LMFDB - Embedded newform 882.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,6,Mod(1,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("882.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	882.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:	$141.458529075$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	882.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} +16.0000 q^{4} -54.0000 q^{5} -64.0000 q^{8} +O(q^{10})$

$q-4.00000 q^{2} +16.0000 q^{4} -54.0000 q^{5} -64.0000 q^{8} +216.000 q^{10} +594.000 q^{11} -26.0000 q^{13} +256.000 q^{16} +534.000 q^{17} +3004.00 q^{19} -864.000 q^{20} -2376.00 q^{22} +3510.00 q^{23} -209.000 q^{25} +104.000 q^{26} +4296.00 q^{29} -8036.00 q^{31} -1024.00 q^{32} -2136.00 q^{34} -502.000 q^{37} -12016.0 q^{38} +3456.00 q^{40} -9870.00 q^{41} +9068.00 q^{43} +9504.00 q^{44} -14040.0 q^{46} -1140.00 q^{47} +836.000 q^{50} -416.000 q^{52} +28356.0 q^{53} -32076.0 q^{55} -17184.0 q^{58} +8196.00 q^{59} -29822.0 q^{61} +32144.0 q^{62} +4096.00 q^{64} +1404.00 q^{65} -62884.0 q^{67} +8544.00 q^{68} -34398.0 q^{71} -56990.0 q^{73} +2008.00 q^{74} +48064.0 q^{76} +49496.0 q^{79} -13824.0 q^{80} +39480.0 q^{82} +52512.0 q^{83} -28836.0 q^{85} -36272.0 q^{86} -38016.0 q^{88} +48282.0 q^{89} +56160.0 q^{92} +4560.00 q^{94} -162216. q^{95} +83938.0 q^{97} +O(q^{100})$

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	16.0000	0.500000
$5$	−54.0000	−0.965981	−0.482991	−	0.875625i	$-0.660450\pi$
$5$	−54.0000	−0.965981	−0.482991	+	0.875625i	$0.660450\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	0	0
$10$	216.000	0.683052
$11$	594.000	1.48015	0.740073	−	0.672526i	$-0.234791\pi$
$11$	594.000	1.48015	0.740073	+	0.672526i	$0.234791\pi$
$12$	0	0
$13$	−26.0000	−0.0426692	−0.0213346	−	0.999772i	$-0.506792\pi$
$13$	−26.0000	−0.0426692	−0.0213346	+	0.999772i	$0.506792\pi$
$14$	0	0
$15$	0	0
$16$	256.000	0.250000
$17$	534.000	0.448145	0.224073	−	0.974572i	$-0.428065\pi$
$17$	534.000	0.448145	0.224073	+	0.974572i	$0.428065\pi$
$18$	0	0
$19$	3004.00	1.90904	0.954522	−	0.298141i	$-0.0963664\pi$
$19$	3004.00	1.90904	0.954522	+	0.298141i	$0.0963664\pi$
$20$	−864.000	−0.482991
$21$	0	0
$22$	−2376.00	−1.04662
$23$	3510.00	1.38353	0.691763	−	0.722124i	$-0.256834\pi$
$23$	3510.00	1.38353	0.691763	+	0.722124i	$0.256834\pi$
$24$	0	0
$25$	−209.000	−0.0668800
$26$	104.000	0.0301717
$27$	0	0
$28$	0	0
$29$	4296.00	0.948570	0.474285	−	0.880371i	$-0.342707\pi$
$29$	4296.00	0.948570	0.474285	+	0.880371i	$0.342707\pi$
$30$	0	0
$31$	−8036.00	−1.50188	−0.750941	−	0.660370i	$-0.770400\pi$
$31$	−8036.00	−1.50188	−0.750941	+	0.660370i	$0.770400\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	−2136.00	−0.316887
$35$	0	0
$36$	0	0
$37$	−502.000	−0.0602836	−0.0301418	−	0.999546i	$-0.509596\pi$
$37$	−502.000	−0.0602836	−0.0301418	+	0.999546i	$0.509596\pi$
$38$	−12016.0	−1.34990
$39$	0	0
$40$	3456.00	0.341526
$41$	−9870.00	−0.916975	−0.458488	−	0.888701i	$-0.651609\pi$
$41$	−9870.00	−0.916975	−0.458488	+	0.888701i	$0.651609\pi$
$42$	0	0
$43$	9068.00	0.747895	0.373947	−	0.927450i	$-0.378004\pi$
$43$	9068.00	0.747895	0.373947	+	0.927450i	$0.378004\pi$
$44$	9504.00	0.740073
$45$	0	0
$46$	−14040.0	−0.978301
$47$	−1140.00	−0.0752766	−0.0376383	−	0.999291i	$-0.511983\pi$
$47$	−1140.00	−0.0752766	−0.0376383	+	0.999291i	$0.511983\pi$
$48$	0	0
$49$	0	0
$50$	836.000	0.0472913
$51$	0	0
$52$	−416.000	−0.0213346
$53$	28356.0	1.38661	0.693307	−	0.720643i	$-0.256153\pi$
$53$	28356.0	1.38661	0.693307	+	0.720643i	$0.256153\pi$
$54$	0	0
$55$	−32076.0	−1.42979
$56$	0	0
$57$	0	0
$58$	−17184.0	−0.670740
$59$	8196.00	0.306529	0.153265	−	0.988185i	$-0.451021\pi$
$59$	8196.00	0.306529	0.153265	+	0.988185i	$0.451021\pi$
$60$	0	0
$61$	−29822.0	−1.02615	−0.513077	−	0.858343i	$-0.671494\pi$
$61$	−29822.0	−1.02615	−0.513077	+	0.858343i	$0.671494\pi$
$62$	32144.0	1.06199
$63$	0	0
$64$	4096.00	0.125000
$65$	1404.00	0.0412177
$66$	0	0
$67$	−62884.0	−1.71141	−0.855703	−	0.517467i	$-0.826875\pi$
$67$	−62884.0	−1.71141	−0.855703	+	0.517467i	$0.826875\pi$
$68$	8544.00	0.224073
$69$	0	0
$70$	0	0
$71$	−34398.0	−0.809818	−0.404909	−	0.914357i	$-0.632697\pi$
$71$	−34398.0	−0.809818	−0.404909	+	0.914357i	$0.632697\pi$
$72$	0	0
$73$	−56990.0	−1.25167	−0.625837	−	0.779954i	$-0.715243\pi$
$73$	−56990.0	−1.25167	−0.625837	+	0.779954i	$0.715243\pi$
$74$	2008.00	0.0426270
$75$	0	0
$76$	48064.0	0.954522
$77$	0	0
$78$	0	0
$79$	49496.0	0.892282	0.446141	−	0.894963i	$-0.352798\pi$
$79$	49496.0	0.892282	0.446141	+	0.894963i	$0.352798\pi$
$80$	−13824.0	−0.241495
$81$	0	0
$82$	39480.0	0.648399
$83$	52512.0	0.836688	0.418344	−	0.908289i	$-0.362611\pi$
$83$	52512.0	0.836688	0.418344	+	0.908289i	$0.362611\pi$
$84$	0	0
$85$	−28836.0	−0.432900
$86$	−36272.0	−0.528841
$87$	0	0
$88$	−38016.0	−0.523311
$89$	48282.0	0.646116	0.323058	−	0.946379i	$-0.395289\pi$
$89$	48282.0	0.646116	0.323058	+	0.946379i	$0.395289\pi$
$90$	0	0
$91$	0	0
$92$	56160.0	0.691763
$93$	0	0
$94$	4560.00	0.0532286
$95$	−162216.	−1.84410
$96$	0	0
$97$	83938.0	0.905794	0.452897	−	0.891563i	$-0.350391\pi$
$97$	83938.0	0.905794	0.452897	+	0.891563i	$0.350391\pi$
$98$	0	0
$99$	0	0
$100$	−3344.00	−0.0334400
$101$	62694.0	0.611537	0.305768	−	0.952106i	$-0.401087\pi$
$101$	62694.0	0.611537	0.305768	+	0.952106i	$0.401087\pi$
$102$	0	0
$103$	30988.0	0.287806	0.143903	−	0.989592i	$-0.454035\pi$
$103$	30988.0	0.287806	0.143903	+	0.989592i	$0.454035\pi$
$104$	1664.00	0.0150859
$105$	0	0
$106$	−113424.	−0.980484
$107$	118218.	0.998215	0.499108	−	0.866540i	$-0.333661\pi$
$107$	118218.	0.998215	0.499108	+	0.866540i	$0.333661\pi$
$108$	0	0
$109$	207362.	1.67172	0.835859	−	0.548944i	$-0.184970\pi$
$109$	207362.	1.67172	0.835859	+	0.548944i	$0.184970\pi$
$110$	128304.	1.01102
$111$	0	0
$112$	0	0
$113$	−136416.	−1.00501	−0.502504	−	0.864575i	$-0.667588\pi$
$113$	−136416.	−1.00501	−0.502504	+	0.864575i	$0.667588\pi$
$114$	0	0
$115$	−189540.	−1.33646
$116$	68736.0	0.474285
$117$	0	0
$118$	−32784.0	−0.216749
$119$	0	0
$120$	0	0
$121$	191785.	1.19083
$122$	119288.	0.725600
$123$	0	0
$124$	−128576.	−0.750941
$125$	180036.	1.03059
$126$	0	0
$127$	−128248.	−0.705572	−0.352786	−	0.935704i	$-0.614766\pi$
$127$	−128248.	−0.705572	−0.352786	+	0.935704i	$0.614766\pi$
$128$	−16384.0	−0.0883883
$129$	0	0
$130$	−5616.00	−0.0291453
$131$	−370296.	−1.88526	−0.942629	−	0.333842i	$-0.891655\pi$
$131$	−370296.	−1.88526	−0.942629	+	0.333842i	$0.891655\pi$
$132$	0	0
$133$	0	0
$134$	251536.	1.21015
$135$	0	0
$136$	−34176.0	−0.158443
$137$	12924.0	0.0588296	0.0294148	−	0.999567i	$-0.490636\pi$
$137$	12924.0	0.0588296	0.0294148	+	0.999567i	$0.490636\pi$
$138$	0	0
$139$	177760.	0.780364	0.390182	−	0.920738i	$-0.372412\pi$
$139$	177760.	0.780364	0.390182	+	0.920738i	$0.372412\pi$
$140$	0	0
$141$	0	0
$142$	137592.	0.572628
$143$	−15444.0	−0.0631567
$144$	0	0
$145$	−231984.	−0.916301
$146$	227960.	0.885068
$147$	0	0
$148$	−8032.00	−0.0301418
$149$	309564.	1.14231	0.571156	−	0.820841i	$-0.306495\pi$
$149$	309564.	1.14231	0.571156	+	0.820841i	$0.306495\pi$
$150$	0	0
$151$	−300136.	−1.07121	−0.535606	−	0.844468i	$-0.679917\pi$
$151$	−300136.	−1.07121	−0.535606	+	0.844468i	$0.679917\pi$
$152$	−192256.	−0.674949
$153$	0	0
$154$	0	0
$155$	433944.	1.45079
$156$	0	0
$157$	−11726.0	−0.0379665	−0.0189833	−	0.999820i	$-0.506043\pi$
$157$	−11726.0	−0.0379665	−0.0189833	+	0.999820i	$0.506043\pi$
$158$	−197984.	−0.630939
$159$	0	0
$160$	55296.0	0.170763
$161$	0	0
$162$	0	0
$163$	−269260.	−0.793785	−0.396892	−	0.917865i	$-0.629911\pi$
$163$	−269260.	−0.793785	−0.396892	+	0.917865i	$0.629911\pi$
$164$	−157920.	−0.458488
$165$	0	0
$166$	−210048.	−0.591627
$167$	−41604.0	−0.115437	−0.0577184	−	0.998333i	$-0.518383\pi$
$167$	−41604.0	−0.115437	−0.0577184	+	0.998333i	$0.518383\pi$
$168$	0	0
$169$	−370617.	−0.998179
$170$	115344.	0.306107
$171$	0	0
$172$	145088.	0.373947
$173$	−286962.	−0.728969	−0.364485	−	0.931209i	$-0.618755\pi$
$173$	−286962.	−0.728969	−0.364485	+	0.931209i	$0.618755\pi$
$174$	0	0
$175$	0	0
$176$	152064.	0.370037
$177$	0	0
$178$	−193128.	−0.456873
$179$	−420186.	−0.980187	−0.490094	−	0.871670i	$-0.663037\pi$
$179$	−420186.	−0.980187	−0.490094	+	0.871670i	$0.663037\pi$
$180$	0	0
$181$	16918.0	0.0383842	0.0191921	−	0.999816i	$-0.493891\pi$
$181$	16918.0	0.0383842	0.0191921	+	0.999816i	$0.493891\pi$
$182$	0	0
$183$	0	0
$184$	−224640.	−0.489151
$185$	27108.0	0.0582329
$186$	0	0
$187$	317196.	0.663321
$188$	−18240.0	−0.0376383
$189$	0	0
$190$	648864.	1.30398
$191$	−134742.	−0.267251	−0.133626	−	0.991032i	$-0.542662\pi$
$191$	−134742.	−0.267251	−0.133626	+	0.991032i	$0.542662\pi$
$192$	0	0
$193$	−314650.	−0.608043	−0.304022	−	0.952665i	$-0.598330\pi$
$193$	−314650.	−0.608043	−0.304022	+	0.952665i	$0.598330\pi$
$194$	−335752.	−0.640493
$195$	0	0
$196$	0	0
$197$	596628.	1.09531	0.547656	−	0.836703i	$-0.315520\pi$
$197$	596628.	1.09531	0.547656	+	0.836703i	$0.315520\pi$
$198$	0	0
$199$	10096.0	0.0180724	0.00903622	−	0.999959i	$-0.497124\pi$
$199$	10096.0	0.0180724	0.00903622	+	0.999959i	$0.497124\pi$
$200$	13376.0	0.0236457
$201$	0	0
$202$	−250776.	−0.432422
$203$	0	0
$204$	0	0
$205$	532980.	0.885781
$206$	−123952.	−0.203510
$207$	0	0
$208$	−6656.00	−0.0106673
$209$	1.78438e6	2.82566
$210$	0	0
$211$	−721324.	−1.11538	−0.557692	−	0.830048i	$-0.688313\pi$
$211$	−721324.	−1.11538	−0.557692	+	0.830048i	$0.688313\pi$
$212$	453696.	0.693307
$213$	0	0
$214$	−472872.	−0.705845
$215$	−489672.	−0.722452
$216$	0	0
$217$	0	0
$218$	−829448.	−1.18208
$219$	0	0
$220$	−513216.	−0.714897
$221$	−13884.0	−0.0191220
$222$	0	0
$223$	536584.	0.722563	0.361281	−	0.932457i	$-0.382339\pi$
$223$	536584.	0.722563	0.361281	+	0.932457i	$0.382339\pi$
$224$	0	0
$225$	0	0
$226$	545664.	0.710647
$227$	1.48698e6	1.91532	0.957658	−	0.287908i	$-0.0929597\pi$
$227$	1.48698e6	1.91532	0.957658	+	0.287908i	$0.0929597\pi$
$228$	0	0
$229$	1.10957e6	1.39818	0.699092	−	0.715032i	$-0.253588\pi$
$229$	1.10957e6	1.39818	0.699092	+	0.715032i	$0.253588\pi$
$230$	758160.	0.945021
$231$	0	0
$232$	−274944.	−0.335370
$233$	1.38796e6	1.67489	0.837444	−	0.546523i	$-0.184049\pi$
$233$	1.38796e6	1.67489	0.837444	+	0.546523i	$0.184049\pi$
$234$	0	0
$235$	61560.0	0.0727158
$236$	131136.	0.153265
$237$	0	0
$238$	0	0
$239$	1.56406e6	1.77117	0.885583	−	0.464481i	$-0.153759\pi$
$239$	1.56406e6	1.77117	0.885583	+	0.464481i	$0.153759\pi$
$240$	0	0
$241$	−1.36319e6	−1.51187	−0.755934	−	0.654648i	$-0.772817\pi$
$241$	−1.36319e6	−1.51187	−0.755934	+	0.654648i	$0.772817\pi$
$242$	−767140.	−0.842047
$243$	0	0
$244$	−477152.	−0.513077
$245$	0	0
$246$	0	0
$247$	−78104.0	−0.0814575
$248$	514304.	0.530995
$249$	0	0
$250$	−720144.	−0.728734
$251$	1.54847e6	1.55138	0.775690	−	0.631115i	$-0.217402\pi$
$251$	1.54847e6	1.55138	0.775690	+	0.631115i	$0.217402\pi$
$252$	0	0
$253$	2.08494e6	2.04782
$254$	512992.	0.498915
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.54147e6	1.45580	0.727899	−	0.685684i	$-0.240497\pi$
$257$	1.54147e6	1.45580	0.727899	+	0.685684i	$0.240497\pi$
$258$	0	0
$259$	0	0
$260$	22464.0	0.0206088
$261$	0	0
$262$	1.48118e6	1.33308
$263$	−2.13251e6	−1.90109	−0.950545	−	0.310588i	$-0.899474\pi$
$263$	−2.13251e6	−1.90109	−0.950545	+	0.310588i	$0.899474\pi$
$264$	0	0
$265$	−1.53122e6	−1.33944
$266$	0	0
$267$	0	0
$268$	−1.00614e6	−0.855703
$269$	−386142.	−0.325362	−0.162681	−	0.986679i	$-0.552014\pi$
$269$	−386142.	−0.325362	−0.162681	+	0.986679i	$0.552014\pi$
$270$	0	0
$271$	1.17581e6	0.972556	0.486278	−	0.873804i	$-0.338354\pi$
$271$	1.17581e6	0.972556	0.486278	+	0.873804i	$0.338354\pi$
$272$	136704.	0.112036
$273$	0	0
$274$	−51696.0	−0.0415988
$275$	−124146.	−0.0989922
$276$	0	0
$277$	417038.	0.326570	0.163285	−	0.986579i	$-0.447791\pi$
$277$	417038.	0.326570	0.163285	+	0.986579i	$0.447791\pi$
$278$	−711040.	−0.551800
$279$	0	0
$280$	0	0
$281$	−523932.	−0.395830	−0.197915	−	0.980219i	$-0.563417\pi$
$281$	−523932.	−0.395830	−0.197915	+	0.980219i	$0.563417\pi$
$282$	0	0
$283$	2.36724e6	1.75702	0.878510	−	0.477723i	$-0.158538\pi$
$283$	2.36724e6	1.75702	0.878510	+	0.477723i	$0.158538\pi$
$284$	−550368.	−0.404909
$285$	0	0
$286$	61776.0	0.0446586
$287$	0	0
$288$	0	0
$289$	−1.13470e6	−0.799166
$290$	927936.	0.647922
$291$	0	0
$292$	−911840.	−0.625837
$293$	2.44630e6	1.66472	0.832360	−	0.554236i	$-0.186989\pi$
$293$	2.44630e6	1.66472	0.832360	+	0.554236i	$0.186989\pi$
$294$	0	0
$295$	−442584.	−0.296102
$296$	32128.0	0.0213135
$297$	0	0
$298$	−1.23826e6	−0.807737
$299$	−91260.0	−0.0590340
$300$	0	0
$301$	0	0
$302$	1.20054e6	0.757462
$303$	0	0
$304$	769024.	0.477261
$305$	1.61039e6	0.991245
$306$	0	0
$307$	969316.	0.586975	0.293487	−	0.955963i	$-0.405184\pi$
$307$	969316.	0.586975	0.293487	+	0.955963i	$0.405184\pi$
$308$	0	0
$309$	0	0
$310$	−1.73578e6	−1.02586
$311$	−2.44765e6	−1.43499	−0.717495	−	0.696564i	$-0.754711\pi$
$311$	−2.44765e6	−1.43499	−0.717495	+	0.696564i	$0.754711\pi$
$312$	0	0
$313$	−2.02541e6	−1.16856	−0.584281	−	0.811551i	$-0.698624\pi$
$313$	−2.02541e6	−1.16856	−0.584281	+	0.811551i	$0.698624\pi$
$314$	46904.0	0.0268464
$315$	0	0
$316$	791936.	0.446141
$317$	2.50379e6	1.39942	0.699712	−	0.714425i	$-0.253312\pi$
$317$	2.50379e6	1.39942	0.699712	+	0.714425i	$0.253312\pi$
$318$	0	0
$319$	2.55182e6	1.40402
$320$	−221184.	−0.120748
$321$	0	0
$322$	0	0
$323$	1.60414e6	0.855529
$324$	0	0
$325$	5434.00	0.00285372
$326$	1.07704e6	0.561291
$327$	0	0
$328$	631680.	0.324200
$329$	0	0
$330$	0	0
$331$	1.28700e6	0.645665	0.322832	−	0.946456i	$-0.395365\pi$
$331$	1.28700e6	0.645665	0.322832	+	0.946456i	$0.395365\pi$
$332$	840192.	0.418344
$333$	0	0
$334$	166416.	0.0816261
$335$	3.39574e6	1.65319
$336$	0	0
$337$	−1.40639e6	−0.674574	−0.337287	−	0.941402i	$-0.609509\pi$
$337$	−1.40639e6	−0.674574	−0.337287	+	0.941402i	$0.609509\pi$
$338$	1.48247e6	0.705819
$339$	0	0
$340$	−461376.	−0.216450
$341$	−4.77338e6	−2.22300
$342$	0	0
$343$	0	0
$344$	−580352.	−0.264421
$345$	0	0
$346$	1.14785e6	0.515459
$347$	−1.25313e6	−0.558692	−0.279346	−	0.960191i	$-0.590118\pi$
$347$	−1.25313e6	−0.558692	−0.279346	+	0.960191i	$0.590118\pi$
$348$	0	0
$349$	−1.66876e6	−0.733381	−0.366691	−	0.930343i	$-0.619509\pi$
$349$	−1.66876e6	−0.733381	−0.366691	+	0.930343i	$0.619509\pi$
$350$	0	0
$351$	0	0
$352$	−608256.	−0.261655
$353$	2.13687e6	0.912728	0.456364	−	0.889793i	$-0.349152\pi$
$353$	2.13687e6	0.912728	0.456364	+	0.889793i	$0.349152\pi$
$354$	0	0
$355$	1.85749e6	0.782269
$356$	772512.	0.323058
$357$	0	0
$358$	1.68074e6	0.693097
$359$	3.60907e6	1.47795	0.738973	−	0.673735i	$-0.235311\pi$
$359$	3.60907e6	1.47795	0.738973	+	0.673735i	$0.235311\pi$
$360$	0	0
$361$	6.54792e6	2.64445
$362$	−67672.0	−0.0271417
$363$	0	0
$364$	0	0
$365$	3.07746e6	1.20909
$366$	0	0
$367$	1.88190e6	0.729344	0.364672	−	0.931136i	$-0.381181\pi$
$367$	1.88190e6	0.729344	0.364672	+	0.931136i	$0.381181\pi$
$368$	898560.	0.345882
$369$	0	0
$370$	−108432.	−0.0411769
$371$	0	0
$372$	0	0
$373$	4.86186e6	1.80938	0.904692	−	0.426067i	$-0.140101\pi$
$373$	4.86186e6	1.80938	0.904692	+	0.426067i	$0.140101\pi$
$374$	−1.26878e6	−0.469039
$375$	0	0
$376$	72960.0	0.0266143
$377$	−111696.	−0.0404748
$378$	0	0
$379$	251300.	0.0898658	0.0449329	−	0.998990i	$-0.485693\pi$
$379$	251300.	0.0898658	0.0449329	+	0.998990i	$0.485693\pi$
$380$	−2.59546e6	−0.922050
$381$	0	0
$382$	538968.	0.188975
$383$	567720.	0.197759	0.0988797	−	0.995099i	$-0.468474\pi$
$383$	567720.	0.197759	0.0988797	+	0.995099i	$0.468474\pi$
$384$	0	0
$385$	0	0
$386$	1.25860e6	0.429951
$387$	0	0
$388$	1.34301e6	0.452897
$389$	−2.34547e6	−0.785880	−0.392940	−	0.919564i	$-0.628542\pi$
$389$	−2.34547e6	−0.785880	−0.392940	+	0.919564i	$0.628542\pi$
$390$	0	0
$391$	1.87434e6	0.620021
$392$	0	0
$393$	0	0
$394$	−2.38651e6	−0.774503
$395$	−2.67278e6	−0.861928
$396$	0	0
$397$	5.25719e6	1.67408	0.837042	−	0.547139i	$-0.184283\pi$
$397$	5.25719e6	1.67408	0.837042	+	0.547139i	$0.184283\pi$
$398$	−40384.0	−0.0127791
$399$	0	0
$400$	−53504.0	−0.0167200
$401$	−2.34140e6	−0.727136	−0.363568	−	0.931568i	$-0.618442\pi$
$401$	−2.34140e6	−0.727136	−0.363568	+	0.931568i	$0.618442\pi$
$402$	0	0
$403$	208936.	0.0640842
$404$	1.00310e6	0.305768
$405$	0	0
$406$	0	0
$407$	−298188.	−0.0892286
$408$	0	0
$409$	−662318.	−0.195775	−0.0978877	−	0.995197i	$-0.531209\pi$
$409$	−662318.	−0.195775	−0.0978877	+	0.995197i	$0.531209\pi$
$410$	−2.13192e6	−0.626342
$411$	0	0
$412$	495808.	0.143903
$413$	0	0
$414$	0	0
$415$	−2.83565e6	−0.808225
$416$	26624.0	0.00754293
$417$	0	0
$418$	−7.13750e6	−1.99805
$419$	−5.27752e6	−1.46857	−0.734285	−	0.678842i	$-0.762482\pi$
$419$	−5.27752e6	−1.46857	−0.734285	+	0.678842i	$0.762482\pi$
$420$	0	0
$421$	1.74817e6	0.480706	0.240353	−	0.970686i	$-0.422737\pi$
$421$	1.74817e6	0.480706	0.240353	+	0.970686i	$0.422737\pi$
$422$	2.88530e6	0.788695
$423$	0	0
$424$	−1.81478e6	−0.490242
$425$	−111606.	−0.0299720
$426$	0	0
$427$	0	0
$428$	1.89149e6	0.499108
$429$	0	0
$430$	1.95869e6	0.510851
$431$	−2.65575e6	−0.688643	−0.344321	−	0.938852i	$-0.611891\pi$
$431$	−2.65575e6	−0.688643	−0.344321	+	0.938852i	$0.611891\pi$
$432$	0	0
$433$	3.12026e6	0.799781	0.399891	−	0.916563i	$-0.369048\pi$
$433$	3.12026e6	0.799781	0.399891	+	0.916563i	$0.369048\pi$
$434$	0	0
$435$	0	0
$436$	3.31779e6	0.835859
$437$	1.05440e7	2.64121
$438$	0	0
$439$	4.02131e6	0.995879	0.497939	−	0.867212i	$-0.334090\pi$
$439$	4.02131e6	0.995879	0.497939	+	0.867212i	$0.334090\pi$
$440$	2.05286e6	0.505509
$441$	0	0
$442$	55536.0	0.0135213
$443$	−766146.	−0.185482	−0.0927411	−	0.995690i	$-0.529563\pi$
$443$	−766146.	−0.185482	−0.0927411	+	0.995690i	$0.529563\pi$
$444$	0	0
$445$	−2.60723e6	−0.624136
$446$	−2.14634e6	−0.510929
$447$	0	0
$448$	0	0
$449$	−3.01961e6	−0.706862	−0.353431	−	0.935461i	$-0.614985\pi$
$449$	−3.01961e6	−0.706862	−0.353431	+	0.935461i	$0.614985\pi$
$450$	0	0
$451$	−5.86278e6	−1.35726
$452$	−2.18266e6	−0.502504
$453$	0	0
$454$	−5.94792e6	−1.35433
$455$	0	0
$456$	0	0
$457$	−223114.	−0.0499731	−0.0249866	−	0.999688i	$-0.507954\pi$
$457$	−223114.	−0.0499731	−0.0249866	+	0.999688i	$0.507954\pi$
$458$	−4.43826e6	−0.988666
$459$	0	0
$460$	−3.03264e6	−0.668230
$461$	4.58050e6	1.00383	0.501916	−	0.864917i	$-0.332629\pi$
$461$	4.58050e6	1.00383	0.501916	+	0.864917i	$0.332629\pi$
$462$	0	0
$463$	−4.23654e6	−0.918458	−0.459229	−	0.888318i	$-0.651874\pi$
$463$	−4.23654e6	−0.918458	−0.459229	+	0.888318i	$0.651874\pi$
$464$	1.09978e6	0.237142
$465$	0	0
$466$	−5.55182e6	−1.18433
$467$	2.74499e6	0.582436	0.291218	−	0.956657i	$-0.405939\pi$
$467$	2.74499e6	0.582436	0.291218	+	0.956657i	$0.405939\pi$
$468$	0	0
$469$	0	0
$470$	−246240.	−0.0514179
$471$	0	0
$472$	−524544.	−0.108374
$473$	5.38639e6	1.10699
$474$	0	0
$475$	−627836.	−0.127677
$476$	0	0
$477$	0	0
$478$	−6.25625e6	−1.25240
$479$	2.67628e6	0.532957	0.266478	−	0.963841i	$-0.414140\pi$
$479$	2.67628e6	0.532957	0.266478	+	0.963841i	$0.414140\pi$
$480$	0	0
$481$	13052.0	0.00257226
$482$	5.45276e6	1.06905
$483$	0	0
$484$	3.06856e6	0.595417
$485$	−4.53265e6	−0.874980
$486$	0	0
$487$	−7.92959e6	−1.51506	−0.757528	−	0.652803i	$-0.773593\pi$
$487$	−7.92959e6	−1.51506	−0.757528	+	0.652803i	$0.773593\pi$
$488$	1.90861e6	0.362800
$489$	0	0
$490$	0	0
$491$	−7.10567e6	−1.33015	−0.665076	−	0.746775i	$-0.731601\pi$
$491$	−7.10567e6	−1.33015	−0.665076	+	0.746775i	$0.731601\pi$
$492$	0	0
$493$	2.29406e6	0.425097
$494$	312416.	0.0575991
$495$	0	0
$496$	−2.05722e6	−0.375470
$497$	0	0
$498$	0	0
$499$	−1.31352e6	−0.236149	−0.118075	−	0.993005i	$-0.537672\pi$
$499$	−1.31352e6	−0.236149	−0.118075	+	0.993005i	$0.537672\pi$
$500$	2.88058e6	0.515293
$501$	0	0
$502$	−6.19387e6	−1.09699
$503$	−3.64608e6	−0.642549	−0.321274	−	0.946986i	$-0.604111\pi$
$503$	−3.64608e6	−0.642549	−0.321274	+	0.946986i	$0.604111\pi$
$504$	0	0
$505$	−3.38548e6	−0.590733
$506$	−8.33976e6	−1.44803
$507$	0	0
$508$	−2.05197e6	−0.352786
$509$	−9.65410e6	−1.65165	−0.825824	−	0.563928i	$-0.809289\pi$
$509$	−9.65410e6	−1.65165	−0.825824	+	0.563928i	$0.809289\pi$
$510$	0	0
$511$	0	0
$512$	−262144.	−0.0441942
$513$	0	0
$514$	−6.16586e6	−1.02940
$515$	−1.67335e6	−0.278016
$516$	0	0
$517$	−677160.	−0.111420
$518$	0	0
$519$	0	0
$520$	−89856.0	−0.0145727
$521$	−7.67870e6	−1.23935	−0.619674	−	0.784859i	$-0.712735\pi$
$521$	−7.67870e6	−1.23935	−0.619674	+	0.784859i	$0.712735\pi$
$522$	0	0
$523$	9.06510e6	1.44917	0.724584	−	0.689187i	$-0.242032\pi$
$523$	9.06510e6	1.44917	0.724584	+	0.689187i	$0.242032\pi$
$524$	−5.92474e6	−0.942629
$525$	0	0
$526$	8.53006e6	1.34427
$527$	−4.29122e6	−0.673061
$528$	0	0
$529$	5.88376e6	0.914146
$530$	6.12490e6	0.947129
$531$	0	0
$532$	0	0
$533$	256620.	0.0391266
$534$	0	0
$535$	−6.38377e6	−0.964257
$536$	4.02458e6	0.605074
$537$	0	0
$538$	1.54457e6	0.230065
$539$	0	0
$540$	0	0
$541$	7.33108e6	1.07690	0.538449	−	0.842658i	$-0.319010\pi$
$541$	7.33108e6	1.07690	0.538449	+	0.842658i	$0.319010\pi$
$542$	−4.70325e6	−0.687701
$543$	0	0
$544$	−546816.	−0.0792217
$545$	−1.11975e7	−1.61485
$546$	0	0
$547$	−3.16498e6	−0.452275	−0.226138	−	0.974095i	$-0.572610\pi$
$547$	−3.16498e6	−0.452275	−0.226138	+	0.974095i	$0.572610\pi$
$548$	206784.	0.0294148
$549$	0	0
$550$	496584.	0.0699981
$551$	1.29052e7	1.81086
$552$	0	0
$553$	0	0
$554$	−1.66815e6	−0.230920
$555$	0	0
$556$	2.84416e6	0.390182
$557$	−118092.	−0.0161281	−0.00806404	−	0.999967i	$-0.502567\pi$
$557$	−118092.	−0.0161281	−0.00806404	+	0.999967i	$0.502567\pi$
$558$	0	0
$559$	−235768.	−0.0319121
$560$	0	0
$561$	0	0
$562$	2.09573e6	0.279894
$563$	−6.43544e6	−0.855672	−0.427836	−	0.903856i	$-0.640724\pi$
$563$	−6.43544e6	−0.855672	−0.427836	+	0.903856i	$0.640724\pi$
$564$	0	0
$565$	7.36646e6	0.970818
$566$	−9.46898e6	−1.24240
$567$	0	0
$568$	2.20147e6	0.286314
$569$	3.22976e6	0.418206	0.209103	−	0.977894i	$-0.432946\pi$
$569$	3.22976e6	0.418206	0.209103	+	0.977894i	$0.432946\pi$
$570$	0	0
$571$	−228556.	−0.0293361	−0.0146680	−	0.999892i	$-0.504669\pi$
$571$	−228556.	−0.0293361	−0.0146680	+	0.999892i	$0.504669\pi$
$572$	−247104.	−0.0315784
$573$	0	0
$574$	0	0
$575$	−733590.	−0.0925303
$576$	0	0
$577$	−1.50817e7	−1.88587	−0.942933	−	0.332983i	$-0.891945\pi$
$577$	−1.50817e7	−1.88587	−0.942933	+	0.332983i	$0.891945\pi$
$578$	4.53880e6	0.565095
$579$	0	0
$580$	−3.71174e6	−0.458150
$581$	0	0
$582$	0	0
$583$	1.68435e7	2.05239
$584$	3.64736e6	0.442534
$585$	0	0
$586$	−9.78521e6	−1.17713
$587$	−8.90044e6	−1.06614	−0.533072	−	0.846070i	$-0.678963\pi$
$587$	−8.90044e6	−1.06614	−0.533072	+	0.846070i	$0.678963\pi$
$588$	0	0
$589$	−2.41401e7	−2.86716
$590$	1.77034e6	0.209375
$591$	0	0
$592$	−128512.	−0.0150709
$593$	−1.34870e6	−0.157499	−0.0787495	−	0.996894i	$-0.525093\pi$
$593$	−1.34870e6	−0.157499	−0.0787495	+	0.996894i	$0.525093\pi$
$594$	0	0
$595$	0	0
$596$	4.95302e6	0.571156
$597$	0	0
$598$	365040.	0.0417434
$599$	1.18444e7	1.34879	0.674395	−	0.738371i	$-0.264405\pi$
$599$	1.18444e7	1.34879	0.674395	+	0.738371i	$0.264405\pi$
$600$	0	0
$601$	9.62671e6	1.08716	0.543578	−	0.839359i	$-0.317069\pi$
$601$	9.62671e6	1.08716	0.543578	+	0.839359i	$0.317069\pi$
$602$	0	0
$603$	0	0
$604$	−4.80218e6	−0.535606
$605$	−1.03564e7	−1.15032
$606$	0	0
$607$	641512.	0.0706697	0.0353348	−	0.999376i	$-0.488750\pi$
$607$	641512.	0.0706697	0.0353348	+	0.999376i	$0.488750\pi$
$608$	−3.07610e6	−0.337474
$609$	0	0
$610$	−6.44155e6	−0.700916
$611$	29640.0	0.00321200
$612$	0	0
$613$	3.72964e6	0.400881	0.200441	−	0.979706i	$-0.435763\pi$
$613$	3.72964e6	0.400881	0.200441	+	0.979706i	$0.435763\pi$
$614$	−3.87726e6	−0.415054
$615$	0	0
$616$	0	0
$617$	−1.18580e7	−1.25400	−0.627000	−	0.779019i	$-0.715718\pi$
$617$	−1.18580e7	−1.25400	−0.627000	+	0.779019i	$0.715718\pi$
$618$	0	0
$619$	−2.60636e6	−0.273406	−0.136703	−	0.990612i	$-0.543651\pi$
$619$	−2.60636e6	−0.273406	−0.136703	+	0.990612i	$0.543651\pi$
$620$	6.94310e6	0.725395
$621$	0	0
$622$	9.79061e6	1.01469
$623$	0	0
$624$	0	0
$625$	−9.06882e6	−0.928647
$626$	8.10164e6	0.826299
$627$	0	0
$628$	−187616.	−0.0189833
$629$	−268068.	−0.0270158
$630$	0	0
$631$	5.15540e6	0.515453	0.257726	−	0.966218i	$-0.417027\pi$
$631$	5.15540e6	0.515453	0.257726	+	0.966218i	$0.417027\pi$
$632$	−3.16774e6	−0.315470
$633$	0	0
$634$	−1.00152e7	−0.989542
$635$	6.92539e6	0.681569
$636$	0	0
$637$	0	0
$638$	−1.02073e7	−0.992794
$639$	0	0
$640$	884736.	0.0853815
$641$	1.42517e7	1.37000	0.685002	−	0.728541i	$-0.259801\pi$
$641$	1.42517e7	1.37000	0.685002	+	0.728541i	$0.259801\pi$
$642$	0	0
$643$	1.24310e7	1.18571	0.592857	−	0.805308i	$-0.298000\pi$
$643$	1.24310e7	1.18571	0.592857	+	0.805308i	$0.298000\pi$
$644$	0	0
$645$	0	0
$646$	−6.41654e6	−0.604951
$647$	−5.71643e6	−0.536864	−0.268432	−	0.963299i	$-0.586505\pi$
$647$	−5.71643e6	−0.536864	−0.268432	+	0.963299i	$0.586505\pi$
$648$	0	0
$649$	4.86842e6	0.453708
$650$	−21736.0	−0.00201788
$651$	0	0
$652$	−4.30816e6	−0.396892
$653$	−2.48479e6	−0.228038	−0.114019	−	0.993479i	$-0.536372\pi$
$653$	−2.48479e6	−0.228038	−0.114019	+	0.993479i	$0.536372\pi$
$654$	0	0
$655$	1.99960e7	1.82112
$656$	−2.52672e6	−0.229244
$657$	0	0
$658$	0	0
$659$	2.87481e6	0.257867	0.128933	−	0.991653i	$-0.458845\pi$
$659$	2.87481e6	0.257867	0.128933	+	0.991653i	$0.458845\pi$
$660$	0	0
$661$	8.18274e6	0.728442	0.364221	−	0.931313i	$-0.381335\pi$
$661$	8.18274e6	0.728442	0.364221	+	0.931313i	$0.381335\pi$
$662$	−5.14798e6	−0.456554
$663$	0	0
$664$	−3.36077e6	−0.295814
$665$	0	0
$666$	0	0
$667$	1.50790e7	1.31237
$668$	−665664.	−0.0577184
$669$	0	0
$670$	−1.35829e7	−1.16898
$671$	−1.77143e7	−1.51886
$672$	0	0
$673$	1.52187e7	1.29521	0.647603	−	0.761978i	$-0.275772\pi$
$673$	1.52187e7	1.29521	0.647603	+	0.761978i	$0.275772\pi$
$674$	5.62554e6	0.476996
$675$	0	0
$676$	−5.92987e6	−0.499090
$677$	1.85942e7	1.55922	0.779609	−	0.626266i	$-0.215418\pi$
$677$	1.85942e7	1.55922	0.779609	+	0.626266i	$0.215418\pi$
$678$	0	0
$679$	0	0
$680$	1.84550e6	0.153053
$681$	0	0
$682$	1.90935e7	1.57190
$683$	−1362.00	−0.000111719 0	−5.58593e−5	−	1.00000i	$-0.500018\pi$
$683$	−1362.00	−0.000111719 0	−5.58593e−5		1.00000i	$0.500018\pi$
$684$	0	0
$685$	−697896.	−0.0568282
$686$	0	0
$687$	0	0
$688$	2.32141e6	0.186974
$689$	−737256.	−0.0591657
$690$	0	0
$691$	−1.83515e7	−1.46210	−0.731048	−	0.682327i	$-0.760968\pi$
$691$	−1.83515e7	−1.46210	−0.731048	+	0.682327i	$0.760968\pi$
$692$	−4.59139e6	−0.364485
$693$	0	0
$694$	5.01252e6	0.395055
$695$	−9.59904e6	−0.753817
$696$	0	0
$697$	−5.27058e6	−0.410938
$698$	6.67503e6	0.518579
$699$	0	0
$700$	0	0
$701$	−1.00448e7	−0.772051	−0.386025	−	0.922488i	$-0.626152\pi$
$701$	−1.00448e7	−0.772051	−0.386025	+	0.922488i	$0.626152\pi$
$702$	0	0
$703$	−1.50801e6	−0.115084
$704$	2.43302e6	0.185018
$705$	0	0
$706$	−8.54748e6	−0.645396
$707$	0	0
$708$	0	0
$709$	−2.11149e6	−0.157752	−0.0788759	−	0.996884i	$-0.525133\pi$
$709$	−2.11149e6	−0.157752	−0.0788759	+	0.996884i	$0.525133\pi$
$710$	−7.42997e6	−0.553148
$711$	0	0
$712$	−3.09005e6	−0.228436
$713$	−2.82064e7	−2.07789
$714$	0	0
$715$	833976.	0.0610082
$716$	−6.72298e6	−0.490094
$717$	0	0
$718$	−1.44363e7	−1.04507
$719$	296016.	0.0213547	0.0106773	−	0.999943i	$-0.496601\pi$
$719$	296016.	0.0213547	0.0106773	+	0.999943i	$0.496601\pi$
$720$	0	0
$721$	0	0
$722$	−2.61917e7	−1.86991
$723$	0	0
$724$	270688.	0.0191921
$725$	−897864.	−0.0634403
$726$	0	0
$727$	90220.0	0.00633092	0.00316546	−	0.999995i	$-0.498992\pi$
$727$	90220.0	0.00633092	0.00316546	+	0.999995i	$0.498992\pi$
$728$	0	0
$729$	0	0
$730$	−1.23098e7	−0.854959
$731$	4.84231e6	0.335166
$732$	0	0
$733$	1.40664e7	0.966992	0.483496	−	0.875347i	$-0.339367\pi$
$733$	1.40664e7	0.966992	0.483496	+	0.875347i	$0.339367\pi$
$734$	−7.52762e6	−0.515724
$735$	0	0
$736$	−3.59424e6	−0.244575
$737$	−3.73531e7	−2.53313
$738$	0	0
$739$	2.20018e7	1.48199	0.740997	−	0.671508i	$-0.234353\pi$
$739$	2.20018e7	1.48199	0.740997	+	0.671508i	$0.234353\pi$
$740$	433728.	0.0291164
$741$	0	0
$742$	0	0
$743$	9.42981e6	0.626658	0.313329	−	0.949645i	$-0.398556\pi$
$743$	9.42981e6	0.626658	0.313329	+	0.949645i	$0.398556\pi$
$744$	0	0
$745$	−1.67165e7	−1.10345
$746$	−1.94474e7	−1.27943
$747$	0	0
$748$	5.07514e6	0.331660
$749$	0	0
$750$	0	0
$751$	5.06420e6	0.327651	0.163825	−	0.986489i	$-0.447617\pi$
$751$	5.06420e6	0.327651	0.163825	+	0.986489i	$0.447617\pi$
$752$	−291840.	−0.0188192
$753$	0	0
$754$	446784.	0.0286200
$755$	1.62073e7	1.03477
$756$	0	0
$757$	−9.41479e6	−0.597133	−0.298566	−	0.954389i	$-0.596508\pi$
$757$	−9.41479e6	−0.597133	−0.298566	+	0.954389i	$0.596508\pi$
$758$	−1.00520e6	−0.0635447
$759$	0	0
$760$	1.03818e7	0.651988
$761$	1.81025e7	1.13313	0.566563	−	0.824019i	$-0.308273\pi$
$761$	1.81025e7	1.13313	0.566563	+	0.824019i	$0.308273\pi$
$762$	0	0
$763$	0	0
$764$	−2.15587e6	−0.133626
$765$	0	0
$766$	−2.27088e6	−0.139837
$767$	−213096.	−0.0130794
$768$	0	0
$769$	−2.37970e7	−1.45113	−0.725566	−	0.688152i	$-0.758422\pi$
$769$	−2.37970e7	−1.45113	−0.725566	+	0.688152i	$0.758422\pi$
$770$	0	0
$771$	0	0
$772$	−5.03440e6	−0.304022
$773$	9.76453e6	0.587763	0.293882	−	0.955842i	$-0.405053\pi$
$773$	9.76453e6	0.587763	0.293882	+	0.955842i	$0.405053\pi$
$774$	0	0
$775$	1.67952e6	0.100446
$776$	−5.37203e6	−0.320246
$777$	0	0
$778$	9.38189e6	0.555701
$779$	−2.96495e7	−1.75055
$780$	0	0
$781$	−2.04324e7	−1.19865
$782$	−7.49736e6	−0.438421
$783$	0	0
$784$	0	0
$785$	633204.	0.0366749
$786$	0	0
$787$	2.69301e6	0.154989	0.0774945	−	0.996993i	$-0.475308\pi$
$787$	2.69301e6	0.154989	0.0774945	+	0.996993i	$0.475308\pi$
$788$	9.54605e6	0.547656
$789$	0	0
$790$	1.06911e7	0.609475
$791$	0	0
$792$	0	0
$793$	775372.	0.0437852
$794$	−2.10287e7	−1.18376
$795$	0	0
$796$	161536.	0.00903622
$797$	2.69834e7	1.50470	0.752352	−	0.658762i	$-0.228919\pi$
$797$	2.69834e7	1.50470	0.752352	+	0.658762i	$0.228919\pi$
$798$	0	0
$799$	−608760.	−0.0337349
$800$	214016.	0.0118228
$801$	0	0
$802$	9.36562e6	0.514163
$803$	−3.38521e7	−1.85266
$804$	0	0
$805$	0	0
$806$	−835744.	−0.0453143
$807$	0	0
$808$	−4.01242e6	−0.216211
$809$	1.30813e7	0.702718	0.351359	−	0.936241i	$-0.385720\pi$
$809$	1.30813e7	0.702718	0.351359	+	0.936241i	$0.385720\pi$
$810$	0	0
$811$	−2.12063e7	−1.13217	−0.566086	−	0.824346i	$-0.691543\pi$
$811$	−2.12063e7	−1.13217	−0.566086	+	0.824346i	$0.691543\pi$
$812$	0	0
$813$	0	0
$814$	1.19275e6	0.0630942
$815$	1.45400e7	0.766781
$816$	0	0
$817$	2.72403e7	1.42776
$818$	2.64927e6	0.138434
$819$	0	0
$820$	8.52768e6	0.442890
$821$	3.76237e7	1.94806	0.974032	−	0.226411i	$-0.0726993\pi$
$821$	3.76237e7	1.94806	0.974032	+	0.226411i	$0.0726993\pi$
$822$	0	0
$823$	4.75582e6	0.244752	0.122376	−	0.992484i	$-0.460949\pi$
$823$	4.75582e6	0.244752	0.122376	+	0.992484i	$0.460949\pi$
$824$	−1.98323e6	−0.101755
$825$	0	0
$826$	0	0
$827$	−2.26167e7	−1.14991	−0.574957	−	0.818184i	$-0.694981\pi$
$827$	−2.26167e7	−1.14991	−0.574957	+	0.818184i	$0.694981\pi$
$828$	0	0
$829$	2.44896e7	1.23764	0.618821	−	0.785532i	$-0.287611\pi$
$829$	2.44896e7	1.23764	0.618821	+	0.785532i	$0.287611\pi$
$830$	1.13426e7	0.571501
$831$	0	0
$832$	−106496.	−0.00533366
$833$	0	0
$834$	0	0
$835$	2.24662e6	0.111510
$836$	2.85500e7	1.41283
$837$	0	0
$838$	2.11101e7	1.03844
$839$	−3.13107e7	−1.53563	−0.767816	−	0.640670i	$-0.778657\pi$
$839$	−3.13107e7	−1.53563	−0.767816	+	0.640670i	$0.778657\pi$
$840$	0	0
$841$	−2.05553e6	−0.100215
$842$	−6.99270e6	−0.339910
$843$	0	0
$844$	−1.15412e7	−0.557692
$845$	2.00133e7	0.964223
$846$	0	0
$847$	0	0
$848$	7.25914e6	0.346653
$849$	0	0
$850$	446424.	0.0211934
$851$	−1.76202e6	−0.0834040
$852$	0	0
$853$	1.59565e7	0.750870	0.375435	−	0.926849i	$-0.377493\pi$
$853$	1.59565e7	0.750870	0.375435	+	0.926849i	$0.377493\pi$
$854$	0	0
$855$	0	0
$856$	−7.56595e6	−0.352922
$857$	−6.51800e6	−0.303153	−0.151577	−	0.988446i	$-0.548435\pi$
$857$	−6.51800e6	−0.303153	−0.151577	+	0.988446i	$0.548435\pi$
$858$	0	0
$859$	1.77405e7	0.820321	0.410161	−	0.912013i	$-0.365473\pi$
$859$	1.77405e7	0.820321	0.410161	+	0.912013i	$0.365473\pi$
$860$	−7.83475e6	−0.361226
$861$	0	0
$862$	1.06230e7	0.486944
$863$	8.57437e6	0.391900	0.195950	−	0.980614i	$-0.437221\pi$
$863$	8.57437e6	0.391900	0.195950	+	0.980614i	$0.437221\pi$
$864$	0	0
$865$	1.54959e7	0.704171
$866$	−1.24810e7	−0.565531
$867$	0	0
$868$	0	0
$869$	2.94006e7	1.32071
$870$	0	0
$871$	1.63498e6	0.0730244
$872$	−1.32712e7	−0.591041
$873$	0	0
$874$	−4.21762e7	−1.86762
$875$	0	0
$876$	0	0
$877$	−3.83551e7	−1.68393	−0.841964	−	0.539533i	$-0.818601\pi$
$877$	−3.83551e7	−1.68393	−0.841964	+	0.539533i	$0.818601\pi$
$878$	−1.60852e7	−0.704193
$879$	0	0
$880$	−8.21146e6	−0.357449
$881$	−3.91651e7	−1.70004	−0.850020	−	0.526751i	$-0.823410\pi$
$881$	−3.91651e7	−1.70004	−0.850020	+	0.526751i	$0.823410\pi$
$882$	0	0
$883$	1.72766e7	0.745688	0.372844	−	0.927894i	$-0.378383\pi$
$883$	1.72766e7	0.745688	0.372844	+	0.927894i	$0.378383\pi$
$884$	−222144.	−0.00956101
$885$	0	0
$886$	3.06458e6	0.131156
$887$	−2.33351e7	−0.995865	−0.497932	−	0.867216i	$-0.665907\pi$
$887$	−2.33351e7	−0.995865	−0.497932	+	0.867216i	$0.665907\pi$
$888$	0	0
$889$	0	0
$890$	1.04289e7	0.441331
$891$	0	0
$892$	8.58534e6	0.361281
$893$	−3.42456e6	−0.143706
$894$	0	0
$895$	2.26900e7	0.946843
$896$	0	0
$897$	0	0
$898$	1.20784e7	0.499827
$899$	−3.45227e7	−1.42464
$900$	0	0
$901$	1.51421e7	0.621404
$902$	2.34511e7	0.959726
$903$	0	0
$904$	8.73062e6	0.355324
$905$	−913572.	−0.0370784
$906$	0	0
$907$	−3.16449e7	−1.27728	−0.638640	−	0.769506i	$-0.720503\pi$
$907$	−3.16449e7	−1.27728	−0.638640	+	0.769506i	$0.720503\pi$
$908$	2.37917e7	0.957658
$909$	0	0
$910$	0	0
$911$	−2.29551e6	−0.0916396	−0.0458198	−	0.998950i	$-0.514590\pi$
$911$	−2.29551e6	−0.0916396	−0.0458198	+	0.998950i	$0.514590\pi$
$912$	0	0
$913$	3.11921e7	1.23842
$914$	892456.	0.0353363
$915$	0	0
$916$	1.77531e7	0.699092
$917$	0	0
$918$	0	0
$919$	−2.80612e7	−1.09602	−0.548008	−	0.836473i	$-0.684614\pi$
$919$	−2.80612e7	−1.09602	−0.548008	+	0.836473i	$0.684614\pi$
$920$	1.21306e7	0.472510
$921$	0	0
$922$	−1.83220e7	−0.709816
$923$	894348.	0.0345543
$924$	0	0
$925$	104918.	0.00403177
$926$	1.69462e7	0.649448
$927$	0	0
$928$	−4.39910e6	−0.167685
$929$	−6.79025e6	−0.258135	−0.129067	−	0.991636i	$-0.541198\pi$
$929$	−6.79025e6	−0.258135	−0.129067	+	0.991636i	$0.541198\pi$
$930$	0	0
$931$	0	0
$932$	2.22073e7	0.837444
$933$	0	0
$934$	−1.09800e7	−0.411844
$935$	−1.71286e7	−0.640756
$936$	0	0
$937$	−3.83161e7	−1.42571	−0.712857	−	0.701310i	$-0.752599\pi$
$937$	−3.83161e7	−1.42571	−0.712857	+	0.701310i	$0.752599\pi$
$938$	0	0
$939$	0	0
$940$	984960.	0.0363579
$941$	−1.16868e7	−0.430250	−0.215125	−	0.976587i	$-0.569016\pi$
$941$	−1.16868e7	−0.430250	−0.215125	+	0.976587i	$0.569016\pi$
$942$	0	0
$943$	−3.46437e7	−1.26866
$944$	2.09818e6	0.0766323
$945$	0	0
$946$	−2.15456e7	−0.782763
$947$	2.08201e7	0.754410	0.377205	−	0.926130i	$-0.376885\pi$
$947$	2.08201e7	0.754410	0.377205	+	0.926130i	$0.376885\pi$
$948$	0	0
$949$	1.48174e6	0.0534080
$950$	2.51134e6	0.0902812
$951$	0	0
$952$	0	0
$953$	−1.41556e7	−0.504888	−0.252444	−	0.967612i	$-0.581234\pi$
$953$	−1.41556e7	−0.504888	−0.252444	+	0.967612i	$0.581234\pi$
$954$	0	0
$955$	7.27607e6	0.258160
$956$	2.50250e7	0.885583
$957$	0	0
$958$	−1.07051e7	−0.376857
$959$	0	0
$960$	0	0
$961$	3.59481e7	1.25565
$962$	−52208.0	−0.00181886
$963$	0	0
$964$	−2.18110e7	−0.755934
$965$	1.69911e7	0.587358
$966$	0	0
$967$	5.29558e7	1.82116	0.910578	−	0.413337i	$-0.135637\pi$
$967$	5.29558e7	1.82116	0.910578	+	0.413337i	$0.135637\pi$
$968$	−1.22742e7	−0.421023
$969$	0	0
$970$	1.81306e7	0.618704
$971$	−1.07845e7	−0.367072	−0.183536	−	0.983013i	$-0.558754\pi$
$971$	−1.07845e7	−0.367072	−0.183536	+	0.983013i	$0.558754\pi$
$972$	0	0
$973$	0	0
$974$	3.17184e7	1.07131
$975$	0	0
$976$	−7.63443e6	−0.256538
$977$	−4.78226e7	−1.60286	−0.801432	−	0.598086i	$-0.795928\pi$
$977$	−4.78226e7	−1.60286	−0.801432	+	0.598086i	$0.795928\pi$
$978$	0	0
$979$	2.86795e7	0.956346
$980$	0	0
$981$	0	0
$982$	2.84227e7	0.940560
$983$	2.96662e7	0.979216	0.489608	−	0.871943i	$-0.337140\pi$
$983$	2.96662e7	0.979216	0.489608	+	0.871943i	$0.337140\pi$
$984$	0	0
$985$	−3.22179e7	−1.05805
$986$	−9.17626e6	−0.300589
$987$	0	0
$988$	−1.24966e6	−0.0407287
$989$	3.18287e7	1.03473
$990$	0	0
$991$	−1.39263e7	−0.450456	−0.225228	−	0.974306i	$-0.572313\pi$
$991$	−1.39263e7	−0.450456	−0.225228	+	0.974306i	$0.572313\pi$
$992$	8.22886e6	0.265498
$993$	0	0
$994$	0	0
$995$	−545184.	−0.0174576
$996$	0	0
$997$	3.59999e6	0.114700	0.0573499	−	0.998354i	$-0.481735\pi$
$997$	3.59999e6	0.114700	0.0573499	+	0.998354i	$0.481735\pi$
$998$	5.25410e6	0.166983
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.6.a.b.1.1		1
3.2	odd	2		882.6.a.w.1.1		1
7.6	odd	2		126.6.a.e.1.1	✓	1
21.20	even	2		126.6.a.g.1.1	yes	1
28.27	even	2		1008.6.a.w.1.1		1
84.83	odd	2		1008.6.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.6.a.e.1.1	✓	1	7.6	odd	2
126.6.a.g.1.1	yes	1	21.20	even	2
882.6.a.b.1.1		1	1.1	even	1	trivial
882.6.a.w.1.1		1	3.2	odd	2
1008.6.a.f.1.1		1	84.83	odd	2
1008.6.a.w.1.1		1	28.27	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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