	0.745388i	$-0.732264\pi$
$937$	−40.8117	−1.33326	−0.666630	+	0.745388i	$0.732264\pi$
$938$	−110.106	−3.59507
$939$	−41.3595	−1.34972
$940$	1.85539	0.0605162
$941$	13.2576	0.432185	0.216093	−	0.976373i	$-0.430669\pi$
$941$	13.2576	0.432185	0.216093	+	0.976373i	$0.430669\pi$
$942$	71.5064	2.32980
$943$	−10.7360	−0.349611
$944$	9.18816	0.299049
$945$	−3.75012	−0.121991
$946$	13.0354	0.423816
$947$	12.1485	0.394773	0.197386	−	0.980326i	$-0.436755\pi$
$947$	12.1485	0.394773	0.197386	+	0.980326i	$0.436755\pi$
$948$	50.2829	1.63311
$949$	−2.41248	−0.0783123
$950$	−28.9639	−0.939712
$951$	26.8900	0.871970
$952$	9.07061	0.293980
$953$	−54.0305	−1.75022	−0.875110	−	0.483923i	$-0.839211\pi$
$953$	−54.0305	−1.75022	−0.875110	+	0.483923i	$0.839211\pi$
$954$	55.4831	1.79633
$955$	33.4328	1.08186
$956$	50.9006	1.64624
$957$	−12.0285	−0.388828
$958$	17.1202	0.553129
$959$	−60.3775	−1.94969
$960$	−35.1078	−1.13310
$961$	1.00000	0.0322581
$962$	10.9598	0.353359
$963$	14.0050	0.451305
$964$	64.0692	2.06353
$965$	−13.3229	−0.428878
$966$	−129.938	−4.18068
$967$	−44.1289	−1.41909	−0.709545	−	0.704660i	$-0.751100\pi$
$967$	−44.1289	−1.41909	−0.709545	+	0.704660i	$0.751100\pi$
$968$	−5.44389	−0.174973
$969$	−35.7381	−1.14807
$970$	−11.3996	−0.366018
$971$	−23.5896	−0.757025	−0.378513	−	0.925596i	$-0.623564\pi$
$971$	−23.5896	−0.757025	−0.378513	+	0.925596i	$0.623564\pi$
$972$	−50.8364	−1.63058
$973$	88.0679	2.82333
$974$	−8.62750	−0.276443
$975$	−7.56081	−0.242140
$976$	−38.3482	−1.22750
$977$	30.5227	0.976507	0.488254	−	0.872702i	$-0.337634\pi$
$977$	30.5227	0.976507	0.488254	+	0.872702i	$0.337634\pi$
$978$	23.0269	0.736319
$979$	11.8142	0.377583
$980$	60.1610	1.92177
$981$	−58.3568	−1.86319
$982$	−41.8584	−1.33575
$983$	−8.75338	−0.279189	−0.139595	−	0.990209i	$-0.544580\pi$
$983$	−8.75338	−0.279189	−0.139595	+	0.990209i	$0.544580\pi$
$984$	−3.09912	−0.0987963
$985$	−5.63220	−0.179457
$986$	−25.1280	−0.800238
$987$	−7.35894	−0.234238
$988$	10.5140	0.334496
$989$	−25.3271	−0.805356
$990$	−11.4931	−0.365276
$991$	−50.0987	−1.59144	−0.795718	−	0.605667i	$-0.792906\pi$
$991$	−50.0987	−1.59144	−0.795718	+	0.605667i	$0.792906\pi$
$992$	8.11353	0.257605
$993$	−74.9262	−2.37771
$994$	139.156	4.41375
$995$	−12.1542	−0.385315
$996$	−75.0258	−2.37728
$997$	23.6112	0.747775	0.373888	−	0.927474i	$-0.378025\pi$
$997$	23.6112	0.747775	0.373888	+	0.927474i	$0.378025\pi$
$998$	39.1998	1.24085
$999$	2.78811	0.0882120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.e.1.7	✓	8
3.2	odd	2		3627.2.a.p.1.2		8
4.3	odd	2		6448.2.a.bd.1.3		8
13.12	even	2		5239.2.a.i.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.e.1.7	✓	8	1.1	even	1	trivial
3627.2.a.p.1.2		8	3.2	odd	2
5239.2.a.i.1.2		8	13.12	even	2
6448.2.a.bd.1.3		8	4.3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q+2.06827 q^{2} +2.49221 q^{3} +2.27774 q^{4} +1.40222 q^{5} +5.15456 q^{6} -5.08294 q^{7} +0.574435 q^{8} +3.21112 q^{9} +2.90017 q^{10} -1.23412 q^{11} +5.67660 q^{12} +1.00000 q^{13} -10.5129 q^{14} +3.49463 q^{15} -3.36739 q^{16} -3.10657 q^{17} +6.64146 q^{18} +4.61601 q^{19} +3.19389 q^{20} -12.6678 q^{21} -2.55250 q^{22} +4.95939 q^{23} +1.43161 q^{24} -3.03378 q^{25} +2.06827 q^{26} +0.526154 q^{27} -11.5776 q^{28} +3.91084 q^{29} +7.22784 q^{30} -1.00000 q^{31} -8.11353 q^{32} -3.07570 q^{33} -6.42521 q^{34} -7.12741 q^{35} +7.31409 q^{36} +5.29904 q^{37} +9.54714 q^{38} +2.49221 q^{39} +0.805485 q^{40} -2.16477 q^{41} -26.2003 q^{42} -5.10691 q^{43} -2.81101 q^{44} +4.50270 q^{45} +10.2574 q^{46} +0.580919 q^{47} -8.39224 q^{48} +18.8363 q^{49} -6.27466 q^{50} -7.74222 q^{51} +2.27774 q^{52} +8.35405 q^{53} +1.08823 q^{54} -1.73051 q^{55} -2.91982 q^{56} +11.5041 q^{57} +8.08866 q^{58} -2.72857 q^{59} +7.95985 q^{60} +11.3881 q^{61} -2.06827 q^{62} -16.3219 q^{63} -10.0462 q^{64} +1.40222 q^{65} -6.36137 q^{66} +10.4734 q^{67} -7.07594 q^{68} +12.3599 q^{69} -14.7414 q^{70} -13.2367 q^{71} +1.84458 q^{72} -2.41248 q^{73} +10.9598 q^{74} -7.56081 q^{75} +10.5140 q^{76} +6.27297 q^{77} +5.15456 q^{78} +8.85793 q^{79} -4.72182 q^{80} -8.32207 q^{81} -4.47733 q^{82} -13.2167 q^{83} -28.8538 q^{84} -4.35609 q^{85} -10.5625 q^{86} +9.74663 q^{87} -0.708924 q^{88} -9.57294 q^{89} +9.31280 q^{90} -5.08294 q^{91} +11.2962 q^{92} -2.49221 q^{93} +1.20150 q^{94} +6.47266 q^{95} -20.2206 q^{96} -3.93065 q^{97} +38.9585 q^{98} -3.96292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9} - 2 q^{10} - 2 q^{11} + 19 q^{12} + 8 q^{13} + 3 q^{14} + 6 q^{15} - 7 q^{16} + 7 q^{17} - 12 q^{18} - 5 q^{19} + 6 q^{20} + 8 q^{21} - 4 q^{22}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9 - 2 * q^10 - 2 * q^11 + 19 * q^12 + 8 * q^13 + 3 * q^14 + 6 * q^15 - 7 * q^16 + 7 * q^17 - 12 * q^18 - 5 * q^19 + 6 * q^20 + 8 * q^21 - 4 * q^22 + 14 * q^23 - 17 * q^24 + 17 * q^25 - q^26 + 7 * q^27 - 9 * q^28 + 12 * q^29 - 9 * q^30 - 8 * q^31 - 21 * q^32 + 10 * q^33 - 12 * q^34 - q^35 + 11 * q^36 + 2 * q^37 + 24 * q^38 + 7 * q^39 - 19 * q^40 + 13 * q^41 - 27 * q^42 - 5 * q^43 + 22 * q^44 + 19 * q^45 + 17 * q^46 + 23 * q^47 + 3 * q^48 + 26 * q^49 - 26 * q^50 + 18 * q^51 + 7 * q^52 + 25 * q^53 - 36 * q^54 - 17 * q^55 + 8 * q^56 - 35 * q^57 - 29 * q^58 - 5 * q^59 + 71 * q^60 - 9 * q^61 + q^62 - 37 * q^63 - 14 * q^64 + 11 * q^65 - 41 * q^66 + 22 * q^67 - 6 * q^68 - 7 * q^69 - 29 * q^70 - 17 * q^71 - 34 * q^72 - 27 * q^73 + 14 * q^74 - 33 * q^75 - 36 * q^76 + 31 * q^77 - 23 * q^79 + 9 * q^80 - 12 * q^81 + 18 * q^82 - 25 * q^83 - 62 * q^84 + 13 * q^85 + 11 * q^86 + 26 * q^87 + 5 * q^88 + 2 * q^89 - 14 * q^90 - 2 * q^91 - 20 * q^92 - 7 * q^93 - 38 * q^94 + 3 * q^95 - 52 * q^96 - 15 * q^97 + 39 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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