LMFDB - Embedded newform 1386.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,4,Mod(1,1386)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1386.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1386.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$81.7766472680$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1386.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +2.00000 q^{10} +11.0000 q^{11} -43.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -100.000 q^{17} -87.0000 q^{19} -4.00000 q^{20} -22.0000 q^{22} +58.0000 q^{23} -124.000 q^{25} +86.0000 q^{26} -28.0000 q^{28} +223.000 q^{29} +88.0000 q^{31} -32.0000 q^{32} +200.000 q^{34} +7.00000 q^{35} +37.0000 q^{37} +174.000 q^{38} +8.00000 q^{40} -128.000 q^{41} -458.000 q^{43} +44.0000 q^{44} -116.000 q^{46} +341.000 q^{47} +49.0000 q^{49} +248.000 q^{50} -172.000 q^{52} +342.000 q^{53} -11.0000 q^{55} +56.0000 q^{56} -446.000 q^{58} +105.000 q^{59} +190.000 q^{61} -176.000 q^{62} +64.0000 q^{64} +43.0000 q^{65} -579.000 q^{67} -400.000 q^{68} -14.0000 q^{70} -128.000 q^{71} -161.000 q^{73} -74.0000 q^{74} -348.000 q^{76} -77.0000 q^{77} -396.000 q^{79} -16.0000 q^{80} +256.000 q^{82} +420.000 q^{83} +100.000 q^{85} +916.000 q^{86} -88.0000 q^{88} +798.000 q^{89} +301.000 q^{91} +232.000 q^{92} -682.000 q^{94} +87.0000 q^{95} +1414.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−1.00000	−0.0894427	−0.0447214	−	0.998999i	$-0.514240\pi$
$5$	−1.00000	−0.0894427	−0.0447214	+	0.998999i	$0.514240\pi$
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	2.00000	0.0632456
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	−43.0000	−0.917389	−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−43.0000	−0.917389	−0.458694	+	0.888594i	$0.651683\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−100.000	−1.42668	−0.713340	−	0.700818i	$-0.752818\pi$
$17$	−100.000	−1.42668	−0.713340	+	0.700818i	$0.752818\pi$
$18$	0	0
$19$	−87.0000	−1.05048	−0.525241	−	0.850953i	$-0.676025\pi$
$19$	−87.0000	−1.05048	−0.525241	+	0.850953i	$0.676025\pi$
$20$	−4.00000	−0.0447214
$21$	0	0
$22$	−22.0000	−0.213201
$23$	58.0000	0.525819	0.262909	−	0.964821i	$-0.415318\pi$
$23$	58.0000	0.525819	0.262909	+	0.964821i	$0.415318\pi$
$24$	0	0
$25$	−124.000	−0.992000
$26$	86.0000	0.648692
$27$	0	0
$28$	−28.0000	−0.188982
$29$	223.000	1.42793	0.713967	−	0.700180i	$-0.246897\pi$
$29$	223.000	1.42793	0.713967	+	0.700180i	$0.246897\pi$
$30$	0	0
$31$	88.0000	0.509847	0.254924	−	0.966961i	$-0.417950\pi$
$31$	88.0000	0.509847	0.254924	+	0.966961i	$0.417950\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	200.000	1.00882
$35$	7.00000	0.0338062
$36$	0	0
$37$	37.0000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	37.0000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	174.000	0.742803
$39$	0	0
$40$	8.00000	0.0316228
$41$	−128.000	−0.487567	−0.243783	−	0.969830i	$-0.578389\pi$
$41$	−128.000	−0.487567	−0.243783	+	0.969830i	$0.578389\pi$
$42$	0	0
$43$	−458.000	−1.62429	−0.812144	−	0.583458i	$-0.801699\pi$
$43$	−458.000	−1.62429	−0.812144	+	0.583458i	$0.801699\pi$
$44$	44.0000	0.150756
$45$	0	0
$46$	−116.000	−0.371810
$47$	341.000	1.05830	0.529149	−	0.848529i	$-0.322511\pi$
$47$	341.000	1.05830	0.529149	+	0.848529i	$0.322511\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	248.000	0.701450
$51$	0	0
$52$	−172.000	−0.458694
$53$	342.000	0.886364	0.443182	−	0.896432i	$-0.353849\pi$
$53$	342.000	0.886364	0.443182	+	0.896432i	$0.353849\pi$
$54$	0	0
$55$	−11.0000	−0.0269680
$56$	56.0000	0.133631
$57$	0	0
$58$	−446.000	−1.00970
$59$	105.000	0.231692	0.115846	−	0.993267i	$-0.463042\pi$
$59$	105.000	0.231692	0.115846	+	0.993267i	$0.463042\pi$
$60$	0	0
$61$	190.000	0.398803	0.199402	−	0.979918i	$-0.436100\pi$
$61$	190.000	0.398803	0.199402	+	0.979918i	$0.436100\pi$
$62$	−176.000	−0.360516
$63$	0	0
$64$	64.0000	0.125000
$65$	43.0000	0.0820537
$66$	0	0
$67$	−579.000	−1.05576	−0.527881	−	0.849318i	$-0.677013\pi$
$67$	−579.000	−1.05576	−0.527881	+	0.849318i	$0.677013\pi$
$68$	−400.000	−0.713340
$69$	0	0
$70$	−14.0000	−0.0239046
$71$	−128.000	−0.213955	−0.106978	−	0.994261i	$-0.534117\pi$
$71$	−128.000	−0.213955	−0.106978	+	0.994261i	$0.534117\pi$
$72$	0	0
$73$	−161.000	−0.258132	−0.129066	−	0.991636i	$-0.541198\pi$
$73$	−161.000	−0.258132	−0.129066	+	0.991636i	$0.541198\pi$
$74$	−74.0000	−0.116248
$75$	0	0
$76$	−348.000	−0.525241
$77$	−77.0000	−0.113961
$78$	0	0
$79$	−396.000	−0.563968	−0.281984	−	0.959419i	$-0.590993\pi$
$79$	−396.000	−0.563968	−0.281984	+	0.959419i	$0.590993\pi$
$80$	−16.0000	−0.0223607
$81$	0	0
$82$	256.000	0.344762
$83$	420.000	0.555434	0.277717	−	0.960663i	$-0.410422\pi$
$83$	420.000	0.555434	0.277717	+	0.960663i	$0.410422\pi$
$84$	0	0
$85$	100.000	0.127606
$86$	916.000	1.14854
$87$	0	0
$88$	−88.0000	−0.106600
$89$	798.000	0.950425	0.475213	−	0.879871i	$-0.342371\pi$
$89$	798.000	0.950425	0.475213	+	0.879871i	$0.342371\pi$
$90$	0	0
$91$	301.000	0.346740
$92$	232.000	0.262909
$93$	0	0
$94$	−682.000	−0.748329
$95$	87.0000	0.0939580
$96$	0	0
$97$	1414.00	1.48010	0.740051	−	0.672550i	$-0.234801\pi$
$97$	1414.00	1.48010	0.740051	+	0.672550i	$0.234801\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	−496.000	−0.496000
$101$	1764.00	1.73787	0.868933	−	0.494929i	$-0.164806\pi$
$101$	1764.00	1.73787	0.868933	+	0.494929i	$0.164806\pi$
$102$	0	0
$103$	978.000	0.935584	0.467792	−	0.883838i	$-0.345050\pi$
$103$	978.000	0.935584	0.467792	+	0.883838i	$0.345050\pi$
$104$	344.000	0.324346
$105$	0	0
$106$	−684.000	−0.626754
$107$	−481.000	−0.434580	−0.217290	−	0.976107i	$-0.569722\pi$
$107$	−481.000	−0.434580	−0.217290	+	0.976107i	$0.569722\pi$
$108$	0	0
$109$	−284.000	−0.249562	−0.124781	−	0.992184i	$-0.539823\pi$
$109$	−284.000	−0.249562	−0.124781	+	0.992184i	$0.539823\pi$
$110$	22.0000	0.0190693
$111$	0	0
$112$	−112.000	−0.0944911
$113$	−1498.00	−1.24708	−0.623540	−	0.781792i	$-0.714306\pi$
$113$	−1498.00	−1.24708	−0.623540	+	0.781792i	$0.714306\pi$
$114$	0	0
$115$	−58.0000	−0.0470307
$116$	892.000	0.713967
$117$	0	0
$118$	−210.000	−0.163831
$119$	700.000	0.539234
$120$	0	0
$121$	121.000	0.0909091
$122$	−380.000	−0.281997
$123$	0	0
$124$	352.000	0.254924
$125$	249.000	0.178170
$126$	0	0
$127$	−616.000	−0.430403	−0.215201	−	0.976570i	$-0.569041\pi$
$127$	−616.000	−0.430403	−0.215201	+	0.976570i	$0.569041\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−86.0000	−0.0580208
$131$	−2748.00	−1.83278	−0.916389	−	0.400289i	$-0.868910\pi$
$131$	−2748.00	−1.83278	−0.916389	+	0.400289i	$0.868910\pi$
$132$	0	0
$133$	609.000	0.397045
$134$	1158.00	0.746537
$135$	0	0
$136$	800.000	0.504408
$137$	−2184.00	−1.36198	−0.680992	−	0.732291i	$-0.738451\pi$
$137$	−2184.00	−1.36198	−0.680992	+	0.732291i	$0.738451\pi$
$138$	0	0
$139$	908.000	0.554069	0.277034	−	0.960860i	$-0.410648\pi$
$139$	908.000	0.554069	0.277034	+	0.960860i	$0.410648\pi$
$140$	28.0000	0.0169031
$141$	0	0
$142$	256.000	0.151289
$143$	−473.000	−0.276603
$144$	0	0
$145$	−223.000	−0.127718
$146$	322.000	0.182527
$147$	0	0
$148$	148.000	0.0821995
$149$	−421.000	−0.231474	−0.115737	−	0.993280i	$-0.536923\pi$
$149$	−421.000	−0.231474	−0.115737	+	0.993280i	$0.536923\pi$
$150$	0	0
$151$	948.000	0.510908	0.255454	−	0.966821i	$-0.417775\pi$
$151$	948.000	0.510908	0.255454	+	0.966821i	$0.417775\pi$
$152$	696.000	0.371402
$153$	0	0
$154$	154.000	0.0805823
$155$	−88.0000	−0.0456021
$156$	0	0
$157$	2368.00	1.20374	0.601869	−	0.798595i	$-0.294423\pi$
$157$	2368.00	1.20374	0.601869	+	0.798595i	$0.294423\pi$
$158$	792.000	0.398786
$159$	0	0
$160$	32.0000	0.0158114
$161$	−406.000	−0.198741
$162$	0	0
$163$	−2603.00	−1.25081	−0.625407	−	0.780299i	$-0.715067\pi$
$163$	−2603.00	−1.25081	−0.625407	+	0.780299i	$0.715067\pi$
$164$	−512.000	−0.243783
$165$	0	0
$166$	−840.000	−0.392751
$167$	1402.00	0.649641	0.324820	−	0.945776i	$-0.394696\pi$
$167$	1402.00	0.649641	0.324820	+	0.945776i	$0.394696\pi$
$168$	0	0
$169$	−348.000	−0.158398
$170$	−200.000	−0.0902312
$171$	0	0
$172$	−1832.00	−0.812144
$173$	−836.000	−0.367398	−0.183699	−	0.982983i	$-0.558807\pi$
$173$	−836.000	−0.367398	−0.183699	+	0.982983i	$0.558807\pi$
$174$	0	0
$175$	868.000	0.374941
$176$	176.000	0.0753778
$177$	0	0
$178$	−1596.00	−0.672052
$179$	3292.00	1.37461	0.687306	−	0.726368i	$-0.258793\pi$
$179$	3292.00	1.37461	0.687306	+	0.726368i	$0.258793\pi$
$180$	0	0
$181$	4838.00	1.98677	0.993386	−	0.114823i	$-0.0366302\pi$
$181$	4838.00	1.98677	0.993386	+	0.114823i	$0.0366302\pi$
$182$	−602.000	−0.245182
$183$	0	0
$184$	−464.000	−0.185905
$185$	−37.0000	−0.0147043
$186$	0	0
$187$	−1100.00	−0.430160
$188$	1364.00	0.529149
$189$	0	0
$190$	−174.000	−0.0664384
$191$	1232.00	0.466725	0.233362	−	0.972390i	$-0.425027\pi$
$191$	1232.00	0.466725	0.233362	+	0.972390i	$0.425027\pi$
$192$	0	0
$193$	2366.00	0.882427	0.441213	−	0.897402i	$-0.354548\pi$
$193$	2366.00	0.882427	0.441213	+	0.897402i	$0.354548\pi$
$194$	−2828.00	−1.04659
$195$	0	0
$196$	196.000	0.0714286
$197$	−318.000	−0.115008	−0.0575040	−	0.998345i	$-0.518314\pi$
$197$	−318.000	−0.115008	−0.0575040	+	0.998345i	$0.518314\pi$
$198$	0	0
$199$	−806.000	−0.287115	−0.143557	−	0.989642i	$-0.545854\pi$
$199$	−806.000	−0.287115	−0.143557	+	0.989642i	$0.545854\pi$
$200$	992.000	0.350725
$201$	0	0
$202$	−3528.00	−1.22886
$203$	−1561.00	−0.539708
$204$	0	0
$205$	128.000	0.0436093
$206$	−1956.00	−0.661558
$207$	0	0
$208$	−688.000	−0.229347
$209$	−957.000	−0.316732
$210$	0	0
$211$	4462.00	1.45581	0.727907	−	0.685676i	$-0.240493\pi$
$211$	4462.00	1.45581	0.727907	+	0.685676i	$0.240493\pi$
$212$	1368.00	0.443182
$213$	0	0
$214$	962.000	0.307294
$215$	458.000	0.145281
$216$	0	0
$217$	−616.000	−0.192704
$218$	568.000	0.176467
$219$	0	0
$220$	−44.0000	−0.0134840
$221$	4300.00	1.30882
$222$	0	0
$223$	3802.00	1.14171	0.570854	−	0.821052i	$-0.306612\pi$
$223$	3802.00	1.14171	0.570854	+	0.821052i	$0.306612\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	2996.00	0.881818
$227$	3370.00	0.985351	0.492676	−	0.870213i	$-0.336019\pi$
$227$	3370.00	0.985351	0.492676	+	0.870213i	$0.336019\pi$
$228$	0	0
$229$	−898.000	−0.259133	−0.129567	−	0.991571i	$-0.541359\pi$
$229$	−898.000	−0.259133	−0.129567	+	0.991571i	$0.541359\pi$
$230$	116.000	0.0332557
$231$	0	0
$232$	−1784.00	−0.504851
$233$	462.000	0.129900	0.0649498	−	0.997889i	$-0.479311\pi$
$233$	462.000	0.129900	0.0649498	+	0.997889i	$0.479311\pi$
$234$	0	0
$235$	−341.000	−0.0946570
$236$	420.000	0.115846
$237$	0	0
$238$	−1400.00	−0.381296
$239$	5665.00	1.53322	0.766608	−	0.642116i	$-0.221943\pi$
$239$	5665.00	1.53322	0.766608	+	0.642116i	$0.221943\pi$
$240$	0	0
$241$	1593.00	0.425785	0.212892	−	0.977076i	$-0.431712\pi$
$241$	1593.00	0.425785	0.212892	+	0.977076i	$0.431712\pi$
$242$	−242.000	−0.0642824
$243$	0	0
$244$	760.000	0.199402
$245$	−49.0000	−0.0127775
$246$	0	0
$247$	3741.00	0.963701
$248$	−704.000	−0.180258
$249$	0	0
$250$	−498.000	−0.125985
$251$	−4545.00	−1.14294	−0.571470	−	0.820623i	$-0.693627\pi$
$251$	−4545.00	−1.14294	−0.571470	+	0.820623i	$0.693627\pi$
$252$	0	0
$253$	638.000	0.158540
$254$	1232.00	0.304341
$255$	0	0
$256$	256.000	0.0625000
$257$	2859.00	0.693928	0.346964	−	0.937878i	$-0.387213\pi$
$257$	2859.00	0.693928	0.346964	+	0.937878i	$0.387213\pi$
$258$	0	0
$259$	−259.000	−0.0621370
$260$	172.000	0.0410269
$261$	0	0
$262$	5496.00	1.29597
$263$	6279.00	1.47217	0.736083	−	0.676891i	$-0.236673\pi$
$263$	6279.00	1.47217	0.736083	+	0.676891i	$0.236673\pi$
$264$	0	0
$265$	−342.000	−0.0792788
$266$	−1218.00	−0.280753
$267$	0	0
$268$	−2316.00	−0.527881
$269$	6270.00	1.42115	0.710574	−	0.703623i	$-0.248435\pi$
$269$	6270.00	1.42115	0.710574	+	0.703623i	$0.248435\pi$
$270$	0	0
$271$	6721.00	1.50654	0.753269	−	0.657713i	$-0.228476\pi$
$271$	6721.00	1.50654	0.753269	+	0.657713i	$0.228476\pi$
$272$	−1600.00	−0.356670
$273$	0	0
$274$	4368.00	0.963068
$275$	−1364.00	−0.299099
$276$	0	0
$277$	−5388.00	−1.16871	−0.584357	−	0.811497i	$-0.698653\pi$
$277$	−5388.00	−1.16871	−0.584357	+	0.811497i	$0.698653\pi$
$278$	−1816.00	−0.391786
$279$	0	0
$280$	−56.0000	−0.0119523
$281$	−4765.00	−1.01159	−0.505794	−	0.862654i	$-0.668800\pi$
$281$	−4765.00	−1.01159	−0.505794	+	0.862654i	$0.668800\pi$
$282$	0	0
$283$	−903.000	−0.189674	−0.0948371	−	0.995493i	$-0.530233\pi$
$283$	−903.000	−0.189674	−0.0948371	+	0.995493i	$0.530233\pi$
$284$	−512.000	−0.106978
$285$	0	0
$286$	946.000	0.195588
$287$	896.000	0.184283
$288$	0	0
$289$	5087.00	1.03542
$290$	446.000	0.0903104
$291$	0	0
$292$	−644.000	−0.129066
$293$	−672.000	−0.133989	−0.0669943	−	0.997753i	$-0.521341\pi$
$293$	−672.000	−0.133989	−0.0669943	+	0.997753i	$0.521341\pi$
$294$	0	0
$295$	−105.000	−0.0207232
$296$	−296.000	−0.0581238
$297$	0	0
$298$	842.000	0.163677
$299$	−2494.00	−0.482380
$300$	0	0
$301$	3206.00	0.613923
$302$	−1896.00	−0.361267
$303$	0	0
$304$	−1392.00	−0.262621
$305$	−190.000	−0.0356701
$306$	0	0
$307$	−1876.00	−0.348759	−0.174379	−	0.984679i	$-0.555792\pi$
$307$	−1876.00	−0.348759	−0.174379	+	0.984679i	$0.555792\pi$
$308$	−308.000	−0.0569803
$309$	0	0
$310$	176.000	0.0322456
$311$	4688.00	0.854766	0.427383	−	0.904071i	$-0.359436\pi$
$311$	4688.00	0.854766	0.427383	+	0.904071i	$0.359436\pi$
$312$	0	0
$313$	4912.00	0.887037	0.443519	−	0.896265i	$-0.353730\pi$
$313$	4912.00	0.887037	0.443519	+	0.896265i	$0.353730\pi$
$314$	−4736.00	−0.851172
$315$	0	0
$316$	−1584.00	−0.281984
$317$	558.000	0.0988656	0.0494328	−	0.998777i	$-0.484259\pi$
$317$	558.000	0.0988656	0.0494328	+	0.998777i	$0.484259\pi$
$318$	0	0
$319$	2453.00	0.430538
$320$	−64.0000	−0.0111803
$321$	0	0
$322$	812.000	0.140531
$323$	8700.00	1.49870
$324$	0	0
$325$	5332.00	0.910050
$326$	5206.00	0.884459
$327$	0	0
$328$	1024.00	0.172381
$329$	−2387.00	−0.399999
$330$	0	0
$331$	4660.00	0.773827	0.386914	−	0.922116i	$-0.373541\pi$
$331$	4660.00	0.773827	0.386914	+	0.922116i	$0.373541\pi$
$332$	1680.00	0.277717
$333$	0	0
$334$	−2804.00	−0.459365
$335$	579.000	0.0944303
$336$	0	0
$337$	−9906.00	−1.60123	−0.800615	−	0.599180i	$-0.795493\pi$
$337$	−9906.00	−1.60123	−0.800615	+	0.599180i	$0.795493\pi$
$338$	696.000	0.112004
$339$	0	0
$340$	400.000	0.0638031
$341$	968.000	0.153725
$342$	0	0
$343$	−343.000	−0.0539949
$344$	3664.00	0.574272
$345$	0	0
$346$	1672.00	0.259790
$347$	10664.0	1.64978	0.824890	−	0.565294i	$-0.191237\pi$
$347$	10664.0	1.64978	0.824890	+	0.565294i	$0.191237\pi$
$348$	0	0
$349$	5489.00	0.841889	0.420945	−	0.907086i	$-0.361699\pi$
$349$	5489.00	0.841889	0.420945	+	0.907086i	$0.361699\pi$
$350$	−1736.00	−0.265123
$351$	0	0
$352$	−352.000	−0.0533002
$353$	1845.00	0.278185	0.139093	−	0.990279i	$-0.455581\pi$
$353$	1845.00	0.278185	0.139093	+	0.990279i	$0.455581\pi$
$354$	0	0
$355$	128.000	0.0191367
$356$	3192.00	0.475213
$357$	0	0
$358$	−6584.00	−0.971998
$359$	848.000	0.124668	0.0623339	−	0.998055i	$-0.480146\pi$
$359$	848.000	0.124668	0.0623339	+	0.998055i	$0.480146\pi$
$360$	0	0
$361$	710.000	0.103514
$362$	−9676.00	−1.40486
$363$	0	0
$364$	1204.00	0.173370
$365$	161.000	0.0230880
$366$	0	0
$367$	−8474.00	−1.20528	−0.602642	−	0.798012i	$-0.705885\pi$
$367$	−8474.00	−1.20528	−0.602642	+	0.798012i	$0.705885\pi$
$368$	928.000	0.131455
$369$	0	0
$370$	74.0000	0.0103975
$371$	−2394.00	−0.335014
$372$	0	0
$373$	11396.0	1.58194	0.790969	−	0.611857i	$-0.209577\pi$
$373$	11396.0	1.58194	0.790969	+	0.611857i	$0.209577\pi$
$374$	2200.00	0.304169
$375$	0	0
$376$	−2728.00	−0.374165
$377$	−9589.00	−1.30997
$378$	0	0
$379$	2155.00	0.292071	0.146036	−	0.989279i	$-0.453349\pi$
$379$	2155.00	0.292071	0.146036	+	0.989279i	$0.453349\pi$
$380$	348.000	0.0469790
$381$	0	0
$382$	−2464.00	−0.330024
$383$	5864.00	0.782340	0.391170	−	0.920318i	$-0.372070\pi$
$383$	5864.00	0.782340	0.391170	+	0.920318i	$0.372070\pi$
$384$	0	0
$385$	77.0000	0.0101929
$386$	−4732.00	−0.623970
$387$	0	0
$388$	5656.00	0.740051
$389$	−10104.0	−1.31695	−0.658474	−	0.752603i	$-0.728798\pi$
$389$	−10104.0	−1.31695	−0.658474	+	0.752603i	$0.728798\pi$
$390$	0	0
$391$	−5800.00	−0.750175
$392$	−392.000	−0.0505076
$393$	0	0
$394$	636.000	0.0813229
$395$	396.000	0.0504428
$396$	0	0
$397$	−5868.00	−0.741830	−0.370915	−	0.928667i	$-0.620956\pi$
$397$	−5868.00	−0.741830	−0.370915	+	0.928667i	$0.620956\pi$
$398$	1612.00	0.203021
$399$	0	0
$400$	−1984.00	−0.248000
$401$	2418.00	0.301120	0.150560	−	0.988601i	$-0.451892\pi$
$401$	2418.00	0.301120	0.150560	+	0.988601i	$0.451892\pi$
$402$	0	0
$403$	−3784.00	−0.467728
$404$	7056.00	0.868933
$405$	0	0
$406$	3122.00	0.381631
$407$	407.000	0.0495682
$408$	0	0
$409$	−2354.00	−0.284591	−0.142296	−	0.989824i	$-0.545448\pi$
$409$	−2354.00	−0.284591	−0.142296	+	0.989824i	$0.545448\pi$
$410$	−256.000	−0.0308364
$411$	0	0
$412$	3912.00	0.467792
$413$	−735.000	−0.0875714
$414$	0	0
$415$	−420.000	−0.0496795
$416$	1376.00	0.162173
$417$	0	0
$418$	1914.00	0.223964
$419$	11443.0	1.33419	0.667097	−	0.744971i	$-0.267537\pi$
$419$	11443.0	1.33419	0.667097	+	0.744971i	$0.267537\pi$
$420$	0	0
$421$	−13325.0	−1.54257	−0.771284	−	0.636492i	$-0.780385\pi$
$421$	−13325.0	−1.54257	−0.771284	+	0.636492i	$0.780385\pi$
$422$	−8924.00	−1.02942
$423$	0	0
$424$	−2736.00	−0.313377
$425$	12400.0	1.41527
$426$	0	0
$427$	−1330.00	−0.150734
$428$	−1924.00	−0.217290
$429$	0	0
$430$	−916.000	−0.102729
$431$	8503.00	0.950290	0.475145	−	0.879907i	$-0.342396\pi$
$431$	8503.00	0.950290	0.475145	+	0.879907i	$0.342396\pi$
$432$	0	0
$433$	4496.00	0.498993	0.249497	−	0.968376i	$-0.419735\pi$
$433$	4496.00	0.498993	0.249497	+	0.968376i	$0.419735\pi$
$434$	1232.00	0.136262
$435$	0	0
$436$	−1136.00	−0.124781
$437$	−5046.00	−0.552364
$438$	0	0
$439$	−7247.00	−0.787883	−0.393941	−	0.919136i	$-0.628889\pi$
$439$	−7247.00	−0.787883	−0.393941	+	0.919136i	$0.628889\pi$
$440$	88.0000	0.00953463
$441$	0	0
$442$	−8600.00	−0.925476
$443$	−8568.00	−0.918912	−0.459456	−	0.888201i	$-0.651956\pi$
$443$	−8568.00	−0.918912	−0.459456	+	0.888201i	$0.651956\pi$
$444$	0	0
$445$	−798.000	−0.0850086
$446$	−7604.00	−0.807309
$447$	0	0
$448$	−448.000	−0.0472456
$449$	7812.00	0.821094	0.410547	−	0.911840i	$-0.365338\pi$
$449$	7812.00	0.821094	0.410547	+	0.911840i	$0.365338\pi$
$450$	0	0
$451$	−1408.00	−0.147007
$452$	−5992.00	−0.623540
$453$	0	0
$454$	−6740.00	−0.696749
$455$	−301.000	−0.0310134
$456$	0	0
$457$	4262.00	0.436254	0.218127	−	0.975920i	$-0.430005\pi$
$457$	4262.00	0.436254	0.218127	+	0.975920i	$0.430005\pi$
$458$	1796.00	0.183235
$459$	0	0
$460$	−232.000	−0.0235153
$461$	−8316.00	−0.840162	−0.420081	−	0.907487i	$-0.637998\pi$
$461$	−8316.00	−0.840162	−0.420081	+	0.907487i	$0.637998\pi$
$462$	0	0
$463$	−16103.0	−1.61635	−0.808175	−	0.588943i	$-0.799544\pi$
$463$	−16103.0	−1.61635	−0.808175	+	0.588943i	$0.799544\pi$
$464$	3568.00	0.356983
$465$	0	0
$466$	−924.000	−0.0918529
$467$	8913.00	0.883179	0.441589	−	0.897217i	$-0.354415\pi$
$467$	8913.00	0.883179	0.441589	+	0.897217i	$0.354415\pi$
$468$	0	0
$469$	4053.00	0.399041
$470$	682.000	0.0669326
$471$	0	0
$472$	−840.000	−0.0819155
$473$	−5038.00	−0.489741
$474$	0	0
$475$	10788.0	1.04208
$476$	2800.00	0.269617
$477$	0	0
$478$	−11330.0	−1.08415
$479$	4100.00	0.391093	0.195547	−	0.980694i	$-0.437352\pi$
$479$	4100.00	0.391093	0.195547	+	0.980694i	$0.437352\pi$
$480$	0	0
$481$	−1591.00	−0.150818
$482$	−3186.00	−0.301075
$483$	0	0
$484$	484.000	0.0454545
$485$	−1414.00	−0.132384
$486$	0	0
$487$	10496.0	0.976631	0.488315	−	0.872667i	$-0.337612\pi$
$487$	10496.0	0.976631	0.488315	+	0.872667i	$0.337612\pi$
$488$	−1520.00	−0.140998
$489$	0	0
$490$	98.0000	0.00903508
$491$	−2625.00	−0.241272	−0.120636	−	0.992697i	$-0.538493\pi$
$491$	−2625.00	−0.241272	−0.120636	+	0.992697i	$0.538493\pi$
$492$	0	0
$493$	−22300.0	−2.03720
$494$	−7482.00	−0.681439
$495$	0	0
$496$	1408.00	0.127462
$497$	896.000	0.0808674
$498$	0	0
$499$	−12397.0	−1.11216	−0.556078	−	0.831130i	$-0.687694\pi$
$499$	−12397.0	−1.11216	−0.556078	+	0.831130i	$0.687694\pi$
$500$	996.000	0.0890849
$501$	0	0
$502$	9090.00	0.808180
$503$	1854.00	0.164345	0.0821727	−	0.996618i	$-0.473814\pi$
$503$	1854.00	0.164345	0.0821727	+	0.996618i	$0.473814\pi$
$504$	0	0
$505$	−1764.00	−0.155440
$506$	−1276.00	−0.112105
$507$	0	0
$508$	−2464.00	−0.215201
$509$	−17530.0	−1.52653	−0.763265	−	0.646086i	$-0.776405\pi$
$509$	−17530.0	−1.52653	−0.763265	+	0.646086i	$0.776405\pi$
$510$	0	0
$511$	1127.00	0.0975647
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−5718.00	−0.490681
$515$	−978.000	−0.0836812
$516$	0	0
$517$	3751.00	0.319089
$518$	518.000	0.0439375
$519$	0	0
$520$	−344.000	−0.0290104
$521$	22255.0	1.87142	0.935709	−	0.352772i	$-0.114761\pi$
$521$	22255.0	1.87142	0.935709	+	0.352772i	$0.114761\pi$
$522$	0	0
$523$	−7789.00	−0.651222	−0.325611	−	0.945504i	$-0.605570\pi$
$523$	−7789.00	−0.651222	−0.325611	+	0.945504i	$0.605570\pi$
$524$	−10992.0	−0.916389
$525$	0	0
$526$	−12558.0	−1.04098
$527$	−8800.00	−0.727389
$528$	0	0
$529$	−8803.00	−0.723514
$530$	684.000	0.0560586
$531$	0	0
$532$	2436.00	0.198523
$533$	5504.00	0.447288
$534$	0	0
$535$	481.000	0.0388700
$536$	4632.00	0.373269
$537$	0	0
$538$	−12540.0	−1.00490
$539$	539.000	0.0430730
$540$	0	0
$541$	8288.00	0.658649	0.329324	−	0.944217i	$-0.393179\pi$
$541$	8288.00	0.658649	0.329324	+	0.944217i	$0.393179\pi$
$542$	−13442.0	−1.06528
$543$	0	0
$544$	3200.00	0.252204
$545$	284.000	0.0223215
$546$	0	0
$547$	−6432.00	−0.502765	−0.251383	−	0.967888i	$-0.580885\pi$
$547$	−6432.00	−0.502765	−0.251383	+	0.967888i	$0.580885\pi$
$548$	−8736.00	−0.680992
$549$	0	0
$550$	2728.00	0.211495
$551$	−19401.0	−1.50002
$552$	0	0
$553$	2772.00	0.213160
$554$	10776.0	0.826405
$555$	0	0
$556$	3632.00	0.277034
$557$	9815.00	0.746634	0.373317	−	0.927704i	$-0.378220\pi$
$557$	9815.00	0.746634	0.373317	+	0.927704i	$0.378220\pi$
$558$	0	0
$559$	19694.0	1.49010
$560$	112.000	0.00845154
$561$	0	0
$562$	9530.00	0.715300
$563$	20042.0	1.50030	0.750151	−	0.661267i	$-0.229981\pi$
$563$	20042.0	1.50030	0.750151	+	0.661267i	$0.229981\pi$
$564$	0	0
$565$	1498.00	0.111542
$566$	1806.00	0.134120
$567$	0	0
$568$	1024.00	0.0756445
$569$	8562.00	0.630822	0.315411	−	0.948955i	$-0.397858\pi$
$569$	8562.00	0.630822	0.315411	+	0.948955i	$0.397858\pi$
$570$	0	0
$571$	27004.0	1.97913	0.989564	−	0.144093i	$-0.0460265\pi$
$571$	27004.0	1.97913	0.989564	+	0.144093i	$0.0460265\pi$
$572$	−1892.00	−0.138302
$573$	0	0
$574$	−1792.00	−0.130308
$575$	−7192.00	−0.521612
$576$	0	0
$577$	14360.0	1.03607	0.518037	−	0.855358i	$-0.326663\pi$
$577$	14360.0	1.03607	0.518037	+	0.855358i	$0.326663\pi$
$578$	−10174.0	−0.732150
$579$	0	0
$580$	−892.000	−0.0638591
$581$	−2940.00	−0.209934
$582$	0	0
$583$	3762.00	0.267249
$584$	1288.00	0.0912634
$585$	0	0
$586$	1344.00	0.0947442
$587$	−15453.0	−1.08656	−0.543282	−	0.839550i	$-0.682819\pi$
$587$	−15453.0	−1.08656	−0.543282	+	0.839550i	$0.682819\pi$
$588$	0	0
$589$	−7656.00	−0.535586
$590$	210.000	0.0146535
$591$	0	0
$592$	592.000	0.0410997
$593$	−18000.0	−1.24649	−0.623247	−	0.782025i	$-0.714187\pi$
$593$	−18000.0	−1.24649	−0.623247	+	0.782025i	$0.714187\pi$
$594$	0	0
$595$	−700.000	−0.0482306
$596$	−1684.00	−0.115737
$597$	0	0
$598$	4988.00	0.341094
$599$	−27180.0	−1.85400	−0.926999	−	0.375064i	$-0.877621\pi$
$599$	−27180.0	−1.85400	−0.926999	+	0.375064i	$0.877621\pi$
$600$	0	0
$601$	−16153.0	−1.09633	−0.548165	−	0.836370i	$-0.684674\pi$
$601$	−16153.0	−1.09633	−0.548165	+	0.836370i	$0.684674\pi$
$602$	−6412.00	−0.434109
$603$	0	0
$604$	3792.00	0.255454
$605$	−121.000	−0.00813116
$606$	0	0
$607$	−11443.0	−0.765168	−0.382584	−	0.923921i	$-0.624966\pi$
$607$	−11443.0	−0.765168	−0.382584	+	0.923921i	$0.624966\pi$
$608$	2784.00	0.185701
$609$	0	0
$610$	380.000	0.0252225
$611$	−14663.0	−0.970870
$612$	0	0
$613$	−9488.00	−0.625150	−0.312575	−	0.949893i	$-0.601191\pi$
$613$	−9488.00	−0.625150	−0.312575	+	0.949893i	$0.601191\pi$
$614$	3752.00	0.246610
$615$	0	0
$616$	616.000	0.0402911
$617$	−22902.0	−1.49433	−0.747164	−	0.664640i	$-0.768585\pi$
$617$	−22902.0	−1.49433	−0.747164	+	0.664640i	$0.768585\pi$
$618$	0	0
$619$	19448.0	1.26281	0.631406	−	0.775452i	$-0.282478\pi$
$619$	19448.0	1.26281	0.631406	+	0.775452i	$0.282478\pi$
$620$	−352.000	−0.0228011
$621$	0	0
$622$	−9376.00	−0.604411
$623$	−5586.00	−0.359227
$624$	0	0
$625$	15251.0	0.976064
$626$	−9824.00	−0.627230
$627$	0	0
$628$	9472.00	0.601869
$629$	−3700.00	−0.234545
$630$	0	0
$631$	−13608.0	−0.858520	−0.429260	−	0.903181i	$-0.641226\pi$
$631$	−13608.0	−0.858520	−0.429260	+	0.903181i	$0.641226\pi$
$632$	3168.00	0.199393
$633$	0	0
$634$	−1116.00	−0.0699086
$635$	616.000	0.0384964
$636$	0	0
$637$	−2107.00	−0.131056
$638$	−4906.00	−0.304436
$639$	0	0
$640$	128.000	0.00790569
$641$	−17628.0	−1.08622	−0.543108	−	0.839663i	$-0.682752\pi$
$641$	−17628.0	−1.08622	−0.543108	+	0.839663i	$0.682752\pi$
$642$	0	0
$643$	−21074.0	−1.29250	−0.646250	−	0.763126i	$-0.723664\pi$
$643$	−21074.0	−1.29250	−0.646250	+	0.763126i	$0.723664\pi$
$644$	−1624.00	−0.0993704
$645$	0	0
$646$	−17400.0	−1.05974
$647$	4899.00	0.297681	0.148840	−	0.988861i	$-0.452446\pi$
$647$	4899.00	0.297681	0.148840	+	0.988861i	$0.452446\pi$
$648$	0	0
$649$	1155.00	0.0698578
$650$	−10664.0	−0.643502
$651$	0	0
$652$	−10412.0	−0.625407
$653$	−7760.00	−0.465042	−0.232521	−	0.972591i	$-0.574697\pi$
$653$	−7760.00	−0.465042	−0.232521	+	0.972591i	$0.574697\pi$
$654$	0	0
$655$	2748.00	0.163929
$656$	−2048.00	−0.121892
$657$	0	0
$658$	4774.00	0.282842
$659$	−18365.0	−1.08558	−0.542791	−	0.839868i	$-0.682633\pi$
$659$	−18365.0	−1.08558	−0.542791	+	0.839868i	$0.682633\pi$
$660$	0	0
$661$	13286.0	0.781794	0.390897	−	0.920435i	$-0.372165\pi$
$661$	13286.0	0.781794	0.390897	+	0.920435i	$0.372165\pi$
$662$	−9320.00	−0.547178
$663$	0	0
$664$	−3360.00	−0.196375
$665$	−609.000	−0.0355128
$666$	0	0
$667$	12934.0	0.750834
$668$	5608.00	0.324820
$669$	0	0
$670$	−1158.00	−0.0667723
$671$	2090.00	0.120244
$672$	0	0
$673$	−15242.0	−0.873010	−0.436505	−	0.899702i	$-0.643784\pi$
$673$	−15242.0	−0.873010	−0.436505	+	0.899702i	$0.643784\pi$
$674$	19812.0	1.13224
$675$	0	0
$676$	−1392.00	−0.0791989
$677$	−14170.0	−0.804427	−0.402214	−	0.915546i	$-0.631759\pi$
$677$	−14170.0	−0.804427	−0.402214	+	0.915546i	$0.631759\pi$
$678$	0	0
$679$	−9898.00	−0.559426
$680$	−800.000	−0.0451156
$681$	0	0
$682$	−1936.00	−0.108700
$683$	7116.00	0.398662	0.199331	−	0.979932i	$-0.436123\pi$
$683$	7116.00	0.398662	0.199331	+	0.979932i	$0.436123\pi$
$684$	0	0
$685$	2184.00	0.121819
$686$	686.000	0.0381802
$687$	0	0
$688$	−7328.00	−0.406072
$689$	−14706.0	−0.813141
$690$	0	0
$691$	2010.00	0.110657	0.0553285	−	0.998468i	$-0.482379\pi$
$691$	2010.00	0.110657	0.0553285	+	0.998468i	$0.482379\pi$
$692$	−3344.00	−0.183699
$693$	0	0
$694$	−21328.0	−1.16657
$695$	−908.000	−0.0495574
$696$	0	0
$697$	12800.0	0.695602
$698$	−10978.0	−0.595306
$699$	0	0
$700$	3472.00	0.187470
$701$	−7794.00	−0.419936	−0.209968	−	0.977708i	$-0.567336\pi$
$701$	−7794.00	−0.419936	−0.209968	+	0.977708i	$0.567336\pi$
$702$	0	0
$703$	−3219.00	−0.172698
$704$	704.000	0.0376889
$705$	0	0
$706$	−3690.00	−0.196707
$707$	−12348.0	−0.656852
$708$	0	0
$709$	29991.0	1.58863	0.794313	−	0.607509i	$-0.207831\pi$
$709$	29991.0	1.58863	0.794313	+	0.607509i	$0.207831\pi$
$710$	−256.000	−0.0135317
$711$	0	0
$712$	−6384.00	−0.336026
$713$	5104.00	0.268087
$714$	0	0
$715$	473.000	0.0247401
$716$	13168.0	0.687306
$717$	0	0
$718$	−1696.00	−0.0881534
$719$	−19613.0	−1.01730	−0.508652	−	0.860972i	$-0.669856\pi$
$719$	−19613.0	−1.01730	−0.508652	+	0.860972i	$0.669856\pi$
$720$	0	0
$721$	−6846.00	−0.353618
$722$	−1420.00	−0.0731952
$723$	0	0
$724$	19352.0	0.993386
$725$	−27652.0	−1.41651
$726$	0	0
$727$	16646.0	0.849197	0.424598	−	0.905382i	$-0.360415\pi$
$727$	16646.0	0.849197	0.424598	+	0.905382i	$0.360415\pi$
$728$	−2408.00	−0.122591
$729$	0	0
$730$	−322.000	−0.0163257
$731$	45800.0	2.31734
$732$	0	0
$733$	−36346.0	−1.83147	−0.915737	−	0.401779i	$-0.868392\pi$
$733$	−36346.0	−1.83147	−0.915737	+	0.401779i	$0.868392\pi$
$734$	16948.0	0.852264
$735$	0	0
$736$	−1856.00	−0.0929525
$737$	−6369.00	−0.318324
$738$	0	0
$739$	−25698.0	−1.27918	−0.639591	−	0.768715i	$-0.720896\pi$
$739$	−25698.0	−1.27918	−0.639591	+	0.768715i	$0.720896\pi$
$740$	−148.000	−0.00735215
$741$	0	0
$742$	4788.00	0.236891
$743$	27543.0	1.35997	0.679983	−	0.733228i	$-0.261987\pi$
$743$	27543.0	1.35997	0.679983	+	0.733228i	$0.261987\pi$
$744$	0	0
$745$	421.000	0.0207037
$746$	−22792.0	−1.11860
$747$	0	0
$748$	−4400.00	−0.215080
$749$	3367.00	0.164256
$750$	0	0
$751$	26005.0	1.26356	0.631782	−	0.775146i	$-0.282324\pi$
$751$	26005.0	1.26356	0.631782	+	0.775146i	$0.282324\pi$
$752$	5456.00	0.264574
$753$	0	0
$754$	19178.0	0.926289
$755$	−948.000	−0.0456970
$756$	0	0
$757$	17621.0	0.846032	0.423016	−	0.906122i	$-0.360971\pi$
$757$	17621.0	0.846032	0.423016	+	0.906122i	$0.360971\pi$
$758$	−4310.00	−0.206525
$759$	0	0
$760$	−696.000	−0.0332192
$761$	−22968.0	−1.09407	−0.547036	−	0.837109i	$-0.684244\pi$
$761$	−22968.0	−1.09407	−0.547036	+	0.837109i	$0.684244\pi$
$762$	0	0
$763$	1988.00	0.0943256
$764$	4928.00	0.233362
$765$	0	0
$766$	−11728.0	−0.553198
$767$	−4515.00	−0.212552
$768$	0	0
$769$	28273.0	1.32581	0.662907	−	0.748702i	$-0.269323\pi$
$769$	28273.0	1.32581	0.662907	+	0.748702i	$0.269323\pi$
$770$	−154.000	−0.00720750
$771$	0	0
$772$	9464.00	0.441213
$773$	13239.0	0.616007	0.308004	−	0.951385i	$-0.400339\pi$
$773$	13239.0	0.616007	0.308004	+	0.951385i	$0.400339\pi$
$774$	0	0
$775$	−10912.0	−0.505769
$776$	−11312.0	−0.523295
$777$	0	0
$778$	20208.0	0.931224
$779$	11136.0	0.512180
$780$	0	0
$781$	−1408.00	−0.0645099
$782$	11600.0	0.530454
$783$	0	0
$784$	784.000	0.0357143
$785$	−2368.00	−0.107666
$786$	0	0
$787$	1775.00	0.0803963	0.0401982	−	0.999192i	$-0.487201\pi$
$787$	1775.00	0.0803963	0.0401982	+	0.999192i	$0.487201\pi$
$788$	−1272.00	−0.0575040
$789$	0	0
$790$	−792.000	−0.0356685
$791$	10486.0	0.471352
$792$	0	0
$793$	−8170.00	−0.365858
$794$	11736.0	0.524553
$795$	0	0
$796$	−3224.00	−0.143557
$797$	16481.0	0.732481	0.366240	−	0.930520i	$-0.380645\pi$
$797$	16481.0	0.732481	0.366240	+	0.930520i	$0.380645\pi$
$798$	0	0
$799$	−34100.0	−1.50985
$800$	3968.00	0.175362
$801$	0	0
$802$	−4836.00	−0.212924
$803$	−1771.00	−0.0778297
$804$	0	0
$805$	406.000	0.0177759
$806$	7568.00	0.330734
$807$	0	0
$808$	−14112.0	−0.614429
$809$	29079.0	1.26374	0.631868	−	0.775076i	$-0.282288\pi$
$809$	29079.0	1.26374	0.631868	+	0.775076i	$0.282288\pi$
$810$	0	0
$811$	−40381.0	−1.74842	−0.874210	−	0.485548i	$-0.838620\pi$
$811$	−40381.0	−1.74842	−0.874210	+	0.485548i	$0.838620\pi$
$812$	−6244.00	−0.269854
$813$	0	0
$814$	−814.000	−0.0350500
$815$	2603.00	0.111876
$816$	0	0
$817$	39846.0	1.70629
$818$	4708.00	0.201236
$819$	0	0
$820$	512.000	0.0218047
$821$	6345.00	0.269722	0.134861	−	0.990865i	$-0.456941\pi$
$821$	6345.00	0.269722	0.134861	+	0.990865i	$0.456941\pi$
$822$	0	0
$823$	7757.00	0.328544	0.164272	−	0.986415i	$-0.447472\pi$
$823$	7757.00	0.328544	0.164272	+	0.986415i	$0.447472\pi$
$824$	−7824.00	−0.330779
$825$	0	0
$826$	1470.00	0.0619223
$827$	15659.0	0.658424	0.329212	−	0.944256i	$-0.393217\pi$
$827$	15659.0	0.658424	0.329212	+	0.944256i	$0.393217\pi$
$828$	0	0
$829$	−5384.00	−0.225566	−0.112783	−	0.993620i	$-0.535976\pi$
$829$	−5384.00	−0.225566	−0.112783	+	0.993620i	$0.535976\pi$
$830$	840.000	0.0351287
$831$	0	0
$832$	−2752.00	−0.114674
$833$	−4900.00	−0.203811
$834$	0	0
$835$	−1402.00	−0.0581056
$836$	−3828.00	−0.158366
$837$	0	0
$838$	−22886.0	−0.943417
$839$	−40395.0	−1.66221	−0.831103	−	0.556119i	$-0.812290\pi$
$839$	−40395.0	−1.66221	−0.831103	+	0.556119i	$0.812290\pi$
$840$	0	0
$841$	25340.0	1.03899
$842$	26650.0	1.09076
$843$	0	0
$844$	17848.0	0.727907
$845$	348.000	0.0141675
$846$	0	0
$847$	−847.000	−0.0343604
$848$	5472.00	0.221591
$849$	0	0
$850$	−24800.0	−1.00074
$851$	2146.00	0.0864441
$852$	0	0
$853$	−33202.0	−1.33273	−0.666363	−	0.745628i	$-0.732150\pi$
$853$	−33202.0	−1.33273	−0.666363	+	0.745628i	$0.732150\pi$
$854$	2660.00	0.106585
$855$	0	0
$856$	3848.00	0.153647
$857$	−21034.0	−0.838399	−0.419199	−	0.907894i	$-0.637689\pi$
$857$	−21034.0	−0.838399	−0.419199	+	0.907894i	$0.637689\pi$
$858$	0	0
$859$	20920.0	0.830944	0.415472	−	0.909606i	$-0.363616\pi$
$859$	20920.0	0.830944	0.415472	+	0.909606i	$0.363616\pi$
$860$	1832.00	0.0726403
$861$	0	0
$862$	−17006.0	−0.671957
$863$	−8354.00	−0.329517	−0.164759	−	0.986334i	$-0.552685\pi$
$863$	−8354.00	−0.329517	−0.164759	+	0.986334i	$0.552685\pi$
$864$	0	0
$865$	836.000	0.0328611
$866$	−8992.00	−0.352841
$867$	0	0
$868$	−2464.00	−0.0963521
$869$	−4356.00	−0.170043
$870$	0	0
$871$	24897.0	0.968545
$872$	2272.00	0.0882335
$873$	0	0
$874$	10092.0	0.390580
$875$	−1743.00	−0.0673419
$876$	0	0
$877$	19564.0	0.753283	0.376642	−	0.926359i	$-0.377079\pi$
$877$	19564.0	0.753283	0.376642	+	0.926359i	$0.377079\pi$
$878$	14494.0	0.557117
$879$	0	0
$880$	−176.000	−0.00674200
$881$	−32061.0	−1.22606	−0.613032	−	0.790058i	$-0.710050\pi$
$881$	−32061.0	−1.22606	−0.613032	+	0.790058i	$0.710050\pi$
$882$	0	0
$883$	46711.0	1.78024	0.890119	−	0.455728i	$-0.150621\pi$
$883$	46711.0	1.78024	0.890119	+	0.455728i	$0.150621\pi$
$884$	17200.0	0.654410
$885$	0	0
$886$	17136.0	0.649769
$887$	7120.00	0.269522	0.134761	−	0.990878i	$-0.456973\pi$
$887$	7120.00	0.269522	0.134761	+	0.990878i	$0.456973\pi$
$888$	0	0
$889$	4312.00	0.162677
$890$	1596.00	0.0601102
$891$	0	0
$892$	15208.0	0.570854
$893$	−29667.0	−1.11172
$894$	0	0
$895$	−3292.00	−0.122949
$896$	896.000	0.0334077
$897$	0	0
$898$	−15624.0	−0.580601
$899$	19624.0	0.728028
$900$	0	0
$901$	−34200.0	−1.26456
$902$	2816.00	0.103950
$903$	0	0
$904$	11984.0	0.440909
$905$	−4838.00	−0.177702
$906$	0	0
$907$	−21940.0	−0.803204	−0.401602	−	0.915814i	$-0.631546\pi$
$907$	−21940.0	−0.803204	−0.401602	+	0.915814i	$0.631546\pi$
$908$	13480.0	0.492676
$909$	0	0
$910$	602.000	0.0219298
$911$	−66.0000	−0.00240030	−0.00120015	−	0.999999i	$-0.500382\pi$
$911$	−66.0000	−0.00240030	−0.00120015	+	0.999999i	$0.500382\pi$
$912$	0	0
$913$	4620.00	0.167470
$914$	−8524.00	−0.308478
$915$	0	0
$916$	−3592.00	−0.129567
$917$	19236.0	0.692725
$918$	0	0
$919$	−42594.0	−1.52889	−0.764443	−	0.644691i	$-0.776986\pi$
$919$	−42594.0	−1.52889	−0.764443	+	0.644691i	$0.776986\pi$
$920$	464.000	0.0166279
$921$	0	0
$922$	16632.0	0.594084
$923$	5504.00	0.196280
$924$	0	0
$925$	−4588.00	−0.163084
$926$	32206.0	1.14293
$927$	0	0
$928$	−7136.00	−0.252425
$929$	6609.00	0.233406	0.116703	−	0.993167i	$-0.462767\pi$
$929$	6609.00	0.233406	0.116703	+	0.993167i	$0.462767\pi$
$930$	0	0
$931$	−4263.00	−0.150069
$932$	1848.00	0.0649498
$933$	0	0
$934$	−17826.0	−0.624502
$935$	1100.00	0.0384747
$936$	0	0
$937$	10098.0	0.352068	0.176034	−	0.984384i	$-0.443673\pi$
$937$	10098.0	0.352068	0.176034	+	0.984384i	$0.443673\pi$
$938$	−8106.00	−0.282164
$939$	0	0
$940$	−1364.00	−0.0473285
$941$	41824.0	1.44891	0.724455	−	0.689323i	$-0.242092\pi$
$941$	41824.0	1.44891	0.724455	+	0.689323i	$0.242092\pi$
$942$	0	0
$943$	−7424.00	−0.256372
$944$	1680.00	0.0579230
$945$	0	0
$946$	10076.0	0.346299
$947$	28838.0	0.989556	0.494778	−	0.869020i	$-0.335249\pi$
$947$	28838.0	0.989556	0.494778	+	0.869020i	$0.335249\pi$
$948$	0	0
$949$	6923.00	0.236807
$950$	−21576.0	−0.736861
$951$	0	0
$952$	−5600.00	−0.190648
$953$	−16165.0	−0.549460	−0.274730	−	0.961521i	$-0.588589\pi$
$953$	−16165.0	−0.549460	−0.274730	+	0.961521i	$0.588589\pi$
$954$	0	0
$955$	−1232.00	−0.0417451
$956$	22660.0	0.766608
$957$	0	0
$958$	−8200.00	−0.276545
$959$	15288.0	0.514781
$960$	0	0
$961$	−22047.0	−0.740056
$962$	3182.00	0.106644
$963$	0	0
$964$	6372.00	0.212892
$965$	−2366.00	−0.0789267
$966$	0	0
$967$	−40114.0	−1.33400	−0.667001	−	0.745057i	$-0.732422\pi$
$967$	−40114.0	−1.33400	−0.667001	+	0.745057i	$0.732422\pi$
$968$	−968.000	−0.0321412
$969$	0	0
$970$	2828.00	0.0936099
$971$	6515.00	0.215321	0.107660	−	0.994188i	$-0.465664\pi$
$971$	6515.00	0.215321	0.107660	+	0.994188i	$0.465664\pi$
$972$	0	0
$973$	−6356.00	−0.209418
$974$	−20992.0	−0.690582
$975$	0	0
$976$	3040.00	0.0997008
$977$	−12790.0	−0.418821	−0.209411	−	0.977828i	$-0.567155\pi$
$977$	−12790.0	−0.418821	−0.209411	+	0.977828i	$0.567155\pi$
$978$	0	0
$979$	8778.00	0.286564
$980$	−196.000	−0.00638877
$981$	0	0
$982$	5250.00	0.170605
$983$	−4788.00	−0.155355	−0.0776773	−	0.996979i	$-0.524750\pi$
$983$	−4788.00	−0.155355	−0.0776773	+	0.996979i	$0.524750\pi$
$984$	0	0
$985$	318.000	0.0102866
$986$	44600.0	1.44052
$987$	0	0
$988$	14964.0	0.481850
$989$	−26564.0	−0.854081
$990$	0	0
$991$	26989.0	0.865120	0.432560	−	0.901605i	$-0.357610\pi$
$991$	26989.0	0.865120	0.432560	+	0.901605i	$0.357610\pi$
$992$	−2816.00	−0.0901291
$993$	0	0
$994$	−1792.00	−0.0571819
$995$	806.000	0.0256803
$996$	0	0
$997$	−55518.0	−1.76356	−0.881782	−	0.471658i	$-0.843656\pi$
$997$	−55518.0	−1.76356	−0.881782	+	0.471658i	$0.843656\pi$
$998$	24794.0	0.786413
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.4.a.d.1.1		1
3.2	odd	2		462.4.a.f.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.a.f.1.1	✓	1	3.2	odd	2
1386.4.a.d.1.1		1	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1386.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more