LMFDB - Embedded newform 961.2.a.i.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(1,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,2,-3,8,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.67362363425$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.2051578125.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 19x^{5} + 14x^{4} - 28x^{3} - 11x^{2} + 6x + 1 $ x^8 - 2x^7 - 9x^6 + 19x^5 + 14x^4 - 28x^3 - 11x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.11562$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.30753 q^{2} -2.54272 q^{3} +3.32468 q^{4} -2.49846 q^{5} -5.86740 q^{6} +1.60188 q^{7} +3.05673 q^{8} +3.46545 q^{9} -5.76526 q^{10} +0.733657 q^{11} -8.45374 q^{12} -1.89598 q^{13} +3.69638 q^{14} +6.35289 q^{15} +0.404135 q^{16} -4.37924 q^{17} +7.99661 q^{18} -4.63803 q^{19} -8.30658 q^{20} -4.07313 q^{21} +1.69293 q^{22} -7.11846 q^{23} -7.77243 q^{24} +1.24230 q^{25} -4.37501 q^{26} -1.18350 q^{27} +5.32573 q^{28} -0.128939 q^{29} +14.6595 q^{30} -5.18091 q^{32} -1.86549 q^{33} -10.1052 q^{34} -4.00223 q^{35} +11.5215 q^{36} +8.42948 q^{37} -10.7024 q^{38} +4.82094 q^{39} -7.63712 q^{40} -7.37398 q^{41} -9.39887 q^{42} +0.230492 q^{43} +2.43917 q^{44} -8.65827 q^{45} -16.4260 q^{46} -8.03652 q^{47} -1.02760 q^{48} -4.43399 q^{49} +2.86664 q^{50} +11.1352 q^{51} -6.30351 q^{52} +5.73424 q^{53} -2.73096 q^{54} -1.83301 q^{55} +4.89652 q^{56} +11.7932 q^{57} -0.297530 q^{58} +9.50372 q^{59} +21.1213 q^{60} -7.84044 q^{61} +5.55122 q^{63} -12.7634 q^{64} +4.73702 q^{65} -4.30466 q^{66} +4.82658 q^{67} -14.5596 q^{68} +18.1003 q^{69} -9.23525 q^{70} -3.40502 q^{71} +10.5929 q^{72} +2.69205 q^{73} +19.4512 q^{74} -3.15882 q^{75} -15.4200 q^{76} +1.17523 q^{77} +11.1245 q^{78} +4.52794 q^{79} -1.00972 q^{80} -7.38702 q^{81} -17.0157 q^{82} +2.67035 q^{83} -13.5419 q^{84} +10.9414 q^{85} +0.531866 q^{86} +0.327856 q^{87} +2.24259 q^{88} -2.20459 q^{89} -19.9792 q^{90} -3.03712 q^{91} -23.6666 q^{92} -18.5445 q^{94} +11.5879 q^{95} +13.1736 q^{96} +12.2899 q^{97} -10.2315 q^{98} +2.54245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{5} - 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} - 18 q^{11} - 8 q^{13} - 9 q^{14} - 18 q^{15} + 4 q^{16} - 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} + q^{21}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^5 - 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 - 18 * q^11 - 8 * q^13 - 9 * q^14 - 18 * q^15 + 4 * q^16 - 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 + q^21 - 4 * q^22 - 22 * q^23 - 30 * q^24 + 13 * q^25 - 9 * q^26 - 18 * q^27 - 5 * q^28 - 12 * q^29 - 11 * q^30 - 21 * q^32 + 6 * q^33 + 7 * q^34 - 12 * q^35 - q^36 + 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 - 18 * q^46 - 18 * q^47 + q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 + q^52 - 6 * q^53 + 7 * q^54 - 28 * q^55 + 30 * q^56 + 17 * q^57 + 5 * q^58 - 4 * q^59 + 40 * q^60 - 30 * q^61 - 23 * q^63 + 9 * q^64 - 3 * q^65 + 10 * q^66 - 13 * q^67 - 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 - 33 * q^76 + 24 * q^77 - 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 - 39 * q^83 - 8 * q^84 + 26 * q^85 + 16 * q^86 - 15 * q^87 + 17 * q^88 - 27 * q^89 + 8 * q^90 - 16 * q^91 - 32 * q^92 + 22 * q^94 - 6 * q^95 + 12 * q^96 + 34 * q^97 + 10 * q^98 - 6 * 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 $

$2$	2.30753	1.63167	0.815834	−	0.578286i	$-0.196278\pi$
$2$	2.30753	1.63167	0.815834	+	0.578286i	$0.196278\pi$
$3$	−2.54272	−1.46804	−0.734021	−	0.679127i	$-0.762359\pi$
$3$	−2.54272	−1.46804	−0.734021	+	0.679127i	$0.762359\pi$
$4$	3.32468	1.66234
$5$	−2.49846	−1.11735	−0.558673	−	0.829388i	$-0.688689\pi$
$5$	−2.49846	−1.11735	−0.558673	+	0.829388i	$0.688689\pi$
$6$	−5.86740	−2.39536
$7$	1.60188	0.605453	0.302727	−	0.953077i	$-0.402103\pi$
$7$	1.60188	0.605453	0.302727	+	0.953077i	$0.402103\pi$
$8$	3.05673	1.08072
$9$	3.46545	1.15515
$10$	−5.76526	−1.82314
$11$	0.733657	0.221206	0.110603	−	0.993865i	$-0.464722\pi$
$11$	0.733657	0.221206	0.110603	+	0.993865i	$0.464722\pi$
$12$	−8.45374	−2.44039
$13$	−1.89598	−0.525849	−0.262925	−	0.964816i	$-0.584687\pi$
$13$	−1.89598	−0.525849	−0.262925	+	0.964816i	$0.584687\pi$
$14$	3.69638	0.987898
$15$	6.35289	1.64031
$16$	0.404135	0.101034
$17$	−4.37924	−1.06212	−0.531061	−	0.847334i	$-0.678206\pi$
$17$	−4.37924	−1.06212	−0.531061	+	0.847334i	$0.678206\pi$
$18$	7.99661	1.88482
$19$	−4.63803	−1.06404	−0.532018	−	0.846733i	$-0.678566\pi$
$19$	−4.63803	−1.06404	−0.532018	+	0.846733i	$0.678566\pi$
$20$	−8.30658	−1.85741
$21$	−4.07313	−0.888831
$22$	1.69293	0.360934
$23$	−7.11846	−1.48430	−0.742151	−	0.670233i	$-0.766194\pi$
$23$	−7.11846	−1.48430	−0.742151	+	0.670233i	$0.766194\pi$
$24$	−7.77243	−1.58654
$25$	1.24230	0.248460
$26$	−4.37501	−0.858011
$27$	−1.18350	−0.227765
$28$	5.32573	1.00647
$29$	−0.128939	−0.0239434	−0.0119717	−	0.999928i	$-0.503811\pi$
$29$	−0.128939	−0.0239434	−0.0119717	+	0.999928i	$0.503811\pi$
$30$	14.6595	2.67644
$31$	0	0
$31$	0	0
$32$	−5.18091	−0.915865
$33$	−1.86549	−0.324740
$34$	−10.1052	−1.73303
$35$	−4.00223	−0.676500
$36$	11.5215	1.92025
$37$	8.42948	1.38580	0.692899	−	0.721035i	$-0.256333\pi$
$37$	8.42948	1.38580	0.692899	+	0.721035i	$0.256333\pi$
$38$	−10.7024	−1.73615
$39$	4.82094	0.771969
$40$	−7.63712	−1.20754
$41$	−7.37398	−1.15162	−0.575811	−	0.817583i	$-0.695314\pi$
$41$	−7.37398	−1.15162	−0.575811	+	0.817583i	$0.695314\pi$
$42$	−9.39887	−1.45028
$43$	0.230492	0.0351497	0.0175748	−	0.999846i	$-0.494405\pi$
$43$	0.230492	0.0351497	0.0175748	+	0.999846i	$0.494405\pi$
$44$	2.43917	0.367719
$45$	−8.65827	−1.29070
$46$	−16.4260	−2.42189
$47$	−8.03652	−1.17225	−0.586124	−	0.810222i	$-0.699347\pi$
$47$	−8.03652	−1.17225	−0.586124	+	0.810222i	$0.699347\pi$
$48$	−1.02760	−0.148322
$49$	−4.43399	−0.633427
$50$	2.86664	0.405404
$51$	11.1352	1.55924
$52$	−6.30351	−0.874140
$53$	5.73424	0.787658	0.393829	−	0.919184i	$-0.371150\pi$
$53$	5.73424	0.787658	0.393829	+	0.919184i	$0.371150\pi$
$54$	−2.73096	−0.371636
$55$	−1.83301	−0.247163
$56$	4.89652	0.654324
$57$	11.7932	1.56205
$58$	−0.297530	−0.0390676
$59$	9.50372	1.23728	0.618639	−	0.785675i	$-0.287684\pi$
$59$	9.50372	1.23728	0.618639	+	0.785675i	$0.287684\pi$
$60$	21.1213	2.72675
$61$	−7.84044	−1.00387	−0.501933	−	0.864907i	$-0.667377\pi$
$61$	−7.84044	−1.00387	−0.501933	+	0.864907i	$0.667377\pi$
$62$	0	0
$63$	5.55122	0.699388
$64$	−12.7634	−1.59542
$65$	4.73702	0.587555
$66$	−4.30466	−0.529867
$67$	4.82658	0.589660	0.294830	−	0.955550i	$-0.404737\pi$
$67$	4.82658	0.589660	0.294830	+	0.955550i	$0.404737\pi$
$68$	−14.5596	−1.76561
$69$	18.1003	2.17902
$70$	−9.23525	−1.10382
$71$	−3.40502	−0.404101	−0.202051	−	0.979375i	$-0.564761\pi$
$71$	−3.40502	−0.404101	−0.202051	+	0.979375i	$0.564761\pi$
$72$	10.5929	1.24839
$73$	2.69205	0.315080	0.157540	−	0.987513i	$-0.449644\pi$
$73$	2.69205	0.315080	0.157540	+	0.987513i	$0.449644\pi$
$74$	19.4512	2.26116
$75$	−3.15882	−0.364750
$76$	−15.4200	−1.76879
$77$	1.17523	0.133930
$78$	11.1245	1.25960
$79$	4.52794	0.509434	0.254717	−	0.967016i	$-0.418018\pi$
$79$	4.52794	0.509434	0.254717	+	0.967016i	$0.418018\pi$
$80$	−1.00972	−0.112890
$81$	−7.38702	−0.820780
$82$	−17.0157	−1.87906
$83$	2.67035	0.293109	0.146554	−	0.989203i	$-0.453182\pi$
$83$	2.67035	0.293109	0.146554	+	0.989203i	$0.453182\pi$
$84$	−13.5419	−1.47754
$85$	10.9414	1.18676
$86$	0.531866	0.0573526
$87$	0.327856	0.0351499
$88$	2.24259	0.239061
$89$	−2.20459	−0.233686	−0.116843	−	0.993150i	$-0.537277\pi$
$89$	−2.20459	−0.233686	−0.116843	+	0.993150i	$0.537277\pi$
$90$	−19.9792	−2.10599
$91$	−3.03712	−0.318377
$92$	−23.6666	−2.46741
$93$	0	0
$94$	−18.5445	−1.91272
$95$	11.5879	1.18890
$96$	13.1736	1.34453
$97$	12.2899	1.24785	0.623923	−	0.781485i	$-0.285538\pi$
$97$	12.2899	1.24785	0.623923	+	0.781485i	$0.285538\pi$
$98$	−10.2315	−1.03354
$99$	2.54245	0.255526
$100$	4.13025	0.413025
$101$	7.34432	0.730787	0.365394	−	0.930853i	$-0.380934\pi$
$101$	7.34432	0.730787	0.365394	+	0.930853i	$0.380934\pi$
$102$	25.6948	2.54416
$103$	5.58875	0.550676	0.275338	−	0.961347i	$-0.411210\pi$
$103$	5.58875	0.550676	0.275338	+	0.961347i	$0.411210\pi$
$104$	−5.79549	−0.568295
$105$	10.1766	0.993131
$106$	13.2319	1.28520
$107$	1.82416	0.176348	0.0881741	−	0.996105i	$-0.471897\pi$
$107$	1.82416	0.176348	0.0881741	+	0.996105i	$0.471897\pi$
$108$	−3.93476	−0.378622
$109$	11.7653	1.12691	0.563455	−	0.826147i	$-0.309472\pi$
$109$	11.7653	1.12691	0.563455	+	0.826147i	$0.309472\pi$
$110$	−4.22972	−0.403288
$111$	−21.4338	−2.03441
$112$	0.647376	0.0611712
$113$	11.0545	1.03992	0.519962	−	0.854190i	$-0.325946\pi$
$113$	11.0545	1.03992	0.519962	+	0.854190i	$0.325946\pi$
$114$	27.2132	2.54875
$115$	17.7852	1.65848
$116$	−0.428681	−0.0398020
$117$	−6.57040	−0.607434
$118$	21.9301	2.01883
$119$	−7.01501	−0.643065
$120$	19.4191	1.77271
$121$	−10.4617	−0.951068
$122$	−18.0920	−1.63797
$123$	18.7500	1.69063
$124$	0	0
$125$	9.38846	0.839730
$126$	12.8096	1.14117
$127$	−1.28703	−0.114206	−0.0571028	−	0.998368i	$-0.518186\pi$
$127$	−1.28703	−0.114206	−0.0571028	+	0.998368i	$0.518186\pi$
$128$	−19.0900	−1.68733
$129$	−0.586077	−0.0516012
$130$	10.9308	0.958694
$131$	−8.02035	−0.700742	−0.350371	−	0.936611i	$-0.613944\pi$
$131$	−8.02035	−0.700742	−0.350371	+	0.936611i	$0.613944\pi$
$132$	−6.20214	−0.539827
$133$	−7.42955	−0.644224
$134$	11.1375	0.962130
$135$	2.95692	0.254492
$136$	−13.3862	−1.14785
$137$	−16.4768	−1.40770	−0.703852	−	0.710347i	$-0.748538\pi$
$137$	−16.4768	−1.40770	−0.703852	+	0.710347i	$0.748538\pi$
$138$	41.7669	3.55543
$139$	7.33982	0.622555	0.311278	−	0.950319i	$-0.399243\pi$
$139$	7.33982	0.622555	0.311278	+	0.950319i	$0.399243\pi$
$140$	−13.3061	−1.12457
$141$	20.4347	1.72091
$142$	−7.85717	−0.659359
$143$	−1.39100	−0.116321
$144$	1.40051	0.116709
$145$	0.322149	0.0267530
$146$	6.21197	0.514106
$147$	11.2744	0.929897
$148$	28.0253	2.30367
$149$	−6.36193	−0.521189	−0.260595	−	0.965448i	$-0.583919\pi$
$149$	−6.36193	−0.521189	−0.260595	+	0.965448i	$0.583919\pi$
$150$	−7.28907	−0.595150
$151$	−5.52473	−0.449596	−0.224798	−	0.974405i	$-0.572172\pi$
$151$	−5.52473	−0.449596	−0.224798	+	0.974405i	$0.572172\pi$
$152$	−14.1772	−1.14992
$153$	−15.1760	−1.22691
$154$	2.71187	0.218529
$155$	0	0
$156$	16.0281	1.28327
$157$	7.99448	0.638029	0.319014	−	0.947750i	$-0.396648\pi$
$157$	7.99448	0.638029	0.319014	+	0.947750i	$0.396648\pi$
$158$	10.4484	0.831226
$159$	−14.5806	−1.15632
$160$	12.9443	1.02334
$161$	−11.4029	−0.898675
$162$	−17.0458	−1.33924
$163$	−17.0654	−1.33667	−0.668333	−	0.743863i	$-0.732992\pi$
$163$	−17.0654	−1.33667	−0.668333	+	0.743863i	$0.732992\pi$
$164$	−24.5161	−1.91439
$165$	4.66084	0.362846
$166$	6.16190	0.478256
$167$	−24.3722	−1.88598	−0.942989	−	0.332824i	$-0.891999\pi$
$167$	−24.3722	−1.88598	−0.942989	+	0.332824i	$0.891999\pi$
$168$	−12.4505	−0.960576
$169$	−9.40528	−0.723483
$170$	25.2475	1.93639
$171$	−16.0728	−1.22912
$172$	0.766311	0.0584307
$173$	8.97360	0.682250	0.341125	−	0.940018i	$-0.389192\pi$
$173$	8.97360	0.682250	0.341125	+	0.940018i	$0.389192\pi$
$174$	0.756537	0.0573529
$175$	1.99001	0.150431
$176$	0.296497	0.0223493
$177$	−24.1653	−1.81638
$178$	−5.08714	−0.381297
$179$	−11.2905	−0.843893	−0.421946	−	0.906621i	$-0.638653\pi$
$179$	−11.2905	−0.843893	−0.421946	+	0.906621i	$0.638653\pi$
$180$	−28.7860	−2.14558
$181$	−14.9410	−1.11056	−0.555279	−	0.831664i	$-0.687389\pi$
$181$	−14.9410	−1.11056	−0.555279	+	0.831664i	$0.687389\pi$
$182$	−7.00824	−0.519485
$183$	19.9361	1.47372
$184$	−21.7592	−1.60411
$185$	−21.0607	−1.54841
$186$	0	0
$187$	−3.21286	−0.234947
$188$	−26.7189	−1.94867
$189$	−1.89582	−0.137901
$190$	26.7394	1.93988
$191$	2.26093	0.163595	0.0817975	−	0.996649i	$-0.473934\pi$
$191$	2.26093	0.163595	0.0817975	+	0.996649i	$0.473934\pi$
$192$	32.4537	2.34215
$193$	25.6643	1.84735	0.923677	−	0.383173i	$-0.125169\pi$
$193$	25.6643	1.84735	0.923677	+	0.383173i	$0.125169\pi$
$194$	28.3592	2.03607
$195$	−12.0449	−0.862555
$196$	−14.7416	−1.05297
$197$	−6.19571	−0.441426	−0.220713	−	0.975339i	$-0.570838\pi$
$197$	−6.19571	−0.441426	−0.220713	+	0.975339i	$0.570838\pi$
$198$	5.86676	0.416933
$199$	−4.56933	−0.323911	−0.161956	−	0.986798i	$-0.551780\pi$
$199$	−4.56933	−0.323911	−0.161956	+	0.986798i	$0.551780\pi$
$200$	3.79738	0.268515
$201$	−12.2727	−0.865647
$202$	16.9472	1.19240
$203$	−0.206545	−0.0144966
$204$	37.0210	2.59199
$205$	18.4236	1.28676
$206$	12.8962	0.898520
$207$	−24.6686	−1.71459
$208$	−0.766231	−0.0531285
$209$	−3.40272	−0.235371
$210$	23.4827	1.62046
$211$	−18.6168	−1.28163	−0.640816	−	0.767695i	$-0.721404\pi$
$211$	−18.6168	−1.28163	−0.640816	+	0.767695i	$0.721404\pi$
$212$	19.0645	1.30936
$213$	8.65802	0.593238
$214$	4.20930	0.287742
$215$	−0.575874	−0.0392743
$216$	−3.61764	−0.246149
$217$	0	0
$218$	27.1487	1.83874
$219$	−6.84513	−0.462551
$220$	−6.09418	−0.410869
$221$	8.30293	0.558516
$222$	−49.4591	−3.31948
$223$	6.21495	0.416184	0.208092	−	0.978109i	$-0.433275\pi$
$223$	6.21495	0.416184	0.208092	+	0.978109i	$0.433275\pi$
$224$	−8.29919	−0.554513
$225$	4.30512	0.287008
$226$	25.5086	1.69681
$227$	−13.0478	−0.866013	−0.433006	−	0.901391i	$-0.642547\pi$
$227$	−13.0478	−0.866013	−0.433006	+	0.901391i	$0.642547\pi$
$228$	39.2087	2.59666
$229$	15.2779	1.00959	0.504797	−	0.863238i	$-0.331567\pi$
$229$	15.2779	1.00959	0.504797	+	0.863238i	$0.331567\pi$
$230$	41.0398	2.70608
$231$	−2.98828	−0.196615
$232$	−0.394132	−0.0258760
$233$	13.0613	0.855671	0.427836	−	0.903857i	$-0.359276\pi$
$233$	13.0613	0.855671	0.427836	+	0.903857i	$0.359276\pi$
$234$	−15.1614	−0.991130
$235$	20.0789	1.30980
$236$	31.5968	2.05678
$237$	−11.5133	−0.747870
$238$	−16.1873	−1.04927
$239$	−23.4422	−1.51635	−0.758176	−	0.652050i	$-0.773909\pi$
$239$	−23.4422	−1.51635	−0.758176	+	0.652050i	$0.773909\pi$
$240$	2.56743	0.165727
$241$	24.7121	1.59185	0.795923	−	0.605398i	$-0.206986\pi$
$241$	24.7121	1.59185	0.795923	+	0.605398i	$0.206986\pi$
$242$	−24.1408	−1.55183
$243$	22.3337	1.43271
$244$	−26.0669	−1.66876
$245$	11.0781	0.707756
$246$	43.2661	2.75855
$247$	8.79358	0.559522
$248$	0	0
$249$	−6.78996	−0.430296
$250$	21.6641	1.37016
$251$	−23.1941	−1.46400	−0.732001	−	0.681304i	$-0.761413\pi$
$251$	−23.1941	−1.46400	−0.732001	+	0.681304i	$0.761413\pi$
$252$	18.4560	1.16262
$253$	−5.22251	−0.328336
$254$	−2.96986	−0.186346
$255$	−27.8208	−1.74221
$256$	−18.5239	−1.15774
$257$	15.3461	0.957264	0.478632	−	0.878016i	$-0.341133\pi$
$257$	15.3461	0.957264	0.478632	+	0.878016i	$0.341133\pi$
$258$	−1.35239	−0.0841960
$259$	13.5030	0.839035
$260$	15.7491	0.976716
$261$	−0.446831	−0.0276581
$262$	−18.5072	−1.14338
$263$	−6.80588	−0.419668	−0.209834	−	0.977737i	$-0.567292\pi$
$263$	−6.80588	−0.419668	−0.209834	+	0.977737i	$0.567292\pi$
$264$	−5.70230	−0.350952
$265$	−14.3268	−0.880086
$266$	−17.1439	−1.05116
$267$	5.60566	0.343061
$268$	16.0468	0.980216
$269$	10.5196	0.641394	0.320697	−	0.947182i	$-0.396083\pi$
$269$	10.5196	0.641394	0.320697	+	0.947182i	$0.396083\pi$
$270$	6.82318	0.415246
$271$	−1.57714	−0.0958044	−0.0479022	−	0.998852i	$-0.515254\pi$
$271$	−1.57714	−0.0958044	−0.0479022	+	0.998852i	$0.515254\pi$
$272$	−1.76981	−0.107310
$273$	7.72256	0.467391
$274$	−38.0206	−2.29691
$275$	0.911421	0.0549608
$276$	60.1776	3.62227
$277$	12.1014	0.727100	0.363550	−	0.931575i	$-0.381565\pi$
$277$	12.1014	0.727100	0.363550	+	0.931575i	$0.381565\pi$
$278$	16.9368	1.01580
$279$	0	0
$280$	−12.2337	−0.731106
$281$	−21.4727	−1.28096	−0.640478	−	0.767976i	$-0.721264\pi$
$281$	−21.4727	−1.28096	−0.640478	+	0.767976i	$0.721264\pi$
$282$	47.1535	2.80795
$283$	−0.688807	−0.0409453	−0.0204726	−	0.999790i	$-0.506517\pi$
$283$	−0.688807	−0.0409453	−0.0204726	+	0.999790i	$0.506517\pi$
$284$	−11.3206	−0.671753
$285$	−29.4649	−1.74535
$286$	−3.20976	−0.189797
$287$	−11.8122	−0.697253
$288$	−17.9542	−1.05796
$289$	2.17774	0.128102
$290$	0.743367	0.0436520
$291$	−31.2497	−1.83189
$292$	8.95019	0.523770
$293$	9.01188	0.526480	0.263240	−	0.964730i	$-0.415209\pi$
$293$	9.01188	0.526480	0.263240	+	0.964730i	$0.415209\pi$
$294$	26.0160	1.51728
$295$	−23.7447	−1.38247
$296$	25.7667	1.49766
$297$	−0.868282	−0.0503828
$298$	−14.6803	−0.850408
$299$	13.4964	0.780519
$300$	−10.5021	−0.606338
$301$	0.369220	0.0212815
$302$	−12.7485	−0.733592
$303$	−18.6746	−1.07283
$304$	−1.87439	−0.107504
$305$	19.5890	1.12166
$306$	−35.0191	−2.00191
$307$	−31.3326	−1.78825	−0.894124	−	0.447819i	$-0.852201\pi$
$307$	−31.3326	−1.78825	−0.894124	+	0.447819i	$0.852201\pi$
$308$	3.90726	0.222637
$309$	−14.2107	−0.808416
$310$	0	0
$311$	−17.7139	−1.00447	−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139	−1.00447	−0.502233	+	0.864732i	$0.667488\pi$
$312$	14.7363	0.834281
$313$	−21.6687	−1.22479	−0.612394	−	0.790553i	$-0.709793\pi$
$313$	−21.6687	−1.22479	−0.612394	+	0.790553i	$0.709793\pi$
$314$	18.4475	1.04105
$315$	−13.8695	−0.781458
$316$	15.0540	0.846852
$317$	1.01605	0.0570669	0.0285334	−	0.999593i	$-0.490916\pi$
$317$	1.01605	0.0570669	0.0285334	+	0.999593i	$0.490916\pi$
$318$	−33.6451	−1.88672
$319$	−0.0945970	−0.00529641
$320$	31.8888	1.78264
$321$	−4.63834	−0.258887
$322$	−26.3125	−1.46634
$323$	20.3110	1.13014
$324$	−24.5595	−1.36442
$325$	−2.35537	−0.130652
$326$	−39.3789	−2.18099
$327$	−29.9159	−1.65435
$328$	−22.5403	−1.24458
$329$	−12.8735	−0.709741
$330$	10.7550	0.592044
$331$	26.6894	1.46698	0.733492	−	0.679698i	$-0.237889\pi$
$331$	26.6894	1.46698	0.733492	+	0.679698i	$0.237889\pi$
$332$	8.87806	0.487247
$333$	29.2119	1.60080
$334$	−56.2395	−3.07729
$335$	−12.0590	−0.658854
$336$	−1.64610	−0.0898020
$337$	31.9415	1.73997	0.869983	−	0.493081i	$-0.164129\pi$
$337$	31.9415	1.73997	0.869983	+	0.493081i	$0.164129\pi$
$338$	−21.7029	−1.18048
$339$	−28.1086	−1.52665
$340$	36.3765	1.97279
$341$	0	0
$342$	−37.0885	−2.00552
$343$	−18.3159	−0.988963
$344$	0.704552	0.0379869
$345$	−45.2228	−2.43472
$346$	20.7068	1.11321
$347$	3.12131	0.167561	0.0837804	−	0.996484i	$-0.473301\pi$
$347$	3.12131	0.167561	0.0837804	+	0.996484i	$0.473301\pi$
$348$	1.09002	0.0584310
$349$	−22.0265	−1.17905	−0.589525	−	0.807750i	$-0.700685\pi$
$349$	−22.0265	−1.17905	−0.589525	+	0.807750i	$0.700685\pi$
$350$	4.59201	0.245453
$351$	2.24389	0.119770
$352$	−3.80101	−0.202595
$353$	4.93239	0.262525	0.131262	−	0.991348i	$-0.458097\pi$
$353$	4.93239	0.262525	0.131262	+	0.991348i	$0.458097\pi$
$354$	−55.7621	−2.96372
$355$	8.50730	0.451520
$356$	−7.32954	−0.388465
$357$	17.8372	0.944046
$358$	−26.0532	−1.37695
$359$	−0.360860	−0.0190455	−0.00952273	−	0.999955i	$-0.503031\pi$
$359$	−0.360860	−0.0190455	−0.00952273	+	0.999955i	$0.503031\pi$
$360$	−26.4660	−1.39488
$361$	2.51129	0.132173
$362$	−34.4769	−1.81206
$363$	26.6013	1.39621
$364$	−10.0975	−0.529251
$365$	−6.72597	−0.352053
$366$	46.0030	2.40462
$367$	−29.3869	−1.53398	−0.766992	−	0.641657i	$-0.778247\pi$
$367$	−29.3869	−1.53398	−0.766992	+	0.641657i	$0.778247\pi$
$368$	−2.87682	−0.149965
$369$	−25.5541	−1.33029
$370$	−48.5981	−2.52650
$371$	9.18555	0.476890
$372$	0	0
$373$	17.7284	0.917941	0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284	0.917941	0.458971	+	0.888451i	$0.348218\pi$
$374$	−7.41376	−0.383356
$375$	−23.8723	−1.23276
$376$	−24.5655	−1.26687
$377$	0.244465	0.0125906
$378$	−4.37466	−0.225008
$379$	−2.46042	−0.126383	−0.0631917	−	0.998001i	$-0.520128\pi$
$379$	−2.46042	−0.126383	−0.0631917	+	0.998001i	$0.520128\pi$
$380$	38.5261	1.97635
$381$	3.27257	0.167659
$382$	5.21715	0.266933
$383$	−19.1179	−0.976880	−0.488440	−	0.872598i	$-0.662434\pi$
$383$	−19.1179	−0.976880	−0.488440	+	0.872598i	$0.662434\pi$
$384$	48.5406	2.47708
$385$	−2.93626	−0.149646
$386$	59.2209	3.01427
$387$	0.798756	0.0406031
$388$	40.8599	2.07435
$389$	5.27106	0.267253	0.133627	−	0.991032i	$-0.457338\pi$
$389$	5.27106	0.267253	0.133627	+	0.991032i	$0.457338\pi$
$390$	−27.7940	−1.40740
$391$	31.1735	1.57651
$392$	−13.5535	−0.684556
$393$	20.3935	1.02872
$394$	−14.2968	−0.720261
$395$	−11.3129	−0.569213
$396$	8.45282	0.424770
$397$	16.9255	0.849467	0.424733	−	0.905319i	$-0.360368\pi$
$397$	16.9255	0.849467	0.424733	+	0.905319i	$0.360368\pi$
$398$	−10.5439	−0.528516
$399$	18.8913	0.945748
$400$	0.502057	0.0251029
$401$	38.0397	1.89961	0.949805	−	0.312843i	$-0.101281\pi$
$401$	38.0397	1.89961	0.949805	+	0.312843i	$0.101281\pi$
$402$	−28.3195	−1.41245
$403$	0	0
$404$	24.4175	1.21482
$405$	18.4562	0.917095
$406$	−0.476607	−0.0236536
$407$	6.18434	0.306546
$408$	34.0373	1.68510
$409$	0.498684	0.0246583	0.0123292	−	0.999924i	$-0.496075\pi$
$409$	0.498684	0.0246583	0.0123292	+	0.999924i	$0.496075\pi$
$410$	42.5129	2.09956
$411$	41.8958	2.06657
$412$	18.5808	0.915411
$413$	15.2238	0.749114
$414$	−56.9235	−2.79764
$415$	−6.67176	−0.327504
$416$	9.82289	0.481607
$417$	−18.6631	−0.913938
$418$	−7.85186	−0.384047
$419$	13.5100	0.660007	0.330003	−	0.943980i	$-0.392950\pi$
$419$	13.5100	0.660007	0.330003	+	0.943980i	$0.392950\pi$
$420$	33.8338	1.65092
$421$	−30.9151	−1.50671	−0.753355	−	0.657614i	$-0.771566\pi$
$421$	−30.9151	−1.50671	−0.753355	+	0.657614i	$0.771566\pi$
$422$	−42.9587	−2.09120
$423$	−27.8501	−1.35412
$424$	17.5280	0.851237
$425$	−5.44033	−0.263895
$426$	19.9786	0.967967
$427$	−12.5594	−0.607793
$428$	6.06475	0.293151
$429$	3.53692	0.170764
$430$	−1.32885	−0.0640826
$431$	−12.0548	−0.580659	−0.290330	−	0.956927i	$-0.593765\pi$
$431$	−12.0548	−0.580659	−0.290330	+	0.956927i	$0.593765\pi$
$432$	−0.478294	−0.0230119
$433$	−32.3919	−1.55665	−0.778327	−	0.627860i	$-0.783931\pi$
$433$	−32.3919	−1.55665	−0.778327	+	0.627860i	$0.783931\pi$
$434$	0	0
$435$	−0.819136	−0.0392745
$436$	39.1158	1.87331
$437$	33.0156	1.57935
$438$	−15.7953	−0.754730
$439$	12.3682	0.590300	0.295150	−	0.955451i	$-0.404630\pi$
$439$	12.3682	0.590300	0.295150	+	0.955451i	$0.404630\pi$
$440$	−5.60303	−0.267114
$441$	−15.3657	−0.731702
$442$	19.1592	0.911312
$443$	−4.72341	−0.224416	−0.112208	−	0.993685i	$-0.535792\pi$
$443$	−4.72341	−0.224416	−0.112208	+	0.993685i	$0.535792\pi$
$444$	−71.2606	−3.38188
$445$	5.50807	0.261108
$446$	14.3412	0.679074
$447$	16.1766	0.765128
$448$	−20.4454	−0.965953
$449$	−15.9842	−0.754341	−0.377170	−	0.926144i	$-0.623103\pi$
$449$	−15.9842	−0.754341	−0.377170	+	0.926144i	$0.623103\pi$
$450$	9.93418	0.468302
$451$	−5.40997	−0.254746
$452$	36.7528	1.72871
$453$	14.0479	0.660027
$454$	−30.1081	−1.41305
$455$	7.58813	0.355737
$456$	36.0487	1.68814
$457$	4.55775	0.213203	0.106601	−	0.994302i	$-0.466003\pi$
$457$	4.55775	0.213203	0.106601	+	0.994302i	$0.466003\pi$
$458$	35.2542	1.64732
$459$	5.18283	0.241914
$460$	59.1301	2.75695
$461$	−16.9910	−0.791349	−0.395675	−	0.918391i	$-0.629489\pi$
$461$	−16.9910	−0.791349	−0.395675	+	0.918391i	$0.629489\pi$
$462$	−6.89554	−0.320810
$463$	27.4279	1.27468	0.637340	−	0.770582i	$-0.280035\pi$
$463$	27.4279	1.27468	0.637340	+	0.770582i	$0.280035\pi$
$464$	−0.0521088	−0.00241909
$465$	0	0
$466$	30.1392	1.39617
$467$	−22.9105	−1.06017	−0.530086	−	0.847944i	$-0.677840\pi$
$467$	−22.9105	−1.06017	−0.530086	+	0.847944i	$0.677840\pi$
$468$	−21.8445	−1.00976
$469$	7.73159	0.357012
$470$	46.3327	2.13717
$471$	−20.3277	−0.936653
$472$	29.0503	1.33715
$473$	0.169102	0.00777531
$474$	−26.5673	−1.22028
$475$	−5.76182	−0.264370
$476$	−23.3227	−1.06899
$477$	19.8717	0.909862
$478$	−54.0936	−2.47418
$479$	9.04705	0.413370	0.206685	−	0.978407i	$-0.433732\pi$
$479$	9.04705	0.413370	0.206685	+	0.978407i	$0.433732\pi$
$480$	−32.9138	−1.50230
$481$	−15.9821	−0.728720
$482$	57.0238	2.59736
$483$	28.9945	1.31929
$484$	−34.7820	−1.58100
$485$	−30.7057	−1.39428
$486$	51.5355	2.33770
$487$	−23.6227	−1.07045	−0.535223	−	0.844711i	$-0.679772\pi$
$487$	−23.6227	−1.07045	−0.535223	+	0.844711i	$0.679772\pi$
$488$	−23.9661	−1.08490
$489$	43.3926	1.96228
$490$	25.5631	1.15482
$491$	9.22692	0.416405	0.208202	−	0.978086i	$-0.433239\pi$
$491$	9.22692	0.416405	0.208202	+	0.978086i	$0.433239\pi$
$492$	62.3377	2.81040
$493$	0.564655	0.0254308
$494$	20.2914	0.912955
$495$	−6.35220	−0.285510
$496$	0	0
$497$	−5.45442	−0.244664
$498$	−15.6680	−0.702101
$499$	28.4139	1.27198	0.635992	−	0.771696i	$-0.280591\pi$
$499$	28.4139	1.27198	0.635992	+	0.771696i	$0.280591\pi$
$500$	31.2136	1.39592
$501$	61.9718	2.76870
$502$	−53.5211	−2.38876
$503$	18.2781	0.814979	0.407489	−	0.913210i	$-0.366404\pi$
$503$	18.2781	0.814979	0.407489	+	0.913210i	$0.366404\pi$
$504$	16.9686	0.755842
$505$	−18.3495	−0.816541
$506$	−12.0511	−0.535736
$507$	23.9150	1.06210
$508$	−4.27897	−0.189849
$509$	10.3864	0.460367	0.230184	−	0.973147i	$-0.426067\pi$
$509$	10.3864	0.460367	0.230184	+	0.973147i	$0.426067\pi$
$510$	−64.1973	−2.84271
$511$	4.31233	0.190766
$512$	−4.56446	−0.201722
$513$	5.48910	0.242350
$514$	35.4116	1.56194
$515$	−13.9633	−0.615295
$516$	−1.94852	−0.0857787
$517$	−5.89605	−0.259308
$518$	31.1585	1.36903
$519$	−22.8174	−1.00157
$520$	14.4798	0.634981
$521$	9.25044	0.405269	0.202635	−	0.979254i	$-0.435050\pi$
$521$	9.25044	0.405269	0.202635	+	0.979254i	$0.435050\pi$
$522$	−1.03107	−0.0451289
$523$	−6.57516	−0.287512	−0.143756	−	0.989613i	$-0.545918\pi$
$523$	−6.57516	−0.287512	−0.143756	+	0.989613i	$0.545918\pi$
$524$	−26.6651	−1.16487
$525$	−5.06005	−0.220839
$526$	−15.7047	−0.684759
$527$	0	0
$528$	−0.753909	−0.0328097
$529$	27.6725	1.20315
$530$	−33.0594	−1.43601
$531$	32.9346	1.42924
$532$	−24.7009	−1.07092
$533$	13.9809	0.605579
$534$	12.9352	0.559761
$535$	−4.55759	−0.197042
$536$	14.7536	0.637257
$537$	28.7087	1.23887
$538$	24.2744	1.04654
$539$	−3.25302	−0.140118
$540$	9.83083	0.423051
$541$	−2.20328	−0.0947262	−0.0473631	−	0.998878i	$-0.515082\pi$
$541$	−2.20328	−0.0947262	−0.0473631	+	0.998878i	$0.515082\pi$
$542$	−3.63929	−0.156321
$543$	37.9909	1.63035
$544$	22.6885	0.972760
$545$	−29.3951	−1.25915
$546$	17.8200	0.762627
$547$	−4.86344	−0.207946	−0.103973	−	0.994580i	$-0.533156\pi$
$547$	−4.86344	−0.207946	−0.103973	+	0.994580i	$0.533156\pi$
$548$	−54.7799	−2.34008
$549$	−27.1706	−1.15961
$550$	2.10313	0.0896777
$551$	0.598022	0.0254766
$552$	55.3277	2.35491
$553$	7.25322	0.308438
$554$	27.9242	1.18639
$555$	53.5516	2.27314
$556$	24.4025	1.03490
$557$	11.0363	0.467623	0.233811	−	0.972282i	$-0.424880\pi$
$557$	11.0363	0.467623	0.233811	+	0.972282i	$0.424880\pi$
$558$	0	0
$559$	−0.437007	−0.0184834
$560$	−1.61744	−0.0683494
$561$	8.16941	0.344913
$562$	−49.5489	−2.09010
$563$	−11.1924	−0.471704	−0.235852	−	0.971789i	$-0.575788\pi$
$563$	−11.1924	−0.471704	−0.235852	+	0.971789i	$0.575788\pi$
$564$	67.9387	2.86074
$565$	−27.6193	−1.16195
$566$	−1.58944	−0.0668091
$567$	−11.8331	−0.496944
$568$	−10.4082	−0.436720
$569$	−46.9220	−1.96707	−0.983536	−	0.180713i	$-0.942160\pi$
$569$	−46.9220	−1.96707	−0.983536	+	0.180713i	$0.942160\pi$
$570$	−67.9910	−2.84783
$571$	−20.4597	−0.856210	−0.428105	−	0.903729i	$-0.640819\pi$
$571$	−20.4597	−0.856210	−0.428105	+	0.903729i	$0.640819\pi$
$572$	−4.62461	−0.193365
$573$	−5.74892	−0.240164
$574$	−27.2570	−1.13769
$575$	−8.84326	−0.368789
$576$	−44.2308	−1.84295
$577$	3.64835	0.151883	0.0759413	−	0.997112i	$-0.475804\pi$
$577$	3.64835	0.151883	0.0759413	+	0.997112i	$0.475804\pi$
$578$	5.02520	0.209021
$579$	−65.2571	−2.71199
$580$	1.07104	0.0444726
$581$	4.27758	0.177464
$582$	−72.1096	−2.98904
$583$	4.20696	0.174235
$584$	8.22887	0.340513
$585$	16.4159	0.678713
$586$	20.7952	0.859040
$587$	−22.8726	−0.944053	−0.472027	−	0.881584i	$-0.656477\pi$
$587$	−22.8726	−0.944053	−0.472027	+	0.881584i	$0.656477\pi$
$588$	37.4838	1.54580
$589$	0	0
$590$	−54.7914	−2.25573
$591$	15.7540	0.648032
$592$	3.40665	0.140012
$593$	−19.4598	−0.799117	−0.399558	−	0.916708i	$-0.630837\pi$
$593$	−19.4598	−0.799117	−0.399558	+	0.916708i	$0.630837\pi$
$594$	−2.00358	−0.0822081
$595$	17.5267	0.718525
$596$	−21.1514	−0.866394
$597$	11.6185	0.475515
$598$	31.1434	1.27355
$599$	35.1718	1.43708	0.718541	−	0.695484i	$-0.244810\pi$
$599$	35.1718	1.43708	0.718541	+	0.695484i	$0.244810\pi$
$600$	−9.65569	−0.394192
$601$	5.88806	0.240179	0.120089	−	0.992763i	$-0.461682\pi$
$601$	5.88806	0.240179	0.120089	+	0.992763i	$0.461682\pi$
$602$	0.851984	0.0347243
$603$	16.7262	0.681145
$604$	−18.3680	−0.747382
$605$	26.1383	1.06267
$606$	−43.0921	−1.75050
$607$	38.8848	1.57829	0.789143	−	0.614209i	$-0.210525\pi$
$607$	38.8848	1.57829	0.789143	+	0.614209i	$0.210525\pi$
$608$	24.0292	0.974513
$609$	0.525186	0.0212816
$610$	45.2022	1.83018
$611$	15.2371	0.616425
$612$	−50.4554	−2.03954
$613$	−45.6024	−1.84186	−0.920931	−	0.389725i	$-0.872570\pi$
$613$	−45.6024	−1.84186	−0.920931	+	0.389725i	$0.872570\pi$
$614$	−72.3009	−2.91783
$615$	−46.8461	−1.88902
$616$	3.59236	0.144740
$617$	−6.62648	−0.266772	−0.133386	−	0.991064i	$-0.542585\pi$
$617$	−6.62648	−0.266772	−0.133386	+	0.991064i	$0.542585\pi$
$618$	−32.7915	−1.31907
$619$	41.5360	1.66947	0.834736	−	0.550650i	$-0.185620\pi$
$619$	41.5360	1.66947	0.834736	+	0.550650i	$0.185620\pi$
$620$	0	0
$621$	8.42469	0.338071
$622$	−40.8754	−1.63895
$623$	−3.53148	−0.141486
$624$	1.94831	0.0779950
$625$	−29.6682	−1.18673
$626$	−50.0011	−1.99845
$627$	8.65218	0.345535
$628$	26.5791	1.06062
$629$	−36.9147	−1.47189
$630$	−32.0042	−1.27508
$631$	11.1447	0.443664	0.221832	−	0.975085i	$-0.428796\pi$
$631$	11.1447	0.443664	0.221832	+	0.975085i	$0.428796\pi$
$632$	13.8407	0.550554
$633$	47.3373	1.88149
$634$	2.34455	0.0931141
$635$	3.21560	0.127607
$636$	−48.4758	−1.92219
$637$	8.40673	0.333087
$638$	−0.218285	−0.00864199
$639$	−11.7999	−0.466797
$640$	47.6956	1.88533
$641$	17.5533	0.693314	0.346657	−	0.937992i	$-0.387317\pi$
$641$	17.5533	0.693314	0.346657	+	0.937992i	$0.387317\pi$
$642$	−10.7031	−0.422417
$643$	−2.19605	−0.0866038	−0.0433019	−	0.999062i	$-0.513788\pi$
$643$	−2.19605	−0.0866038	−0.0433019	+	0.999062i	$0.513788\pi$
$644$	−37.9110	−1.49390
$645$	1.46429	0.0576563
$646$	46.8682	1.84401
$647$	−32.4446	−1.27553	−0.637764	−	0.770232i	$-0.720140\pi$
$647$	−32.4446	−1.27553	−0.637764	+	0.770232i	$0.720140\pi$
$648$	−22.5802	−0.887033
$649$	6.97247	0.273693
$650$	−5.43508	−0.213181
$651$	0	0
$652$	−56.7370	−2.22199
$653$	16.4900	0.645302	0.322651	−	0.946518i	$-0.395426\pi$
$653$	16.4900	0.645302	0.322651	+	0.946518i	$0.395426\pi$
$654$	−69.0317	−2.69935
$655$	20.0385	0.782970
$656$	−2.98009	−0.116353
$657$	9.32914	0.363964
$658$	−29.7060	−1.15806
$659$	−19.7414	−0.769015	−0.384508	−	0.923122i	$-0.625629\pi$
$659$	−19.7414	−0.769015	−0.384508	+	0.923122i	$0.625629\pi$
$660$	15.4958	0.603173
$661$	11.7808	0.458221	0.229110	−	0.973400i	$-0.426418\pi$
$661$	11.7808	0.458221	0.229110	+	0.973400i	$0.426418\pi$
$662$	61.5866	2.39363
$663$	−21.1121	−0.819925
$664$	8.16255	0.316768
$665$	18.5624	0.719820
$666$	67.4072	2.61198
$667$	0.917847	0.0355392
$668$	−81.0298	−3.13514
$669$	−15.8029	−0.610976
$670$	−27.8265	−1.07503
$671$	−5.75219	−0.222061
$672$	21.1026	0.814049
$673$	50.3821	1.94209	0.971044	−	0.238901i	$-0.0767871\pi$
$673$	50.3821	1.94209	0.971044	+	0.238901i	$0.0767871\pi$
$674$	73.7060	2.83905
$675$	−1.47026	−0.0565903
$676$	−31.2695	−1.20267
$677$	−3.97995	−0.152962	−0.0764810	−	0.997071i	$-0.524368\pi$
$677$	−3.97995	−0.152962	−0.0764810	+	0.997071i	$0.524368\pi$
$678$	−64.8614	−2.49099
$679$	19.6869	0.755513
$680$	33.4448	1.28255
$681$	33.1770	1.27134
$682$	0	0
$683$	5.23244	0.200214	0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244	0.200214	0.100107	+	0.994977i	$0.468082\pi$
$684$	−53.4370	−2.04321
$685$	41.1665	1.57289
$686$	−42.2643	−1.61366
$687$	−38.8476	−1.48213
$688$	0.0931499	0.00355130
$689$	−10.8720	−0.414189
$690$	−104.353	−3.97265
$691$	9.19553	0.349815	0.174907	−	0.984585i	$-0.444037\pi$
$691$	9.19553	0.349815	0.174907	+	0.984585i	$0.444037\pi$
$692$	29.8344	1.13413
$693$	4.07269	0.154709
$694$	7.20251	0.273404
$695$	−18.3382	−0.695609
$696$	1.00217	0.0379871
$697$	32.2924	1.22316
$698$	−50.8266	−1.92382
$699$	−33.2112	−1.25616
$700$	6.61615	0.250067
$701$	−40.5543	−1.53172	−0.765858	−	0.643010i	$-0.777685\pi$
$701$	−40.5543	−1.53172	−0.765858	+	0.643010i	$0.777685\pi$
$702$	5.17783	0.195424
$703$	−39.0961	−1.47454
$704$	−9.36393	−0.352916
$705$	−51.0552	−1.92285
$706$	11.3816	0.428353
$707$	11.7647	0.442457
$708$	−80.3420	−3.01944
$709$	−37.2861	−1.40031	−0.700154	−	0.713992i	$-0.746885\pi$
$709$	−37.2861	−1.40031	−0.700154	+	0.713992i	$0.746885\pi$
$710$	19.6308	0.736731
$711$	15.6913	0.588471
$712$	−6.73883	−0.252548
$713$	0	0
$714$	41.1599	1.54037
$715$	3.47535	0.129971
$716$	−37.5374	−1.40284
$717$	59.6071	2.22607
$718$	−0.832694	−0.0310759
$719$	−18.5799	−0.692912	−0.346456	−	0.938066i	$-0.612615\pi$
$719$	−18.5799	−0.692912	−0.346456	+	0.938066i	$0.612615\pi$
$720$	−3.49911	−0.130404
$721$	8.95250	0.333409
$722$	5.79486	0.215662
$723$	−62.8360	−2.33690
$724$	−49.6742	−1.84613
$725$	−0.160181	−0.00594897
$726$	61.3833	2.27815
$727$	16.3772	0.607396	0.303698	−	0.952768i	$-0.401779\pi$
$727$	16.3772	0.607396	0.303698	+	0.952768i	$0.401779\pi$
$728$	−9.28367	−0.344076
$729$	−34.6273	−1.28249
$730$	−15.5203	−0.574434
$731$	−1.00938	−0.0373332
$732$	66.2810	2.44982
$733$	−1.15134	−0.0425256	−0.0212628	−	0.999774i	$-0.506769\pi$
$733$	−1.15134	−0.0425256	−0.0212628	+	0.999774i	$0.506769\pi$
$734$	−67.8111	−2.50295
$735$	−28.1686	−1.03902
$736$	36.8801	1.35942
$737$	3.54105	0.130436
$738$	−58.9668	−2.17060
$739$	−20.7158	−0.762043	−0.381022	−	0.924566i	$-0.624428\pi$
$739$	−20.7158	−0.762043	−0.381022	+	0.924566i	$0.624428\pi$
$740$	−70.0201	−2.57399
$741$	−22.3597	−0.821403
$742$	21.1959	0.778126
$743$	−35.2367	−1.29271	−0.646354	−	0.763038i	$-0.723707\pi$
$743$	−35.2367	−1.29271	−0.646354	+	0.763038i	$0.723707\pi$
$744$	0	0
$745$	15.8950	0.582348
$746$	40.9087	1.49778
$747$	9.25395	0.338584
$748$	−10.6817	−0.390563
$749$	2.92208	0.106771
$750$	−55.0859	−2.01145
$751$	−43.1459	−1.57441	−0.787207	−	0.616688i	$-0.788474\pi$
$751$	−43.1459	−1.57441	−0.787207	+	0.616688i	$0.788474\pi$
$752$	−3.24784	−0.118437
$753$	58.9763	2.14922
$754$	0.564110	0.0205437
$755$	13.8033	0.502354
$756$	−6.30300	−0.229238
$757$	−27.3386	−0.993637	−0.496819	−	0.867854i	$-0.665499\pi$
$757$	−27.3386	−0.993637	−0.496819	+	0.867854i	$0.665499\pi$
$758$	−5.67749	−0.206216
$759$	13.2794	0.482011
$760$	35.4212	1.28486
$761$	17.1920	0.623208	0.311604	−	0.950212i	$-0.399134\pi$
$761$	17.1920	0.623208	0.311604	+	0.950212i	$0.399134\pi$
$762$	7.55154	0.273563
$763$	18.8466	0.682291
$764$	7.51686	0.271951
$765$	37.9167	1.37088
$766$	−44.1151	−1.59394
$767$	−18.0188	−0.650622
$768$	47.1012	1.69962
$769$	14.0567	0.506899	0.253450	−	0.967349i	$-0.418435\pi$
$769$	14.0567	0.506899	0.253450	+	0.967349i	$0.418435\pi$
$770$	−6.77550	−0.244172
$771$	−39.0209	−1.40530
$772$	85.3254	3.07093
$773$	−22.2368	−0.799803	−0.399902	−	0.916558i	$-0.630956\pi$
$773$	−22.2368	−0.799803	−0.399902	+	0.916558i	$0.630956\pi$
$774$	1.84315	0.0662507
$775$	0	0
$776$	37.5668	1.34857
$777$	−34.3344	−1.23174
$778$	12.1631	0.436069
$779$	34.2007	1.22537
$780$	−40.0455	−1.43386
$781$	−2.49811	−0.0893895
$782$	71.9336	2.57234
$783$	0.152599	0.00545345
$784$	−1.79193	−0.0639975
$785$	−19.9739	−0.712898
$786$	47.0587	1.67853
$787$	32.0338	1.14188	0.570941	−	0.820991i	$-0.306578\pi$
$787$	32.0338	1.14188	0.570941	+	0.820991i	$0.306578\pi$
$788$	−20.5988	−0.733800
$789$	17.3055	0.616091
$790$	−26.1048	−0.928767
$791$	17.7080	0.629625
$792$	7.77158	0.276151
$793$	14.8653	0.527881
$794$	39.0560	1.38605
$795$	36.4290	1.29200
$796$	−15.1916	−0.538451
$797$	26.0493	0.922712	0.461356	−	0.887215i	$-0.347363\pi$
$797$	26.0493	0.922712	0.461356	+	0.887215i	$0.347363\pi$
$798$	43.5922	1.54315
$799$	35.1939	1.24507
$800$	−6.43625	−0.227556
$801$	−7.63987	−0.269942
$802$	87.7775	3.09953
$803$	1.97504	0.0696976
$804$	−40.8027	−1.43900
$805$	28.4897	1.00413
$806$	0	0
$807$	−26.7486	−0.941594
$808$	22.4496	0.789775
$809$	−8.72941	−0.306910	−0.153455	−	0.988156i	$-0.549040\pi$
$809$	−8.72941	−0.306910	−0.153455	+	0.988156i	$0.549040\pi$
$810$	42.5881	1.49639
$811$	−50.0784	−1.75849	−0.879245	−	0.476369i	$-0.841953\pi$
$811$	−50.0784	−1.75849	−0.879245	+	0.476369i	$0.841953\pi$
$812$	−0.686695	−0.0240983
$813$	4.01023	0.140645
$814$	14.2705	0.500182
$815$	42.6372	1.49352
$816$	4.50013	0.157536
$817$	−1.06903	−0.0374005
$818$	1.15073	0.0402342
$819$	−10.5250	−0.367773
$820$	61.2525	2.13903
$821$	−50.7831	−1.77234	−0.886171	−	0.463359i	$-0.846644\pi$
$821$	−50.7831	−1.77234	−0.886171	+	0.463359i	$0.846644\pi$
$822$	96.6758	3.37195
$823$	−6.32920	−0.220622	−0.110311	−	0.993897i	$-0.535185\pi$
$823$	−6.32920	−0.220622	−0.110311	+	0.993897i	$0.535185\pi$
$824$	17.0833	0.595126
$825$	−2.31749	−0.0806847
$826$	35.1293	1.22231
$827$	3.69745	0.128573	0.0642865	−	0.997931i	$-0.479523\pi$
$827$	3.69745	0.128573	0.0642865	+	0.997931i	$0.479523\pi$
$828$	−82.0153	−2.85023
$829$	26.0416	0.904461	0.452230	−	0.891901i	$-0.350628\pi$
$829$	26.0416	0.904461	0.452230	+	0.891901i	$0.350628\pi$
$830$	−15.3953	−0.534377
$831$	−30.7704	−1.06741
$832$	24.1990	0.838951
$833$	19.4175	0.672776
$834$	−43.0657	−1.49124
$835$	60.8930	2.10729
$836$	−11.3130	−0.391267
$837$	0	0
$838$	31.1747	1.07691
$839$	7.49300	0.258687	0.129343	−	0.991600i	$-0.458713\pi$
$839$	7.49300	0.258687	0.129343	+	0.991600i	$0.458713\pi$
$840$	31.1070	1.07329
$841$	−28.9834	−0.999427
$842$	−71.3374	−2.45845
$843$	54.5992	1.88050
$844$	−61.8948	−2.13051
$845$	23.4987	0.808380
$846$	−64.2649	−2.20947
$847$	−16.7584	−0.575827
$848$	2.31741	0.0795801
$849$	1.75144	0.0601094
$850$	−12.5537	−0.430588
$851$	−60.0049	−2.05694
$852$	28.7851	0.986163
$853$	−43.5869	−1.49239	−0.746194	−	0.665728i	$-0.768121\pi$
$853$	−43.5869	−1.49239	−0.746194	+	0.665728i	$0.768121\pi$
$854$	−28.9812	−0.991717
$855$	40.1573	1.37335
$856$	5.57597	0.190583
$857$	39.2228	1.33982	0.669912	−	0.742440i	$-0.266332\pi$
$857$	39.2228	1.33982	0.669912	+	0.742440i	$0.266332\pi$
$858$	8.16153	0.278630
$859$	−18.2013	−0.621020	−0.310510	−	0.950570i	$-0.600500\pi$
$859$	−18.2013	−0.621020	−0.310510	+	0.950570i	$0.600500\pi$
$860$	−1.91460	−0.0652872
$861$	30.0352	1.02360
$862$	−27.8168	−0.947443
$863$	44.9477	1.53004	0.765018	−	0.644009i	$-0.222730\pi$
$863$	44.9477	1.53004	0.765018	+	0.644009i	$0.222730\pi$
$864$	6.13161	0.208602
$865$	−22.4202	−0.762309
$866$	−74.7451	−2.53994
$867$	−5.53740	−0.188060
$868$	0	0
$869$	3.32196	0.112690
$870$	−1.89018	−0.0640830
$871$	−9.15108	−0.310072
$872$	35.9633	1.21787
$873$	42.5899	1.44145
$874$	76.1844	2.57698
$875$	15.0392	0.508417
$876$	−22.7579	−0.768917
$877$	−42.6511	−1.44022	−0.720112	−	0.693858i	$-0.755910\pi$
$877$	−42.6511	−1.44022	−0.720112	+	0.693858i	$0.755910\pi$
$878$	28.5399	0.963173
$879$	−22.9147	−0.772894
$880$	−0.740785	−0.0249718
$881$	−8.91652	−0.300405	−0.150203	−	0.988655i	$-0.547993\pi$
$881$	−8.91652	−0.300405	−0.150203	+	0.988655i	$0.547993\pi$
$882$	−35.4568	−1.19389
$883$	47.0683	1.58398	0.791988	−	0.610537i	$-0.209046\pi$
$883$	47.0683	1.58398	0.791988	+	0.610537i	$0.209046\pi$
$884$	27.6046	0.928443
$885$	60.3761	2.02952
$886$	−10.8994	−0.366172
$887$	3.15657	0.105987	0.0529936	−	0.998595i	$-0.483124\pi$
$887$	3.15657	0.105987	0.0529936	+	0.998595i	$0.483124\pi$
$888$	−65.5175	−2.19862
$889$	−2.06167	−0.0691462
$890$	12.7100	0.426041
$891$	−5.41954	−0.181561
$892$	20.6627	0.691839
$893$	37.2736	1.24731
$894$	37.3280	1.24843
$895$	28.2089	0.942920
$896$	−30.5798	−1.02160
$897$	−34.3177	−1.14583
$898$	−36.8840	−1.23083
$899$	0	0
$900$	14.3131	0.477105
$901$	−25.1116	−0.836589
$902$	−12.4836	−0.415660
$903$	−0.938824	−0.0312421
$904$	33.7908	1.12386
$905$	37.3296	1.24088
$906$	32.4158	1.07694
$907$	26.9632	0.895297	0.447649	−	0.894210i	$-0.352262\pi$
$907$	26.9632	0.895297	0.447649	+	0.894210i	$0.352262\pi$
$908$	−43.3797	−1.43961
$909$	25.4513	0.844168
$910$	17.5098	0.580444
$911$	5.07802	0.168242	0.0841212	−	0.996456i	$-0.473192\pi$
$911$	5.07802	0.168242	0.0841212	+	0.996456i	$0.473192\pi$
$912$	4.76606	0.157820
$913$	1.95912	0.0648374
$914$	10.5171	0.347876
$915$	−49.8095	−1.64665
$916$	50.7942	1.67829
$917$	−12.8476	−0.424266
$918$	11.9595	0.394723
$919$	−49.2770	−1.62550	−0.812749	−	0.582615i	$-0.802030\pi$
$919$	−49.2770	−1.62550	−0.812749	+	0.582615i	$0.802030\pi$
$920$	54.3646	1.79235
$921$	79.6703	2.62522
$922$	−39.2072	−1.29122
$923$	6.45583	0.212496
$924$	−9.93508	−0.326840
$925$	10.4719	0.344315
$926$	63.2905	2.07986
$927$	19.3675	0.636113
$928$	0.668022	0.0219289
$929$	−39.9606	−1.31107	−0.655533	−	0.755167i	$-0.727556\pi$
$929$	−39.9606	−1.31107	−0.655533	+	0.755167i	$0.727556\pi$
$930$	0	0
$931$	20.5649	0.673989
$932$	43.4245	1.42242
$933$	45.0417	1.47460
$934$	−52.8666	−1.72985
$935$	8.02720	0.262517
$936$	−20.0840	−0.656465
$937$	45.0893	1.47300	0.736502	−	0.676436i	$-0.236476\pi$
$937$	45.0893	1.47300	0.736502	+	0.676436i	$0.236476\pi$
$938$	17.8409	0.582525
$939$	55.0975	1.79804
$940$	66.7560	2.17734
$941$	50.1923	1.63622	0.818112	−	0.575060i	$-0.195021\pi$
$941$	50.1923	1.63622	0.818112	+	0.575060i	$0.195021\pi$
$942$	−46.9068	−1.52831
$943$	52.4914	1.70936
$944$	3.84079	0.125007
$945$	4.73663	0.154083
$946$	0.390207	0.0126867
$947$	30.3259	0.985461	0.492730	−	0.870182i	$-0.335999\pi$
$947$	30.3259	0.985461	0.492730	+	0.870182i	$0.335999\pi$
$948$	−38.2781	−1.24321
$949$	−5.10405	−0.165685
$950$	−13.2955	−0.431365
$951$	−2.58353	−0.0837766
$952$	−21.4430	−0.694972
$953$	−35.4775	−1.14923	−0.574614	−	0.818425i	$-0.694848\pi$
$953$	−35.4775	−1.14923	−0.574614	+	0.818425i	$0.694848\pi$
$954$	45.8545	1.48459
$955$	−5.64884	−0.182792
$956$	−77.9379	−2.52069
$957$	0.240534	0.00777536
$958$	20.8763	0.674483
$959$	−26.3938	−0.852299
$960$	−81.0843	−2.61698
$961$	0	0
$962$	−36.8791	−1.18903
$963$	6.32153	0.203708
$964$	82.1598	2.64619
$965$	−64.1211	−2.06413
$966$	66.9055	2.15265
$967$	−35.4443	−1.13981	−0.569906	−	0.821710i	$-0.693021\pi$
$967$	−35.4443	−1.13981	−0.569906	+	0.821710i	$0.693021\pi$
$968$	−31.9788	−1.02784
$969$	−51.6453	−1.65909
$970$	−70.8543	−2.27499
$971$	−40.0972	−1.28678	−0.643391	−	0.765538i	$-0.722473\pi$
$971$	−40.0972	−1.28678	−0.643391	+	0.765538i	$0.722473\pi$
$972$	74.2523	2.38164
$973$	11.7575	0.376928
$974$	−54.5099	−1.74661
$975$	5.98905	0.191803
$976$	−3.16860	−0.101424
$977$	−38.6708	−1.23719	−0.618595	−	0.785710i	$-0.712298\pi$
$977$	−38.6708	−1.23719	−0.618595	+	0.785710i	$0.712298\pi$
$978$	100.130	3.20179
$979$	−1.61741	−0.0516926
$980$	36.8312	1.17653
$981$	40.7720	1.30175
$982$	21.2914	0.679434
$983$	−21.5796	−0.688282	−0.344141	−	0.938918i	$-0.611830\pi$
$983$	−21.5796	−0.688282	−0.344141	+	0.938918i	$0.611830\pi$
$984$	57.3137	1.82710
$985$	15.4797	0.493225
$986$	1.30296	0.0414946
$987$	32.7338	1.04193
$988$	29.2359	0.930116
$989$	−1.64075	−0.0521727
$990$	−14.6579	−0.465858
$991$	46.8764	1.48908	0.744538	−	0.667580i	$-0.232670\pi$
$991$	46.8764	1.48908	0.744538	+	0.667580i	$0.232670\pi$
$992$	0	0
$993$	−67.8639	−2.15360
$994$	−12.5862	−0.399211
$995$	11.4163	0.361921
$996$	−22.5744	−0.715299
$997$	44.5389	1.41056	0.705281	−	0.708928i	$-0.250821\pi$
$997$	44.5389	1.41056	0.705281	+	0.708928i	$0.250821\pi$
$998$	65.5659	2.07545
$999$	−9.97628	−0.315636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.i.1.8		8
3.2	odd	2		8649.2.a.bf.1.1		8
31.2	even	5		961.2.d.p.531.4		16
31.3	odd	30		961.2.g.m.846.2		16
31.4	even	5		961.2.d.o.388.1		16
31.5	even	3		961.2.c.j.521.8		16
31.6	odd	6		961.2.c.i.439.8		16
31.7	even	15		31.2.g.a.18.1	✓	16
31.8	even	5		961.2.d.o.374.1		16
31.9	even	15		31.2.g.a.19.1	yes	16
31.10	even	15		961.2.g.s.844.2		16
31.11	odd	30		961.2.g.j.338.1		16
31.12	odd	30		961.2.g.n.547.2		16
31.13	odd	30		961.2.g.n.448.2		16
31.14	even	15		961.2.g.k.816.1		16
31.15	odd	10		961.2.d.q.628.4		16
31.16	even	5		961.2.d.p.628.4		16
31.17	odd	30		961.2.g.j.816.1		16
31.18	even	15		961.2.g.t.448.2		16
31.19	even	15		961.2.g.t.547.2		16
31.20	even	15		961.2.g.k.338.1		16
31.21	odd	30		961.2.g.m.844.2		16
31.22	odd	30		961.2.g.l.732.1		16
31.23	odd	10		961.2.d.n.374.1		16
31.24	odd	30		961.2.g.l.235.1		16
31.25	even	3		961.2.c.j.439.8		16
31.26	odd	6		961.2.c.i.521.8		16
31.27	odd	10		961.2.d.n.388.1		16
31.28	even	15		961.2.g.s.846.2		16
31.29	odd	10		961.2.d.q.531.4		16
31.30	odd	2		961.2.a.j.1.8		8
93.38	odd	30		279.2.y.c.235.2		16
93.71	odd	30		279.2.y.c.19.2		16
93.92	even	2		8649.2.a.be.1.1		8
124.7	odd	30		496.2.bg.c.49.2		16
124.71	odd	30		496.2.bg.c.81.2		16
155.7	odd	60		775.2.ck.a.49.1		32
155.9	even	30		775.2.bl.a.701.2		16
155.38	odd	60		775.2.ck.a.49.4		32
155.69	even	30		775.2.bl.a.576.2		16
155.102	odd	60		775.2.ck.a.174.4		32
155.133	odd	60		775.2.ck.a.174.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.7	even	15
31.2.g.a.19.1	yes	16	31.9	even	15
279.2.y.c.19.2		16	93.71	odd	30
279.2.y.c.235.2		16	93.38	odd	30
496.2.bg.c.49.2		16	124.7	odd	30
496.2.bg.c.81.2		16	124.71	odd	30
775.2.bl.a.576.2		16	155.69	even	30
775.2.bl.a.701.2		16	155.9	even	30
775.2.ck.a.49.1		32	155.7	odd	60
775.2.ck.a.49.4		32	155.38	odd	60
775.2.ck.a.174.1		32	155.133	odd	60
775.2.ck.a.174.4		32	155.102	odd	60
961.2.a.i.1.8		8	1.1	even	1	trivial
961.2.a.j.1.8		8	31.30	odd	2
961.2.c.i.439.8		16	31.6	odd	6
961.2.c.i.521.8		16	31.26	odd	6
961.2.c.j.439.8		16	31.25	even	3
961.2.c.j.521.8		16	31.5	even	3
961.2.d.n.374.1		16	31.23	odd	10
961.2.d.n.388.1		16	31.27	odd	10
961.2.d.o.374.1		16	31.8	even	5
961.2.d.o.388.1		16	31.4	even	5
961.2.d.p.531.4		16	31.2	even	5
961.2.d.p.628.4		16	31.16	even	5
961.2.d.q.531.4		16	31.29	odd	10
961.2.d.q.628.4		16	31.15	odd	10
961.2.g.j.338.1		16	31.11	odd	30
961.2.g.j.816.1		16	31.17	odd	30
961.2.g.k.338.1		16	31.20	even	15
961.2.g.k.816.1		16	31.14	even	15
961.2.g.l.235.1		16	31.24	odd	30
961.2.g.l.732.1		16	31.22	odd	30
961.2.g.m.844.2		16	31.21	odd	30
961.2.g.m.846.2		16	31.3	odd	30
961.2.g.n.448.2		16	31.13	odd	30
961.2.g.n.547.2		16	31.12	odd	30
961.2.g.s.844.2		16	31.10	even	15
961.2.g.s.846.2		16	31.28	even	15
961.2.g.t.448.2		16	31.18	even	15
961.2.g.t.547.2		16	31.19	even	15
8649.2.a.be.1.1		8	93.92	even	2
8649.2.a.bf.1.1		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q+2.30753 q^{2} -2.54272 q^{3} +3.32468 q^{4} -2.49846 q^{5} -5.86740 q^{6} +1.60188 q^{7} +3.05673 q^{8} +3.46545 q^{9} -5.76526 q^{10} +0.733657 q^{11} -8.45374 q^{12} -1.89598 q^{13} +3.69638 q^{14} +6.35289 q^{15} +0.404135 q^{16} -4.37924 q^{17} +7.99661 q^{18} -4.63803 q^{19} -8.30658 q^{20} -4.07313 q^{21} +1.69293 q^{22} -7.11846 q^{23} -7.77243 q^{24} +1.24230 q^{25} -4.37501 q^{26} -1.18350 q^{27} +5.32573 q^{28} -0.128939 q^{29} +14.6595 q^{30} -5.18091 q^{32} -1.86549 q^{33} -10.1052 q^{34} -4.00223 q^{35} +11.5215 q^{36} +8.42948 q^{37} -10.7024 q^{38} +4.82094 q^{39} -7.63712 q^{40} -7.37398 q^{41} -9.39887 q^{42} +0.230492 q^{43} +2.43917 q^{44} -8.65827 q^{45} -16.4260 q^{46} -8.03652 q^{47} -1.02760 q^{48} -4.43399 q^{49} +2.86664 q^{50} +11.1352 q^{51} -6.30351 q^{52} +5.73424 q^{53} -2.73096 q^{54} -1.83301 q^{55} +4.89652 q^{56} +11.7932 q^{57} -0.297530 q^{58} +9.50372 q^{59} +21.1213 q^{60} -7.84044 q^{61} +5.55122 q^{63} -12.7634 q^{64} +4.73702 q^{65} -4.30466 q^{66} +4.82658 q^{67} -14.5596 q^{68} +18.1003 q^{69} -9.23525 q^{70} -3.40502 q^{71} +10.5929 q^{72} +2.69205 q^{73} +19.4512 q^{74} -3.15882 q^{75} -15.4200 q^{76} +1.17523 q^{77} +11.1245 q^{78} +4.52794 q^{79} -1.00972 q^{80} -7.38702 q^{81} -17.0157 q^{82} +2.67035 q^{83} -13.5419 q^{84} +10.9414 q^{85} +0.531866 q^{86} +0.327856 q^{87} +2.24259 q^{88} -2.20459 q^{89} -19.9792 q^{90} -3.03712 q^{91} -23.6666 q^{92} -18.5445 q^{94} +11.5879 q^{95} +13.1736 q^{96} +12.2899 q^{97} -10.2315 q^{98} +2.54245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{5} - 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} - 18 q^{11} - 8 q^{13} - 9 q^{14} - 18 q^{15} + 4 q^{16} - 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} + q^{21}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^5 - 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 - 18 * q^11 - 8 * q^13 - 9 * q^14 - 18 * q^15 + 4 * q^16 - 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 + q^21 - 4 * q^22 - 22 * q^23 - 30 * q^24 + 13 * q^25 - 9 * q^26 - 18 * q^27 - 5 * q^28 - 12 * q^29 - 11 * q^30 - 21 * q^32 + 6 * q^33 + 7 * q^34 - 12 * q^35 - q^36 + 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 - 18 * q^46 - 18 * q^47 + q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 + q^52 - 6 * q^53 + 7 * q^54 - 28 * q^55 + 30 * q^56 + 17 * q^57 + 5 * q^58 - 4 * q^59 + 40 * q^60 - 30 * q^61 - 23 * q^63 + 9 * q^64 - 3 * q^65 + 10 * q^66 - 13 * q^67 - 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 - 33 * q^76 + 24 * q^77 - 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 - 39 * q^83 - 8 * q^84 + 26 * q^85 + 16 * q^86 - 15 * q^87 + 17 * q^88 - 27 * q^89 + 8 * q^90 - 16 * q^91 - 32 * q^92 + 22 * q^94 - 6 * q^95 + 12 * q^96 + 34 * q^97 + 10 * q^98 - 6 * q^99

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