LMFDB - Embedded newform 2156.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2156,4,Mod(1,2156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2156.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2156 = 2^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2156.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:	$127.208117972$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2156.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{3} +7.00000 q^{5} -2.00000 q^{9} +O(q^{10})$

$q+5.00000 q^{3} +7.00000 q^{5} -2.00000 q^{9} -11.0000 q^{11} -52.0000 q^{13} +35.0000 q^{15} -46.0000 q^{17} +96.0000 q^{19} +27.0000 q^{23} -76.0000 q^{25} -145.000 q^{27} +16.0000 q^{29} +293.000 q^{31} -55.0000 q^{33} -29.0000 q^{37} -260.000 q^{39} +472.000 q^{41} -110.000 q^{43} -14.0000 q^{45} +224.000 q^{47} -230.000 q^{51} +754.000 q^{53} -77.0000 q^{55} +480.000 q^{57} -825.000 q^{59} +548.000 q^{61} -364.000 q^{65} -123.000 q^{67} +135.000 q^{69} +1001.00 q^{71} +1020.00 q^{73} -380.000 q^{75} +526.000 q^{79} -671.000 q^{81} +158.000 q^{83} -322.000 q^{85} +80.0000 q^{87} +1217.00 q^{89} +1465.00 q^{93} +672.000 q^{95} +263.000 q^{97} +22.0000 q^{99} +O(q^{100})$

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
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	0	0
$5$	7.00000	0.626099	0.313050	−	0.949737i	$-0.398649\pi$
$5$	7.00000	0.626099	0.313050	+	0.949737i	$0.398649\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	0	0
$13$	−52.0000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−52.0000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	35.0000	0.602464
$16$	0	0
$17$	−46.0000	−0.656273	−0.328136	−	0.944630i	$-0.606421\pi$
$17$	−46.0000	−0.656273	−0.328136	+	0.944630i	$0.606421\pi$
$18$	0	0
$19$	96.0000	1.15915	0.579577	−	0.814918i	$-0.303218\pi$
$19$	96.0000	1.15915	0.579577	+	0.814918i	$0.303218\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	27.0000	0.244778	0.122389	−	0.992482i	$-0.460944\pi$
$23$	27.0000	0.244778	0.122389	+	0.992482i	$0.460944\pi$
$24$	0	0
$25$	−76.0000	−0.608000
$26$	0	0
$27$	−145.000	−1.03353
$28$	0	0
$29$	16.0000	0.102453	0.0512263	−	0.998687i	$-0.483687\pi$
$29$	16.0000	0.102453	0.0512263	+	0.998687i	$0.483687\pi$
$30$	0	0
$31$	293.000	1.69756	0.848780	−	0.528746i	$-0.177338\pi$
$31$	293.000	1.69756	0.848780	+	0.528746i	$0.177338\pi$
$32$	0	0
$33$	−55.0000	−0.290129
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−29.0000	−0.128853	−0.0644266	−	0.997922i	$-0.520522\pi$
$37$	−29.0000	−0.128853	−0.0644266	+	0.997922i	$0.520522\pi$
$38$	0	0
$39$	−260.000	−1.06752
$40$	0	0
$41$	472.000	1.79790	0.898951	−	0.438048i	$-0.144330\pi$
$41$	472.000	1.79790	0.898951	+	0.438048i	$0.144330\pi$
$42$	0	0
$43$	−110.000	−0.390113	−0.195056	−	0.980792i	$-0.562489\pi$
$43$	−110.000	−0.390113	−0.195056	+	0.980792i	$0.562489\pi$
$44$	0	0
$45$	−14.0000	−0.0463777
$46$	0	0
$47$	224.000	0.695186	0.347593	−	0.937645i	$-0.386999\pi$
$47$	224.000	0.695186	0.347593	+	0.937645i	$0.386999\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−230.000	−0.631499
$52$	0	0
$53$	754.000	1.95415	0.977074	−	0.212899i	$-0.0682905\pi$
$53$	754.000	1.95415	0.977074	+	0.212899i	$0.0682905\pi$
$54$	0	0
$55$	−77.0000	−0.188776
$56$	0	0
$57$	480.000	1.11540
$58$	0	0
$59$	−825.000	−1.82044	−0.910219	−	0.414127i	$-0.864087\pi$
$59$	−825.000	−1.82044	−0.910219	+	0.414127i	$0.864087\pi$
$60$	0	0
$61$	548.000	1.15023	0.575116	−	0.818072i	$-0.304957\pi$
$61$	548.000	1.15023	0.575116	+	0.818072i	$0.304957\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−364.000	−0.694595
$66$	0	0
$67$	−123.000	−0.224281	−0.112141	−	0.993692i	$-0.535771\pi$
$67$	−123.000	−0.224281	−0.112141	+	0.993692i	$0.535771\pi$
$68$	0	0
$69$	135.000	0.235538
$70$	0	0
$71$	1001.00	1.67319	0.836597	−	0.547818i	$-0.184541\pi$
$71$	1001.00	1.67319	0.836597	+	0.547818i	$0.184541\pi$
$72$	0	0
$73$	1020.00	1.63537	0.817685	−	0.575666i	$-0.195257\pi$
$73$	1020.00	1.63537	0.817685	+	0.575666i	$0.195257\pi$
$74$	0	0
$75$	−380.000	−0.585048
$76$	0	0
$77$	0	0
$78$	0	0
$79$	526.000	0.749109	0.374555	−	0.927205i	$-0.377796\pi$
$79$	526.000	0.749109	0.374555	+	0.927205i	$0.377796\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	0	0
$83$	158.000	0.208949	0.104474	−	0.994528i	$-0.466684\pi$
$83$	158.000	0.208949	0.104474	+	0.994528i	$0.466684\pi$
$84$	0	0
$85$	−322.000	−0.410892
$86$	0	0
$87$	80.0000	0.0985851
$88$	0	0
$89$	1217.00	1.44946	0.724729	−	0.689034i	$-0.241965\pi$
$89$	1217.00	1.44946	0.724729	+	0.689034i	$0.241965\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1465.00	1.63348
$94$	0	0
$95$	672.000	0.725745
$96$	0	0
$97$	263.000	0.275295	0.137647	−	0.990481i	$-0.456046\pi$
$97$	263.000	0.275295	0.137647	+	0.990481i	$0.456046\pi$
$98$	0	0
$99$	22.0000	0.0223342
$100$	0	0
$101$	814.000	0.801941	0.400970	−	0.916091i	$-0.368673\pi$
$101$	814.000	0.801941	0.400970	+	0.916091i	$0.368673\pi$
$102$	0	0
$103$	−376.000	−0.359693	−0.179847	−	0.983695i	$-0.557560\pi$
$103$	−376.000	−0.359693	−0.179847	+	0.983695i	$0.557560\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1494.00	−1.34982	−0.674909	−	0.737901i	$-0.735817\pi$
$107$	−1494.00	−1.34982	−0.674909	+	0.737901i	$0.735817\pi$
$108$	0	0
$109$	842.000	0.739899	0.369949	−	0.929052i	$-0.379375\pi$
$109$	842.000	0.739899	0.369949	+	0.929052i	$0.379375\pi$
$110$	0	0
$111$	−145.000	−0.123989
$112$	0	0
$113$	1281.00	1.06643	0.533214	−	0.845980i	$-0.320984\pi$
$113$	1281.00	1.06643	0.533214	+	0.845980i	$0.320984\pi$
$114$	0	0
$115$	189.000	0.153255
$116$	0	0
$117$	104.000	0.0821778
$118$	0	0
$119$	0	0
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	2360.00	1.73003
$124$	0	0
$125$	−1407.00	−1.00677
$126$	0	0
$127$	1736.00	1.21295	0.606477	−	0.795101i	$-0.292582\pi$
$127$	1736.00	1.21295	0.606477	+	0.795101i	$0.292582\pi$
$128$	0	0
$129$	−550.000	−0.375386
$130$	0	0
$131$	−6.00000	−0.00400170	−0.00200085	−	0.999998i	$-0.500637\pi$
$131$	−6.00000	−0.00400170	−0.00200085	+	0.999998i	$0.500637\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1015.00	−0.647091
$136$	0	0
$137$	−1439.00	−0.897387	−0.448694	−	0.893686i	$-0.648111\pi$
$137$	−1439.00	−0.897387	−0.448694	+	0.893686i	$0.648111\pi$
$138$	0	0
$139$	318.000	0.194046	0.0970231	−	0.995282i	$-0.469068\pi$
$139$	318.000	0.194046	0.0970231	+	0.995282i	$0.469068\pi$
$140$	0	0
$141$	1120.00	0.668943
$142$	0	0
$143$	572.000	0.334497
$144$	0	0
$145$	112.000	0.0641455
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−922.000	−0.506934	−0.253467	−	0.967344i	$-0.581571\pi$
$149$	−922.000	−0.506934	−0.253467	+	0.967344i	$0.581571\pi$
$150$	0	0
$151$	−1030.00	−0.555101	−0.277550	−	0.960711i	$-0.589523\pi$
$151$	−1030.00	−0.555101	−0.277550	+	0.960711i	$0.589523\pi$
$152$	0	0
$153$	92.0000	0.0486128
$154$	0	0
$155$	2051.00	1.06284
$156$	0	0
$157$	−1017.00	−0.516977	−0.258489	−	0.966014i	$-0.583224\pi$
$157$	−1017.00	−0.516977	−0.258489	+	0.966014i	$0.583224\pi$
$158$	0	0
$159$	3770.00	1.88038
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−2444.00	−1.17441	−0.587205	−	0.809438i	$-0.699772\pi$
$163$	−2444.00	−1.17441	−0.587205	+	0.809438i	$0.699772\pi$
$164$	0	0
$165$	−385.000	−0.181650
$166$	0	0
$167$	1452.00	0.672809	0.336405	−	0.941718i	$-0.390789\pi$
$167$	1452.00	0.672809	0.336405	+	0.941718i	$0.390789\pi$
$168$	0	0
$169$	507.000	0.230769
$170$	0	0
$171$	−192.000	−0.0858632
$172$	0	0
$173$	−1914.00	−0.841149	−0.420574	−	0.907258i	$-0.638171\pi$
$173$	−1914.00	−0.841149	−0.420574	+	0.907258i	$0.638171\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−4125.00	−1.75172
$178$	0	0
$179$	1293.00	0.539907	0.269954	−	0.962873i	$-0.412992\pi$
$179$	1293.00	0.539907	0.269954	+	0.962873i	$0.412992\pi$
$180$	0	0
$181$	−455.000	−0.186850	−0.0934251	−	0.995626i	$-0.529782\pi$
$181$	−455.000	−0.186850	−0.0934251	+	0.995626i	$0.529782\pi$
$182$	0	0
$183$	2740.00	1.10681
$184$	0	0
$185$	−203.000	−0.0806749
$186$	0	0
$187$	506.000	0.197874
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1115.00	−0.422401	−0.211200	−	0.977443i	$-0.567737\pi$
$191$	−1115.00	−0.422401	−0.211200	+	0.977443i	$0.567737\pi$
$192$	0	0
$193$	5012.00	1.86928	0.934642	−	0.355591i	$-0.115720\pi$
$193$	5012.00	1.86928	0.934642	+	0.355591i	$0.115720\pi$
$194$	0	0
$195$	−1820.00	−0.668374
$196$	0	0
$197$	−4146.00	−1.49944	−0.749721	−	0.661753i	$-0.769813\pi$
$197$	−4146.00	−1.49944	−0.749721	+	0.661753i	$0.769813\pi$
$198$	0	0
$199$	1240.00	0.441715	0.220857	−	0.975306i	$-0.429114\pi$
$199$	1240.00	0.441715	0.220857	+	0.975306i	$0.429114\pi$
$200$	0	0
$201$	−615.000	−0.215815
$202$	0	0
$203$	0	0
$204$	0	0
$205$	3304.00	1.12567
$206$	0	0
$207$	−54.0000	−0.0181317
$208$	0	0
$209$	−1056.00	−0.349498
$210$	0	0
$211$	−2820.00	−0.920080	−0.460040	−	0.887898i	$-0.652165\pi$
$211$	−2820.00	−0.920080	−0.460040	+	0.887898i	$0.652165\pi$
$212$	0	0
$213$	5005.00	1.61003
$214$	0	0
$215$	−770.000	−0.244249
$216$	0	0
$217$	0	0
$218$	0	0
$219$	5100.00	1.57363
$220$	0	0
$221$	2392.00	0.728069
$222$	0	0
$223$	−3695.00	−1.10958	−0.554788	−	0.831992i	$-0.687201\pi$
$223$	−3695.00	−1.10958	−0.554788	+	0.831992i	$0.687201\pi$
$224$	0	0
$225$	152.000	0.0450370
$226$	0	0
$227$	486.000	0.142101	0.0710506	−	0.997473i	$-0.477365\pi$
$227$	486.000	0.142101	0.0710506	+	0.997473i	$0.477365\pi$
$228$	0	0
$229$	−4231.00	−1.22093	−0.610464	−	0.792044i	$-0.709017\pi$
$229$	−4231.00	−1.22093	−0.610464	+	0.792044i	$0.709017\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−3336.00	−0.937977	−0.468988	−	0.883204i	$-0.655381\pi$
$233$	−3336.00	−0.937977	−0.468988	+	0.883204i	$0.655381\pi$
$234$	0	0
$235$	1568.00	0.435255
$236$	0	0
$237$	2630.00	0.720831
$238$	0	0
$239$	3610.00	0.977036	0.488518	−	0.872554i	$-0.337538\pi$
$239$	3610.00	0.977036	0.488518	+	0.872554i	$0.337538\pi$
$240$	0	0
$241$	6408.00	1.71276	0.856381	−	0.516345i	$-0.172708\pi$
$241$	6408.00	1.71276	0.856381	+	0.516345i	$0.172708\pi$
$242$	0	0
$243$	560.000	0.147835
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−4992.00	−1.28596
$248$	0	0
$249$	790.000	0.201061
$250$	0	0
$251$	1787.00	0.449380	0.224690	−	0.974430i	$-0.427863\pi$
$251$	1787.00	0.449380	0.224690	+	0.974430i	$0.427863\pi$
$252$	0	0
$253$	−297.000	−0.0738033
$254$	0	0
$255$	−1610.00	−0.395381
$256$	0	0
$257$	354.000	0.0859218	0.0429609	−	0.999077i	$-0.486321\pi$
$257$	354.000	0.0859218	0.0429609	+	0.999077i	$0.486321\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−32.0000	−0.00758908
$262$	0	0
$263$	−2026.00	−0.475013	−0.237507	−	0.971386i	$-0.576330\pi$
$263$	−2026.00	−0.475013	−0.237507	+	0.971386i	$0.576330\pi$
$264$	0	0
$265$	5278.00	1.22349
$266$	0	0
$267$	6085.00	1.39474
$268$	0	0
$269$	8750.00	1.98326	0.991630	−	0.129112i	$-0.0412128\pi$
$269$	8750.00	1.98326	0.991630	+	0.129112i	$0.0412128\pi$
$270$	0	0
$271$	5036.00	1.12884	0.564419	−	0.825488i	$-0.309100\pi$
$271$	5036.00	1.12884	0.564419	+	0.825488i	$0.309100\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	836.000	0.183319
$276$	0	0
$277$	−4306.00	−0.934016	−0.467008	−	0.884253i	$-0.654668\pi$
$277$	−4306.00	−0.934016	−0.467008	+	0.884253i	$0.654668\pi$
$278$	0	0
$279$	−586.000	−0.125745
$280$	0	0
$281$	−1202.00	−0.255179	−0.127590	−	0.991827i	$-0.540724\pi$
$281$	−1202.00	−0.255179	−0.127590	+	0.991827i	$0.540724\pi$
$282$	0	0
$283$	6620.00	1.39052	0.695262	−	0.718757i	$-0.255288\pi$
$283$	6620.00	1.39052	0.695262	+	0.718757i	$0.255288\pi$
$284$	0	0
$285$	3360.00	0.698348
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−2797.00	−0.569306
$290$	0	0
$291$	1315.00	0.264903
$292$	0	0
$293$	−6968.00	−1.38933	−0.694667	−	0.719331i	$-0.744448\pi$
$293$	−6968.00	−1.38933	−0.694667	+	0.719331i	$0.744448\pi$
$294$	0	0
$295$	−5775.00	−1.13977
$296$	0	0
$297$	1595.00	0.311620
$298$	0	0
$299$	−1404.00	−0.271557
$300$	0	0
$301$	0	0
$302$	0	0
$303$	4070.00	0.771668
$304$	0	0
$305$	3836.00	0.720160
$306$	0	0
$307$	−7640.00	−1.42032	−0.710159	−	0.704041i	$-0.751377\pi$
$307$	−7640.00	−1.42032	−0.710159	+	0.704041i	$0.751377\pi$
$308$	0	0
$309$	−1880.00	−0.346115
$310$	0	0
$311$	652.000	0.118880	0.0594398	−	0.998232i	$-0.481069\pi$
$311$	652.000	0.118880	0.0594398	+	0.998232i	$0.481069\pi$
$312$	0	0
$313$	−8055.00	−1.45462	−0.727309	−	0.686310i	$-0.759229\pi$
$313$	−8055.00	−1.45462	−0.727309	+	0.686310i	$0.759229\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−5675.00	−1.00549	−0.502744	−	0.864435i	$-0.667676\pi$
$317$	−5675.00	−1.00549	−0.502744	+	0.864435i	$0.667676\pi$
$318$	0	0
$319$	−176.000	−0.0308906
$320$	0	0
$321$	−7470.00	−1.29886
$322$	0	0
$323$	−4416.00	−0.760721
$324$	0	0
$325$	3952.00	0.674515
$326$	0	0
$327$	4210.00	0.711968
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−2245.00	−0.372799	−0.186399	−	0.982474i	$-0.559682\pi$
$331$	−2245.00	−0.372799	−0.186399	+	0.982474i	$0.559682\pi$
$332$	0	0
$333$	58.0000	0.00954469
$334$	0	0
$335$	−861.000	−0.140422
$336$	0	0
$337$	−694.000	−0.112180	−0.0560899	−	0.998426i	$-0.517863\pi$
$337$	−694.000	−0.112180	−0.0560899	+	0.998426i	$0.517863\pi$
$338$	0	0
$339$	6405.00	1.02617
$340$	0	0
$341$	−3223.00	−0.511834
$342$	0	0
$343$	0	0
$344$	0	0
$345$	945.000	0.147470
$346$	0	0
$347$	4092.00	0.633055	0.316527	−	0.948583i	$-0.397483\pi$
$347$	4092.00	0.633055	0.316527	+	0.948583i	$0.397483\pi$
$348$	0	0
$349$	−334.000	−0.0512281	−0.0256141	−	0.999672i	$-0.508154\pi$
$349$	−334.000	−0.0512281	−0.0256141	+	0.999672i	$0.508154\pi$
$350$	0	0
$351$	7540.00	1.14660
$352$	0	0
$353$	−891.000	−0.134343	−0.0671716	−	0.997741i	$-0.521397\pi$
$353$	−891.000	−0.134343	−0.0671716	+	0.997741i	$0.521397\pi$
$354$	0	0
$355$	7007.00	1.04759
$356$	0	0
$357$	0	0
$358$	0	0
$359$	2476.00	0.364006	0.182003	−	0.983298i	$-0.441742\pi$
$359$	2476.00	0.364006	0.182003	+	0.983298i	$0.441742\pi$
$360$	0	0
$361$	2357.00	0.343636
$362$	0	0
$363$	605.000	0.0874773
$364$	0	0
$365$	7140.00	1.02390
$366$	0	0
$367$	−1379.00	−0.196140	−0.0980698	−	0.995180i	$-0.531267\pi$
$367$	−1379.00	−0.196140	−0.0980698	+	0.995180i	$0.531267\pi$
$368$	0	0
$369$	−944.000	−0.133178
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−6266.00	−0.869816	−0.434908	−	0.900475i	$-0.643219\pi$
$373$	−6266.00	−0.869816	−0.434908	+	0.900475i	$0.643219\pi$
$374$	0	0
$375$	−7035.00	−0.968762
$376$	0	0
$377$	−832.000	−0.113661
$378$	0	0
$379$	151.000	0.0204653	0.0102327	−	0.999948i	$-0.496743\pi$
$379$	151.000	0.0204653	0.0102327	+	0.999948i	$0.496743\pi$
$380$	0	0
$381$	8680.00	1.16717
$382$	0	0
$383$	1989.00	0.265361	0.132680	−	0.991159i	$-0.457642\pi$
$383$	1989.00	0.265361	0.132680	+	0.991159i	$0.457642\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	220.000	0.0288972
$388$	0	0
$389$	6817.00	0.888523	0.444262	−	0.895897i	$-0.353466\pi$
$389$	6817.00	0.888523	0.444262	+	0.895897i	$0.353466\pi$
$390$	0	0
$391$	−1242.00	−0.160641
$392$	0	0
$393$	−30.0000	−0.00385064
$394$	0	0
$395$	3682.00	0.469017
$396$	0	0
$397$	4170.00	0.527170	0.263585	−	0.964636i	$-0.415095\pi$
$397$	4170.00	0.527170	0.263585	+	0.964636i	$0.415095\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	10914.0	1.35915	0.679575	−	0.733606i	$-0.262164\pi$
$401$	10914.0	1.35915	0.679575	+	0.733606i	$0.262164\pi$
$402$	0	0
$403$	−15236.0	−1.88327
$404$	0	0
$405$	−4697.00	−0.576286
$406$	0	0
$407$	319.000	0.0388507
$408$	0	0
$409$	1102.00	0.133228	0.0666142	−	0.997779i	$-0.478780\pi$
$409$	1102.00	0.133228	0.0666142	+	0.997779i	$0.478780\pi$
$410$	0	0
$411$	−7195.00	−0.863511
$412$	0	0
$413$	0	0
$414$	0	0
$415$	1106.00	0.130823
$416$	0	0
$417$	1590.00	0.186721
$418$	0	0
$419$	−11028.0	−1.28581	−0.642903	−	0.765947i	$-0.722270\pi$
$419$	−11028.0	−1.28581	−0.642903	+	0.765947i	$0.722270\pi$
$420$	0	0
$421$	2622.00	0.303536	0.151768	−	0.988416i	$-0.451503\pi$
$421$	2622.00	0.303536	0.151768	+	0.988416i	$0.451503\pi$
$422$	0	0
$423$	−448.000	−0.0514953
$424$	0	0
$425$	3496.00	0.399014
$426$	0	0
$427$	0	0
$428$	0	0
$429$	2860.00	0.321870
$430$	0	0
$431$	16598.0	1.85498	0.927491	−	0.373845i	$-0.121961\pi$
$431$	16598.0	1.85498	0.927491	+	0.373845i	$0.121961\pi$
$432$	0	0
$433$	5763.00	0.639612	0.319806	−	0.947483i	$-0.396382\pi$
$433$	5763.00	0.639612	0.319806	+	0.947483i	$0.396382\pi$
$434$	0	0
$435$	560.000	0.0617240
$436$	0	0
$437$	2592.00	0.283735
$438$	0	0
$439$	3128.00	0.340071	0.170036	−	0.985438i	$-0.445612\pi$
$439$	3128.00	0.340071	0.170036	+	0.985438i	$0.445612\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	6369.00	0.683071	0.341535	−	0.939869i	$-0.389053\pi$
$443$	6369.00	0.683071	0.341535	+	0.939869i	$0.389053\pi$
$444$	0	0
$445$	8519.00	0.907504
$446$	0	0
$447$	−4610.00	−0.487798
$448$	0	0
$449$	8691.00	0.913483	0.456741	−	0.889600i	$-0.349017\pi$
$449$	8691.00	0.913483	0.456741	+	0.889600i	$0.349017\pi$
$450$	0	0
$451$	−5192.00	−0.542088
$452$	0	0
$453$	−5150.00	−0.534146
$454$	0	0
$455$	0	0
$456$	0	0
$457$	2260.00	0.231331	0.115666	−	0.993288i	$-0.463100\pi$
$457$	2260.00	0.231331	0.115666	+	0.993288i	$0.463100\pi$
$458$	0	0
$459$	6670.00	0.678277
$460$	0	0
$461$	12756.0	1.28873	0.644367	−	0.764717i	$-0.277121\pi$
$461$	12756.0	1.28873	0.644367	+	0.764717i	$0.277121\pi$
$462$	0	0
$463$	−6887.00	−0.691287	−0.345644	−	0.938366i	$-0.612339\pi$
$463$	−6887.00	−0.691287	−0.345644	+	0.938366i	$0.612339\pi$
$464$	0	0
$465$	10255.0	1.02272
$466$	0	0
$467$	1535.00	0.152101	0.0760507	−	0.997104i	$-0.475769\pi$
$467$	1535.00	0.152101	0.0760507	+	0.997104i	$0.475769\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−5085.00	−0.497462
$472$	0	0
$473$	1210.00	0.117623
$474$	0	0
$475$	−7296.00	−0.704765
$476$	0	0
$477$	−1508.00	−0.144752
$478$	0	0
$479$	17564.0	1.67541	0.837703	−	0.546126i	$-0.183898\pi$
$479$	17564.0	1.67541	0.837703	+	0.546126i	$0.183898\pi$
$480$	0	0
$481$	1508.00	0.142950
$482$	0	0
$483$	0	0
$484$	0	0
$485$	1841.00	0.172362
$486$	0	0
$487$	−7541.00	−0.701674	−0.350837	−	0.936437i	$-0.614103\pi$
$487$	−7541.00	−0.701674	−0.350837	+	0.936437i	$0.614103\pi$
$488$	0	0
$489$	−12220.0	−1.13008
$490$	0	0
$491$	12552.0	1.15369	0.576847	−	0.816852i	$-0.304283\pi$
$491$	12552.0	1.15369	0.576847	+	0.816852i	$0.304283\pi$
$492$	0	0
$493$	−736.000	−0.0672369
$494$	0	0
$495$	154.000	0.0139834
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−8396.00	−0.753220	−0.376610	−	0.926372i	$-0.622910\pi$
$499$	−8396.00	−0.753220	−0.376610	+	0.926372i	$0.622910\pi$
$500$	0	0
$501$	7260.00	0.647411
$502$	0	0
$503$	12194.0	1.08092	0.540461	−	0.841369i	$-0.318250\pi$
$503$	12194.0	1.08092	0.540461	+	0.841369i	$0.318250\pi$
$504$	0	0
$505$	5698.00	0.502094
$506$	0	0
$507$	2535.00	0.222058
$508$	0	0
$509$	−18295.0	−1.59315	−0.796573	−	0.604542i	$-0.793356\pi$
$509$	−18295.0	−1.59315	−0.796573	+	0.604542i	$0.793356\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−13920.0	−1.19802
$514$	0	0
$515$	−2632.00	−0.225203
$516$	0	0
$517$	−2464.00	−0.209607
$518$	0	0
$519$	−9570.00	−0.809396
$520$	0	0
$521$	−7101.00	−0.597122	−0.298561	−	0.954391i	$-0.596507\pi$
$521$	−7101.00	−0.597122	−0.298561	+	0.954391i	$0.596507\pi$
$522$	0	0
$523$	4912.00	0.410682	0.205341	−	0.978690i	$-0.434170\pi$
$523$	4912.00	0.410682	0.205341	+	0.978690i	$0.434170\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−13478.0	−1.11406
$528$	0	0
$529$	−11438.0	−0.940084
$530$	0	0
$531$	1650.00	0.134847
$532$	0	0
$533$	−24544.0	−1.99459
$534$	0	0
$535$	−10458.0	−0.845119
$536$	0	0
$537$	6465.00	0.519526
$538$	0	0
$539$	0	0
$540$	0	0
$541$	11496.0	0.913589	0.456794	−	0.889572i	$-0.348997\pi$
$541$	11496.0	0.913589	0.456794	+	0.889572i	$0.348997\pi$
$542$	0	0
$543$	−2275.00	−0.179797
$544$	0	0
$545$	5894.00	0.463250
$546$	0	0
$547$	19048.0	1.48891	0.744455	−	0.667673i	$-0.232709\pi$
$547$	19048.0	1.48891	0.744455	+	0.667673i	$0.232709\pi$
$548$	0	0
$549$	−1096.00	−0.0852024
$550$	0	0
$551$	1536.00	0.118758
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−1015.00	−0.0776295
$556$	0	0
$557$	10718.0	0.815325	0.407663	−	0.913133i	$-0.366344\pi$
$557$	10718.0	0.815325	0.407663	+	0.913133i	$0.366344\pi$
$558$	0	0
$559$	5720.00	0.432791
$560$	0	0
$561$	2530.00	0.190404
$562$	0	0
$563$	−6660.00	−0.498553	−0.249277	−	0.968432i	$-0.580193\pi$
$563$	−6660.00	−0.498553	−0.249277	+	0.968432i	$0.580193\pi$
$564$	0	0
$565$	8967.00	0.667689
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−10960.0	−0.807499	−0.403750	−	0.914870i	$-0.632293\pi$
$569$	−10960.0	−0.807499	−0.403750	+	0.914870i	$0.632293\pi$
$570$	0	0
$571$	18596.0	1.36290	0.681452	−	0.731863i	$-0.261349\pi$
$571$	18596.0	1.36290	0.681452	+	0.731863i	$0.261349\pi$
$572$	0	0
$573$	−5575.00	−0.406455
$574$	0	0
$575$	−2052.00	−0.148825
$576$	0	0
$577$	21119.0	1.52374	0.761868	−	0.647733i	$-0.224283\pi$
$577$	21119.0	1.52374	0.761868	+	0.647733i	$0.224283\pi$
$578$	0	0
$579$	25060.0	1.79872
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−8294.00	−0.589198
$584$	0	0
$585$	728.000	0.0514514
$586$	0	0
$587$	2836.00	0.199411	0.0997055	−	0.995017i	$-0.468210\pi$
$587$	2836.00	0.199411	0.0997055	+	0.995017i	$0.468210\pi$
$588$	0	0
$589$	28128.0	1.96773
$590$	0	0
$591$	−20730.0	−1.44284
$592$	0	0
$593$	−18044.0	−1.24954	−0.624771	−	0.780808i	$-0.714808\pi$
$593$	−18044.0	−1.24954	−0.624771	+	0.780808i	$0.714808\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	6200.00	0.425040
$598$	0	0
$599$	−9264.00	−0.631914	−0.315957	−	0.948773i	$-0.602326\pi$
$599$	−9264.00	−0.631914	−0.315957	+	0.948773i	$0.602326\pi$
$600$	0	0
$601$	19326.0	1.31169	0.655844	−	0.754897i	$-0.272313\pi$
$601$	19326.0	1.31169	0.655844	+	0.754897i	$0.272313\pi$
$602$	0	0
$603$	246.000	0.0166134
$604$	0	0
$605$	847.000	0.0569181
$606$	0	0
$607$	−10082.0	−0.674161	−0.337081	−	0.941476i	$-0.609439\pi$
$607$	−10082.0	−0.674161	−0.337081	+	0.941476i	$0.609439\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−11648.0	−0.771240
$612$	0	0
$613$	13088.0	0.862348	0.431174	−	0.902269i	$-0.358100\pi$
$613$	13088.0	0.862348	0.431174	+	0.902269i	$0.358100\pi$
$614$	0	0
$615$	16520.0	1.08317
$616$	0	0
$617$	23426.0	1.52852	0.764259	−	0.644910i	$-0.223105\pi$
$617$	23426.0	1.52852	0.764259	+	0.644910i	$0.223105\pi$
$618$	0	0
$619$	−23587.0	−1.53157	−0.765785	−	0.643097i	$-0.777649\pi$
$619$	−23587.0	−1.53157	−0.765785	+	0.643097i	$0.777649\pi$
$620$	0	0
$621$	−3915.00	−0.252985
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−349.000	−0.0223360
$626$	0	0
$627$	−5280.00	−0.336304
$628$	0	0
$629$	1334.00	0.0845629
$630$	0	0
$631$	19683.0	1.24179	0.620894	−	0.783895i	$-0.286770\pi$
$631$	19683.0	1.24179	0.620894	+	0.783895i	$0.286770\pi$
$632$	0	0
$633$	−14100.0	−0.885347
$634$	0	0
$635$	12152.0	0.759429
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−2002.00	−0.123940
$640$	0	0
$641$	375.000	0.0231070	0.0115535	−	0.999933i	$-0.496322\pi$
$641$	375.000	0.0231070	0.0115535	+	0.999933i	$0.496322\pi$
$642$	0	0
$643$	21055.0	1.29133	0.645667	−	0.763619i	$-0.276579\pi$
$643$	21055.0	1.29133	0.645667	+	0.763619i	$0.276579\pi$
$644$	0	0
$645$	−3850.00	−0.235029
$646$	0	0
$647$	6427.00	0.390528	0.195264	−	0.980751i	$-0.437444\pi$
$647$	6427.00	0.390528	0.195264	+	0.980751i	$0.437444\pi$
$648$	0	0
$649$	9075.00	0.548883
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−7617.00	−0.456472	−0.228236	−	0.973606i	$-0.573296\pi$
$653$	−7617.00	−0.456472	−0.228236	+	0.973606i	$0.573296\pi$
$654$	0	0
$655$	−42.0000	−0.00250546
$656$	0	0
$657$	−2040.00	−0.121138
$658$	0	0
$659$	−17630.0	−1.04214	−0.521068	−	0.853515i	$-0.674466\pi$
$659$	−17630.0	−1.04214	−0.521068	+	0.853515i	$0.674466\pi$
$660$	0	0
$661$	−4605.00	−0.270974	−0.135487	−	0.990779i	$-0.543260\pi$
$661$	−4605.00	−0.270974	−0.135487	+	0.990779i	$0.543260\pi$
$662$	0	0
$663$	11960.0	0.700585
$664$	0	0
$665$	0	0
$666$	0	0
$667$	432.000	0.0250781
$668$	0	0
$669$	−18475.0	−1.06769
$670$	0	0
$671$	−6028.00	−0.346808
$672$	0	0
$673$	−2818.00	−0.161406	−0.0807028	−	0.996738i	$-0.525716\pi$
$673$	−2818.00	−0.161406	−0.0807028	+	0.996738i	$0.525716\pi$
$674$	0	0
$675$	11020.0	0.628385
$676$	0	0
$677$	−8438.00	−0.479023	−0.239512	−	0.970894i	$-0.576987\pi$
$677$	−8438.00	−0.479023	−0.239512	+	0.970894i	$0.576987\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	2430.00	0.136737
$682$	0	0
$683$	−17344.0	−0.971669	−0.485834	−	0.874051i	$-0.661484\pi$
$683$	−17344.0	−0.971669	−0.485834	+	0.874051i	$0.661484\pi$
$684$	0	0
$685$	−10073.0	−0.561853
$686$	0	0
$687$	−21155.0	−1.17484
$688$	0	0
$689$	−39208.0	−2.16793
$690$	0	0
$691$	3947.00	0.217295	0.108648	−	0.994080i	$-0.465348\pi$
$691$	3947.00	0.217295	0.108648	+	0.994080i	$0.465348\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	2226.00	0.121492
$696$	0	0
$697$	−21712.0	−1.17991
$698$	0	0
$699$	−16680.0	−0.902569
$700$	0	0
$701$	−7998.00	−0.430928	−0.215464	−	0.976512i	$-0.569126\pi$
$701$	−7998.00	−0.430928	−0.215464	+	0.976512i	$0.569126\pi$
$702$	0	0
$703$	−2784.00	−0.149361
$704$	0	0
$705$	7840.00	0.418825
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−881.000	−0.0466666	−0.0233333	−	0.999728i	$-0.507428\pi$
$709$	−881.000	−0.0466666	−0.0233333	+	0.999728i	$0.507428\pi$
$710$	0	0
$711$	−1052.00	−0.0554896
$712$	0	0
$713$	7911.00	0.415525
$714$	0	0
$715$	4004.00	0.209428
$716$	0	0
$717$	18050.0	0.940153
$718$	0	0
$719$	26093.0	1.35341	0.676707	−	0.736252i	$-0.263406\pi$
$719$	26093.0	1.35341	0.676707	+	0.736252i	$0.263406\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	32040.0	1.64811
$724$	0	0
$725$	−1216.00	−0.0622912
$726$	0	0
$727$	7481.00	0.381644	0.190822	−	0.981625i	$-0.438885\pi$
$727$	7481.00	0.381644	0.190822	+	0.981625i	$0.438885\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	0	0
$731$	5060.00	0.256020
$732$	0	0
$733$	−17788.0	−0.896337	−0.448168	−	0.893949i	$-0.647923\pi$
$733$	−17788.0	−0.896337	−0.448168	+	0.893949i	$0.647923\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	1353.00	0.0676233
$738$	0	0
$739$	−32182.0	−1.60194	−0.800970	−	0.598704i	$-0.795683\pi$
$739$	−32182.0	−1.60194	−0.800970	+	0.598704i	$0.795683\pi$
$740$	0	0
$741$	−24960.0	−1.23742
$742$	0	0
$743$	−32044.0	−1.58221	−0.791104	−	0.611682i	$-0.790493\pi$
$743$	−32044.0	−1.58221	−0.791104	+	0.611682i	$0.790493\pi$
$744$	0	0
$745$	−6454.00	−0.317391
$746$	0	0
$747$	−316.000	−0.0154777
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−33779.0	−1.64130	−0.820648	−	0.571434i	$-0.806387\pi$
$751$	−33779.0	−1.64130	−0.820648	+	0.571434i	$0.806387\pi$
$752$	0	0
$753$	8935.00	0.432416
$754$	0	0
$755$	−7210.00	−0.347548
$756$	0	0
$757$	−15630.0	−0.750439	−0.375219	−	0.926936i	$-0.622433\pi$
$757$	−15630.0	−0.750439	−0.375219	+	0.926936i	$0.622433\pi$
$758$	0	0
$759$	−1485.00	−0.0710172
$760$	0	0
$761$	−1948.00	−0.0927923	−0.0463962	−	0.998923i	$-0.514774\pi$
$761$	−1948.00	−0.0927923	−0.0463962	+	0.998923i	$0.514774\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	644.000	0.0304364
$766$	0	0
$767$	42900.0	2.01959
$768$	0	0
$769$	17420.0	0.816881	0.408440	−	0.912785i	$-0.366073\pi$
$769$	17420.0	0.816881	0.408440	+	0.912785i	$0.366073\pi$
$770$	0	0
$771$	1770.00	0.0826783
$772$	0	0
$773$	−11122.0	−0.517504	−0.258752	−	0.965944i	$-0.583311\pi$
$773$	−11122.0	−0.517504	−0.258752	+	0.965944i	$0.583311\pi$
$774$	0	0
$775$	−22268.0	−1.03212
$776$	0	0
$777$	0	0
$778$	0	0
$779$	45312.0	2.08404
$780$	0	0
$781$	−11011.0	−0.504487
$782$	0	0
$783$	−2320.00	−0.105888
$784$	0	0
$785$	−7119.00	−0.323679
$786$	0	0
$787$	−29648.0	−1.34287	−0.671434	−	0.741064i	$-0.734321\pi$
$787$	−29648.0	−1.34287	−0.671434	+	0.741064i	$0.734321\pi$
$788$	0	0
$789$	−10130.0	−0.457082
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−28496.0	−1.27607
$794$	0	0
$795$	26390.0	1.17730
$796$	0	0
$797$	23219.0	1.03194	0.515972	−	0.856606i	$-0.327431\pi$
$797$	23219.0	1.03194	0.515972	+	0.856606i	$0.327431\pi$
$798$	0	0
$799$	−10304.0	−0.456232
$800$	0	0
$801$	−2434.00	−0.107367
$802$	0	0
$803$	−11220.0	−0.493082
$804$	0	0
$805$	0	0
$806$	0	0
$807$	43750.0	1.90839
$808$	0	0
$809$	9232.00	0.401211	0.200606	−	0.979672i	$-0.435709\pi$
$809$	9232.00	0.401211	0.200606	+	0.979672i	$0.435709\pi$
$810$	0	0
$811$	32286.0	1.39792	0.698961	−	0.715160i	$-0.253646\pi$
$811$	32286.0	1.39792	0.698961	+	0.715160i	$0.253646\pi$
$812$	0	0
$813$	25180.0	1.08623
$814$	0	0
$815$	−17108.0	−0.735297
$816$	0	0
$817$	−10560.0	−0.452200
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−31706.0	−1.34780	−0.673902	−	0.738821i	$-0.735383\pi$
$821$	−31706.0	−1.34780	−0.673902	+	0.738821i	$0.735383\pi$
$822$	0	0
$823$	41139.0	1.74242	0.871212	−	0.490906i	$-0.163334\pi$
$823$	41139.0	1.74242	0.871212	+	0.490906i	$0.163334\pi$
$824$	0	0
$825$	4180.00	0.176399
$826$	0	0
$827$	−15252.0	−0.641311	−0.320655	−	0.947196i	$-0.603903\pi$
$827$	−15252.0	−0.641311	−0.320655	+	0.947196i	$0.603903\pi$
$828$	0	0
$829$	−369.000	−0.0154595	−0.00772973	−	0.999970i	$-0.502460\pi$
$829$	−369.000	−0.0154595	−0.00772973	+	0.999970i	$0.502460\pi$
$830$	0	0
$831$	−21530.0	−0.898757
$832$	0	0
$833$	0	0
$834$	0	0
$835$	10164.0	0.421245
$836$	0	0
$837$	−42485.0	−1.75448
$838$	0	0
$839$	10257.0	0.422063	0.211032	−	0.977479i	$-0.432318\pi$
$839$	10257.0	0.422063	0.211032	+	0.977479i	$0.432318\pi$
$840$	0	0
$841$	−24133.0	−0.989503
$842$	0	0
$843$	−6010.00	−0.245546
$844$	0	0
$845$	3549.00	0.144484
$846$	0	0
$847$	0	0
$848$	0	0
$849$	33100.0	1.33803
$850$	0	0
$851$	−783.000	−0.0315404
$852$	0	0
$853$	34386.0	1.38025	0.690126	−	0.723690i	$-0.257555\pi$
$853$	34386.0	1.38025	0.690126	+	0.723690i	$0.257555\pi$
$854$	0	0
$855$	−1344.00	−0.0537589
$856$	0	0
$857$	23464.0	0.935257	0.467628	−	0.883925i	$-0.345109\pi$
$857$	23464.0	0.935257	0.467628	+	0.883925i	$0.345109\pi$
$858$	0	0
$859$	22475.0	0.892709	0.446355	−	0.894856i	$-0.352722\pi$
$859$	22475.0	0.892709	0.446355	+	0.894856i	$0.352722\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	2880.00	0.113599	0.0567997	−	0.998386i	$-0.481910\pi$
$863$	2880.00	0.113599	0.0567997	+	0.998386i	$0.481910\pi$
$864$	0	0
$865$	−13398.0	−0.526642
$866$	0	0
$867$	−13985.0	−0.547815
$868$	0	0
$869$	−5786.00	−0.225865
$870$	0	0
$871$	6396.00	0.248818
$872$	0	0
$873$	−526.000	−0.0203922
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−11084.0	−0.426773	−0.213387	−	0.976968i	$-0.568449\pi$
$877$	−11084.0	−0.426773	−0.213387	+	0.976968i	$0.568449\pi$
$878$	0	0
$879$	−34840.0	−1.33689
$880$	0	0
$881$	−41797.0	−1.59838	−0.799192	−	0.601076i	$-0.794739\pi$
$881$	−41797.0	−1.59838	−0.799192	+	0.601076i	$0.794739\pi$
$882$	0	0
$883$	23780.0	0.906298	0.453149	−	0.891435i	$-0.350301\pi$
$883$	23780.0	0.906298	0.453149	+	0.891435i	$0.350301\pi$
$884$	0	0
$885$	−28875.0	−1.09675
$886$	0	0
$887$	14334.0	0.542603	0.271301	−	0.962494i	$-0.412546\pi$
$887$	14334.0	0.542603	0.271301	+	0.962494i	$0.412546\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	7381.00	0.277523
$892$	0	0
$893$	21504.0	0.805827
$894$	0	0
$895$	9051.00	0.338035
$896$	0	0
$897$	−7020.00	−0.261305
$898$	0	0
$899$	4688.00	0.173919
$900$	0	0
$901$	−34684.0	−1.28245
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−3185.00	−0.116987
$906$	0	0
$907$	25716.0	0.941440	0.470720	−	0.882283i	$-0.343994\pi$
$907$	25716.0	0.941440	0.470720	+	0.882283i	$0.343994\pi$
$908$	0	0
$909$	−1628.00	−0.0594030
$910$	0	0
$911$	−28300.0	−1.02922	−0.514611	−	0.857424i	$-0.672064\pi$
$911$	−28300.0	−1.02922	−0.514611	+	0.857424i	$0.672064\pi$
$912$	0	0
$913$	−1738.00	−0.0630004
$914$	0	0
$915$	19180.0	0.692974
$916$	0	0
$917$	0	0
$918$	0	0
$919$	21410.0	0.768499	0.384250	−	0.923229i	$-0.374460\pi$
$919$	21410.0	0.768499	0.384250	+	0.923229i	$0.374460\pi$
$920$	0	0
$921$	−38200.0	−1.36670
$922$	0	0
$923$	−52052.0	−1.85624
$924$	0	0
$925$	2204.00	0.0783428
$926$	0	0
$927$	752.000	0.0266439
$928$	0	0
$929$	−19938.0	−0.704138	−0.352069	−	0.935974i	$-0.614522\pi$
$929$	−19938.0	−0.704138	−0.352069	+	0.935974i	$0.614522\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	3260.00	0.114392
$934$	0	0
$935$	3542.00	0.123889
$936$	0	0
$937$	−26728.0	−0.931874	−0.465937	−	0.884818i	$-0.654283\pi$
$937$	−26728.0	−0.931874	−0.465937	+	0.884818i	$0.654283\pi$
$938$	0	0
$939$	−40275.0	−1.39971
$940$	0	0
$941$	−8634.00	−0.299108	−0.149554	−	0.988754i	$-0.547784\pi$
$941$	−8634.00	−0.299108	−0.149554	+	0.988754i	$0.547784\pi$
$942$	0	0
$943$	12744.0	0.440087
$944$	0	0
$945$	0	0
$946$	0	0
$947$	24841.0	0.852401	0.426201	−	0.904629i	$-0.359852\pi$
$947$	24841.0	0.852401	0.426201	+	0.904629i	$0.359852\pi$
$948$	0	0
$949$	−53040.0	−1.81428
$950$	0	0
$951$	−28375.0	−0.967531
$952$	0	0
$953$	51234.0	1.74148	0.870741	−	0.491742i	$-0.163640\pi$
$953$	51234.0	1.74148	0.870741	+	0.491742i	$0.163640\pi$
$954$	0	0
$955$	−7805.00	−0.264465
$956$	0	0
$957$	−880.000	−0.0297245
$958$	0	0
$959$	0	0
$960$	0	0
$961$	56058.0	1.88171
$962$	0	0
$963$	2988.00	0.0999865
$964$	0	0
$965$	35084.0	1.17036
$966$	0	0
$967$	−26752.0	−0.889645	−0.444822	−	0.895619i	$-0.646733\pi$
$967$	−26752.0	−0.889645	−0.444822	+	0.895619i	$0.646733\pi$
$968$	0	0
$969$	−22080.0	−0.732004
$970$	0	0
$971$	−21155.0	−0.699172	−0.349586	−	0.936904i	$-0.613678\pi$
$971$	−21155.0	−0.699172	−0.349586	+	0.936904i	$0.613678\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	19760.0	0.649053
$976$	0	0
$977$	−56323.0	−1.84435	−0.922176	−	0.386770i	$-0.873591\pi$
$977$	−56323.0	−1.84435	−0.922176	+	0.386770i	$0.873591\pi$
$978$	0	0
$979$	−13387.0	−0.437028
$980$	0	0
$981$	−1684.00	−0.0548073
$982$	0	0
$983$	−24683.0	−0.800880	−0.400440	−	0.916323i	$-0.631143\pi$
$983$	−24683.0	−0.800880	−0.400440	+	0.916323i	$0.631143\pi$
$984$	0	0
$985$	−29022.0	−0.938800
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−2970.00	−0.0954909
$990$	0	0
$991$	−26816.0	−0.859574	−0.429787	−	0.902930i	$-0.641411\pi$
$991$	−26816.0	−0.859574	−0.429787	+	0.902930i	$0.641411\pi$
$992$	0	0
$993$	−11225.0	−0.358726
$994$	0	0
$995$	8680.00	0.276557
$996$	0	0
$997$	−18614.0	−0.591285	−0.295643	−	0.955299i	$-0.595534\pi$
$997$	−18614.0	−0.591285	−0.295643	+	0.955299i	$0.595534\pi$
$998$	0	0
$999$	4205.00	0.133173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.4.a.b.1.1		1
7.6	odd	2		44.4.a.a.1.1	✓	1
21.20	even	2		396.4.a.e.1.1		1
28.27	even	2		176.4.a.e.1.1		1
35.13	even	4		1100.4.b.c.749.1		2
35.27	even	4		1100.4.b.c.749.2		2
35.34	odd	2		1100.4.a.d.1.1		1
56.13	odd	2		704.4.a.j.1.1		1
56.27	even	2		704.4.a.c.1.1		1
77.76	even	2		484.4.a.a.1.1		1
84.83	odd	2		1584.4.a.p.1.1		1
308.307	odd	2		1936.4.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.a.a.1.1	✓	1	7.6	odd	2
176.4.a.e.1.1		1	28.27	even	2
396.4.a.e.1.1		1	21.20	even	2
484.4.a.a.1.1		1	77.76	even	2
704.4.a.c.1.1		1	56.27	even	2
704.4.a.j.1.1		1	56.13	odd	2
1100.4.a.d.1.1		1	35.34	odd	2
1100.4.b.c.749.1		2	35.13	even	4
1100.4.b.c.749.2		2	35.27	even	4
1584.4.a.p.1.1		1	84.83	odd	2
1936.4.a.m.1.1		1	308.307	odd	2
2156.4.a.b.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:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2156.a (trivial)

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