LMFDB - Embedded newform 1600.4.a.bp.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,4,Mod(1,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1600.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1600.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:	$94.4030560092$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 800)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1600.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{3} +10.0000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+5.00000 q^{3} +10.0000 q^{7} -2.00000 q^{9} -15.0000 q^{11} +8.00000 q^{13} +21.0000 q^{17} +105.000 q^{19} +50.0000 q^{21} +10.0000 q^{23} -145.000 q^{27} +20.0000 q^{29} +230.000 q^{31} -75.0000 q^{33} -54.0000 q^{37} +40.0000 q^{39} -195.000 q^{41} -300.000 q^{43} +480.000 q^{47} -243.000 q^{49} +105.000 q^{51} +322.000 q^{53} +525.000 q^{57} +560.000 q^{59} +730.000 q^{61} -20.0000 q^{63} +255.000 q^{67} +50.0000 q^{69} +40.0000 q^{71} -317.000 q^{73} -150.000 q^{77} +830.000 q^{79} -671.000 q^{81} +75.0000 q^{83} +100.000 q^{87} -705.000 q^{89} +80.0000 q^{91} +1150.00 q^{93} +1434.00 q^{97} +30.0000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	10.0000	0.539949	0.269975	−	0.962867i	$-0.412985\pi$
$7$	10.0000	0.539949	0.269975	+	0.962867i	$0.412985\pi$
$8$	0	0
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	−15.0000	−0.411152	−0.205576	−	0.978641i	$-0.565907\pi$
$11$	−15.0000	−0.411152	−0.205576	+	0.978641i	$0.565907\pi$
$12$	0	0
$13$	8.00000	0.170677	0.0853385	−	0.996352i	$-0.472803\pi$
$13$	8.00000	0.170677	0.0853385	+	0.996352i	$0.472803\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	21.0000	0.299603	0.149801	−	0.988716i	$-0.452137\pi$
$17$	21.0000	0.299603	0.149801	+	0.988716i	$0.452137\pi$
$18$	0	0
$19$	105.000	1.26782	0.633912	−	0.773405i	$-0.281448\pi$
$19$	105.000	1.26782	0.633912	+	0.773405i	$0.281448\pi$
$20$	0	0
$21$	50.0000	0.519566
$22$	0	0
$23$	10.0000	0.0906584	0.0453292	−	0.998972i	$-0.485566\pi$
$23$	10.0000	0.0906584	0.0453292	+	0.998972i	$0.485566\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−145.000	−1.03353
$28$	0	0
$29$	20.0000	0.128066	0.0640329	−	0.997948i	$-0.479604\pi$
$29$	20.0000	0.128066	0.0640329	+	0.997948i	$0.479604\pi$
$30$	0	0
$31$	230.000	1.33256	0.666278	−	0.745704i	$-0.267887\pi$
$31$	230.000	1.33256	0.666278	+	0.745704i	$0.267887\pi$
$32$	0	0
$33$	−75.0000	−0.395631
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−54.0000	−0.239934	−0.119967	−	0.992778i	$-0.538279\pi$
$37$	−54.0000	−0.239934	−0.119967	+	0.992778i	$0.538279\pi$
$38$	0	0
$39$	40.0000	0.164234
$40$	0	0
$41$	−195.000	−0.742778	−0.371389	−	0.928477i	$-0.621118\pi$
$41$	−195.000	−0.742778	−0.371389	+	0.928477i	$0.621118\pi$
$42$	0	0
$43$	−300.000	−1.06394	−0.531972	−	0.846762i	$-0.678549\pi$
$43$	−300.000	−1.06394	−0.531972	+	0.846762i	$0.678549\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	480.000	1.48969	0.744843	−	0.667240i	$-0.232525\pi$
$47$	480.000	1.48969	0.744843	+	0.667240i	$0.232525\pi$
$48$	0	0
$49$	−243.000	−0.708455
$50$	0	0
$51$	105.000	0.288293
$52$	0	0
$53$	322.000	0.834530	0.417265	−	0.908785i	$-0.362989\pi$
$53$	322.000	0.834530	0.417265	+	0.908785i	$0.362989\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	525.000	1.21996
$58$	0	0
$59$	560.000	1.23569	0.617846	−	0.786299i	$-0.288006\pi$
$59$	560.000	1.23569	0.617846	+	0.786299i	$0.288006\pi$
$60$	0	0
$61$	730.000	1.53224	0.766122	−	0.642695i	$-0.222184\pi$
$61$	730.000	1.53224	0.766122	+	0.642695i	$0.222184\pi$
$62$	0	0
$63$	−20.0000	−0.0399962
$64$	0	0
$65$	0	0
$66$	0	0
$67$	255.000	0.464973	0.232487	−	0.972600i	$-0.425314\pi$
$67$	255.000	0.464973	0.232487	+	0.972600i	$0.425314\pi$
$68$	0	0
$69$	50.0000	0.0872361
$70$	0	0
$71$	40.0000	0.0668609	0.0334305	−	0.999441i	$-0.489357\pi$
$71$	40.0000	0.0668609	0.0334305	+	0.999441i	$0.489357\pi$
$72$	0	0
$73$	−317.000	−0.508247	−0.254124	−	0.967172i	$-0.581787\pi$
$73$	−317.000	−0.508247	−0.254124	+	0.967172i	$0.581787\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−150.000	−0.222001
$78$	0	0
$79$	830.000	1.18205	0.591027	−	0.806652i	$-0.298723\pi$
$79$	830.000	1.18205	0.591027	+	0.806652i	$0.298723\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	0	0
$83$	75.0000	0.0991846	0.0495923	−	0.998770i	$-0.484208\pi$
$83$	75.0000	0.0991846	0.0495923	+	0.998770i	$0.484208\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	100.000	0.123231
$88$	0	0
$89$	−705.000	−0.839661	−0.419831	−	0.907602i	$-0.637911\pi$
$89$	−705.000	−0.839661	−0.419831	+	0.907602i	$0.637911\pi$
$90$	0	0
$91$	80.0000	0.0921569
$92$	0	0
$93$	1150.00	1.28225
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1434.00	1.50104	0.750519	−	0.660849i	$-0.229804\pi$
$97$	1434.00	1.50104	0.750519	+	0.660849i	$0.229804\pi$
$98$	0	0
$99$	30.0000	0.0304557
$100$	0	0
$101$	1902.00	1.87382	0.936911	−	0.349567i	$-0.113671\pi$
$101$	1902.00	1.87382	0.936911	+	0.349567i	$0.113671\pi$
$102$	0	0
$103$	−1480.00	−1.41581	−0.707906	−	0.706306i	$-0.750360\pi$
$103$	−1480.00	−1.41581	−0.707906	+	0.706306i	$0.750360\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1945.00	1.75729	0.878646	−	0.477474i	$-0.158447\pi$
$107$	1945.00	1.75729	0.878646	+	0.477474i	$0.158447\pi$
$108$	0	0
$109$	246.000	0.216170	0.108085	−	0.994142i	$-0.465528\pi$
$109$	246.000	0.216170	0.108085	+	0.994142i	$0.465528\pi$
$110$	0	0
$111$	−270.000	−0.230876
$112$	0	0
$113$	−753.000	−0.626870	−0.313435	−	0.949610i	$-0.601480\pi$
$113$	−753.000	−0.626870	−0.313435	+	0.949610i	$0.601480\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−16.0000	−0.0126427
$118$	0	0
$119$	210.000	0.161770
$120$	0	0
$121$	−1106.00	−0.830954
$122$	0	0
$123$	−975.000	−0.714738
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−1490.00	−1.04107	−0.520536	−	0.853840i	$-0.674268\pi$
$127$	−1490.00	−1.04107	−0.520536	+	0.853840i	$0.674268\pi$
$128$	0	0
$129$	−1500.00	−1.02378
$130$	0	0
$131$	780.000	0.520221	0.260110	−	0.965579i	$-0.416241\pi$
$131$	780.000	0.520221	0.260110	+	0.965579i	$0.416241\pi$
$132$	0	0
$133$	1050.00	0.684561
$134$	0	0
$135$	0	0
$136$	0	0
$137$	2749.00	1.71433	0.857164	−	0.515044i	$-0.172224\pi$
$137$	2749.00	1.71433	0.857164	+	0.515044i	$0.172224\pi$
$138$	0	0
$139$	−735.000	−0.448503	−0.224251	−	0.974531i	$-0.571994\pi$
$139$	−735.000	−0.448503	−0.224251	+	0.974531i	$0.571994\pi$
$140$	0	0
$141$	2400.00	1.43345
$142$	0	0
$143$	−120.000	−0.0701742
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−1215.00	−0.681711
$148$	0	0
$149$	−836.000	−0.459650	−0.229825	−	0.973232i	$-0.573815\pi$
$149$	−836.000	−0.459650	−0.229825	+	0.973232i	$0.573815\pi$
$150$	0	0
$151$	−1790.00	−0.964690	−0.482345	−	0.875981i	$-0.660215\pi$
$151$	−1790.00	−0.964690	−0.482345	+	0.875981i	$0.660215\pi$
$152$	0	0
$153$	−42.0000	−0.0221928
$154$	0	0
$155$	0	0
$156$	0	0
$157$	1374.00	0.698453	0.349227	−	0.937038i	$-0.386444\pi$
$157$	1374.00	0.698453	0.349227	+	0.937038i	$0.386444\pi$
$158$	0	0
$159$	1610.00	0.803027
$160$	0	0
$161$	100.000	0.0489510
$162$	0	0
$163$	1895.00	0.910600	0.455300	−	0.890338i	$-0.349532\pi$
$163$	1895.00	0.910600	0.455300	+	0.890338i	$0.349532\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	720.000	0.333624	0.166812	−	0.985989i	$-0.446653\pi$
$167$	720.000	0.333624	0.166812	+	0.985989i	$0.446653\pi$
$168$	0	0
$169$	−2133.00	−0.970869
$170$	0	0
$171$	−210.000	−0.0939129
$172$	0	0
$173$	2512.00	1.10395	0.551976	−	0.833860i	$-0.313874\pi$
$173$	2512.00	1.10395	0.551976	+	0.833860i	$0.313874\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	2800.00	1.18904
$178$	0	0
$179$	165.000	0.0688976	0.0344488	−	0.999406i	$-0.489032\pi$
$179$	165.000	0.0688976	0.0344488	+	0.999406i	$0.489032\pi$
$180$	0	0
$181$	3158.00	1.29686	0.648432	−	0.761273i	$-0.275425\pi$
$181$	3158.00	1.29686	0.648432	+	0.761273i	$0.275425\pi$
$182$	0	0
$183$	3650.00	1.47440
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−315.000	−0.123182
$188$	0	0
$189$	−1450.00	−0.558053
$190$	0	0
$191$	3290.00	1.24637	0.623183	−	0.782076i	$-0.285839\pi$
$191$	3290.00	1.24637	0.623183	+	0.782076i	$0.285839\pi$
$192$	0	0
$193$	197.000	0.0734734	0.0367367	−	0.999325i	$-0.488304\pi$
$193$	197.000	0.0734734	0.0367367	+	0.999325i	$0.488304\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	1746.00	0.631459	0.315729	−	0.948849i	$-0.397751\pi$
$197$	1746.00	0.631459	0.315729	+	0.948849i	$0.397751\pi$
$198$	0	0
$199$	−4660.00	−1.65999	−0.829997	−	0.557768i	$-0.811658\pi$
$199$	−4660.00	−1.65999	−0.829997	+	0.557768i	$0.811658\pi$
$200$	0	0
$201$	1275.00	0.447421
$202$	0	0
$203$	200.000	0.0691490
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−20.0000	−0.00671544
$208$	0	0
$209$	−1575.00	−0.521268
$210$	0	0
$211$	−265.000	−0.0864614	−0.0432307	−	0.999065i	$-0.513765\pi$
$211$	−265.000	−0.0864614	−0.0432307	+	0.999065i	$0.513765\pi$
$212$	0	0
$213$	200.000	0.0643370
$214$	0	0
$215$	0	0
$216$	0	0
$217$	2300.00	0.719512
$218$	0	0
$219$	−1585.00	−0.489061
$220$	0	0
$221$	168.000	0.0511353
$222$	0	0
$223$	1060.00	0.318309	0.159154	−	0.987254i	$-0.449123\pi$
$223$	1060.00	0.318309	0.159154	+	0.987254i	$0.449123\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−4660.00	−1.36253	−0.681267	−	0.732035i	$-0.738571\pi$
$227$	−4660.00	−1.36253	−0.681267	+	0.732035i	$0.738571\pi$
$228$	0	0
$229$	−1660.00	−0.479021	−0.239511	−	0.970894i	$-0.576987\pi$
$229$	−1660.00	−0.479021	−0.239511	+	0.970894i	$0.576987\pi$
$230$	0	0
$231$	−750.000	−0.213621
$232$	0	0
$233$	3462.00	0.973404	0.486702	−	0.873568i	$-0.338200\pi$
$233$	3462.00	0.973404	0.486702	+	0.873568i	$0.338200\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	4150.00	1.13743
$238$	0	0
$239$	−4020.00	−1.08800	−0.544000	−	0.839085i	$-0.683091\pi$
$239$	−4020.00	−1.08800	−0.544000	+	0.839085i	$0.683091\pi$
$240$	0	0
$241$	3985.00	1.06513	0.532565	−	0.846389i	$-0.321228\pi$
$241$	3985.00	1.06513	0.532565	+	0.846389i	$0.321228\pi$
$242$	0	0
$243$	560.000	0.147835
$244$	0	0
$245$	0	0
$246$	0	0
$247$	840.000	0.216388
$248$	0	0
$249$	375.000	0.0954404
$250$	0	0
$251$	−6625.00	−1.66600	−0.833001	−	0.553272i	$-0.813379\pi$
$251$	−6625.00	−1.66600	−0.833001	+	0.553272i	$0.813379\pi$
$252$	0	0
$253$	−150.000	−0.0372744
$254$	0	0
$255$	0	0
$256$	0	0
$257$	2246.00	0.545143	0.272571	−	0.962136i	$-0.412126\pi$
$257$	2246.00	0.545143	0.272571	+	0.962136i	$0.412126\pi$
$258$	0	0
$259$	−540.000	−0.129552
$260$	0	0
$261$	−40.0000	−0.00948635
$262$	0	0
$263$	−3950.00	−0.926112	−0.463056	−	0.886329i	$-0.653247\pi$
$263$	−3950.00	−0.926112	−0.463056	+	0.886329i	$0.653247\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−3525.00	−0.807964
$268$	0	0
$269$	−2656.00	−0.602004	−0.301002	−	0.953623i	$-0.597321\pi$
$269$	−2656.00	−0.602004	−0.301002	+	0.953623i	$0.597321\pi$
$270$	0	0
$271$	3110.00	0.697118	0.348559	−	0.937287i	$-0.386671\pi$
$271$	3110.00	0.697118	0.348559	+	0.937287i	$0.386671\pi$
$272$	0	0
$273$	400.000	0.0886780
$274$	0	0
$275$	0	0
$276$	0	0
$277$	6884.00	1.49321	0.746606	−	0.665267i	$-0.231682\pi$
$277$	6884.00	1.49321	0.746606	+	0.665267i	$0.231682\pi$
$278$	0	0
$279$	−460.000	−0.0987078
$280$	0	0
$281$	4630.00	0.982928	0.491464	−	0.870898i	$-0.336462\pi$
$281$	4630.00	0.982928	0.491464	+	0.870898i	$0.336462\pi$
$282$	0	0
$283$	215.000	0.0451605	0.0225803	−	0.999745i	$-0.492812\pi$
$283$	215.000	0.0451605	0.0225803	+	0.999745i	$0.492812\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−1950.00	−0.401062
$288$	0	0
$289$	−4472.00	−0.910238
$290$	0	0
$291$	7170.00	1.44437
$292$	0	0
$293$	−1602.00	−0.319419	−0.159710	−	0.987164i	$-0.551056\pi$
$293$	−1602.00	−0.319419	−0.159710	+	0.987164i	$0.551056\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	2175.00	0.424937
$298$	0	0
$299$	80.0000	0.0154733
$300$	0	0
$301$	−3000.00	−0.574475
$302$	0	0
$303$	9510.00	1.80309
$304$	0	0
$305$	0	0
$306$	0	0
$307$	1885.00	0.350432	0.175216	−	0.984530i	$-0.443938\pi$
$307$	1885.00	0.350432	0.175216	+	0.984530i	$0.443938\pi$
$308$	0	0
$309$	−7400.00	−1.36237
$310$	0	0
$311$	−9250.00	−1.68656	−0.843279	−	0.537476i	$-0.819378\pi$
$311$	−9250.00	−1.68656	−0.843279	+	0.537476i	$0.819378\pi$
$312$	0	0
$313$	8162.00	1.47394	0.736970	−	0.675925i	$-0.236256\pi$
$313$	8162.00	1.47394	0.736970	+	0.675925i	$0.236256\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	6924.00	1.22678	0.613392	−	0.789779i	$-0.289805\pi$
$317$	6924.00	1.22678	0.613392	+	0.789779i	$0.289805\pi$
$318$	0	0
$319$	−300.000	−0.0526545
$320$	0	0
$321$	9725.00	1.69096
$322$	0	0
$323$	2205.00	0.379844
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1230.00	0.208010
$328$	0	0
$329$	4800.00	0.804354
$330$	0	0
$331$	−8075.00	−1.34091	−0.670456	−	0.741949i	$-0.733902\pi$
$331$	−8075.00	−1.34091	−0.670456	+	0.741949i	$0.733902\pi$
$332$	0	0
$333$	108.000	0.0177729
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−4741.00	−0.766346	−0.383173	−	0.923677i	$-0.625169\pi$
$337$	−4741.00	−0.766346	−0.383173	+	0.923677i	$0.625169\pi$
$338$	0	0
$339$	−3765.00	−0.603206
$340$	0	0
$341$	−3450.00	−0.547883
$342$	0	0
$343$	−5860.00	−0.922479
$344$	0	0
$345$	0	0
$346$	0	0
$347$	8705.00	1.34671	0.673356	−	0.739319i	$-0.264852\pi$
$347$	8705.00	1.34671	0.673356	+	0.739319i	$0.264852\pi$
$348$	0	0
$349$	1470.00	0.225465	0.112733	−	0.993625i	$-0.464040\pi$
$349$	1470.00	0.225465	0.112733	+	0.993625i	$0.464040\pi$
$350$	0	0
$351$	−1160.00	−0.176399
$352$	0	0
$353$	1998.00	0.301254	0.150627	−	0.988591i	$-0.451871\pi$
$353$	1998.00	0.301254	0.150627	+	0.988591i	$0.451871\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	1050.00	0.155664
$358$	0	0
$359$	8190.00	1.20404	0.602022	−	0.798480i	$-0.294362\pi$
$359$	8190.00	1.20404	0.602022	+	0.798480i	$0.294362\pi$
$360$	0	0
$361$	4166.00	0.607377
$362$	0	0
$363$	−5530.00	−0.799586
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−5340.00	−0.759525	−0.379763	−	0.925084i	$-0.623994\pi$
$367$	−5340.00	−0.759525	−0.379763	+	0.925084i	$0.623994\pi$
$368$	0	0
$369$	390.000	0.0550206
$370$	0	0
$371$	3220.00	0.450604
$372$	0	0
$373$	−9378.00	−1.30181	−0.650904	−	0.759160i	$-0.725610\pi$
$373$	−9378.00	−1.30181	−0.650904	+	0.759160i	$0.725610\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	160.000	0.0218579
$378$	0	0
$379$	−4045.00	−0.548226	−0.274113	−	0.961697i	$-0.588384\pi$
$379$	−4045.00	−0.548226	−0.274113	+	0.961697i	$0.588384\pi$
$380$	0	0
$381$	−7450.00	−1.00177
$382$	0	0
$383$	−8090.00	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$383$	−8090.00	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	600.000	0.0788106
$388$	0	0
$389$	−6574.00	−0.856851	−0.428425	−	0.903577i	$-0.640932\pi$
$389$	−6574.00	−0.856851	−0.428425	+	0.903577i	$0.640932\pi$
$390$	0	0
$391$	210.000	0.0271615
$392$	0	0
$393$	3900.00	0.500583
$394$	0	0
$395$	0	0
$396$	0	0
$397$	7036.00	0.889488	0.444744	−	0.895658i	$-0.353295\pi$
$397$	7036.00	0.889488	0.444744	+	0.895658i	$0.353295\pi$
$398$	0	0
$399$	5250.00	0.658719
$400$	0	0
$401$	8277.00	1.03076	0.515379	−	0.856963i	$-0.327651\pi$
$401$	8277.00	1.03076	0.515379	+	0.856963i	$0.327651\pi$
$402$	0	0
$403$	1840.00	0.227437
$404$	0	0
$405$	0	0
$406$	0	0
$407$	810.000	0.0986492
$408$	0	0
$409$	−2179.00	−0.263434	−0.131717	−	0.991287i	$-0.542049\pi$
$409$	−2179.00	−0.263434	−0.131717	+	0.991287i	$0.542049\pi$
$410$	0	0
$411$	13745.0	1.64961
$412$	0	0
$413$	5600.00	0.667211
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−3675.00	−0.431572
$418$	0	0
$419$	12245.0	1.42770	0.713851	−	0.700297i	$-0.246949\pi$
$419$	12245.0	1.42770	0.713851	+	0.700297i	$0.246949\pi$
$420$	0	0
$421$	660.000	0.0764048	0.0382024	−	0.999270i	$-0.487837\pi$
$421$	660.000	0.0764048	0.0382024	+	0.999270i	$0.487837\pi$
$422$	0	0
$423$	−960.000	−0.110347
$424$	0	0
$425$	0	0
$426$	0	0
$427$	7300.00	0.827334
$428$	0	0
$429$	−600.000	−0.0675251
$430$	0	0
$431$	7470.00	0.834843	0.417421	−	0.908713i	$-0.362934\pi$
$431$	7470.00	0.834843	0.417421	+	0.908713i	$0.362934\pi$
$432$	0	0
$433$	1173.00	0.130187	0.0650933	−	0.997879i	$-0.479266\pi$
$433$	1173.00	0.130187	0.0650933	+	0.997879i	$0.479266\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1050.00	0.114939
$438$	0	0
$439$	−5660.00	−0.615346	−0.307673	−	0.951492i	$-0.599550\pi$
$439$	−5660.00	−0.615346	−0.307673	+	0.951492i	$0.599550\pi$
$440$	0	0
$441$	486.000	0.0524781
$442$	0	0
$443$	1115.00	0.119583	0.0597915	−	0.998211i	$-0.480956\pi$
$443$	1115.00	0.119583	0.0597915	+	0.998211i	$0.480956\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−4180.00	−0.442298
$448$	0	0
$449$	4089.00	0.429781	0.214891	−	0.976638i	$-0.431060\pi$
$449$	4089.00	0.429781	0.214891	+	0.976638i	$0.431060\pi$
$450$	0	0
$451$	2925.00	0.305394
$452$	0	0
$453$	−8950.00	−0.928273
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−4519.00	−0.462560	−0.231280	−	0.972887i	$-0.574291\pi$
$457$	−4519.00	−0.462560	−0.231280	+	0.972887i	$0.574291\pi$
$458$	0	0
$459$	−3045.00	−0.309648
$460$	0	0
$461$	−10068.0	−1.01717	−0.508583	−	0.861013i	$-0.669830\pi$
$461$	−10068.0	−1.01717	−0.508583	+	0.861013i	$0.669830\pi$
$462$	0	0
$463$	−1460.00	−0.146548	−0.0732742	−	0.997312i	$-0.523345\pi$
$463$	−1460.00	−0.146548	−0.0732742	+	0.997312i	$0.523345\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	4740.00	0.469681	0.234841	−	0.972034i	$-0.424543\pi$
$467$	4740.00	0.469681	0.234841	+	0.972034i	$0.424543\pi$
$468$	0	0
$469$	2550.00	0.251062
$470$	0	0
$471$	6870.00	0.672087
$472$	0	0
$473$	4500.00	0.437442
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−644.000	−0.0618171
$478$	0	0
$479$	8610.00	0.821296	0.410648	−	0.911794i	$-0.365302\pi$
$479$	8610.00	0.821296	0.410648	+	0.911794i	$0.365302\pi$
$480$	0	0
$481$	−432.000	−0.0409512
$482$	0	0
$483$	500.000	0.0471031
$484$	0	0
$485$	0	0
$486$	0	0
$487$	17710.0	1.64788	0.823939	−	0.566678i	$-0.191772\pi$
$487$	17710.0	1.64788	0.823939	+	0.566678i	$0.191772\pi$
$488$	0	0
$489$	9475.00	0.876226
$490$	0	0
$491$	−8660.00	−0.795968	−0.397984	−	0.917392i	$-0.630290\pi$
$491$	−8660.00	−0.795968	−0.397984	+	0.917392i	$0.630290\pi$
$492$	0	0
$493$	420.000	0.0383689
$494$	0	0
$495$	0	0
$496$	0	0
$497$	400.000	0.0361015
$498$	0	0
$499$	17300.0	1.55201	0.776006	−	0.630725i	$-0.217242\pi$
$499$	17300.0	1.55201	0.776006	+	0.630725i	$0.217242\pi$
$500$	0	0
$501$	3600.00	0.321030
$502$	0	0
$503$	−1860.00	−0.164877	−0.0824387	−	0.996596i	$-0.526271\pi$
$503$	−1860.00	−0.164877	−0.0824387	+	0.996596i	$0.526271\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−10665.0	−0.934219
$508$	0	0
$509$	5870.00	0.511165	0.255583	−	0.966787i	$-0.417733\pi$
$509$	5870.00	0.511165	0.255583	+	0.966787i	$0.417733\pi$
$510$	0	0
$511$	−3170.00	−0.274428
$512$	0	0
$513$	−15225.0	−1.31033
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−7200.00	−0.612487
$518$	0	0
$519$	12560.0	1.06228
$520$	0	0
$521$	−12187.0	−1.02480	−0.512401	−	0.858746i	$-0.671244\pi$
$521$	−12187.0	−1.02480	−0.512401	+	0.858746i	$0.671244\pi$
$522$	0	0
$523$	−5315.00	−0.444376	−0.222188	−	0.975004i	$-0.571320\pi$
$523$	−5315.00	−0.444376	−0.222188	+	0.975004i	$0.571320\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	4830.00	0.399237
$528$	0	0
$529$	−12067.0	−0.991781
$530$	0	0
$531$	−1120.00	−0.0915327
$532$	0	0
$533$	−1560.00	−0.126775
$534$	0	0
$535$	0	0
$536$	0	0
$537$	825.000	0.0662968
$538$	0	0
$539$	3645.00	0.291282
$540$	0	0
$541$	1672.00	0.132874	0.0664371	−	0.997791i	$-0.478837\pi$
$541$	1672.00	0.132874	0.0664371	+	0.997791i	$0.478837\pi$
$542$	0	0
$543$	15790.0	1.24791
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−10595.0	−0.828171	−0.414085	−	0.910238i	$-0.635899\pi$
$547$	−10595.0	−0.828171	−0.414085	+	0.910238i	$0.635899\pi$
$548$	0	0
$549$	−1460.00	−0.113500
$550$	0	0
$551$	2100.00	0.162365
$552$	0	0
$553$	8300.00	0.638249
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−15264.0	−1.16114	−0.580571	−	0.814209i	$-0.697171\pi$
$557$	−15264.0	−1.16114	−0.580571	+	0.814209i	$0.697171\pi$
$558$	0	0
$559$	−2400.00	−0.181591
$560$	0	0
$561$	−1575.00	−0.118532
$562$	0	0
$563$	−15400.0	−1.15281	−0.576406	−	0.817164i	$-0.695545\pi$
$563$	−15400.0	−1.15281	−0.576406	+	0.817164i	$0.695545\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−6710.00	−0.496990
$568$	0	0
$569$	14569.0	1.07340	0.536700	−	0.843773i	$-0.319671\pi$
$569$	14569.0	1.07340	0.536700	+	0.843773i	$0.319671\pi$
$570$	0	0
$571$	−7780.00	−0.570198	−0.285099	−	0.958498i	$-0.592026\pi$
$571$	−7780.00	−0.570198	−0.285099	+	0.958498i	$0.592026\pi$
$572$	0	0
$573$	16450.0	1.19932
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−19829.0	−1.43066	−0.715331	−	0.698786i	$-0.753724\pi$
$577$	−19829.0	−1.43066	−0.715331	+	0.698786i	$0.753724\pi$
$578$	0	0
$579$	985.000	0.0706998
$580$	0	0
$581$	750.000	0.0535546
$582$	0	0
$583$	−4830.00	−0.343119
$584$	0	0
$585$	0	0
$586$	0	0
$587$	795.000	0.0558998	0.0279499	−	0.999609i	$-0.491102\pi$
$587$	795.000	0.0558998	0.0279499	+	0.999609i	$0.491102\pi$
$588$	0	0
$589$	24150.0	1.68945
$590$	0	0
$591$	8730.00	0.607621
$592$	0	0
$593$	−21457.0	−1.48589	−0.742946	−	0.669352i	$-0.766572\pi$
$593$	−21457.0	−1.48589	−0.742946	+	0.669352i	$0.766572\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−23300.0	−1.59733
$598$	0	0
$599$	−26570.0	−1.81239	−0.906194	−	0.422862i	$-0.861026\pi$
$599$	−26570.0	−1.81239	−0.906194	+	0.422862i	$0.861026\pi$
$600$	0	0
$601$	−25245.0	−1.71342	−0.856710	−	0.515799i	$-0.827495\pi$
$601$	−25245.0	−1.71342	−0.856710	+	0.515799i	$0.827495\pi$
$602$	0	0
$603$	−510.000	−0.0344425
$604$	0	0
$605$	0	0
$606$	0	0
$607$	14040.0	0.938824	0.469412	−	0.882979i	$-0.344466\pi$
$607$	14040.0	0.938824	0.469412	+	0.882979i	$0.344466\pi$
$608$	0	0
$609$	1000.00	0.0665387
$610$	0	0
$611$	3840.00	0.254255
$612$	0	0
$613$	−19502.0	−1.28496	−0.642478	−	0.766304i	$-0.722094\pi$
$613$	−19502.0	−1.28496	−0.642478	+	0.766304i	$0.722094\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	6286.00	0.410154	0.205077	−	0.978746i	$-0.434256\pi$
$617$	6286.00	0.410154	0.205077	+	0.978746i	$0.434256\pi$
$618$	0	0
$619$	2420.00	0.157137	0.0785687	−	0.996909i	$-0.474965\pi$
$619$	2420.00	0.157137	0.0785687	+	0.996909i	$0.474965\pi$
$620$	0	0
$621$	−1450.00	−0.0936981
$622$	0	0
$623$	−7050.00	−0.453374
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−7875.00	−0.501590
$628$	0	0
$629$	−1134.00	−0.0718848
$630$	0	0
$631$	−2290.00	−0.144475	−0.0722373	−	0.997387i	$-0.523014\pi$
$631$	−2290.00	−0.144475	−0.0722373	+	0.997387i	$0.523014\pi$
$632$	0	0
$633$	−1325.00	−0.0831975
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−1944.00	−0.120917
$638$	0	0
$639$	−80.0000	−0.00495266
$640$	0	0
$641$	−15150.0	−0.933524	−0.466762	−	0.884383i	$-0.654580\pi$
$641$	−15150.0	−0.933524	−0.466762	+	0.884383i	$0.654580\pi$
$642$	0	0
$643$	7860.00	0.482066	0.241033	−	0.970517i	$-0.422514\pi$
$643$	7860.00	0.482066	0.241033	+	0.970517i	$0.422514\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	2420.00	0.147048	0.0735240	−	0.997293i	$-0.476575\pi$
$647$	2420.00	0.147048	0.0735240	+	0.997293i	$0.476575\pi$
$648$	0	0
$649$	−8400.00	−0.508057
$650$	0	0
$651$	11500.0	0.692351
$652$	0	0
$653$	20462.0	1.22625	0.613124	−	0.789987i	$-0.289913\pi$
$653$	20462.0	1.22625	0.613124	+	0.789987i	$0.289913\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	634.000	0.0376479
$658$	0	0
$659$	−32205.0	−1.90369	−0.951843	−	0.306587i	$-0.900813\pi$
$659$	−32205.0	−1.90369	−0.951843	+	0.306587i	$0.900813\pi$
$660$	0	0
$661$	27100.0	1.59466	0.797328	−	0.603546i	$-0.206246\pi$
$661$	27100.0	1.59466	0.797328	+	0.603546i	$0.206246\pi$
$662$	0	0
$663$	840.000	0.0492050
$664$	0	0
$665$	0	0
$666$	0	0
$667$	200.000	0.0116102
$668$	0	0
$669$	5300.00	0.306293
$670$	0	0
$671$	−10950.0	−0.629985
$672$	0	0
$673$	−24182.0	−1.38506	−0.692532	−	0.721387i	$-0.743505\pi$
$673$	−24182.0	−1.38506	−0.692532	+	0.721387i	$0.743505\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−25704.0	−1.45921	−0.729605	−	0.683869i	$-0.760296\pi$
$677$	−25704.0	−1.45921	−0.729605	+	0.683869i	$0.760296\pi$
$678$	0	0
$679$	14340.0	0.810484
$680$	0	0
$681$	−23300.0	−1.31110
$682$	0	0
$683$	6525.00	0.365552	0.182776	−	0.983155i	$-0.441492\pi$
$683$	6525.00	0.365552	0.182776	+	0.983155i	$0.441492\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−8300.00	−0.460939
$688$	0	0
$689$	2576.00	0.142435
$690$	0	0
$691$	−28955.0	−1.59407	−0.797033	−	0.603935i	$-0.793599\pi$
$691$	−28955.0	−1.59407	−0.797033	+	0.603935i	$0.793599\pi$
$692$	0	0
$693$	300.000	0.0164445
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−4095.00	−0.222538
$698$	0	0
$699$	17310.0	0.936659
$700$	0	0
$701$	−9720.00	−0.523708	−0.261854	−	0.965107i	$-0.584334\pi$
$701$	−9720.00	−0.523708	−0.261854	+	0.965107i	$0.584334\pi$
$702$	0	0
$703$	−5670.00	−0.304194
$704$	0	0
$705$	0	0
$706$	0	0
$707$	19020.0	1.01177
$708$	0	0
$709$	25140.0	1.33167	0.665834	−	0.746100i	$-0.268076\pi$
$709$	25140.0	1.33167	0.665834	+	0.746100i	$0.268076\pi$
$710$	0	0
$711$	−1660.00	−0.0875596
$712$	0	0
$713$	2300.00	0.120807
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−20100.0	−1.04693
$718$	0	0
$719$	−30030.0	−1.55762	−0.778811	−	0.627259i	$-0.784177\pi$
$719$	−30030.0	−1.55762	−0.778811	+	0.627259i	$0.784177\pi$
$720$	0	0
$721$	−14800.0	−0.764467
$722$	0	0
$723$	19925.0	1.02492
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−36100.0	−1.84164	−0.920822	−	0.389984i	$-0.872481\pi$
$727$	−36100.0	−1.84164	−0.920822	+	0.389984i	$0.872481\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	0	0
$731$	−6300.00	−0.318760
$732$	0	0
$733$	−5368.00	−0.270493	−0.135247	−	0.990812i	$-0.543183\pi$
$733$	−5368.00	−0.270493	−0.135247	+	0.990812i	$0.543183\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3825.00	−0.191175
$738$	0	0
$739$	−25540.0	−1.27132	−0.635659	−	0.771970i	$-0.719272\pi$
$739$	−25540.0	−1.27132	−0.635659	+	0.771970i	$0.719272\pi$
$740$	0	0
$741$	4200.00	0.208220
$742$	0	0
$743$	18730.0	0.924814	0.462407	−	0.886668i	$-0.346986\pi$
$743$	18730.0	0.924814	0.462407	+	0.886668i	$0.346986\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−150.000	−0.00734701
$748$	0	0
$749$	19450.0	0.948849
$750$	0	0
$751$	−29940.0	−1.45476	−0.727381	−	0.686234i	$-0.759263\pi$
$751$	−29940.0	−1.45476	−0.727381	+	0.686234i	$0.759263\pi$
$752$	0	0
$753$	−33125.0	−1.60311
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−16216.0	−0.778574	−0.389287	−	0.921117i	$-0.627279\pi$
$757$	−16216.0	−0.778574	−0.389287	+	0.921117i	$0.627279\pi$
$758$	0	0
$759$	−750.000	−0.0358673
$760$	0	0
$761$	−25843.0	−1.23102	−0.615511	−	0.788128i	$-0.711050\pi$
$761$	−25843.0	−1.23102	−0.615511	+	0.788128i	$0.711050\pi$
$762$	0	0
$763$	2460.00	0.116721
$764$	0	0
$765$	0	0
$766$	0	0
$767$	4480.00	0.210904
$768$	0	0
$769$	−27475.0	−1.28839	−0.644196	−	0.764860i	$-0.722808\pi$
$769$	−27475.0	−1.28839	−0.644196	+	0.764860i	$0.722808\pi$
$770$	0	0
$771$	11230.0	0.524564
$772$	0	0
$773$	3948.00	0.183699	0.0918497	−	0.995773i	$-0.470722\pi$
$773$	3948.00	0.183699	0.0918497	+	0.995773i	$0.470722\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−2700.00	−0.124661
$778$	0	0
$779$	−20475.0	−0.941711
$780$	0	0
$781$	−600.000	−0.0274900
$782$	0	0
$783$	−2900.00	−0.132360
$784$	0	0
$785$	0	0
$786$	0	0
$787$	22100.0	1.00099	0.500496	−	0.865739i	$-0.333151\pi$
$787$	22100.0	1.00099	0.500496	+	0.865739i	$0.333151\pi$
$788$	0	0
$789$	−19750.0	−0.891152
$790$	0	0
$791$	−7530.00	−0.338478
$792$	0	0
$793$	5840.00	0.261519
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−16026.0	−0.712259	−0.356129	−	0.934437i	$-0.615904\pi$
$797$	−16026.0	−0.712259	−0.356129	+	0.934437i	$0.615904\pi$
$798$	0	0
$799$	10080.0	0.446314
$800$	0	0
$801$	1410.00	0.0621971
$802$	0	0
$803$	4755.00	0.208967
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−13280.0	−0.579279
$808$	0	0
$809$	35770.0	1.55452	0.777260	−	0.629180i	$-0.216609\pi$
$809$	35770.0	1.55452	0.777260	+	0.629180i	$0.216609\pi$
$810$	0	0
$811$	30620.0	1.32579	0.662894	−	0.748714i	$-0.269328\pi$
$811$	30620.0	1.32579	0.662894	+	0.748714i	$0.269328\pi$
$812$	0	0
$813$	15550.0	0.670802
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−31500.0	−1.34889
$818$	0	0
$819$	−160.000	−0.00682644
$820$	0	0
$821$	9150.00	0.388961	0.194481	−	0.980906i	$-0.437698\pi$
$821$	9150.00	0.388961	0.194481	+	0.980906i	$0.437698\pi$
$822$	0	0
$823$	28940.0	1.22574	0.612871	−	0.790183i	$-0.290015\pi$
$823$	28940.0	1.22574	0.612871	+	0.790183i	$0.290015\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−25765.0	−1.08336	−0.541679	−	0.840586i	$-0.682211\pi$
$827$	−25765.0	−1.08336	−0.541679	+	0.840586i	$0.682211\pi$
$828$	0	0
$829$	41584.0	1.74219	0.871093	−	0.491118i	$-0.163412\pi$
$829$	41584.0	1.74219	0.871093	+	0.491118i	$0.163412\pi$
$830$	0	0
$831$	34420.0	1.43684
$832$	0	0
$833$	−5103.00	−0.212255
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−33350.0	−1.37723
$838$	0	0
$839$	20320.0	0.836143	0.418072	−	0.908414i	$-0.362706\pi$
$839$	20320.0	0.836143	0.418072	+	0.908414i	$0.362706\pi$
$840$	0	0
$841$	−23989.0	−0.983599
$842$	0	0
$843$	23150.0	0.945822
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−11060.0	−0.448673
$848$	0	0
$849$	1075.00	0.0434557
$850$	0	0
$851$	−540.000	−0.0217520
$852$	0	0
$853$	−38882.0	−1.56072	−0.780360	−	0.625330i	$-0.784964\pi$
$853$	−38882.0	−1.56072	−0.780360	+	0.625330i	$0.784964\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	15269.0	0.608610	0.304305	−	0.952575i	$-0.401576\pi$
$857$	15269.0	0.608610	0.304305	+	0.952575i	$0.401576\pi$
$858$	0	0
$859$	−19375.0	−0.769577	−0.384788	−	0.923005i	$-0.625726\pi$
$859$	−19375.0	−0.769577	−0.384788	+	0.923005i	$0.625726\pi$
$860$	0	0
$861$	−9750.00	−0.385922
$862$	0	0
$863$	−22900.0	−0.903274	−0.451637	−	0.892202i	$-0.649160\pi$
$863$	−22900.0	−0.903274	−0.451637	+	0.892202i	$0.649160\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−22360.0	−0.875877
$868$	0	0
$869$	−12450.0	−0.486004
$870$	0	0
$871$	2040.00	0.0793602
$872$	0	0
$873$	−2868.00	−0.111188
$874$	0	0
$875$	0	0
$876$	0	0
$877$	23444.0	0.902677	0.451338	−	0.892353i	$-0.350947\pi$
$877$	23444.0	0.902677	0.451338	+	0.892353i	$0.350947\pi$
$878$	0	0
$879$	−8010.00	−0.307361
$880$	0	0
$881$	3750.00	0.143406	0.0717030	−	0.997426i	$-0.477157\pi$
$881$	3750.00	0.143406	0.0717030	+	0.997426i	$0.477157\pi$
$882$	0	0
$883$	−37595.0	−1.43281	−0.716406	−	0.697684i	$-0.754214\pi$
$883$	−37595.0	−1.43281	−0.716406	+	0.697684i	$0.754214\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−11420.0	−0.432295	−0.216148	−	0.976361i	$-0.569349\pi$
$887$	−11420.0	−0.432295	−0.216148	+	0.976361i	$0.569349\pi$
$888$	0	0
$889$	−14900.0	−0.562126
$890$	0	0
$891$	10065.0	0.378440
$892$	0	0
$893$	50400.0	1.88866
$894$	0	0
$895$	0	0
$896$	0	0
$897$	400.000	0.0148892
$898$	0	0
$899$	4600.00	0.170655
$900$	0	0
$901$	6762.00	0.250028
$902$	0	0
$903$	−15000.0	−0.552789
$904$	0	0
$905$	0	0
$906$	0	0
$907$	2620.00	0.0959158	0.0479579	−	0.998849i	$-0.484729\pi$
$907$	2620.00	0.0959158	0.0479579	+	0.998849i	$0.484729\pi$
$908$	0	0
$909$	−3804.00	−0.138802
$910$	0	0
$911$	−46500.0	−1.69112	−0.845562	−	0.533877i	$-0.820734\pi$
$911$	−46500.0	−1.69112	−0.845562	+	0.533877i	$0.820734\pi$
$912$	0	0
$913$	−1125.00	−0.0407799
$914$	0	0
$915$	0	0
$916$	0	0
$917$	7800.00	0.280893
$918$	0	0
$919$	−45190.0	−1.62207	−0.811034	−	0.584999i	$-0.801095\pi$
$919$	−45190.0	−1.62207	−0.811034	+	0.584999i	$0.801095\pi$
$920$	0	0
$921$	9425.00	0.337203
$922$	0	0
$923$	320.000	0.0114116
$924$	0	0
$925$	0	0
$926$	0	0
$927$	2960.00	0.104875
$928$	0	0
$929$	15166.0	0.535609	0.267804	−	0.963473i	$-0.413702\pi$
$929$	15166.0	0.535609	0.267804	+	0.963473i	$0.413702\pi$
$930$	0	0
$931$	−25515.0	−0.898196
$932$	0	0
$933$	−46250.0	−1.62289
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−23789.0	−0.829405	−0.414703	−	0.909957i	$-0.636114\pi$
$937$	−23789.0	−0.829405	−0.414703	+	0.909957i	$0.636114\pi$
$938$	0	0
$939$	40810.0	1.41830
$940$	0	0
$941$	−47472.0	−1.64457	−0.822286	−	0.569074i	$-0.807302\pi$
$941$	−47472.0	−1.64457	−0.822286	+	0.569074i	$0.807302\pi$
$942$	0	0
$943$	−1950.00	−0.0673391
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−19760.0	−0.678050	−0.339025	−	0.940777i	$-0.610097\pi$
$947$	−19760.0	−0.678050	−0.339025	+	0.940777i	$0.610097\pi$
$948$	0	0
$949$	−2536.00	−0.0867461
$950$	0	0
$951$	34620.0	1.18047
$952$	0	0
$953$	36337.0	1.23512	0.617561	−	0.786523i	$-0.288121\pi$
$953$	36337.0	1.23512	0.617561	+	0.786523i	$0.288121\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−1500.00	−0.0506668
$958$	0	0
$959$	27490.0	0.925650
$960$	0	0
$961$	23109.0	0.775704
$962$	0	0
$963$	−3890.00	−0.130170
$964$	0	0
$965$	0	0
$966$	0	0
$967$	33880.0	1.12669	0.563344	−	0.826222i	$-0.309515\pi$
$967$	33880.0	1.12669	0.563344	+	0.826222i	$0.309515\pi$
$968$	0	0
$969$	11025.0	0.365505
$970$	0	0
$971$	−17175.0	−0.567633	−0.283817	−	0.958879i	$-0.591601\pi$
$971$	−17175.0	−0.567633	−0.283817	+	0.958879i	$0.591601\pi$
$972$	0	0
$973$	−7350.00	−0.242169
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−13311.0	−0.435882	−0.217941	−	0.975962i	$-0.569934\pi$
$977$	−13311.0	−0.435882	−0.217941	+	0.975962i	$0.569934\pi$
$978$	0	0
$979$	10575.0	0.345228
$980$	0	0
$981$	−492.000	−0.0160126
$982$	0	0
$983$	53110.0	1.72324	0.861621	−	0.507553i	$-0.169450\pi$
$983$	53110.0	1.72324	0.861621	+	0.507553i	$0.169450\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	24000.0	0.773990
$988$	0	0
$989$	−3000.00	−0.0964555
$990$	0	0
$991$	8990.00	0.288170	0.144085	−	0.989565i	$-0.453976\pi$
$991$	8990.00	0.288170	0.144085	+	0.989565i	$0.453976\pi$
$992$	0	0
$993$	−40375.0	−1.29029
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−1236.00	−0.0392623	−0.0196311	−	0.999807i	$-0.506249\pi$
$997$	−1236.00	−0.0392623	−0.0196311	+	0.999807i	$0.506249\pi$
$998$	0	0
$999$	7830.00	0.247978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.4.a.bp.1.1		1
4.3	odd	2		1600.4.a.l.1.1		1
5.4	even	2		1600.4.a.k.1.1		1
8.3	odd	2		800.4.a.i.1.1	yes	1
8.5	even	2		800.4.a.c.1.1	yes	1
20.19	odd	2		1600.4.a.bq.1.1		1
40.3	even	4		800.4.c.c.449.2		2
40.13	odd	4		800.4.c.d.449.1		2
40.19	odd	2		800.4.a.b.1.1	✓	1
40.27	even	4		800.4.c.c.449.1		2
40.29	even	2		800.4.a.j.1.1	yes	1
40.37	odd	4		800.4.c.d.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.4.a.b.1.1	✓	1	40.19	odd	2
800.4.a.c.1.1	yes	1	8.5	even	2
800.4.a.i.1.1	yes	1	8.3	odd	2
800.4.a.j.1.1	yes	1	40.29	even	2
800.4.c.c.449.1		2	40.27	even	4
800.4.c.c.449.2		2	40.3	even	4
800.4.c.d.449.1		2	40.13	odd	4
800.4.c.d.449.2		2	40.37	odd	4
1600.4.a.k.1.1		1	5.4	even	2
1600.4.a.l.1.1		1	4.3	odd	2
1600.4.a.bp.1.1		1	1.1	even	1	trivial
1600.4.a.bq.1.1		1	20.19	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1600.a (trivial)

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