LMFDB - Embedded newform 961.2.a.i.1.4

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			1.4
Root			$-1.04940$ 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)

$f(q)$	$=$	\(q+0.351432 q^{2} -2.89329 q^{3} -1.87650 q^{4} +2.97323 q^{5} -1.01680 q^{6} -1.08213 q^{7} -1.36233 q^{8} +5.37114 q^{9} +1.04489 q^{10} -2.43137 q^{11} +5.42925 q^{12} +2.87365 q^{13} -0.380294 q^{14} -8.60242 q^{15} +3.27422 q^{16} -1.82477 q^{17} +1.88759 q^{18} +2.11827 q^{19} -5.57925 q^{20} +3.13091 q^{21} -0.854462 q^{22} -0.442216 q^{23} +3.94161 q^{24} +3.84010 q^{25} +1.00989 q^{26} -6.86040 q^{27} +2.03060 q^{28} -3.15914 q^{29} -3.02317 q^{30} +3.87532 q^{32} +7.03466 q^{33} -0.641282 q^{34} -3.21741 q^{35} -10.0789 q^{36} +3.14675 q^{37} +0.744430 q^{38} -8.31432 q^{39} -4.05051 q^{40} -6.94624 q^{41} +1.10030 q^{42} -8.41238 q^{43} +4.56245 q^{44} +15.9696 q^{45} -0.155409 q^{46} -7.96205 q^{47} -9.47329 q^{48} -5.82900 q^{49} +1.34953 q^{50} +5.27958 q^{51} -5.39239 q^{52} -4.97700 q^{53} -2.41097 q^{54} -7.22902 q^{55} +1.47421 q^{56} -6.12878 q^{57} -1.11022 q^{58} -12.0139 q^{59} +16.1424 q^{60} -14.4351 q^{61} -5.81225 q^{63} -5.18654 q^{64} +8.54403 q^{65} +2.47221 q^{66} -6.43759 q^{67} +3.42416 q^{68} +1.27946 q^{69} -1.13070 q^{70} +1.67787 q^{71} -7.31724 q^{72} +14.3602 q^{73} +1.10587 q^{74} -11.1105 q^{75} -3.97493 q^{76} +2.63105 q^{77} -2.92192 q^{78} -3.44764 q^{79} +9.73502 q^{80} +3.73571 q^{81} -2.44113 q^{82} +12.8536 q^{83} -5.87513 q^{84} -5.42545 q^{85} -2.95638 q^{86} +9.14030 q^{87} +3.31232 q^{88} +2.25938 q^{89} +5.61225 q^{90} -3.10965 q^{91} +0.829816 q^{92} -2.79812 q^{94} +6.29811 q^{95} -11.2124 q^{96} +3.41286 q^{97} -2.04850 q^{98} -13.0592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.351432	0.248500	0.124250	−	0.992251i	$-0.460347\pi$
$2$	0.351432	0.248500	0.124250	+	0.992251i	$0.460347\pi$
$3$	−2.89329	−1.67044	−0.835221	−	0.549914i	$-0.814661\pi$
$3$	−2.89329	−1.67044	−0.835221	+	0.549914i	$0.814661\pi$
$4$	−1.87650	−0.938248
$5$	2.97323	1.32967	0.664834	−	0.746991i	$-0.268502\pi$
$5$	2.97323	1.32967	0.664834	+	0.746991i	$0.268502\pi$
$6$	−1.01680	−0.415106
$7$	−1.08213	−0.409005	−0.204503	−	0.978866i	$-0.565558\pi$
$7$	−1.08213	−0.409005	−0.204503	+	0.978866i	$0.565558\pi$
$8$	−1.36233	−0.481655
$9$	5.37114	1.79038
$10$	1.04489	0.330423
$11$	−2.43137	−0.733086	−0.366543	−	0.930401i	$-0.619459\pi$
$11$	−2.43137	−0.733086	−0.366543	+	0.930401i	$0.619459\pi$
$12$	5.42925	1.56729
$13$	2.87365	0.797008	0.398504	−	0.917167i	$-0.369530\pi$
$13$	2.87365	0.797008	0.398504	+	0.917167i	$0.369530\pi$
$14$	−0.380294	−0.101638
$15$	−8.60242	−2.22114
$16$	3.27422	0.818556
$17$	−1.82477	−0.442571	−0.221285	−	0.975209i	$-0.571025\pi$
$17$	−1.82477	−0.442571	−0.221285	+	0.975209i	$0.571025\pi$
$18$	1.88759	0.444910
$19$	2.11827	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$19$	2.11827	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$20$	−5.57925	−1.24756
$21$	3.13091	0.683220
$22$	−0.854462	−0.182172
$23$	−0.442216	−0.0922083	−0.0461042	−	0.998937i	$-0.514681\pi$
$23$	−0.442216	−0.0922083	−0.0461042	+	0.998937i	$0.514681\pi$
$24$	3.94161	0.804577
$25$	3.84010	0.768019
$26$	1.00989	0.198057
$27$	−6.86040	−1.32028
$28$	2.03060	0.383748
$29$	−3.15914	−0.586637	−0.293318	−	0.956015i	$-0.594760\pi$
$29$	−3.15914	−0.586637	−0.293318	+	0.956015i	$0.594760\pi$
$30$	−3.02317	−0.551953
$31$	0	0
$31$	0	0
$32$	3.87532	0.685067
$33$	7.03466	1.22458
$34$	−0.641282	−0.109979
$35$	−3.21741	−0.543841
$36$	−10.0789	−1.67982
$37$	3.14675	0.517323	0.258661	−	0.965968i	$-0.416719\pi$
$37$	3.14675	0.517323	0.258661	+	0.965968i	$0.416719\pi$
$38$	0.744430	0.120763
$39$	−8.31432	−1.33136
$40$	−4.05051	−0.640442
$41$	−6.94624	−1.08482	−0.542410	−	0.840114i	$-0.682488\pi$
$41$	−6.94624	−1.08482	−0.542410	+	0.840114i	$0.682488\pi$
$42$	1.10030	0.169780
$43$	−8.41238	−1.28288	−0.641438	−	0.767175i	$-0.721662\pi$
$43$	−8.41238	−1.28288	−0.641438	+	0.767175i	$0.721662\pi$
$44$	4.56245	0.687816
$45$	15.9696	2.38061
$46$	−0.155409	−0.0229138
$47$	−7.96205	−1.16138	−0.580692	−	0.814123i	$-0.697218\pi$
$47$	−7.96205	−1.16138	−0.580692	+	0.814123i	$0.697218\pi$
$48$	−9.47329	−1.36735
$49$	−5.82900	−0.832715
$50$	1.34953	0.190853
$51$	5.27958	0.739289
$52$	−5.39239	−0.747791
$53$	−4.97700	−0.683643	−0.341822	−	0.939765i	$-0.611044\pi$
$53$	−4.97700	−0.683643	−0.341822	+	0.939765i	$0.611044\pi$
$54$	−2.41097	−0.328091
$55$	−7.22902	−0.974761
$56$	1.47421	0.196999
$57$	−6.12878	−0.811777
$58$	−1.11022	−0.145779
$59$	−12.0139	−1.56408	−0.782041	−	0.623227i	$-0.785821\pi$
$59$	−12.0139	−1.56408	−0.782041	+	0.623227i	$0.785821\pi$
$60$	16.1424	2.08398
$61$	−14.4351	−1.84823	−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351	−1.84823	−0.924115	+	0.382115i	$0.875196\pi$
$62$	0	0
$63$	−5.81225	−0.732274
$64$	−5.18654	−0.648317
$65$	8.54403	1.05976
$66$	2.47221	0.304308
$67$	−6.43759	−0.786476	−0.393238	−	0.919437i	$-0.628645\pi$
$67$	−6.43759	−0.786476	−0.393238	+	0.919437i	$0.628645\pi$
$68$	3.42416	0.415241
$69$	1.27946	0.154029
$70$	−1.13070	−0.135145
$71$	1.67787	0.199127	0.0995635	−	0.995031i	$-0.468255\pi$
$71$	1.67787	0.199127	0.0995635	+	0.995031i	$0.468255\pi$
$72$	−7.31724	−0.862345
$73$	14.3602	1.68073	0.840365	−	0.542021i	$-0.182341\pi$
$73$	14.3602	1.68073	0.840365	+	0.542021i	$0.182341\pi$
$74$	1.10587	0.128555
$75$	−11.1105	−1.28293
$76$	−3.97493	−0.455956
$77$	2.63105	0.299836
$78$	−2.92192	−0.330842
$79$	−3.44764	−0.387890	−0.193945	−	0.981012i	$-0.562128\pi$
$79$	−3.44764	−0.387890	−0.193945	+	0.981012i	$0.562128\pi$
$80$	9.73502	1.08841
$81$	3.73571	0.415079
$82$	−2.44113	−0.269578
$83$	12.8536	1.41087	0.705434	−	0.708776i	$-0.250752\pi$
$83$	12.8536	1.41087	0.705434	+	0.708776i	$0.250752\pi$
$84$	−5.87513	−0.641029
$85$	−5.42545	−0.588472
$86$	−2.95638	−0.318795
$87$	9.14030	0.979943
$88$	3.31232	0.353094
$89$	2.25938	0.239494	0.119747	−	0.992804i	$-0.461792\pi$
$89$	2.25938	0.239494	0.119747	+	0.992804i	$0.461792\pi$
$90$	5.61225	0.591583
$91$	−3.10965	−0.325980
$92$	0.829816	0.0865143
$93$	0	0
$94$	−2.79812	−0.288604
$95$	6.29811	0.646173
$96$	−11.2124	−1.14436
$97$	3.41286	0.346523	0.173262	−	0.984876i	$-0.444569\pi$
$97$	3.41286	0.346523	0.173262	+	0.984876i	$0.444569\pi$
$98$	−2.04850	−0.206930
$99$	−13.0592	−1.31250
$100$	−7.20592	−0.720592
$101$	17.7173	1.76294	0.881469	−	0.472243i	$-0.156555\pi$
$101$	17.7173	1.76294	0.881469	+	0.472243i	$0.156555\pi$
$102$	1.85542	0.183713
$103$	8.07385	0.795540	0.397770	−	0.917485i	$-0.369784\pi$
$103$	8.07385	0.795540	0.397770	+	0.917485i	$0.369784\pi$
$104$	−3.91485	−0.383883
$105$	9.30890	0.908456
$106$	−1.74908	−0.169886
$107$	−12.1512	−1.17470	−0.587350	−	0.809333i	$-0.699829\pi$
$107$	−12.1512	−1.17470	−0.587350	+	0.809333i	$0.699829\pi$
$108$	12.8735	1.23875
$109$	−0.632102	−0.0605444	−0.0302722	−	0.999542i	$-0.509637\pi$
$109$	−0.632102	−0.0605444	−0.0302722	+	0.999542i	$0.509637\pi$
$110$	−2.54051	−0.242228
$111$	−9.10447	−0.864158
$112$	−3.54312	−0.334794
$113$	−11.3003	−1.06305	−0.531523	−	0.847044i	$-0.678380\pi$
$113$	−11.3003	−1.06305	−0.531523	+	0.847044i	$0.678380\pi$
$114$	−2.15385	−0.201727
$115$	−1.31481	−0.122607
$116$	5.92810	0.550411
$117$	15.4348	1.42695
$118$	−4.22209	−0.388675
$119$	1.97463	0.181014
$120$	11.7193	1.06982
$121$	−5.08844	−0.462585
$122$	−5.07297	−0.459286
$123$	20.0975	1.81213
$124$	0	0
$125$	−3.44866	−0.308458
$126$	−2.04261	−0.181970
$127$	0.117806	0.0104536	0.00522680	−	0.999986i	$-0.498336\pi$
$127$	0.117806	0.0104536	0.00522680	+	0.999986i	$0.498336\pi$
$128$	−9.57336	−0.846173
$129$	24.3395	2.14297
$130$	3.00265	0.263350
$131$	5.78395	0.505346	0.252673	−	0.967552i	$-0.418690\pi$
$131$	5.78395	0.505346	0.252673	+	0.967552i	$0.418690\pi$
$132$	−13.2005	−1.14896
$133$	−2.29224	−0.198762
$134$	−2.26238	−0.195440
$135$	−20.3975	−1.75554
$136$	2.48593	0.213166
$137$	11.8054	1.00861	0.504303	−	0.863527i	$-0.331750\pi$
$137$	11.8054	1.00861	0.504303	+	0.863527i	$0.331750\pi$
$138$	0.449643	0.0382762
$139$	−15.4220	−1.30808	−0.654039	−	0.756461i	$-0.726927\pi$
$139$	−15.4220	−1.30808	−0.654039	+	0.756461i	$0.726927\pi$
$140$	6.03745	0.510258
$141$	23.0365	1.94003
$142$	0.589660	0.0494831
$143$	−6.98691	−0.584275
$144$	17.5863	1.46553
$145$	−9.39284	−0.780033
$146$	5.04663	0.417662
$147$	16.8650	1.39100
$148$	−5.90486	−0.485377
$149$	−11.9502	−0.979001	−0.489500	−	0.872003i	$-0.662821\pi$
$149$	−11.9502	−0.979001	−0.489500	+	0.872003i	$0.662821\pi$
$150$	−3.90460	−0.318809
$151$	−4.32213	−0.351730	−0.175865	−	0.984414i	$-0.556272\pi$
$151$	−4.32213	−0.351730	−0.175865	+	0.984414i	$0.556272\pi$
$152$	−2.88578	−0.234068
$153$	−9.80107	−0.792369
$154$	0.924636	0.0745093
$155$	0	0
$156$	15.6018	1.24914
$157$	−8.70444	−0.694690	−0.347345	−	0.937737i	$-0.612917\pi$
$157$	−8.70444	−0.694690	−0.347345	+	0.937737i	$0.612917\pi$
$158$	−1.21161	−0.0963908
$159$	14.3999	1.14199
$160$	11.5222	0.910912
$161$	0.478533	0.0377137
$162$	1.31285	0.103147
$163$	3.12790	0.244996	0.122498	−	0.992469i	$-0.460909\pi$
$163$	3.12790	0.244996	0.122498	+	0.992469i	$0.460909\pi$
$164$	13.0346	1.01783
$165$	20.9157	1.62828
$166$	4.51718	0.350601
$167$	−13.3549	−1.03344	−0.516718	−	0.856156i	$-0.672846\pi$
$167$	−13.3549	−1.03344	−0.516718	+	0.856156i	$0.672846\pi$
$168$	−4.26532	−0.329076
$169$	−4.74212	−0.364779
$170$	−1.90668	−0.146236
$171$	11.3775	0.870062
$172$	15.7858	1.20366
$173$	19.0447	1.44794	0.723972	−	0.689829i	$-0.242314\pi$
$173$	19.0447	1.44794	0.723972	+	0.689829i	$0.242314\pi$
$174$	3.21220	0.243516
$175$	−4.15547	−0.314124
$176$	−7.96085	−0.600072
$177$	34.7598	2.61271
$178$	0.794021	0.0595144
$179$	−0.0793300	−0.00592940	−0.00296470	−	0.999996i	$-0.500944\pi$
$179$	−0.0793300	−0.00592940	−0.00296470	+	0.999996i	$0.500944\pi$
$180$	−29.9669	−2.23360
$181$	2.16285	0.160763	0.0803817	−	0.996764i	$-0.474386\pi$
$181$	2.16285	0.160763	0.0803817	+	0.996764i	$0.474386\pi$
$182$	−1.09283	−0.0810062
$183$	41.7651	3.08736
$184$	0.602442	0.0444126
$185$	9.35601	0.687868
$186$	0	0
$187$	4.43668	0.324442
$188$	14.9408	1.08967
$189$	7.42381	0.540003
$190$	2.21336	0.160574
$191$	−5.34169	−0.386511	−0.193256	−	0.981148i	$-0.561905\pi$
$191$	−5.34169	−0.386511	−0.193256	+	0.981148i	$0.561905\pi$
$192$	15.0062	1.08298
$193$	−2.13368	−0.153585	−0.0767927	−	0.997047i	$-0.524468\pi$
$193$	−2.13368	−0.153585	−0.0767927	+	0.997047i	$0.524468\pi$
$194$	1.19939	0.0861112
$195$	−24.7204	−1.77026
$196$	10.9381	0.781293
$197$	−5.87573	−0.418628	−0.209314	−	0.977848i	$-0.567123\pi$
$197$	−5.87573	−0.418628	−0.209314	+	0.977848i	$0.567123\pi$
$198$	−4.58944	−0.326157
$199$	6.92796	0.491110	0.245555	−	0.969383i	$-0.421030\pi$
$199$	6.92796	0.491110	0.245555	+	0.969383i	$0.421030\pi$
$200$	−5.23146	−0.369920
$201$	18.6258	1.31376
$202$	6.22643	0.438090
$203$	3.41858	0.239937
$204$	−9.90710	−0.693636
$205$	−20.6528	−1.44245
$206$	2.83741	0.197692
$207$	−2.37520	−0.165088
$208$	9.40898	0.652396
$209$	−5.15031	−0.356254
$210$	3.27145	0.225752
$211$	16.7087	1.15028	0.575139	−	0.818056i	$-0.304948\pi$
$211$	16.7087	1.15028	0.575139	+	0.818056i	$0.304948\pi$
$212$	9.33931	0.641427
$213$	−4.85458	−0.332630
$214$	−4.27032	−0.291913
$215$	−25.0119	−1.70580
$216$	9.34610	0.635921
$217$	0	0
$218$	−0.222141	−0.0150453
$219$	−41.5482	−2.80756
$220$	13.5652	0.914567
$221$	−5.24374	−0.352732
$222$	−3.19961	−0.214744
$223$	−6.26156	−0.419305	−0.209653	−	0.977776i	$-0.567233\pi$
$223$	−6.26156	−0.419305	−0.209653	+	0.977776i	$0.567233\pi$
$224$	−4.19359	−0.280196
$225$	20.6257	1.37505
$226$	−3.97131	−0.264167
$227$	−7.84751	−0.520858	−0.260429	−	0.965493i	$-0.583864\pi$
$227$	−7.84751	−0.520858	−0.260429	+	0.965493i	$0.583864\pi$
$228$	11.5006	0.761648
$229$	12.7730	0.844063	0.422031	−	0.906581i	$-0.361317\pi$
$229$	12.7730	0.844063	0.422031	+	0.906581i	$0.361317\pi$
$230$	−0.462067	−0.0304678
$231$	−7.61239	−0.500859
$232$	4.30377	0.282557
$233$	12.7175	0.833150	0.416575	−	0.909101i	$-0.363230\pi$
$233$	12.7175	0.833150	0.416575	+	0.909101i	$0.363230\pi$
$234$	5.42428	0.354597
$235$	−23.6730	−1.54426
$236$	22.5441	1.46750
$237$	9.97504	0.647949
$238$	0.693948	0.0449819
$239$	−25.4246	−1.64458	−0.822291	−	0.569068i	$-0.807304\pi$
$239$	−25.4246	−1.64458	−0.822291	+	0.569068i	$0.807304\pi$
$240$	−28.1663	−1.81812
$241$	2.36098	0.152084	0.0760421	−	0.997105i	$-0.475772\pi$
$241$	2.36098	0.152084	0.0760421	+	0.997105i	$0.475772\pi$
$242$	−1.78824	−0.114953
$243$	9.77268	0.626918
$244$	27.0875	1.73410
$245$	−17.3310	−1.10723
$246$	7.06291	0.450315
$247$	6.08718	0.387318
$248$	0	0
$249$	−37.1893	−2.35677
$250$	−1.21197	−0.0766518
$251$	2.35664	0.148750	0.0743748	−	0.997230i	$-0.476304\pi$
$251$	2.35664	0.148750	0.0743748	+	0.997230i	$0.476304\pi$
$252$	10.9067	0.687055
$253$	1.07519	0.0675966
$254$	0.0414009	0.00259772
$255$	15.6974	0.983009
$256$	7.00868	0.438043
$257$	−26.0140	−1.62271	−0.811355	−	0.584554i	$-0.801269\pi$
$257$	−26.0140	−1.62271	−0.811355	+	0.584554i	$0.801269\pi$
$258$	8.55368	0.532529
$259$	−3.40518	−0.211588
$260$	−16.0328	−0.994314
$261$	−16.9682	−1.05030
$262$	2.03267	0.125579
$263$	22.9355	1.41427	0.707133	−	0.707080i	$-0.249988\pi$
$263$	22.9355	1.41427	0.707133	+	0.707080i	$0.249988\pi$
$264$	−9.58351	−0.589824
$265$	−14.7978	−0.909019
$266$	−0.805567	−0.0493925
$267$	−6.53706	−0.400062
$268$	12.0801	0.737910
$269$	−17.0473	−1.03939	−0.519697	−	0.854351i	$-0.673955\pi$
$269$	−17.0473	−1.03939	−0.519697	+	0.854351i	$0.673955\pi$
$270$	−7.16836	−0.436252
$271$	7.24651	0.440194	0.220097	−	0.975478i	$-0.429363\pi$
$271$	7.24651	0.440194	0.220097	+	0.975478i	$0.429363\pi$
$272$	−5.97469	−0.362269
$273$	8.99714	0.544531
$274$	4.14881	0.250639
$275$	−9.33669	−0.563024
$276$	−2.40090	−0.144517
$277$	15.1033	0.907468	0.453734	−	0.891137i	$-0.350092\pi$
$277$	15.1033	0.907468	0.453734	+	0.891137i	$0.350092\pi$
$278$	−5.41979	−0.325058
$279$	0	0
$280$	4.38316	0.261944
$281$	−2.48708	−0.148367	−0.0741834	−	0.997245i	$-0.523635\pi$
$281$	−2.48708	−0.148367	−0.0741834	+	0.997245i	$0.523635\pi$
$282$	8.09579	0.482097
$283$	−4.72636	−0.280953	−0.140476	−	0.990084i	$-0.544863\pi$
$283$	−4.72636	−0.280953	−0.140476	+	0.990084i	$0.544863\pi$
$284$	−3.14852	−0.186831
$285$	−18.2223	−1.07939
$286$	−2.45543	−0.145193
$287$	7.51670	0.443697
$288$	20.8149	1.22653
$289$	−13.6702	−0.804131
$290$	−3.30095	−0.193838
$291$	−9.87440	−0.578848
$292$	−26.9468	−1.57694
$293$	−10.5489	−0.616273	−0.308136	−	0.951342i	$-0.599705\pi$
$293$	−10.5489	−0.616273	−0.308136	+	0.951342i	$0.599705\pi$
$294$	5.92691	0.345665
$295$	−35.7202	−2.07971
$296$	−4.28690	−0.249171
$297$	16.6802	0.967881
$298$	−4.19970	−0.243282
$299$	−1.27077	−0.0734908
$300$	20.8488	1.20371
$301$	9.10325	0.524703
$302$	−1.51894	−0.0874050
$303$	−51.2613	−2.94489
$304$	6.93570	0.397790
$305$	−42.9190	−2.45753
$306$	−3.44441	−0.196904
$307$	2.64850	0.151158	0.0755790	−	0.997140i	$-0.475919\pi$
$307$	2.64850	0.151158	0.0755790	+	0.997140i	$0.475919\pi$
$308$	−4.93715	−0.281320
$309$	−23.3600	−1.32890
$310$	0	0
$311$	5.51283	0.312604	0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283	0.312604	0.156302	+	0.987709i	$0.450043\pi$
$312$	11.3268	0.641254
$313$	−26.6755	−1.50779	−0.753893	−	0.656997i	$-0.771826\pi$
$313$	−26.6755	−1.50779	−0.753893	+	0.656997i	$0.771826\pi$
$314$	−3.05902	−0.172631
$315$	−17.2811	−0.973682
$316$	6.46949	0.363937
$317$	10.7402	0.603232	0.301616	−	0.953430i	$-0.402474\pi$
$317$	10.7402	0.603232	0.301616	+	0.953430i	$0.402474\pi$
$318$	5.06060	0.283784
$319$	7.68103	0.430055
$320$	−15.4208	−0.862047
$321$	35.1570	1.96227
$322$	0.168172	0.00937186
$323$	−3.86535	−0.215074
$324$	−7.01005	−0.389447
$325$	11.0351	0.612117
$326$	1.09925	0.0608816
$327$	1.82886	0.101136
$328$	9.46304	0.522509
$329$	8.61594	0.475012
$330$	7.35045	0.404629
$331$	19.6476	1.07993	0.539965	−	0.841687i	$-0.318437\pi$
$331$	19.6476	1.07993	0.539965	+	0.841687i	$0.318437\pi$
$332$	−24.1197	−1.32374
$333$	16.9016	0.926204
$334$	−4.69336	−0.256809
$335$	−19.1404	−1.04575
$336$	10.2513	0.559254
$337$	19.1787	1.04473	0.522366	−	0.852721i	$-0.325050\pi$
$337$	19.1787	1.04473	0.522366	+	0.852721i	$0.325050\pi$
$338$	−1.66654	−0.0906476
$339$	32.6952	1.77576
$340$	10.1808	0.552133
$341$	0	0
$342$	3.99844	0.216211
$343$	13.8826	0.749590
$344$	11.4604	0.617904
$345$	3.80413	0.204807
$346$	6.69294	0.359815
$347$	10.6600	0.572257	0.286128	−	0.958191i	$-0.407632\pi$
$347$	10.6600	0.572257	0.286128	+	0.958191i	$0.407632\pi$
$348$	−17.1517	−0.919429
$349$	−18.7016	−1.00107	−0.500536	−	0.865716i	$-0.666864\pi$
$349$	−18.7016	−1.00107	−0.500536	+	0.865716i	$0.666864\pi$
$350$	−1.46037	−0.0780598
$351$	−19.7144	−1.05228
$352$	−9.42234	−0.502212
$353$	−12.6622	−0.673943	−0.336972	−	0.941515i	$-0.609403\pi$
$353$	−12.6622	−0.673943	−0.336972	+	0.941515i	$0.609403\pi$
$354$	12.2157	0.649259
$355$	4.98871	0.264773
$356$	−4.23973	−0.224705
$357$	−5.71317	−0.302373
$358$	−0.0278791	−0.00147346
$359$	−22.6781	−1.19691	−0.598453	−	0.801158i	$-0.704218\pi$
$359$	−22.6781	−1.19691	−0.598453	+	0.801158i	$0.704218\pi$
$360$	−21.7558	−1.14663
$361$	−14.5129	−0.763838
$362$	0.760096	0.0399498
$363$	14.7223	0.772722
$364$	5.83525	0.305850
$365$	42.6961	2.23481
$366$	14.6776	0.767210
$367$	8.71968	0.455164	0.227582	−	0.973759i	$-0.426918\pi$
$367$	8.71968	0.455164	0.227582	+	0.973759i	$0.426918\pi$
$368$	−1.44791	−0.0754777
$369$	−37.3092	−1.94224
$370$	3.28801	0.170935
$371$	5.38574	0.279614
$372$	0	0
$373$	25.4134	1.31586	0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134	1.31586	0.657928	+	0.753081i	$0.271433\pi$
$374$	1.55919	0.0806240
$375$	9.97799	0.515261
$376$	10.8469	0.559387
$377$	−9.07826	−0.467554
$378$	2.60897	0.134191
$379$	22.0979	1.13509	0.567546	−	0.823342i	$-0.307893\pi$
$379$	22.0979	1.13509	0.567546	+	0.823342i	$0.307893\pi$
$380$	−11.8184	−0.606270
$381$	−0.340848	−0.0174622
$382$	−1.87724	−0.0960482
$383$	−26.6426	−1.36137	−0.680687	−	0.732574i	$-0.738319\pi$
$383$	−26.6426	−1.36137	−0.680687	+	0.732574i	$0.738319\pi$
$384$	27.6985	1.41348
$385$	7.82271	0.398682
$386$	−0.749843	−0.0381660
$387$	−45.1841	−2.29683
$388$	−6.40422	−0.325125
$389$	−12.9551	−0.656847	−0.328424	−	0.944531i	$-0.606517\pi$
$389$	−12.9551	−0.656847	−0.328424	+	0.944531i	$0.606517\pi$
$390$	−8.68754	−0.439911
$391$	0.806940	0.0408087
$392$	7.94100	0.401081
$393$	−16.7347	−0.844152
$394$	−2.06492	−0.104029
$395$	−10.2506	−0.515766
$396$	24.5056	1.23145
$397$	−2.92725	−0.146915	−0.0734574	−	0.997298i	$-0.523403\pi$
$397$	−2.92725	−0.146915	−0.0734574	+	0.997298i	$0.523403\pi$
$398$	2.43471	0.122041
$399$	6.63212	0.332021
$400$	12.5733	0.628667
$401$	−12.2745	−0.612957	−0.306479	−	0.951878i	$-0.599151\pi$
$401$	−12.2745	−0.612957	−0.306479	+	0.951878i	$0.599151\pi$
$402$	6.54572	0.326471
$403$	0	0
$404$	−33.2464	−1.65407
$405$	11.1071	0.551918
$406$	1.20140	0.0596245
$407$	−7.65092	−0.379242
$408$	−7.19251	−0.356082
$409$	−17.1972	−0.850348	−0.425174	−	0.905112i	$-0.639787\pi$
$409$	−17.1972	−0.850348	−0.425174	+	0.905112i	$0.639787\pi$
$410$	−7.25805	−0.358450
$411$	−34.1565	−1.68482
$412$	−15.1505	−0.746413
$413$	13.0006	0.639717
$414$	−0.834723	−0.0410244
$415$	38.2167	1.87599
$416$	11.1363	0.546003
$417$	44.6204	2.18507
$418$	−1.80999	−0.0885293
$419$	23.1455	1.13073	0.565366	−	0.824840i	$-0.308735\pi$
$419$	23.1455	1.13073	0.565366	+	0.824840i	$0.308735\pi$
$420$	−17.4681	−0.852357
$421$	29.1822	1.42226	0.711128	−	0.703063i	$-0.248185\pi$
$421$	29.1822	1.42226	0.711128	+	0.703063i	$0.248185\pi$
$422$	5.87200	0.285844
$423$	−42.7653	−2.07932
$424$	6.78030	0.329280
$425$	−7.00727	−0.339903
$426$	−1.70606	−0.0826588
$427$	15.6206	0.755935
$428$	22.8017	1.10216
$429$	20.2152	0.975998
$430$	−8.79001	−0.423892
$431$	30.3522	1.46201	0.731007	−	0.682369i	$-0.239050\pi$
$431$	30.3522	1.46201	0.731007	+	0.682369i	$0.239050\pi$
$432$	−22.4625	−1.08073
$433$	−13.8400	−0.665107	−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400	−0.665107	−0.332553	+	0.943084i	$0.607910\pi$
$434$	0	0
$435$	27.1762	1.30300
$436$	1.18614	0.0568057
$437$	−0.936734	−0.0448101
$438$	−14.6014	−0.697680
$439$	12.9201	0.616644	0.308322	−	0.951282i	$-0.400233\pi$
$439$	12.9201	0.616644	0.308322	+	0.951282i	$0.400233\pi$
$440$	9.84829	0.469499
$441$	−31.3084	−1.49088
$442$	−1.84282	−0.0876540
$443$	23.7583	1.12879	0.564395	−	0.825505i	$-0.309110\pi$
$443$	23.7583	1.12879	0.564395	+	0.825505i	$0.309110\pi$
$444$	17.0845	0.810794
$445$	6.71767	0.318448
$446$	−2.20052	−0.104197
$447$	34.5755	1.63536
$448$	5.61248	0.265165
$449$	−19.4129	−0.916151	−0.458075	−	0.888913i	$-0.651461\pi$
$449$	−19.4129	−0.916151	−0.458075	+	0.888913i	$0.651461\pi$
$450$	7.24854	0.341699
$451$	16.8889	0.795266
$452$	21.2050	0.997401
$453$	12.5052	0.587545
$454$	−2.75787	−0.129433
$455$	−9.24571	−0.433446
$456$	8.34940	0.390997
$457$	24.3420	1.13867	0.569334	−	0.822106i	$-0.307201\pi$
$457$	24.3420	1.13867	0.569334	+	0.822106i	$0.307201\pi$
$458$	4.48884	0.209750
$459$	12.5186	0.584319
$460$	2.46723	0.115035
$461$	−38.3431	−1.78582	−0.892908	−	0.450239i	$-0.851339\pi$
$461$	−38.3431	−1.78582	−0.892908	+	0.450239i	$0.851339\pi$
$462$	−2.67524	−0.124464
$463$	−6.59429	−0.306463	−0.153231	−	0.988190i	$-0.548968\pi$
$463$	−6.59429	−0.306463	−0.153231	+	0.988190i	$0.548968\pi$
$464$	−10.3437	−0.480195
$465$	0	0
$466$	4.46933	0.207038
$467$	38.4014	1.77701	0.888503	−	0.458871i	$-0.151746\pi$
$467$	38.4014	1.77701	0.888503	+	0.458871i	$0.151746\pi$
$468$	−28.9633	−1.33883
$469$	6.96628	0.321673
$470$	−8.31947	−0.383748
$471$	25.1845	1.16044
$472$	16.3669	0.753348
$473$	20.4536	0.940458
$474$	3.50555	0.161015
$475$	8.13437	0.373231
$476$	−3.70538	−0.169836
$477$	−26.7321	−1.22398
$478$	−8.93503	−0.408679
$479$	7.52515	0.343833	0.171916	−	0.985112i	$-0.445004\pi$
$479$	7.52515	0.343833	0.171916	+	0.985112i	$0.445004\pi$
$480$	−33.3372	−1.52163
$481$	9.04267	0.412310
$482$	0.829725	0.0377930
$483$	−1.38454	−0.0629986
$484$	9.54843	0.434020
$485$	10.1472	0.460761
$486$	3.43444	0.155789
$487$	25.0323	1.13432	0.567160	−	0.823608i	$-0.308042\pi$
$487$	25.0323	1.13432	0.567160	+	0.823608i	$0.308042\pi$
$488$	19.6654	0.890209
$489$	−9.04993	−0.409252
$490$	−6.09066	−0.275148
$491$	−39.7100	−1.79209	−0.896044	−	0.443964i	$-0.853572\pi$
$491$	−39.7100	−1.79209	−0.896044	+	0.443964i	$0.853572\pi$
$492$	−37.7128	−1.70023
$493$	5.76468	0.259628
$494$	2.13923	0.0962487
$495$	−38.8281	−1.74519
$496$	0	0
$497$	−1.81567	−0.0814440
$498$	−13.0695	−0.585659
$499$	−23.6541	−1.05890	−0.529451	−	0.848341i	$-0.677602\pi$
$499$	−23.6541	−1.05890	−0.529451	+	0.848341i	$0.677602\pi$
$500$	6.47140	0.289410
$501$	38.6397	1.72630
$502$	0.828199	0.0369643
$503$	−20.1864	−0.900068	−0.450034	−	0.893011i	$-0.648588\pi$
$503$	−20.1864	−0.900068	−0.450034	+	0.893011i	$0.648588\pi$
$504$	7.91818	0.352704
$505$	52.6776	2.34412
$506$	0.377857	0.0167978
$507$	13.7203	0.609342
$508$	−0.221063	−0.00980807
$509$	11.8390	0.524755	0.262377	−	0.964965i	$-0.415493\pi$
$509$	11.8390	0.524755	0.262377	+	0.964965i	$0.415493\pi$
$510$	5.51658	0.244278
$511$	−15.5395	−0.687427
$512$	21.6098	0.955027
$513$	−14.5322	−0.641612
$514$	−9.14217	−0.403244
$515$	24.0054	1.05780
$516$	−45.6729	−2.01064
$517$	19.3587	0.851395
$518$	−1.19669	−0.0525796
$519$	−55.1020	−2.41871
$520$	−11.6398	−0.510437
$521$	−32.7484	−1.43474	−0.717368	−	0.696695i	$-0.754653\pi$
$521$	−32.7484	−1.43474	−0.717368	+	0.696695i	$0.754653\pi$
$522$	−5.96316	−0.261000
$523$	−29.5027	−1.29006	−0.645031	−	0.764157i	$-0.723155\pi$
$523$	−29.5027	−1.29006	−0.645031	+	0.764157i	$0.723155\pi$
$524$	−10.8536	−0.474140
$525$	12.0230	0.524726
$526$	8.06030	0.351446
$527$	0	0
$528$	23.0331	1.00239
$529$	−22.8044	−0.991498
$530$	−5.20041	−0.225892
$531$	−64.5285	−2.80030
$532$	4.30138	0.186488
$533$	−19.9611	−0.864610
$534$	−2.29734	−0.0994154
$535$	−36.1283	−1.56196
$536$	8.77009	0.378810
$537$	0.229525	0.00990472
$538$	−5.99098	−0.258290
$539$	14.1725	0.610451
$540$	38.2759	1.64713
$541$	13.2658	0.570342	0.285171	−	0.958477i	$-0.407950\pi$
$541$	13.2658	0.570342	0.285171	+	0.958477i	$0.407950\pi$
$542$	2.54666	0.109388
$543$	−6.25776	−0.268546
$544$	−7.07155	−0.303190
$545$	−1.87939	−0.0805040
$546$	3.16189	0.135316
$547$	37.7639	1.61467	0.807333	−	0.590096i	$-0.200910\pi$
$547$	37.7639	1.61467	0.807333	+	0.590096i	$0.200910\pi$
$548$	−22.1528	−0.946321
$549$	−77.5331	−3.30903
$550$	−3.28122	−0.139912
$551$	−6.69191	−0.285085
$552$	−1.74304	−0.0741887
$553$	3.73078	0.158649
$554$	5.30778	0.225506
$555$	−27.0697	−1.14904
$556$	28.9393	1.22730
$557$	−11.3637	−0.481496	−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637	−0.481496	−0.240748	+	0.970588i	$0.577393\pi$
$558$	0	0
$559$	−24.1743	−1.02246
$560$	−10.5345	−0.445165
$561$	−12.8366	−0.541962
$562$	−0.874041	−0.0368692
$563$	−20.1865	−0.850762	−0.425381	−	0.905014i	$-0.639860\pi$
$563$	−20.1865	−0.850762	−0.425381	+	0.905014i	$0.639860\pi$
$564$	−43.2280	−1.82023
$565$	−33.5985	−1.41350
$566$	−1.66100	−0.0698169
$567$	−4.04251	−0.169770
$568$	−2.28581	−0.0959106
$569$	−30.9897	−1.29915	−0.649577	−	0.760296i	$-0.725054\pi$
$569$	−30.9897	−1.29915	−0.649577	+	0.760296i	$0.725054\pi$
$570$	−6.40390	−0.268230
$571$	−10.3997	−0.435214	−0.217607	−	0.976036i	$-0.569825\pi$
$571$	−10.3997	−0.435214	−0.217607	+	0.976036i	$0.569825\pi$
$572$	13.1109	0.548195
$573$	15.4551	0.645645
$574$	2.64161	0.110259
$575$	−1.69815	−0.0708178
$576$	−27.8576	−1.16073
$577$	5.41386	0.225382	0.112691	−	0.993630i	$-0.464053\pi$
$577$	5.41386	0.225382	0.112691	+	0.993630i	$0.464053\pi$
$578$	−4.80416	−0.199827
$579$	6.17335	0.256556
$580$	17.6256	0.731864
$581$	−13.9092	−0.577052
$582$	−3.47019	−0.143844
$583$	12.1009	0.501169
$584$	−19.5632	−0.809532
$585$	45.8912	1.89737
$586$	−3.70722	−0.153144
$587$	−12.5628	−0.518523	−0.259261	−	0.965807i	$-0.583479\pi$
$587$	−12.5628	−0.518523	−0.259261	+	0.965807i	$0.583479\pi$
$588$	−31.6471	−1.30510
$589$	0	0
$590$	−12.5532	−0.516809
$591$	17.0002	0.699295
$592$	10.3032	0.423458
$593$	27.0700	1.11163	0.555816	−	0.831305i	$-0.312406\pi$
$593$	27.0700	1.11163	0.555816	+	0.831305i	$0.312406\pi$
$594$	5.86195	0.240519
$595$	5.87102	0.240688
$596$	22.4245	0.918545
$597$	−20.0446	−0.820372
$598$	−0.446591	−0.0182625
$599$	−14.3551	−0.586533	−0.293266	−	0.956031i	$-0.594742\pi$
$599$	−14.3551	−0.586533	−0.293266	+	0.956031i	$0.594742\pi$
$600$	15.1362	0.617931
$601$	0.640017	0.0261068	0.0130534	−	0.999915i	$-0.495845\pi$
$601$	0.640017	0.0261068	0.0130534	+	0.999915i	$0.495845\pi$
$602$	3.19918	0.130389
$603$	−34.5772	−1.40809
$604$	8.11046	0.330010
$605$	−15.1291	−0.615085
$606$	−18.0149	−0.731805
$607$	−6.51782	−0.264550	−0.132275	−	0.991213i	$-0.542228\pi$
$607$	−6.51782	−0.264550	−0.132275	+	0.991213i	$0.542228\pi$
$608$	8.20899	0.332919
$609$	−9.89096	−0.400802
$610$	−15.0831	−0.610698
$611$	−22.8802	−0.925633
$612$	18.3917	0.743439
$613$	10.4453	0.421883	0.210941	−	0.977499i	$-0.432347\pi$
$613$	10.4453	0.421883	0.210941	+	0.977499i	$0.432347\pi$
$614$	0.930770	0.0375628
$615$	59.7545	2.40953
$616$	−3.58435	−0.144417
$617$	21.7034	0.873744	0.436872	−	0.899524i	$-0.356086\pi$
$617$	21.7034	0.873744	0.436872	+	0.899524i	$0.356086\pi$
$618$	−8.20946	−0.330233
$619$	28.5478	1.14743	0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478	1.14743	0.573716	+	0.819054i	$0.305501\pi$
$620$	0	0
$621$	3.03377	0.121741
$622$	1.93739	0.0776822
$623$	−2.44494	−0.0979544
$624$	−27.2229	−1.08979
$625$	−29.4541	−1.17817
$626$	−9.37462	−0.374685
$627$	14.9013	0.595102
$628$	16.3338	0.651791
$629$	−5.74208	−0.228952
$630$	−6.07316	−0.241960
$631$	27.2405	1.08443	0.542214	−	0.840241i	$-0.317586\pi$
$631$	27.2405	1.08443	0.542214	+	0.840241i	$0.317586\pi$
$632$	4.69682	0.186829
$633$	−48.3433	−1.92147
$634$	3.77447	0.149903
$635$	0.350265	0.0138998
$636$	−27.0214	−1.07147
$637$	−16.7505	−0.663680
$638$	2.69936	0.106869
$639$	9.01210	0.356513
$640$	−28.4638	−1.12513
$641$	41.2081	1.62762	0.813811	−	0.581130i	$-0.197389\pi$
$641$	41.2081	1.62762	0.813811	+	0.581130i	$0.197389\pi$
$642$	12.3553	0.487625
$643$	−30.8124	−1.21512	−0.607562	−	0.794273i	$-0.707852\pi$
$643$	−30.8124	−1.21512	−0.607562	+	0.794273i	$0.707852\pi$
$644$	−0.897965	−0.0353848
$645$	72.3668	2.84944
$646$	−1.35841	−0.0534459
$647$	8.91617	0.350531	0.175265	−	0.984521i	$-0.443922\pi$
$647$	8.91617	0.350531	0.175265	+	0.984521i	$0.443922\pi$
$648$	−5.08926	−0.199925
$649$	29.2103	1.14661
$650$	3.87809	0.152111
$651$	0	0
$652$	−5.86949	−0.229867
$653$	39.2414	1.53563	0.767817	−	0.640669i	$-0.221343\pi$
$653$	39.2414	1.53563	0.767817	+	0.640669i	$0.221343\pi$
$654$	0.642719	0.0251323
$655$	17.1970	0.671943
$656$	−22.7435	−0.887986
$657$	77.1304	3.00914
$658$	3.02792	0.118041
$659$	32.9535	1.28369	0.641844	−	0.766835i	$-0.278170\pi$
$659$	32.9535	1.28369	0.641844	+	0.766835i	$0.278170\pi$
$660$	−39.2482	−1.52773
$661$	−0.169675	−0.00659960	−0.00329980	−	0.999995i	$-0.501050\pi$
$661$	−0.169675	−0.00659960	−0.00329980	+	0.999995i	$0.501050\pi$
$662$	6.90481	0.268363
$663$	15.1717	0.589219
$664$	−17.5108	−0.679551
$665$	−6.81535	−0.264288
$666$	5.93978	0.230162
$667$	1.39702	0.0540928
$668$	25.0605	0.969619
$669$	18.1165	0.700426
$670$	−6.72657	−0.259870
$671$	35.0972	1.35491
$672$	12.1333	0.468051
$673$	−14.5863	−0.562262	−0.281131	−	0.959669i	$-0.590710\pi$
$673$	−14.5863	−0.562262	−0.281131	+	0.959669i	$0.590710\pi$
$674$	6.74003	0.259616
$675$	−26.3446	−1.01400
$676$	8.89857	0.342253
$677$	15.7668	0.605968	0.302984	−	0.952996i	$-0.402017\pi$
$677$	15.7668	0.605968	0.302984	+	0.952996i	$0.402017\pi$
$678$	11.4902	0.441277
$679$	−3.69314	−0.141730
$680$	7.39123	0.283441
$681$	22.7051	0.870063
$682$	0	0
$683$	20.5935	0.787988	0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935	0.787988	0.393994	+	0.919113i	$0.371093\pi$
$684$	−21.3499	−0.816334
$685$	35.1002	1.34111
$686$	4.87880	0.186273
$687$	−36.9560	−1.40996
$688$	−27.5440	−1.05011
$689$	−14.3022	−0.544869
$690$	1.33689	0.0508947
$691$	−5.95171	−0.226414	−0.113207	−	0.993571i	$-0.536112\pi$
$691$	−5.95171	−0.226414	−0.113207	+	0.993571i	$0.536112\pi$
$692$	−35.7374	−1.35853
$693$	14.1317	0.536820
$694$	3.74626	0.142206
$695$	−45.8532	−1.73931
$696$	−12.4521	−0.471995
$697$	12.6752	0.480109
$698$	−6.57233	−0.248767
$699$	−36.7954	−1.39173
$700$	7.79771	0.294726
$701$	−26.6304	−1.00582	−0.502908	−	0.864340i	$-0.667737\pi$
$701$	−26.6304	−1.00582	−0.502908	+	0.864340i	$0.667737\pi$
$702$	−6.92828	−0.261491
$703$	6.66568	0.251401
$704$	12.6104	0.475272
$705$	68.4929	2.57959
$706$	−4.44992	−0.167475
$707$	−19.1723	−0.721050
$708$	−65.2266	−2.45137
$709$	−2.64278	−0.0992515	−0.0496258	−	0.998768i	$-0.515803\pi$
$709$	−2.64278	−0.0992515	−0.0496258	+	0.998768i	$0.515803\pi$
$710$	1.75319	0.0657962
$711$	−18.5178	−0.694471
$712$	−3.07802	−0.115354
$713$	0	0
$714$	−2.00779	−0.0751398
$715$	−20.7737	−0.776892
$716$	0.148862	0.00556325
$717$	73.5608	2.74718
$718$	−7.96983	−0.297431
$719$	5.19824	0.193862	0.0969308	−	0.995291i	$-0.469097\pi$
$719$	5.19824	0.193862	0.0969308	+	0.995291i	$0.469097\pi$
$720$	52.2882	1.94866
$721$	−8.73692	−0.325380
$722$	−5.10031	−0.189814
$723$	−6.83101	−0.254048
$724$	−4.05858	−0.150836
$725$	−12.1314	−0.450548
$726$	5.17391	0.192022
$727$	24.2064	0.897767	0.448884	−	0.893590i	$-0.351822\pi$
$727$	24.2064	0.897767	0.448884	+	0.893590i	$0.351822\pi$
$728$	4.23636	0.157010
$729$	−39.4824	−1.46231
$730$	15.0048	0.555352
$731$	15.3506	0.567763
$732$	−78.3719	−2.89671
$733$	40.3628	1.49083	0.745416	−	0.666599i	$-0.232251\pi$
$733$	40.3628	1.49083	0.745416	+	0.666599i	$0.232251\pi$
$734$	3.06438	0.113108
$735$	50.1435	1.84957
$736$	−1.71373	−0.0631689
$737$	15.6522	0.576555
$738$	−13.1117	−0.482647
$739$	6.09785	0.224313	0.112157	−	0.993691i	$-0.464224\pi$
$739$	6.09785	0.224313	0.112157	+	0.993691i	$0.464224\pi$
$740$	−17.5565	−0.645390
$741$	−17.6120	−0.646993
$742$	1.89272	0.0694841
$743$	16.2263	0.595284	0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263	0.595284	0.297642	+	0.954678i	$0.403800\pi$
$744$	0	0
$745$	−35.5308	−1.30175
$746$	8.93109	0.326990
$747$	69.0385	2.52599
$748$	−8.32541	−0.304407
$749$	13.1491	0.480458
$750$	3.50659	0.128043
$751$	36.4445	1.32988	0.664939	−	0.746898i	$-0.268458\pi$
$751$	36.4445	1.32988	0.664939	+	0.746898i	$0.268458\pi$
$752$	−26.0695	−0.950659
$753$	−6.81844	−0.248478
$754$	−3.19039	−0.116187
$755$	−12.8507	−0.467684
$756$	−13.9307	−0.506656
$757$	43.5622	1.58329	0.791647	−	0.610978i	$-0.209224\pi$
$757$	43.5622	1.58329	0.791647	+	0.610978i	$0.209224\pi$
$758$	7.76591	0.282071
$759$	−3.11084	−0.112916
$760$	−8.58009	−0.311232
$761$	3.29928	0.119599	0.0597994	−	0.998210i	$-0.480954\pi$
$761$	3.29928	0.119599	0.0597994	+	0.998210i	$0.480954\pi$
$762$	−0.119785	−0.00433935
$763$	0.684014	0.0247630
$764$	10.0237	0.362643
$765$	−29.1408	−1.05359
$766$	−9.36309	−0.338302
$767$	−34.5239	−1.24658
$768$	−20.2782	−0.731725
$769$	−45.7136	−1.64847	−0.824237	−	0.566244i	$-0.808396\pi$
$769$	−45.7136	−1.64847	−0.824237	+	0.566244i	$0.808396\pi$
$770$	2.74916	0.0990727
$771$	75.2661	2.71064
$772$	4.00383	0.144101
$773$	30.0007	1.07905	0.539524	−	0.841970i	$-0.318604\pi$
$773$	30.0007	1.07905	0.539524	+	0.841970i	$0.318604\pi$
$774$	−15.8791	−0.570764
$775$	0	0
$776$	−4.64943	−0.166905
$777$	9.85218	0.353445
$778$	−4.55283	−0.163227
$779$	−14.7140	−0.527185
$780$	46.3877	1.66094
$781$	−4.07953	−0.145977
$782$	0.283585	0.0101410
$783$	21.6729	0.774527
$784$	−19.0855	−0.681624
$785$	−25.8803	−0.923707
$786$	−5.88110	−0.209772
$787$	−43.2320	−1.54105	−0.770527	−	0.637408i	$-0.780007\pi$
$787$	−43.2320	−1.54105	−0.770527	+	0.637408i	$0.780007\pi$
$788$	11.0258	0.392777
$789$	−66.3592	−2.36245
$790$	−3.60241	−0.128168
$791$	12.2284	0.434792
$792$	17.7909	0.632173
$793$	−41.4816	−1.47305
$794$	−1.02873	−0.0365083
$795$	42.8142	1.51846
$796$	−13.0003	−0.460783
$797$	22.8237	0.808458	0.404229	−	0.914658i	$-0.367540\pi$
$797$	22.8237	0.808458	0.404229	+	0.914658i	$0.367540\pi$
$798$	2.33074	0.0825073
$799$	14.5289	0.513995
$800$	14.8816	0.526144
$801$	12.1355	0.428786
$802$	−4.31364	−0.152320
$803$	−34.9149	−1.23212
$804$	−34.9513	−1.23264
$805$	1.42279	0.0501467
$806$	0	0
$807$	49.3229	1.73625
$808$	−24.1367	−0.849128
$809$	−21.2384	−0.746703	−0.373352	−	0.927690i	$-0.621791\pi$
$809$	−21.2384	−0.746703	−0.373352	+	0.927690i	$0.621791\pi$
$810$	3.90341	0.137152
$811$	2.12314	0.0745534	0.0372767	−	0.999305i	$-0.488132\pi$
$811$	2.12314	0.0745534	0.0372767	+	0.999305i	$0.488132\pi$
$812$	−6.41495	−0.225121
$813$	−20.9663	−0.735319
$814$	−2.68878	−0.0942417
$815$	9.29997	0.325764
$816$	17.2865	0.605149
$817$	−17.8197	−0.623433
$818$	−6.04366	−0.211312
$819$	−16.7024	−0.583628
$820$	38.7548	1.35338
$821$	41.7919	1.45855	0.729274	−	0.684222i	$-0.239858\pi$
$821$	41.7919	1.45855	0.729274	+	0.684222i	$0.239858\pi$
$822$	−12.0037	−0.418678
$823$	16.2985	0.568130	0.284065	−	0.958805i	$-0.408317\pi$
$823$	16.2985	0.568130	0.284065	+	0.958805i	$0.408317\pi$
$824$	−10.9992	−0.383176
$825$	27.0138	0.940499
$826$	4.56883	0.158970
$827$	−31.0895	−1.08109	−0.540544	−	0.841316i	$-0.681782\pi$
$827$	−31.0895	−1.08109	−0.540544	+	0.841316i	$0.681782\pi$
$828$	4.45705	0.154893
$829$	−28.0488	−0.974176	−0.487088	−	0.873353i	$-0.661941\pi$
$829$	−28.0488	−0.974176	−0.487088	+	0.873353i	$0.661941\pi$
$830$	13.4306	0.466183
$831$	−43.6982	−1.51587
$832$	−14.9043	−0.516714
$833$	10.6366	0.368535
$834$	15.6810	0.542990
$835$	−39.7073	−1.37413
$836$	9.66453	0.334255
$837$	0	0
$838$	8.13409	0.280987
$839$	−23.0676	−0.796382	−0.398191	−	0.917302i	$-0.630362\pi$
$839$	−23.0676	−0.796382	−0.398191	+	0.917302i	$0.630362\pi$
$840$	−12.6818	−0.437562
$841$	−19.0199	−0.655857
$842$	10.2556	0.353431
$843$	7.19585	0.247838
$844$	−31.3539	−1.07925
$845$	−14.0994	−0.485035
$846$	−15.0291	−0.516711
$847$	5.50633	0.189200
$848$	−16.2958	−0.559600
$849$	13.6747	0.469316
$850$	−2.46258	−0.0844659
$851$	−1.39154	−0.0477015
$852$	9.10960	0.312090
$853$	30.0209	1.02790	0.513948	−	0.857821i	$-0.328182\pi$
$853$	30.0209	1.02790	0.513948	+	0.857821i	$0.328182\pi$
$854$	5.48960	0.187850
$855$	33.8280	1.15689
$856$	16.5539	0.565800
$857$	−54.5874	−1.86467	−0.932335	−	0.361596i	$-0.882232\pi$
$857$	−54.5874	−1.86467	−0.932335	+	0.361596i	$0.882232\pi$
$858$	7.10427	0.242536
$859$	9.33641	0.318554	0.159277	−	0.987234i	$-0.449084\pi$
$859$	9.33641	0.318554	0.159277	+	0.987234i	$0.449084\pi$
$860$	46.9348	1.60046
$861$	−21.7480	−0.741170
$862$	10.6668	0.363311
$863$	13.3167	0.453307	0.226653	−	0.973975i	$-0.427222\pi$
$863$	13.3167	0.453307	0.226653	+	0.973975i	$0.427222\pi$
$864$	−26.5862	−0.904482
$865$	56.6244	1.92529
$866$	−4.86382	−0.165279
$867$	39.5520	1.34326
$868$	0	0
$869$	8.38250	0.284357
$870$	9.55061	0.323796
$871$	−18.4994	−0.626828
$872$	0.861129	0.0291615
$873$	18.3309	0.620409
$874$	−0.329199	−0.0111353
$875$	3.73189	0.126161
$876$	77.9649	2.63419
$877$	−42.5661	−1.43735	−0.718677	−	0.695344i	$-0.755252\pi$
$877$	−42.5661	−1.43735	−0.718677	+	0.695344i	$0.755252\pi$
$878$	4.54055	0.153236
$879$	30.5210	1.02945
$880$	−23.6694	−0.797897
$881$	−5.77313	−0.194502	−0.0972509	−	0.995260i	$-0.531005\pi$
$881$	−5.77313	−0.194502	−0.0972509	+	0.995260i	$0.531005\pi$
$882$	−11.0028	−0.370483
$883$	27.1971	0.915255	0.457627	−	0.889144i	$-0.348699\pi$
$883$	27.1971	0.915255	0.457627	+	0.889144i	$0.348699\pi$
$884$	9.83985	0.330950
$885$	103.349	3.47404
$886$	8.34943	0.280504
$887$	−7.37169	−0.247517	−0.123759	−	0.992312i	$-0.539495\pi$
$887$	−7.37169	−0.247517	−0.123759	+	0.992312i	$0.539495\pi$
$888$	12.4033	0.416226
$889$	−0.127481	−0.00427558
$890$	2.36081	0.0791345
$891$	−9.08290	−0.304289
$892$	11.7498	0.393412
$893$	−16.8658	−0.564393
$894$	12.1510	0.406389
$895$	−0.235866	−0.00788414
$896$	10.3596	0.346089
$897$	3.67672	0.122762
$898$	−6.82232	−0.227664
$899$	0	0
$900$	−38.7040	−1.29013
$901$	9.08185	0.302560
$902$	5.93530	0.197624
$903$	−26.3384	−0.876486
$904$	15.3948	0.512022
$905$	6.43065	0.213762
$906$	4.39473	0.146005
$907$	16.4830	0.547310	0.273655	−	0.961828i	$-0.411767\pi$
$907$	16.4830	0.547310	0.273655	+	0.961828i	$0.411767\pi$
$908$	14.7258	0.488694
$909$	95.1621	3.15633
$910$	−3.24924	−0.107711
$911$	44.8070	1.48452	0.742262	−	0.670110i	$-0.233753\pi$
$911$	44.8070	1.48452	0.742262	+	0.670110i	$0.233753\pi$
$912$	−20.0670	−0.664485
$913$	−31.2519	−1.03429
$914$	8.55455	0.282959
$915$	124.177	4.10517
$916$	−23.9684	−0.791940
$917$	−6.25896	−0.206689
$918$	4.39945	0.145203
$919$	−10.3568	−0.341640	−0.170820	−	0.985302i	$-0.554642\pi$
$919$	−10.3568	−0.341640	−0.170820	+	0.985302i	$0.554642\pi$
$920$	1.79120	0.0590541
$921$	−7.66289	−0.252501
$922$	−13.4750	−0.443776
$923$	4.82163	0.158706
$924$	14.2846	0.469929
$925$	12.0838	0.397314
$926$	−2.31745	−0.0761561
$927$	43.3658	1.42432
$928$	−12.2427	−0.401885
$929$	44.0624	1.44564	0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624	1.44564	0.722820	+	0.691037i	$0.242846\pi$
$930$	0	0
$931$	−12.3474	−0.404671
$932$	−23.8643	−0.781701
$933$	−15.9502	−0.522187
$934$	13.4955	0.441586
$935$	13.1913	0.431401
$936$	−21.0272	−0.687296
$937$	−34.5669	−1.12925	−0.564626	−	0.825347i	$-0.690980\pi$
$937$	−34.5669	−1.12925	−0.564626	+	0.825347i	$0.690980\pi$
$938$	2.44818	0.0799358
$939$	77.1799	2.51867
$940$	44.4223	1.44890
$941$	−22.1491	−0.722039	−0.361020	−	0.932558i	$-0.617571\pi$
$941$	−22.1491	−0.722039	−0.361020	+	0.932558i	$0.617571\pi$
$942$	8.85064	0.288370
$943$	3.07173	0.100029
$944$	−39.3363	−1.28029
$945$	22.0727	0.718025
$946$	7.18806	0.233704
$947$	−28.0826	−0.912560	−0.456280	−	0.889836i	$-0.650819\pi$
$947$	−28.0826	−0.912560	−0.456280	+	0.889836i	$0.650819\pi$
$948$	−18.7181	−0.607936
$949$	41.2661	1.33956
$950$	2.85868	0.0927479
$951$	−31.0746	−1.00766
$952$	−2.69008	−0.0871861
$953$	7.66676	0.248351	0.124175	−	0.992260i	$-0.460371\pi$
$953$	7.66676	0.248351	0.124175	+	0.992260i	$0.460371\pi$
$954$	−9.39455	−0.304160
$955$	−15.8821	−0.513932
$956$	47.7092	1.54302
$957$	−22.2235	−0.718382
$958$	2.64458	0.0854426
$959$	−12.7750	−0.412525
$960$	44.6168	1.44000
$961$	0	0
$962$	3.17789	0.102459
$963$	−65.2657	−2.10316
$964$	−4.43037	−0.142693
$965$	−6.34391	−0.204218
$966$	−0.486571	−0.0156552
$967$	−1.85036	−0.0595037	−0.0297518	−	0.999557i	$-0.509472\pi$
$967$	−1.85036	−0.0595037	−0.0297518	+	0.999557i	$0.509472\pi$
$968$	6.93211	0.222807
$969$	11.1836	0.359269
$970$	3.56606	0.114499
$971$	49.3715	1.58441	0.792203	−	0.610258i	$-0.208934\pi$
$971$	49.3715	1.58441	0.792203	+	0.610258i	$0.208934\pi$
$972$	−18.3384	−0.588204
$973$	16.6885	0.535010
$974$	8.79715	0.281879
$975$	−31.9278	−1.02251
$976$	−47.2639	−1.51288
$977$	−35.6224	−1.13966	−0.569831	−	0.821762i	$-0.692992\pi$
$977$	−35.6224	−1.13966	−0.569831	+	0.821762i	$0.692992\pi$
$978$	−3.18044	−0.101699
$979$	−5.49340	−0.175570
$980$	32.5215	1.03886
$981$	−3.39511	−0.108397
$982$	−13.9554	−0.445335
$983$	−6.38359	−0.203605	−0.101802	−	0.994805i	$-0.532461\pi$
$983$	−6.38359	−0.203605	−0.101802	+	0.994805i	$0.532461\pi$
$984$	−27.3793	−0.872821
$985$	−17.4699	−0.556637
$986$	2.02590	0.0645177
$987$	−24.9284	−0.793481
$988$	−11.4226	−0.363400
$989$	3.72009	0.118292
$990$	−13.6454	−0.433681
$991$	−44.2919	−1.40698	−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919	−1.40698	−0.703489	+	0.710706i	$0.748376\pi$
$992$	0	0
$993$	−56.8463	−1.80396
$994$	−0.638086	−0.0202389
$995$	20.5984	0.653014
$996$	69.7855	2.21124
$997$	5.32316	0.168586	0.0842931	−	0.996441i	$-0.473137\pi$
$997$	5.32316	0.168586	0.0842931	+	0.996441i	$0.473137\pi$
$998$	−8.31281	−0.263137
$999$	−21.5880	−0.683013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.i.1.4		8
3.2	odd	2		8649.2.a.bf.1.5		8
31.2	even	5		961.2.d.p.531.2		16
31.3	odd	30		961.2.g.n.846.1		16
31.4	even	5		961.2.d.o.388.3		16
31.5	even	3		961.2.c.j.521.4		16
31.6	odd	6		961.2.c.i.439.4		16
31.7	even	15		961.2.g.k.235.2		16
31.8	even	5		961.2.d.o.374.3		16
31.9	even	15		961.2.g.k.732.2		16
31.10	even	15		961.2.g.t.844.1		16
31.11	odd	30		961.2.g.l.338.2		16
31.12	odd	30		961.2.g.m.547.1		16
31.13	odd	30		961.2.g.m.448.1		16
31.14	even	15		31.2.g.a.10.2	✓	16
31.15	odd	10		961.2.d.q.628.2		16
31.16	even	5		961.2.d.p.628.2		16
31.17	odd	30		961.2.g.l.816.2		16
31.18	even	15		961.2.g.s.448.1		16
31.19	even	15		961.2.g.s.547.1		16
31.20	even	15		31.2.g.a.28.2	yes	16
31.21	odd	30		961.2.g.n.844.1		16
31.22	odd	30		961.2.g.j.732.2		16
31.23	odd	10		961.2.d.n.374.3		16
31.24	odd	30		961.2.g.j.235.2		16
31.25	even	3		961.2.c.j.439.4		16
31.26	odd	6		961.2.c.i.521.4		16
31.27	odd	10		961.2.d.n.388.3		16
31.28	even	15		961.2.g.t.846.1		16
31.29	odd	10		961.2.d.q.531.2		16
31.30	odd	2		961.2.a.j.1.4		8
93.14	odd	30		279.2.y.c.10.1		16
93.20	odd	30		279.2.y.c.28.1		16
93.92	even	2		8649.2.a.be.1.5		8
124.51	odd	30		496.2.bg.c.369.1		16
124.107	odd	30		496.2.bg.c.289.1		16
155.14	even	30		775.2.bl.a.351.1		16
155.82	odd	60		775.2.ck.a.524.2		32
155.107	odd	60		775.2.ck.a.599.3		32
155.113	odd	60		775.2.ck.a.524.3		32
155.138	odd	60		775.2.ck.a.599.2		32
155.144	even	30		775.2.bl.a.276.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.14	even	15
31.2.g.a.28.2	yes	16	31.20	even	15
279.2.y.c.10.1		16	93.14	odd	30
279.2.y.c.28.1		16	93.20	odd	30
496.2.bg.c.289.1		16	124.107	odd	30
496.2.bg.c.369.1		16	124.51	odd	30
775.2.bl.a.276.1		16	155.144	even	30
775.2.bl.a.351.1		16	155.14	even	30
775.2.ck.a.524.2		32	155.82	odd	60
775.2.ck.a.524.3		32	155.113	odd	60
775.2.ck.a.599.2		32	155.138	odd	60
775.2.ck.a.599.3		32	155.107	odd	60
961.2.a.i.1.4		8	1.1	even	1	trivial
961.2.a.j.1.4		8	31.30	odd	2
961.2.c.i.439.4		16	31.6	odd	6
961.2.c.i.521.4		16	31.26	odd	6
961.2.c.j.439.4		16	31.25	even	3
961.2.c.j.521.4		16	31.5	even	3
961.2.d.n.374.3		16	31.23	odd	10
961.2.d.n.388.3		16	31.27	odd	10
961.2.d.o.374.3		16	31.8	even	5
961.2.d.o.388.3		16	31.4	even	5
961.2.d.p.531.2		16	31.2	even	5
961.2.d.p.628.2		16	31.16	even	5
961.2.d.q.531.2		16	31.29	odd	10
961.2.d.q.628.2		16	31.15	odd	10
961.2.g.j.235.2		16	31.24	odd	30
961.2.g.j.732.2		16	31.22	odd	30
961.2.g.k.235.2		16	31.7	even	15
961.2.g.k.732.2		16	31.9	even	15
961.2.g.l.338.2		16	31.11	odd	30
961.2.g.l.816.2		16	31.17	odd	30
961.2.g.m.448.1		16	31.13	odd	30
961.2.g.m.547.1		16	31.12	odd	30
961.2.g.n.844.1		16	31.21	odd	30
961.2.g.n.846.1		16	31.3	odd	30
961.2.g.s.448.1		16	31.18	even	15
961.2.g.s.547.1		16	31.19	even	15
961.2.g.t.844.1		16	31.10	even	15
961.2.g.t.846.1		16	31.28	even	15
8649.2.a.be.1.5		8	93.92	even	2
8649.2.a.bf.1.5		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)

\(f(q)\)	\(=\)	\(q+0.351432 q^{2} -2.89329 q^{3} -1.87650 q^{4} +2.97323 q^{5} -1.01680 q^{6} -1.08213 q^{7} -1.36233 q^{8} +5.37114 q^{9} +1.04489 q^{10} -2.43137 q^{11} +5.42925 q^{12} +2.87365 q^{13} -0.380294 q^{14} -8.60242 q^{15} +3.27422 q^{16} -1.82477 q^{17} +1.88759 q^{18} +2.11827 q^{19} -5.57925 q^{20} +3.13091 q^{21} -0.854462 q^{22} -0.442216 q^{23} +3.94161 q^{24} +3.84010 q^{25} +1.00989 q^{26} -6.86040 q^{27} +2.03060 q^{28} -3.15914 q^{29} -3.02317 q^{30} +3.87532 q^{32} +7.03466 q^{33} -0.641282 q^{34} -3.21741 q^{35} -10.0789 q^{36} +3.14675 q^{37} +0.744430 q^{38} -8.31432 q^{39} -4.05051 q^{40} -6.94624 q^{41} +1.10030 q^{42} -8.41238 q^{43} +4.56245 q^{44} +15.9696 q^{45} -0.155409 q^{46} -7.96205 q^{47} -9.47329 q^{48} -5.82900 q^{49} +1.34953 q^{50} +5.27958 q^{51} -5.39239 q^{52} -4.97700 q^{53} -2.41097 q^{54} -7.22902 q^{55} +1.47421 q^{56} -6.12878 q^{57} -1.11022 q^{58} -12.0139 q^{59} +16.1424 q^{60} -14.4351 q^{61} -5.81225 q^{63} -5.18654 q^{64} +8.54403 q^{65} +2.47221 q^{66} -6.43759 q^{67} +3.42416 q^{68} +1.27946 q^{69} -1.13070 q^{70} +1.67787 q^{71} -7.31724 q^{72} +14.3602 q^{73} +1.10587 q^{74} -11.1105 q^{75} -3.97493 q^{76} +2.63105 q^{77} -2.92192 q^{78} -3.44764 q^{79} +9.73502 q^{80} +3.73571 q^{81} -2.44113 q^{82} +12.8536 q^{83} -5.87513 q^{84} -5.42545 q^{85} -2.95638 q^{86} +9.14030 q^{87} +3.31232 q^{88} +2.25938 q^{89} +5.61225 q^{90} -3.10965 q^{91} +0.829816 q^{92} -2.79812 q^{94} +6.29811 q^{95} -11.2124 q^{96} +3.41286 q^{97} -2.04850 q^{98} -13.0592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{5} - 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} - 18 q^{11} - 8 q^{13} - 9 q^{14} - 18 q^{15} + 4 q^{16} - 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} + q^{21}+ \cdots - 6 q^{99}+O(q^{100}) \) 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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