LMFDB - Embedded newform 400.6.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,6,Mod(1,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("400.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	400.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:	$64.1535279252$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+6.00000 q^{3} -118.000 q^{7} -207.000 q^{9} +O(q^{10})$

$q+6.00000 q^{3} -118.000 q^{7} -207.000 q^{9} -192.000 q^{11} -1106.00 q^{13} -762.000 q^{17} +2740.00 q^{19} -708.000 q^{21} +1566.00 q^{23} -2700.00 q^{27} +5910.00 q^{29} +6868.00 q^{31} -1152.00 q^{33} +5518.00 q^{37} -6636.00 q^{39} -378.000 q^{41} -2434.00 q^{43} +13122.0 q^{47} -2883.00 q^{49} -4572.00 q^{51} +9174.00 q^{53} +16440.0 q^{57} +34980.0 q^{59} -9838.00 q^{61} +24426.0 q^{63} +33722.0 q^{67} +9396.00 q^{69} -70212.0 q^{71} -21986.0 q^{73} +22656.0 q^{77} -4520.00 q^{79} +34101.0 q^{81} -109074. q^{83} +35460.0 q^{87} +38490.0 q^{89} +130508. q^{91} +41208.0 q^{93} +1918.00 q^{97} +39744.0 q^{99} +O(q^{100})$

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
$3$	6.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	6.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−118.000	−0.910200	−0.455100	−	0.890440i	$-0.650397\pi$
$7$	−118.000	−0.910200	−0.455100	+	0.890440i	$0.650397\pi$
$8$	0	0
$9$	−207.000	−0.851852
$10$	0	0
$11$	−192.000	−0.478431	−0.239216	−	0.970966i	$-0.576890\pi$
$11$	−192.000	−0.478431	−0.239216	+	0.970966i	$0.576890\pi$
$12$	0	0
$13$	−1106.00	−1.81508	−0.907542	−	0.419961i	$-0.862044\pi$
$13$	−1106.00	−1.81508	−0.907542	+	0.419961i	$0.862044\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−762.000	−0.639488	−0.319744	−	0.947504i	$-0.603597\pi$
$17$	−762.000	−0.639488	−0.319744	+	0.947504i	$0.603597\pi$
$18$	0	0
$19$	2740.00	1.74127	0.870636	−	0.491928i	$-0.163708\pi$
$19$	2740.00	1.74127	0.870636	+	0.491928i	$0.163708\pi$
$20$	0	0
$21$	−708.000	−0.350336
$22$	0	0
$23$	1566.00	0.617266	0.308633	−	0.951181i	$-0.400129\pi$
$23$	1566.00	0.617266	0.308633	+	0.951181i	$0.400129\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−2700.00	−0.712778
$28$	0	0
$29$	5910.00	1.30495	0.652473	−	0.757812i	$-0.273732\pi$
$29$	5910.00	1.30495	0.652473	+	0.757812i	$0.273732\pi$
$30$	0	0
$31$	6868.00	1.28359	0.641795	−	0.766877i	$-0.278190\pi$
$31$	6868.00	1.28359	0.641795	+	0.766877i	$0.278190\pi$
$32$	0	0
$33$	−1152.00	−0.184148
$34$	0	0
$35$	0	0
$36$	0	0
$37$	5518.00	0.662640	0.331320	−	0.943519i	$-0.392506\pi$
$37$	5518.00	0.662640	0.331320	+	0.943519i	$0.392506\pi$
$38$	0	0
$39$	−6636.00	−0.698626
$40$	0	0
$41$	−378.000	−0.0351182	−0.0175591	−	0.999846i	$-0.505590\pi$
$41$	−378.000	−0.0351182	−0.0175591	+	0.999846i	$0.505590\pi$
$42$	0	0
$43$	−2434.00	−0.200747	−0.100374	−	0.994950i	$-0.532004\pi$
$43$	−2434.00	−0.200747	−0.100374	+	0.994950i	$0.532004\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	13122.0	0.866474	0.433237	−	0.901280i	$-0.357371\pi$
$47$	13122.0	0.866474	0.433237	+	0.901280i	$0.357371\pi$
$48$	0	0
$49$	−2883.00	−0.171536
$50$	0	0
$51$	−4572.00	−0.246139
$52$	0	0
$53$	9174.00	0.448610	0.224305	−	0.974519i	$-0.427989\pi$
$53$	9174.00	0.448610	0.224305	+	0.974519i	$0.427989\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	16440.0	0.670216
$58$	0	0
$59$	34980.0	1.30825	0.654124	−	0.756388i	$-0.273038\pi$
$59$	34980.0	1.30825	0.654124	+	0.756388i	$0.273038\pi$
$60$	0	0
$61$	−9838.00	−0.338518	−0.169259	−	0.985572i	$-0.554137\pi$
$61$	−9838.00	−0.338518	−0.169259	+	0.985572i	$0.554137\pi$
$62$	0	0
$63$	24426.0	0.775356
$64$	0	0
$65$	0	0
$66$	0	0
$67$	33722.0	0.917754	0.458877	−	0.888500i	$-0.348252\pi$
$67$	33722.0	0.917754	0.458877	+	0.888500i	$0.348252\pi$
$68$	0	0
$69$	9396.00	0.237586
$70$	0	0
$71$	−70212.0	−1.65297	−0.826486	−	0.562957i	$-0.809664\pi$
$71$	−70212.0	−1.65297	−0.826486	+	0.562957i	$0.809664\pi$
$72$	0	0
$73$	−21986.0	−0.482880	−0.241440	−	0.970416i	$-0.577620\pi$
$73$	−21986.0	−0.482880	−0.241440	+	0.970416i	$0.577620\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	22656.0	0.435468
$78$	0	0
$79$	−4520.00	−0.0814837	−0.0407418	−	0.999170i	$-0.512972\pi$
$79$	−4520.00	−0.0814837	−0.0407418	+	0.999170i	$0.512972\pi$
$80$	0	0
$81$	34101.0	0.577503
$82$	0	0
$83$	−109074.	−1.73790	−0.868952	−	0.494896i	$-0.835206\pi$
$83$	−109074.	−1.73790	−0.868952	+	0.494896i	$0.835206\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	35460.0	0.502274
$88$	0	0
$89$	38490.0	0.515078	0.257539	−	0.966268i	$-0.417088\pi$
$89$	38490.0	0.515078	0.257539	+	0.966268i	$0.417088\pi$
$90$	0	0
$91$	130508.	1.65209
$92$	0	0
$93$	41208.0	0.494054
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1918.00	0.0206976	0.0103488	−	0.999946i	$-0.496706\pi$
$97$	1918.00	0.0206976	0.0103488	+	0.999946i	$0.496706\pi$
$98$	0	0
$99$	39744.0	0.407553
$100$	0	0
$101$	77622.0	0.757149	0.378575	−	0.925571i	$-0.376414\pi$
$101$	77622.0	0.757149	0.378575	+	0.925571i	$0.376414\pi$
$102$	0	0
$103$	−46714.0	−0.433864	−0.216932	−	0.976187i	$-0.569605\pi$
$103$	−46714.0	−0.433864	−0.216932	+	0.976187i	$0.569605\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1038.00	−0.00876472	−0.00438236	−	0.999990i	$-0.501395\pi$
$107$	−1038.00	−0.00876472	−0.00438236	+	0.999990i	$0.501395\pi$
$108$	0	0
$109$	206930.	1.66823	0.834117	−	0.551587i	$-0.185977\pi$
$109$	206930.	1.66823	0.834117	+	0.551587i	$0.185977\pi$
$110$	0	0
$111$	33108.0	0.255050
$112$	0	0
$113$	−139386.	−1.02689	−0.513444	−	0.858123i	$-0.671631\pi$
$113$	−139386.	−1.02689	−0.513444	+	0.858123i	$0.671631\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	228942.	1.54618
$118$	0	0
$119$	89916.0	0.582062
$120$	0	0
$121$	−124187.	−0.771104
$122$	0	0
$123$	−2268.00	−0.0135170
$124$	0	0
$125$	0	0
$126$	0	0
$127$	299882.	1.64984	0.824919	−	0.565252i	$-0.191221\pi$
$127$	299882.	1.64984	0.824919	+	0.565252i	$0.191221\pi$
$128$	0	0
$129$	−14604.0	−0.0772676
$130$	0	0
$131$	−7872.00	−0.0400781	−0.0200390	−	0.999799i	$-0.506379\pi$
$131$	−7872.00	−0.0400781	−0.0200390	+	0.999799i	$0.506379\pi$
$132$	0	0
$133$	−323320.	−1.58491
$134$	0	0
$135$	0	0
$136$	0	0
$137$	164238.	0.747605	0.373803	−	0.927508i	$-0.378054\pi$
$137$	164238.	0.747605	0.373803	+	0.927508i	$0.378054\pi$
$138$	0	0
$139$	282100.	1.23841	0.619207	−	0.785228i	$-0.287454\pi$
$139$	282100.	1.23841	0.619207	+	0.785228i	$0.287454\pi$
$140$	0	0
$141$	78732.0	0.333506
$142$	0	0
$143$	212352.	0.868393
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−17298.0	−0.0660241
$148$	0	0
$149$	−388950.	−1.43525	−0.717626	−	0.696429i	$-0.754771\pi$
$149$	−388950.	−1.43525	−0.717626	+	0.696429i	$0.754771\pi$
$150$	0	0
$151$	97948.0	0.349585	0.174793	−	0.984605i	$-0.444074\pi$
$151$	97948.0	0.349585	0.174793	+	0.984605i	$0.444074\pi$
$152$	0	0
$153$	157734.	0.544749
$154$	0	0
$155$	0	0
$156$	0	0
$157$	3718.00	0.0120382	0.00601908	−	0.999982i	$-0.498084\pi$
$157$	3718.00	0.0120382	0.00601908	+	0.999982i	$0.498084\pi$
$158$	0	0
$159$	55044.0	0.172670
$160$	0	0
$161$	−184788.	−0.561835
$162$	0	0
$163$	−43234.0	−0.127455	−0.0637274	−	0.997967i	$-0.520299\pi$
$163$	−43234.0	−0.127455	−0.0637274	+	0.997967i	$0.520299\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	186522.	0.517534	0.258767	−	0.965940i	$-0.416684\pi$
$167$	186522.	0.517534	0.258767	+	0.965940i	$0.416684\pi$
$168$	0	0
$169$	851943.	2.29453
$170$	0	0
$171$	−567180.	−1.48331
$172$	0	0
$173$	374454.	0.951225	0.475612	−	0.879655i	$-0.342226\pi$
$173$	374454.	0.951225	0.475612	+	0.879655i	$0.342226\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	209880.	0.503545
$178$	0	0
$179$	−272100.	−0.634740	−0.317370	−	0.948302i	$-0.602800\pi$
$179$	−272100.	−0.634740	−0.317370	+	0.948302i	$0.602800\pi$
$180$	0	0
$181$	−75418.0	−0.171111	−0.0855556	−	0.996333i	$-0.527267\pi$
$181$	−75418.0	−0.171111	−0.0855556	+	0.996333i	$0.527267\pi$
$182$	0	0
$183$	−59028.0	−0.130296
$184$	0	0
$185$	0	0
$186$	0	0
$187$	146304.	0.305951
$188$	0	0
$189$	318600.	0.648771
$190$	0	0
$191$	356988.	0.708060	0.354030	−	0.935234i	$-0.384811\pi$
$191$	356988.	0.708060	0.354030	+	0.935234i	$0.384811\pi$
$192$	0	0
$193$	438694.	0.847751	0.423876	−	0.905720i	$-0.360669\pi$
$193$	438694.	0.847751	0.423876	+	0.905720i	$0.360669\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	156798.	0.287856	0.143928	−	0.989588i	$-0.454027\pi$
$197$	156798.	0.287856	0.143928	+	0.989588i	$0.454027\pi$
$198$	0	0
$199$	162520.	0.290920	0.145460	−	0.989364i	$-0.453534\pi$
$199$	162520.	0.290920	0.145460	+	0.989364i	$0.453534\pi$
$200$	0	0
$201$	202332.	0.353244
$202$	0	0
$203$	−697380.	−1.18776
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−324162.	−0.525819
$208$	0	0
$209$	−526080.	−0.833079
$210$	0	0
$211$	181648.	0.280882	0.140441	−	0.990089i	$-0.455148\pi$
$211$	181648.	0.280882	0.140441	+	0.990089i	$0.455148\pi$
$212$	0	0
$213$	−421272.	−0.636229
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−810424.	−1.16832
$218$	0	0
$219$	−131916.	−0.185861
$220$	0	0
$221$	842772.	1.16073
$222$	0	0
$223$	−288274.	−0.388189	−0.194095	−	0.980983i	$-0.562177\pi$
$223$	−288274.	−0.388189	−0.194095	+	0.980983i	$0.562177\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	1.12552e6	1.44974	0.724869	−	0.688887i	$-0.241900\pi$
$227$	1.12552e6	1.44974	0.724869	+	0.688887i	$0.241900\pi$
$228$	0	0
$229$	−415810.	−0.523970	−0.261985	−	0.965072i	$-0.584377\pi$
$229$	−415810.	−0.523970	−0.261985	+	0.965072i	$0.584377\pi$
$230$	0	0
$231$	135936.	0.167612
$232$	0	0
$233$	−770586.	−0.929889	−0.464945	−	0.885340i	$-0.653926\pi$
$233$	−770586.	−0.929889	−0.464945	+	0.885340i	$0.653926\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−27120.0	−0.0313631
$238$	0	0
$239$	595320.	0.674149	0.337074	−	0.941478i	$-0.390563\pi$
$239$	595320.	0.674149	0.337074	+	0.941478i	$0.390563\pi$
$240$	0	0
$241$	273902.	0.303775	0.151888	−	0.988398i	$-0.451465\pi$
$241$	273902.	0.303775	0.151888	+	0.988398i	$0.451465\pi$
$242$	0	0
$243$	860706.	0.935059
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−3.03044e6	−3.16055
$248$	0	0
$249$	−654444.	−0.668920
$250$	0	0
$251$	−850752.	−0.852351	−0.426176	−	0.904640i	$-0.640139\pi$
$251$	−850752.	−0.852351	−0.426176	+	0.904640i	$0.640139\pi$
$252$	0	0
$253$	−300672.	−0.295319
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−825402.	−0.779530	−0.389765	−	0.920914i	$-0.627444\pi$
$257$	−825402.	−0.779530	−0.389765	+	0.920914i	$0.627444\pi$
$258$	0	0
$259$	−651124.	−0.603135
$260$	0	0
$261$	−1.22337e6	−1.11162
$262$	0	0
$263$	1.36465e6	1.21655	0.608276	−	0.793726i	$-0.291861\pi$
$263$	1.36465e6	1.21655	0.608276	+	0.793726i	$0.291861\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	230940.	0.198254
$268$	0	0
$269$	−113310.	−0.0954745	−0.0477373	−	0.998860i	$-0.515201\pi$
$269$	−113310.	−0.0954745	−0.0477373	+	0.998860i	$0.515201\pi$
$270$	0	0
$271$	849628.	0.702758	0.351379	−	0.936233i	$-0.385713\pi$
$271$	849628.	0.702758	0.351379	+	0.936233i	$0.385713\pi$
$272$	0	0
$273$	783048.	0.635890
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−438602.	−0.343456	−0.171728	−	0.985144i	$-0.554935\pi$
$277$	−438602.	−0.343456	−0.171728	+	0.985144i	$0.554935\pi$
$278$	0	0
$279$	−1.42168e6	−1.09343
$280$	0	0
$281$	−1.45670e6	−1.10053	−0.550267	−	0.834989i	$-0.685474\pi$
$281$	−1.45670e6	−1.10053	−0.550267	+	0.834989i	$0.685474\pi$
$282$	0	0
$283$	−120394.	−0.0893591	−0.0446795	−	0.999001i	$-0.514227\pi$
$283$	−120394.	−0.0893591	−0.0446795	+	0.999001i	$0.514227\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	44604.0	0.0319646
$288$	0	0
$289$	−839213.	−0.591055
$290$	0	0
$291$	11508.0	0.00796650
$292$	0	0
$293$	2.64209e6	1.79796	0.898978	−	0.437993i	$-0.144311\pi$
$293$	2.64209e6	1.79796	0.898978	+	0.437993i	$0.144311\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	518400.	0.341015
$298$	0	0
$299$	−1.73200e6	−1.12039
$300$	0	0
$301$	287212.	0.182720
$302$	0	0
$303$	465732.	0.291427
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−1.44756e6	−0.876577	−0.438288	−	0.898834i	$-0.644415\pi$
$307$	−1.44756e6	−0.876577	−0.438288	+	0.898834i	$0.644415\pi$
$308$	0	0
$309$	−280284.	−0.166994
$310$	0	0
$311$	928068.	0.544100	0.272050	−	0.962283i	$-0.412298\pi$
$311$	928068.	0.544100	0.272050	+	0.962283i	$0.412298\pi$
$312$	0	0
$313$	−2.29563e6	−1.32446	−0.662232	−	0.749299i	$-0.730391\pi$
$313$	−2.29563e6	−1.32446	−0.662232	+	0.749299i	$0.730391\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−2.73652e6	−1.52950	−0.764752	−	0.644324i	$-0.777139\pi$
$317$	−2.73652e6	−1.52950	−0.764752	+	0.644324i	$0.777139\pi$
$318$	0	0
$319$	−1.13472e6	−0.624327
$320$	0	0
$321$	−6228.00	−0.00337354
$322$	0	0
$323$	−2.08788e6	−1.11352
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1.24158e6	0.642104
$328$	0	0
$329$	−1.54840e6	−0.788665
$330$	0	0
$331$	−3.81879e6	−1.91583	−0.957913	−	0.287059i	$-0.907322\pi$
$331$	−3.81879e6	−1.91583	−0.957913	+	0.287059i	$0.907322\pi$
$332$	0	0
$333$	−1.14223e6	−0.564471
$334$	0	0
$335$	0	0
$336$	0	0
$337$	2.21088e6	1.06045	0.530225	−	0.847857i	$-0.322108\pi$
$337$	2.21088e6	1.06045	0.530225	+	0.847857i	$0.322108\pi$
$338$	0	0
$339$	−836316.	−0.395249
$340$	0	0
$341$	−1.31866e6	−0.614109
$342$	0	0
$343$	2.32342e6	1.06633
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−2.32724e6	−1.03757	−0.518785	−	0.854905i	$-0.673615\pi$
$347$	−2.32724e6	−1.03757	−0.518785	+	0.854905i	$0.673615\pi$
$348$	0	0
$349$	−311290.	−0.136805	−0.0684024	−	0.997658i	$-0.521790\pi$
$349$	−311290.	−0.136805	−0.0684024	+	0.997658i	$0.521790\pi$
$350$	0	0
$351$	2.98620e6	1.29375
$352$	0	0
$353$	3.08657e6	1.31838	0.659189	−	0.751977i	$-0.270900\pi$
$353$	3.08657e6	1.31838	0.659189	+	0.751977i	$0.270900\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	539496.	0.224036
$358$	0	0
$359$	3.53076e6	1.44588	0.722940	−	0.690911i	$-0.242790\pi$
$359$	3.53076e6	1.44588	0.722940	+	0.690911i	$0.242790\pi$
$360$	0	0
$361$	5.03150e6	2.03203
$362$	0	0
$363$	−745122.	−0.296798
$364$	0	0
$365$	0	0
$366$	0	0
$367$	35762.0	0.0138598	0.00692989	−	0.999976i	$-0.497794\pi$
$367$	35762.0	0.0138598	0.00692989	+	0.999976i	$0.497794\pi$
$368$	0	0
$369$	78246.0	0.0299155
$370$	0	0
$371$	−1.08253e6	−0.408325
$372$	0	0
$373$	1.71525e6	0.638346	0.319173	−	0.947696i	$-0.396595\pi$
$373$	1.71525e6	0.638346	0.319173	+	0.947696i	$0.396595\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−6.53646e6	−2.36859
$378$	0	0
$379$	3.10174e6	1.10919	0.554597	−	0.832119i	$-0.312873\pi$
$379$	3.10174e6	1.10919	0.554597	+	0.832119i	$0.312873\pi$
$380$	0	0
$381$	1.79929e6	0.635023
$382$	0	0
$383$	5.31949e6	1.85299	0.926494	−	0.376309i	$-0.122807\pi$
$383$	5.31949e6	1.85299	0.926494	+	0.376309i	$0.122807\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	503838.	0.171007
$388$	0	0
$389$	1.16145e6	0.389158	0.194579	−	0.980887i	$-0.437666\pi$
$389$	1.16145e6	0.389158	0.194579	+	0.980887i	$0.437666\pi$
$390$	0	0
$391$	−1.19329e6	−0.394734
$392$	0	0
$393$	−47232.0	−0.0154261
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−628562.	−0.200157	−0.100079	−	0.994980i	$-0.531909\pi$
$397$	−628562.	−0.200157	−0.100079	+	0.994980i	$0.531909\pi$
$398$	0	0
$399$	−1.93992e6	−0.610031
$400$	0	0
$401$	−2.72432e6	−0.846052	−0.423026	−	0.906118i	$-0.639032\pi$
$401$	−2.72432e6	−0.846052	−0.423026	+	0.906118i	$0.639032\pi$
$402$	0	0
$403$	−7.59601e6	−2.32982
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−1.05946e6	−0.317027
$408$	0	0
$409$	1.78019e6	0.526209	0.263104	−	0.964767i	$-0.415254\pi$
$409$	1.78019e6	0.526209	0.263104	+	0.964767i	$0.415254\pi$
$410$	0	0
$411$	985428.	0.287753
$412$	0	0
$413$	−4.12764e6	−1.19077
$414$	0	0
$415$	0	0
$416$	0	0
$417$	1.69260e6	0.476666
$418$	0	0
$419$	−650580.	−0.181036	−0.0905181	−	0.995895i	$-0.528852\pi$
$419$	−650580.	−0.181036	−0.0905181	+	0.995895i	$0.528852\pi$
$420$	0	0
$421$	−3.54060e6	−0.973579	−0.486790	−	0.873519i	$-0.661832\pi$
$421$	−3.54060e6	−0.973579	−0.486790	+	0.873519i	$0.661832\pi$
$422$	0	0
$423$	−2.71625e6	−0.738107
$424$	0	0
$425$	0	0
$426$	0	0
$427$	1.16088e6	0.308119
$428$	0	0
$429$	1.27411e6	0.334245
$430$	0	0
$431$	548748.	0.142292	0.0711459	−	0.997466i	$-0.477334\pi$
$431$	548748.	0.142292	0.0711459	+	0.997466i	$0.477334\pi$
$432$	0	0
$433$	1.49241e6	0.382534	0.191267	−	0.981538i	$-0.438740\pi$
$433$	1.49241e6	0.382534	0.191267	+	0.981538i	$0.438740\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	4.29084e6	1.07483
$438$	0	0
$439$	−4.86212e6	−1.20411	−0.602053	−	0.798456i	$-0.705650\pi$
$439$	−4.86212e6	−1.20411	−0.602053	+	0.798456i	$0.705650\pi$
$440$	0	0
$441$	596781.	0.146123
$442$	0	0
$443$	−1.86155e6	−0.450678	−0.225339	−	0.974280i	$-0.572349\pi$
$443$	−1.86155e6	−0.450678	−0.225339	+	0.974280i	$0.572349\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−2.33370e6	−0.552429
$448$	0	0
$449$	3.73719e6	0.874841	0.437421	−	0.899257i	$-0.355892\pi$
$449$	3.73719e6	0.874841	0.437421	+	0.899257i	$0.355892\pi$
$450$	0	0
$451$	72576.0	0.0168016
$452$	0	0
$453$	587688.	0.134555
$454$	0	0
$455$	0	0
$456$	0	0
$457$	6.48276e6	1.45201	0.726005	−	0.687690i	$-0.241375\pi$
$457$	6.48276e6	1.45201	0.726005	+	0.687690i	$0.241375\pi$
$458$	0	0
$459$	2.05740e6	0.455813
$460$	0	0
$461$	1.50910e6	0.330724	0.165362	−	0.986233i	$-0.447121\pi$
$461$	1.50910e6	0.330724	0.165362	+	0.986233i	$0.447121\pi$
$462$	0	0
$463$	8.68401e6	1.88264	0.941321	−	0.337513i	$-0.109586\pi$
$463$	8.68401e6	1.88264	0.941321	+	0.337513i	$0.109586\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	6.96412e6	1.47766	0.738829	−	0.673893i	$-0.235379\pi$
$467$	6.96412e6	1.47766	0.738829	+	0.673893i	$0.235379\pi$
$468$	0	0
$469$	−3.97920e6	−0.835340
$470$	0	0
$471$	22308.0	0.00463349
$472$	0	0
$473$	467328.	0.0960437
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1.89902e6	−0.382149
$478$	0	0
$479$	5.51052e6	1.09737	0.548686	−	0.836029i	$-0.315128\pi$
$479$	5.51052e6	1.09737	0.548686	+	0.836029i	$0.315128\pi$
$480$	0	0
$481$	−6.10291e6	−1.20275
$482$	0	0
$483$	−1.10873e6	−0.216251
$484$	0	0
$485$	0	0
$486$	0	0
$487$	5.51808e6	1.05430	0.527152	−	0.849771i	$-0.323260\pi$
$487$	5.51808e6	1.05430	0.527152	+	0.849771i	$0.323260\pi$
$488$	0	0
$489$	−259404.	−0.0490574
$490$	0	0
$491$	1.51277e6	0.283184	0.141592	−	0.989925i	$-0.454778\pi$
$491$	1.51277e6	0.283184	0.141592	+	0.989925i	$0.454778\pi$
$492$	0	0
$493$	−4.50342e6	−0.834498
$494$	0	0
$495$	0	0
$496$	0	0
$497$	8.28502e6	1.50454
$498$	0	0
$499$	1.93042e6	0.347057	0.173528	−	0.984829i	$-0.444483\pi$
$499$	1.93042e6	0.347057	0.173528	+	0.984829i	$0.444483\pi$
$500$	0	0
$501$	1.11913e6	0.199199
$502$	0	0
$503$	6.73105e6	1.18621	0.593106	−	0.805124i	$-0.297901\pi$
$503$	6.73105e6	1.18621	0.593106	+	0.805124i	$0.297901\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	5.11166e6	0.883165
$508$	0	0
$509$	−556650.	−0.0952331	−0.0476165	−	0.998866i	$-0.515163\pi$
$509$	−556650.	−0.0952331	−0.0476165	+	0.998866i	$0.515163\pi$
$510$	0	0
$511$	2.59435e6	0.439517
$512$	0	0
$513$	−7.39800e6	−1.24114
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−2.51942e6	−0.414548
$518$	0	0
$519$	2.24672e6	0.366127
$520$	0	0
$521$	1.01110e7	1.63192	0.815962	−	0.578106i	$-0.196208\pi$
$521$	1.01110e7	1.63192	0.815962	+	0.578106i	$0.196208\pi$
$522$	0	0
$523$	−7.03719e6	−1.12498	−0.562491	−	0.826804i	$-0.690157\pi$
$523$	−7.03719e6	−1.12498	−0.562491	+	0.826804i	$0.690157\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−5.23342e6	−0.820840
$528$	0	0
$529$	−3.98399e6	−0.618983
$530$	0	0
$531$	−7.24086e6	−1.11443
$532$	0	0
$533$	418068.	0.0637425
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−1.63260e6	−0.244312
$538$	0	0
$539$	553536.	0.0820680
$540$	0	0
$541$	−4.23114e6	−0.621533	−0.310766	−	0.950486i	$-0.600586\pi$
$541$	−4.23114e6	−0.621533	−0.310766	+	0.950486i	$0.600586\pi$
$542$	0	0
$543$	−452508.	−0.0658608
$544$	0	0
$545$	0	0
$546$	0	0
$547$	4.44024e6	0.634510	0.317255	−	0.948340i	$-0.397239\pi$
$547$	4.44024e6	0.634510	0.317255	+	0.948340i	$0.397239\pi$
$548$	0	0
$549$	2.03647e6	0.288367
$550$	0	0
$551$	1.61934e7	2.27227
$552$	0	0
$553$	533360.	0.0741665
$554$	0	0
$555$	0	0
$556$	0	0
$557$	9.01448e6	1.23113	0.615563	−	0.788088i	$-0.288929\pi$
$557$	9.01448e6	1.23113	0.615563	+	0.788088i	$0.288929\pi$
$558$	0	0
$559$	2.69200e6	0.364373
$560$	0	0
$561$	877824.	0.117761
$562$	0	0
$563$	−9.81287e6	−1.30474	−0.652372	−	0.757899i	$-0.726226\pi$
$563$	−9.81287e6	−1.30474	−0.652372	+	0.757899i	$0.726226\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−4.02392e6	−0.525644
$568$	0	0
$569$	1.33152e7	1.72412	0.862061	−	0.506804i	$-0.169173\pi$
$569$	1.33152e7	1.72412	0.862061	+	0.506804i	$0.169173\pi$
$570$	0	0
$571$	−9.95895e6	−1.27827	−0.639136	−	0.769094i	$-0.720708\pi$
$571$	−9.95895e6	−1.27827	−0.639136	+	0.769094i	$0.720708\pi$
$572$	0	0
$573$	2.14193e6	0.272533
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−4.50372e6	−0.563160	−0.281580	−	0.959538i	$-0.590859\pi$
$577$	−4.50372e6	−0.563160	−0.281580	+	0.959538i	$0.590859\pi$
$578$	0	0
$579$	2.63216e6	0.326300
$580$	0	0
$581$	1.28707e7	1.58184
$582$	0	0
$583$	−1.76141e6	−0.214629
$584$	0	0
$585$	0	0
$586$	0	0
$587$	625842.	0.0749669	0.0374834	−	0.999297i	$-0.488066\pi$
$587$	625842.	0.0749669	0.0374834	+	0.999297i	$0.488066\pi$
$588$	0	0
$589$	1.88183e7	2.23508
$590$	0	0
$591$	940788.	0.110796
$592$	0	0
$593$	2.50385e6	0.292397	0.146198	−	0.989255i	$-0.453296\pi$
$593$	2.50385e6	0.292397	0.146198	+	0.989255i	$0.453296\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	975120.	0.111975
$598$	0	0
$599$	756480.	0.0861451	0.0430725	−	0.999072i	$-0.486285\pi$
$599$	756480.	0.0861451	0.0430725	+	0.999072i	$0.486285\pi$
$600$	0	0
$601$	−1.38565e7	−1.56483	−0.782413	−	0.622760i	$-0.786011\pi$
$601$	−1.38565e7	−1.56483	−0.782413	+	0.622760i	$0.786011\pi$
$602$	0	0
$603$	−6.98045e6	−0.781791
$604$	0	0
$605$	0	0
$606$	0	0
$607$	1.13772e7	1.25333	0.626663	−	0.779291i	$-0.284420\pi$
$607$	1.13772e7	1.25333	0.626663	+	0.779291i	$0.284420\pi$
$608$	0	0
$609$	−4.18428e6	−0.457170
$610$	0	0
$611$	−1.45129e7	−1.57272
$612$	0	0
$613$	7.00161e6	0.752570	0.376285	−	0.926504i	$-0.377201\pi$
$613$	7.00161e6	0.752570	0.376285	+	0.926504i	$0.377201\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−7.90300e6	−0.835755	−0.417878	−	0.908503i	$-0.637226\pi$
$617$	−7.90300e6	−0.835755	−0.417878	+	0.908503i	$0.637226\pi$
$618$	0	0
$619$	−4.02362e6	−0.422076	−0.211038	−	0.977478i	$-0.567684\pi$
$619$	−4.02362e6	−0.422076	−0.211038	+	0.977478i	$0.567684\pi$
$620$	0	0
$621$	−4.22820e6	−0.439974
$622$	0	0
$623$	−4.54182e6	−0.468824
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−3.15648e6	−0.320652
$628$	0	0
$629$	−4.20472e6	−0.423750
$630$	0	0
$631$	1.00227e7	1.00210	0.501049	−	0.865419i	$-0.332948\pi$
$631$	1.00227e7	1.00210	0.501049	+	0.865419i	$0.332948\pi$
$632$	0	0
$633$	1.08989e6	0.108112
$634$	0	0
$635$	0	0
$636$	0	0
$637$	3.18860e6	0.311352
$638$	0	0
$639$	1.45339e7	1.40809
$640$	0	0
$641$	6.37390e6	0.612718	0.306359	−	0.951916i	$-0.400889\pi$
$641$	6.37390e6	0.612718	0.306359	+	0.951916i	$0.400889\pi$
$642$	0	0
$643$	5.00457e6	0.477352	0.238676	−	0.971099i	$-0.423287\pi$
$643$	5.00457e6	0.477352	0.238676	+	0.971099i	$0.423287\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−8.71928e6	−0.818879	−0.409440	−	0.912337i	$-0.634276\pi$
$647$	−8.71928e6	−0.818879	−0.409440	+	0.912337i	$0.634276\pi$
$648$	0	0
$649$	−6.71616e6	−0.625906
$650$	0	0
$651$	−4.86254e6	−0.449688
$652$	0	0
$653$	1.58477e6	0.145440	0.0727201	−	0.997352i	$-0.476832\pi$
$653$	1.58477e6	0.145440	0.0727201	+	0.997352i	$0.476832\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	4.55110e6	0.411342
$658$	0	0
$659$	−1.26410e7	−1.13388	−0.566940	−	0.823759i	$-0.691873\pi$
$659$	−1.26410e7	−1.13388	−0.566940	+	0.823759i	$0.691873\pi$
$660$	0	0
$661$	−3.61572e6	−0.321878	−0.160939	−	0.986964i	$-0.551452\pi$
$661$	−3.61572e6	−0.321878	−0.160939	+	0.986964i	$0.551452\pi$
$662$	0	0
$663$	5.05663e6	0.446763
$664$	0	0
$665$	0	0
$666$	0	0
$667$	9.25506e6	0.805498
$668$	0	0
$669$	−1.72964e6	−0.149414
$670$	0	0
$671$	1.88890e6	0.161958
$672$	0	0
$673$	−1.11313e7	−0.947349	−0.473675	−	0.880700i	$-0.657073\pi$
$673$	−1.11313e7	−0.947349	−0.473675	+	0.880700i	$0.657073\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	235518.	0.0197493	0.00987467	−	0.999951i	$-0.496857\pi$
$677$	235518.	0.0197493	0.00987467	+	0.999951i	$0.496857\pi$
$678$	0	0
$679$	−226324.	−0.0188389
$680$	0	0
$681$	6.75313e6	0.558004
$682$	0	0
$683$	2.05830e7	1.68833	0.844164	−	0.536084i	$-0.180097\pi$
$683$	2.05830e7	1.68833	0.844164	+	0.536084i	$0.180097\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−2.49486e6	−0.201676
$688$	0	0
$689$	−1.01464e7	−0.814265
$690$	0	0
$691$	9.54825e6	0.760727	0.380363	−	0.924837i	$-0.375799\pi$
$691$	9.54825e6	0.760727	0.380363	+	0.924837i	$0.375799\pi$
$692$	0	0
$693$	−4.68979e6	−0.370954
$694$	0	0
$695$	0	0
$696$	0	0
$697$	288036.	0.0224577
$698$	0	0
$699$	−4.62352e6	−0.357915
$700$	0	0
$701$	1.29304e6	0.0993843	0.0496921	−	0.998765i	$-0.484176\pi$
$701$	1.29304e6	0.0993843	0.0496921	+	0.998765i	$0.484176\pi$
$702$	0	0
$703$	1.51193e7	1.15384
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−9.15940e6	−0.689157
$708$	0	0
$709$	−2.12720e7	−1.58926	−0.794628	−	0.607097i	$-0.792334\pi$
$709$	−2.12720e7	−1.58926	−0.794628	+	0.607097i	$0.792334\pi$
$710$	0	0
$711$	935640.	0.0694120
$712$	0	0
$713$	1.07553e7	0.792316
$714$	0	0
$715$	0	0
$716$	0	0
$717$	3.57192e6	0.259480
$718$	0	0
$719$	−8.31732e6	−0.600014	−0.300007	−	0.953937i	$-0.596989\pi$
$719$	−8.31732e6	−0.600014	−0.300007	+	0.953937i	$0.596989\pi$
$720$	0	0
$721$	5.51225e6	0.394903
$722$	0	0
$723$	1.64341e6	0.116923
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−4.36740e6	−0.306469	−0.153235	−	0.988190i	$-0.548969\pi$
$727$	−4.36740e6	−0.306469	−0.153235	+	0.988190i	$0.548969\pi$
$728$	0	0
$729$	−3.12231e6	−0.217599
$730$	0	0
$731$	1.85471e6	0.128375
$732$	0	0
$733$	4.05645e6	0.278860	0.139430	−	0.990232i	$-0.455473\pi$
$733$	4.05645e6	0.278860	0.139430	+	0.990232i	$0.455473\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−6.47462e6	−0.439082
$738$	0	0
$739$	−768260.	−0.0517484	−0.0258742	−	0.999665i	$-0.508237\pi$
$739$	−768260.	−0.0517484	−0.0258742	+	0.999665i	$0.508237\pi$
$740$	0	0
$741$	−1.81826e7	−1.21650
$742$	0	0
$743$	6.18781e6	0.411211	0.205605	−	0.978635i	$-0.434084\pi$
$743$	6.18781e6	0.411211	0.205605	+	0.978635i	$0.434084\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	2.25783e7	1.48044
$748$	0	0
$749$	122484.	0.00797765
$750$	0	0
$751$	−1.81698e7	−1.17557	−0.587787	−	0.809016i	$-0.700001\pi$
$751$	−1.81698e7	−1.17557	−0.587787	+	0.809016i	$0.700001\pi$
$752$	0	0
$753$	−5.10451e6	−0.328070
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−1.93494e7	−1.22724	−0.613618	−	0.789603i	$-0.710286\pi$
$757$	−1.93494e7	−1.22724	−0.613618	+	0.789603i	$0.710286\pi$
$758$	0	0
$759$	−1.80403e6	−0.113668
$760$	0	0
$761$	−3.01992e7	−1.89031	−0.945155	−	0.326621i	$-0.894090\pi$
$761$	−3.01992e7	−1.89031	−0.945155	+	0.326621i	$0.894090\pi$
$762$	0	0
$763$	−2.44177e7	−1.51843
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−3.86879e7	−2.37458
$768$	0	0
$769$	2.15854e7	1.31627	0.658134	−	0.752901i	$-0.271346\pi$
$769$	2.15854e7	1.31627	0.658134	+	0.752901i	$0.271346\pi$
$770$	0	0
$771$	−4.95241e6	−0.300041
$772$	0	0
$773$	−3.90895e6	−0.235294	−0.117647	−	0.993055i	$-0.537535\pi$
$773$	−3.90895e6	−0.235294	−0.117647	+	0.993055i	$0.537535\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−3.90674e6	−0.232147
$778$	0	0
$779$	−1.03572e6	−0.0611503
$780$	0	0
$781$	1.34807e7	0.790833
$782$	0	0
$783$	−1.59570e7	−0.930137
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−2.65082e7	−1.52561	−0.762806	−	0.646628i	$-0.776179\pi$
$787$	−2.65082e7	−1.52561	−0.762806	+	0.646628i	$0.776179\pi$
$788$	0	0
$789$	8.18788e6	0.468251
$790$	0	0
$791$	1.64475e7	0.934674
$792$	0	0
$793$	1.08808e7	0.614439
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−1.07940e7	−0.601919	−0.300960	−	0.953637i	$-0.597307\pi$
$797$	−1.07940e7	−0.601919	−0.300960	+	0.953637i	$0.597307\pi$
$798$	0	0
$799$	−9.99896e6	−0.554100
$800$	0	0
$801$	−7.96743e6	−0.438770
$802$	0	0
$803$	4.22131e6	0.231025
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−679860.	−0.0367482
$808$	0	0
$809$	−1.11446e7	−0.598675	−0.299338	−	0.954147i	$-0.596766\pi$
$809$	−1.11446e7	−0.598675	−0.299338	+	0.954147i	$0.596766\pi$
$810$	0	0
$811$	1.14866e7	0.613253	0.306626	−	0.951830i	$-0.400800\pi$
$811$	1.14866e7	0.613253	0.306626	+	0.951830i	$0.400800\pi$
$812$	0	0
$813$	5.09777e6	0.270492
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−6.66916e6	−0.349555
$818$	0	0
$819$	−2.70152e7	−1.40734
$820$	0	0
$821$	3.04347e7	1.57584	0.787918	−	0.615781i	$-0.211159\pi$
$821$	3.04347e7	1.57584	0.787918	+	0.615781i	$0.211159\pi$
$822$	0	0
$823$	4.09773e6	0.210884	0.105442	−	0.994425i	$-0.466374\pi$
$823$	4.09773e6	0.210884	0.105442	+	0.994425i	$0.466374\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−1.70652e7	−0.867654	−0.433827	−	0.900996i	$-0.642837\pi$
$827$	−1.70652e7	−0.867654	−0.433827	+	0.900996i	$0.642837\pi$
$828$	0	0
$829$	−2.47617e7	−1.25139	−0.625697	−	0.780066i	$-0.715185\pi$
$829$	−2.47617e7	−1.25139	−0.625697	+	0.780066i	$0.715185\pi$
$830$	0	0
$831$	−2.63161e6	−0.132196
$832$	0	0
$833$	2.19685e6	0.109695
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1.85436e7	−0.914914
$838$	0	0
$839$	−3.16529e7	−1.55242	−0.776208	−	0.630476i	$-0.782860\pi$
$839$	−3.16529e7	−1.55242	−0.776208	+	0.630476i	$0.782860\pi$
$840$	0	0
$841$	1.44170e7	0.702884
$842$	0	0
$843$	−8.74019e6	−0.423596
$844$	0	0
$845$	0	0
$846$	0	0
$847$	1.46541e7	0.701859
$848$	0	0
$849$	−722364.	−0.0343943
$850$	0	0
$851$	8.64119e6	0.409025
$852$	0	0
$853$	−2.82671e7	−1.33017	−0.665087	−	0.746765i	$-0.731606\pi$
$853$	−2.82671e7	−1.33017	−0.665087	+	0.746765i	$0.731606\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−2.60870e7	−1.21331	−0.606655	−	0.794966i	$-0.707489\pi$
$857$	−2.60870e7	−1.21331	−0.606655	+	0.794966i	$0.707489\pi$
$858$	0	0
$859$	3.38111e7	1.56342	0.781710	−	0.623642i	$-0.214348\pi$
$859$	3.38111e7	1.56342	0.781710	+	0.623642i	$0.214348\pi$
$860$	0	0
$861$	267624.	0.0123032
$862$	0	0
$863$	2.22817e7	1.01841	0.509204	−	0.860646i	$-0.329940\pi$
$863$	2.22817e7	1.01841	0.509204	+	0.860646i	$0.329940\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−5.03528e6	−0.227497
$868$	0	0
$869$	867840.	0.0389843
$870$	0	0
$871$	−3.72965e7	−1.66580
$872$	0	0
$873$	−397026.	−0.0176313
$874$	0	0
$875$	0	0
$876$	0	0
$877$	3.46748e7	1.52235	0.761177	−	0.648545i	$-0.224622\pi$
$877$	3.46748e7	1.52235	0.761177	+	0.648545i	$0.224622\pi$
$878$	0	0
$879$	1.58526e7	0.692034
$880$	0	0
$881$	1.42603e7	0.618998	0.309499	−	0.950900i	$-0.399839\pi$
$881$	1.42603e7	0.618998	0.309499	+	0.950900i	$0.399839\pi$
$882$	0	0
$883$	−3.75177e7	−1.61933	−0.809663	−	0.586895i	$-0.800350\pi$
$883$	−3.75177e7	−1.61933	−0.809663	+	0.586895i	$0.800350\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	4.07657e7	1.73975	0.869873	−	0.493275i	$-0.164200\pi$
$887$	4.07657e7	1.73975	0.869873	+	0.493275i	$0.164200\pi$
$888$	0	0
$889$	−3.53861e7	−1.50168
$890$	0	0
$891$	−6.54739e6	−0.276296
$892$	0	0
$893$	3.59543e7	1.50877
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−1.03920e7	−0.431238
$898$	0	0
$899$	4.05899e7	1.67501
$900$	0	0
$901$	−6.99059e6	−0.286881
$902$	0	0
$903$	1.72327e6	0.0703290
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−3.57116e7	−1.44142	−0.720712	−	0.693235i	$-0.756185\pi$
$907$	−3.57116e7	−1.44142	−0.720712	+	0.693235i	$0.756185\pi$
$908$	0	0
$909$	−1.60678e7	−0.644979
$910$	0	0
$911$	2.11389e7	0.843893	0.421947	−	0.906621i	$-0.361347\pi$
$911$	2.11389e7	0.843893	0.421947	+	0.906621i	$0.361347\pi$
$912$	0	0
$913$	2.09422e7	0.831468
$914$	0	0
$915$	0	0
$916$	0	0
$917$	928896.	0.0364791
$918$	0	0
$919$	−1.85996e7	−0.726465	−0.363233	−	0.931698i	$-0.618327\pi$
$919$	−1.85996e7	−0.726465	−0.363233	+	0.931698i	$0.618327\pi$
$920$	0	0
$921$	−8.68535e6	−0.337395
$922$	0	0
$923$	7.76545e7	3.00028
$924$	0	0
$925$	0	0
$926$	0	0
$927$	9.66980e6	0.369588
$928$	0	0
$929$	4.45110e7	1.69211	0.846055	−	0.533096i	$-0.178972\pi$
$929$	4.45110e7	1.69211	0.846055	+	0.533096i	$0.178972\pi$
$930$	0	0
$931$	−7.89942e6	−0.298690
$932$	0	0
$933$	5.56841e6	0.209424
$934$	0	0
$935$	0	0
$936$	0	0
$937$	2.19419e7	0.816441	0.408221	−	0.912883i	$-0.366149\pi$
$937$	2.19419e7	0.816441	0.408221	+	0.912883i	$0.366149\pi$
$938$	0	0
$939$	−1.37738e7	−0.509787
$940$	0	0
$941$	−7.77722e6	−0.286319	−0.143160	−	0.989700i	$-0.545726\pi$
$941$	−7.77722e6	−0.286319	−0.143160	+	0.989700i	$0.545726\pi$
$942$	0	0
$943$	−591948.	−0.0216773
$944$	0	0
$945$	0	0
$946$	0	0
$947$	3.17199e7	1.14936	0.574681	−	0.818378i	$-0.305126\pi$
$947$	3.17199e7	1.14936	0.574681	+	0.818378i	$0.305126\pi$
$948$	0	0
$949$	2.43165e7	0.876468
$950$	0	0
$951$	−1.64191e7	−0.588707
$952$	0	0
$953$	5.60285e6	0.199838	0.0999188	−	0.994996i	$-0.468142\pi$
$953$	5.60285e6	0.199838	0.0999188	+	0.994996i	$0.468142\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−6.80832e6	−0.240304
$958$	0	0
$959$	−1.93801e7	−0.680470
$960$	0	0
$961$	1.85403e7	0.647601
$962$	0	0
$963$	214866.	0.00746624
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−2.03532e7	−0.699949	−0.349975	−	0.936759i	$-0.613810\pi$
$967$	−2.03532e7	−0.699949	−0.349975	+	0.936759i	$0.613810\pi$
$968$	0	0
$969$	−1.25273e7	−0.428595
$970$	0	0
$971$	2.34306e7	0.797510	0.398755	−	0.917057i	$-0.369442\pi$
$971$	2.34306e7	0.797510	0.398755	+	0.917057i	$0.369442\pi$
$972$	0	0
$973$	−3.32878e7	−1.12721
$974$	0	0
$975$	0	0
$976$	0	0
$977$	4.30412e7	1.44261	0.721303	−	0.692619i	$-0.243543\pi$
$977$	4.30412e7	1.44261	0.721303	+	0.692619i	$0.243543\pi$
$978$	0	0
$979$	−7.39008e6	−0.246429
$980$	0	0
$981$	−4.28345e7	−1.42109
$982$	0	0
$983$	−4.75003e7	−1.56788	−0.783940	−	0.620837i	$-0.786793\pi$
$983$	−4.75003e7	−1.56788	−0.783940	+	0.620837i	$0.786793\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−9.29038e6	−0.303557
$988$	0	0
$989$	−3.81164e6	−0.123914
$990$	0	0
$991$	−2.09231e7	−0.676770	−0.338385	−	0.941008i	$-0.609881\pi$
$991$	−2.09231e7	−0.676770	−0.338385	+	0.941008i	$0.609881\pi$
$992$	0	0
$993$	−2.29128e7	−0.737402
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−2.96332e7	−0.944148	−0.472074	−	0.881559i	$-0.656495\pi$
$997$	−2.96332e7	−0.944148	−0.472074	+	0.881559i	$0.656495\pi$
$998$	0	0
$999$	−1.48986e7	−0.472315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.6.a.i.1.1		1
4.3	odd	2		50.6.a.b.1.1		1
5.2	odd	4		400.6.c.i.49.1		2
5.3	odd	4		400.6.c.i.49.2		2
5.4	even	2		80.6.a.c.1.1		1
12.11	even	2		450.6.a.u.1.1		1
15.14	odd	2		720.6.a.v.1.1		1
20.3	even	4		50.6.b.b.49.2		2
20.7	even	4		50.6.b.b.49.1		2
20.19	odd	2		10.6.a.c.1.1	✓	1
40.19	odd	2		320.6.a.f.1.1		1
40.29	even	2		320.6.a.k.1.1		1
60.23	odd	4		450.6.c.f.199.1		2
60.47	odd	4		450.6.c.f.199.2		2
60.59	even	2		90.6.a.b.1.1		1
140.139	even	2		490.6.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.a.c.1.1	✓	1	20.19	odd	2
50.6.a.b.1.1		1	4.3	odd	2
50.6.b.b.49.1		2	20.7	even	4
50.6.b.b.49.2		2	20.3	even	4
80.6.a.c.1.1		1	5.4	even	2
90.6.a.b.1.1		1	60.59	even	2
320.6.a.f.1.1		1	40.19	odd	2
320.6.a.k.1.1		1	40.29	even	2
400.6.a.i.1.1		1	1.1	even	1	trivial
400.6.c.i.49.1		2	5.2	odd	4
400.6.c.i.49.2		2	5.3	odd	4
450.6.a.u.1.1		1	12.11	even	2
450.6.c.f.199.1		2	60.23	odd	4
450.6.c.f.199.2		2	60.47	odd	4
490.6.a.k.1.1		1	140.139	even	2
720.6.a.v.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	400.a (trivial)

Introduction

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