LMFDB - Embedded newform 722.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +3.00000 q^{5} +10.0000 q^{6} -32.0000 q^{7} +8.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +3.00000 q^{5} +10.0000 q^{6} -32.0000 q^{7} +8.00000 q^{8} -2.00000 q^{9} +6.00000 q^{10} +4.00000 q^{11} +20.0000 q^{12} -69.0000 q^{13} -64.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} +19.0000 q^{17} -4.00000 q^{18} +12.0000 q^{20} -160.000 q^{21} +8.00000 q^{22} +67.0000 q^{23} +40.0000 q^{24} -116.000 q^{25} -138.000 q^{26} -145.000 q^{27} -128.000 q^{28} +51.0000 q^{29} +30.0000 q^{30} -132.000 q^{31} +32.0000 q^{32} +20.0000 q^{33} +38.0000 q^{34} -96.0000 q^{35} -8.00000 q^{36} -14.0000 q^{37} -345.000 q^{39} +24.0000 q^{40} -413.000 q^{41} -320.000 q^{42} +129.000 q^{43} +16.0000 q^{44} -6.00000 q^{45} +134.000 q^{46} -617.000 q^{47} +80.0000 q^{48} +681.000 q^{49} -232.000 q^{50} +95.0000 q^{51} -276.000 q^{52} +383.000 q^{53} -290.000 q^{54} +12.0000 q^{55} -256.000 q^{56} +102.000 q^{58} -599.000 q^{59} +60.0000 q^{60} -217.000 q^{61} -264.000 q^{62} +64.0000 q^{63} +64.0000 q^{64} -207.000 q^{65} +40.0000 q^{66} -225.000 q^{67} +76.0000 q^{68} +335.000 q^{69} -192.000 q^{70} +701.000 q^{71} -16.0000 q^{72} +1015.00 q^{73} -28.0000 q^{74} -580.000 q^{75} -128.000 q^{77} -690.000 q^{78} +349.000 q^{79} +48.0000 q^{80} -671.000 q^{81} -826.000 q^{82} -592.000 q^{83} -640.000 q^{84} +57.0000 q^{85} +258.000 q^{86} +255.000 q^{87} +32.0000 q^{88} -1349.00 q^{89} -12.0000 q^{90} +2208.00 q^{91} +268.000 q^{92} -660.000 q^{93} -1234.00 q^{94} +160.000 q^{96} -613.000 q^{97} +1362.00 q^{98} -8.00000 q^{99} +O(q^{100})\)

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
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	4.00000	0.500000
$5$	3.00000	0.268328	0.134164	−	0.990959i	$-0.457165\pi$
$5$	3.00000	0.268328	0.134164	+	0.990959i	$0.457165\pi$
$6$	10.0000	0.680414
$7$	−32.0000	−1.72784	−0.863919	−	0.503631i	$-0.831997\pi$
$7$	−32.0000	−1.72784	−0.863919	+	0.503631i	$0.831997\pi$
$8$	8.00000	0.353553
$9$	−2.00000	−0.0740741
$10$	6.00000	0.189737
$11$	4.00000	0.109640	0.0548202	−	0.998496i	$-0.482541\pi$
$11$	4.00000	0.109640	0.0548202	+	0.998496i	$0.482541\pi$
$12$	20.0000	0.481125
$13$	−69.0000	−1.47209	−0.736044	−	0.676933i	$-0.763309\pi$
$13$	−69.0000	−1.47209	−0.736044	+	0.676933i	$0.763309\pi$
$14$	−64.0000	−1.22177
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	19.0000	0.271069	0.135535	−	0.990773i	$-0.456725\pi$
$17$	19.0000	0.271069	0.135535	+	0.990773i	$0.456725\pi$
$18$	−4.00000	−0.0523783
$19$	0	0
$19$	0	0
$20$	12.0000	0.134164
$21$	−160.000	−1.66261
$22$	8.00000	0.0775275
$23$	67.0000	0.607412	0.303706	−	0.952766i	$-0.401776\pi$
$23$	67.0000	0.607412	0.303706	+	0.952766i	$0.401776\pi$
$24$	40.0000	0.340207
$25$	−116.000	−0.928000
$26$	−138.000	−1.04092
$27$	−145.000	−1.03353
$28$	−128.000	−0.863919
$29$	51.0000	0.326568	0.163284	−	0.986579i	$-0.447791\pi$
$29$	51.0000	0.326568	0.163284	+	0.986579i	$0.447791\pi$
$30$	30.0000	0.182574
$31$	−132.000	−0.764771	−0.382385	−	0.924003i	$-0.624897\pi$
$31$	−132.000	−0.764771	−0.382385	+	0.924003i	$0.624897\pi$
$32$	32.0000	0.176777
$33$	20.0000	0.105502
$34$	38.0000	0.191675
$35$	−96.0000	−0.463627
$36$	−8.00000	−0.0370370
$37$	−14.0000	−0.0622050	−0.0311025	−	0.999516i	$-0.509902\pi$
$37$	−14.0000	−0.0622050	−0.0311025	+	0.999516i	$0.509902\pi$
$38$	0	0
$39$	−345.000	−1.41652
$40$	24.0000	0.0948683
$41$	−413.000	−1.57316	−0.786582	−	0.617485i	$-0.788152\pi$
$41$	−413.000	−1.57316	−0.786582	+	0.617485i	$0.788152\pi$
$42$	−320.000	−1.17564
$43$	129.000	0.457496	0.228748	−	0.973486i	$-0.426537\pi$
$43$	129.000	0.457496	0.228748	+	0.973486i	$0.426537\pi$
$44$	16.0000	0.0548202
$45$	−6.00000	−0.0198762
$46$	134.000	0.429505
$47$	−617.000	−1.91487	−0.957433	−	0.288656i	$-0.906792\pi$
$47$	−617.000	−1.91487	−0.957433	+	0.288656i	$0.906792\pi$
$48$	80.0000	0.240563
$49$	681.000	1.98542
$50$	−232.000	−0.656195
$51$	95.0000	0.260836
$52$	−276.000	−0.736044
$53$	383.000	0.992624	0.496312	−	0.868144i	$-0.334687\pi$
$53$	383.000	0.992624	0.496312	+	0.868144i	$0.334687\pi$
$54$	−290.000	−0.730815
$55$	12.0000	0.0294196
$56$	−256.000	−0.610883
$57$	0	0
$58$	102.000	0.230918
$59$	−599.000	−1.32175	−0.660874	−	0.750497i	$-0.729814\pi$
$59$	−599.000	−1.32175	−0.660874	+	0.750497i	$0.729814\pi$
$60$	60.0000	0.129099
$61$	−217.000	−0.455475	−0.227738	−	0.973723i	$-0.573133\pi$
$61$	−217.000	−0.455475	−0.227738	+	0.973723i	$0.573133\pi$
$62$	−264.000	−0.540775
$63$	64.0000	0.127988
$64$	64.0000	0.125000
$65$	−207.000	−0.395003
$66$	40.0000	0.0746009
$67$	−225.000	−0.410271	−0.205135	−	0.978734i	$-0.565763\pi$
$67$	−225.000	−0.410271	−0.205135	+	0.978734i	$0.565763\pi$
$68$	76.0000	0.135535
$69$	335.000	0.584482
$70$	−192.000	−0.327834
$71$	701.000	1.17174	0.585869	−	0.810406i	$-0.300753\pi$
$71$	701.000	1.17174	0.585869	+	0.810406i	$0.300753\pi$
$72$	−16.0000	−0.0261891
$73$	1015.00	1.62735	0.813676	−	0.581318i	$-0.197463\pi$
$73$	1015.00	1.62735	0.813676	+	0.581318i	$0.197463\pi$
$74$	−28.0000	−0.0439856
$75$	−580.000	−0.892968
$76$	0	0
$77$	−128.000	−0.189441
$78$	−690.000	−1.00163
$79$	349.000	0.497033	0.248516	−	0.968628i	$-0.420057\pi$
$79$	349.000	0.497033	0.248516	+	0.968628i	$0.420057\pi$
$80$	48.0000	0.0670820
$81$	−671.000	−0.920439
$82$	−826.000	−1.11240
$83$	−592.000	−0.782897	−0.391448	−	0.920200i	$-0.628026\pi$
$83$	−592.000	−0.782897	−0.391448	+	0.920200i	$0.628026\pi$
$84$	−640.000	−0.831306
$85$	57.0000	0.0727355
$86$	258.000	0.323498
$87$	255.000	0.314240
$88$	32.0000	0.0387638
$89$	−1349.00	−1.60667	−0.803335	−	0.595527i	$-0.796943\pi$
$89$	−1349.00	−1.60667	−0.803335	+	0.595527i	$0.796943\pi$
$90$	−12.0000	−0.0140546
$91$	2208.00	2.54353
$92$	268.000	0.303706
$93$	−660.000	−0.735901
$94$	−1234.00	−1.35401
$95$	0	0
$96$	160.000	0.170103
$97$	−613.000	−0.641657	−0.320828	−	0.947137i	$-0.603961\pi$
$97$	−613.000	−0.641657	−0.320828	+	0.947137i	$0.603961\pi$
$98$	1362.00	1.40391
$99$	−8.00000	−0.00812152
$100$	−464.000	−0.464000
$101$	1235.00	1.21670	0.608352	−	0.793667i	$-0.291831\pi$
$101$	1235.00	1.21670	0.608352	+	0.793667i	$0.291831\pi$
$102$	190.000	0.184439
$103$	1632.00	1.56122	0.780610	−	0.625018i	$-0.214908\pi$
$103$	1632.00	1.56122	0.780610	+	0.625018i	$0.214908\pi$
$104$	−552.000	−0.520462
$105$	−480.000	−0.446126
$106$	766.000	0.701891
$107$	2060.00	1.86119	0.930597	−	0.366046i	$-0.119289\pi$
$107$	2060.00	1.86119	0.930597	+	0.366046i	$0.119289\pi$
$108$	−580.000	−0.516764
$109$	1055.00	0.927070	0.463535	−	0.886079i	$-0.346581\pi$
$109$	1055.00	0.927070	0.463535	+	0.886079i	$0.346581\pi$
$110$	24.0000	0.0208028
$111$	−70.0000	−0.0598568
$112$	−512.000	−0.431959
$113$	1006.00	0.837491	0.418746	−	0.908104i	$-0.362470\pi$
$113$	1006.00	0.837491	0.418746	+	0.908104i	$0.362470\pi$
$114$	0	0
$115$	201.000	0.162986
$116$	204.000	0.163284
$117$	138.000	0.109044
$118$	−1198.00	−0.934617
$119$	−608.000	−0.468364
$120$	120.000	0.0912871
$121$	−1315.00	−0.987979
$122$	−434.000	−0.322070
$123$	−2065.00	−1.51378
$124$	−528.000	−0.382385
$125$	−723.000	−0.517337
$126$	128.000	0.0905012
$127$	1987.00	1.38833	0.694164	−	0.719817i	$-0.255774\pi$
$127$	1987.00	1.38833	0.694164	+	0.719817i	$0.255774\pi$
$128$	128.000	0.0883883
$129$	645.000	0.440225
$130$	−414.000	−0.279309
$131$	−1803.00	−1.20251	−0.601255	−	0.799057i	$-0.705332\pi$
$131$	−1803.00	−1.20251	−0.601255	+	0.799057i	$0.705332\pi$
$132$	80.0000	0.0527508
$133$	0	0
$134$	−450.000	−0.290105
$135$	−435.000	−0.277325
$136$	152.000	0.0958374
$137$	−669.000	−0.417201	−0.208600	−	0.978001i	$-0.566891\pi$
$137$	−669.000	−0.417201	−0.208600	+	0.978001i	$0.566891\pi$
$138$	670.000	0.413291
$139$	−2725.00	−1.66282	−0.831408	−	0.555662i	$-0.812465\pi$
$139$	−2725.00	−1.66282	−0.831408	+	0.555662i	$0.812465\pi$
$140$	−384.000	−0.231814
$141$	−3085.00	−1.84258
$142$	1402.00	0.828544
$143$	−276.000	−0.161401
$144$	−32.0000	−0.0185185
$145$	153.000	0.0876273
$146$	2030.00	1.15071
$147$	3405.00	1.91047
$148$	−56.0000	−0.0311025
$149$	71.0000	0.0390372	0.0195186	−	0.999809i	$-0.493787\pi$
$149$	71.0000	0.0390372	0.0195186	+	0.999809i	$0.493787\pi$
$150$	−1160.00	−0.631424
$151$	−656.000	−0.353540	−0.176770	−	0.984252i	$-0.556565\pi$
$151$	−656.000	−0.353540	−0.176770	+	0.984252i	$0.556565\pi$
$152$	0	0
$153$	−38.0000	−0.0200792
$154$	−256.000	−0.133955
$155$	−396.000	−0.205210
$156$	−1380.00	−0.708259
$157$	−1053.00	−0.535277	−0.267639	−	0.963519i	$-0.586243\pi$
$157$	−1053.00	−0.535277	−0.267639	+	0.963519i	$0.586243\pi$
$158$	698.000	0.351455
$159$	1915.00	0.955153
$160$	96.0000	0.0474342
$161$	−2144.00	−1.04951
$162$	−1342.00	−0.650849
$163$	68.0000	0.0326759	0.0163379	−	0.999867i	$-0.494799\pi$
$163$	68.0000	0.0326759	0.0163379	+	0.999867i	$0.494799\pi$
$164$	−1652.00	−0.786582
$165$	60.0000	0.0283091
$166$	−1184.00	−0.553592
$167$	−921.000	−0.426761	−0.213381	−	0.976969i	$-0.568447\pi$
$167$	−921.000	−0.426761	−0.213381	+	0.976969i	$0.568447\pi$
$168$	−1280.00	−0.587822
$169$	2564.00	1.16705
$170$	114.000	0.0514318
$171$	0	0
$172$	516.000	0.228748
$173$	−1893.00	−0.831920	−0.415960	−	0.909383i	$-0.636554\pi$
$173$	−1893.00	−0.831920	−0.415960	+	0.909383i	$0.636554\pi$
$174$	510.000	0.222201
$175$	3712.00	1.60343
$176$	64.0000	0.0274101
$177$	−2995.00	−1.27185
$178$	−2698.00	−1.13609
$179$	−20.0000	−0.00835123	−0.00417562	−	0.999991i	$-0.501329\pi$
$179$	−20.0000	−0.00835123	−0.00417562	+	0.999991i	$0.501329\pi$
$180$	−24.0000	−0.00993808
$181$	1839.00	0.755203	0.377602	−	0.925968i	$-0.376749\pi$
$181$	1839.00	0.755203	0.377602	+	0.925968i	$0.376749\pi$
$182$	4416.00	1.79855
$183$	−1085.00	−0.438281
$184$	536.000	0.214752
$185$	−42.0000	−0.0166914
$186$	−1320.00	−0.520361
$187$	76.0000	0.0297202
$188$	−2468.00	−0.957433
$189$	4640.00	1.78577
$190$	0	0
$191$	2992.00	1.13347	0.566737	−	0.823899i	$-0.308206\pi$
$191$	2992.00	1.13347	0.566737	+	0.823899i	$0.308206\pi$
$192$	320.000	0.120281
$193$	−1393.00	−0.519535	−0.259768	−	0.965671i	$-0.583646\pi$
$193$	−1393.00	−0.519535	−0.259768	+	0.965671i	$0.583646\pi$
$194$	−1226.00	−0.453720
$195$	−1035.00	−0.380092
$196$	2724.00	0.992711
$197$	−4214.00	−1.52404	−0.762018	−	0.647556i	$-0.775791\pi$
$197$	−4214.00	−1.52404	−0.762018	+	0.647556i	$0.775791\pi$
$198$	−16.0000	−0.00574278
$199$	767.000	0.273222	0.136611	−	0.990625i	$-0.456379\pi$
$199$	767.000	0.273222	0.136611	+	0.990625i	$0.456379\pi$
$200$	−928.000	−0.328098
$201$	−1125.00	−0.394783
$202$	2470.00	0.860340
$203$	−1632.00	−0.564256
$204$	380.000	0.130418
$205$	−1239.00	−0.422124
$206$	3264.00	1.10395
$207$	−134.000	−0.0449934
$208$	−1104.00	−0.368022
$209$	0	0
$210$	−960.000	−0.315459
$211$	2365.00	0.771627	0.385814	−	0.922577i	$-0.373921\pi$
$211$	2365.00	0.771627	0.385814	+	0.922577i	$0.373921\pi$
$212$	1532.00	0.496312
$213$	3505.00	1.12751
$214$	4120.00	1.31606
$215$	387.000	0.122759
$216$	−1160.00	−0.365407
$217$	4224.00	1.32140
$218$	2110.00	0.655538
$219$	5075.00	1.56592
$220$	48.0000	0.0147098
$221$	−1311.00	−0.399038
$222$	−140.000	−0.0423252
$223$	−2439.00	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$223$	−2439.00	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$224$	−1024.00	−0.305441
$225$	232.000	0.0687407
$226$	2012.00	0.592196
$227$	−1708.00	−0.499401	−0.249700	−	0.968323i	$-0.580332\pi$
$227$	−1708.00	−0.499401	−0.249700	+	0.968323i	$0.580332\pi$
$228$	0	0
$229$	4618.00	1.33260	0.666301	−	0.745683i	$-0.267876\pi$
$229$	4618.00	1.33260	0.666301	+	0.745683i	$0.267876\pi$
$230$	402.000	0.115248
$231$	−640.000	−0.182290
$232$	408.000	0.115459
$233$	3219.00	0.905080	0.452540	−	0.891744i	$-0.350518\pi$
$233$	3219.00	0.905080	0.452540	+	0.891744i	$0.350518\pi$
$234$	276.000	0.0771055
$235$	−1851.00	−0.513812
$236$	−2396.00	−0.660874
$237$	1745.00	0.478270
$238$	−1216.00	−0.331183
$239$	−4236.00	−1.14646	−0.573230	−	0.819394i	$-0.694310\pi$
$239$	−4236.00	−1.14646	−0.573230	+	0.819394i	$0.694310\pi$
$240$	240.000	0.0645497
$241$	−2429.00	−0.649235	−0.324618	−	0.945845i	$-0.605236\pi$
$241$	−2429.00	−0.649235	−0.324618	+	0.945845i	$0.605236\pi$
$242$	−2630.00	−0.698607
$243$	560.000	0.147835
$244$	−868.000	−0.227738
$245$	2043.00	0.532745
$246$	−4130.00	−1.07040
$247$	0	0
$248$	−1056.00	−0.270387
$249$	−2960.00	−0.753343
$250$	−1446.00	−0.365812
$251$	243.000	0.0611077	0.0305538	−	0.999533i	$-0.490273\pi$
$251$	243.000	0.0611077	0.0305538	+	0.999533i	$0.490273\pi$
$252$	256.000	0.0639940
$253$	268.000	0.0665969
$254$	3974.00	0.981697
$255$	285.000	0.0699898
$256$	256.000	0.0625000
$257$	1047.00	0.254125	0.127062	−	0.991895i	$-0.459445\pi$
$257$	1047.00	0.254125	0.127062	+	0.991895i	$0.459445\pi$
$258$	1290.00	0.311286
$259$	448.000	0.107480
$260$	−828.000	−0.197501
$261$	−102.000	−0.0241902
$262$	−3606.00	−0.850303
$263$	1905.00	0.446644	0.223322	−	0.974745i	$-0.428310\pi$
$263$	1905.00	0.446644	0.223322	+	0.974745i	$0.428310\pi$
$264$	160.000	0.0373005
$265$	1149.00	0.266349
$266$	0	0
$267$	−6745.00	−1.54602
$268$	−900.000	−0.205135
$269$	−5833.00	−1.32210	−0.661049	−	0.750343i	$-0.729888\pi$
$269$	−5833.00	−1.32210	−0.661049	+	0.750343i	$0.729888\pi$
$270$	−870.000	−0.196098
$271$	−3727.00	−0.835421	−0.417711	−	0.908580i	$-0.637167\pi$
$271$	−3727.00	−0.835421	−0.417711	+	0.908580i	$0.637167\pi$
$272$	304.000	0.0677673
$273$	11040.0	2.44751
$274$	−1338.00	−0.295006
$275$	−464.000	−0.101746
$276$	1340.00	0.292241
$277$	−5294.00	−1.14832	−0.574162	−	0.818742i	$-0.694672\pi$
$277$	−5294.00	−1.14832	−0.574162	+	0.818742i	$0.694672\pi$
$278$	−5450.00	−1.17579
$279$	264.000	0.0566497
$280$	−768.000	−0.163917
$281$	1375.00	0.291906	0.145953	−	0.989292i	$-0.453375\pi$
$281$	1375.00	0.291906	0.145953	+	0.989292i	$0.453375\pi$
$282$	−6170.00	−1.30290
$283$	−1307.00	−0.274534	−0.137267	−	0.990534i	$-0.543832\pi$
$283$	−1307.00	−0.274534	−0.137267	+	0.990534i	$0.543832\pi$
$284$	2804.00	0.585869
$285$	0	0
$286$	−552.000	−0.114127
$287$	13216.0	2.71817
$288$	−64.0000	−0.0130946
$289$	−4552.00	−0.926521
$290$	306.000	0.0619619
$291$	−3065.00	−0.617435
$292$	4060.00	0.813676
$293$	3818.00	0.761263	0.380631	−	0.924727i	$-0.375707\pi$
$293$	3818.00	0.761263	0.380631	+	0.924727i	$0.375707\pi$
$294$	6810.00	1.35091
$295$	−1797.00	−0.354662
$296$	−112.000	−0.0219928
$297$	−580.000	−0.113317
$298$	142.000	0.0276035
$299$	−4623.00	−0.894164
$300$	−2320.00	−0.446484
$301$	−4128.00	−0.790478
$302$	−1312.00	−0.249990
$303$	6175.00	1.17077
$304$	0	0
$305$	−651.000	−0.122217
$306$	−76.0000	−0.0141981
$307$	873.000	0.162296	0.0811478	−	0.996702i	$-0.474141\pi$
$307$	873.000	0.162296	0.0811478	+	0.996702i	$0.474141\pi$
$308$	−512.000	−0.0947205
$309$	8160.00	1.50229
$310$	−792.000	−0.145105
$311$	4180.00	0.762142	0.381071	−	0.924546i	$-0.375555\pi$
$311$	4180.00	0.762142	0.381071	+	0.924546i	$0.375555\pi$
$312$	−2760.00	−0.500815
$313$	−3165.00	−0.571554	−0.285777	−	0.958296i	$-0.592252\pi$
$313$	−3165.00	−0.571554	−0.285777	+	0.958296i	$0.592252\pi$
$314$	−2106.00	−0.378498
$315$	192.000	0.0343428
$316$	1396.00	0.248516
$317$	4539.00	0.804213	0.402107	−	0.915593i	$-0.368278\pi$
$317$	4539.00	0.804213	0.402107	+	0.915593i	$0.368278\pi$
$318$	3830.00	0.675395
$319$	204.000	0.0358050
$320$	192.000	0.0335410
$321$	10300.0	1.79093
$322$	−4288.00	−0.742115
$323$	0	0
$324$	−2684.00	−0.460219
$325$	8004.00	1.36610
$326$	136.000	0.0231053
$327$	5275.00	0.892074
$328$	−3304.00	−0.556198
$329$	19744.0	3.30858
$330$	120.000	0.0200175
$331$	3660.00	0.607770	0.303885	−	0.952709i	$-0.401716\pi$
$331$	3660.00	0.607770	0.303885	+	0.952709i	$0.401716\pi$
$332$	−2368.00	−0.391448
$333$	28.0000	0.00460778
$334$	−1842.00	−0.301766
$335$	−675.000	−0.110087
$336$	−2560.00	−0.415653
$337$	−5173.00	−0.836176	−0.418088	−	0.908407i	$-0.637300\pi$
$337$	−5173.00	−0.836176	−0.418088	+	0.908407i	$0.637300\pi$
$338$	5128.00	0.825226
$339$	5030.00	0.805876
$340$	228.000	0.0363678
$341$	−528.000	−0.0838499
$342$	0	0
$343$	−10816.0	−1.70265
$344$	1032.00	0.161749
$345$	1005.00	0.156833
$346$	−3786.00	−0.588256
$347$	−8591.00	−1.32908	−0.664538	−	0.747255i	$-0.731371\pi$
$347$	−8591.00	−1.32908	−0.664538	+	0.747255i	$0.731371\pi$
$348$	1020.00	0.157120
$349$	6946.00	1.06536	0.532680	−	0.846317i	$-0.321185\pi$
$349$	6946.00	1.06536	0.532680	+	0.846317i	$0.321185\pi$
$350$	7424.00	1.13380
$351$	10005.0	1.52145
$352$	128.000	0.0193819
$353$	−8226.00	−1.24030	−0.620150	−	0.784483i	$-0.712928\pi$
$353$	−8226.00	−1.24030	−0.620150	+	0.784483i	$0.712928\pi$
$354$	−5990.00	−0.899336
$355$	2103.00	0.314410
$356$	−5396.00	−0.803335
$357$	−3040.00	−0.450683
$358$	−40.0000	−0.00590521
$359$	11385.0	1.67375	0.836876	−	0.547392i	$-0.184379\pi$
$359$	11385.0	1.67375	0.836876	+	0.547392i	$0.184379\pi$
$360$	−48.0000	−0.00702728
$361$	0	0
$362$	3678.00	0.534009
$363$	−6575.00	−0.950683
$364$	8832.00	1.27177
$365$	3045.00	0.436665
$366$	−2170.00	−0.309912
$367$	−2953.00	−0.420015	−0.210007	−	0.977700i	$-0.567349\pi$
$367$	−2953.00	−0.420015	−0.210007	+	0.977700i	$0.567349\pi$
$368$	1072.00	0.151853
$369$	826.000	0.116531
$370$	−84.0000	−0.0118026
$371$	−12256.0	−1.71509
$372$	−2640.00	−0.367951
$373$	5006.00	0.694908	0.347454	−	0.937697i	$-0.387046\pi$
$373$	5006.00	0.694908	0.347454	+	0.937697i	$0.387046\pi$
$374$	152.000	0.0210153
$375$	−3615.00	−0.497807
$376$	−4936.00	−0.677007
$377$	−3519.00	−0.480737
$378$	9280.00	1.26273
$379$	6764.00	0.916737	0.458369	−	0.888762i	$-0.348434\pi$
$379$	6764.00	0.916737	0.458369	+	0.888762i	$0.348434\pi$
$380$	0	0
$381$	9935.00	1.33592
$382$	5984.00	0.801487
$383$	−4963.00	−0.662134	−0.331067	−	0.943607i	$-0.607409\pi$
$383$	−4963.00	−0.662134	−0.331067	+	0.943607i	$0.607409\pi$
$384$	640.000	0.0850517
$385$	−384.000	−0.0508323
$386$	−2786.00	−0.367367
$387$	−258.000	−0.0338886
$388$	−2452.00	−0.320828
$389$	3623.00	0.472220	0.236110	−	0.971726i	$-0.424128\pi$
$389$	3623.00	0.472220	0.236110	+	0.971726i	$0.424128\pi$
$390$	−2070.00	−0.268765
$391$	1273.00	0.164651
$392$	5448.00	0.701953
$393$	−9015.00	−1.15712
$394$	−8428.00	−1.07766
$395$	1047.00	0.133368
$396$	−32.0000	−0.00406076
$397$	−7629.00	−0.964455	−0.482227	−	0.876046i	$-0.660172\pi$
$397$	−7629.00	−0.964455	−0.482227	+	0.876046i	$0.660172\pi$
$398$	1534.00	0.193197
$399$	0	0
$400$	−1856.00	−0.232000
$401$	−9117.00	−1.13536	−0.567682	−	0.823248i	$-0.692160\pi$
$401$	−9117.00	−1.13536	−0.567682	+	0.823248i	$0.692160\pi$
$402$	−2250.00	−0.279154
$403$	9108.00	1.12581
$404$	4940.00	0.608352
$405$	−2013.00	−0.246980
$406$	−3264.00	−0.398989
$407$	−56.0000	−0.00682019
$408$	760.000	0.0922196
$409$	4935.00	0.596626	0.298313	−	0.954468i	$-0.403576\pi$
$409$	4935.00	0.596626	0.298313	+	0.954468i	$0.403576\pi$
$410$	−2478.00	−0.298487
$411$	−3345.00	−0.401452
$412$	6528.00	0.780610
$413$	19168.0	2.28377
$414$	−268.000	−0.0318152
$415$	−1776.00	−0.210073
$416$	−2208.00	−0.260231
$417$	−13625.0	−1.60005
$418$	0	0
$419$	6516.00	0.759731	0.379866	−	0.925042i	$-0.375970\pi$
$419$	6516.00	0.759731	0.379866	+	0.925042i	$0.375970\pi$
$420$	−1920.00	−0.223063
$421$	10915.0	1.26357	0.631787	−	0.775142i	$-0.282322\pi$
$421$	10915.0	1.26357	0.631787	+	0.775142i	$0.282322\pi$
$422$	4730.00	0.545623
$423$	1234.00	0.141842
$424$	3064.00	0.350946
$425$	−2204.00	−0.251552
$426$	7010.00	0.797267
$427$	6944.00	0.786988
$428$	8240.00	0.930597
$429$	−1380.00	−0.155308
$430$	774.000	0.0868037
$431$	−5509.00	−0.615683	−0.307841	−	0.951438i	$-0.599607\pi$
$431$	−5509.00	−0.615683	−0.307841	+	0.951438i	$0.599607\pi$
$432$	−2320.00	−0.258382
$433$	−3753.00	−0.416530	−0.208265	−	0.978072i	$-0.566782\pi$
$433$	−3753.00	−0.416530	−0.208265	+	0.978072i	$0.566782\pi$
$434$	8448.00	0.934371
$435$	765.000	0.0843194
$436$	4220.00	0.463535
$437$	0	0
$438$	10150.0	1.10727
$439$	7813.00	0.849417	0.424709	−	0.905330i	$-0.360377\pi$
$439$	7813.00	0.849417	0.424709	+	0.905330i	$0.360377\pi$
$440$	96.0000	0.0104014
$441$	−1362.00	−0.147068
$442$	−2622.00	−0.282162
$443$	−6117.00	−0.656044	−0.328022	−	0.944670i	$-0.606382\pi$
$443$	−6117.00	−0.656044	−0.328022	+	0.944670i	$0.606382\pi$
$444$	−280.000	−0.0299284
$445$	−4047.00	−0.431115
$446$	−4878.00	−0.517892
$447$	355.000	0.0375636
$448$	−2048.00	−0.215980
$449$	−7146.00	−0.751093	−0.375546	−	0.926804i	$-0.622545\pi$
$449$	−7146.00	−0.751093	−0.375546	+	0.926804i	$0.622545\pi$
$450$	464.000	0.0486070
$451$	−1652.00	−0.172483
$452$	4024.00	0.418746
$453$	−3280.00	−0.340194
$454$	−3416.00	−0.353130
$455$	6624.00	0.682501
$456$	0	0
$457$	−18118.0	−1.85454	−0.927269	−	0.374395i	$-0.877851\pi$
$457$	−18118.0	−1.85454	−0.927269	+	0.374395i	$0.877851\pi$
$458$	9236.00	0.942292
$459$	−2755.00	−0.280158
$460$	804.000	0.0814928
$461$	16935.0	1.71094	0.855468	−	0.517856i	$-0.173270\pi$
$461$	16935.0	1.71094	0.855468	+	0.517856i	$0.173270\pi$
$462$	−1280.00	−0.128898
$463$	−7788.00	−0.781726	−0.390863	−	0.920449i	$-0.627823\pi$
$463$	−7788.00	−0.781726	−0.390863	+	0.920449i	$0.627823\pi$
$464$	816.000	0.0816419
$465$	−1980.00	−0.197463
$466$	6438.00	0.639988
$467$	12500.0	1.23861	0.619305	−	0.785150i	$-0.287414\pi$
$467$	12500.0	1.23861	0.619305	+	0.785150i	$0.287414\pi$
$468$	552.000	0.0545218
$469$	7200.00	0.708881
$470$	−3702.00	−0.363320
$471$	−5265.00	−0.515071
$472$	−4792.00	−0.467309
$473$	516.000	0.0501601
$474$	3490.00	0.338188
$475$	0	0
$476$	−2432.00	−0.234182
$477$	−766.000	−0.0735277
$478$	−8472.00	−0.810670
$479$	−12105.0	−1.15468	−0.577340	−	0.816504i	$-0.695909\pi$
$479$	−12105.0	−1.15468	−0.577340	+	0.816504i	$0.695909\pi$
$480$	480.000	0.0456435
$481$	966.000	0.0915713
$482$	−4858.00	−0.459078
$483$	−10720.0	−1.00989
$484$	−5260.00	−0.493989
$485$	−1839.00	−0.172175
$486$	1120.00	0.104535
$487$	296.000	0.0275422	0.0137711	−	0.999905i	$-0.495616\pi$
$487$	296.000	0.0275422	0.0137711	+	0.999905i	$0.495616\pi$
$488$	−1736.00	−0.161035
$489$	340.000	0.0314424
$490$	4086.00	0.376707
$491$	3213.00	0.295317	0.147659	−	0.989038i	$-0.452826\pi$
$491$	3213.00	0.295317	0.147659	+	0.989038i	$0.452826\pi$
$492$	−8260.00	−0.756889
$493$	969.000	0.0885224
$494$	0	0
$495$	−24.0000	−0.00217923
$496$	−2112.00	−0.191193
$497$	−22432.0	−2.02457
$498$	−5920.00	−0.532694
$499$	3017.00	0.270660	0.135330	−	0.990801i	$-0.456790\pi$
$499$	3017.00	0.270660	0.135330	+	0.990801i	$0.456790\pi$
$500$	−2892.00	−0.258668
$501$	−4605.00	−0.410651
$502$	486.000	0.0432096
$503$	−7277.00	−0.645060	−0.322530	−	0.946559i	$-0.604533\pi$
$503$	−7277.00	−0.645060	−0.322530	+	0.946559i	$0.604533\pi$
$504$	512.000	0.0452506
$505$	3705.00	0.326476
$506$	536.000	0.0470911
$507$	12820.0	1.12299
$508$	7948.00	0.694164
$509$	−10693.0	−0.931157	−0.465578	−	0.885007i	$-0.654154\pi$
$509$	−10693.0	−0.931157	−0.465578	+	0.885007i	$0.654154\pi$
$510$	570.000	0.0494902
$511$	−32480.0	−2.81180
$512$	512.000	0.0441942
$513$	0	0
$514$	2094.00	0.179693
$515$	4896.00	0.418919
$516$	2580.00	0.220113
$517$	−2468.00	−0.209947
$518$	896.000	0.0760000
$519$	−9465.00	−0.800515
$520$	−1656.00	−0.139655
$521$	−7190.00	−0.604606	−0.302303	−	0.953212i	$-0.597755\pi$
$521$	−7190.00	−0.604606	−0.302303	+	0.953212i	$0.597755\pi$
$522$	−204.000	−0.0171051
$523$	8647.00	0.722958	0.361479	−	0.932380i	$-0.382272\pi$
$523$	8647.00	0.722958	0.361479	+	0.932380i	$0.382272\pi$
$524$	−7212.00	−0.601255
$525$	18560.0	1.54290
$526$	3810.00	0.315825
$527$	−2508.00	−0.207306
$528$	320.000	0.0263754
$529$	−7678.00	−0.631051
$530$	2298.00	0.188337
$531$	1198.00	0.0979073
$532$	0	0
$533$	28497.0	2.31584
$534$	−13490.0	−1.09320
$535$	6180.00	0.499411
$536$	−1800.00	−0.145053
$537$	−100.000	−0.00803597
$538$	−11666.0	−0.934864
$539$	2724.00	0.217683
$540$	−1740.00	−0.138662
$541$	4043.00	0.321298	0.160649	−	0.987012i	$-0.448641\pi$
$541$	4043.00	0.321298	0.160649	+	0.987012i	$0.448641\pi$
$542$	−7454.00	−0.590732
$543$	9195.00	0.726695
$544$	608.000	0.0479187
$545$	3165.00	0.248759
$546$	22080.0	1.73065
$547$	−5389.00	−0.421238	−0.210619	−	0.977568i	$-0.567548\pi$
$547$	−5389.00	−0.421238	−0.210619	+	0.977568i	$0.567548\pi$
$548$	−2676.00	−0.208600
$549$	434.000	0.0337389
$550$	−928.000	−0.0719456
$551$	0	0
$552$	2680.00	0.206646
$553$	−11168.0	−0.858791
$554$	−10588.0	−0.811987
$555$	−210.000	−0.0160613
$556$	−10900.0	−0.831408
$557$	6727.00	0.511727	0.255864	−	0.966713i	$-0.417640\pi$
$557$	6727.00	0.511727	0.255864	+	0.966713i	$0.417640\pi$
$558$	528.000	0.0400574
$559$	−8901.00	−0.673474
$560$	−1536.00	−0.115907
$561$	380.000	0.0285982
$562$	2750.00	0.206409
$563$	−19908.0	−1.49027	−0.745135	−	0.666914i	$-0.767615\pi$
$563$	−19908.0	−1.49027	−0.745135	+	0.666914i	$0.767615\pi$
$564$	−12340.0	−0.921290
$565$	3018.00	0.224723
$566$	−2614.00	−0.194125
$567$	21472.0	1.59037
$568$	5608.00	0.414272
$569$	−8730.00	−0.643200	−0.321600	−	0.946876i	$-0.604221\pi$
$569$	−8730.00	−0.643200	−0.321600	+	0.946876i	$0.604221\pi$
$570$	0	0
$571$	−4732.00	−0.346809	−0.173405	−	0.984851i	$-0.555477\pi$
$571$	−4732.00	−0.346809	−0.173405	+	0.984851i	$0.555477\pi$
$572$	−1104.00	−0.0807003
$573$	14960.0	1.09069
$574$	26432.0	1.92204
$575$	−7772.00	−0.563678
$576$	−128.000	−0.00925926
$577$	−23882.0	−1.72309	−0.861543	−	0.507685i	$-0.830502\pi$
$577$	−23882.0	−1.72309	−0.861543	+	0.507685i	$0.830502\pi$
$578$	−9104.00	−0.655150
$579$	−6965.00	−0.499923
$580$	612.000	0.0438136
$581$	18944.0	1.35272
$582$	−6130.00	−0.436592
$583$	1532.00	0.108832
$584$	8120.00	0.575356
$585$	414.000	0.0292595
$586$	7636.00	0.538294
$587$	−16547.0	−1.16349	−0.581744	−	0.813372i	$-0.697630\pi$
$587$	−16547.0	−1.16349	−0.581744	+	0.813372i	$0.697630\pi$
$588$	13620.0	0.955237
$589$	0	0
$590$	−3594.00	−0.250784
$591$	−21070.0	−1.46650
$592$	−224.000	−0.0155513
$593$	−15029.0	−1.04075	−0.520377	−	0.853937i	$-0.674209\pi$
$593$	−15029.0	−1.04075	−0.520377	+	0.853937i	$0.674209\pi$
$594$	−1160.00	−0.0801269
$595$	−1824.00	−0.125675
$596$	284.000	0.0195186
$597$	3835.00	0.262908
$598$	−9246.00	−0.632269
$599$	13787.0	0.940437	0.470218	−	0.882550i	$-0.344175\pi$
$599$	13787.0	0.940437	0.470218	+	0.882550i	$0.344175\pi$
$600$	−4640.00	−0.315712
$601$	11382.0	0.772515	0.386257	−	0.922391i	$-0.373768\pi$
$601$	11382.0	0.772515	0.386257	+	0.922391i	$0.373768\pi$
$602$	−8256.00	−0.558953
$603$	450.000	0.0303904
$604$	−2624.00	−0.176770
$605$	−3945.00	−0.265103
$606$	12350.0	0.827862
$607$	−25312.0	−1.69256	−0.846279	−	0.532740i	$-0.821162\pi$
$607$	−25312.0	−1.69256	−0.846279	+	0.532740i	$0.821162\pi$
$608$	0	0
$609$	−8160.00	−0.542955
$610$	−1302.00	−0.0864204
$611$	42573.0	2.81885
$612$	−152.000	−0.0100396
$613$	−23497.0	−1.54818	−0.774090	−	0.633075i	$-0.781792\pi$
$613$	−23497.0	−1.54818	−0.774090	+	0.633075i	$0.781792\pi$
$614$	1746.00	0.114760
$615$	−6195.00	−0.406189
$616$	−1024.00	−0.0669775
$617$	−13221.0	−0.862654	−0.431327	−	0.902196i	$-0.641954\pi$
$617$	−13221.0	−0.862654	−0.431327	+	0.902196i	$0.641954\pi$
$618$	16320.0	1.06228
$619$	15316.0	0.994511	0.497255	−	0.867604i	$-0.334341\pi$
$619$	15316.0	0.994511	0.497255	+	0.867604i	$0.334341\pi$
$620$	−1584.00	−0.102605
$621$	−9715.00	−0.627777
$622$	8360.00	0.538916
$623$	43168.0	2.77607
$624$	−5520.00	−0.354130
$625$	12331.0	0.789184
$626$	−6330.00	−0.404150
$627$	0	0
$628$	−4212.00	−0.267639
$629$	−266.000	−0.0168619
$630$	384.000	0.0242840
$631$	−6049.00	−0.381627	−0.190814	−	0.981626i	$-0.561113\pi$
$631$	−6049.00	−0.381627	−0.190814	+	0.981626i	$0.561113\pi$
$632$	2792.00	0.175728
$633$	11825.0	0.742499
$634$	9078.00	0.568665
$635$	5961.00	0.372528
$636$	7660.00	0.477577
$637$	−46989.0	−2.92272
$638$	408.000	0.0253180
$639$	−1402.00	−0.0867954
$640$	384.000	0.0237171
$641$	−24089.0	−1.48433	−0.742167	−	0.670215i	$-0.766202\pi$
$641$	−24089.0	−1.48433	−0.742167	+	0.670215i	$0.766202\pi$
$642$	20600.0	1.26638
$643$	1633.00	0.100154	0.0500772	−	0.998745i	$-0.484053\pi$
$643$	1633.00	0.100154	0.0500772	+	0.998745i	$0.484053\pi$
$644$	−8576.00	−0.524754
$645$	1935.00	0.118125
$646$	0	0
$647$	14592.0	0.886663	0.443331	−	0.896358i	$-0.353797\pi$
$647$	14592.0	0.886663	0.443331	+	0.896358i	$0.353797\pi$
$648$	−5368.00	−0.325424
$649$	−2396.00	−0.144917
$650$	16008.0	0.965978
$651$	21120.0	1.27152
$652$	272.000	0.0163379
$653$	−23430.0	−1.40411	−0.702057	−	0.712121i	$-0.747735\pi$
$653$	−23430.0	−1.40411	−0.702057	+	0.712121i	$0.747735\pi$
$654$	10550.0	0.630792
$655$	−5409.00	−0.322667
$656$	−6608.00	−0.393291
$657$	−2030.00	−0.120545
$658$	39488.0	2.33952
$659$	4135.00	0.244426	0.122213	−	0.992504i	$-0.461001\pi$
$659$	4135.00	0.244426	0.122213	+	0.992504i	$0.461001\pi$
$660$	240.000	0.0141545
$661$	−8285.00	−0.487518	−0.243759	−	0.969836i	$-0.578381\pi$
$661$	−8285.00	−0.487518	−0.243759	+	0.969836i	$0.578381\pi$
$662$	7320.00	0.429758
$663$	−6555.00	−0.383975
$664$	−4736.00	−0.276796
$665$	0	0
$666$	56.0000	0.00325819
$667$	3417.00	0.198361
$668$	−3684.00	−0.213381
$669$	−12195.0	−0.704762
$670$	−1350.00	−0.0778434
$671$	−868.000	−0.0499386
$672$	−5120.00	−0.293911
$673$	23990.0	1.37407	0.687033	−	0.726626i	$-0.258913\pi$
$673$	23990.0	1.37407	0.687033	+	0.726626i	$0.258913\pi$
$674$	−10346.0	−0.591266
$675$	16820.0	0.959114
$676$	10256.0	0.583523
$677$	690.000	0.0391711	0.0195856	−	0.999808i	$-0.493765\pi$
$677$	690.000	0.0391711	0.0195856	+	0.999808i	$0.493765\pi$
$678$	10060.0	0.569841
$679$	19616.0	1.10868
$680$	456.000	0.0257159
$681$	−8540.00	−0.480548
$682$	−1056.00	−0.0592908
$683$	5760.00	0.322694	0.161347	−	0.986898i	$-0.448416\pi$
$683$	5760.00	0.322694	0.161347	+	0.986898i	$0.448416\pi$
$684$	0	0
$685$	−2007.00	−0.111947
$686$	−21632.0	−1.20396
$687$	23090.0	1.28230
$688$	2064.00	0.114374
$689$	−26427.0	−1.46123
$690$	2010.00	0.110898
$691$	4348.00	0.239372	0.119686	−	0.992812i	$-0.461811\pi$
$691$	4348.00	0.239372	0.119686	+	0.992812i	$0.461811\pi$
$692$	−7572.00	−0.415960
$693$	256.000	0.0140327
$694$	−17182.0	−0.939798
$695$	−8175.00	−0.446180
$696$	2040.00	0.111101
$697$	−7847.00	−0.426437
$698$	13892.0	0.753324
$699$	16095.0	0.870914
$700$	14848.0	0.801717
$701$	−10289.0	−0.554365	−0.277183	−	0.960817i	$-0.589401\pi$
$701$	−10289.0	−0.554365	−0.277183	+	0.960817i	$0.589401\pi$
$702$	20010.0	1.07582
$703$	0	0
$704$	256.000	0.0137051
$705$	−9255.00	−0.494416
$706$	−16452.0	−0.877024
$707$	−39520.0	−2.10227
$708$	−11980.0	−0.635927
$709$	−30745.0	−1.62857	−0.814283	−	0.580469i	$-0.802869\pi$
$709$	−30745.0	−1.62857	−0.814283	+	0.580469i	$0.802869\pi$
$710$	4206.00	0.222322
$711$	−698.000	−0.0368172
$712$	−10792.0	−0.568044
$713$	−8844.00	−0.464531
$714$	−6080.00	−0.318681
$715$	−828.000	−0.0433083
$716$	−80.0000	−0.00417562
$717$	−21180.0	−1.10318
$718$	22770.0	1.18352
$719$	841.000	0.0436217	0.0218109	−	0.999762i	$-0.493057\pi$
$719$	841.000	0.0436217	0.0218109	+	0.999762i	$0.493057\pi$
$720$	−96.0000	−0.00496904
$721$	−52224.0	−2.69754
$722$	0	0
$723$	−12145.0	−0.624727
$724$	7356.00	0.377602
$725$	−5916.00	−0.303055
$726$	−13150.0	−0.672235
$727$	−271.000	−0.0138251	−0.00691254	−	0.999976i	$-0.502200\pi$
$727$	−271.000	−0.0138251	−0.00691254	+	0.999976i	$0.502200\pi$
$728$	17664.0	0.899274
$729$	20917.0	1.06269
$730$	6090.00	0.308769
$731$	2451.00	0.124013
$732$	−4340.00	−0.219141
$733$	−8102.00	−0.408259	−0.204130	−	0.978944i	$-0.565436\pi$
$733$	−8102.00	−0.408259	−0.204130	+	0.978944i	$0.565436\pi$
$734$	−5906.00	−0.296995
$735$	10215.0	0.512634
$736$	2144.00	0.107376
$737$	−900.000	−0.0449823
$738$	1652.00	0.0823997
$739$	15649.0	0.778969	0.389484	−	0.921033i	$-0.372653\pi$
$739$	15649.0	0.778969	0.389484	+	0.921033i	$0.372653\pi$
$740$	−168.000	−0.00834568
$741$	0	0
$742$	−24512.0	−1.21275
$743$	−10335.0	−0.510302	−0.255151	−	0.966901i	$-0.582125\pi$
$743$	−10335.0	−0.510302	−0.255151	+	0.966901i	$0.582125\pi$
$744$	−5280.00	−0.260180
$745$	213.000	0.0104748
$746$	10012.0	0.491374
$747$	1184.00	0.0579924
$748$	304.000	0.0148601
$749$	−65920.0	−3.21584
$750$	−7230.00	−0.352003
$751$	−14669.0	−0.712756	−0.356378	−	0.934342i	$-0.615988\pi$
$751$	−14669.0	−0.712756	−0.356378	+	0.934342i	$0.615988\pi$
$752$	−9872.00	−0.478716
$753$	1215.00	0.0588009
$754$	−7038.00	−0.339932
$755$	−1968.00	−0.0948647
$756$	18560.0	0.892884
$757$	−41437.0	−1.98950	−0.994751	−	0.102323i	$-0.967373\pi$
$757$	−41437.0	−1.98950	−0.994751	+	0.102323i	$0.967373\pi$
$758$	13528.0	0.648231
$759$	1340.00	0.0640829
$760$	0	0
$761$	−34258.0	−1.63187	−0.815934	−	0.578145i	$-0.803777\pi$
$761$	−34258.0	−1.63187	−0.815934	+	0.578145i	$0.803777\pi$
$762$	19870.0	0.944638
$763$	−33760.0	−1.60183
$764$	11968.0	0.566737
$765$	−114.000	−0.00538782
$766$	−9926.00	−0.468200
$767$	41331.0	1.94573
$768$	1280.00	0.0601407
$769$	6855.00	0.321453	0.160727	−	0.986999i	$-0.448616\pi$
$769$	6855.00	0.321453	0.160727	+	0.986999i	$0.448616\pi$
$770$	−768.000	−0.0359439
$771$	5235.00	0.244532
$772$	−5572.00	−0.259768
$773$	−29457.0	−1.37063	−0.685313	−	0.728248i	$-0.740335\pi$
$773$	−29457.0	−1.37063	−0.685313	+	0.728248i	$0.740335\pi$
$774$	−516.000	−0.0239628
$775$	15312.0	0.709707
$776$	−4904.00	−0.226860
$777$	2240.00	0.103423
$778$	7246.00	0.333910
$779$	0	0
$780$	−4140.00	−0.190046
$781$	2804.00	0.128470
$782$	2546.00	0.116426
$783$	−7395.00	−0.337517
$784$	10896.0	0.496356
$785$	−3159.00	−0.143630
$786$	−18030.0	−0.818205
$787$	20716.0	0.938305	0.469152	−	0.883117i	$-0.344560\pi$
$787$	20716.0	0.938305	0.469152	+	0.883117i	$0.344560\pi$
$788$	−16856.0	−0.762018
$789$	9525.00	0.429783
$790$	2094.00	0.0943053
$791$	−32192.0	−1.44705
$792$	−64.0000	−0.00287139
$793$	14973.0	0.670500
$794$	−15258.0	−0.681972
$795$	5745.00	0.256295
$796$	3068.00	0.136611
$797$	3722.00	0.165420	0.0827102	−	0.996574i	$-0.473642\pi$
$797$	3722.00	0.165420	0.0827102	+	0.996574i	$0.473642\pi$
$798$	0	0
$799$	−11723.0	−0.519061
$800$	−3712.00	−0.164049
$801$	2698.00	0.119013
$802$	−18234.0	−0.802824
$803$	4060.00	0.178424
$804$	−4500.00	−0.197391
$805$	−6432.00	−0.281613
$806$	18216.0	0.796069
$807$	−29165.0	−1.27219
$808$	9880.00	0.430170
$809$	11358.0	0.493604	0.246802	−	0.969066i	$-0.420620\pi$
$809$	11358.0	0.493604	0.246802	+	0.969066i	$0.420620\pi$
$810$	−4026.00	−0.174641
$811$	8479.00	0.367124	0.183562	−	0.983008i	$-0.441237\pi$
$811$	8479.00	0.367124	0.183562	+	0.983008i	$0.441237\pi$
$812$	−6528.00	−0.282128
$813$	−18635.0	−0.803884
$814$	−112.000	−0.00482260
$815$	204.000	0.00876786
$816$	1520.00	0.0652091
$817$	0	0
$818$	9870.00	0.421878
$819$	−4416.00	−0.188410
$820$	−4956.00	−0.211062
$821$	13371.0	0.568394	0.284197	−	0.958766i	$-0.408273\pi$
$821$	13371.0	0.568394	0.284197	+	0.958766i	$0.408273\pi$
$822$	−6690.00	−0.283869
$823$	−26585.0	−1.12600	−0.562998	−	0.826458i	$-0.690352\pi$
$823$	−26585.0	−1.12600	−0.562998	+	0.826458i	$0.690352\pi$
$824$	13056.0	0.551975
$825$	−2320.00	−0.0979055
$826$	38336.0	1.61487
$827$	36603.0	1.53907	0.769535	−	0.638605i	$-0.220488\pi$
$827$	36603.0	1.53907	0.769535	+	0.638605i	$0.220488\pi$
$828$	−536.000	−0.0224967
$829$	31238.0	1.30873	0.654367	−	0.756177i	$-0.272935\pi$
$829$	31238.0	1.30873	0.654367	+	0.756177i	$0.272935\pi$
$830$	−3552.00	−0.148544
$831$	−26470.0	−1.10497
$832$	−4416.00	−0.184011
$833$	12939.0	0.538187
$834$	−27250.0	−1.13140
$835$	−2763.00	−0.114512
$836$	0	0
$837$	19140.0	0.790412
$838$	13032.0	0.537211
$839$	30657.0	1.26150	0.630749	−	0.775987i	$-0.282748\pi$
$839$	30657.0	1.26150	0.630749	+	0.775987i	$0.282748\pi$
$840$	−3840.00	−0.157729
$841$	−21788.0	−0.893354
$842$	21830.0	0.893482
$843$	6875.00	0.280887
$844$	9460.00	0.385814
$845$	7692.00	0.313151
$846$	2468.00	0.100297
$847$	42080.0	1.70707
$848$	6128.00	0.248156
$849$	−6535.00	−0.264170
$850$	−4408.00	−0.177874
$851$	−938.000	−0.0377840
$852$	14020.0	0.563753
$853$	4443.00	0.178342	0.0891708	−	0.996016i	$-0.471578\pi$
$853$	4443.00	0.178342	0.0891708	+	0.996016i	$0.471578\pi$
$854$	13888.0	0.556484
$855$	0	0
$856$	16480.0	0.658031
$857$	−6969.00	−0.277779	−0.138889	−	0.990308i	$-0.544353\pi$
$857$	−6969.00	−0.277779	−0.138889	+	0.990308i	$0.544353\pi$
$858$	−2760.00	−0.109819
$859$	39319.0	1.56175	0.780877	−	0.624685i	$-0.214772\pi$
$859$	39319.0	1.56175	0.780877	+	0.624685i	$0.214772\pi$
$860$	1548.00	0.0613795
$861$	66080.0	2.61556
$862$	−11018.0	−0.435353
$863$	9380.00	0.369987	0.184994	−	0.982740i	$-0.440774\pi$
$863$	9380.00	0.369987	0.184994	+	0.982740i	$0.440774\pi$
$864$	−4640.00	−0.182704
$865$	−5679.00	−0.223228
$866$	−7506.00	−0.294531
$867$	−22760.0	−0.891546
$868$	16896.0	0.660700
$869$	1396.00	0.0544949
$870$	1530.00	0.0596228
$871$	15525.0	0.603955
$872$	8440.00	0.327769
$873$	1226.00	0.0475301
$874$	0	0
$875$	23136.0	0.893874
$876$	20300.0	0.782961
$877$	−10249.0	−0.394623	−0.197311	−	0.980341i	$-0.563221\pi$
$877$	−10249.0	−0.394623	−0.197311	+	0.980341i	$0.563221\pi$
$878$	15626.0	0.600629
$879$	19090.0	0.732525
$880$	192.000	0.00735491
$881$	−28698.0	−1.09746	−0.548729	−	0.836000i	$-0.684888\pi$
$881$	−28698.0	−1.09746	−0.548729	+	0.836000i	$0.684888\pi$
$882$	−2724.00	−0.103993
$883$	31779.0	1.21115	0.605577	−	0.795787i	$-0.292942\pi$
$883$	31779.0	1.21115	0.605577	+	0.795787i	$0.292942\pi$
$884$	−5244.00	−0.199519
$885$	−8985.00	−0.341274
$886$	−12234.0	−0.463893
$887$	3567.00	0.135026	0.0675130	−	0.997718i	$-0.478494\pi$
$887$	3567.00	0.135026	0.0675130	+	0.997718i	$0.478494\pi$
$888$	−560.000	−0.0211626
$889$	−63584.0	−2.39881
$890$	−8094.00	−0.304844
$891$	−2684.00	−0.100917
$892$	−9756.00	−0.366205
$893$	0	0
$894$	710.000	0.0265615
$895$	−60.0000	−0.00224087
$896$	−4096.00	−0.152721
$897$	−23115.0	−0.860410
$898$	−14292.0	−0.531103
$899$	−6732.00	−0.249749
$900$	928.000	0.0343704
$901$	7277.00	0.269070
$902$	−3304.00	−0.121964
$903$	−20640.0	−0.760638
$904$	8048.00	0.296098
$905$	5517.00	0.202642
$906$	−6560.00	−0.240553
$907$	−31079.0	−1.13777	−0.568887	−	0.822416i	$-0.692626\pi$
$907$	−31079.0	−1.13777	−0.568887	+	0.822416i	$0.692626\pi$
$908$	−6832.00	−0.249700
$909$	−2470.00	−0.0901262
$910$	13248.0	0.482601
$911$	32856.0	1.19492	0.597458	−	0.801900i	$-0.296178\pi$
$911$	32856.0	1.19492	0.597458	+	0.801900i	$0.296178\pi$
$912$	0	0
$913$	−2368.00	−0.0858372
$914$	−36236.0	−1.31136
$915$	−3255.00	−0.117603
$916$	18472.0	0.666301
$917$	57696.0	2.07774
$918$	−5510.00	−0.198101
$919$	−7736.00	−0.277679	−0.138840	−	0.990315i	$-0.544337\pi$
$919$	−7736.00	−0.277679	−0.138840	+	0.990315i	$0.544337\pi$
$920$	1608.00	0.0576241
$921$	4365.00	0.156169
$922$	33870.0	1.20981
$923$	−48369.0	−1.72490
$924$	−2560.00	−0.0911448
$925$	1624.00	0.0577263
$926$	−15576.0	−0.552764
$927$	−3264.00	−0.115646
$928$	1632.00	0.0577296
$929$	30519.0	1.07782	0.538911	−	0.842363i	$-0.318836\pi$
$929$	30519.0	1.07782	0.538911	+	0.842363i	$0.318836\pi$
$930$	−3960.00	−0.139627
$931$	0	0
$932$	12876.0	0.452540
$933$	20900.0	0.733371
$934$	25000.0	0.875830
$935$	228.000	0.00797476
$936$	1104.00	0.0385527
$937$	9407.00	0.327976	0.163988	−	0.986462i	$-0.447564\pi$
$937$	9407.00	0.327976	0.163988	+	0.986462i	$0.447564\pi$
$938$	14400.0	0.501254
$939$	−15825.0	−0.549978
$940$	−7404.00	−0.256906
$941$	26815.0	0.928952	0.464476	−	0.885586i	$-0.346243\pi$
$941$	26815.0	0.928952	0.464476	+	0.885586i	$0.346243\pi$
$942$	−10530.0	−0.364210
$943$	−27671.0	−0.955559
$944$	−9584.00	−0.330437
$945$	13920.0	0.479172
$946$	1032.00	0.0354685
$947$	17449.0	0.598750	0.299375	−	0.954136i	$-0.403222\pi$
$947$	17449.0	0.598750	0.299375	+	0.954136i	$0.403222\pi$
$948$	6980.00	0.239135
$949$	−70035.0	−2.39561
$950$	0	0
$951$	22695.0	0.773855
$952$	−4864.00	−0.165592
$953$	−39873.0	−1.35531	−0.677656	−	0.735379i	$-0.737004\pi$
$953$	−39873.0	−1.35531	−0.677656	+	0.735379i	$0.737004\pi$
$954$	−1532.00	−0.0519920
$955$	8976.00	0.304143
$956$	−16944.0	−0.573230
$957$	1020.00	0.0344534
$958$	−24210.0	−0.816482
$959$	21408.0	0.720855
$960$	960.000	0.0322749
$961$	−12367.0	−0.415125
$962$	1932.00	0.0647507
$963$	−4120.00	−0.137866
$964$	−9716.00	−0.324618
$965$	−4179.00	−0.139406
$966$	−21440.0	−0.714100
$967$	−11979.0	−0.398365	−0.199182	−	0.979962i	$-0.563829\pi$
$967$	−11979.0	−0.398365	−0.199182	+	0.979962i	$0.563829\pi$
$968$	−10520.0	−0.349303
$969$	0	0
$970$	−3678.00	−0.121746
$971$	18201.0	0.601543	0.300771	−	0.953696i	$-0.402756\pi$
$971$	18201.0	0.601543	0.300771	+	0.953696i	$0.402756\pi$
$972$	2240.00	0.0739177
$973$	87200.0	2.87308
$974$	592.000	0.0194753
$975$	40020.0	1.31453
$976$	−3472.00	−0.113869
$977$	37398.0	1.22463	0.612317	−	0.790612i	$-0.290238\pi$
$977$	37398.0	1.22463	0.612317	+	0.790612i	$0.290238\pi$
$978$	680.000	0.0222331
$979$	−5396.00	−0.176156
$980$	8172.00	0.266372
$981$	−2110.00	−0.0686719
$982$	6426.00	0.208821
$983$	44037.0	1.42885	0.714426	−	0.699711i	$-0.246688\pi$
$983$	44037.0	1.42885	0.714426	+	0.699711i	$0.246688\pi$
$984$	−16520.0	−0.535202
$985$	−12642.0	−0.408942
$986$	1938.00	0.0625948
$987$	98720.0	3.18368
$988$	0	0
$989$	8643.00	0.277888
$990$	−48.0000	−0.00154095
$991$	9829.00	0.315064	0.157532	−	0.987514i	$-0.449646\pi$
$991$	9829.00	0.315064	0.157532	+	0.987514i	$0.449646\pi$
$992$	−4224.00	−0.135194
$993$	18300.0	0.584827
$994$	−44864.0	−1.43159
$995$	2301.00	0.0733132
$996$	−11840.0	−0.376671
$997$	39983.0	1.27008	0.635042	−	0.772477i	$-0.280983\pi$
$997$	39983.0	1.27008	0.635042	+	0.772477i	$0.280983\pi$
$998$	6034.00	0.191386
$999$	2030.00	0.0642906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.e.1.1		1
19.7	even	3		38.4.c.a.11.1	yes	2
19.11	even	3		38.4.c.a.7.1	✓	2
19.18	odd	2		722.4.a.a.1.1		1
57.11	odd	6		342.4.g.d.235.1		2
57.26	odd	6		342.4.g.d.163.1		2
76.7	odd	6		304.4.i.b.49.1		2
76.11	odd	6		304.4.i.b.273.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.a.7.1	✓	2	19.11	even	3
38.4.c.a.11.1	yes	2	19.7	even	3
304.4.i.b.49.1		2	76.7	odd	6
304.4.i.b.273.1		2	76.11	odd	6
342.4.g.d.163.1		2	57.26	odd	6
342.4.g.d.235.1		2	57.11	odd	6
722.4.a.a.1.1		1	19.18	odd	2
722.4.a.e.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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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