LMFDB - Embedded newform 5929.2.a.ca.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5929,2,Mod(1,5929)] 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("5929.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5929, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,0,0,16,0,0,0,0,20,0,0,0,0,0,28,16,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	yes
Analytic conductor:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 28x^{10} + 279x^{8} - 1174x^{6} + 1857x^{4} - 752x^{2} + 16 $ x^12 - 28x^10 + 279x^8 - 1174x^6 + 1857x^4 - 752*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.150034$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.390854 q^{2} -0.150034 q^{3} -1.84723 q^{4} +1.62035 q^{5} -0.0586413 q^{6} -1.50370 q^{8} -2.97749 q^{9} +0.633321 q^{10} +0.277148 q^{12} +6.47530 q^{13} -0.243108 q^{15} +3.10674 q^{16} +4.38277 q^{17} -1.16376 q^{18} +4.11799 q^{19} -2.99317 q^{20} -5.37685 q^{23} +0.225607 q^{24} -2.37446 q^{25} +2.53090 q^{26} +0.896826 q^{27} -5.92658 q^{29} -0.0950195 q^{30} +1.38975 q^{31} +4.22169 q^{32} +1.71302 q^{34} +5.50012 q^{36} +1.62655 q^{37} +1.60953 q^{38} -0.971515 q^{39} -2.43653 q^{40} +0.566034 q^{41} +6.93016 q^{43} -4.82458 q^{45} -2.10156 q^{46} +7.62601 q^{47} -0.466116 q^{48} -0.928065 q^{50} -0.657564 q^{51} -11.9614 q^{52} -8.36462 q^{53} +0.350528 q^{54} -0.617838 q^{57} -2.31642 q^{58} -9.96152 q^{59} +0.449077 q^{60} -2.87463 q^{61} +0.543188 q^{62} -4.56341 q^{64} +10.4923 q^{65} -7.57680 q^{67} -8.09600 q^{68} +0.806709 q^{69} +13.6302 q^{71} +4.47727 q^{72} -1.35649 q^{73} +0.635743 q^{74} +0.356249 q^{75} -7.60689 q^{76} -0.379720 q^{78} -15.9894 q^{79} +5.03401 q^{80} +8.79792 q^{81} +0.221237 q^{82} -3.49831 q^{83} +7.10163 q^{85} +2.70868 q^{86} +0.889187 q^{87} +14.0768 q^{89} -1.88571 q^{90} +9.93229 q^{92} -0.208509 q^{93} +2.98065 q^{94} +6.67260 q^{95} -0.633396 q^{96} +11.2806 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{4} + 20 q^{9} + 28 q^{15} + 16 q^{16} - 4 q^{18} + 36 q^{23} + 24 q^{25} - 12 q^{29} + 84 q^{30} - 40 q^{32} + 60 q^{36} + 20 q^{37} - 16 q^{39} + 12 q^{43} - 24 q^{46} + 4 q^{50} - 24 q^{51}+ \cdots + 12 q^{95}+O(q^{100}) $ 12 * q + 16 * q^4 + 20 * q^9 + 28 * q^15 + 16 * q^16 - 4 * q^18 + 36 * q^23 + 24 * q^25 - 12 * q^29 + 84 * q^30 - 40 * q^32 + 60 * q^36 + 20 * q^37 - 16 * q^39 + 12 * q^43 - 24 * q^46 + 4 * q^50 - 24 * q^51 + 16 * q^53 - 60 * q^57 - 16 * q^58 - 44 * q^60 - 36 * q^64 + 52 * q^65 + 24 * q^67 + 72 * q^71 - 36 * q^72 + 52 * q^74 + 20 * q^78 + 4 * q^79 + 56 * q^81 + 4 * q^85 + 12 * q^86 + 156 * q^92 + 32 * q^93 + 12 * q^95

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 $

$2$	0.390854	0.276375	0.138188	−	0.990406i	$-0.455872\pi$
$2$	0.390854	0.276375	0.138188	+	0.990406i	$0.455872\pi$
$3$	−0.150034	−0.0866221	−0.0433110	−	0.999062i	$-0.513791\pi$
$3$	−0.150034	−0.0866221	−0.0433110	+	0.999062i	$0.513791\pi$
$4$	−1.84723	−0.923617
$5$	1.62035	0.724644	0.362322	−	0.932053i	$-0.381984\pi$
$5$	1.62035	0.724644	0.362322	+	0.932053i	$0.381984\pi$
$6$	−0.0586413	−0.0239402
$7$	0	0
$7$	0	0
$8$	−1.50370	−0.531640
$9$	−2.97749	−0.992497
$10$	0.633321	0.200274
$11$	0	0
$11$	0	0
$12$	0.277148	0.0800056
$13$	6.47530	1.79593	0.897963	−	0.440071i	$-0.145047\pi$
$13$	6.47530	1.79593	0.897963	+	0.440071i	$0.145047\pi$
$14$	0	0
$15$	−0.243108	−0.0627702
$16$	3.10674	0.776685
$17$	4.38277	1.06298	0.531489	−	0.847065i	$-0.321633\pi$
$17$	4.38277	1.06298	0.531489	+	0.847065i	$0.321633\pi$
$18$	−1.16376	−0.274301
$19$	4.11799	0.944731	0.472366	−	0.881403i	$-0.343400\pi$
$19$	4.11799	0.944731	0.472366	+	0.881403i	$0.343400\pi$
$20$	−2.99317	−0.669293
$21$	0	0
$22$	0	0
$23$	−5.37685	−1.12115	−0.560575	−	0.828104i	$-0.689420\pi$
$23$	−5.37685	−1.12115	−0.560575	+	0.828104i	$0.689420\pi$
$24$	0.225607	0.0460518
$25$	−2.37446	−0.474891
$26$	2.53090	0.496349
$27$	0.896826	0.172594
$28$	0	0
$29$	−5.92658	−1.10054	−0.550269	−	0.834987i	$-0.685475\pi$
$29$	−5.92658	−1.10054	−0.550269	+	0.834987i	$0.685475\pi$
$30$	−0.0950195	−0.0173481
$31$	1.38975	0.249606	0.124803	−	0.992182i	$-0.460170\pi$
$31$	1.38975	0.249606	0.124803	+	0.992182i	$0.460170\pi$
$32$	4.22169	0.746296
$33$	0	0
$34$	1.71302	0.293781
$35$	0	0
$36$	5.50012	0.916686
$37$	1.62655	0.267403	0.133702	−	0.991022i	$-0.457314\pi$
$37$	1.62655	0.267403	0.133702	+	0.991022i	$0.457314\pi$
$38$	1.60953	0.261100
$39$	−0.971515	−0.155567
$40$	−2.43653	−0.385250
$41$	0.566034	0.0883997	0.0441999	−	0.999023i	$-0.485926\pi$
$41$	0.566034	0.0883997	0.0441999	+	0.999023i	$0.485926\pi$
$42$	0	0
$43$	6.93016	1.05684	0.528420	−	0.848983i	$-0.322785\pi$
$43$	6.93016	1.05684	0.528420	+	0.848983i	$0.322785\pi$
$44$	0	0
$45$	−4.82458	−0.719207
$46$	−2.10156	−0.309858
$47$	7.62601	1.11237	0.556184	−	0.831059i	$-0.312265\pi$
$47$	7.62601	1.11237	0.556184	+	0.831059i	$0.312265\pi$
$48$	−0.466116	−0.0672780
$49$	0	0
$50$	−0.928065	−0.131248
$51$	−0.657564	−0.0920773
$52$	−11.9614	−1.65875
$53$	−8.36462	−1.14897	−0.574484	−	0.818516i	$-0.694797\pi$
$53$	−8.36462	−1.14897	−0.574484	+	0.818516i	$0.694797\pi$
$54$	0.350528	0.0477008
$55$	0	0
$56$	0	0
$57$	−0.617838	−0.0818346
$58$	−2.31642	−0.304161
$59$	−9.96152	−1.29688	−0.648439	−	0.761266i	$-0.724578\pi$
$59$	−9.96152	−1.29688	−0.648439	+	0.761266i	$0.724578\pi$
$60$	0.449077	0.0579756
$61$	−2.87463	−0.368058	−0.184029	−	0.982921i	$-0.558914\pi$
$61$	−2.87463	−0.368058	−0.184029	+	0.982921i	$0.558914\pi$
$62$	0.543188	0.0689850
$63$	0	0
$64$	−4.56341	−0.570427
$65$	10.4923	1.30141
$66$	0	0
$67$	−7.57680	−0.925653	−0.462827	−	0.886449i	$-0.653165\pi$
$67$	−7.57680	−0.925653	−0.462827	+	0.886449i	$0.653165\pi$
$68$	−8.09600	−0.981784
$69$	0.806709	0.0971163
$70$	0	0
$71$	13.6302	1.61761	0.808806	−	0.588076i	$-0.200114\pi$
$71$	13.6302	1.61761	0.808806	+	0.588076i	$0.200114\pi$
$72$	4.47727	0.527651
$73$	−1.35649	−0.158765	−0.0793825	−	0.996844i	$-0.525295\pi$
$73$	−1.35649	−0.158765	−0.0793825	+	0.996844i	$0.525295\pi$
$74$	0.635743	0.0739037
$75$	0.356249	0.0411361
$76$	−7.60689	−0.872570
$77$	0	0
$78$	−0.379720	−0.0429948
$79$	−15.9894	−1.79895	−0.899473	−	0.436975i	$-0.856050\pi$
$79$	−15.9894	−1.79895	−0.899473	+	0.436975i	$0.856050\pi$
$80$	5.03401	0.562820
$81$	8.79792	0.977546
$82$	0.221237	0.0244315
$83$	−3.49831	−0.383989	−0.191995	−	0.981396i	$-0.561496\pi$
$83$	−3.49831	−0.383989	−0.191995	+	0.981396i	$0.561496\pi$
$84$	0	0
$85$	7.10163	0.770280
$86$	2.70868	0.292084
$87$	0.889187	0.0953309
$88$	0	0
$89$	14.0768	1.49214	0.746071	−	0.665866i	$-0.231938\pi$
$89$	14.0768	1.49214	0.746071	+	0.665866i	$0.231938\pi$
$90$	−1.88571	−0.198771
$91$	0	0
$92$	9.93229	1.03551
$93$	−0.208509	−0.0216214
$94$	2.98065	0.307431
$95$	6.67260	0.684594
$96$	−0.633396	−0.0646457
$97$	11.2806	1.14537	0.572686	−	0.819775i	$-0.305901\pi$
$97$	11.2806	1.14537	0.572686	+	0.819775i	$0.305901\pi$
$98$	0	0
$99$	0	0
$100$	4.38618	0.438618
$101$	0.960584	0.0955816	0.0477908	−	0.998857i	$-0.484782\pi$
$101$	0.960584	0.0955816	0.0477908	+	0.998857i	$0.484782\pi$
$102$	−0.257011	−0.0254479
$103$	16.5567	1.63138	0.815689	−	0.578490i	$-0.196358\pi$
$103$	16.5567	1.63138	0.815689	+	0.578490i	$0.196358\pi$
$104$	−9.73694	−0.954786
$105$	0	0
$106$	−3.26934	−0.317547
$107$	−3.94786	−0.381654	−0.190827	−	0.981624i	$-0.561117\pi$
$107$	−3.94786	−0.381654	−0.190827	+	0.981624i	$0.561117\pi$
$108$	−1.65665	−0.159411
$109$	−5.49990	−0.526795	−0.263397	−	0.964687i	$-0.584843\pi$
$109$	−5.49990	−0.526795	−0.263397	+	0.964687i	$0.584843\pi$
$110$	0	0
$111$	−0.244038	−0.0231630
$112$	0	0
$113$	2.31863	0.218118	0.109059	−	0.994035i	$-0.465216\pi$
$113$	2.31863	0.218118	0.109059	+	0.994035i	$0.465216\pi$
$114$	−0.241484	−0.0226171
$115$	−8.71239	−0.812434
$116$	10.9478	1.01648
$117$	−19.2801	−1.78245
$118$	−3.89349	−0.358425
$119$	0	0
$120$	0.365562	0.0333711
$121$	0	0
$122$	−1.12356	−0.101722
$123$	−0.0849243	−0.00765737
$124$	−2.56719	−0.230541
$125$	−11.9492	−1.06877
$126$	0	0
$127$	13.0605	1.15893	0.579467	−	0.814996i	$-0.303261\pi$
$127$	13.0605	1.15893	0.579467	+	0.814996i	$0.303261\pi$
$128$	−10.2270	−0.903948
$129$	−1.03976	−0.0915457
$130$	4.10094	0.359677
$131$	19.1739	1.67523	0.837617	−	0.546258i	$-0.183948\pi$
$131$	19.1739	1.67523	0.837617	+	0.546258i	$0.183948\pi$
$132$	0	0
$133$	0	0
$134$	−2.96142	−0.255828
$135$	1.45317	0.125069
$136$	−6.59039	−0.565121
$137$	10.3760	0.886486	0.443243	−	0.896402i	$-0.353828\pi$
$137$	10.3760	0.886486	0.443243	+	0.896402i	$0.353828\pi$
$138$	0.315305	0.0268405
$139$	14.7997	1.25530	0.627648	−	0.778497i	$-0.284018\pi$
$139$	14.7997	1.25530	0.627648	+	0.778497i	$0.284018\pi$
$140$	0	0
$141$	−1.14416	−0.0963556
$142$	5.32743	0.447068
$143$	0	0
$144$	−9.25028	−0.770857
$145$	−9.60315	−0.797498
$146$	−0.530189	−0.0438787
$147$	0	0
$148$	−3.00462	−0.246978
$149$	0.0904789	0.00741232	0.00370616	−	0.999993i	$-0.498820\pi$
$149$	0.0904789	0.00741232	0.00370616	+	0.999993i	$0.498820\pi$
$150$	0.139241	0.0113690
$151$	4.65886	0.379133	0.189566	−	0.981868i	$-0.439292\pi$
$151$	4.65886	0.379133	0.189566	+	0.981868i	$0.439292\pi$
$152$	−6.19224	−0.502257
$153$	−13.0497	−1.05500
$154$	0	0
$155$	2.25188	0.180876
$156$	1.79461	0.143684
$157$	−18.1474	−1.44832	−0.724159	−	0.689633i	$-0.757772\pi$
$157$	−18.1474	−1.44832	−0.724159	+	0.689633i	$0.757772\pi$
$158$	−6.24951	−0.497184
$159$	1.25498	0.0995261
$160$	6.84063	0.540799
$161$	0	0
$162$	3.43870	0.270170
$163$	−9.64052	−0.755104	−0.377552	−	0.925988i	$-0.623234\pi$
$163$	−9.64052	−0.755104	−0.377552	+	0.925988i	$0.623234\pi$
$164$	−1.04560	−0.0816475
$165$	0	0
$166$	−1.36733	−0.106125
$167$	14.7298	1.13982	0.569912	−	0.821705i	$-0.306977\pi$
$167$	14.7298	1.13982	0.569912	+	0.821705i	$0.306977\pi$
$168$	0	0
$169$	28.9295	2.22535
$170$	2.77570	0.212886
$171$	−12.2613	−0.937643
$172$	−12.8016	−0.976115
$173$	19.6782	1.49611	0.748054	−	0.663638i	$-0.230988\pi$
$173$	19.6782	1.49611	0.748054	+	0.663638i	$0.230988\pi$
$174$	0.347542	0.0263471
$175$	0	0
$176$	0	0
$177$	1.49456	0.112338
$178$	5.50199	0.412391
$179$	9.40597	0.703035	0.351518	−	0.936181i	$-0.385666\pi$
$179$	9.40597	0.703035	0.351518	+	0.936181i	$0.385666\pi$
$180$	8.91213	0.664271
$181$	11.9270	0.886528	0.443264	−	0.896391i	$-0.353820\pi$
$181$	11.9270	0.886528	0.443264	+	0.896391i	$0.353820\pi$
$182$	0	0
$183$	0.431291	0.0318820
$184$	8.08519	0.596048
$185$	2.63559	0.193772
$186$	−0.0814966	−0.00597562
$187$	0	0
$188$	−14.0870	−1.02740
$189$	0	0
$190$	2.60801	0.189205
$191$	23.7059	1.71530	0.857648	−	0.514237i	$-0.171925\pi$
$191$	23.7059	1.71530	0.857648	+	0.514237i	$0.171925\pi$
$192$	0.684667	0.0494116
$193$	−2.59815	−0.187019	−0.0935095	−	0.995618i	$-0.529809\pi$
$193$	−2.59815	−0.187019	−0.0935095	+	0.995618i	$0.529809\pi$
$194$	4.40907	0.316553
$195$	−1.57420	−0.112731
$196$	0	0
$197$	23.5003	1.67433	0.837163	−	0.546953i	$-0.184212\pi$
$197$	23.5003	1.67433	0.837163	+	0.546953i	$0.184212\pi$
$198$	0	0
$199$	1.53318	0.108684	0.0543422	−	0.998522i	$-0.482694\pi$
$199$	1.53318	0.108684	0.0543422	+	0.998522i	$0.482694\pi$
$200$	3.57048	0.252471
$201$	1.13678	0.0801820
$202$	0.375448	0.0264164
$203$	0	0
$204$	1.21467	0.0850442
$205$	0.917176	0.0640583
$206$	6.47124	0.450873
$207$	16.0095	1.11274
$208$	20.1171	1.39487
$209$	0	0
$210$	0	0
$211$	−26.6554	−1.83503	−0.917516	−	0.397700i	$-0.869809\pi$
$211$	−26.6554	−1.83503	−0.917516	+	0.397700i	$0.869809\pi$
$212$	15.4514	1.06121
$213$	−2.04500	−0.140121
$214$	−1.54303	−0.105480
$215$	11.2293	0.765833
$216$	−1.34856	−0.0917580
$217$	0	0
$218$	−2.14965	−0.145593
$219$	0.203519	0.0137526
$220$	0	0
$221$	28.3798	1.90903
$222$	−0.0953830	−0.00640169
$223$	−7.38239	−0.494362	−0.247181	−	0.968969i	$-0.579504\pi$
$223$	−7.38239	−0.494362	−0.247181	+	0.968969i	$0.579504\pi$
$224$	0	0
$225$	7.06992	0.471328
$226$	0.906244	0.0602825
$227$	18.2778	1.21314	0.606568	−	0.795031i	$-0.292546\pi$
$227$	18.2778	1.21314	0.606568	+	0.795031i	$0.292546\pi$
$228$	1.14129	0.0755838
$229$	−8.30699	−0.548941	−0.274471	−	0.961596i	$-0.588503\pi$
$229$	−8.30699	−0.548941	−0.274471	+	0.961596i	$0.588503\pi$
$230$	−3.40527	−0.224537
$231$	0	0
$232$	8.91183	0.585090
$233$	12.4590	0.816215	0.408107	−	0.912934i	$-0.366189\pi$
$233$	12.4590	0.816215	0.408107	+	0.912934i	$0.366189\pi$
$234$	−7.53571	−0.492625
$235$	12.3568	0.806071
$236$	18.4012	1.19782
$237$	2.39895	0.155829
$238$	0	0
$239$	6.93875	0.448831	0.224415	−	0.974494i	$-0.427953\pi$
$239$	6.93875	0.448831	0.224415	+	0.974494i	$0.427953\pi$
$240$	−0.755272	−0.0487526
$241$	−26.4038	−1.70082	−0.850410	−	0.526121i	$-0.823646\pi$
$241$	−26.4038	−1.70082	−0.850410	+	0.526121i	$0.823646\pi$
$242$	0	0
$243$	−4.01046	−0.257271
$244$	5.31011	0.339945
$245$	0	0
$246$	−0.0331930	−0.00211631
$247$	26.6652	1.69667
$248$	−2.08977	−0.132701
$249$	0.524865	0.0332620
$250$	−4.67040	−0.295382
$251$	−16.4261	−1.03681	−0.518404	−	0.855136i	$-0.673474\pi$
$251$	−16.4261	−1.03681	−0.518404	+	0.855136i	$0.673474\pi$
$252$	0	0
$253$	0	0
$254$	5.10475	0.320301
$255$	−1.06549	−0.0667233
$256$	5.12957	0.320598
$257$	23.0935	1.44053	0.720267	−	0.693697i	$-0.244019\pi$
$257$	23.0935	1.44053	0.720267	+	0.693697i	$0.244019\pi$
$258$	−0.406394	−0.0253010
$259$	0	0
$260$	−19.3817	−1.20200
$261$	17.6463	1.09228
$262$	7.49420	0.462993
$263$	15.5989	0.961871	0.480936	−	0.876756i	$-0.340297\pi$
$263$	15.5989	0.961871	0.480936	+	0.876756i	$0.340297\pi$
$264$	0	0
$265$	−13.5536	−0.832593
$266$	0	0
$267$	−2.11200	−0.129253
$268$	13.9961	0.854949
$269$	−17.3982	−1.06079	−0.530393	−	0.847752i	$-0.677956\pi$
$269$	−17.3982	−1.06079	−0.530393	+	0.847752i	$0.677956\pi$
$270$	0.567978	0.0345661
$271$	−18.2149	−1.10648	−0.553239	−	0.833022i	$-0.686608\pi$
$271$	−18.2149	−1.10648	−0.553239	+	0.833022i	$0.686608\pi$
$272$	13.6161	0.825598
$273$	0	0
$274$	4.05552	0.245003
$275$	0	0
$276$	−1.49018	−0.0896983
$277$	1.55924	0.0936858	0.0468429	−	0.998902i	$-0.485084\pi$
$277$	1.55924	0.0936858	0.0468429	+	0.998902i	$0.485084\pi$
$278$	5.78453	0.346933
$279$	−4.13796	−0.247733
$280$	0	0
$281$	−27.9232	−1.66576	−0.832878	−	0.553457i	$-0.813308\pi$
$281$	−27.9232	−1.66576	−0.832878	+	0.553457i	$0.813308\pi$
$282$	−0.447199	−0.0266303
$283$	10.9002	0.647949	0.323974	−	0.946066i	$-0.394981\pi$
$283$	10.9002	0.647949	0.323974	+	0.946066i	$0.394981\pi$
$284$	−25.1782	−1.49405
$285$	−1.00112	−0.0593009
$286$	0	0
$287$	0	0
$288$	−12.5700	−0.740697
$289$	2.20867	0.129922
$290$	−3.75343	−0.220409
$291$	−1.69247	−0.0992146
$292$	2.50575	0.146638
$293$	16.5313	0.965768	0.482884	−	0.875684i	$-0.339589\pi$
$293$	16.5313	0.965768	0.482884	+	0.875684i	$0.339589\pi$
$294$	0	0
$295$	−16.1412	−0.939775
$296$	−2.44585	−0.142162
$297$	0	0
$298$	0.0353640	0.00204858
$299$	−34.8167	−2.01350
$300$	−0.658075	−0.0379940
$301$	0	0
$302$	1.82093	0.104783
$303$	−0.144120	−0.00827948
$304$	12.7935	0.733758
$305$	−4.65791	−0.266711
$306$	−5.10050	−0.291576
$307$	1.73356	0.0989392	0.0494696	−	0.998776i	$-0.484247\pi$
$307$	1.73356	0.0989392	0.0494696	+	0.998776i	$0.484247\pi$
$308$	0	0
$309$	−2.48406	−0.141313
$310$	0.880157	0.0499895
$311$	27.3012	1.54811	0.774055	−	0.633118i	$-0.218225\pi$
$311$	27.3012	1.54811	0.774055	+	0.633118i	$0.218225\pi$
$312$	1.46087	0.0827055
$313$	17.5897	0.994229	0.497114	−	0.867685i	$-0.334393\pi$
$313$	17.5897	0.994229	0.497114	+	0.867685i	$0.334393\pi$
$314$	−7.09297	−0.400279
$315$	0	0
$316$	29.5361	1.66154
$317$	3.35447	0.188406	0.0942030	−	0.995553i	$-0.469970\pi$
$317$	3.35447	0.188406	0.0942030	+	0.995553i	$0.469970\pi$
$318$	0.490512	0.0275065
$319$	0	0
$320$	−7.39434	−0.413356
$321$	0.592312	0.0330597
$322$	0	0
$323$	18.0482	1.00423
$324$	−16.2518	−0.902878
$325$	−15.3753	−0.852869
$326$	−3.76803	−0.208692
$327$	0.825171	0.0456320
$328$	−0.851149	−0.0469968
$329$	0	0
$330$	0	0
$331$	20.4149	1.12210	0.561051	−	0.827781i	$-0.310397\pi$
$331$	20.4149	1.12210	0.561051	+	0.827781i	$0.310397\pi$
$332$	6.46220	0.354659
$333$	−4.84304	−0.265397
$334$	5.75719	0.315019
$335$	−12.2771	−0.670769
$336$	0	0
$337$	−7.34145	−0.399914	−0.199957	−	0.979805i	$-0.564080\pi$
$337$	−7.34145	−0.399914	−0.199957	+	0.979805i	$0.564080\pi$
$338$	11.3072	0.615031
$339$	−0.347873	−0.0188939
$340$	−13.1184	−0.711444
$341$	0	0
$342$	−4.79236	−0.259141
$343$	0	0
$344$	−10.4209	−0.561859
$345$	1.30715	0.0703748
$346$	7.69130	0.413487
$347$	−29.6156	−1.58985	−0.794925	−	0.606708i	$-0.792490\pi$
$347$	−29.6156	−1.58985	−0.794925	+	0.606708i	$0.792490\pi$
$348$	−1.64254	−0.0880492
$349$	−34.6627	−1.85545	−0.927727	−	0.373260i	$-0.878240\pi$
$349$	−34.6627	−1.85545	−0.927727	+	0.373260i	$0.878240\pi$
$350$	0	0
$351$	5.80722	0.309966
$352$	0	0
$353$	15.5315	0.826657	0.413328	−	0.910582i	$-0.364366\pi$
$353$	15.5315	0.826657	0.413328	+	0.910582i	$0.364366\pi$
$354$	0.584156	0.0310475
$355$	22.0858	1.17219
$356$	−26.0032	−1.37817
$357$	0	0
$358$	3.67636	0.194301
$359$	−32.0749	−1.69285	−0.846425	−	0.532509i	$-0.821249\pi$
$359$	−32.0749	−1.69285	−0.846425	+	0.532509i	$0.821249\pi$
$360$	7.25475	0.382359
$361$	−2.04217	−0.107483
$362$	4.66171	0.245014
$363$	0	0
$364$	0	0
$365$	−2.19799	−0.115048
$366$	0.168572	0.00881139
$367$	14.6368	0.764037	0.382019	−	0.924155i	$-0.375229\pi$
$367$	14.6368	0.764037	0.382019	+	0.924155i	$0.375229\pi$
$368$	−16.7045	−0.870780
$369$	−1.68536	−0.0877364
$370$	1.03013	0.0535538
$371$	0	0
$372$	0.385165	0.0199699
$373$	9.05631	0.468918	0.234459	−	0.972126i	$-0.424668\pi$
$373$	9.05631	0.468918	0.234459	+	0.972126i	$0.424668\pi$
$374$	0	0
$375$	1.79279	0.0925792
$376$	−11.4673	−0.591379
$377$	−38.3764	−1.97648
$378$	0	0
$379$	12.6037	0.647411	0.323705	−	0.946158i	$-0.395071\pi$
$379$	12.6037	0.647411	0.323705	+	0.946158i	$0.395071\pi$
$380$	−12.3258	−0.632302
$381$	−1.95952	−0.100389
$382$	9.26552	0.474065
$383$	−9.42359	−0.481523	−0.240762	−	0.970584i	$-0.577397\pi$
$383$	−9.42359	−0.481523	−0.240762	+	0.970584i	$0.577397\pi$
$384$	1.53440	0.0783019
$385$	0	0
$386$	−1.01550	−0.0516874
$387$	−20.6345	−1.04891
$388$	−20.8379	−1.05789
$389$	−2.01979	−0.102408	−0.0512038	−	0.998688i	$-0.516306\pi$
$389$	−2.01979	−0.102408	−0.0512038	+	0.998688i	$0.516306\pi$
$390$	−0.615280	−0.0311559
$391$	−23.5655	−1.19176
$392$	0	0
$393$	−2.87674	−0.145112
$394$	9.18518	0.462742
$395$	−25.9085	−1.30360
$396$	0	0
$397$	15.4181	0.773812	0.386906	−	0.922119i	$-0.373544\pi$
$397$	15.4181	0.773812	0.386906	+	0.922119i	$0.373544\pi$
$398$	0.599249	0.0300376
$399$	0	0
$400$	−7.37681	−0.368841
$401$	−11.8274	−0.590633	−0.295317	−	0.955399i	$-0.595425\pi$
$401$	−11.8274	−0.590633	−0.295317	+	0.955399i	$0.595425\pi$
$402$	0.444313	0.0221603
$403$	8.99904	0.448274
$404$	−1.77442	−0.0882808
$405$	14.2557	0.708373
$406$	0	0
$407$	0	0
$408$	0.988782	0.0489520
$409$	11.7016	0.578607	0.289304	−	0.957237i	$-0.406576\pi$
$409$	11.7016	0.578607	0.289304	+	0.957237i	$0.406576\pi$
$410$	0.358481	0.0177041
$411$	−1.55676	−0.0767892
$412$	−30.5841	−1.50677
$413$	0	0
$414$	6.25737	0.307533
$415$	−5.66850	−0.278256
$416$	27.3367	1.34029
$417$	−2.22046	−0.108736
$418$	0	0
$419$	25.6328	1.25224	0.626122	−	0.779725i	$-0.284641\pi$
$419$	25.6328	1.25224	0.626122	+	0.779725i	$0.284641\pi$
$420$	0	0
$421$	26.3965	1.28649	0.643243	−	0.765662i	$-0.277589\pi$
$421$	26.3965	1.28649	0.643243	+	0.765662i	$0.277589\pi$
$422$	−10.4183	−0.507157
$423$	−22.7064	−1.10402
$424$	12.5779	0.610838
$425$	−10.4067	−0.504799
$426$	−0.799294	−0.0387259
$427$	0	0
$428$	7.29262	0.352502
$429$	0	0
$430$	4.38902	0.211657
$431$	19.6410	0.946072	0.473036	−	0.881043i	$-0.343158\pi$
$431$	19.6410	0.946072	0.473036	+	0.881043i	$0.343158\pi$
$432$	2.78620	0.134051
$433$	−9.98232	−0.479720	−0.239860	−	0.970808i	$-0.577101\pi$
$433$	−9.98232	−0.479720	−0.239860	+	0.970808i	$0.577101\pi$
$434$	0	0
$435$	1.44080	0.0690809
$436$	10.1596	0.486556
$437$	−22.1418	−1.05919
$438$	0.0795463	0.00380087
$439$	37.9959	1.81345	0.906723	−	0.421727i	$-0.138576\pi$
$439$	37.9959	1.81345	0.906723	+	0.421727i	$0.138576\pi$
$440$	0	0
$441$	0	0
$442$	11.0923	0.527608
$443$	14.5129	0.689530	0.344765	−	0.938689i	$-0.387959\pi$
$443$	14.5129	0.689530	0.344765	+	0.938689i	$0.387959\pi$
$444$	0.450795	0.0213938
$445$	22.8095	1.08127
$446$	−2.88543	−0.136629
$447$	−0.0135749	−0.000642070 0
$448$	0	0
$449$	−7.19788	−0.339689	−0.169844	−	0.985471i	$-0.554327\pi$
$449$	−7.19788	−0.339689	−0.169844	+	0.985471i	$0.554327\pi$
$450$	2.76330	0.130263
$451$	0	0
$452$	−4.28305	−0.201458
$453$	−0.698987	−0.0328413
$454$	7.14392	0.335281
$455$	0	0
$456$	0.929046	0.0435065
$457$	−22.4301	−1.04924	−0.524618	−	0.851338i	$-0.675792\pi$
$457$	−22.4301	−1.04924	−0.524618	+	0.851338i	$0.675792\pi$
$458$	−3.24682	−0.151714
$459$	3.93058	0.183464
$460$	16.0938	0.750378
$461$	7.01660	0.326796	0.163398	−	0.986560i	$-0.447755\pi$
$461$	7.01660	0.326796	0.163398	+	0.986560i	$0.447755\pi$
$462$	0	0
$463$	3.85090	0.178966	0.0894832	−	0.995988i	$-0.471478\pi$
$463$	3.85090	0.178966	0.0894832	+	0.995988i	$0.471478\pi$
$464$	−18.4123	−0.854771
$465$	−0.337859	−0.0156678
$466$	4.86963	0.225581
$467$	−6.50146	−0.300852	−0.150426	−	0.988621i	$-0.548064\pi$
$467$	−6.50146	−0.300852	−0.150426	+	0.988621i	$0.548064\pi$
$468$	35.6149	1.64630
$469$	0	0
$470$	4.82971	0.222778
$471$	2.72272	0.125456
$472$	14.9792	0.689473
$473$	0	0
$474$	0.937638	0.0430671
$475$	−9.77798	−0.448645
$476$	0	0
$477$	24.9056	1.14035
$478$	2.71204	0.124046
$479$	34.0519	1.55587	0.777935	−	0.628344i	$-0.216267\pi$
$479$	34.0519	1.55587	0.777935	+	0.628344i	$0.216267\pi$
$480$	−1.02633	−0.0468451
$481$	10.5324	0.480237
$482$	−10.3200	−0.470064
$483$	0	0
$484$	0	0
$485$	18.2786	0.829987
$486$	−1.56750	−0.0711034
$487$	−1.13879	−0.0516035	−0.0258017	−	0.999667i	$-0.508214\pi$
$487$	−1.13879	−0.0516035	−0.0258017	+	0.999667i	$0.508214\pi$
$488$	4.32259	0.195675
$489$	1.44640	0.0654087
$490$	0	0
$491$	−6.99706	−0.315773	−0.157886	−	0.987457i	$-0.550468\pi$
$491$	−6.99706	−0.315773	−0.157886	+	0.987457i	$0.550468\pi$
$492$	0.156875	0.00707247
$493$	−25.9748	−1.16985
$494$	10.4222	0.468917
$495$	0	0
$496$	4.31759	0.193865
$497$	0	0
$498$	0.205145	0.00919278
$499$	9.42232	0.421801	0.210901	−	0.977508i	$-0.432360\pi$
$499$	9.42232	0.421801	0.210901	+	0.977508i	$0.432360\pi$
$500$	22.0730	0.987135
$501$	−2.20997	−0.0987340
$502$	−6.42021	−0.286548
$503$	−17.1632	−0.765270	−0.382635	−	0.923900i	$-0.624983\pi$
$503$	−17.1632	−0.765270	−0.382635	+	0.923900i	$0.624983\pi$
$504$	0	0
$505$	1.55648	0.0692626
$506$	0	0
$507$	−4.34041	−0.192764
$508$	−24.1258	−1.07041
$509$	−23.5858	−1.04542	−0.522711	−	0.852510i	$-0.675079\pi$
$509$	−23.5858	−1.04542	−0.522711	+	0.852510i	$0.675079\pi$
$510$	−0.416449	−0.0184407
$511$	0	0
$512$	22.4589	0.992554
$513$	3.69312	0.163055
$514$	9.02618	0.398128
$515$	26.8277	1.18217
$516$	1.92068	0.0845531
$517$	0	0
$518$	0	0
$519$	−2.95240	−0.129596
$520$	−15.7773	−0.691880
$521$	−20.1506	−0.882814	−0.441407	−	0.897307i	$-0.645521\pi$
$521$	−20.1506	−0.882814	−0.441407	+	0.897307i	$0.645521\pi$
$522$	6.89713	0.301879
$523$	−4.76234	−0.208243	−0.104121	−	0.994565i	$-0.533203\pi$
$523$	−4.76234	−0.208243	−0.104121	+	0.994565i	$0.533203\pi$
$524$	−35.4187	−1.54727
$525$	0	0
$526$	6.09690	0.265837
$527$	6.09095	0.265326
$528$	0	0
$529$	5.91047	0.256977
$530$	−5.29749	−0.230108
$531$	29.6603	1.28715
$532$	0	0
$533$	3.66524	0.158759
$534$	−0.825484	−0.0357222
$535$	−6.39692	−0.276563
$536$	11.3933	0.492114
$537$	−1.41121	−0.0608984
$538$	−6.80015	−0.293175
$539$	0	0
$540$	−2.68435	−0.115516
$541$	0.667605	0.0287026	0.0143513	−	0.999897i	$-0.495432\pi$
$541$	0.667605	0.0287026	0.0143513	+	0.999897i	$0.495432\pi$
$542$	−7.11937	−0.305803
$543$	−1.78946	−0.0767929
$544$	18.5027	0.793296
$545$	−8.91177	−0.381738
$546$	0	0
$547$	−33.9259	−1.45057	−0.725283	−	0.688451i	$-0.758291\pi$
$547$	−33.9259	−1.45057	−0.725283	+	0.688451i	$0.758291\pi$
$548$	−19.1670	−0.818773
$549$	8.55917	0.365297
$550$	0	0
$551$	−24.4056	−1.03971
$552$	−1.21305	−0.0516309
$553$	0	0
$554$	0.609436	0.0258924
$555$	−0.395427	−0.0167850
$556$	−27.3386	−1.15941
$557$	−18.0539	−0.764967	−0.382484	−	0.923962i	$-0.624931\pi$
$557$	−18.0539	−0.764967	−0.382484	+	0.923962i	$0.624931\pi$
$558$	−1.61734	−0.0684674
$559$	44.8749	1.89801
$560$	0	0
$561$	0	0
$562$	−10.9139	−0.460374
$563$	30.7445	1.29573	0.647863	−	0.761757i	$-0.275663\pi$
$563$	30.7445	1.29573	0.647863	+	0.761757i	$0.275663\pi$
$564$	2.11353	0.0889957
$565$	3.75700	0.158058
$566$	4.26038	0.179077
$567$	0	0
$568$	−20.4959	−0.859987
$569$	−11.6065	−0.486569	−0.243285	−	0.969955i	$-0.578225\pi$
$569$	−11.6065	−0.486569	−0.243285	+	0.969955i	$0.578225\pi$
$570$	−0.391289	−0.0163893
$571$	6.86083	0.287117	0.143558	−	0.989642i	$-0.454146\pi$
$571$	6.86083	0.287117	0.143558	+	0.989642i	$0.454146\pi$
$572$	0	0
$573$	−3.55668	−0.148582
$574$	0	0
$575$	12.7671	0.532424
$576$	13.5875	0.566147
$577$	6.29056	0.261879	0.130940	−	0.991390i	$-0.458201\pi$
$577$	6.29056	0.261879	0.130940	+	0.991390i	$0.458201\pi$
$578$	0.863266	0.0359071
$579$	0.389810	0.0162000
$580$	17.7393	0.736583
$581$	0	0
$582$	−0.661509	−0.0274205
$583$	0	0
$584$	2.03976	0.0844059
$585$	−31.2406	−1.29164
$586$	6.46131	0.266914
$587$	19.0046	0.784405	0.392203	−	0.919879i	$-0.371713\pi$
$587$	19.0046	0.784405	0.392203	+	0.919879i	$0.371713\pi$
$588$	0	0
$589$	5.72297	0.235811
$590$	−6.30883	−0.259731
$591$	−3.52584	−0.145034
$592$	5.05327	0.207688
$593$	−38.7873	−1.59280	−0.796401	−	0.604769i	$-0.793265\pi$
$593$	−38.7873	−1.59280	−0.796401	+	0.604769i	$0.793265\pi$
$594$	0	0
$595$	0	0
$596$	−0.167136	−0.00684614
$597$	−0.230029	−0.00941446
$598$	−13.6082	−0.556482
$599$	5.73320	0.234252	0.117126	−	0.993117i	$-0.462632\pi$
$599$	5.73320	0.234252	0.117126	+	0.993117i	$0.462632\pi$
$600$	−0.535693	−0.0218696
$601$	28.4836	1.16187	0.580934	−	0.813950i	$-0.302687\pi$
$601$	28.4836	1.16187	0.580934	+	0.813950i	$0.302687\pi$
$602$	0	0
$603$	22.5598	0.918708
$604$	−8.60600	−0.350173
$605$	0	0
$606$	−0.0563298	−0.00228824
$607$	34.6147	1.40497	0.702484	−	0.711700i	$-0.252074\pi$
$607$	34.6147	1.40497	0.702484	+	0.711700i	$0.252074\pi$
$608$	17.3849	0.705050
$609$	0	0
$610$	−1.82056	−0.0737124
$611$	49.3807	1.99773
$612$	24.1058	0.974417
$613$	−20.5920	−0.831702	−0.415851	−	0.909433i	$-0.636516\pi$
$613$	−20.5920	−0.831702	−0.415851	+	0.909433i	$0.636516\pi$
$614$	0.677566	0.0273443
$615$	−0.137607	−0.00554887
$616$	0	0
$617$	38.5159	1.55059	0.775296	−	0.631598i	$-0.217601\pi$
$617$	38.5159	1.55059	0.775296	+	0.631598i	$0.217601\pi$
$618$	−0.970905	−0.0390555
$619$	21.6451	0.869991	0.434995	−	0.900433i	$-0.356750\pi$
$619$	21.6451	0.869991	0.434995	+	0.900433i	$0.356750\pi$
$620$	−4.15975	−0.167060
$621$	−4.82209	−0.193504
$622$	10.6708	0.427859
$623$	0	0
$624$	−3.01824	−0.120826
$625$	−7.48968	−0.299587
$626$	6.87500	0.274780
$627$	0	0
$628$	33.5224	1.33769
$629$	7.12880	0.284244
$630$	0	0
$631$	−32.4472	−1.29170	−0.645850	−	0.763464i	$-0.723497\pi$
$631$	−32.4472	−1.29170	−0.645850	+	0.763464i	$0.723497\pi$
$632$	24.0433	0.956392
$633$	3.99921	0.158954
$634$	1.31111	0.0520707
$635$	21.1627	0.839814
$636$	−2.31823	−0.0919239
$637$	0	0
$638$	0	0
$639$	−40.5839	−1.60547
$640$	−16.5714	−0.655041
$641$	−10.4994	−0.414701	−0.207351	−	0.978267i	$-0.566484\pi$
$641$	−10.4994	−0.414701	−0.207351	+	0.978267i	$0.566484\pi$
$642$	0.231507	0.00913687
$643$	49.7066	1.96024	0.980119	−	0.198411i	$-0.0635781\pi$
$643$	49.7066	1.96024	0.980119	+	0.198411i	$0.0635781\pi$
$644$	0	0
$645$	−1.68478	−0.0663380
$646$	7.05420	0.277544
$647$	7.53355	0.296174	0.148087	−	0.988974i	$-0.452688\pi$
$647$	7.53355	0.296174	0.148087	+	0.988974i	$0.452688\pi$
$648$	−13.2295	−0.519703
$649$	0	0
$650$	−6.00950	−0.235712
$651$	0	0
$652$	17.8083	0.697427
$653$	−14.8697	−0.581895	−0.290947	−	0.956739i	$-0.593970\pi$
$653$	−14.8697	−0.581895	−0.290947	+	0.956739i	$0.593970\pi$
$654$	0.322521	0.0126116
$655$	31.0685	1.21395
$656$	1.75852	0.0686587
$657$	4.03893	0.157574
$658$	0	0
$659$	5.75268	0.224093	0.112046	−	0.993703i	$-0.464259\pi$
$659$	5.75268	0.224093	0.112046	+	0.993703i	$0.464259\pi$
$660$	0	0
$661$	−37.5643	−1.46108	−0.730540	−	0.682870i	$-0.760732\pi$
$661$	−37.5643	−1.46108	−0.730540	+	0.682870i	$0.760732\pi$
$662$	7.97922	0.310121
$663$	−4.25792	−0.165364
$664$	5.26043	0.204144
$665$	0	0
$666$	−1.89292	−0.0733491
$667$	31.8663	1.23387
$668$	−27.2094	−1.05276
$669$	1.10761	0.0428226
$670$	−4.79854	−0.185384
$671$	0	0
$672$	0	0
$673$	−15.9009	−0.612934	−0.306467	−	0.951881i	$-0.599147\pi$
$673$	−15.9009	−0.612934	−0.306467	+	0.951881i	$0.599147\pi$
$674$	−2.86943	−0.110526
$675$	−2.12947	−0.0819635
$676$	−53.4396	−2.05537
$677$	17.1999	0.661044	0.330522	−	0.943798i	$-0.392775\pi$
$677$	17.1999	0.661044	0.330522	+	0.943798i	$0.392775\pi$
$678$	−0.135967	−0.00522179
$679$	0	0
$680$	−10.6788	−0.409512
$681$	−2.74228	−0.105084
$682$	0	0
$683$	−15.8072	−0.604847	−0.302423	−	0.953174i	$-0.597796\pi$
$683$	−15.8072	−0.604847	−0.302423	+	0.953174i	$0.597796\pi$
$684$	22.6494	0.866023
$685$	16.8129	0.642386
$686$	0	0
$687$	1.24633	0.0475504
$688$	21.5302	0.820832
$689$	−54.1634	−2.06346
$690$	0.510905	0.0194498
$691$	−31.6899	−1.20554	−0.602770	−	0.797915i	$-0.705936\pi$
$691$	−31.6899	−1.20554	−0.602770	+	0.797915i	$0.705936\pi$
$692$	−36.3503	−1.38183
$693$	0	0
$694$	−11.5754	−0.439395
$695$	23.9808	0.909643
$696$	−1.33708	−0.0506817
$697$	2.48080	0.0939669
$698$	−13.5481	−0.512801
$699$	−1.86927	−0.0707022
$700$	0	0
$701$	−2.90049	−0.109550	−0.0547750	−	0.998499i	$-0.517444\pi$
$701$	−2.90049	−0.109550	−0.0547750	+	0.998499i	$0.517444\pi$
$702$	2.26977	0.0856670
$703$	6.69812	0.252624
$704$	0	0
$705$	−1.85394	−0.0698235
$706$	6.07053	0.228467
$707$	0	0
$708$	−2.76081	−0.103758
$709$	−8.27951	−0.310944	−0.155472	−	0.987840i	$-0.549690\pi$
$709$	−8.27951	−0.310944	−0.155472	+	0.987840i	$0.549690\pi$
$710$	8.63231	0.323965
$711$	47.6082	1.78545
$712$	−21.1674	−0.793283
$713$	−7.47246	−0.279846
$714$	0	0
$715$	0	0
$716$	−17.3750	−0.649335
$717$	−1.04105	−0.0388786
$718$	−12.5366	−0.467862
$719$	16.7701	0.625419	0.312709	−	0.949849i	$-0.398763\pi$
$719$	16.7701	0.625419	0.312709	+	0.949849i	$0.398763\pi$
$720$	−14.9887	−0.558597
$721$	0	0
$722$	−0.798189	−0.0297055
$723$	3.96147	0.147328
$724$	−22.0320	−0.818812
$725$	14.0724	0.522636
$726$	0	0
$727$	7.41874	0.275146	0.137573	−	0.990492i	$-0.456070\pi$
$727$	7.41874	0.275146	0.137573	+	0.990492i	$0.456070\pi$
$728$	0	0
$729$	−25.7920	−0.955261
$730$	−0.859093	−0.0317965
$731$	30.3733	1.12340
$732$	−0.796696	−0.0294467
$733$	37.9087	1.40019	0.700095	−	0.714050i	$-0.253141\pi$
$733$	37.9087	1.40019	0.700095	+	0.714050i	$0.253141\pi$
$734$	5.72087	0.211161
$735$	0	0
$736$	−22.6994	−0.836710
$737$	0	0
$738$	−0.658730	−0.0242482
$739$	−31.6278	−1.16345	−0.581724	−	0.813386i	$-0.697622\pi$
$739$	−31.6278	−1.16345	−0.581724	+	0.813386i	$0.697622\pi$
$740$	−4.86855	−0.178971
$741$	−4.00069	−0.146969
$742$	0	0
$743$	−0.547186	−0.0200743	−0.0100372	−	0.999950i	$-0.503195\pi$
$743$	−0.547186	−0.0200743	−0.0100372	+	0.999950i	$0.503195\pi$
$744$	0.313537	0.0114948
$745$	0.146608	0.00537129
$746$	3.53969	0.129597
$747$	10.4162	0.381108
$748$	0	0
$749$	0	0
$750$	0.700717	0.0255866
$751$	−15.3541	−0.560280	−0.280140	−	0.959959i	$-0.590381\pi$
$751$	−15.3541	−0.560280	−0.280140	+	0.959959i	$0.590381\pi$
$752$	23.6920	0.863959
$753$	2.46448	0.0898105
$754$	−14.9995	−0.546251
$755$	7.54900	0.274736
$756$	0	0
$757$	38.2354	1.38969	0.694845	−	0.719160i	$-0.255473\pi$
$757$	38.2354	1.38969	0.694845	+	0.719160i	$0.255473\pi$
$758$	4.92622	0.178928
$759$	0	0
$760$	−10.0336	−0.363957
$761$	13.9482	0.505622	0.252811	−	0.967516i	$-0.418645\pi$
$761$	13.9482	0.505622	0.252811	+	0.967516i	$0.418645\pi$
$762$	−0.765885	−0.0277451
$763$	0	0
$764$	−43.7903	−1.58428
$765$	−21.1450	−0.764501
$766$	−3.68325	−0.133081
$767$	−64.5038	−2.32910
$768$	−0.769609	−0.0277709
$769$	5.40411	0.194877	0.0974385	−	0.995242i	$-0.468935\pi$
$769$	5.40411	0.194877	0.0974385	+	0.995242i	$0.468935\pi$
$770$	0	0
$771$	−3.46481	−0.124782
$772$	4.79939	0.172734
$773$	29.2118	1.05067	0.525337	−	0.850894i	$-0.323939\pi$
$773$	29.2118	1.05067	0.525337	+	0.850894i	$0.323939\pi$
$774$	−8.06507	−0.289893
$775$	−3.29990	−0.118536
$776$	−16.9627	−0.608926
$777$	0	0
$778$	−0.789444	−0.0283029
$779$	2.33092	0.0835140
$780$	2.90791	0.104120
$781$	0	0
$782$	−9.21065	−0.329372
$783$	−5.31511	−0.189946
$784$	0	0
$785$	−29.4052	−1.04952
$786$	−1.12438	−0.0401054
$787$	22.8478	0.814435	0.407217	−	0.913331i	$-0.366499\pi$
$787$	22.8478	0.814435	0.407217	+	0.913331i	$0.366499\pi$
$788$	−43.4105	−1.54644
$789$	−2.34037	−0.0833193
$790$	−10.1264	−0.360282
$791$	0	0
$792$	0	0
$793$	−18.6141	−0.661005
$794$	6.02622	0.213863
$795$	2.03350	0.0721210
$796$	−2.83214	−0.100383
$797$	−14.3818	−0.509429	−0.254715	−	0.967016i	$-0.581981\pi$
$797$	−14.3818	−0.509429	−0.254715	+	0.967016i	$0.581981\pi$
$798$	0	0
$799$	33.4230	1.18242
$800$	−10.0242	−0.354410
$801$	−41.9137	−1.48095
$802$	−4.62279	−0.163236
$803$	0	0
$804$	−2.09989	−0.0740575
$805$	0	0
$806$	3.51731	0.123892
$807$	2.61032	0.0918876
$808$	−1.44443	−0.0508150
$809$	−34.0006	−1.19540	−0.597699	−	0.801721i	$-0.703918\pi$
$809$	−34.0006	−1.19540	−0.597699	+	0.801721i	$0.703918\pi$
$810$	5.57190	0.195777
$811$	19.7225	0.692552	0.346276	−	0.938133i	$-0.387446\pi$
$811$	19.7225	0.692552	0.346276	+	0.938133i	$0.387446\pi$
$812$	0	0
$813$	2.73286	0.0958454
$814$	0	0
$815$	−15.6210	−0.547181
$816$	−2.04288	−0.0715151
$817$	28.5383	0.998430
$818$	4.57362	0.159913
$819$	0	0
$820$	−1.69424	−0.0591653
$821$	−0.307769	−0.0107412	−0.00537061	−	0.999986i	$-0.501710\pi$
$821$	−0.307769	−0.0107412	−0.00537061	+	0.999986i	$0.501710\pi$
$822$	−0.608465	−0.0212226
$823$	−19.8794	−0.692953	−0.346477	−	0.938059i	$-0.612622\pi$
$823$	−19.8794	−0.692953	−0.346477	+	0.938059i	$0.612622\pi$
$824$	−24.8964	−0.867306
$825$	0	0
$826$	0	0
$827$	46.0495	1.60130	0.800648	−	0.599134i	$-0.204488\pi$
$827$	46.0495	1.60130	0.800648	+	0.599134i	$0.204488\pi$
$828$	−29.5733	−1.02774
$829$	−15.2483	−0.529595	−0.264798	−	0.964304i	$-0.585305\pi$
$829$	−15.2483	−0.529595	−0.264798	+	0.964304i	$0.585305\pi$
$830$	−2.21555	−0.0769030
$831$	−0.233939	−0.00811526
$832$	−29.5495	−1.02444
$833$	0	0
$834$	−0.867875	−0.0300520
$835$	23.8675	0.825967
$836$	0	0
$837$	1.24636	0.0430806
$838$	10.0187	0.346089
$839$	−43.6834	−1.50812	−0.754060	−	0.656806i	$-0.771907\pi$
$839$	−43.6834	−1.50812	−0.754060	+	0.656806i	$0.771907\pi$
$840$	0	0
$841$	6.12433	0.211184
$842$	10.3172	0.355553
$843$	4.18942	0.144291
$844$	49.2387	1.69487
$845$	46.8761	1.61259
$846$	−8.87487	−0.305124
$847$	0	0
$848$	−25.9867	−0.892386
$849$	−1.63540	−0.0561267
$850$	−4.06749	−0.139514
$851$	−8.74572	−0.299799
$852$	3.77759	0.129418
$853$	−12.6550	−0.433298	−0.216649	−	0.976250i	$-0.569513\pi$
$853$	−12.6550	−0.433298	−0.216649	+	0.976250i	$0.569513\pi$
$854$	0	0
$855$	−19.8676	−0.679457
$856$	5.93642	0.202902
$857$	38.8928	1.32855	0.664277	−	0.747486i	$-0.268739\pi$
$857$	38.8928	1.32855	0.664277	+	0.747486i	$0.268739\pi$
$858$	0	0
$859$	−0.833120	−0.0284257	−0.0142128	−	0.999899i	$-0.504524\pi$
$859$	−0.833120	−0.0284257	−0.0142128	+	0.999899i	$0.504524\pi$
$860$	−20.7432	−0.707336
$861$	0	0
$862$	7.67674	0.261471
$863$	−1.64405	−0.0559640	−0.0279820	−	0.999608i	$-0.508908\pi$
$863$	−1.64405	−0.0559640	−0.0279820	+	0.999608i	$0.508908\pi$
$864$	3.78612	0.128806
$865$	31.8857	1.08415
$866$	−3.90162	−0.132583
$867$	−0.331375	−0.0112541
$868$	0	0
$869$	0	0
$870$	0.563141	0.0190923
$871$	−49.0621	−1.66240
$872$	8.27022	0.280065
$873$	−33.5879	−1.13678
$874$	−8.65420	−0.292733
$875$	0	0
$876$	−0.375948	−0.0127021
$877$	−47.2358	−1.59504	−0.797520	−	0.603293i	$-0.793855\pi$
$877$	−47.2358	−1.59504	−0.797520	+	0.603293i	$0.793855\pi$
$878$	14.8508	0.501191
$879$	−2.48025	−0.0836568
$880$	0	0
$881$	30.6325	1.03203	0.516017	−	0.856578i	$-0.327414\pi$
$881$	30.6325	1.03203	0.516017	+	0.856578i	$0.327414\pi$
$882$	0	0
$883$	−45.2525	−1.52287	−0.761434	−	0.648242i	$-0.775504\pi$
$883$	−45.2525	−1.52287	−0.761434	+	0.648242i	$0.775504\pi$
$884$	−52.4240	−1.76321
$885$	2.42172	0.0814053
$886$	5.67243	0.190569
$887$	−24.1232	−0.809977	−0.404988	−	0.914322i	$-0.632724\pi$
$887$	−24.1232	−0.809977	−0.404988	+	0.914322i	$0.632724\pi$
$888$	0.366961	0.0123144
$889$	0	0
$890$	8.91516	0.298837
$891$	0	0
$892$	13.6370	0.456601
$893$	31.4038	1.05089
$894$	−0.00530579	−0.000177452 0
$895$	15.2410	0.509450
$896$	0	0
$897$	5.22368	0.174414
$898$	−2.81332	−0.0938816
$899$	−8.23646	−0.274701
$900$	−13.0598	−0.435326
$901$	−36.6602	−1.22133
$902$	0	0
$903$	0	0
$904$	−3.48653	−0.115960
$905$	19.3260	0.642417
$906$	−0.273201	−0.00907651
$907$	23.9188	0.794209	0.397105	−	0.917773i	$-0.370015\pi$
$907$	23.9188	0.794209	0.397105	+	0.917773i	$0.370015\pi$
$908$	−33.7633	−1.12047
$909$	−2.86013	−0.0948645
$910$	0	0
$911$	−3.68709	−0.122159	−0.0610794	−	0.998133i	$-0.519454\pi$
$911$	−3.68709	−0.122159	−0.0610794	+	0.998133i	$0.519454\pi$
$912$	−1.91946	−0.0635597
$913$	0	0
$914$	−8.76689	−0.289983
$915$	0.698844	0.0231031
$916$	15.3449	0.507011
$917$	0	0
$918$	1.53628	0.0507048
$919$	−25.3877	−0.837464	−0.418732	−	0.908110i	$-0.637525\pi$
$919$	−25.3877	−0.837464	−0.418732	+	0.908110i	$0.637525\pi$
$920$	13.1009	0.431923
$921$	−0.260092	−0.00857032
$922$	2.74246	0.0903182
$923$	88.2599	2.90511
$924$	0	0
$925$	−3.86218	−0.126988
$926$	1.50514	0.0494619
$927$	−49.2973	−1.61914
$928$	−25.0202	−0.821328
$929$	−56.4056	−1.85061	−0.925304	−	0.379226i	$-0.876190\pi$
$929$	−56.4056	−1.85061	−0.925304	+	0.379226i	$0.876190\pi$
$930$	−0.132053	−0.00433020
$931$	0	0
$932$	−23.0146	−0.753869
$933$	−4.09611	−0.134101
$934$	−2.54112	−0.0831480
$935$	0	0
$936$	28.9917	0.947622
$937$	−20.4951	−0.669547	−0.334774	−	0.942299i	$-0.608660\pi$
$937$	−20.4951	−0.669547	−0.334774	+	0.942299i	$0.608660\pi$
$938$	0	0
$939$	−2.63905	−0.0861222
$940$	−22.8259	−0.744500
$941$	27.7752	0.905444	0.452722	−	0.891652i	$-0.350453\pi$
$941$	27.7752	0.905444	0.452722	+	0.891652i	$0.350453\pi$
$942$	1.06419	0.0346730
$943$	−3.04348	−0.0991093
$944$	−30.9478	−1.00727
$945$	0	0
$946$	0	0
$947$	41.8885	1.36119	0.680597	−	0.732658i	$-0.261721\pi$
$947$	41.8885	1.36119	0.680597	+	0.732658i	$0.261721\pi$
$948$	−4.43142	−0.143926
$949$	−8.78368	−0.285130
$950$	−3.82176	−0.123994
$951$	−0.503284	−0.0163201
$952$	0	0
$953$	34.0129	1.10179	0.550893	−	0.834576i	$-0.314287\pi$
$953$	34.0129	1.10179	0.550893	+	0.834576i	$0.314287\pi$
$954$	9.73443	0.315164
$955$	38.4119	1.24298
$956$	−12.8175	−0.414547
$957$	0	0
$958$	13.3093	0.430004
$959$	0	0
$960$	1.10940	0.0358058
$961$	−29.0686	−0.937697
$962$	4.11663	0.132726
$963$	11.7547	0.378790
$964$	48.7740	1.57091
$965$	−4.20992	−0.135522
$966$	0	0
$967$	−28.6521	−0.921390	−0.460695	−	0.887558i	$-0.652400\pi$
$967$	−28.6521	−0.921390	−0.460695	+	0.887558i	$0.652400\pi$
$968$	0	0
$969$	−2.70784	−0.0869884
$970$	7.14425	0.229388
$971$	−51.0701	−1.63892	−0.819459	−	0.573137i	$-0.805726\pi$
$971$	−51.0701	−1.63892	−0.819459	+	0.573137i	$0.805726\pi$
$972$	7.40826	0.237620
$973$	0	0
$974$	−0.445100	−0.0142619
$975$	2.30682	0.0738773
$976$	−8.93072	−0.285865
$977$	−7.34009	−0.234830	−0.117415	−	0.993083i	$-0.537461\pi$
$977$	−7.34009	−0.234830	−0.117415	+	0.993083i	$0.537461\pi$
$978$	0.565332	0.0180773
$979$	0	0
$980$	0	0
$981$	16.3759	0.522842
$982$	−2.73483	−0.0872718
$983$	29.0560	0.926741	0.463370	−	0.886165i	$-0.346640\pi$
$983$	29.0560	0.926741	0.463370	+	0.886165i	$0.346640\pi$
$984$	0.127701	0.00407096
$985$	38.0788	1.21329
$986$	−10.1524	−0.323317
$987$	0	0
$988$	−49.2569	−1.56707
$989$	−37.2624	−1.18488
$990$	0	0
$991$	17.5473	0.557407	0.278703	−	0.960377i	$-0.410095\pi$
$991$	17.5473	0.557407	0.278703	+	0.960377i	$0.410095\pi$
$992$	5.86709	0.186280
$993$	−3.06292	−0.0971988
$994$	0	0
$995$	2.48429	0.0787574
$996$	−0.969548	−0.0307213
$997$	24.9683	0.790753	0.395376	−	0.918519i	$-0.370614\pi$
$997$	24.9683	0.790753	0.395376	+	0.918519i	$0.370614\pi$
$998$	3.68275	0.116575
$999$	1.45873	0.0461523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.ca.1.7	✓	12
7.6	odd	2	inner	5929.2.a.ca.1.8	yes	12
11.10	odd	2		5929.2.a.cb.1.5	yes	12
77.76	even	2		5929.2.a.cb.1.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5929.2.a.ca.1.7	✓	12	1.1	even	1	trivial
5929.2.a.ca.1.8	yes	12	7.6	odd	2	inner
5929.2.a.cb.1.5	yes	12	11.10	odd	2
5929.2.a.cb.1.6	yes	12	77.76	even	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+0.390854 q^{2} -0.150034 q^{3} -1.84723 q^{4} +1.62035 q^{5} -0.0586413 q^{6} -1.50370 q^{8} -2.97749 q^{9} +0.633321 q^{10} +0.277148 q^{12} +6.47530 q^{13} -0.243108 q^{15} +3.10674 q^{16} +4.38277 q^{17} -1.16376 q^{18} +4.11799 q^{19} -2.99317 q^{20} -5.37685 q^{23} +0.225607 q^{24} -2.37446 q^{25} +2.53090 q^{26} +0.896826 q^{27} -5.92658 q^{29} -0.0950195 q^{30} +1.38975 q^{31} +4.22169 q^{32} +1.71302 q^{34} +5.50012 q^{36} +1.62655 q^{37} +1.60953 q^{38} -0.971515 q^{39} -2.43653 q^{40} +0.566034 q^{41} +6.93016 q^{43} -4.82458 q^{45} -2.10156 q^{46} +7.62601 q^{47} -0.466116 q^{48} -0.928065 q^{50} -0.657564 q^{51} -11.9614 q^{52} -8.36462 q^{53} +0.350528 q^{54} -0.617838 q^{57} -2.31642 q^{58} -9.96152 q^{59} +0.449077 q^{60} -2.87463 q^{61} +0.543188 q^{62} -4.56341 q^{64} +10.4923 q^{65} -7.57680 q^{67} -8.09600 q^{68} +0.806709 q^{69} +13.6302 q^{71} +4.47727 q^{72} -1.35649 q^{73} +0.635743 q^{74} +0.356249 q^{75} -7.60689 q^{76} -0.379720 q^{78} -15.9894 q^{79} +5.03401 q^{80} +8.79792 q^{81} +0.221237 q^{82} -3.49831 q^{83} +7.10163 q^{85} +2.70868 q^{86} +0.889187 q^{87} +14.0768 q^{89} -1.88571 q^{90} +9.93229 q^{92} -0.208509 q^{93} +2.98065 q^{94} +6.67260 q^{95} -0.633396 q^{96} +11.2806 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{4} + 20 q^{9} + 28 q^{15} + 16 q^{16} - 4 q^{18} + 36 q^{23} + 24 q^{25} - 12 q^{29} + 84 q^{30} - 40 q^{32} + 60 q^{36} + 20 q^{37} - 16 q^{39} + 12 q^{43} - 24 q^{46} + 4 q^{50} - 24 q^{51}+ \cdots + 12 q^{95}+O(q^{100}) \) 12 * q + 16 * q^4 + 20 * q^9 + 28 * q^15 + 16 * q^16 - 4 * q^18 + 36 * q^23 + 24 * q^25 - 12 * q^29 + 84 * q^30 - 40 * q^32 + 60 * q^36 + 20 * q^37 - 16 * q^39 + 12 * q^43 - 24 * q^46 + 4 * q^50 - 24 * q^51 + 16 * q^53 - 60 * q^57 - 16 * q^58 - 44 * q^60 - 36 * q^64 + 52 * q^65 + 24 * q^67 + 72 * q^71 - 36 * q^72 + 52 * q^74 + 20 * q^78 + 4 * q^79 + 56 * q^81 + 4 * q^85 + 12 * q^86 + 156 * q^92 + 32 * q^93 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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