LMFDB - Embedded newform 80.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(1,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, 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("80.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.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:	$12.8307055850$
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	$\chi$	$=$	80.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-6.00000 q^{3} -25.0000 q^{5} +118.000 q^{7} -207.000 q^{9} +O(q^{10})$

$q-6.00000 q^{3} -25.0000 q^{5} +118.000 q^{7} -207.000 q^{9} -192.000 q^{11} +1106.00 q^{13} +150.000 q^{15} +762.000 q^{17} +2740.00 q^{19} -708.000 q^{21} -1566.00 q^{23} +625.000 q^{25} +2700.00 q^{27} +5910.00 q^{29} +6868.00 q^{31} +1152.00 q^{33} -2950.00 q^{35} -5518.00 q^{37} -6636.00 q^{39} -378.000 q^{41} +2434.00 q^{43} +5175.00 q^{45} -13122.0 q^{47} -2883.00 q^{49} -4572.00 q^{51} -9174.00 q^{53} +4800.00 q^{55} -16440.0 q^{57} +34980.0 q^{59} -9838.00 q^{61} -24426.0 q^{63} -27650.0 q^{65} -33722.0 q^{67} +9396.00 q^{69} -70212.0 q^{71} +21986.0 q^{73} -3750.00 q^{75} -22656.0 q^{77} -4520.00 q^{79} +34101.0 q^{81} +109074. q^{83} -19050.0 q^{85} -35460.0 q^{87} +38490.0 q^{89} +130508. q^{91} -41208.0 q^{93} -68500.0 q^{95} -1918.00 q^{97} +39744.0 q^{99} +O(q^{100})$

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	$-0.561643\pi$
$3$	−6.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	0	0
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	118.000	0.910200	0.455100	−	0.890440i	$-0.349603\pi$
$7$	118.000	0.910200	0.455100	+	0.890440i	$0.349603\pi$
$8$	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	$-0.137956\pi$
$13$	1106.00	1.81508	0.907542	+	0.419961i	$0.137956\pi$
$14$	0	0
$15$	150.000	0.172133
$16$	0	0
$17$	762.000	0.639488	0.319744	−	0.947504i	$-0.396403\pi$
$17$	762.000	0.639488	0.319744	+	0.947504i	$0.396403\pi$
$18$	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	$-0.599871\pi$
$23$	−1566.00	−0.617266	−0.308633	+	0.951181i	$0.599871\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	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
$35$	−2950.00	−0.407054
$36$	0	0
$37$	−5518.00	−0.662640	−0.331320	−	0.943519i	$-0.607494\pi$
$37$	−5518.00	−0.662640	−0.331320	+	0.943519i	$0.607494\pi$
$38$	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	$-0.467996\pi$
$43$	2434.00	0.200747	0.100374	+	0.994950i	$0.467996\pi$
$44$	0	0
$45$	5175.00	0.380960
$46$	0	0
$47$	−13122.0	−0.866474	−0.433237	−	0.901280i	$-0.642629\pi$
$47$	−13122.0	−0.866474	−0.433237	+	0.901280i	$0.642629\pi$
$48$	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	$-0.572011\pi$
$53$	−9174.00	−0.448610	−0.224305	+	0.974519i	$0.572011\pi$
$54$	0	0
$55$	4800.00	0.213961
$56$	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
$65$	−27650.0	−0.811730
$66$	0	0
$67$	−33722.0	−0.917754	−0.458877	−	0.888500i	$-0.651748\pi$
$67$	−33722.0	−0.917754	−0.458877	+	0.888500i	$0.651748\pi$
$68$	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	$-0.422380\pi$
$73$	21986.0	0.482880	0.241440	+	0.970416i	$0.422380\pi$
$74$	0	0
$75$	−3750.00	−0.0769800
$76$	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	$-0.164794\pi$
$83$	109074.	1.73790	0.868952	+	0.494896i	$0.164794\pi$
$84$	0	0
$85$	−19050.0	−0.285988
$86$	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
$95$	−68500.0	−0.778720
$96$	0	0
$97$	−1918.00	−0.0206976	−0.0103488	−	0.999946i	$-0.503294\pi$
$97$	−1918.00	−0.0206976	−0.0103488	+	0.999946i	$0.503294\pi$
$98$	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	$-0.430395\pi$
$103$	46714.0	0.433864	0.216932	+	0.976187i	$0.430395\pi$
$104$	0	0
$105$	17700.0	0.156675
$106$	0	0
$107$	1038.00	0.00876472	0.00438236	−	0.999990i	$-0.498605\pi$
$107$	1038.00	0.00876472	0.00438236	+	0.999990i	$0.498605\pi$
$108$	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	$-0.328369\pi$
$113$	139386.	1.02689	0.513444	+	0.858123i	$0.328369\pi$
$114$	0	0
$115$	39150.0	0.276050
$116$	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
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−299882.	−1.64984	−0.824919	−	0.565252i	$-0.808779\pi$
$127$	−299882.	−1.64984	−0.824919	+	0.565252i	$0.808779\pi$
$128$	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
$135$	−67500.0	−0.318764
$136$	0	0
$137$	−164238.	−0.747605	−0.373803	−	0.927508i	$-0.621946\pi$
$137$	−164238.	−0.747605	−0.373803	+	0.927508i	$0.621946\pi$
$138$	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
$145$	−147750.	−0.583590
$146$	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
$155$	−171700.	−0.574039
$156$	0	0
$157$	−3718.00	−0.0120382	−0.00601908	−	0.999982i	$-0.501916\pi$
$157$	−3718.00	−0.0120382	−0.00601908	+	0.999982i	$0.501916\pi$
$158$	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	$-0.479701\pi$
$163$	43234.0	0.127455	0.0637274	+	0.997967i	$0.479701\pi$
$164$	0	0
$165$	−28800.0	−0.0823536
$166$	0	0
$167$	−186522.	−0.517534	−0.258767	−	0.965940i	$-0.583316\pi$
$167$	−186522.	−0.517534	−0.258767	+	0.965940i	$0.583316\pi$
$168$	0	0
$169$	851943.	2.29453
$170$	0	0
$171$	−567180.	−1.48331
$172$	0	0
$173$	−374454.	−0.951225	−0.475612	−	0.879655i	$-0.657774\pi$
$173$	−374454.	−0.951225	−0.475612	+	0.879655i	$0.657774\pi$
$174$	0	0
$175$	73750.0	0.182040
$176$	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
$185$	137950.	0.296341
$186$	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	$-0.639331\pi$
$193$	−438694.	−0.847751	−0.423876	+	0.905720i	$0.639331\pi$
$194$	0	0
$195$	165900.	0.312435
$196$	0	0
$197$	−156798.	−0.287856	−0.143928	−	0.989588i	$-0.545973\pi$
$197$	−156798.	−0.287856	−0.143928	+	0.989588i	$0.545973\pi$
$198$	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
$205$	9450.00	0.0157053
$206$	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
$215$	−60850.0	−0.0897769
$216$	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	$-0.437823\pi$
$223$	288274.	0.388189	0.194095	+	0.980983i	$0.437823\pi$
$224$	0	0
$225$	−129375.	−0.170370
$226$	0	0
$227$	−1.12552e6	−1.44974	−0.724869	−	0.688887i	$-0.758100\pi$
$227$	−1.12552e6	−1.44974	−0.724869	+	0.688887i	$0.758100\pi$
$228$	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	$-0.346074\pi$
$233$	770586.	0.929889	0.464945	+	0.885340i	$0.346074\pi$
$234$	0	0
$235$	328050.	0.387499
$236$	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
$245$	72075.0	0.0767131
$246$	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
$255$	114300.	0.110077
$256$	0	0
$257$	825402.	0.779530	0.389765	−	0.920914i	$-0.372556\pi$
$257$	825402.	0.779530	0.389765	+	0.920914i	$0.372556\pi$
$258$	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	$-0.708139\pi$
$263$	−1.36465e6	−1.21655	−0.608276	+	0.793726i	$0.708139\pi$
$264$	0	0
$265$	229350.	0.200625
$266$	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
$275$	−120000.	−0.0956862
$276$	0	0
$277$	438602.	0.343456	0.171728	−	0.985144i	$-0.445065\pi$
$277$	438602.	0.343456	0.171728	+	0.985144i	$0.445065\pi$
$278$	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	$-0.485773\pi$
$283$	120394.	0.0893591	0.0446795	+	0.999001i	$0.485773\pi$
$284$	0	0
$285$	411000.	0.299730
$286$	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	$-0.855689\pi$
$293$	−2.64209e6	−1.79796	−0.898978	+	0.437993i	$0.855689\pi$
$294$	0	0
$295$	−874500.	−0.585066
$296$	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
$305$	245950.	0.151390
$306$	0	0
$307$	1.44756e6	0.876577	0.438288	−	0.898834i	$-0.355585\pi$
$307$	1.44756e6	0.876577	0.438288	+	0.898834i	$0.355585\pi$
$308$	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	$-0.269609\pi$
$313$	2.29563e6	1.32446	0.662232	+	0.749299i	$0.269609\pi$
$314$	0	0
$315$	610650.	0.346750
$316$	0	0
$317$	2.73652e6	1.52950	0.764752	−	0.644324i	$-0.222861\pi$
$317$	2.73652e6	1.52950	0.764752	+	0.644324i	$0.222861\pi$
$318$	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
$325$	691250.	0.363017
$326$	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
$335$	843050.	0.410432
$336$	0	0
$337$	−2.21088e6	−1.06045	−0.530225	−	0.847857i	$-0.677892\pi$
$337$	−2.21088e6	−1.06045	−0.530225	+	0.847857i	$0.677892\pi$
$338$	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
$345$	−234900.	−0.106252
$346$	0	0
$347$	2.32724e6	1.03757	0.518785	−	0.854905i	$-0.326385\pi$
$347$	2.32724e6	1.03757	0.518785	+	0.854905i	$0.326385\pi$
$348$	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	$-0.729100\pi$
$353$	−3.08657e6	−1.31838	−0.659189	+	0.751977i	$0.729100\pi$
$354$	0	0
$355$	1.75530e6	0.739232
$356$	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
$365$	−549650.	−0.215950
$366$	0	0
$367$	−35762.0	−0.0138598	−0.00692989	−	0.999976i	$-0.502206\pi$
$367$	−35762.0	−0.0138598	−0.00692989	+	0.999976i	$0.502206\pi$
$368$	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	$-0.603405\pi$
$373$	−1.71525e6	−0.638346	−0.319173	+	0.947696i	$0.603405\pi$
$374$	0	0
$375$	93750.0	0.0344265
$376$	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	$-0.877193\pi$
$383$	−5.31949e6	−1.85299	−0.926494	+	0.376309i	$0.877193\pi$
$384$	0	0
$385$	566400.	0.194747
$386$	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
$395$	113000.	0.0364406
$396$	0	0
$397$	628562.	0.200157	0.100079	−	0.994980i	$-0.468091\pi$
$397$	628562.	0.200157	0.100079	+	0.994980i	$0.468091\pi$
$398$	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
$405$	−852525.	−0.258267
$406$	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
$415$	−2.72685e6	−0.777215
$416$	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
$425$	476250.	0.127898
$426$	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	$-0.561260\pi$
$433$	−1.49241e6	−0.382534	−0.191267	+	0.981538i	$0.561260\pi$
$434$	0	0
$435$	886500.	0.224624
$436$	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	$-0.427651\pi$
$443$	1.86155e6	0.450678	0.225339	+	0.974280i	$0.427651\pi$
$444$	0	0
$445$	−962250.	−0.230350
$446$	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
$455$	−3.26270e6	−0.738837
$456$	0	0
$457$	−6.48276e6	−1.45201	−0.726005	−	0.687690i	$-0.758625\pi$
$457$	−6.48276e6	−1.45201	−0.726005	+	0.687690i	$0.758625\pi$
$458$	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	$-0.890414\pi$
$463$	−8.68401e6	−1.88264	−0.941321	+	0.337513i	$0.890414\pi$
$464$	0	0
$465$	1.03020e6	0.220948
$466$	0	0
$467$	−6.96412e6	−1.47766	−0.738829	−	0.673893i	$-0.764621\pi$
$467$	−6.96412e6	−1.47766	−0.738829	+	0.673893i	$0.764621\pi$
$468$	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
$475$	1.71250e6	0.348254
$476$	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
$485$	47950.0	0.00925623
$486$	0	0
$487$	−5.51808e6	−1.05430	−0.527152	−	0.849771i	$-0.676740\pi$
$487$	−5.51808e6	−1.05430	−0.527152	+	0.849771i	$0.676740\pi$
$488$	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
$495$	−993600.	−0.182263
$496$	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	$-0.702099\pi$
$503$	−6.73105e6	−1.18621	−0.593106	+	0.805124i	$0.702099\pi$
$504$	0	0
$505$	−1.94055e6	−0.338607
$506$	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
$515$	−1.16785e6	−0.194030
$516$	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	$-0.309843\pi$
$523$	7.03719e6	1.12498	0.562491	+	0.826804i	$0.309843\pi$
$524$	0	0
$525$	−442500.	−0.0700672
$526$	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
$535$	−25950.0	−0.00391970
$536$	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
$545$	−5.17325e6	−0.746057
$546$	0	0
$547$	−4.44024e6	−0.634510	−0.317255	−	0.948340i	$-0.602761\pi$
$547$	−4.44024e6	−0.634510	−0.317255	+	0.948340i	$0.602761\pi$
$548$	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
$555$	−827700.	−0.114062
$556$	0	0
$557$	−9.01448e6	−1.23113	−0.615563	−	0.788088i	$-0.711071\pi$
$557$	−9.01448e6	−1.23113	−0.615563	+	0.788088i	$0.711071\pi$
$558$	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	$-0.273774\pi$
$563$	9.81287e6	1.30474	0.652372	+	0.757899i	$0.273774\pi$
$564$	0	0
$565$	−3.48465e6	−0.459238
$566$	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
$575$	−978750.	−0.123453
$576$	0	0
$577$	4.50372e6	0.563160	0.281580	−	0.959538i	$-0.409141\pi$
$577$	4.50372e6	0.563160	0.281580	+	0.959538i	$0.409141\pi$
$578$	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
$585$	5.72355e6	0.691474
$586$	0	0
$587$	−625842.	−0.0749669	−0.0374834	−	0.999297i	$-0.511934\pi$
$587$	−625842.	−0.0749669	−0.0374834	+	0.999297i	$0.511934\pi$
$588$	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	$-0.546704\pi$
$593$	−2.50385e6	−0.292397	−0.146198	+	0.989255i	$0.546704\pi$
$594$	0	0
$595$	−2.24790e6	−0.260306
$596$	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
$605$	3.10468e6	0.344848
$606$	0	0
$607$	−1.13772e7	−1.25333	−0.626663	−	0.779291i	$-0.715580\pi$
$607$	−1.13772e7	−1.25333	−0.626663	+	0.779291i	$0.715580\pi$
$608$	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	$-0.622799\pi$
$613$	−7.00161e6	−0.752570	−0.376285	+	0.926504i	$0.622799\pi$
$614$	0	0
$615$	−56700.0	−0.00604499
$616$	0	0
$617$	7.90300e6	0.835755	0.417878	−	0.908503i	$-0.362774\pi$
$617$	7.90300e6	0.835755	0.417878	+	0.908503i	$0.362774\pi$
$618$	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
$625$	390625.	0.0400000
$626$	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
$635$	7.49705e6	0.737830
$636$	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	$-0.576713\pi$
$643$	−5.00457e6	−0.477352	−0.238676	+	0.971099i	$0.576713\pi$
$644$	0	0
$645$	365100.	0.0345551
$646$	0	0
$647$	8.71928e6	0.818879	0.409440	−	0.912337i	$-0.365724\pi$
$647$	8.71928e6	0.818879	0.409440	+	0.912337i	$0.365724\pi$
$648$	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	$-0.523168\pi$
$653$	−1.58477e6	−0.145440	−0.0727201	+	0.997352i	$0.523168\pi$
$654$	0	0
$655$	196800.	0.0179235
$656$	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
$665$	−8.08300e6	−0.708791
$666$	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	$-0.342927\pi$
$673$	1.11313e7	0.947349	0.473675	+	0.880700i	$0.342927\pi$
$674$	0	0
$675$	1.68750e6	0.142556
$676$	0	0
$677$	−235518.	−0.0197493	−0.00987467	−	0.999951i	$-0.503143\pi$
$677$	−235518.	−0.0197493	−0.00987467	+	0.999951i	$0.503143\pi$
$678$	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	$-0.819903\pi$
$683$	−2.05830e7	−1.68833	−0.844164	+	0.536084i	$0.819903\pi$
$684$	0	0
$685$	4.10595e6	0.334339
$686$	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
$695$	−7.05250e6	−0.553836
$696$	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
$705$	−1.96830e6	−0.149148
$706$	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
$715$	5.30880e6	0.388357
$716$	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
$725$	3.69375e6	0.260989
$726$	0	0
$727$	4.36740e6	0.306469	0.153235	−	0.988190i	$-0.451031\pi$
$727$	4.36740e6	0.306469	0.153235	+	0.988190i	$0.451031\pi$
$728$	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	$-0.544527\pi$
$733$	−4.05645e6	−0.278860	−0.139430	+	0.990232i	$0.544527\pi$
$734$	0	0
$735$	−432450.	−0.0295269
$736$	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	$-0.565916\pi$
$743$	−6.18781e6	−0.411211	−0.205605	+	0.978635i	$0.565916\pi$
$744$	0	0
$745$	9.72375e6	0.641864
$746$	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
$755$	−2.44870e6	−0.156339
$756$	0	0
$757$	1.93494e7	1.22724	0.613618	−	0.789603i	$-0.289714\pi$
$757$	1.93494e7	1.22724	0.613618	+	0.789603i	$0.289714\pi$
$758$	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
$765$	3.94335e6	0.243619
$766$	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	$-0.462465\pi$
$773$	3.90895e6	0.235294	0.117647	+	0.993055i	$0.462465\pi$
$774$	0	0
$775$	4.29250e6	0.256718
$776$	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
$785$	92950.0	0.00538363
$786$	0	0
$787$	2.65082e7	1.52561	0.762806	−	0.646628i	$-0.223821\pi$
$787$	2.65082e7	1.52561	0.762806	+	0.646628i	$0.223821\pi$
$788$	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
$795$	−1.37610e6	−0.0772204
$796$	0	0
$797$	1.07940e7	0.601919	0.300960	−	0.953637i	$-0.402693\pi$
$797$	1.07940e7	0.601919	0.300960	+	0.953637i	$0.402693\pi$
$798$	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
$805$	4.61970e6	0.251260
$806$	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
$815$	−1.08085e6	−0.0569995
$816$	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	$-0.533626\pi$
$823$	−4.09773e6	−0.210884	−0.105442	+	0.994425i	$0.533626\pi$
$824$	0	0
$825$	720000.	0.0368297
$826$	0	0
$827$	1.70652e7	0.867654	0.433827	−	0.900996i	$-0.357163\pi$
$827$	1.70652e7	0.867654	0.433827	+	0.900996i	$0.357163\pi$
$828$	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
$835$	4.66305e6	0.231448
$836$	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
$845$	−2.12986e7	−1.02615
$846$	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	$-0.268394\pi$
$853$	2.82671e7	1.33017	0.665087	+	0.746765i	$0.268394\pi$
$854$	0	0
$855$	1.41795e7	0.663354
$856$	0	0
$857$	2.60870e7	1.21331	0.606655	−	0.794966i	$-0.292511\pi$
$857$	2.60870e7	1.21331	0.606655	+	0.794966i	$0.292511\pi$
$858$	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	$-0.670060\pi$
$863$	−2.22817e7	−1.01841	−0.509204	+	0.860646i	$0.670060\pi$
$864$	0	0
$865$	9.36135e6	0.425401
$866$	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
$875$	−1.84375e6	−0.0814108
$876$	0	0
$877$	−3.46748e7	−1.52235	−0.761177	−	0.648545i	$-0.775378\pi$
$877$	−3.46748e7	−1.52235	−0.761177	+	0.648545i	$0.775378\pi$
$878$	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	$-0.199650\pi$
$883$	3.75177e7	1.61933	0.809663	+	0.586895i	$0.199650\pi$
$884$	0	0
$885$	5.24700e6	0.225192
$886$	0	0
$887$	−4.07657e7	−1.73975	−0.869873	−	0.493275i	$-0.835800\pi$
$887$	−4.07657e7	−1.73975	−0.869873	+	0.493275i	$0.835800\pi$
$888$	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
$895$	6.80250e6	0.283864
$896$	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
$905$	1.88545e6	0.0765233
$906$	0	0
$907$	3.57116e7	1.44142	0.720712	−	0.693235i	$-0.243815\pi$
$907$	3.57116e7	1.44142	0.720712	+	0.693235i	$0.243815\pi$
$908$	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
$915$	−1.47570e6	−0.0582700
$916$	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
$925$	−3.44875e6	−0.132528
$926$	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
$935$	3.65760e6	0.136826
$936$	0	0
$937$	−2.19419e7	−0.816441	−0.408221	−	0.912883i	$-0.633851\pi$
$937$	−2.19419e7	−0.816441	−0.408221	+	0.912883i	$0.633851\pi$
$938$	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
$945$	−7.96500e6	−0.290139
$946$	0	0
$947$	−3.17199e7	−1.14936	−0.574681	−	0.818378i	$-0.694874\pi$
$947$	−3.17199e7	−1.14936	−0.574681	+	0.818378i	$0.694874\pi$
$948$	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	$-0.531858\pi$
$953$	−5.60285e6	−0.199838	−0.0999188	+	0.994996i	$0.531858\pi$
$954$	0	0
$955$	−8.92470e6	−0.316654
$956$	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
$965$	1.09674e7	0.379126
$966$	0	0
$967$	2.03532e7	0.699949	0.349975	−	0.936759i	$-0.386190\pi$
$967$	2.03532e7	0.699949	0.349975	+	0.936759i	$0.386190\pi$
$968$	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
$975$	−4.14750e6	−0.139725
$976$	0	0
$977$	−4.30412e7	−1.44261	−0.721303	−	0.692619i	$-0.756457\pi$
$977$	−4.30412e7	−1.44261	−0.721303	+	0.692619i	$0.756457\pi$
$978$	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	$-0.213207\pi$
$983$	4.75003e7	1.56788	0.783940	+	0.620837i	$0.213207\pi$
$984$	0	0
$985$	3.91995e6	0.128733
$986$	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
$995$	−4.06300e6	−0.130104
$996$	0	0
$997$	2.96332e7	0.944148	0.472074	−	0.881559i	$-0.343505\pi$
$997$	2.96332e7	0.944148	0.472074	+	0.881559i	$0.343505\pi$
$998$	0	0
$999$	−1.48986e7	−0.472315

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.a.c.1.1	✓	1	4.3	odd	2
50.6.a.b.1.1		1	20.19	odd	2
50.6.b.b.49.1		2	20.3	even	4
50.6.b.b.49.2		2	20.7	even	4
80.6.a.c.1.1		1	1.1	even	1	trivial
90.6.a.b.1.1		1	12.11	even	2
320.6.a.f.1.1		1	8.3	odd	2
320.6.a.k.1.1		1	8.5	even	2
400.6.a.i.1.1		1	5.4	even	2
400.6.c.i.49.1		2	5.3	odd	4
400.6.c.i.49.2		2	5.2	odd	4
450.6.a.u.1.1		1	60.59	even	2
450.6.c.f.199.1		2	60.47	odd	4
450.6.c.f.199.2		2	60.23	odd	4
490.6.a.k.1.1		1	28.27	even	2
720.6.a.v.1.1		1	3.2	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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