LMFDB - Embedded newform 1232.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,4,Mod(1,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, 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("1232.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1232.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:	$72.6903531271$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +O(q^{10})$

$q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +11.0000 q^{11} +56.0000 q^{13} +36.0000 q^{15} +36.0000 q^{17} +28.0000 q^{19} -14.0000 q^{21} -180.000 q^{23} +199.000 q^{25} -100.000 q^{27} -54.0000 q^{29} +334.000 q^{31} +22.0000 q^{33} -126.000 q^{35} +386.000 q^{37} +112.000 q^{39} -444.000 q^{41} +316.000 q^{43} -414.000 q^{45} +402.000 q^{47} +49.0000 q^{49} +72.0000 q^{51} -486.000 q^{53} +198.000 q^{55} +56.0000 q^{57} +282.000 q^{59} +380.000 q^{61} +161.000 q^{63} +1008.00 q^{65} -176.000 q^{67} -360.000 q^{69} +324.000 q^{71} +800.000 q^{73} +398.000 q^{75} -77.0000 q^{77} +1144.00 q^{79} +421.000 q^{81} -468.000 q^{83} +648.000 q^{85} -108.000 q^{87} -870.000 q^{89} -392.000 q^{91} +668.000 q^{93} +504.000 q^{95} -1330.00 q^{97} -253.000 q^{99} +O(q^{100})$

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
$3$	2.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	2.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	0	0
$5$	18.0000	1.60997	0.804984	−	0.593296i	$-0.202174\pi$
$5$	18.0000	1.60997	0.804984	+	0.593296i	$0.202174\pi$
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	0	0
$9$	−23.0000	−0.851852
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	56.0000	1.19474	0.597369	−	0.801966i	$-0.296213\pi$
$13$	56.0000	1.19474	0.597369	+	0.801966i	$0.296213\pi$
$14$	0	0
$15$	36.0000	0.619677
$16$	0	0
$17$	36.0000	0.513605	0.256802	−	0.966464i	$-0.417331\pi$
$17$	36.0000	0.513605	0.256802	+	0.966464i	$0.417331\pi$
$18$	0	0
$19$	28.0000	0.338086	0.169043	−	0.985609i	$-0.445932\pi$
$19$	28.0000	0.338086	0.169043	+	0.985609i	$0.445932\pi$
$20$	0	0
$21$	−14.0000	−0.145479
$22$	0	0
$23$	−180.000	−1.63185	−0.815926	−	0.578156i	$-0.803772\pi$
$23$	−180.000	−1.63185	−0.815926	+	0.578156i	$0.803772\pi$
$24$	0	0
$25$	199.000	1.59200
$26$	0	0
$27$	−100.000	−0.712778
$28$	0	0
$29$	−54.0000	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$29$	−54.0000	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$30$	0	0
$31$	334.000	1.93510	0.967551	−	0.252675i	$-0.0813104\pi$
$31$	334.000	1.93510	0.967551	+	0.252675i	$0.0813104\pi$
$32$	0	0
$33$	22.0000	0.116052
$34$	0	0
$35$	−126.000	−0.608511
$36$	0	0
$37$	386.000	1.71508	0.857541	−	0.514416i	$-0.171991\pi$
$37$	386.000	1.71508	0.857541	+	0.514416i	$0.171991\pi$
$38$	0	0
$39$	112.000	0.459855
$40$	0	0
$41$	−444.000	−1.69125	−0.845624	−	0.533779i	$-0.820771\pi$
$41$	−444.000	−1.69125	−0.845624	+	0.533779i	$0.820771\pi$
$42$	0	0
$43$	316.000	1.12069	0.560344	−	0.828260i	$-0.310669\pi$
$43$	316.000	1.12069	0.560344	+	0.828260i	$0.310669\pi$
$44$	0	0
$45$	−414.000	−1.37146
$46$	0	0
$47$	402.000	1.24761	0.623806	−	0.781580i	$-0.285586\pi$
$47$	402.000	1.24761	0.623806	+	0.781580i	$0.285586\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	72.0000	0.197687
$52$	0	0
$53$	−486.000	−1.25957	−0.629785	−	0.776769i	$-0.716857\pi$
$53$	−486.000	−1.25957	−0.629785	+	0.776769i	$0.716857\pi$
$54$	0	0
$55$	198.000	0.485424
$56$	0	0
$57$	56.0000	0.130129
$58$	0	0
$59$	282.000	0.622259	0.311129	−	0.950368i	$-0.399293\pi$
$59$	282.000	0.622259	0.311129	+	0.950368i	$0.399293\pi$
$60$	0	0
$61$	380.000	0.797607	0.398803	−	0.917036i	$-0.369426\pi$
$61$	380.000	0.797607	0.398803	+	0.917036i	$0.369426\pi$
$62$	0	0
$63$	161.000	0.321970
$64$	0	0
$65$	1008.00	1.92349
$66$	0	0
$67$	−176.000	−0.320923	−0.160461	−	0.987042i	$-0.551298\pi$
$67$	−176.000	−0.320923	−0.160461	+	0.987042i	$0.551298\pi$
$68$	0	0
$69$	−360.000	−0.628100
$70$	0	0
$71$	324.000	0.541574	0.270787	−	0.962639i	$-0.412716\pi$
$71$	324.000	0.541574	0.270787	+	0.962639i	$0.412716\pi$
$72$	0	0
$73$	800.000	1.28264	0.641321	−	0.767272i	$-0.278387\pi$
$73$	800.000	1.28264	0.641321	+	0.767272i	$0.278387\pi$
$74$	0	0
$75$	398.000	0.612761
$76$	0	0
$77$	−77.0000	−0.113961
$78$	0	0
$79$	1144.00	1.62924	0.814621	−	0.579994i	$-0.196945\pi$
$79$	1144.00	1.62924	0.814621	+	0.579994i	$0.196945\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	0	0
$83$	−468.000	−0.618912	−0.309456	−	0.950914i	$-0.600147\pi$
$83$	−468.000	−0.618912	−0.309456	+	0.950914i	$0.600147\pi$
$84$	0	0
$85$	648.000	0.826888
$86$	0	0
$87$	−108.000	−0.133090
$88$	0	0
$89$	−870.000	−1.03618	−0.518089	−	0.855327i	$-0.673356\pi$
$89$	−870.000	−1.03618	−0.518089	+	0.855327i	$0.673356\pi$
$90$	0	0
$91$	−392.000	−0.451569
$92$	0	0
$93$	668.000	0.744821
$94$	0	0
$95$	504.000	0.544309
$96$	0	0
$97$	−1330.00	−1.39218	−0.696088	−	0.717957i	$-0.745078\pi$
$97$	−1330.00	−1.39218	−0.696088	+	0.717957i	$0.745078\pi$
$98$	0	0
$99$	−253.000	−0.256843
$100$	0	0
$101$	−120.000	−0.118222	−0.0591111	−	0.998251i	$-0.518827\pi$
$101$	−120.000	−0.118222	−0.0591111	+	0.998251i	$0.518827\pi$
$102$	0	0
$103$	1210.00	1.15752	0.578761	−	0.815497i	$-0.303536\pi$
$103$	1210.00	1.15752	0.578761	+	0.815497i	$0.303536\pi$
$104$	0	0
$105$	−252.000	−0.234216
$106$	0	0
$107$	−1236.00	−1.11672	−0.558358	−	0.829600i	$-0.688568\pi$
$107$	−1236.00	−1.11672	−0.558358	+	0.829600i	$0.688568\pi$
$108$	0	0
$109$	−694.000	−0.609845	−0.304923	−	0.952377i	$-0.598631\pi$
$109$	−694.000	−0.609845	−0.304923	+	0.952377i	$0.598631\pi$
$110$	0	0
$111$	772.000	0.660135
$112$	0	0
$113$	978.000	0.814181	0.407091	−	0.913388i	$-0.366543\pi$
$113$	978.000	0.814181	0.407091	+	0.913388i	$0.366543\pi$
$114$	0	0
$115$	−3240.00	−2.62723
$116$	0	0
$117$	−1288.00	−1.01774
$118$	0	0
$119$	−252.000	−0.194124
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	−888.000	−0.650961
$124$	0	0
$125$	1332.00	0.953102
$126$	0	0
$127$	1216.00	0.849626	0.424813	−	0.905281i	$-0.360340\pi$
$127$	1216.00	0.849626	0.424813	+	0.905281i	$0.360340\pi$
$128$	0	0
$129$	632.000	0.431353
$130$	0	0
$131$	−1680.00	−1.12048	−0.560238	−	0.828332i	$-0.689290\pi$
$131$	−1680.00	−1.12048	−0.560238	+	0.828332i	$0.689290\pi$
$132$	0	0
$133$	−196.000	−0.127785
$134$	0	0
$135$	−1800.00	−1.14755
$136$	0	0
$137$	1062.00	0.662283	0.331142	−	0.943581i	$-0.392566\pi$
$137$	1062.00	0.662283	0.331142	+	0.943581i	$0.392566\pi$
$138$	0	0
$139$	508.000	0.309986	0.154993	−	0.987916i	$-0.450465\pi$
$139$	508.000	0.309986	0.154993	+	0.987916i	$0.450465\pi$
$140$	0	0
$141$	804.000	0.480206
$142$	0	0
$143$	616.000	0.360227
$144$	0	0
$145$	−972.000	−0.556691
$146$	0	0
$147$	98.0000	0.0549857
$148$	0	0
$149$	2598.00	1.42843	0.714216	−	0.699925i	$-0.246783\pi$
$149$	2598.00	1.42843	0.714216	+	0.699925i	$0.246783\pi$
$150$	0	0
$151$	−2648.00	−1.42709	−0.713547	−	0.700607i	$-0.752912\pi$
$151$	−2648.00	−1.42709	−0.713547	+	0.700607i	$0.752912\pi$
$152$	0	0
$153$	−828.000	−0.437515
$154$	0	0
$155$	6012.00	3.11545
$156$	0	0
$157$	−790.000	−0.401585	−0.200793	−	0.979634i	$-0.564352\pi$
$157$	−790.000	−0.401585	−0.200793	+	0.979634i	$0.564352\pi$
$158$	0	0
$159$	−972.000	−0.484809
$160$	0	0
$161$	1260.00	0.616782
$162$	0	0
$163$	160.000	0.0768845	0.0384422	−	0.999261i	$-0.487760\pi$
$163$	160.000	0.0768845	0.0384422	+	0.999261i	$0.487760\pi$
$164$	0	0
$165$	396.000	0.186840
$166$	0	0
$167$	−264.000	−0.122329	−0.0611645	−	0.998128i	$-0.519481\pi$
$167$	−264.000	−0.122329	−0.0611645	+	0.998128i	$0.519481\pi$
$168$	0	0
$169$	939.000	0.427401
$170$	0	0
$171$	−644.000	−0.287999
$172$	0	0
$173$	1632.00	0.717218	0.358609	−	0.933488i	$-0.383251\pi$
$173$	1632.00	0.717218	0.358609	+	0.933488i	$0.383251\pi$
$174$	0	0
$175$	−1393.00	−0.601719
$176$	0	0
$177$	564.000	0.239508
$178$	0	0
$179$	708.000	0.295634	0.147817	−	0.989015i	$-0.452775\pi$
$179$	708.000	0.295634	0.147817	+	0.989015i	$0.452775\pi$
$180$	0	0
$181$	902.000	0.370415	0.185208	−	0.982699i	$-0.440704\pi$
$181$	902.000	0.370415	0.185208	+	0.982699i	$0.440704\pi$
$182$	0	0
$183$	760.000	0.306999
$184$	0	0
$185$	6948.00	2.76123
$186$	0	0
$187$	396.000	0.154858
$188$	0	0
$189$	700.000	0.269405
$190$	0	0
$191$	−1824.00	−0.690995	−0.345497	−	0.938420i	$-0.612290\pi$
$191$	−1824.00	−0.690995	−0.345497	+	0.938420i	$0.612290\pi$
$192$	0	0
$193$	2090.00	0.779490	0.389745	−	0.920923i	$-0.372563\pi$
$193$	2090.00	0.779490	0.389745	+	0.920923i	$0.372563\pi$
$194$	0	0
$195$	2016.00	0.740353
$196$	0	0
$197$	−1602.00	−0.579380	−0.289690	−	0.957121i	$-0.593552\pi$
$197$	−1602.00	−0.579380	−0.289690	+	0.957121i	$0.593552\pi$
$198$	0	0
$199$	3274.00	1.16627	0.583135	−	0.812375i	$-0.301826\pi$
$199$	3274.00	1.16627	0.583135	+	0.812375i	$0.301826\pi$
$200$	0	0
$201$	−352.000	−0.123523
$202$	0	0
$203$	378.000	0.130692
$204$	0	0
$205$	−7992.00	−2.72286
$206$	0	0
$207$	4140.00	1.39010
$208$	0	0
$209$	308.000	0.101937
$210$	0	0
$211$	4948.00	1.61438	0.807190	−	0.590291i	$-0.200987\pi$
$211$	4948.00	1.61438	0.807190	+	0.590291i	$0.200987\pi$
$212$	0	0
$213$	648.000	0.208452
$214$	0	0
$215$	5688.00	1.80427
$216$	0	0
$217$	−2338.00	−0.731400
$218$	0	0
$219$	1600.00	0.493689
$220$	0	0
$221$	2016.00	0.613624
$222$	0	0
$223$	−2342.00	−0.703282	−0.351641	−	0.936135i	$-0.614376\pi$
$223$	−2342.00	−0.703282	−0.351641	+	0.936135i	$0.614376\pi$
$224$	0	0
$225$	−4577.00	−1.35615
$226$	0	0
$227$	−2064.00	−0.603491	−0.301746	−	0.953388i	$-0.597569\pi$
$227$	−2064.00	−0.603491	−0.301746	+	0.953388i	$0.597569\pi$
$228$	0	0
$229$	−1666.00	−0.480753	−0.240376	−	0.970680i	$-0.577271\pi$
$229$	−1666.00	−0.480753	−0.240376	+	0.970680i	$0.577271\pi$
$230$	0	0
$231$	−154.000	−0.0438634
$232$	0	0
$233$	4158.00	1.16910	0.584549	−	0.811359i	$-0.301272\pi$
$233$	4158.00	1.16910	0.584549	+	0.811359i	$0.301272\pi$
$234$	0	0
$235$	7236.00	2.00862
$236$	0	0
$237$	2288.00	0.627095
$238$	0	0
$239$	−72.0000	−0.0194866	−0.00974329	−	0.999953i	$-0.503101\pi$
$239$	−72.0000	−0.0194866	−0.00974329	+	0.999953i	$0.503101\pi$
$240$	0	0
$241$	6860.00	1.83357	0.916787	−	0.399376i	$-0.130773\pi$
$241$	6860.00	1.83357	0.916787	+	0.399376i	$0.130773\pi$
$242$	0	0
$243$	3542.00	0.935059
$244$	0	0
$245$	882.000	0.229996
$246$	0	0
$247$	1568.00	0.403925
$248$	0	0
$249$	−936.000	−0.238219
$250$	0	0
$251$	150.000	0.0377208	0.0188604	−	0.999822i	$-0.493996\pi$
$251$	150.000	0.0377208	0.0188604	+	0.999822i	$0.493996\pi$
$252$	0	0
$253$	−1980.00	−0.492022
$254$	0	0
$255$	1296.00	0.318269
$256$	0	0
$257$	−2430.00	−0.589802	−0.294901	−	0.955528i	$-0.595287\pi$
$257$	−2430.00	−0.589802	−0.294901	+	0.955528i	$0.595287\pi$
$258$	0	0
$259$	−2702.00	−0.648240
$260$	0	0
$261$	1242.00	0.294551
$262$	0	0
$263$	−3048.00	−0.714630	−0.357315	−	0.933984i	$-0.616308\pi$
$263$	−3048.00	−0.714630	−0.357315	+	0.933984i	$0.616308\pi$
$264$	0	0
$265$	−8748.00	−2.02787
$266$	0	0
$267$	−1740.00	−0.398825
$268$	0	0
$269$	−3834.00	−0.869008	−0.434504	−	0.900670i	$-0.643076\pi$
$269$	−3834.00	−0.869008	−0.434504	+	0.900670i	$0.643076\pi$
$270$	0	0
$271$	3508.00	0.786331	0.393166	−	0.919468i	$-0.371380\pi$
$271$	3508.00	0.786331	0.393166	+	0.919468i	$0.371380\pi$
$272$	0	0
$273$	−784.000	−0.173809
$274$	0	0
$275$	2189.00	0.480006
$276$	0	0
$277$	8294.00	1.79905	0.899527	−	0.436864i	$-0.143911\pi$
$277$	8294.00	1.79905	0.899527	+	0.436864i	$0.143911\pi$
$278$	0	0
$279$	−7682.00	−1.64842
$280$	0	0
$281$	8022.00	1.70303	0.851517	−	0.524327i	$-0.175683\pi$
$281$	8022.00	1.70303	0.851517	+	0.524327i	$0.175683\pi$
$282$	0	0
$283$	−392.000	−0.0823392	−0.0411696	−	0.999152i	$-0.513108\pi$
$283$	−392.000	−0.0823392	−0.0411696	+	0.999152i	$0.513108\pi$
$284$	0	0
$285$	1008.00	0.209504
$286$	0	0
$287$	3108.00	0.639231
$288$	0	0
$289$	−3617.00	−0.736210
$290$	0	0
$291$	−2660.00	−0.535849
$292$	0	0
$293$	−2748.00	−0.547918	−0.273959	−	0.961741i	$-0.588333\pi$
$293$	−2748.00	−0.547918	−0.273959	+	0.961741i	$0.588333\pi$
$294$	0	0
$295$	5076.00	1.00182
$296$	0	0
$297$	−1100.00	−0.214911
$298$	0	0
$299$	−10080.0	−1.94964
$300$	0	0
$301$	−2212.00	−0.423580
$302$	0	0
$303$	−240.000	−0.0455038
$304$	0	0
$305$	6840.00	1.28412
$306$	0	0
$307$	3064.00	0.569615	0.284807	−	0.958585i	$-0.408070\pi$
$307$	3064.00	0.569615	0.284807	+	0.958585i	$0.408070\pi$
$308$	0	0
$309$	2420.00	0.445531
$310$	0	0
$311$	−4062.00	−0.740627	−0.370313	−	0.928907i	$-0.620750\pi$
$311$	−4062.00	−0.740627	−0.370313	+	0.928907i	$0.620750\pi$
$312$	0	0
$313$	−4870.00	−0.879453	−0.439726	−	0.898132i	$-0.644925\pi$
$313$	−4870.00	−0.879453	−0.439726	+	0.898132i	$0.644925\pi$
$314$	0	0
$315$	2898.00	0.518361
$316$	0	0
$317$	4806.00	0.851520	0.425760	−	0.904836i	$-0.360007\pi$
$317$	4806.00	0.851520	0.425760	+	0.904836i	$0.360007\pi$
$318$	0	0
$319$	−594.000	−0.104256
$320$	0	0
$321$	−2472.00	−0.429824
$322$	0	0
$323$	1008.00	0.173643
$324$	0	0
$325$	11144.0	1.90202
$326$	0	0
$327$	−1388.00	−0.234730
$328$	0	0
$329$	−2814.00	−0.471553
$330$	0	0
$331$	−6620.00	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−6620.00	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	0	0
$333$	−8878.00	−1.46100
$334$	0	0
$335$	−3168.00	−0.516676
$336$	0	0
$337$	1094.00	0.176837	0.0884184	−	0.996083i	$-0.471819\pi$
$337$	1094.00	0.176837	0.0884184	+	0.996083i	$0.471819\pi$
$338$	0	0
$339$	1956.00	0.313379
$340$	0	0
$341$	3674.00	0.583455
$342$	0	0
$343$	−343.000	−0.0539949
$344$	0	0
$345$	−6480.00	−1.01122
$346$	0	0
$347$	−3468.00	−0.536519	−0.268259	−	0.963347i	$-0.586448\pi$
$347$	−3468.00	−0.536519	−0.268259	+	0.963347i	$0.586448\pi$
$348$	0	0
$349$	−8188.00	−1.25586	−0.627928	−	0.778272i	$-0.716097\pi$
$349$	−8188.00	−1.25586	−0.627928	+	0.778272i	$0.716097\pi$
$350$	0	0
$351$	−5600.00	−0.851584
$352$	0	0
$353$	−5070.00	−0.764444	−0.382222	−	0.924070i	$-0.624841\pi$
$353$	−5070.00	−0.764444	−0.382222	+	0.924070i	$0.624841\pi$
$354$	0	0
$355$	5832.00	0.871917
$356$	0	0
$357$	−504.000	−0.0747185
$358$	0	0
$359$	−1656.00	−0.243455	−0.121727	−	0.992564i	$-0.538843\pi$
$359$	−1656.00	−0.243455	−0.121727	+	0.992564i	$0.538843\pi$
$360$	0	0
$361$	−6075.00	−0.885698
$362$	0	0
$363$	242.000	0.0349909
$364$	0	0
$365$	14400.0	2.06501
$366$	0	0
$367$	−10166.0	−1.44594	−0.722971	−	0.690878i	$-0.757224\pi$
$367$	−10166.0	−1.44594	−0.722971	+	0.690878i	$0.757224\pi$
$368$	0	0
$369$	10212.0	1.44069
$370$	0	0
$371$	3402.00	0.476073
$372$	0	0
$373$	−2722.00	−0.377855	−0.188927	−	0.981991i	$-0.560501\pi$
$373$	−2722.00	−0.377855	−0.188927	+	0.981991i	$0.560501\pi$
$374$	0	0
$375$	2664.00	0.366849
$376$	0	0
$377$	−3024.00	−0.413114
$378$	0	0
$379$	5872.00	0.795843	0.397921	−	0.917420i	$-0.369732\pi$
$379$	5872.00	0.795843	0.397921	+	0.917420i	$0.369732\pi$
$380$	0	0
$381$	2432.00	0.327021
$382$	0	0
$383$	−12330.0	−1.64500	−0.822498	−	0.568768i	$-0.807420\pi$
$383$	−12330.0	−1.64500	−0.822498	+	0.568768i	$0.807420\pi$
$384$	0	0
$385$	−1386.00	−0.183473
$386$	0	0
$387$	−7268.00	−0.954659
$388$	0	0
$389$	−14586.0	−1.90113	−0.950565	−	0.310526i	$-0.899495\pi$
$389$	−14586.0	−1.90113	−0.950565	+	0.310526i	$0.899495\pi$
$390$	0	0
$391$	−6480.00	−0.838127
$392$	0	0
$393$	−3360.00	−0.431271
$394$	0	0
$395$	20592.0	2.62303
$396$	0	0
$397$	1874.00	0.236910	0.118455	−	0.992959i	$-0.462206\pi$
$397$	1874.00	0.236910	0.118455	+	0.992959i	$0.462206\pi$
$398$	0	0
$399$	−392.000	−0.0491843
$400$	0	0
$401$	13338.0	1.66102	0.830509	−	0.557006i	$-0.188050\pi$
$401$	13338.0	1.66102	0.830509	+	0.557006i	$0.188050\pi$
$402$	0	0
$403$	18704.0	2.31194
$404$	0	0
$405$	7578.00	0.929763
$406$	0	0
$407$	4246.00	0.517116
$408$	0	0
$409$	−8200.00	−0.991354	−0.495677	−	0.868507i	$-0.665080\pi$
$409$	−8200.00	−0.991354	−0.495677	+	0.868507i	$0.665080\pi$
$410$	0	0
$411$	2124.00	0.254913
$412$	0	0
$413$	−1974.00	−0.235192
$414$	0	0
$415$	−8424.00	−0.996429
$416$	0	0
$417$	1016.00	0.119314
$418$	0	0
$419$	7362.00	0.858370	0.429185	−	0.903216i	$-0.358801\pi$
$419$	7362.00	0.858370	0.429185	+	0.903216i	$0.358801\pi$
$420$	0	0
$421$	−11710.0	−1.35561	−0.677803	−	0.735243i	$-0.737068\pi$
$421$	−11710.0	−1.35561	−0.677803	+	0.735243i	$0.737068\pi$
$422$	0	0
$423$	−9246.00	−1.06278
$424$	0	0
$425$	7164.00	0.817659
$426$	0	0
$427$	−2660.00	−0.301467
$428$	0	0
$429$	1232.00	0.138652
$430$	0	0
$431$	936.000	0.104607	0.0523034	−	0.998631i	$-0.483344\pi$
$431$	936.000	0.104607	0.0523034	+	0.998631i	$0.483344\pi$
$432$	0	0
$433$	9038.00	1.00309	0.501546	−	0.865131i	$-0.332765\pi$
$433$	9038.00	1.00309	0.501546	+	0.865131i	$0.332765\pi$
$434$	0	0
$435$	−1944.00	−0.214270
$436$	0	0
$437$	−5040.00	−0.551707
$438$	0	0
$439$	−1964.00	−0.213523	−0.106762	−	0.994285i	$-0.534048\pi$
$439$	−1964.00	−0.213523	−0.106762	+	0.994285i	$0.534048\pi$
$440$	0	0
$441$	−1127.00	−0.121693
$442$	0	0
$443$	−10068.0	−1.07979	−0.539893	−	0.841734i	$-0.681535\pi$
$443$	−10068.0	−1.07979	−0.539893	+	0.841734i	$0.681535\pi$
$444$	0	0
$445$	−15660.0	−1.66821
$446$	0	0
$447$	5196.00	0.549804
$448$	0	0
$449$	3270.00	0.343699	0.171849	−	0.985123i	$-0.445026\pi$
$449$	3270.00	0.343699	0.171849	+	0.985123i	$0.445026\pi$
$450$	0	0
$451$	−4884.00	−0.509930
$452$	0	0
$453$	−5296.00	−0.549289
$454$	0	0
$455$	−7056.00	−0.727012
$456$	0	0
$457$	−15526.0	−1.58922	−0.794612	−	0.607117i	$-0.792326\pi$
$457$	−15526.0	−1.58922	−0.794612	+	0.607117i	$0.792326\pi$
$458$	0	0
$459$	−3600.00	−0.366086
$460$	0	0
$461$	10548.0	1.06566	0.532830	−	0.846222i	$-0.321128\pi$
$461$	10548.0	1.06566	0.532830	+	0.846222i	$0.321128\pi$
$462$	0	0
$463$	3796.00	0.381026	0.190513	−	0.981685i	$-0.438985\pi$
$463$	3796.00	0.381026	0.190513	+	0.981685i	$0.438985\pi$
$464$	0	0
$465$	12024.0	1.19914
$466$	0	0
$467$	−7122.00	−0.705711	−0.352855	−	0.935678i	$-0.614789\pi$
$467$	−7122.00	−0.705711	−0.352855	+	0.935678i	$0.614789\pi$
$468$	0	0
$469$	1232.00	0.121297
$470$	0	0
$471$	−1580.00	−0.154570
$472$	0	0
$473$	3476.00	0.337900
$474$	0	0
$475$	5572.00	0.538233
$476$	0	0
$477$	11178.0	1.07297
$478$	0	0
$479$	−2292.00	−0.218631	−0.109315	−	0.994007i	$-0.534866\pi$
$479$	−2292.00	−0.218631	−0.109315	+	0.994007i	$0.534866\pi$
$480$	0	0
$481$	21616.0	2.04907
$482$	0	0
$483$	2520.00	0.237400
$484$	0	0
$485$	−23940.0	−2.24136
$486$	0	0
$487$	−5132.00	−0.477522	−0.238761	−	0.971078i	$-0.576741\pi$
$487$	−5132.00	−0.477522	−0.238761	+	0.971078i	$0.576741\pi$
$488$	0	0
$489$	320.000	0.0295928
$490$	0	0
$491$	−4188.00	−0.384932	−0.192466	−	0.981304i	$-0.561649\pi$
$491$	−4188.00	−0.384932	−0.192466	+	0.981304i	$0.561649\pi$
$492$	0	0
$493$	−1944.00	−0.177593
$494$	0	0
$495$	−4554.00	−0.413509
$496$	0	0
$497$	−2268.00	−0.204696
$498$	0	0
$499$	−3848.00	−0.345211	−0.172605	−	0.984991i	$-0.555219\pi$
$499$	−3848.00	−0.345211	−0.172605	+	0.984991i	$0.555219\pi$
$500$	0	0
$501$	−528.000	−0.0470844
$502$	0	0
$503$	1068.00	0.0946715	0.0473358	−	0.998879i	$-0.484927\pi$
$503$	1068.00	0.0946715	0.0473358	+	0.998879i	$0.484927\pi$
$504$	0	0
$505$	−2160.00	−0.190334
$506$	0	0
$507$	1878.00	0.164507
$508$	0	0
$509$	−6162.00	−0.536593	−0.268297	−	0.963336i	$-0.586461\pi$
$509$	−6162.00	−0.536593	−0.268297	+	0.963336i	$0.586461\pi$
$510$	0	0
$511$	−5600.00	−0.484793
$512$	0	0
$513$	−2800.00	−0.240981
$514$	0	0
$515$	21780.0	1.86358
$516$	0	0
$517$	4422.00	0.376169
$518$	0	0
$519$	3264.00	0.276057
$520$	0	0
$521$	−20946.0	−1.76135	−0.880673	−	0.473725i	$-0.842909\pi$
$521$	−20946.0	−1.76135	−0.880673	+	0.473725i	$0.842909\pi$
$522$	0	0
$523$	4696.00	0.392623	0.196311	−	0.980542i	$-0.437104\pi$
$523$	4696.00	0.392623	0.196311	+	0.980542i	$0.437104\pi$
$524$	0	0
$525$	−2786.00	−0.231602
$526$	0	0
$527$	12024.0	0.993878
$528$	0	0
$529$	20233.0	1.66294
$530$	0	0
$531$	−6486.00	−0.530072
$532$	0	0
$533$	−24864.0	−2.02060
$534$	0	0
$535$	−22248.0	−1.79788
$536$	0	0
$537$	1416.00	0.113789
$538$	0	0
$539$	539.000	0.0430730
$540$	0	0
$541$	19358.0	1.53838	0.769192	−	0.639018i	$-0.220659\pi$
$541$	19358.0	1.53838	0.769192	+	0.639018i	$0.220659\pi$
$542$	0	0
$543$	1804.00	0.142573
$544$	0	0
$545$	−12492.0	−0.981832
$546$	0	0
$547$	−18020.0	−1.40855	−0.704277	−	0.709925i	$-0.748729\pi$
$547$	−18020.0	−1.40855	−0.704277	+	0.709925i	$0.748729\pi$
$548$	0	0
$549$	−8740.00	−0.679443
$550$	0	0
$551$	−1512.00	−0.116903
$552$	0	0
$553$	−8008.00	−0.615795
$554$	0	0
$555$	13896.0	1.06280
$556$	0	0
$557$	14622.0	1.11231	0.556153	−	0.831080i	$-0.312277\pi$
$557$	14622.0	1.11231	0.556153	+	0.831080i	$0.312277\pi$
$558$	0	0
$559$	17696.0	1.33893
$560$	0	0
$561$	792.000	0.0596048
$562$	0	0
$563$	2244.00	0.167981	0.0839905	−	0.996467i	$-0.473233\pi$
$563$	2244.00	0.167981	0.0839905	+	0.996467i	$0.473233\pi$
$564$	0	0
$565$	17604.0	1.31081
$566$	0	0
$567$	−2947.00	−0.218276
$568$	0	0
$569$	−3258.00	−0.240039	−0.120020	−	0.992772i	$-0.538296\pi$
$569$	−3258.00	−0.240039	−0.120020	+	0.992772i	$0.538296\pi$
$570$	0	0
$571$	6604.00	0.484008	0.242004	−	0.970275i	$-0.422195\pi$
$571$	6604.00	0.484008	0.242004	+	0.970275i	$0.422195\pi$
$572$	0	0
$573$	−3648.00	−0.265964
$574$	0	0
$575$	−35820.0	−2.59791
$576$	0	0
$577$	−16594.0	−1.19726	−0.598628	−	0.801027i	$-0.704287\pi$
$577$	−16594.0	−1.19726	−0.598628	+	0.801027i	$0.704287\pi$
$578$	0	0
$579$	4180.00	0.300026
$580$	0	0
$581$	3276.00	0.233927
$582$	0	0
$583$	−5346.00	−0.379775
$584$	0	0
$585$	−23184.0	−1.63853
$586$	0	0
$587$	19062.0	1.34033	0.670164	−	0.742213i	$-0.266224\pi$
$587$	19062.0	1.34033	0.670164	+	0.742213i	$0.266224\pi$
$588$	0	0
$589$	9352.00	0.654232
$590$	0	0
$591$	−3204.00	−0.223003
$592$	0	0
$593$	−4776.00	−0.330737	−0.165368	−	0.986232i	$-0.552881\pi$
$593$	−4776.00	−0.330737	−0.165368	+	0.986232i	$0.552881\pi$
$594$	0	0
$595$	−4536.00	−0.312534
$596$	0	0
$597$	6548.00	0.448897
$598$	0	0
$599$	−7956.00	−0.542693	−0.271347	−	0.962482i	$-0.587469\pi$
$599$	−7956.00	−0.542693	−0.271347	+	0.962482i	$0.587469\pi$
$600$	0	0
$601$	14348.0	0.973822	0.486911	−	0.873452i	$-0.338124\pi$
$601$	14348.0	0.973822	0.486911	+	0.873452i	$0.338124\pi$
$602$	0	0
$603$	4048.00	0.273379
$604$	0	0
$605$	2178.00	0.146361
$606$	0	0
$607$	−24488.0	−1.63746	−0.818729	−	0.574180i	$-0.805321\pi$
$607$	−24488.0	−1.63746	−0.818729	+	0.574180i	$0.805321\pi$
$608$	0	0
$609$	756.000	0.0503032
$610$	0	0
$611$	22512.0	1.49057
$612$	0	0
$613$	−19654.0	−1.29497	−0.647486	−	0.762078i	$-0.724179\pi$
$613$	−19654.0	−1.29497	−0.647486	+	0.762078i	$0.724179\pi$
$614$	0	0
$615$	−15984.0	−1.04803
$616$	0	0
$617$	2694.00	0.175780	0.0878901	−	0.996130i	$-0.471988\pi$
$617$	2694.00	0.175780	0.0878901	+	0.996130i	$0.471988\pi$
$618$	0	0
$619$	−10178.0	−0.660886	−0.330443	−	0.943826i	$-0.607198\pi$
$619$	−10178.0	−0.660886	−0.330443	+	0.943826i	$0.607198\pi$
$620$	0	0
$621$	18000.0	1.16315
$622$	0	0
$623$	6090.00	0.391638
$624$	0	0
$625$	−899.000	−0.0575360
$626$	0	0
$627$	616.000	0.0392355
$628$	0	0
$629$	13896.0	0.880874
$630$	0	0
$631$	7648.00	0.482507	0.241254	−	0.970462i	$-0.422441\pi$
$631$	7648.00	0.482507	0.241254	+	0.970462i	$0.422441\pi$
$632$	0	0
$633$	9896.00	0.621375
$634$	0	0
$635$	21888.0	1.36787
$636$	0	0
$637$	2744.00	0.170677
$638$	0	0
$639$	−7452.00	−0.461340
$640$	0	0
$641$	270.000	0.0166371	0.00831853	−	0.999965i	$-0.497352\pi$
$641$	270.000	0.0166371	0.00831853	+	0.999965i	$0.497352\pi$
$642$	0	0
$643$	−16250.0	−0.996637	−0.498318	−	0.866994i	$-0.666049\pi$
$643$	−16250.0	−0.996637	−0.498318	+	0.866994i	$0.666049\pi$
$644$	0	0
$645$	11376.0	0.694464
$646$	0	0
$647$	−10242.0	−0.622341	−0.311170	−	0.950354i	$-0.600721\pi$
$647$	−10242.0	−0.622341	−0.311170	+	0.950354i	$0.600721\pi$
$648$	0	0
$649$	3102.00	0.187618
$650$	0	0
$651$	−4676.00	−0.281516
$652$	0	0
$653$	−17322.0	−1.03807	−0.519037	−	0.854752i	$-0.673709\pi$
$653$	−17322.0	−1.03807	−0.519037	+	0.854752i	$0.673709\pi$
$654$	0	0
$655$	−30240.0	−1.80393
$656$	0	0
$657$	−18400.0	−1.09262
$658$	0	0
$659$	−11676.0	−0.690186	−0.345093	−	0.938569i	$-0.612153\pi$
$659$	−11676.0	−0.690186	−0.345093	+	0.938569i	$0.612153\pi$
$660$	0	0
$661$	−20710.0	−1.21865	−0.609323	−	0.792922i	$-0.708559\pi$
$661$	−20710.0	−1.21865	−0.609323	+	0.792922i	$0.708559\pi$
$662$	0	0
$663$	4032.00	0.236184
$664$	0	0
$665$	−3528.00	−0.205729
$666$	0	0
$667$	9720.00	0.564258
$668$	0	0
$669$	−4684.00	−0.270693
$670$	0	0
$671$	4180.00	0.240487
$672$	0	0
$673$	−10354.0	−0.593042	−0.296521	−	0.955026i	$-0.595827\pi$
$673$	−10354.0	−0.593042	−0.296521	+	0.955026i	$0.595827\pi$
$674$	0	0
$675$	−19900.0	−1.13474
$676$	0	0
$677$	−10920.0	−0.619926	−0.309963	−	0.950749i	$-0.600317\pi$
$677$	−10920.0	−0.619926	−0.309963	+	0.950749i	$0.600317\pi$
$678$	0	0
$679$	9310.00	0.526193
$680$	0	0
$681$	−4128.00	−0.232284
$682$	0	0
$683$	−27804.0	−1.55767	−0.778836	−	0.627227i	$-0.784190\pi$
$683$	−27804.0	−1.55767	−0.778836	+	0.627227i	$0.784190\pi$
$684$	0	0
$685$	19116.0	1.06626
$686$	0	0
$687$	−3332.00	−0.185042
$688$	0	0
$689$	−27216.0	−1.50486
$690$	0	0
$691$	25834.0	1.42225	0.711123	−	0.703068i	$-0.248187\pi$
$691$	25834.0	1.42225	0.711123	+	0.703068i	$0.248187\pi$
$692$	0	0
$693$	1771.00	0.0970775
$694$	0	0
$695$	9144.00	0.499067
$696$	0	0
$697$	−15984.0	−0.868633
$698$	0	0
$699$	8316.00	0.449986
$700$	0	0
$701$	−10590.0	−0.570583	−0.285292	−	0.958441i	$-0.592090\pi$
$701$	−10590.0	−0.570583	−0.285292	+	0.958441i	$0.592090\pi$
$702$	0	0
$703$	10808.0	0.579846
$704$	0	0
$705$	14472.0	0.773116
$706$	0	0
$707$	840.000	0.0446838
$708$	0	0
$709$	−6802.00	−0.360302	−0.180151	−	0.983639i	$-0.557659\pi$
$709$	−6802.00	−0.360302	−0.180151	+	0.983639i	$0.557659\pi$
$710$	0	0
$711$	−26312.0	−1.38787
$712$	0	0
$713$	−60120.0	−3.15780
$714$	0	0
$715$	11088.0	0.579955
$716$	0	0
$717$	−144.000	−0.00750039
$718$	0	0
$719$	−23010.0	−1.19350	−0.596751	−	0.802426i	$-0.703542\pi$
$719$	−23010.0	−1.19350	−0.596751	+	0.802426i	$0.703542\pi$
$720$	0	0
$721$	−8470.00	−0.437502
$722$	0	0
$723$	13720.0	0.705743
$724$	0	0
$725$	−10746.0	−0.550478
$726$	0	0
$727$	−4682.00	−0.238853	−0.119426	−	0.992843i	$-0.538106\pi$
$727$	−4682.00	−0.238853	−0.119426	+	0.992843i	$0.538106\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	0	0
$731$	11376.0	0.575590
$732$	0	0
$733$	−17860.0	−0.899965	−0.449982	−	0.893037i	$-0.648570\pi$
$733$	−17860.0	−0.899965	−0.449982	+	0.893037i	$0.648570\pi$
$734$	0	0
$735$	1764.00	0.0885253
$736$	0	0
$737$	−1936.00	−0.0967618
$738$	0	0
$739$	−6860.00	−0.341474	−0.170737	−	0.985317i	$-0.554615\pi$
$739$	−6860.00	−0.341474	−0.170737	+	0.985317i	$0.554615\pi$
$740$	0	0
$741$	3136.00	0.155471
$742$	0	0
$743$	22752.0	1.12341	0.561703	−	0.827339i	$-0.310147\pi$
$743$	22752.0	1.12341	0.561703	+	0.827339i	$0.310147\pi$
$744$	0	0
$745$	46764.0	2.29973
$746$	0	0
$747$	10764.0	0.527221
$748$	0	0
$749$	8652.00	0.422079
$750$	0	0
$751$	−7364.00	−0.357811	−0.178906	−	0.983866i	$-0.557256\pi$
$751$	−7364.00	−0.357811	−0.178906	+	0.983866i	$0.557256\pi$
$752$	0	0
$753$	300.000	0.0145187
$754$	0	0
$755$	−47664.0	−2.29758
$756$	0	0
$757$	−34378.0	−1.65058	−0.825290	−	0.564709i	$-0.808989\pi$
$757$	−34378.0	−1.65058	−0.825290	+	0.564709i	$0.808989\pi$
$758$	0	0
$759$	−3960.00	−0.189379
$760$	0	0
$761$	27456.0	1.30786	0.653929	−	0.756556i	$-0.273120\pi$
$761$	27456.0	1.30786	0.653929	+	0.756556i	$0.273120\pi$
$762$	0	0
$763$	4858.00	0.230500
$764$	0	0
$765$	−14904.0	−0.704386
$766$	0	0
$767$	15792.0	0.743437
$768$	0	0
$769$	7952.00	0.372895	0.186448	−	0.982465i	$-0.440303\pi$
$769$	7952.00	0.372895	0.186448	+	0.982465i	$0.440303\pi$
$770$	0	0
$771$	−4860.00	−0.227015
$772$	0	0
$773$	−4986.00	−0.231997	−0.115999	−	0.993249i	$-0.537007\pi$
$773$	−4986.00	−0.231997	−0.115999	+	0.993249i	$0.537007\pi$
$774$	0	0
$775$	66466.0	3.08068
$776$	0	0
$777$	−5404.00	−0.249508
$778$	0	0
$779$	−12432.0	−0.571788
$780$	0	0
$781$	3564.00	0.163291
$782$	0	0
$783$	5400.00	0.246463
$784$	0	0
$785$	−14220.0	−0.646540
$786$	0	0
$787$	42748.0	1.93622	0.968108	−	0.250534i	$-0.0806062\pi$
$787$	42748.0	1.93622	0.968108	+	0.250534i	$0.0806062\pi$
$788$	0	0
$789$	−6096.00	−0.275061
$790$	0	0
$791$	−6846.00	−0.307732
$792$	0	0
$793$	21280.0	0.952932
$794$	0	0
$795$	−17496.0	−0.780527
$796$	0	0
$797$	35610.0	1.58265	0.791324	−	0.611397i	$-0.209392\pi$
$797$	35610.0	1.58265	0.791324	+	0.611397i	$0.209392\pi$
$798$	0	0
$799$	14472.0	0.640779
$800$	0	0
$801$	20010.0	0.882670
$802$	0	0
$803$	8800.00	0.386731
$804$	0	0
$805$	22680.0	0.993000
$806$	0	0
$807$	−7668.00	−0.334481
$808$	0	0
$809$	−17046.0	−0.740798	−0.370399	−	0.928873i	$-0.620779\pi$
$809$	−17046.0	−0.740798	−0.370399	+	0.928873i	$0.620779\pi$
$810$	0	0
$811$	2176.00	0.0942166	0.0471083	−	0.998890i	$-0.484999\pi$
$811$	2176.00	0.0942166	0.0471083	+	0.998890i	$0.484999\pi$
$812$	0	0
$813$	7016.00	0.302659
$814$	0	0
$815$	2880.00	0.123782
$816$	0	0
$817$	8848.00	0.378889
$818$	0	0
$819$	9016.00	0.384670
$820$	0	0
$821$	2094.00	0.0890147	0.0445074	−	0.999009i	$-0.485828\pi$
$821$	2094.00	0.0890147	0.0445074	+	0.999009i	$0.485828\pi$
$822$	0	0
$823$	−7328.00	−0.310374	−0.155187	−	0.987885i	$-0.549598\pi$
$823$	−7328.00	−0.310374	−0.155187	+	0.987885i	$0.549598\pi$
$824$	0	0
$825$	4378.00	0.184754
$826$	0	0
$827$	12492.0	0.525259	0.262630	−	0.964897i	$-0.415410\pi$
$827$	12492.0	0.525259	0.262630	+	0.964897i	$0.415410\pi$
$828$	0	0
$829$	−37486.0	−1.57050	−0.785249	−	0.619180i	$-0.787465\pi$
$829$	−37486.0	−1.57050	−0.785249	+	0.619180i	$0.787465\pi$
$830$	0	0
$831$	16588.0	0.692456
$832$	0	0
$833$	1764.00	0.0733721
$834$	0	0
$835$	−4752.00	−0.196946
$836$	0	0
$837$	−33400.0	−1.37930
$838$	0	0
$839$	17574.0	0.723149	0.361574	−	0.932343i	$-0.382239\pi$
$839$	17574.0	0.723149	0.361574	+	0.932343i	$0.382239\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	0	0
$843$	16044.0	0.655498
$844$	0	0
$845$	16902.0	0.688102
$846$	0	0
$847$	−847.000	−0.0343604
$848$	0	0
$849$	−784.000	−0.0316924
$850$	0	0
$851$	−69480.0	−2.79876
$852$	0	0
$853$	9440.00	0.378921	0.189460	−	0.981888i	$-0.439326\pi$
$853$	9440.00	0.378921	0.189460	+	0.981888i	$0.439326\pi$
$854$	0	0
$855$	−11592.0	−0.463670
$856$	0	0
$857$	−28440.0	−1.13360	−0.566798	−	0.823857i	$-0.691818\pi$
$857$	−28440.0	−1.13360	−0.566798	+	0.823857i	$0.691818\pi$
$858$	0	0
$859$	24334.0	0.966549	0.483274	−	0.875469i	$-0.339447\pi$
$859$	24334.0	0.966549	0.483274	+	0.875469i	$0.339447\pi$
$860$	0	0
$861$	6216.00	0.246040
$862$	0	0
$863$	−39264.0	−1.54874	−0.774370	−	0.632733i	$-0.781933\pi$
$863$	−39264.0	−1.54874	−0.774370	+	0.632733i	$0.781933\pi$
$864$	0	0
$865$	29376.0	1.15470
$866$	0	0
$867$	−7234.00	−0.283367
$868$	0	0
$869$	12584.0	0.491235
$870$	0	0
$871$	−9856.00	−0.383419
$872$	0	0
$873$	30590.0	1.18593
$874$	0	0
$875$	−9324.00	−0.360239
$876$	0	0
$877$	32114.0	1.23650	0.618251	−	0.785981i	$-0.287841\pi$
$877$	32114.0	1.23650	0.618251	+	0.785981i	$0.287841\pi$
$878$	0	0
$879$	−5496.00	−0.210894
$880$	0	0
$881$	41454.0	1.58527	0.792634	−	0.609698i	$-0.208709\pi$
$881$	41454.0	1.58527	0.792634	+	0.609698i	$0.208709\pi$
$882$	0	0
$883$	−2876.00	−0.109609	−0.0548047	−	0.998497i	$-0.517454\pi$
$883$	−2876.00	−0.109609	−0.0548047	+	0.998497i	$0.517454\pi$
$884$	0	0
$885$	10152.0	0.385600
$886$	0	0
$887$	−13932.0	−0.527385	−0.263693	−	0.964607i	$-0.584940\pi$
$887$	−13932.0	−0.527385	−0.263693	+	0.964607i	$0.584940\pi$
$888$	0	0
$889$	−8512.00	−0.321129
$890$	0	0
$891$	4631.00	0.174124
$892$	0	0
$893$	11256.0	0.421800
$894$	0	0
$895$	12744.0	0.475961
$896$	0	0
$897$	−20160.0	−0.750416
$898$	0	0
$899$	−18036.0	−0.669115
$900$	0	0
$901$	−17496.0	−0.646921
$902$	0	0
$903$	−4424.00	−0.163036
$904$	0	0
$905$	16236.0	0.596357
$906$	0	0
$907$	19768.0	0.723689	0.361844	−	0.932239i	$-0.382147\pi$
$907$	19768.0	0.723689	0.361844	+	0.932239i	$0.382147\pi$
$908$	0	0
$909$	2760.00	0.100708
$910$	0	0
$911$	−43836.0	−1.59424	−0.797119	−	0.603822i	$-0.793644\pi$
$911$	−43836.0	−1.59424	−0.797119	+	0.603822i	$0.793644\pi$
$912$	0	0
$913$	−5148.00	−0.186609
$914$	0	0
$915$	13680.0	0.494259
$916$	0	0
$917$	11760.0	0.423500
$918$	0	0
$919$	−31544.0	−1.13225	−0.566127	−	0.824318i	$-0.691559\pi$
$919$	−31544.0	−1.13225	−0.566127	+	0.824318i	$0.691559\pi$
$920$	0	0
$921$	6128.00	0.219245
$922$	0	0
$923$	18144.0	0.647039
$924$	0	0
$925$	76814.0	2.73041
$926$	0	0
$927$	−27830.0	−0.986038
$928$	0	0
$929$	11118.0	0.392648	0.196324	−	0.980539i	$-0.437100\pi$
$929$	11118.0	0.392648	0.196324	+	0.980539i	$0.437100\pi$
$930$	0	0
$931$	1372.00	0.0482980
$932$	0	0
$933$	−8124.00	−0.285067
$934$	0	0
$935$	7128.00	0.249316
$936$	0	0
$937$	10568.0	0.368454	0.184227	−	0.982884i	$-0.441022\pi$
$937$	10568.0	0.368454	0.184227	+	0.982884i	$0.441022\pi$
$938$	0	0
$939$	−9740.00	−0.338501
$940$	0	0
$941$	14964.0	0.518398	0.259199	−	0.965824i	$-0.416541\pi$
$941$	14964.0	0.518398	0.259199	+	0.965824i	$0.416541\pi$
$942$	0	0
$943$	79920.0	2.75987
$944$	0	0
$945$	12600.0	0.433733
$946$	0	0
$947$	−3324.00	−0.114061	−0.0570304	−	0.998372i	$-0.518163\pi$
$947$	−3324.00	−0.114061	−0.0570304	+	0.998372i	$0.518163\pi$
$948$	0	0
$949$	44800.0	1.53242
$950$	0	0
$951$	9612.00	0.327750
$952$	0	0
$953$	3906.00	0.132768	0.0663839	−	0.997794i	$-0.478854\pi$
$953$	3906.00	0.132768	0.0663839	+	0.997794i	$0.478854\pi$
$954$	0	0
$955$	−32832.0	−1.11248
$956$	0	0
$957$	−1188.00	−0.0401281
$958$	0	0
$959$	−7434.00	−0.250319
$960$	0	0
$961$	81765.0	2.74462
$962$	0	0
$963$	28428.0	0.951277
$964$	0	0
$965$	37620.0	1.25495
$966$	0	0
$967$	36448.0	1.21209	0.606044	−	0.795431i	$-0.292756\pi$
$967$	36448.0	1.21209	0.606044	+	0.795431i	$0.292756\pi$
$968$	0	0
$969$	2016.00	0.0668351
$970$	0	0
$971$	20526.0	0.678384	0.339192	−	0.940717i	$-0.389846\pi$
$971$	20526.0	0.678384	0.339192	+	0.940717i	$0.389846\pi$
$972$	0	0
$973$	−3556.00	−0.117164
$974$	0	0
$975$	22288.0	0.732089
$976$	0	0
$977$	37434.0	1.22581	0.612907	−	0.790155i	$-0.290000\pi$
$977$	37434.0	1.22581	0.612907	+	0.790155i	$0.290000\pi$
$978$	0	0
$979$	−9570.00	−0.312419
$980$	0	0
$981$	15962.0	0.519498
$982$	0	0
$983$	52194.0	1.69352	0.846760	−	0.531975i	$-0.178550\pi$
$983$	52194.0	1.69352	0.846760	+	0.531975i	$0.178550\pi$
$984$	0	0
$985$	−28836.0	−0.932783
$986$	0	0
$987$	−5628.00	−0.181501
$988$	0	0
$989$	−56880.0	−1.82880
$990$	0	0
$991$	15220.0	0.487870	0.243935	−	0.969792i	$-0.421562\pi$
$991$	15220.0	0.487870	0.243935	+	0.969792i	$0.421562\pi$
$992$	0	0
$993$	−13240.0	−0.423121
$994$	0	0
$995$	58932.0	1.87766
$996$	0	0
$997$	37664.0	1.19642	0.598210	−	0.801339i	$-0.295879\pi$
$997$	37664.0	1.19642	0.598210	+	0.801339i	$0.295879\pi$
$998$	0	0
$999$	−38600.0	−1.22247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.4.a.f.1.1		1
4.3	odd	2		154.4.a.d.1.1	✓	1
12.11	even	2		1386.4.a.a.1.1		1
28.27	even	2		1078.4.a.g.1.1		1
44.43	even	2		1694.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.d.1.1	✓	1	4.3	odd	2
1078.4.a.g.1.1		1	28.27	even	2
1232.4.a.f.1.1		1	1.1	even	1	trivial
1386.4.a.a.1.1		1	12.11	even	2
1694.4.a.c.1.1		1	44.43	even	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1232.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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