LMFDB - Embedded newform 660.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [660,4,Mod(1,660)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(660, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("660.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	660.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:	$38.9412606038$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	660.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} +5.00000 q^{5} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} +5.00000 q^{5} +9.00000 q^{9} +11.0000 q^{11} -42.0000 q^{13} -15.0000 q^{15} -14.0000 q^{17} -52.0000 q^{19} +96.0000 q^{23} +25.0000 q^{25} -27.0000 q^{27} -26.0000 q^{29} -144.000 q^{31} -33.0000 q^{33} +126.000 q^{37} +126.000 q^{39} +58.0000 q^{41} +364.000 q^{43} +45.0000 q^{45} -328.000 q^{47} -343.000 q^{49} +42.0000 q^{51} -50.0000 q^{53} +55.0000 q^{55} +156.000 q^{57} -284.000 q^{59} -794.000 q^{61} -210.000 q^{65} -316.000 q^{67} -288.000 q^{69} -280.000 q^{71} -358.000 q^{73} -75.0000 q^{75} +784.000 q^{79} +81.0000 q^{81} +324.000 q^{83} -70.0000 q^{85} +78.0000 q^{87} -1398.00 q^{89} +432.000 q^{93} -260.000 q^{95} -894.000 q^{97} +99.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	−42.0000	−0.896054	−0.448027	−	0.894020i	$-0.647873\pi$
$13$	−42.0000	−0.896054	−0.448027	+	0.894020i	$0.647873\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	0	0
$17$	−14.0000	−0.199735	−0.0998676	−	0.995001i	$-0.531842\pi$
$17$	−14.0000	−0.199735	−0.0998676	+	0.995001i	$0.531842\pi$
$18$	0	0
$19$	−52.0000	−0.627875	−0.313937	−	0.949444i	$-0.601648\pi$
$19$	−52.0000	−0.627875	−0.313937	+	0.949444i	$0.601648\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	96.0000	0.870321	0.435161	−	0.900353i	$-0.356692\pi$
$23$	96.0000	0.870321	0.435161	+	0.900353i	$0.356692\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−26.0000	−0.166485	−0.0832427	−	0.996529i	$-0.526528\pi$
$29$	−26.0000	−0.166485	−0.0832427	+	0.996529i	$0.526528\pi$
$30$	0	0
$31$	−144.000	−0.834296	−0.417148	−	0.908839i	$-0.636970\pi$
$31$	−144.000	−0.834296	−0.417148	+	0.908839i	$0.636970\pi$
$32$	0	0
$33$	−33.0000	−0.174078
$34$	0	0
$35$	0	0
$36$	0	0
$37$	126.000	0.559845	0.279923	−	0.960023i	$-0.409691\pi$
$37$	126.000	0.559845	0.279923	+	0.960023i	$0.409691\pi$
$38$	0	0
$39$	126.000	0.517337
$40$	0	0
$41$	58.0000	0.220929	0.110464	−	0.993880i	$-0.464766\pi$
$41$	58.0000	0.220929	0.110464	+	0.993880i	$0.464766\pi$
$42$	0	0
$43$	364.000	1.29092	0.645459	−	0.763795i	$-0.276666\pi$
$43$	364.000	1.29092	0.645459	+	0.763795i	$0.276666\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	0	0
$47$	−328.000	−1.01795	−0.508976	−	0.860781i	$-0.669976\pi$
$47$	−328.000	−1.01795	−0.508976	+	0.860781i	$0.669976\pi$
$48$	0	0
$49$	−343.000	−1.00000
$50$	0	0
$51$	42.0000	0.115317
$52$	0	0
$53$	−50.0000	−0.129585	−0.0647927	−	0.997899i	$-0.520639\pi$
$53$	−50.0000	−0.129585	−0.0647927	+	0.997899i	$0.520639\pi$
$54$	0	0
$55$	55.0000	0.134840
$56$	0	0
$57$	156.000	0.362504
$58$	0	0
$59$	−284.000	−0.626672	−0.313336	−	0.949642i	$-0.601447\pi$
$59$	−284.000	−0.626672	−0.313336	+	0.949642i	$0.601447\pi$
$60$	0	0
$61$	−794.000	−1.66658	−0.833289	−	0.552837i	$-0.813545\pi$
$61$	−794.000	−1.66658	−0.833289	+	0.552837i	$0.813545\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−210.000	−0.400728
$66$	0	0
$67$	−316.000	−0.576202	−0.288101	−	0.957600i	$-0.593024\pi$
$67$	−316.000	−0.576202	−0.288101	+	0.957600i	$0.593024\pi$
$68$	0	0
$69$	−288.000	−0.502480
$70$	0	0
$71$	−280.000	−0.468027	−0.234013	−	0.972233i	$-0.575186\pi$
$71$	−280.000	−0.468027	−0.234013	+	0.972233i	$0.575186\pi$
$72$	0	0
$73$	−358.000	−0.573983	−0.286991	−	0.957933i	$-0.592655\pi$
$73$	−358.000	−0.573983	−0.286991	+	0.957933i	$0.592655\pi$
$74$	0	0
$75$	−75.0000	−0.115470
$76$	0	0
$77$	0	0
$78$	0	0
$79$	784.000	1.11654	0.558271	−	0.829658i	$-0.311465\pi$
$79$	784.000	1.11654	0.558271	+	0.829658i	$0.311465\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	324.000	0.428477	0.214239	−	0.976781i	$-0.431273\pi$
$83$	324.000	0.428477	0.214239	+	0.976781i	$0.431273\pi$
$84$	0	0
$85$	−70.0000	−0.0893243
$86$	0	0
$87$	78.0000	0.0961204
$88$	0	0
$89$	−1398.00	−1.66503	−0.832515	−	0.554002i	$-0.813100\pi$
$89$	−1398.00	−1.66503	−0.832515	+	0.554002i	$0.813100\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	432.000	0.481681
$94$	0	0
$95$	−260.000	−0.280794
$96$	0	0
$97$	−894.000	−0.935793	−0.467897	−	0.883783i	$-0.654988\pi$
$97$	−894.000	−0.935793	−0.467897	+	0.883783i	$0.654988\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	0	0
$101$	−1730.00	−1.70437	−0.852185	−	0.523240i	$-0.824723\pi$
$101$	−1730.00	−1.70437	−0.852185	+	0.523240i	$0.824723\pi$
$102$	0	0
$103$	−1424.00	−1.36224	−0.681121	−	0.732171i	$-0.738507\pi$
$103$	−1424.00	−1.36224	−0.681121	+	0.732171i	$0.738507\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−260.000	−0.234908	−0.117454	−	0.993078i	$-0.537473\pi$
$107$	−260.000	−0.234908	−0.117454	+	0.993078i	$0.537473\pi$
$108$	0	0
$109$	374.000	0.328649	0.164324	−	0.986406i	$-0.447456\pi$
$109$	374.000	0.328649	0.164324	+	0.986406i	$0.447456\pi$
$110$	0	0
$111$	−378.000	−0.323227
$112$	0	0
$113$	−494.000	−0.411253	−0.205627	−	0.978631i	$-0.565923\pi$
$113$	−494.000	−0.411253	−0.205627	+	0.978631i	$0.565923\pi$
$114$	0	0
$115$	480.000	0.389219
$116$	0	0
$117$	−378.000	−0.298685
$118$	0	0
$119$	0	0
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	−174.000	−0.127553
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−280.000	−0.195638	−0.0978188	−	0.995204i	$-0.531187\pi$
$127$	−280.000	−0.195638	−0.0978188	+	0.995204i	$0.531187\pi$
$128$	0	0
$129$	−1092.00	−0.745312
$130$	0	0
$131$	1420.00	0.947069	0.473534	−	0.880775i	$-0.342978\pi$
$131$	1420.00	0.947069	0.473534	+	0.880775i	$0.342978\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−135.000	−0.0860663
$136$	0	0
$137$	−1830.00	−1.14122	−0.570611	−	0.821220i	$-0.693294\pi$
$137$	−1830.00	−1.14122	−0.570611	+	0.821220i	$0.693294\pi$
$138$	0	0
$139$	−1772.00	−1.08129	−0.540644	−	0.841251i	$-0.681819\pi$
$139$	−1772.00	−1.08129	−0.540644	+	0.841251i	$0.681819\pi$
$140$	0	0
$141$	984.000	0.587715
$142$	0	0
$143$	−462.000	−0.270170
$144$	0	0
$145$	−130.000	−0.0744546
$146$	0	0
$147$	1029.00	0.577350
$148$	0	0
$149$	−2514.00	−1.38225	−0.691124	−	0.722736i	$-0.742884\pi$
$149$	−2514.00	−1.38225	−0.691124	+	0.722736i	$0.742884\pi$
$150$	0	0
$151$	248.000	0.133655	0.0668277	−	0.997765i	$-0.478712\pi$
$151$	248.000	0.133655	0.0668277	+	0.997765i	$0.478712\pi$
$152$	0	0
$153$	−126.000	−0.0665784
$154$	0	0
$155$	−720.000	−0.373108
$156$	0	0
$157$	870.000	0.442252	0.221126	−	0.975245i	$-0.429027\pi$
$157$	870.000	0.442252	0.221126	+	0.975245i	$0.429027\pi$
$158$	0	0
$159$	150.000	0.0748162
$160$	0	0
$161$	0	0
$162$	0	0
$163$	2548.00	1.22439	0.612193	−	0.790709i	$-0.290288\pi$
$163$	2548.00	1.22439	0.612193	+	0.790709i	$0.290288\pi$
$164$	0	0
$165$	−165.000	−0.0778499
$166$	0	0
$167$	−384.000	−0.177933	−0.0889665	−	0.996035i	$-0.528356\pi$
$167$	−384.000	−0.177933	−0.0889665	+	0.996035i	$0.528356\pi$
$168$	0	0
$169$	−433.000	−0.197087
$170$	0	0
$171$	−468.000	−0.209292
$172$	0	0
$173$	22.0000	0.00966838	0.00483419	−	0.999988i	$-0.498461\pi$
$173$	22.0000	0.00966838	0.00483419	+	0.999988i	$0.498461\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	852.000	0.361809
$178$	0	0
$179$	1548.00	0.646385	0.323193	−	0.946333i	$-0.395244\pi$
$179$	1548.00	0.646385	0.323193	+	0.946333i	$0.395244\pi$
$180$	0	0
$181$	−754.000	−0.309637	−0.154819	−	0.987943i	$-0.549479\pi$
$181$	−754.000	−0.309637	−0.154819	+	0.987943i	$0.549479\pi$
$182$	0	0
$183$	2382.00	0.962199
$184$	0	0
$185$	630.000	0.250370
$186$	0	0
$187$	−154.000	−0.0602224
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−2640.00	−1.00012	−0.500062	−	0.865990i	$-0.666689\pi$
$191$	−2640.00	−1.00012	−0.500062	+	0.865990i	$0.666689\pi$
$192$	0	0
$193$	4738.00	1.76709	0.883546	−	0.468345i	$-0.155149\pi$
$193$	4738.00	1.76709	0.883546	+	0.468345i	$0.155149\pi$
$194$	0	0
$195$	630.000	0.231360
$196$	0	0
$197$	−1410.00	−0.509941	−0.254970	−	0.966949i	$-0.582066\pi$
$197$	−1410.00	−0.509941	−0.254970	+	0.966949i	$0.582066\pi$
$198$	0	0
$199$	2360.00	0.840683	0.420342	−	0.907366i	$-0.361910\pi$
$199$	2360.00	0.840683	0.420342	+	0.907366i	$0.361910\pi$
$200$	0	0
$201$	948.000	0.332670
$202$	0	0
$203$	0	0
$204$	0	0
$205$	290.000	0.0988023
$206$	0	0
$207$	864.000	0.290107
$208$	0	0
$209$	−572.000	−0.189311
$210$	0	0
$211$	2044.00	0.666895	0.333447	−	0.942769i	$-0.391788\pi$
$211$	2044.00	0.666895	0.333447	+	0.942769i	$0.391788\pi$
$212$	0	0
$213$	840.000	0.270215
$214$	0	0
$215$	1820.00	0.577316
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1074.00	0.331389
$220$	0	0
$221$	588.000	0.178974
$222$	0	0
$223$	3864.00	1.16033	0.580163	−	0.814501i	$-0.302989\pi$
$223$	3864.00	1.16033	0.580163	+	0.814501i	$0.302989\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	0	0
$227$	68.0000	0.0198825	0.00994123	−	0.999951i	$-0.496836\pi$
$227$	68.0000	0.0198825	0.00994123	+	0.999951i	$0.496836\pi$
$228$	0	0
$229$	−1058.00	−0.305304	−0.152652	−	0.988280i	$-0.548781\pi$
$229$	−1058.00	−0.305304	−0.152652	+	0.988280i	$0.548781\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	3258.00	0.916046	0.458023	−	0.888940i	$-0.348558\pi$
$233$	3258.00	0.916046	0.458023	+	0.888940i	$0.348558\pi$
$234$	0	0
$235$	−1640.00	−0.455242
$236$	0	0
$237$	−2352.00	−0.644636
$238$	0	0
$239$	−5392.00	−1.45933	−0.729664	−	0.683806i	$-0.760324\pi$
$239$	−5392.00	−1.45933	−0.729664	+	0.683806i	$0.760324\pi$
$240$	0	0
$241$	978.000	0.261405	0.130702	−	0.991422i	$-0.458277\pi$
$241$	978.000	0.261405	0.130702	+	0.991422i	$0.458277\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	−1715.00	−0.447214
$246$	0	0
$247$	2184.00	0.562610
$248$	0	0
$249$	−972.000	−0.247382
$250$	0	0
$251$	−5420.00	−1.36298	−0.681489	−	0.731829i	$-0.738667\pi$
$251$	−5420.00	−1.36298	−0.681489	+	0.731829i	$0.738667\pi$
$252$	0	0
$253$	1056.00	0.262412
$254$	0	0
$255$	210.000	0.0515714
$256$	0	0
$257$	−1150.00	−0.279125	−0.139562	−	0.990213i	$-0.544570\pi$
$257$	−1150.00	−0.279125	−0.139562	+	0.990213i	$0.544570\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−234.000	−0.0554952
$262$	0	0
$263$	4464.00	1.04662	0.523312	−	0.852141i	$-0.324696\pi$
$263$	4464.00	1.04662	0.523312	+	0.852141i	$0.324696\pi$
$264$	0	0
$265$	−250.000	−0.0579524
$266$	0	0
$267$	4194.00	0.961306
$268$	0	0
$269$	−10.0000	−0.00226658	−0.00113329	−	0.999999i	$-0.500361\pi$
$269$	−10.0000	−0.00226658	−0.00113329	+	0.999999i	$0.500361\pi$
$270$	0	0
$271$	5440.00	1.21940	0.609698	−	0.792634i	$-0.291291\pi$
$271$	5440.00	1.21940	0.609698	+	0.792634i	$0.291291\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	275.000	0.0603023
$276$	0	0
$277$	4878.00	1.05809	0.529044	−	0.848594i	$-0.322550\pi$
$277$	4878.00	1.05809	0.529044	+	0.848594i	$0.322550\pi$
$278$	0	0
$279$	−1296.00	−0.278099
$280$	0	0
$281$	−630.000	−0.133746	−0.0668730	−	0.997761i	$-0.521302\pi$
$281$	−630.000	−0.133746	−0.0668730	+	0.997761i	$0.521302\pi$
$282$	0	0
$283$	1596.00	0.335238	0.167619	−	0.985852i	$-0.446392\pi$
$283$	1596.00	0.335238	0.167619	+	0.985852i	$0.446392\pi$
$284$	0	0
$285$	780.000	0.162117
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−4717.00	−0.960106
$290$	0	0
$291$	2682.00	0.540280
$292$	0	0
$293$	−4866.00	−0.970221	−0.485111	−	0.874453i	$-0.661221\pi$
$293$	−4866.00	−0.970221	−0.485111	+	0.874453i	$0.661221\pi$
$294$	0	0
$295$	−1420.00	−0.280256
$296$	0	0
$297$	−297.000	−0.0580259
$298$	0	0
$299$	−4032.00	−0.779855
$300$	0	0
$301$	0	0
$302$	0	0
$303$	5190.00	0.984019
$304$	0	0
$305$	−3970.00	−0.745317
$306$	0	0
$307$	4084.00	0.759238	0.379619	−	0.925143i	$-0.376055\pi$
$307$	4084.00	0.759238	0.379619	+	0.925143i	$0.376055\pi$
$308$	0	0
$309$	4272.00	0.786491
$310$	0	0
$311$	7128.00	1.29965	0.649826	−	0.760083i	$-0.274842\pi$
$311$	7128.00	1.29965	0.649826	+	0.760083i	$0.274842\pi$
$312$	0	0
$313$	−1110.00	−0.200450	−0.100225	−	0.994965i	$-0.531956\pi$
$313$	−1110.00	−0.200450	−0.100225	+	0.994965i	$0.531956\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	3814.00	0.675759	0.337879	−	0.941189i	$-0.390290\pi$
$317$	3814.00	0.675759	0.337879	+	0.941189i	$0.390290\pi$
$318$	0	0
$319$	−286.000	−0.0501973
$320$	0	0
$321$	780.000	0.135624
$322$	0	0
$323$	728.000	0.125409
$324$	0	0
$325$	−1050.00	−0.179211
$326$	0	0
$327$	−1122.00	−0.189745
$328$	0	0
$329$	0	0
$330$	0	0
$331$	9188.00	1.52573	0.762867	−	0.646555i	$-0.223791\pi$
$331$	9188.00	1.52573	0.762867	+	0.646555i	$0.223791\pi$
$332$	0	0
$333$	1134.00	0.186615
$334$	0	0
$335$	−1580.00	−0.257685
$336$	0	0
$337$	−6638.00	−1.07298	−0.536491	−	0.843906i	$-0.680250\pi$
$337$	−6638.00	−1.07298	−0.536491	+	0.843906i	$0.680250\pi$
$338$	0	0
$339$	1482.00	0.237437
$340$	0	0
$341$	−1584.00	−0.251550
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−1440.00	−0.224716
$346$	0	0
$347$	3276.00	0.506815	0.253408	−	0.967360i	$-0.418449\pi$
$347$	3276.00	0.506815	0.253408	+	0.967360i	$0.418449\pi$
$348$	0	0
$349$	1638.00	0.251232	0.125616	−	0.992079i	$-0.459909\pi$
$349$	1638.00	0.251232	0.125616	+	0.992079i	$0.459909\pi$
$350$	0	0
$351$	1134.00	0.172446
$352$	0	0
$353$	2786.00	0.420067	0.210034	−	0.977694i	$-0.432643\pi$
$353$	2786.00	0.420067	0.210034	+	0.977694i	$0.432643\pi$
$354$	0	0
$355$	−1400.00	−0.209308
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−4744.00	−0.697434	−0.348717	−	0.937228i	$-0.613383\pi$
$359$	−4744.00	−0.697434	−0.348717	+	0.937228i	$0.613383\pi$
$360$	0	0
$361$	−4155.00	−0.605773
$362$	0	0
$363$	−363.000	−0.0524864
$364$	0	0
$365$	−1790.00	−0.256693
$366$	0	0
$367$	−3368.00	−0.479041	−0.239521	−	0.970891i	$-0.576990\pi$
$367$	−3368.00	−0.479041	−0.239521	+	0.970891i	$0.576990\pi$
$368$	0	0
$369$	522.000	0.0736429
$370$	0	0
$371$	0	0
$372$	0	0
$373$	8430.00	1.17021	0.585106	−	0.810957i	$-0.301053\pi$
$373$	8430.00	1.17021	0.585106	+	0.810957i	$0.301053\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	0	0
$377$	1092.00	0.149180
$378$	0	0
$379$	−2556.00	−0.346419	−0.173210	−	0.984885i	$-0.555414\pi$
$379$	−2556.00	−0.346419	−0.173210	+	0.984885i	$0.555414\pi$
$380$	0	0
$381$	840.000	0.112951
$382$	0	0
$383$	4664.00	0.622244	0.311122	−	0.950370i	$-0.399295\pi$
$383$	4664.00	0.622244	0.311122	+	0.950370i	$0.399295\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	3276.00	0.430306
$388$	0	0
$389$	−3426.00	−0.446543	−0.223271	−	0.974756i	$-0.571674\pi$
$389$	−3426.00	−0.446543	−0.223271	+	0.974756i	$0.571674\pi$
$390$	0	0
$391$	−1344.00	−0.173834
$392$	0	0
$393$	−4260.00	−0.546790
$394$	0	0
$395$	3920.00	0.499333
$396$	0	0
$397$	3862.00	0.488232	0.244116	−	0.969746i	$-0.421502\pi$
$397$	3862.00	0.488232	0.244116	+	0.969746i	$0.421502\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	1330.00	0.165629	0.0828143	−	0.996565i	$-0.473609\pi$
$401$	1330.00	0.165629	0.0828143	+	0.996565i	$0.473609\pi$
$402$	0	0
$403$	6048.00	0.747574
$404$	0	0
$405$	405.000	0.0496904
$406$	0	0
$407$	1386.00	0.168800
$408$	0	0
$409$	−2486.00	−0.300550	−0.150275	−	0.988644i	$-0.548016\pi$
$409$	−2486.00	−0.300550	−0.150275	+	0.988644i	$0.548016\pi$
$410$	0	0
$411$	5490.00	0.658885
$412$	0	0
$413$	0	0
$414$	0	0
$415$	1620.00	0.191621
$416$	0	0
$417$	5316.00	0.624282
$418$	0	0
$419$	−10788.0	−1.25782	−0.628912	−	0.777476i	$-0.716499\pi$
$419$	−10788.0	−1.25782	−0.628912	+	0.777476i	$0.716499\pi$
$420$	0	0
$421$	13886.0	1.60751	0.803756	−	0.594960i	$-0.202832\pi$
$421$	13886.0	1.60751	0.803756	+	0.594960i	$0.202832\pi$
$422$	0	0
$423$	−2952.00	−0.339317
$424$	0	0
$425$	−350.000	−0.0399470
$426$	0	0
$427$	0	0
$428$	0	0
$429$	1386.00	0.155983
$430$	0	0
$431$	6752.00	0.754600	0.377300	−	0.926091i	$-0.376853\pi$
$431$	6752.00	0.754600	0.377300	+	0.926091i	$0.376853\pi$
$432$	0	0
$433$	5618.00	0.623519	0.311760	−	0.950161i	$-0.399082\pi$
$433$	5618.00	0.623519	0.311760	+	0.950161i	$0.399082\pi$
$434$	0	0
$435$	390.000	0.0429864
$436$	0	0
$437$	−4992.00	−0.546453
$438$	0	0
$439$	104.000	0.0113067	0.00565336	−	0.999984i	$-0.498200\pi$
$439$	104.000	0.0113067	0.00565336	+	0.999984i	$0.498200\pi$
$440$	0	0
$441$	−3087.00	−0.333333
$442$	0	0
$443$	−16420.0	−1.76103	−0.880517	−	0.474015i	$-0.842804\pi$
$443$	−16420.0	−1.76103	−0.880517	+	0.474015i	$0.842804\pi$
$444$	0	0
$445$	−6990.00	−0.744624
$446$	0	0
$447$	7542.00	0.798041
$448$	0	0
$449$	−10110.0	−1.06263	−0.531314	−	0.847175i	$-0.678302\pi$
$449$	−10110.0	−1.06263	−0.531314	+	0.847175i	$0.678302\pi$
$450$	0	0
$451$	638.000	0.0666125
$452$	0	0
$453$	−744.000	−0.0771659
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−8454.00	−0.865342	−0.432671	−	0.901552i	$-0.642429\pi$
$457$	−8454.00	−0.865342	−0.432671	+	0.901552i	$0.642429\pi$
$458$	0	0
$459$	378.000	0.0384391
$460$	0	0
$461$	5622.00	0.567988	0.283994	−	0.958826i	$-0.408340\pi$
$461$	5622.00	0.567988	0.283994	+	0.958826i	$0.408340\pi$
$462$	0	0
$463$	7912.00	0.794172	0.397086	−	0.917781i	$-0.370021\pi$
$463$	7912.00	0.794172	0.397086	+	0.917781i	$0.370021\pi$
$464$	0	0
$465$	2160.00	0.215414
$466$	0	0
$467$	3412.00	0.338091	0.169046	−	0.985608i	$-0.445932\pi$
$467$	3412.00	0.338091	0.169046	+	0.985608i	$0.445932\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−2610.00	−0.255334
$472$	0	0
$473$	4004.00	0.389226
$474$	0	0
$475$	−1300.00	−0.125575
$476$	0	0
$477$	−450.000	−0.0431951
$478$	0	0
$479$	−5376.00	−0.512809	−0.256405	−	0.966570i	$-0.582538\pi$
$479$	−5376.00	−0.512809	−0.256405	+	0.966570i	$0.582538\pi$
$480$	0	0
$481$	−5292.00	−0.501652
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−4470.00	−0.418499
$486$	0	0
$487$	4608.00	0.428765	0.214382	−	0.976750i	$-0.431226\pi$
$487$	4608.00	0.428765	0.214382	+	0.976750i	$0.431226\pi$
$488$	0	0
$489$	−7644.00	−0.706899
$490$	0	0
$491$	−6300.00	−0.579053	−0.289526	−	0.957170i	$-0.593498\pi$
$491$	−6300.00	−0.579053	−0.289526	+	0.957170i	$0.593498\pi$
$492$	0	0
$493$	364.000	0.0332530
$494$	0	0
$495$	495.000	0.0449467
$496$	0	0
$497$	0	0
$498$	0	0
$499$	620.000	0.0556213	0.0278106	−	0.999613i	$-0.491146\pi$
$499$	620.000	0.0556213	0.0278106	+	0.999613i	$0.491146\pi$
$500$	0	0
$501$	1152.00	0.102730
$502$	0	0
$503$	−3552.00	−0.314863	−0.157431	−	0.987530i	$-0.550321\pi$
$503$	−3552.00	−0.314863	−0.157431	+	0.987530i	$0.550321\pi$
$504$	0	0
$505$	−8650.00	−0.762218
$506$	0	0
$507$	1299.00	0.113788
$508$	0	0
$509$	550.000	0.0478945	0.0239473	−	0.999713i	$-0.492377\pi$
$509$	550.000	0.0478945	0.0239473	+	0.999713i	$0.492377\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	1404.00	0.120835
$514$	0	0
$515$	−7120.00	−0.609213
$516$	0	0
$517$	−3608.00	−0.306924
$518$	0	0
$519$	−66.0000	−0.00558204
$520$	0	0
$521$	−1318.00	−0.110830	−0.0554152	−	0.998463i	$-0.517648\pi$
$521$	−1318.00	−0.110830	−0.0554152	+	0.998463i	$0.517648\pi$
$522$	0	0
$523$	10508.0	0.878552	0.439276	−	0.898352i	$-0.355235\pi$
$523$	10508.0	0.878552	0.439276	+	0.898352i	$0.355235\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	2016.00	0.166638
$528$	0	0
$529$	−2951.00	−0.242541
$530$	0	0
$531$	−2556.00	−0.208891
$532$	0	0
$533$	−2436.00	−0.197964
$534$	0	0
$535$	−1300.00	−0.105054
$536$	0	0
$537$	−4644.00	−0.373191
$538$	0	0
$539$	−3773.00	−0.301511
$540$	0	0
$541$	−10970.0	−0.871788	−0.435894	−	0.899998i	$-0.643568\pi$
$541$	−10970.0	−0.871788	−0.435894	+	0.899998i	$0.643568\pi$
$542$	0	0
$543$	2262.00	0.178769
$544$	0	0
$545$	1870.00	0.146976
$546$	0	0
$547$	−10492.0	−0.820120	−0.410060	−	0.912059i	$-0.634492\pi$
$547$	−10492.0	−0.820120	−0.410060	+	0.912059i	$0.634492\pi$
$548$	0	0
$549$	−7146.00	−0.555526
$550$	0	0
$551$	1352.00	0.104532
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−1890.00	−0.144551
$556$	0	0
$557$	−12138.0	−0.923346	−0.461673	−	0.887050i	$-0.652751\pi$
$557$	−12138.0	−0.923346	−0.461673	+	0.887050i	$0.652751\pi$
$558$	0	0
$559$	−15288.0	−1.15673
$560$	0	0
$561$	462.000	0.0347694
$562$	0	0
$563$	7908.00	0.591976	0.295988	−	0.955192i	$-0.404351\pi$
$563$	7908.00	0.591976	0.295988	+	0.955192i	$0.404351\pi$
$564$	0	0
$565$	−2470.00	−0.183918
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−19542.0	−1.43979	−0.719897	−	0.694080i	$-0.755811\pi$
$569$	−19542.0	−1.43979	−0.719897	+	0.694080i	$0.755811\pi$
$570$	0	0
$571$	22068.0	1.61737	0.808684	−	0.588243i	$-0.200180\pi$
$571$	22068.0	1.61737	0.808684	+	0.588243i	$0.200180\pi$
$572$	0	0
$573$	7920.00	0.577422
$574$	0	0
$575$	2400.00	0.174064
$576$	0	0
$577$	−13246.0	−0.955699	−0.477849	−	0.878442i	$-0.658584\pi$
$577$	−13246.0	−0.955699	−0.477849	+	0.878442i	$0.658584\pi$
$578$	0	0
$579$	−14214.0	−1.02023
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−550.000	−0.0390715
$584$	0	0
$585$	−1890.00	−0.133576
$586$	0	0
$587$	17244.0	1.21250	0.606249	−	0.795275i	$-0.292674\pi$
$587$	17244.0	1.21250	0.606249	+	0.795275i	$0.292674\pi$
$588$	0	0
$589$	7488.00	0.523833
$590$	0	0
$591$	4230.00	0.294414
$592$	0	0
$593$	3922.00	0.271597	0.135799	−	0.990736i	$-0.456640\pi$
$593$	3922.00	0.271597	0.135799	+	0.990736i	$0.456640\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−7080.00	−0.485369
$598$	0	0
$599$	−10296.0	−0.702309	−0.351155	−	0.936318i	$-0.614211\pi$
$599$	−10296.0	−0.702309	−0.351155	+	0.936318i	$0.614211\pi$
$600$	0	0
$601$	−6582.00	−0.446731	−0.223366	−	0.974735i	$-0.571704\pi$
$601$	−6582.00	−0.446731	−0.223366	+	0.974735i	$0.571704\pi$
$602$	0	0
$603$	−2844.00	−0.192067
$604$	0	0
$605$	605.000	0.0406558
$606$	0	0
$607$	−7352.00	−0.491612	−0.245806	−	0.969319i	$-0.579053\pi$
$607$	−7352.00	−0.491612	−0.245806	+	0.969319i	$0.579053\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	13776.0	0.912140
$612$	0	0
$613$	−24098.0	−1.58778	−0.793890	−	0.608061i	$-0.791947\pi$
$613$	−24098.0	−1.58778	−0.793890	+	0.608061i	$0.791947\pi$
$614$	0	0
$615$	−870.000	−0.0570436
$616$	0	0
$617$	13786.0	0.899519	0.449760	−	0.893150i	$-0.351510\pi$
$617$	13786.0	0.899519	0.449760	+	0.893150i	$0.351510\pi$
$618$	0	0
$619$	−7468.00	−0.484918	−0.242459	−	0.970162i	$-0.577954\pi$
$619$	−7468.00	−0.484918	−0.242459	+	0.970162i	$0.577954\pi$
$620$	0	0
$621$	−2592.00	−0.167493
$622$	0	0
$623$	0	0
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	1716.00	0.109299
$628$	0	0
$629$	−1764.00	−0.111821
$630$	0	0
$631$	1464.00	0.0923628	0.0461814	−	0.998933i	$-0.485295\pi$
$631$	1464.00	0.0923628	0.0461814	+	0.998933i	$0.485295\pi$
$632$	0	0
$633$	−6132.00	−0.385032
$634$	0	0
$635$	−1400.00	−0.0874918
$636$	0	0
$637$	14406.0	0.896054
$638$	0	0
$639$	−2520.00	−0.156009
$640$	0	0
$641$	−10878.0	−0.670289	−0.335144	−	0.942167i	$-0.608785\pi$
$641$	−10878.0	−0.670289	−0.335144	+	0.942167i	$0.608785\pi$
$642$	0	0
$643$	532.000	0.0326284	0.0163142	−	0.999867i	$-0.494807\pi$
$643$	532.000	0.0326284	0.0163142	+	0.999867i	$0.494807\pi$
$644$	0	0
$645$	−5460.00	−0.333314
$646$	0	0
$647$	−30240.0	−1.83749	−0.918746	−	0.394850i	$-0.870797\pi$
$647$	−30240.0	−1.83749	−0.918746	+	0.394850i	$0.870797\pi$
$648$	0	0
$649$	−3124.00	−0.188949
$650$	0	0
$651$	0	0
$652$	0	0
$653$	7702.00	0.461566	0.230783	−	0.973005i	$-0.425871\pi$
$653$	7702.00	0.461566	0.230783	+	0.973005i	$0.425871\pi$
$654$	0	0
$655$	7100.00	0.423542
$656$	0	0
$657$	−3222.00	−0.191328
$658$	0	0
$659$	16620.0	0.982433	0.491216	−	0.871038i	$-0.336552\pi$
$659$	16620.0	0.982433	0.491216	+	0.871038i	$0.336552\pi$
$660$	0	0
$661$	−8242.00	−0.484987	−0.242494	−	0.970153i	$-0.577965\pi$
$661$	−8242.00	−0.484987	−0.242494	+	0.970153i	$0.577965\pi$
$662$	0	0
$663$	−1764.00	−0.103330
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−2496.00	−0.144896
$668$	0	0
$669$	−11592.0	−0.669914
$670$	0	0
$671$	−8734.00	−0.502492
$672$	0	0
$673$	−1054.00	−0.0603696	−0.0301848	−	0.999544i	$-0.509610\pi$
$673$	−1054.00	−0.0603696	−0.0301848	+	0.999544i	$0.509610\pi$
$674$	0	0
$675$	−675.000	−0.0384900
$676$	0	0
$677$	12254.0	0.695657	0.347828	−	0.937558i	$-0.386919\pi$
$677$	12254.0	0.695657	0.347828	+	0.937558i	$0.386919\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−204.000	−0.0114791
$682$	0	0
$683$	9100.00	0.509812	0.254906	−	0.966966i	$-0.417955\pi$
$683$	9100.00	0.509812	0.254906	+	0.966966i	$0.417955\pi$
$684$	0	0
$685$	−9150.00	−0.510370
$686$	0	0
$687$	3174.00	0.176267
$688$	0	0
$689$	2100.00	0.116116
$690$	0	0
$691$	8764.00	0.482487	0.241243	−	0.970465i	$-0.422445\pi$
$691$	8764.00	0.482487	0.241243	+	0.970465i	$0.422445\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−8860.00	−0.483567
$696$	0	0
$697$	−812.000	−0.0441272
$698$	0	0
$699$	−9774.00	−0.528879
$700$	0	0
$701$	10022.0	0.539980	0.269990	−	0.962863i	$-0.412980\pi$
$701$	10022.0	0.539980	0.269990	+	0.962863i	$0.412980\pi$
$702$	0	0
$703$	−6552.00	−0.351513
$704$	0	0
$705$	4920.00	0.262834
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−9154.00	−0.484888	−0.242444	−	0.970165i	$-0.577949\pi$
$709$	−9154.00	−0.484888	−0.242444	+	0.970165i	$0.577949\pi$
$710$	0	0
$711$	7056.00	0.372181
$712$	0	0
$713$	−13824.0	−0.726105
$714$	0	0
$715$	−2310.00	−0.120824
$716$	0	0
$717$	16176.0	0.842544
$718$	0	0
$719$	−30544.0	−1.58428	−0.792141	−	0.610338i	$-0.791034\pi$
$719$	−30544.0	−1.58428	−0.792141	+	0.610338i	$0.791034\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−2934.00	−0.150922
$724$	0	0
$725$	−650.000	−0.0332971
$726$	0	0
$727$	−12496.0	−0.637484	−0.318742	−	0.947841i	$-0.603260\pi$
$727$	−12496.0	−0.637484	−0.318742	+	0.947841i	$0.603260\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	−5096.00	−0.257842
$732$	0	0
$733$	1254.00	0.0631890	0.0315945	−	0.999501i	$-0.489941\pi$
$733$	1254.00	0.0631890	0.0315945	+	0.999501i	$0.489941\pi$
$734$	0	0
$735$	5145.00	0.258199
$736$	0	0
$737$	−3476.00	−0.173731
$738$	0	0
$739$	12700.0	0.632175	0.316087	−	0.948730i	$-0.397631\pi$
$739$	12700.0	0.632175	0.316087	+	0.948730i	$0.397631\pi$
$740$	0	0
$741$	−6552.00	−0.324823
$742$	0	0
$743$	22128.0	1.09259	0.546297	−	0.837591i	$-0.316037\pi$
$743$	22128.0	1.09259	0.546297	+	0.837591i	$0.316037\pi$
$744$	0	0
$745$	−12570.0	−0.618160
$746$	0	0
$747$	2916.00	0.142826
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−2080.00	−0.101066	−0.0505328	−	0.998722i	$-0.516092\pi$
$751$	−2080.00	−0.101066	−0.0505328	+	0.998722i	$0.516092\pi$
$752$	0	0
$753$	16260.0	0.786915
$754$	0	0
$755$	1240.00	0.0597725
$756$	0	0
$757$	−30994.0	−1.48811	−0.744053	−	0.668121i	$-0.767099\pi$
$757$	−30994.0	−1.48811	−0.744053	+	0.668121i	$0.767099\pi$
$758$	0	0
$759$	−3168.00	−0.151503
$760$	0	0
$761$	25578.0	1.21840	0.609200	−	0.793017i	$-0.291491\pi$
$761$	25578.0	1.21840	0.609200	+	0.793017i	$0.291491\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−630.000	−0.0297748
$766$	0	0
$767$	11928.0	0.561532
$768$	0	0
$769$	2882.00	0.135146	0.0675732	−	0.997714i	$-0.478474\pi$
$769$	2882.00	0.135146	0.0675732	+	0.997714i	$0.478474\pi$
$770$	0	0
$771$	3450.00	0.161153
$772$	0	0
$773$	31358.0	1.45908	0.729540	−	0.683938i	$-0.239734\pi$
$773$	31358.0	1.45908	0.729540	+	0.683938i	$0.239734\pi$
$774$	0	0
$775$	−3600.00	−0.166859
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−3016.00	−0.138716
$780$	0	0
$781$	−3080.00	−0.141115
$782$	0	0
$783$	702.000	0.0320401
$784$	0	0
$785$	4350.00	0.197781
$786$	0	0
$787$	20596.0	0.932869	0.466435	−	0.884556i	$-0.345538\pi$
$787$	20596.0	0.932869	0.466435	+	0.884556i	$0.345538\pi$
$788$	0	0
$789$	−13392.0	−0.604268
$790$	0	0
$791$	0	0
$792$	0	0
$793$	33348.0	1.49334
$794$	0	0
$795$	750.000	0.0334588
$796$	0	0
$797$	33606.0	1.49358	0.746791	−	0.665058i	$-0.231593\pi$
$797$	33606.0	1.49358	0.746791	+	0.665058i	$0.231593\pi$
$798$	0	0
$799$	4592.00	0.203321
$800$	0	0
$801$	−12582.0	−0.555010
$802$	0	0
$803$	−3938.00	−0.173062
$804$	0	0
$805$	0	0
$806$	0	0
$807$	30.0000	0.00130861
$808$	0	0
$809$	32058.0	1.39320	0.696600	−	0.717459i	$-0.254695\pi$
$809$	32058.0	1.39320	0.696600	+	0.717459i	$0.254695\pi$
$810$	0	0
$811$	3556.00	0.153968	0.0769840	−	0.997032i	$-0.475471\pi$
$811$	3556.00	0.153968	0.0769840	+	0.997032i	$0.475471\pi$
$812$	0	0
$813$	−16320.0	−0.704019
$814$	0	0
$815$	12740.0	0.547562
$816$	0	0
$817$	−18928.0	−0.810535
$818$	0	0
$819$	0	0
$820$	0	0
$821$	846.000	0.0359630	0.0179815	−	0.999838i	$-0.494276\pi$
$821$	846.000	0.0359630	0.0179815	+	0.999838i	$0.494276\pi$
$822$	0	0
$823$	−29248.0	−1.23879	−0.619393	−	0.785081i	$-0.712621\pi$
$823$	−29248.0	−1.23879	−0.619393	+	0.785081i	$0.712621\pi$
$824$	0	0
$825$	−825.000	−0.0348155
$826$	0	0
$827$	24172.0	1.01638	0.508188	−	0.861246i	$-0.330316\pi$
$827$	24172.0	1.01638	0.508188	+	0.861246i	$0.330316\pi$
$828$	0	0
$829$	28870.0	1.20953	0.604763	−	0.796406i	$-0.293268\pi$
$829$	28870.0	1.20953	0.604763	+	0.796406i	$0.293268\pi$
$830$	0	0
$831$	−14634.0	−0.610888
$832$	0	0
$833$	4802.00	0.199735
$834$	0	0
$835$	−1920.00	−0.0795741
$836$	0	0
$837$	3888.00	0.160560
$838$	0	0
$839$	−26472.0	−1.08929	−0.544645	−	0.838666i	$-0.683336\pi$
$839$	−26472.0	−1.08929	−0.544645	+	0.838666i	$0.683336\pi$
$840$	0	0
$841$	−23713.0	−0.972283
$842$	0	0
$843$	1890.00	0.0772183
$844$	0	0
$845$	−2165.00	−0.0881400
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−4788.00	−0.193550
$850$	0	0
$851$	12096.0	0.487245
$852$	0	0
$853$	15982.0	0.641516	0.320758	−	0.947161i	$-0.396062\pi$
$853$	15982.0	0.641516	0.320758	+	0.947161i	$0.396062\pi$
$854$	0	0
$855$	−2340.00	−0.0935980
$856$	0	0
$857$	31594.0	1.25931	0.629656	−	0.776874i	$-0.283196\pi$
$857$	31594.0	1.25931	0.629656	+	0.776874i	$0.283196\pi$
$858$	0	0
$859$	20676.0	0.821253	0.410626	−	0.911804i	$-0.365310\pi$
$859$	20676.0	0.821253	0.410626	+	0.911804i	$0.365310\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−22728.0	−0.896489	−0.448245	−	0.893911i	$-0.647951\pi$
$863$	−22728.0	−0.896489	−0.448245	+	0.893911i	$0.647951\pi$
$864$	0	0
$865$	110.000	0.00432383
$866$	0	0
$867$	14151.0	0.554317
$868$	0	0
$869$	8624.00	0.336650
$870$	0	0
$871$	13272.0	0.516308
$872$	0	0
$873$	−8046.00	−0.311931
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−28330.0	−1.09081	−0.545403	−	0.838174i	$-0.683623\pi$
$877$	−28330.0	−1.09081	−0.545403	+	0.838174i	$0.683623\pi$
$878$	0	0
$879$	14598.0	0.560157
$880$	0	0
$881$	29074.0	1.11184	0.555918	−	0.831237i	$-0.312367\pi$
$881$	29074.0	1.11184	0.555918	+	0.831237i	$0.312367\pi$
$882$	0	0
$883$	38340.0	1.46120	0.730602	−	0.682803i	$-0.239239\pi$
$883$	38340.0	1.46120	0.730602	+	0.682803i	$0.239239\pi$
$884$	0	0
$885$	4260.00	0.161806
$886$	0	0
$887$	−368.000	−0.0139304	−0.00696518	−	0.999976i	$-0.502217\pi$
$887$	−368.000	−0.0139304	−0.00696518	+	0.999976i	$0.502217\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	891.000	0.0335013
$892$	0	0
$893$	17056.0	0.639146
$894$	0	0
$895$	7740.00	0.289072
$896$	0	0
$897$	12096.0	0.450249
$898$	0	0
$899$	3744.00	0.138898
$900$	0	0
$901$	700.000	0.0258828
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−3770.00	−0.138474
$906$	0	0
$907$	−17892.0	−0.655010	−0.327505	−	0.944849i	$-0.606208\pi$
$907$	−17892.0	−0.655010	−0.327505	+	0.944849i	$0.606208\pi$
$908$	0	0
$909$	−15570.0	−0.568124
$910$	0	0
$911$	−8448.00	−0.307239	−0.153619	−	0.988130i	$-0.549093\pi$
$911$	−8448.00	−0.307239	−0.153619	+	0.988130i	$0.549093\pi$
$912$	0	0
$913$	3564.00	0.129191
$914$	0	0
$915$	11910.0	0.430309
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−2456.00	−0.0881567	−0.0440783	−	0.999028i	$-0.514035\pi$
$919$	−2456.00	−0.0881567	−0.0440783	+	0.999028i	$0.514035\pi$
$920$	0	0
$921$	−12252.0	−0.438346
$922$	0	0
$923$	11760.0	0.419377
$924$	0	0
$925$	3150.00	0.111969
$926$	0	0
$927$	−12816.0	−0.454081
$928$	0	0
$929$	45346.0	1.60146	0.800729	−	0.599027i	$-0.204446\pi$
$929$	45346.0	1.60146	0.800729	+	0.599027i	$0.204446\pi$
$930$	0	0
$931$	17836.0	0.627875
$932$	0	0
$933$	−21384.0	−0.750354
$934$	0	0
$935$	−770.000	−0.0269323
$936$	0	0
$937$	−10438.0	−0.363922	−0.181961	−	0.983306i	$-0.558244\pi$
$937$	−10438.0	−0.363922	−0.181961	+	0.983306i	$0.558244\pi$
$938$	0	0
$939$	3330.00	0.115730
$940$	0	0
$941$	−3050.00	−0.105661	−0.0528306	−	0.998603i	$-0.516824\pi$
$941$	−3050.00	−0.105661	−0.0528306	+	0.998603i	$0.516824\pi$
$942$	0	0
$943$	5568.00	0.192279
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−6444.00	−0.221121	−0.110561	−	0.993869i	$-0.535265\pi$
$947$	−6444.00	−0.221121	−0.110561	+	0.993869i	$0.535265\pi$
$948$	0	0
$949$	15036.0	0.514320
$950$	0	0
$951$	−11442.0	−0.390150
$952$	0	0
$953$	24522.0	0.833521	0.416760	−	0.909016i	$-0.363165\pi$
$953$	24522.0	0.833521	0.416760	+	0.909016i	$0.363165\pi$
$954$	0	0
$955$	−13200.0	−0.447269
$956$	0	0
$957$	858.000	0.0289814
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−9055.00	−0.303951
$962$	0	0
$963$	−2340.00	−0.0783026
$964$	0	0
$965$	23690.0	0.790267
$966$	0	0
$967$	−32448.0	−1.07907	−0.539533	−	0.841964i	$-0.681399\pi$
$967$	−32448.0	−1.07907	−0.539533	+	0.841964i	$0.681399\pi$
$968$	0	0
$969$	−2184.00	−0.0724047
$970$	0	0
$971$	6948.00	0.229631	0.114816	−	0.993387i	$-0.463372\pi$
$971$	6948.00	0.229631	0.114816	+	0.993387i	$0.463372\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	3150.00	0.103467
$976$	0	0
$977$	33042.0	1.08199	0.540997	−	0.841025i	$-0.318047\pi$
$977$	33042.0	1.08199	0.540997	+	0.841025i	$0.318047\pi$
$978$	0	0
$979$	−15378.0	−0.502026
$980$	0	0
$981$	3366.00	0.109550
$982$	0	0
$983$	50400.0	1.63531	0.817655	−	0.575708i	$-0.195274\pi$
$983$	50400.0	1.63531	0.817655	+	0.575708i	$0.195274\pi$
$984$	0	0
$985$	−7050.00	−0.228052
$986$	0	0
$987$	0	0
$988$	0	0
$989$	34944.0	1.12351
$990$	0	0
$991$	−2960.00	−0.0948814	−0.0474407	−	0.998874i	$-0.515107\pi$
$991$	−2960.00	−0.0948814	−0.0474407	+	0.998874i	$0.515107\pi$
$992$	0	0
$993$	−27564.0	−0.880883
$994$	0	0
$995$	11800.0	0.375965
$996$	0	0
$997$	55774.0	1.77170	0.885848	−	0.463976i	$-0.153578\pi$
$997$	55774.0	1.77170	0.885848	+	0.463976i	$0.153578\pi$
$998$	0	0
$999$	−3402.00	−0.107742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.4.a.a.1.1	✓	1
3.2	odd	2		1980.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.4.a.a.1.1	✓	1	1.1	even	1	trivial
1980.4.a.a.1.1		1	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	660.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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