LMFDB - Embedded newform 882.6.a.a.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
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)

$f(q)$

$=$

$q-4.00000 q^{2} +16.0000 q^{4} -66.0000 q^{5} -64.0000 q^{8} +O(q^{10})$

$q-4.00000 q^{2} +16.0000 q^{4} -66.0000 q^{5} -64.0000 q^{8} +264.000 q^{10} +60.0000 q^{11} +658.000 q^{13} +256.000 q^{16} -414.000 q^{17} -956.000 q^{19} -1056.00 q^{20} -240.000 q^{22} -600.000 q^{23} +1231.00 q^{25} -2632.00 q^{26} -5574.00 q^{29} +3592.00 q^{31} -1024.00 q^{32} +1656.00 q^{34} -8458.00 q^{37} +3824.00 q^{38} +4224.00 q^{40} +19194.0 q^{41} +13316.0 q^{43} +960.000 q^{44} +2400.00 q^{46} -19680.0 q^{47} -4924.00 q^{50} +10528.0 q^{52} +31266.0 q^{53} -3960.00 q^{55} +22296.0 q^{58} +26340.0 q^{59} +31090.0 q^{61} -14368.0 q^{62} +4096.00 q^{64} -43428.0 q^{65} -16804.0 q^{67} -6624.00 q^{68} -6120.00 q^{71} +25558.0 q^{73} +33832.0 q^{74} -15296.0 q^{76} +74408.0 q^{79} -16896.0 q^{80} -76776.0 q^{82} -6468.00 q^{83} +27324.0 q^{85} -53264.0 q^{86} -3840.00 q^{88} -32742.0 q^{89} -9600.00 q^{92} +78720.0 q^{94} +63096.0 q^{95} -166082. q^{97} +O(q^{100})$

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
$5$	−66.0000	−1.18064	−0.590322	−	0.807168i	$-0.700999\pi$
$5$	−66.0000	−1.18064	−0.590322	+	0.807168i	$0.700999\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	0	0
$10$	264.000	0.834841
$11$	60.0000	0.149510	0.0747549	−	0.997202i	$-0.476183\pi$
$11$	60.0000	0.149510	0.0747549	+	0.997202i	$0.476183\pi$
$12$	0	0
$13$	658.000	1.07986	0.539930	−	0.841710i	$-0.318451\pi$
$13$	658.000	1.07986	0.539930	+	0.841710i	$0.318451\pi$
$14$	0	0
$15$	0	0
$16$	256.000	0.250000
$17$	−414.000	−0.347439	−0.173719	−	0.984795i	$-0.555579\pi$
$17$	−414.000	−0.347439	−0.173719	+	0.984795i	$0.555579\pi$
$18$	0	0
$19$	−956.000	−0.607539	−0.303769	−	0.952746i	$-0.598245\pi$
$19$	−956.000	−0.607539	−0.303769	+	0.952746i	$0.598245\pi$
$20$	−1056.00	−0.590322
$21$	0	0
$22$	−240.000	−0.105719
$23$	−600.000	−0.236500	−0.118250	−	0.992984i	$-0.537728\pi$
$23$	−600.000	−0.236500	−0.118250	+	0.992984i	$0.537728\pi$
$24$	0	0
$25$	1231.00	0.393920
$26$	−2632.00	−0.763576
$27$	0	0
$28$	0	0
$29$	−5574.00	−1.23076	−0.615378	−	0.788232i	$-0.710997\pi$
$29$	−5574.00	−1.23076	−0.615378	+	0.788232i	$0.710997\pi$
$30$	0	0
$31$	3592.00	0.671324	0.335662	−	0.941983i	$-0.391040\pi$
$31$	3592.00	0.671324	0.335662	+	0.941983i	$0.391040\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	1656.00	0.245676
$35$	0	0
$36$	0	0
$37$	−8458.00	−1.01570	−0.507848	−	0.861447i	$-0.669559\pi$
$37$	−8458.00	−1.01570	−0.507848	+	0.861447i	$0.669559\pi$
$38$	3824.00	0.429595
$39$	0	0
$40$	4224.00	0.417421
$41$	19194.0	1.78322	0.891612	−	0.452800i	$-0.149575\pi$
$41$	19194.0	1.78322	0.891612	+	0.452800i	$0.149575\pi$
$42$	0	0
$43$	13316.0	1.09825	0.549127	−	0.835739i	$-0.314960\pi$
$43$	13316.0	1.09825	0.549127	+	0.835739i	$0.314960\pi$
$44$	960.000	0.0747549
$45$	0	0
$46$	2400.00	0.167231
$47$	−19680.0	−1.29951	−0.649756	−	0.760143i	$-0.725129\pi$
$47$	−19680.0	−1.29951	−0.649756	+	0.760143i	$0.725129\pi$
$48$	0	0
$49$	0	0
$50$	−4924.00	−0.278544
$51$	0	0
$52$	10528.0	0.539930
$53$	31266.0	1.52891	0.764456	−	0.644676i	$-0.223008\pi$
$53$	31266.0	1.52891	0.764456	+	0.644676i	$0.223008\pi$
$54$	0	0
$55$	−3960.00	−0.176518
$56$	0	0
$57$	0	0
$58$	22296.0	0.870276
$59$	26340.0	0.985112	0.492556	−	0.870281i	$-0.336063\pi$
$59$	26340.0	0.985112	0.492556	+	0.870281i	$0.336063\pi$
$60$	0	0
$61$	31090.0	1.06978	0.534892	−	0.844920i	$-0.320352\pi$
$61$	31090.0	1.06978	0.534892	+	0.844920i	$0.320352\pi$
$62$	−14368.0	−0.474698
$63$	0	0
$64$	4096.00	0.125000
$65$	−43428.0	−1.27493
$66$	0	0
$67$	−16804.0	−0.457326	−0.228663	−	0.973506i	$-0.573435\pi$
$67$	−16804.0	−0.457326	−0.228663	+	0.973506i	$0.573435\pi$
$68$	−6624.00	−0.173719
$69$	0	0
$70$	0	0
$71$	−6120.00	−0.144081	−0.0720403	−	0.997402i	$-0.522951\pi$
$71$	−6120.00	−0.144081	−0.0720403	+	0.997402i	$0.522951\pi$
$72$	0	0
$73$	25558.0	0.561332	0.280666	−	0.959806i	$-0.409445\pi$
$73$	25558.0	0.561332	0.280666	+	0.959806i	$0.409445\pi$
$74$	33832.0	0.718205
$75$	0	0
$76$	−15296.0	−0.303769
$77$	0	0
$78$	0	0
$79$	74408.0	1.34138	0.670690	−	0.741738i	$-0.265998\pi$
$79$	74408.0	1.34138	0.670690	+	0.741738i	$0.265998\pi$
$80$	−16896.0	−0.295161
$81$	0	0
$82$	−76776.0	−1.26093
$83$	−6468.00	−0.103056	−0.0515282	−	0.998672i	$-0.516409\pi$
$83$	−6468.00	−0.103056	−0.0515282	+	0.998672i	$0.516409\pi$
$84$	0	0
$85$	27324.0	0.410201
$86$	−53264.0	−0.776583
$87$	0	0
$88$	−3840.00	−0.0528597
$89$	−32742.0	−0.438157	−0.219079	−	0.975707i	$-0.570305\pi$
$89$	−32742.0	−0.438157	−0.219079	+	0.975707i	$0.570305\pi$
$90$	0	0
$91$	0	0
$92$	−9600.00	−0.118250
$93$	0	0
$94$	78720.0	0.918894
$95$	63096.0	0.717287
$96$	0	0
$97$	−166082.	−1.79223	−0.896114	−	0.443824i	$-0.853622\pi$
$97$	−166082.	−1.79223	−0.896114	+	0.443824i	$0.853622\pi$
$98$	0	0
$99$	0	0
$100$	19696.0	0.196960
$101$	−22002.0	−0.214614	−0.107307	−	0.994226i	$-0.534223\pi$
$101$	−22002.0	−0.214614	−0.107307	+	0.994226i	$0.534223\pi$
$102$	0	0
$103$	79264.0	0.736178	0.368089	−	0.929791i	$-0.380012\pi$
$103$	79264.0	0.736178	0.368089	+	0.929791i	$0.380012\pi$
$104$	−42112.0	−0.381788
$105$	0	0
$106$	−125064.	−1.08110
$107$	−227988.	−1.92510	−0.962548	−	0.271110i	$-0.912609\pi$
$107$	−227988.	−1.92510	−0.962548	+	0.271110i	$0.912609\pi$
$108$	0	0
$109$	−8530.00	−0.0687674	−0.0343837	−	0.999409i	$-0.510947\pi$
$109$	−8530.00	−0.0687674	−0.0343837	+	0.999409i	$0.510947\pi$
$110$	15840.0	0.124817
$111$	0	0
$112$	0	0
$113$	195438.	1.43984	0.719918	−	0.694059i	$-0.244179\pi$
$113$	195438.	1.43984	0.719918	+	0.694059i	$0.244179\pi$
$114$	0	0
$115$	39600.0	0.279223
$116$	−89184.0	−0.615378
$117$	0	0
$118$	−105360.	−0.696580
$119$	0	0
$120$	0	0
$121$	−157451.	−0.977647
$122$	−124360.	−0.756452
$123$	0	0
$124$	57472.0	0.335662
$125$	125004.	0.715565
$126$	0	0
$127$	173000.	0.951780	0.475890	−	0.879505i	$-0.342126\pi$
$127$	173000.	0.951780	0.475890	+	0.879505i	$0.342126\pi$
$128$	−16384.0	−0.0883883
$129$	0	0
$130$	173712.	0.901512
$131$	151260.	0.770098	0.385049	−	0.922896i	$-0.374185\pi$
$131$	151260.	0.770098	0.385049	+	0.922896i	$0.374185\pi$
$132$	0	0
$133$	0	0
$134$	67216.0	0.323378
$135$	0	0
$136$	26496.0	0.122838
$137$	128454.	0.584718	0.292359	−	0.956309i	$-0.405560\pi$
$137$	128454.	0.584718	0.292359	+	0.956309i	$0.405560\pi$
$138$	0	0
$139$	−154196.	−0.676918	−0.338459	−	0.940981i	$-0.609906\pi$
$139$	−154196.	−0.676918	−0.338459	+	0.940981i	$0.609906\pi$
$140$	0	0
$141$	0	0
$142$	24480.0	0.101880
$143$	39480.0	0.161450
$144$	0	0
$145$	367884.	1.45308
$146$	−102232.	−0.396922
$147$	0	0
$148$	−135328.	−0.507848
$149$	−29454.0	−0.108687	−0.0543436	−	0.998522i	$-0.517307\pi$
$149$	−29454.0	−0.108687	−0.0543436	+	0.998522i	$0.517307\pi$
$150$	0	0
$151$	−203872.	−0.727638	−0.363819	−	0.931470i	$-0.618527\pi$
$151$	−203872.	−0.727638	−0.363819	+	0.931470i	$0.618527\pi$
$152$	61184.0	0.214797
$153$	0	0
$154$	0	0
$155$	−237072.	−0.792594
$156$	0	0
$157$	−136142.	−0.440801	−0.220401	−	0.975409i	$-0.570737\pi$
$157$	−136142.	−0.440801	−0.220401	+	0.975409i	$0.570737\pi$
$158$	−297632.	−0.948499
$159$	0	0
$160$	67584.0	0.208710
$161$	0	0
$162$	0	0
$163$	−171124.	−0.504478	−0.252239	−	0.967665i	$-0.581167\pi$
$163$	−171124.	−0.504478	−0.252239	+	0.967665i	$0.581167\pi$
$164$	307104.	0.891612
$165$	0	0
$166$	25872.0	0.0728718
$167$	−676200.	−1.87622	−0.938110	−	0.346336i	$-0.887426\pi$
$167$	−676200.	−1.87622	−0.938110	+	0.346336i	$0.887426\pi$
$168$	0	0
$169$	61671.0	0.166098
$170$	−109296.	−0.290056
$171$	0	0
$172$	213056.	0.549127
$173$	133158.	0.338261	0.169131	−	0.985594i	$-0.445904\pi$
$173$	133158.	0.338261	0.169131	+	0.985594i	$0.445904\pi$
$174$	0	0
$175$	0	0
$176$	15360.0	0.0373774
$177$	0	0
$178$	130968.	0.309824
$179$	693396.	1.61752	0.808758	−	0.588141i	$-0.200140\pi$
$179$	693396.	1.61752	0.808758	+	0.588141i	$0.200140\pi$
$180$	0	0
$181$	−377174.	−0.855747	−0.427873	−	0.903839i	$-0.640737\pi$
$181$	−377174.	−0.855747	−0.427873	+	0.903839i	$0.640737\pi$
$182$	0	0
$183$	0	0
$184$	38400.0	0.0836155
$185$	558228.	1.19917
$186$	0	0
$187$	−24840.0	−0.0519455
$188$	−314880.	−0.649756
$189$	0	0
$190$	−252384.	−0.507198
$191$	265344.	0.526291	0.263145	−	0.964756i	$-0.415240\pi$
$191$	265344.	0.526291	0.263145	+	0.964756i	$0.415240\pi$
$192$	0	0
$193$	295298.	0.570647	0.285323	−	0.958431i	$-0.407899\pi$
$193$	295298.	0.570647	0.285323	+	0.958431i	$0.407899\pi$
$194$	664328.	1.26730
$195$	0	0
$196$	0	0
$197$	−201294.	−0.369543	−0.184772	−	0.982781i	$-0.559155\pi$
$197$	−201294.	−0.369543	−0.184772	+	0.982781i	$0.559155\pi$
$198$	0	0
$199$	−652448.	−1.16792	−0.583960	−	0.811782i	$-0.698498\pi$
$199$	−652448.	−1.16792	−0.583960	+	0.811782i	$0.698498\pi$
$200$	−78784.0	−0.139272
$201$	0	0
$202$	88008.0	0.151755
$203$	0	0
$204$	0	0
$205$	−1.26680e6	−2.10535
$206$	−317056.	−0.520557
$207$	0	0
$208$	168448.	0.269965
$209$	−57360.0	−0.0908330
$210$	0	0
$211$	−1.14706e6	−1.77370	−0.886850	−	0.462058i	$-0.847111\pi$
$211$	−1.14706e6	−1.77370	−0.886850	+	0.462058i	$0.847111\pi$
$212$	500256.	0.764456
$213$	0	0
$214$	911952.	1.36125
$215$	−878856.	−1.29665
$216$	0	0
$217$	0	0
$218$	34120.0	0.0486259
$219$	0	0
$220$	−63360.0	−0.0882589
$221$	−272412.	−0.375185
$222$	0	0
$223$	−701960.	−0.945258	−0.472629	−	0.881262i	$-0.656695\pi$
$223$	−701960.	−0.945258	−0.472629	+	0.881262i	$0.656695\pi$
$224$	0	0
$225$	0	0
$226$	−781752.	−1.01812
$227$	1.23611e6	1.59218	0.796089	−	0.605179i	$-0.206899\pi$
$227$	1.23611e6	1.59218	0.796089	+	0.605179i	$0.206899\pi$
$228$	0	0
$229$	−105830.	−0.133358	−0.0666792	−	0.997774i	$-0.521240\pi$
$229$	−105830.	−0.133358	−0.0666792	+	0.997774i	$0.521240\pi$
$230$	−158400.	−0.197440
$231$	0	0
$232$	356736.	0.435138
$233$	438678.	0.529366	0.264683	−	0.964335i	$-0.414733\pi$
$233$	438678.	0.529366	0.264683	+	0.964335i	$0.414733\pi$
$234$	0	0
$235$	1.29888e6	1.53426
$236$	421440.	0.492556
$237$	0	0
$238$	0	0
$239$	−28464.0	−0.0322330	−0.0161165	−	0.999870i	$-0.505130\pi$
$239$	−28464.0	−0.0322330	−0.0161165	+	0.999870i	$0.505130\pi$
$240$	0	0
$241$	−892562.	−0.989910	−0.494955	−	0.868919i	$-0.664815\pi$
$241$	−892562.	−0.989910	−0.494955	+	0.868919i	$0.664815\pi$
$242$	629804.	0.691301
$243$	0	0
$244$	497440.	0.534892
$245$	0	0
$246$	0	0
$247$	−629048.	−0.656057
$248$	−229888.	−0.237349
$249$	0	0
$250$	−500016.	−0.505981
$251$	−110124.	−0.110331	−0.0551655	−	0.998477i	$-0.517569\pi$
$251$	−110124.	−0.110331	−0.0551655	+	0.998477i	$0.517569\pi$
$252$	0	0
$253$	−36000.0	−0.0353591
$254$	−692000.	−0.673010
$255$	0	0
$256$	65536.0	0.0625000
$257$	140802.	0.132977	0.0664884	−	0.997787i	$-0.478820\pi$
$257$	140802.	0.132977	0.0664884	+	0.997787i	$0.478820\pi$
$258$	0	0
$259$	0	0
$260$	−694848.	−0.637465
$261$	0	0
$262$	−605040.	−0.544541
$263$	938760.	0.836884	0.418442	−	0.908244i	$-0.362576\pi$
$263$	938760.	0.836884	0.418442	+	0.908244i	$0.362576\pi$
$264$	0	0
$265$	−2.06356e6	−1.80510
$266$	0	0
$267$	0	0
$268$	−268864.	−0.228663
$269$	−1.11451e6	−0.939078	−0.469539	−	0.882912i	$-0.655580\pi$
$269$	−1.11451e6	−0.939078	−0.469539	+	0.882912i	$0.655580\pi$
$270$	0	0
$271$	−567704.	−0.469568	−0.234784	−	0.972048i	$-0.575438\pi$
$271$	−567704.	−0.469568	−0.234784	+	0.972048i	$0.575438\pi$
$272$	−105984.	−0.0868596
$273$	0	0
$274$	−513816.	−0.413458
$275$	73860.0	0.0588949
$276$	0	0
$277$	−1.21326e6	−0.950066	−0.475033	−	0.879968i	$-0.657564\pi$
$277$	−1.21326e6	−0.950066	−0.475033	+	0.879968i	$0.657564\pi$
$278$	616784.	0.478653
$279$	0	0
$280$	0	0
$281$	−687738.	−0.519586	−0.259793	−	0.965664i	$-0.583654\pi$
$281$	−687738.	−0.519586	−0.259793	+	0.965664i	$0.583654\pi$
$282$	0	0
$283$	830908.	0.616718	0.308359	−	0.951270i	$-0.400220\pi$
$283$	830908.	0.616718	0.308359	+	0.951270i	$0.400220\pi$
$284$	−97920.0	−0.0720403
$285$	0	0
$286$	−157920.	−0.114162
$287$	0	0
$288$	0	0
$289$	−1.24846e6	−0.879286
$290$	−1.47154e6	−1.02749
$291$	0	0
$292$	408928.	0.280666
$293$	−1.31263e6	−0.893248	−0.446624	−	0.894722i	$-0.647374\pi$
$293$	−1.31263e6	−0.893248	−0.446624	+	0.894722i	$0.647374\pi$
$294$	0	0
$295$	−1.73844e6	−1.16307
$296$	541312.	0.359102
$297$	0	0
$298$	117816.	0.0768535
$299$	−394800.	−0.255387
$300$	0	0
$301$	0	0
$302$	815488.	0.514518
$303$	0	0
$304$	−244736.	−0.151885
$305$	−2.05194e6	−1.26303
$306$	0	0
$307$	−1.69022e6	−1.02352	−0.511761	−	0.859128i	$-0.671007\pi$
$307$	−1.69022e6	−1.02352	−0.511761	+	0.859128i	$0.671007\pi$
$308$	0	0
$309$	0	0
$310$	948288.	0.560449
$311$	−1.50204e6	−0.880604	−0.440302	−	0.897850i	$-0.645129\pi$
$311$	−1.50204e6	−0.880604	−0.440302	+	0.897850i	$0.645129\pi$
$312$	0	0
$313$	−810842.	−0.467816	−0.233908	−	0.972259i	$-0.575152\pi$
$313$	−810842.	−0.467816	−0.233908	+	0.972259i	$0.575152\pi$
$314$	544568.	0.311694
$315$	0	0
$316$	1.19053e6	0.670690
$317$	−903558.	−0.505019	−0.252510	−	0.967594i	$-0.581256\pi$
$317$	−903558.	−0.505019	−0.252510	+	0.967594i	$0.581256\pi$
$318$	0	0
$319$	−334440.	−0.184010
$320$	−270336.	−0.147580
$321$	0	0
$322$	0	0
$323$	395784.	0.211082
$324$	0	0
$325$	809998.	0.425379
$326$	684496.	0.356720
$327$	0	0
$328$	−1.22842e6	−0.630465
$329$	0	0
$330$	0	0
$331$	1.12197e6	0.562875	0.281438	−	0.959580i	$-0.409189\pi$
$331$	1.12197e6	0.562875	0.281438	+	0.959580i	$0.409189\pi$
$332$	−103488.	−0.0515282
$333$	0	0
$334$	2.70480e6	1.32669
$335$	1.10906e6	0.539939
$336$	0	0
$337$	−2.75217e6	−1.32008	−0.660041	−	0.751229i	$-0.729461\pi$
$337$	−2.75217e6	−1.32008	−0.660041	+	0.751229i	$0.729461\pi$
$338$	−246684.	−0.117449
$339$	0	0
$340$	437184.	0.205101
$341$	215520.	0.100369
$342$	0	0
$343$	0	0
$344$	−852224.	−0.388291
$345$	0	0
$346$	−532632.	−0.239187
$347$	−1.91749e6	−0.854889	−0.427445	−	0.904042i	$-0.640586\pi$
$347$	−1.91749e6	−0.854889	−0.427445	+	0.904042i	$0.640586\pi$
$348$	0	0
$349$	−1.83659e6	−0.807140	−0.403570	−	0.914949i	$-0.632231\pi$
$349$	−1.83659e6	−0.807140	−0.403570	+	0.914949i	$0.632231\pi$
$350$	0	0
$351$	0	0
$352$	−61440.0	−0.0264298
$353$	−622014.	−0.265683	−0.132841	−	0.991137i	$-0.542410\pi$
$353$	−622014.	−0.265683	−0.132841	+	0.991137i	$0.542410\pi$
$354$	0	0
$355$	403920.	0.170108
$356$	−523872.	−0.219079
$357$	0	0
$358$	−2.77358e6	−1.14376
$359$	−3.74062e6	−1.53182	−0.765909	−	0.642949i	$-0.777711\pi$
$359$	−3.74062e6	−1.53182	−0.765909	+	0.642949i	$0.777711\pi$
$360$	0	0
$361$	−1.56216e6	−0.630897
$362$	1.50870e6	0.605104
$363$	0	0
$364$	0	0
$365$	−1.68683e6	−0.662733
$366$	0	0
$367$	−16232.0	−0.00629081	−0.00314541	−	0.999995i	$-0.501001\pi$
$367$	−16232.0	−0.00629081	−0.00314541	+	0.999995i	$0.501001\pi$
$368$	−153600.	−0.0591251
$369$	0	0
$370$	−2.23291e6	−0.847944
$371$	0	0
$372$	0	0
$373$	293606.	0.109268	0.0546340	−	0.998506i	$-0.482601\pi$
$373$	293606.	0.109268	0.0546340	+	0.998506i	$0.482601\pi$
$374$	99360.0	0.0367310
$375$	0	0
$376$	1.25952e6	0.459447
$377$	−3.66769e6	−1.32904
$378$	0	0
$379$	3.18012e6	1.13722	0.568611	−	0.822607i	$-0.307481\pi$
$379$	3.18012e6	1.13722	0.568611	+	0.822607i	$0.307481\pi$
$380$	1.00954e6	0.358643
$381$	0	0
$382$	−1.06138e6	−0.372144
$383$	−2.97984e6	−1.03800	−0.518998	−	0.854775i	$-0.673695\pi$
$383$	−2.97984e6	−1.03800	−0.518998	+	0.854775i	$0.673695\pi$
$384$	0	0
$385$	0	0
$386$	−1.18119e6	−0.403508
$387$	0	0
$388$	−2.65731e6	−0.896114
$389$	−3.45977e6	−1.15924	−0.579620	−	0.814887i	$-0.696799\pi$
$389$	−3.45977e6	−1.15924	−0.579620	+	0.814887i	$0.696799\pi$
$390$	0	0
$391$	248400.	0.0821693
$392$	0	0
$393$	0	0
$394$	805176.	0.261307
$395$	−4.91093e6	−1.58369
$396$	0	0
$397$	3.90416e6	1.24323	0.621615	−	0.783323i	$-0.286477\pi$
$397$	3.90416e6	1.24323	0.621615	+	0.783323i	$0.286477\pi$
$398$	2.60979e6	0.825844
$399$	0	0
$400$	315136.	0.0984800
$401$	−5.44115e6	−1.68978	−0.844890	−	0.534940i	$-0.820334\pi$
$401$	−5.44115e6	−1.68978	−0.844890	+	0.534940i	$0.820334\pi$
$402$	0	0
$403$	2.36354e6	0.724936
$404$	−352032.	−0.107307
$405$	0	0
$406$	0	0
$407$	−507480.	−0.151856
$408$	0	0
$409$	−1.96995e6	−0.582299	−0.291150	−	0.956678i	$-0.594038\pi$
$409$	−1.96995e6	−0.582299	−0.291150	+	0.956678i	$0.594038\pi$
$410$	5.06722e6	1.48871
$411$	0	0
$412$	1.26822e6	0.368089
$413$	0	0
$414$	0	0
$415$	426888.	0.121673
$416$	−673792.	−0.190894
$417$	0	0
$418$	229440.	0.0642286
$419$	139020.	0.0386850	0.0193425	−	0.999813i	$-0.493843\pi$
$419$	139020.	0.0386850	0.0193425	+	0.999813i	$0.493843\pi$
$420$	0	0
$421$	4.32743e6	1.18994	0.594970	−	0.803748i	$-0.297164\pi$
$421$	4.32743e6	1.18994	0.594970	+	0.803748i	$0.297164\pi$
$422$	4.58824e6	1.25419
$423$	0	0
$424$	−2.00102e6	−0.540552
$425$	−509634.	−0.136863
$426$	0	0
$427$	0	0
$428$	−3.64781e6	−0.962548
$429$	0	0
$430$	3.51542e6	0.916867
$431$	2.79936e6	0.725881	0.362941	−	0.931812i	$-0.381773\pi$
$431$	2.79936e6	0.725881	0.362941	+	0.931812i	$0.381773\pi$
$432$	0	0
$433$	5.90241e6	1.51290	0.756449	−	0.654052i	$-0.226932\pi$
$433$	5.90241e6	1.51290	0.756449	+	0.654052i	$0.226932\pi$
$434$	0	0
$435$	0	0
$436$	−136480.	−0.0343837
$437$	573600.	0.143683
$438$	0	0
$439$	446512.	0.110579	0.0552894	−	0.998470i	$-0.482392\pi$
$439$	446512.	0.110579	0.0552894	+	0.998470i	$0.482392\pi$
$440$	253440.	0.0624085
$441$	0	0
$442$	1.08965e6	0.265296
$443$	−3.49525e6	−0.846193	−0.423096	−	0.906085i	$-0.639057\pi$
$443$	−3.49525e6	−0.846193	−0.423096	+	0.906085i	$0.639057\pi$
$444$	0	0
$445$	2.16097e6	0.517308
$446$	2.80784e6	0.668398
$447$	0	0
$448$	0	0
$449$	1.20613e6	0.282343	0.141171	−	0.989985i	$-0.454913\pi$
$449$	1.20613e6	0.282343	0.141171	+	0.989985i	$0.454913\pi$
$450$	0	0
$451$	1.15164e6	0.266609
$452$	3.12701e6	0.719918
$453$	0	0
$454$	−4.94443e6	−1.12584
$455$	0	0
$456$	0	0
$457$	233546.	0.0523097	0.0261548	−	0.999658i	$-0.491674\pi$
$457$	233546.	0.0523097	0.0261548	+	0.999658i	$0.491674\pi$
$458$	423320.	0.0942986
$459$	0	0
$460$	633600.	0.139611
$461$	−1.74489e6	−0.382398	−0.191199	−	0.981551i	$-0.561238\pi$
$461$	−1.74489e6	−0.382398	−0.191199	+	0.981551i	$0.561238\pi$
$462$	0	0
$463$	−2.91786e6	−0.632576	−0.316288	−	0.948663i	$-0.602437\pi$
$463$	−2.91786e6	−0.632576	−0.316288	+	0.948663i	$0.602437\pi$
$464$	−1.42694e6	−0.307689
$465$	0	0
$466$	−1.75471e6	−0.374318
$467$	−5.31076e6	−1.12684	−0.563422	−	0.826169i	$-0.690516\pi$
$467$	−5.31076e6	−1.12684	−0.563422	+	0.826169i	$0.690516\pi$
$468$	0	0
$469$	0	0
$470$	−5.19552e6	−1.08489
$471$	0	0
$472$	−1.68576e6	−0.348290
$473$	798960.	0.164200
$474$	0	0
$475$	−1.17684e6	−0.239322
$476$	0	0
$477$	0	0
$478$	113856.	0.0227922
$479$	2.34466e6	0.466918	0.233459	−	0.972367i	$-0.424996\pi$
$479$	2.34466e6	0.466918	0.233459	+	0.972367i	$0.424996\pi$
$480$	0	0
$481$	−5.56536e6	−1.09681
$482$	3.57025e6	0.699972
$483$	0	0
$484$	−2.51922e6	−0.488823
$485$	1.09614e7	2.11598
$486$	0	0
$487$	9.81531e6	1.87535	0.937674	−	0.347517i	$-0.112975\pi$
$487$	9.81531e6	1.87535	0.937674	+	0.347517i	$0.112975\pi$
$488$	−1.98976e6	−0.378226
$489$	0	0
$490$	0	0
$491$	5.94520e6	1.11292	0.556458	−	0.830876i	$-0.312160\pi$
$491$	5.94520e6	1.11292	0.556458	+	0.830876i	$0.312160\pi$
$492$	0	0
$493$	2.30764e6	0.427612
$494$	2.51619e6	0.463902
$495$	0	0
$496$	919552.	0.167831
$497$	0	0
$498$	0	0
$499$	6.47832e6	1.16469	0.582346	−	0.812941i	$-0.302135\pi$
$499$	6.47832e6	1.16469	0.582346	+	0.812941i	$0.302135\pi$
$500$	2.00006e6	0.357782
$501$	0	0
$502$	440496.	0.0780158
$503$	4.71794e6	0.831444	0.415722	−	0.909492i	$-0.363529\pi$
$503$	4.71794e6	0.831444	0.415722	+	0.909492i	$0.363529\pi$
$504$	0	0
$505$	1.45213e6	0.253383
$506$	144000.	0.0250027
$507$	0	0
$508$	2.76800e6	0.475890
$509$	−1.90771e6	−0.326375	−0.163188	−	0.986595i	$-0.552178\pi$
$509$	−1.90771e6	−0.326375	−0.163188	+	0.986595i	$0.552178\pi$
$510$	0	0
$511$	0	0
$512$	−262144.	−0.0441942
$513$	0	0
$514$	−563208.	−0.0940288
$515$	−5.23142e6	−0.869164
$516$	0	0
$517$	−1.18080e6	−0.194290
$518$	0	0
$519$	0	0
$520$	2.77939e6	0.450756
$521$	8.01974e6	1.29439	0.647196	−	0.762324i	$-0.275941\pi$
$521$	8.01974e6	1.29439	0.647196	+	0.762324i	$0.275941\pi$
$522$	0	0
$523$	−1.91162e6	−0.305596	−0.152798	−	0.988257i	$-0.548828\pi$
$523$	−1.91162e6	−0.305596	−0.152798	+	0.988257i	$0.548828\pi$
$524$	2.42016e6	0.385049
$525$	0	0
$526$	−3.75504e6	−0.591766
$527$	−1.48709e6	−0.233244
$528$	0	0
$529$	−6.07634e6	−0.944068
$530$	8.25422e6	1.27640
$531$	0	0
$532$	0	0
$533$	1.26297e7	1.92563
$534$	0	0
$535$	1.50472e7	2.27285
$536$	1.07546e6	0.161689
$537$	0	0
$538$	4.45802e6	0.664028
$539$	0	0
$540$	0	0
$541$	−1.19900e7	−1.76128	−0.880639	−	0.473788i	$-0.842886\pi$
$541$	−1.19900e7	−1.76128	−0.880639	+	0.473788i	$0.842886\pi$
$542$	2.27082e6	0.332035
$543$	0	0
$544$	423936.	0.0614190
$545$	562980.	0.0811898
$546$	0	0
$547$	4.45809e6	0.637061	0.318530	−	0.947913i	$-0.396811\pi$
$547$	4.45809e6	0.637061	0.318530	+	0.947913i	$0.396811\pi$
$548$	2.05526e6	0.292359
$549$	0	0
$550$	−295440.	−0.0416450
$551$	5.32874e6	0.747732
$552$	0	0
$553$	0	0
$554$	4.85303e6	0.671798
$555$	0	0
$556$	−2.46714e6	−0.338459
$557$	−9.02612e6	−1.23272	−0.616358	−	0.787466i	$-0.711393\pi$
$557$	−9.02612e6	−1.23272	−0.616358	+	0.787466i	$0.711393\pi$
$558$	0	0
$559$	8.76193e6	1.18596
$560$	0	0
$561$	0	0
$562$	2.75095e6	0.367403
$563$	6.84899e6	0.910658	0.455329	−	0.890323i	$-0.349522\pi$
$563$	6.84899e6	0.910658	0.455329	+	0.890323i	$0.349522\pi$
$564$	0	0
$565$	−1.28989e7	−1.69993
$566$	−3.32363e6	−0.436086
$567$	0	0
$568$	391680.	0.0509402
$569$	5.46322e6	0.707405	0.353703	−	0.935358i	$-0.384923\pi$
$569$	5.46322e6	0.707405	0.353703	+	0.935358i	$0.384923\pi$
$570$	0	0
$571$	−1.02324e7	−1.31337	−0.656684	−	0.754166i	$-0.728041\pi$
$571$	−1.02324e7	−1.31337	−0.656684	+	0.754166i	$0.728041\pi$
$572$	631680.	0.0807248
$573$	0	0
$574$	0	0
$575$	−738600.	−0.0931622
$576$	0	0
$577$	−1.59437e7	−1.99365	−0.996825	−	0.0796186i	$-0.974630\pi$
$577$	−1.59437e7	−1.99365	−0.996825	+	0.0796186i	$0.974630\pi$
$578$	4.99384e6	0.621749
$579$	0	0
$580$	5.88614e6	0.726542
$581$	0	0
$582$	0	0
$583$	1.87596e6	0.228587
$584$	−1.63571e6	−0.198461
$585$	0	0
$586$	5.25050e6	0.631622
$587$	−9.47713e6	−1.13522	−0.567612	−	0.823296i	$-0.692133\pi$
$587$	−9.47713e6	−1.13522	−0.567612	+	0.823296i	$0.692133\pi$
$588$	0	0
$589$	−3.43395e6	−0.407855
$590$	6.95376e6	0.822412
$591$	0	0
$592$	−2.16525e6	−0.253924
$593$	2.45349e6	0.286515	0.143258	−	0.989685i	$-0.454242\pi$
$593$	2.45349e6	0.286515	0.143258	+	0.989685i	$0.454242\pi$
$594$	0	0
$595$	0	0
$596$	−471264.	−0.0543436
$597$	0	0
$598$	1.57920e6	0.180586
$599$	9.29978e6	1.05902	0.529512	−	0.848302i	$-0.322375\pi$
$599$	9.29978e6	1.05902	0.529512	+	0.848302i	$0.322375\pi$
$600$	0	0
$601$	1.14617e7	1.29438	0.647192	−	0.762327i	$-0.275943\pi$
$601$	1.14617e7	1.29438	0.647192	+	0.762327i	$0.275943\pi$
$602$	0	0
$603$	0	0
$604$	−3.26195e6	−0.363819
$605$	1.03918e7	1.15425
$606$	0	0
$607$	−1.12784e7	−1.24244	−0.621219	−	0.783637i	$-0.713362\pi$
$607$	−1.12784e7	−1.24244	−0.621219	+	0.783637i	$0.713362\pi$
$608$	978944.	0.107399
$609$	0	0
$610$	8.20776e6	0.893100
$611$	−1.29494e7	−1.40329
$612$	0	0
$613$	93782.0	0.0100802	0.00504009	−	0.999987i	$-0.498396\pi$
$613$	93782.0	0.0100802	0.00504009	+	0.999987i	$0.498396\pi$
$614$	6.76088e6	0.723740
$615$	0	0
$616$	0	0
$617$	1.49642e7	1.58248	0.791242	−	0.611504i	$-0.209435\pi$
$617$	1.49642e7	1.58248	0.791242	+	0.611504i	$0.209435\pi$
$618$	0	0
$619$	5.06888e6	0.531723	0.265861	−	0.964011i	$-0.414344\pi$
$619$	5.06888e6	0.531723	0.265861	+	0.964011i	$0.414344\pi$
$620$	−3.79315e6	−0.396297
$621$	0	0
$622$	6.00816e6	0.622681
$623$	0	0
$624$	0	0
$625$	−1.20971e7	−1.23875
$626$	3.24337e6	0.330796
$627$	0	0
$628$	−2.17827e6	−0.220401
$629$	3.50161e6	0.352892
$630$	0	0
$631$	1.55919e7	1.55892	0.779462	−	0.626450i	$-0.215493\pi$
$631$	1.55919e7	1.55892	0.779462	+	0.626450i	$0.215493\pi$
$632$	−4.76211e6	−0.474250
$633$	0	0
$634$	3.61423e6	0.357102
$635$	−1.14180e7	−1.12371
$636$	0	0
$637$	0	0
$638$	1.33776e6	0.130115
$639$	0	0
$640$	1.08134e6	0.104355
$641$	−1.09701e7	−1.05455	−0.527274	−	0.849695i	$-0.676786\pi$
$641$	−1.09701e7	−1.05455	−0.527274	+	0.849695i	$0.676786\pi$
$642$	0	0
$643$	2.83704e6	0.270607	0.135303	−	0.990804i	$-0.456799\pi$
$643$	2.83704e6	0.270607	0.135303	+	0.990804i	$0.456799\pi$
$644$	0	0
$645$	0	0
$646$	−1.58314e6	−0.149258
$647$	−6.05686e6	−0.568835	−0.284418	−	0.958700i	$-0.591800\pi$
$647$	−6.05686e6	−0.568835	−0.284418	+	0.958700i	$0.591800\pi$
$648$	0	0
$649$	1.58040e6	0.147284
$650$	−3.23999e6	−0.300788
$651$	0	0
$652$	−2.73798e6	−0.252239
$653$	1.08892e6	0.0999341	0.0499671	−	0.998751i	$-0.484088\pi$
$653$	1.08892e6	0.0999341	0.0499671	+	0.998751i	$0.484088\pi$
$654$	0	0
$655$	−9.98316e6	−0.909211
$656$	4.91366e6	0.445806
$657$	0	0
$658$	0	0
$659$	−7.41803e6	−0.665388	−0.332694	−	0.943035i	$-0.607958\pi$
$659$	−7.41803e6	−0.665388	−0.332694	+	0.943035i	$0.607958\pi$
$660$	0	0
$661$	−767654.	−0.0683379	−0.0341690	−	0.999416i	$-0.510878\pi$
$661$	−767654.	−0.0683379	−0.0341690	+	0.999416i	$0.510878\pi$
$662$	−4.48789e6	−0.398013
$663$	0	0
$664$	413952.	0.0364359
$665$	0	0
$666$	0	0
$667$	3.34440e6	0.291074
$668$	−1.08192e7	−0.938110
$669$	0	0
$670$	−4.43626e6	−0.381794
$671$	1.86540e6	0.159943
$672$	0	0
$673$	1.42263e6	0.121075	0.0605373	−	0.998166i	$-0.480719\pi$
$673$	1.42263e6	0.121075	0.0605373	+	0.998166i	$0.480719\pi$
$674$	1.10087e7	0.933439
$675$	0	0
$676$	986736.	0.0830490
$677$	−6.16231e6	−0.516739	−0.258370	−	0.966046i	$-0.583185\pi$
$677$	−6.16231e6	−0.516739	−0.258370	+	0.966046i	$0.583185\pi$
$678$	0	0
$679$	0	0
$680$	−1.74874e6	−0.145028
$681$	0	0
$682$	−862080.	−0.0709719
$683$	−1.50621e7	−1.23548	−0.617739	−	0.786383i	$-0.711951\pi$
$683$	−1.50621e7	−1.23548	−0.617739	+	0.786383i	$0.711951\pi$
$684$	0	0
$685$	−8.47796e6	−0.690343
$686$	0	0
$687$	0	0
$688$	3.40890e6	0.274563
$689$	2.05730e7	1.65101
$690$	0	0
$691$	5.87636e6	0.468180	0.234090	−	0.972215i	$-0.424789\pi$
$691$	5.87636e6	0.468180	0.234090	+	0.972215i	$0.424789\pi$
$692$	2.13053e6	0.169131
$693$	0	0
$694$	7.66997e6	0.604498
$695$	1.01769e7	0.799199
$696$	0	0
$697$	−7.94632e6	−0.619561
$698$	7.34636e6	0.570734
$699$	0	0
$700$	0	0
$701$	−3.60077e6	−0.276758	−0.138379	−	0.990379i	$-0.544189\pi$
$701$	−3.60077e6	−0.276758	−0.138379	+	0.990379i	$0.544189\pi$
$702$	0	0
$703$	8.08585e6	0.617074
$704$	245760.	0.0186887
$705$	0	0
$706$	2.48806e6	0.187866
$707$	0	0
$708$	0	0
$709$	9.22516e6	0.689221	0.344610	−	0.938746i	$-0.388011\pi$
$709$	9.22516e6	0.689221	0.344610	+	0.938746i	$0.388011\pi$
$710$	−1.61568e6	−0.120284
$711$	0	0
$712$	2.09549e6	0.154912
$713$	−2.15520e6	−0.158768
$714$	0	0
$715$	−2.60568e6	−0.190615
$716$	1.10943e7	0.808758
$717$	0	0
$718$	1.49625e7	1.08316
$719$	−2.63923e7	−1.90395	−0.951975	−	0.306177i	$-0.900950\pi$
$719$	−2.63923e7	−1.90395	−0.951975	+	0.306177i	$0.900950\pi$
$720$	0	0
$721$	0	0
$722$	6.24865e6	0.446111
$723$	0	0
$724$	−6.03478e6	−0.427873
$725$	−6.86159e6	−0.484819
$726$	0	0
$727$	9.79485e6	0.687324	0.343662	−	0.939093i	$-0.388333\pi$
$727$	9.79485e6	0.687324	0.343662	+	0.939093i	$0.388333\pi$
$728$	0	0
$729$	0	0
$730$	6.74731e6	0.468623
$731$	−5.51282e6	−0.381576
$732$	0	0
$733$	−4.07584e6	−0.280193	−0.140096	−	0.990138i	$-0.544741\pi$
$733$	−4.07584e6	−0.280193	−0.140096	+	0.990138i	$0.544741\pi$
$734$	64928.0	0.00444828
$735$	0	0
$736$	614400.	0.0418077
$737$	−1.00824e6	−0.0683747
$738$	0	0
$739$	−1.65709e7	−1.11618	−0.558089	−	0.829781i	$-0.688465\pi$
$739$	−1.65709e7	−1.11618	−0.558089	+	0.829781i	$0.688465\pi$
$740$	8.93165e6	0.599587
$741$	0	0
$742$	0	0
$743$	−1.44141e7	−0.957892	−0.478946	−	0.877844i	$-0.658981\pi$
$743$	−1.44141e7	−0.957892	−0.478946	+	0.877844i	$0.658981\pi$
$744$	0	0
$745$	1.94396e6	0.128321
$746$	−1.17442e6	−0.0772641
$747$	0	0
$748$	−397440.	−0.0259727
$749$	0	0
$750$	0	0
$751$	1.67944e7	1.08659	0.543295	−	0.839542i	$-0.317177\pi$
$751$	1.67944e7	1.08659	0.543295	+	0.839542i	$0.317177\pi$
$752$	−5.03808e6	−0.324878
$753$	0	0
$754$	1.46708e7	0.939776
$755$	1.34556e7	0.859081
$756$	0	0
$757$	1.32943e7	0.843188	0.421594	−	0.906785i	$-0.361471\pi$
$757$	1.32943e7	0.843188	0.421594	+	0.906785i	$0.361471\pi$
$758$	−1.27205e7	−0.804137
$759$	0	0
$760$	−4.03814e6	−0.253599
$761$	−2.14786e6	−0.134445	−0.0672225	−	0.997738i	$-0.521414\pi$
$761$	−2.14786e6	−0.134445	−0.0672225	+	0.997738i	$0.521414\pi$
$762$	0	0
$763$	0	0
$764$	4.24550e6	0.263145
$765$	0	0
$766$	1.19194e7	0.733975
$767$	1.73317e7	1.06378
$768$	0	0
$769$	1.31059e7	0.799193	0.399596	−	0.916691i	$-0.369150\pi$
$769$	1.31059e7	0.799193	0.399596	+	0.916691i	$0.369150\pi$
$770$	0	0
$771$	0	0
$772$	4.72477e6	0.285323
$773$	−2.37154e7	−1.42752	−0.713759	−	0.700392i	$-0.753009\pi$
$773$	−2.37154e7	−1.42752	−0.713759	+	0.700392i	$0.753009\pi$
$774$	0	0
$775$	4.42175e6	0.264448
$776$	1.06292e7	0.633648
$777$	0	0
$778$	1.38391e7	0.819707
$779$	−1.83495e7	−1.08338
$780$	0	0
$781$	−367200.	−0.0215415
$782$	−993600.	−0.0581025
$783$	0	0
$784$	0	0
$785$	8.98537e6	0.520430
$786$	0	0
$787$	8.40048e6	0.483468	0.241734	−	0.970343i	$-0.422284\pi$
$787$	8.40048e6	0.483468	0.241734	+	0.970343i	$0.422284\pi$
$788$	−3.22070e6	−0.184772
$789$	0	0
$790$	1.96437e7	1.11984
$791$	0	0
$792$	0	0
$793$	2.04572e7	1.15522
$794$	−1.56166e7	−0.879097
$795$	0	0
$796$	−1.04392e7	−0.583960
$797$	5.41023e6	0.301696	0.150848	−	0.988557i	$-0.451800\pi$
$797$	5.41023e6	0.301696	0.150848	+	0.988557i	$0.451800\pi$
$798$	0	0
$799$	8.14752e6	0.451501
$800$	−1.26054e6	−0.0696359
$801$	0	0
$802$	2.17646e7	1.19485
$803$	1.53348e6	0.0839246
$804$	0	0
$805$	0	0
$806$	−9.45414e6	−0.512607
$807$	0	0
$808$	1.40813e6	0.0758776
$809$	2.60777e7	1.40087	0.700436	−	0.713715i	$-0.252989\pi$
$809$	2.60777e7	1.40087	0.700436	+	0.713715i	$0.252989\pi$
$810$	0	0
$811$	−1.90021e7	−1.01449	−0.507247	−	0.861800i	$-0.669337\pi$
$811$	−1.90021e7	−1.01449	−0.507247	+	0.861800i	$0.669337\pi$
$812$	0	0
$813$	0	0
$814$	2.02992e6	0.107379
$815$	1.12942e7	0.595608
$816$	0	0
$817$	−1.27301e7	−0.667231
$818$	7.87978e6	0.411748
$819$	0	0
$820$	−2.02689e7	−1.05268
$821$	3.10173e7	1.60600	0.803001	−	0.595978i	$-0.203236\pi$
$821$	3.10173e7	1.60600	0.803001	+	0.595978i	$0.203236\pi$
$822$	0	0
$823$	−1.56290e7	−0.804323	−0.402162	−	0.915569i	$-0.631741\pi$
$823$	−1.56290e7	−0.804323	−0.402162	+	0.915569i	$0.631741\pi$
$824$	−5.07290e6	−0.260278
$825$	0	0
$826$	0	0
$827$	−1.58421e7	−0.805467	−0.402733	−	0.915317i	$-0.631940\pi$
$827$	−1.58421e7	−0.805467	−0.402733	+	0.915317i	$0.631940\pi$
$828$	0	0
$829$	−2.06176e6	−0.104196	−0.0520980	−	0.998642i	$-0.516591\pi$
$829$	−2.06176e6	−0.104196	−0.0520980	+	0.998642i	$0.516591\pi$
$830$	−1.70755e6	−0.0860357
$831$	0	0
$832$	2.69517e6	0.134983
$833$	0	0
$834$	0	0
$835$	4.46292e7	2.21515
$836$	−917760.	−0.0454165
$837$	0	0
$838$	−556080.	−0.0273544
$839$	3.03900e7	1.49048	0.745240	−	0.666796i	$-0.232335\pi$
$839$	3.03900e7	1.49048	0.745240	+	0.666796i	$0.232335\pi$
$840$	0	0
$841$	1.05583e7	0.514760
$842$	−1.73097e7	−0.841414
$843$	0	0
$844$	−1.83530e7	−0.886850
$845$	−4.07029e6	−0.196103
$846$	0	0
$847$	0	0
$848$	8.00410e6	0.382228
$849$	0	0
$850$	2.03854e6	0.0967768
$851$	5.07480e6	0.240212
$852$	0	0
$853$	2.97738e7	1.40108	0.700538	−	0.713615i	$-0.252944\pi$
$853$	2.97738e7	1.40108	0.700538	+	0.713615i	$0.252944\pi$
$854$	0	0
$855$	0	0
$856$	1.45912e7	0.680624
$857$	8.64100e6	0.401894	0.200947	−	0.979602i	$-0.435598\pi$
$857$	8.64100e6	0.401894	0.200947	+	0.979602i	$0.435598\pi$
$858$	0	0
$859$	3.35663e7	1.55210	0.776051	−	0.630670i	$-0.217220\pi$
$859$	3.35663e7	1.55210	0.776051	+	0.630670i	$0.217220\pi$
$860$	−1.40617e7	−0.648323
$861$	0	0
$862$	−1.11974e7	−0.513276
$863$	−3.90191e7	−1.78341	−0.891703	−	0.452621i	$-0.850489\pi$
$863$	−3.90191e7	−1.78341	−0.891703	+	0.452621i	$0.850489\pi$
$864$	0	0
$865$	−8.78843e6	−0.399366
$866$	−2.36097e7	−1.06978
$867$	0	0
$868$	0	0
$869$	4.46448e6	0.200549
$870$	0	0
$871$	−1.10570e7	−0.493848
$872$	545920.	0.0243130
$873$	0	0
$874$	−2.29440e6	−0.101599
$875$	0	0
$876$	0	0
$877$	−1.81382e7	−0.796333	−0.398166	−	0.917313i	$-0.630353\pi$
$877$	−1.81382e7	−0.796333	−0.398166	+	0.917313i	$0.630353\pi$
$878$	−1.78605e6	−0.0781910
$879$	0	0
$880$	−1.01376e6	−0.0441294
$881$	3.05312e7	1.32527	0.662634	−	0.748943i	$-0.269438\pi$
$881$	3.05312e7	1.32527	0.662634	+	0.748943i	$0.269438\pi$
$882$	0	0
$883$	−4.35533e7	−1.87983	−0.939916	−	0.341405i	$-0.889097\pi$
$883$	−4.35533e7	−1.87983	−0.939916	+	0.341405i	$0.889097\pi$
$884$	−4.35859e6	−0.187593
$885$	0	0
$886$	1.39810e7	0.598348
$887$	−1.34152e7	−0.572515	−0.286257	−	0.958153i	$-0.592411\pi$
$887$	−1.34152e7	−0.572515	−0.286257	+	0.958153i	$0.592411\pi$
$888$	0	0
$889$	0	0
$890$	−8.64389e6	−0.365792
$891$	0	0
$892$	−1.12314e7	−0.472629
$893$	1.88141e7	0.789504
$894$	0	0
$895$	−4.57641e7	−1.90971
$896$	0	0
$897$	0	0
$898$	−4.82450e6	−0.199647
$899$	−2.00218e7	−0.826236
$900$	0	0
$901$	−1.29441e7	−0.531203
$902$	−4.60656e6	−0.188521
$903$	0	0
$904$	−1.25080e7	−0.509059
$905$	2.48935e7	1.01033
$906$	0	0
$907$	3.10816e6	0.125454	0.0627272	−	0.998031i	$-0.480020\pi$
$907$	3.10816e6	0.125454	0.0627272	+	0.998031i	$0.480020\pi$
$908$	1.97777e7	0.796089
$909$	0	0
$910$	0	0
$911$	−1.19035e6	−0.0475203	−0.0237602	−	0.999718i	$-0.507564\pi$
$911$	−1.19035e6	−0.0475203	−0.0237602	+	0.999718i	$0.507564\pi$
$912$	0	0
$913$	−388080.	−0.0154079
$914$	−934184.	−0.0369885
$915$	0	0
$916$	−1.69328e6	−0.0666792
$917$	0	0
$918$	0	0
$919$	−4.71996e7	−1.84353	−0.921764	−	0.387752i	$-0.873252\pi$
$919$	−4.71996e7	−1.84353	−0.921764	+	0.387752i	$0.873252\pi$
$920$	−2.53440e6	−0.0987201
$921$	0	0
$922$	6.97956e6	0.270396
$923$	−4.02696e6	−0.155587
$924$	0	0
$925$	−1.04118e7	−0.400103
$926$	1.16715e7	0.447299
$927$	0	0
$928$	5.70778e6	0.217569
$929$	1.33595e6	0.0507870	0.0253935	−	0.999678i	$-0.491916\pi$
$929$	1.33595e6	0.0507870	0.0253935	+	0.999678i	$0.491916\pi$
$930$	0	0
$931$	0	0
$932$	7.01885e6	0.264683
$933$	0	0
$934$	2.12430e7	0.796800
$935$	1.63944e6	0.0613291
$936$	0	0
$937$	−1.47238e7	−0.547861	−0.273931	−	0.961749i	$-0.588324\pi$
$937$	−1.47238e7	−0.547861	−0.273931	+	0.961749i	$0.588324\pi$
$938$	0	0
$939$	0	0
$940$	2.07821e7	0.767131
$941$	−2.69196e7	−0.991049	−0.495525	−	0.868594i	$-0.665024\pi$
$941$	−2.69196e7	−0.991049	−0.495525	+	0.868594i	$0.665024\pi$
$942$	0	0
$943$	−1.15164e7	−0.421733
$944$	6.74304e6	0.246278
$945$	0	0
$946$	−3.19584e6	−0.116107
$947$	3.73160e6	0.135214	0.0676068	−	0.997712i	$-0.478464\pi$
$947$	3.73160e6	0.135214	0.0676068	+	0.997712i	$0.478464\pi$
$948$	0	0
$949$	1.68172e7	0.606160
$950$	4.70734e6	0.169226
$951$	0	0
$952$	0	0
$953$	−2.18735e7	−0.780166	−0.390083	−	0.920780i	$-0.627554\pi$
$953$	−2.18735e7	−0.780166	−0.390083	+	0.920780i	$0.627554\pi$
$954$	0	0
$955$	−1.75127e7	−0.621362
$956$	−455424.	−0.0161165
$957$	0	0
$958$	−9.37862e6	−0.330161
$959$	0	0
$960$	0	0
$961$	−1.57267e7	−0.549324
$962$	2.22615e7	0.775561
$963$	0	0
$964$	−1.42810e7	−0.494955
$965$	−1.94897e7	−0.673730
$966$	0	0
$967$	1.76025e7	0.605352	0.302676	−	0.953093i	$-0.402120\pi$
$967$	1.76025e7	0.605352	0.302676	+	0.953093i	$0.402120\pi$
$968$	1.00769e7	0.345650
$969$	0	0
$970$	−4.38456e7	−1.49623
$971$	1.67317e7	0.569497	0.284749	−	0.958602i	$-0.408090\pi$
$971$	1.67317e7	0.569497	0.284749	+	0.958602i	$0.408090\pi$
$972$	0	0
$973$	0	0
$974$	−3.92612e7	−1.32607
$975$	0	0
$976$	7.95904e6	0.267446
$977$	−5.55382e7	−1.86147	−0.930733	−	0.365699i	$-0.880830\pi$
$977$	−5.55382e7	−1.86147	−0.930733	+	0.365699i	$0.880830\pi$
$978$	0	0
$979$	−1.96452e6	−0.0655088
$980$	0	0
$981$	0	0
$982$	−2.37808e7	−0.786951
$983$	−3.86784e7	−1.27669	−0.638344	−	0.769751i	$-0.720380\pi$
$983$	−3.86784e7	−1.27669	−0.638344	+	0.769751i	$0.720380\pi$
$984$	0	0
$985$	1.32854e7	0.436299
$986$	−9.23054e6	−0.302367
$987$	0	0
$988$	−1.00648e7	−0.328028
$989$	−7.98960e6	−0.259737
$990$	0	0
$991$	9.58498e6	0.310033	0.155016	−	0.987912i	$-0.450457\pi$
$991$	9.58498e6	0.310033	0.155016	+	0.987912i	$0.450457\pi$
$992$	−3.67821e6	−0.118674
$993$	0	0
$994$	0	0
$995$	4.30616e7	1.37890
$996$	0	0
$997$	1.03650e7	0.330242	0.165121	−	0.986273i	$-0.447198\pi$
$997$	1.03650e7	0.330242	0.165121	+	0.986273i	$0.447198\pi$
$998$	−2.59133e7	−0.823561
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.6.a.a.1.1		1
3.2	odd	2		294.6.a.m.1.1		1
7.6	odd	2		18.6.a.b.1.1		1
21.2	odd	6		294.6.e.a.67.1		2
21.5	even	6		294.6.e.g.67.1		2
21.11	odd	6		294.6.e.a.79.1		2
21.17	even	6		294.6.e.g.79.1		2
21.20	even	2		6.6.a.a.1.1	✓	1
28.27	even	2		144.6.a.j.1.1		1
35.13	even	4		450.6.c.j.199.2		2
35.27	even	4		450.6.c.j.199.1		2
35.34	odd	2		450.6.a.m.1.1		1
56.13	odd	2		576.6.a.j.1.1		1
56.27	even	2		576.6.a.i.1.1		1
63.13	odd	6		162.6.c.h.55.1		2
63.20	even	6		162.6.c.e.109.1		2
63.34	odd	6		162.6.c.h.109.1		2
63.41	even	6		162.6.c.e.55.1		2
84.83	odd	2		48.6.a.c.1.1		1
105.62	odd	4		150.6.c.b.49.2		2
105.83	odd	4		150.6.c.b.49.1		2
105.104	even	2		150.6.a.d.1.1		1
168.83	odd	2		192.6.a.g.1.1		1
168.125	even	2		192.6.a.o.1.1		1
231.230	odd	2		726.6.a.a.1.1		1
273.272	even	2		1014.6.a.c.1.1		1
336.83	odd	4		768.6.d.p.385.2		2
336.125	even	4		768.6.d.c.385.1		2
336.251	odd	4		768.6.d.p.385.1		2
336.293	even	4		768.6.d.c.385.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.6.a.a.1.1	✓	1	21.20	even	2
18.6.a.b.1.1		1	7.6	odd	2
48.6.a.c.1.1		1	84.83	odd	2
144.6.a.j.1.1		1	28.27	even	2
150.6.a.d.1.1		1	105.104	even	2
150.6.c.b.49.1		2	105.83	odd	4
150.6.c.b.49.2		2	105.62	odd	4
162.6.c.e.55.1		2	63.41	even	6
162.6.c.e.109.1		2	63.20	even	6
162.6.c.h.55.1		2	63.13	odd	6
162.6.c.h.109.1		2	63.34	odd	6
192.6.a.g.1.1		1	168.83	odd	2
192.6.a.o.1.1		1	168.125	even	2
294.6.a.m.1.1		1	3.2	odd	2
294.6.e.a.67.1		2	21.2	odd	6
294.6.e.a.79.1		2	21.11	odd	6
294.6.e.g.67.1		2	21.5	even	6
294.6.e.g.79.1		2	21.17	even	6
450.6.a.m.1.1		1	35.34	odd	2
450.6.c.j.199.1		2	35.27	even	4
450.6.c.j.199.2		2	35.13	even	4
576.6.a.i.1.1		1	56.27	even	2
576.6.a.j.1.1		1	56.13	odd	2
726.6.a.a.1.1		1	231.230	odd	2
768.6.d.c.385.1		2	336.125	even	4
768.6.d.c.385.2		2	336.293	even	4
768.6.d.p.385.1		2	336.251	odd	4
768.6.d.p.385.2		2	336.83	odd	4
882.6.a.a.1.1		1	1.1	even	1	trivial
1014.6.a.c.1.1		1	273.272	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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