LMFDB - Embedded newform 1856.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1856,2,Mod(1,1856)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1856, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1856.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1856 = 2^{6} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1856.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:	$14.8202346151$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 928)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1856.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} +1.00000 q^{5} -2.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} +1.00000 q^{5} -2.00000 q^{9} +5.00000 q^{11} -1.00000 q^{13} -1.00000 q^{15} -6.00000 q^{17} -4.00000 q^{19} -6.00000 q^{23} -4.00000 q^{25} +5.00000 q^{27} +1.00000 q^{29} +9.00000 q^{31} -5.00000 q^{33} +1.00000 q^{39} -8.00000 q^{41} +1.00000 q^{43} -2.00000 q^{45} +9.00000 q^{47} -7.00000 q^{49} +6.00000 q^{51} +9.00000 q^{53} +5.00000 q^{55} +4.00000 q^{57} -14.0000 q^{59} -10.0000 q^{61} -1.00000 q^{65} +4.00000 q^{67} +6.00000 q^{69} -6.00000 q^{71} -4.00000 q^{73} +4.00000 q^{75} -17.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} -6.00000 q^{85} -1.00000 q^{87} -9.00000 q^{93} -4.00000 q^{95} -4.00000 q^{97} -10.0000 q^{99} +O(q^{100})$

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
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0	0
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	5.00000	0.962250
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	9.00000	1.61645	0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000	1.61645	0.808224	+	0.588875i	$0.200429\pi$
$32$	0	0
$33$	−5.00000	−0.870388
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	0	0
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	6.00000	0.840168
$52$	0	0
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	5.00000	0.674200
$56$	0	0
$57$	4.00000	0.529813
$58$	0	0
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.00000	−0.124035
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	0	0
$75$	4.00000	0.461880
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−17.0000	−1.91265	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−17.0000	−1.91265	−0.956325	+	0.292306i	$0.905577\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	0	0
$87$	−1.00000	−0.107211
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−9.00000	−0.933257
$94$	0	0
$95$	−4.00000	−0.410391
$96$	0	0
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	0	0
$99$	−10.0000	−1.00504
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	2.00000	0.197066	0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000	0.197066	0.0985329	+	0.995134i	$0.468585\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	8.00000	0.721336
$124$	0	0
$125$	−9.00000	−0.804984
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	0	0
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	5.00000	0.430331
$136$	0	0
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	−9.00000	−0.757937
$142$	0	0
$143$	−5.00000	−0.418121
$144$	0	0
$145$	1.00000	0.0830455
$146$	0	0
$147$	7.00000	0.577350
$148$	0	0
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	0	0
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	0	0
$153$	12.0000	0.970143
$154$	0	0
$155$	9.00000	0.722897
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	−9.00000	−0.713746
$160$	0	0
$161$	0	0
$162$	0	0
$163$	5.00000	0.391630	0.195815	−	0.980641i	$-0.437265\pi$
$163$	5.00000	0.391630	0.195815	+	0.980641i	$0.437265\pi$
$164$	0	0
$165$	−5.00000	−0.389249
$166$	0	0
$167$	10.0000	0.773823	0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000	0.773823	0.386912	+	0.922117i	$0.373542\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	8.00000	0.611775
$172$	0	0
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	14.0000	1.05230
$178$	0	0
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	0	0
$181$	−21.0000	−1.56092	−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000	−1.56092	−0.780459	+	0.625207i	$0.785014\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−30.0000	−2.19382
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	0	0
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	0	0
$195$	1.00000	0.0716115
$196$	0	0
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−8.00000	−0.558744
$206$	0	0
$207$	12.0000	0.834058
$208$	0	0
$209$	−20.0000	−1.38343
$210$	0	0
$211$	1.00000	0.0688428	0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000	0.0688428	0.0344214	+	0.999407i	$0.489041\pi$
$212$	0	0
$213$	6.00000	0.411113
$214$	0	0
$215$	1.00000	0.0681994
$216$	0	0
$217$	0	0
$218$	0	0
$219$	4.00000	0.270295
$220$	0	0
$221$	6.00000	0.403604
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	0	0
$227$	22.0000	1.46019	0.730096	−	0.683345i	$-0.239475\pi$
$227$	22.0000	1.46019	0.730096	+	0.683345i	$0.239475\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	15.0000	0.982683	0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000	0.982683	0.491341	+	0.870967i	$0.336507\pi$
$234$	0	0
$235$	9.00000	0.587095
$236$	0	0
$237$	17.0000	1.10427
$238$	0	0
$239$	22.0000	1.42306	0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000	1.42306	0.711531	+	0.702655i	$0.248002\pi$
$240$	0	0
$241$	1.00000	0.0644157	0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000	0.0644157	0.0322078	+	0.999481i	$0.489746\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	0	0
$245$	−7.00000	−0.447214
$246$	0	0
$247$	4.00000	0.254514
$248$	0	0
$249$	6.00000	0.380235
$250$	0	0
$251$	−13.0000	−0.820553	−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000	−0.820553	−0.410276	+	0.911961i	$0.634568\pi$
$252$	0	0
$253$	−30.0000	−1.88608
$254$	0	0
$255$	6.00000	0.375735
$256$	0	0
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−2.00000	−0.123797
$262$	0	0
$263$	5.00000	0.308313	0.154157	−	0.988046i	$-0.450734\pi$
$263$	5.00000	0.308313	0.154157	+	0.988046i	$0.450734\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	11.0000	0.668202	0.334101	−	0.942537i	$-0.391567\pi$
$271$	11.0000	0.668202	0.334101	+	0.942537i	$0.391567\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−20.0000	−1.20605
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	−18.0000	−1.07763
$280$	0	0
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	0	0
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	0	0
$285$	4.00000	0.236940
$286$	0	0
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	4.00000	0.234484
$292$	0	0
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	−14.0000	−0.815112
$296$	0	0
$297$	25.0000	1.45065
$298$	0	0
$299$	6.00000	0.346989
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	−10.0000	−0.572598
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	0	0
$309$	−2.00000	−0.113776
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	17.0000	0.960897	0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000	0.960897	0.480448	+	0.877023i	$0.340474\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	0	0
$321$	12.0000	0.669775
$322$	0	0
$323$	24.0000	1.33540
$324$	0	0
$325$	4.00000	0.221880
$326$	0	0
$327$	−1.00000	−0.0553001
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−7.00000	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	4.00000	0.218543
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	0	0
$339$	18.0000	0.977626
$340$	0	0
$341$	45.0000	2.43689
$342$	0	0
$343$	0	0
$344$	0	0
$345$	6.00000	0.323029
$346$	0	0
$347$	34.0000	1.82522	0.912608	−	0.408836i	$-0.134065\pi$
$347$	34.0000	1.82522	0.912608	+	0.408836i	$0.134065\pi$
$348$	0	0
$349$	25.0000	1.33822	0.669110	−	0.743164i	$-0.266676\pi$
$349$	25.0000	1.33822	0.669110	+	0.743164i	$0.266676\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	−6.00000	−0.318447
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−5.00000	−0.263890	−0.131945	−	0.991257i	$-0.542122\pi$
$359$	−5.00000	−0.263890	−0.131945	+	0.991257i	$0.542122\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	−14.0000	−0.734809
$364$	0	0
$365$	−4.00000	−0.209370
$366$	0	0
$367$	−12.0000	−0.626395	−0.313197	−	0.949688i	$-0.601400\pi$
$367$	−12.0000	−0.626395	−0.313197	+	0.949688i	$0.601400\pi$
$368$	0	0
$369$	16.0000	0.832927
$370$	0	0
$371$	0	0
$372$	0	0
$373$	7.00000	0.362446	0.181223	−	0.983442i	$-0.441994\pi$
$373$	7.00000	0.362446	0.181223	+	0.983442i	$0.441994\pi$
$374$	0	0
$375$	9.00000	0.464758
$376$	0	0
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	0	0
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−2.00000	−0.101666
$388$	0	0
$389$	32.0000	1.62246	0.811232	−	0.584724i	$-0.198797\pi$
$389$	32.0000	1.62246	0.811232	+	0.584724i	$0.198797\pi$
$390$	0	0
$391$	36.0000	1.82060
$392$	0	0
$393$	−4.00000	−0.201773
$394$	0	0
$395$	−17.0000	−0.855363
$396$	0	0
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	0	0
$403$	−9.00000	−0.448322
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	−8.00000	−0.394611
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−14.0000	−0.685583
$418$	0	0
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	0	0
$423$	−18.0000	−0.875190
$424$	0	0
$425$	24.0000	1.16417
$426$	0	0
$427$	0	0
$428$	0	0
$429$	5.00000	0.241402
$430$	0	0
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	0	0
$433$	−40.0000	−1.92228	−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000	−1.92228	−0.961139	+	0.276066i	$0.910969\pi$
$434$	0	0
$435$	−1.00000	−0.0479463
$436$	0	0
$437$	24.0000	1.14808
$438$	0	0
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	0	0
$441$	14.0000	0.666667
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	5.00000	0.236492
$448$	0	0
$449$	−26.0000	−1.22702	−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000	−1.22702	−0.613508	+	0.789689i	$0.710242\pi$
$450$	0	0
$451$	−40.0000	−1.88353
$452$	0	0
$453$	12.0000	0.563809
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	0	0
$459$	−30.0000	−1.40028
$460$	0	0
$461$	22.0000	1.02464	0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000	1.02464	0.512321	+	0.858794i	$0.328786\pi$
$462$	0	0
$463$	−14.0000	−0.650635	−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000	−0.650635	−0.325318	+	0.945605i	$0.605471\pi$
$464$	0	0
$465$	−9.00000	−0.417365
$466$	0	0
$467$	−15.0000	−0.694117	−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000	−0.694117	−0.347059	+	0.937843i	$0.612820\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	5.00000	0.229900
$474$	0	0
$475$	16.0000	0.734130
$476$	0	0
$477$	−18.0000	−0.824163
$478$	0	0
$479$	−33.0000	−1.50781	−0.753904	−	0.656984i	$-0.771832\pi$
$479$	−33.0000	−1.50781	−0.753904	+	0.656984i	$0.771832\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−4.00000	−0.181631
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	0	0
$489$	−5.00000	−0.226108
$490$	0	0
$491$	−29.0000	−1.30875	−0.654376	−	0.756169i	$-0.727069\pi$
$491$	−29.0000	−1.30875	−0.654376	+	0.756169i	$0.727069\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	0	0
$495$	−10.0000	−0.449467
$496$	0	0
$497$	0	0
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	0	0
$501$	−10.0000	−0.446767
$502$	0	0
$503$	−25.0000	−1.11469	−0.557347	−	0.830279i	$-0.688181\pi$
$503$	−25.0000	−1.11469	−0.557347	+	0.830279i	$0.688181\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	12.0000	0.532939
$508$	0	0
$509$	−3.00000	−0.132973	−0.0664863	−	0.997787i	$-0.521179\pi$
$509$	−3.00000	−0.132973	−0.0664863	+	0.997787i	$0.521179\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−20.0000	−0.883022
$514$	0	0
$515$	2.00000	0.0881305
$516$	0	0
$517$	45.0000	1.97910
$518$	0	0
$519$	14.0000	0.614532
$520$	0	0
$521$	39.0000	1.70862	0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000	1.70862	0.854311	+	0.519763i	$0.173980\pi$
$522$	0	0
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−54.0000	−2.35228
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	28.0000	1.21510
$532$	0	0
$533$	8.00000	0.346518
$534$	0	0
$535$	−12.0000	−0.518805
$536$	0	0
$537$	10.0000	0.431532
$538$	0	0
$539$	−35.0000	−1.50756
$540$	0	0
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	0	0
$543$	21.0000	0.901196
$544$	0	0
$545$	1.00000	0.0428353
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	0	0
$549$	20.0000	0.853579
$550$	0	0
$551$	−4.00000	−0.170406
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	0	0
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	30.0000	1.26660
$562$	0	0
$563$	−3.00000	−0.126435	−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000	−0.126435	−0.0632175	+	0.998000i	$0.520136\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	24.0000	1.00261
$574$	0	0
$575$	24.0000	1.00087
$576$	0	0
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	0	0
$579$	−12.0000	−0.498703
$580$	0	0
$581$	0	0
$582$	0	0
$583$	45.0000	1.86371
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	0	0
$589$	−36.0000	−1.48335
$590$	0	0
$591$	−22.0000	−0.904959
$592$	0	0
$593$	3.00000	0.123195	0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000	0.123195	0.0615976	+	0.998101i	$0.480380\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	20.0000	0.818546
$598$	0	0
$599$	23.0000	0.939755	0.469877	−	0.882732i	$-0.344298\pi$
$599$	23.0000	0.939755	0.469877	+	0.882732i	$0.344298\pi$
$600$	0	0
$601$	−4.00000	−0.163163	−0.0815817	−	0.996667i	$-0.525997\pi$
$601$	−4.00000	−0.163163	−0.0815817	+	0.996667i	$0.525997\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	0	0
$605$	14.0000	0.569181
$606$	0	0
$607$	23.0000	0.933541	0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000	0.933541	0.466771	+	0.884378i	$0.345417\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−9.00000	−0.364101
$612$	0	0
$613$	−31.0000	−1.25208	−0.626039	−	0.779792i	$-0.715325\pi$
$613$	−31.0000	−1.25208	−0.626039	+	0.779792i	$0.715325\pi$
$614$	0	0
$615$	8.00000	0.322591
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	0	0
$619$	−35.0000	−1.40677	−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000	−1.40677	−0.703384	+	0.710810i	$0.748329\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	0	0
$623$	0	0
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	20.0000	0.798723
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−14.0000	−0.557331	−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000	−0.557331	−0.278666	+	0.960388i	$0.589892\pi$
$632$	0	0
$633$	−1.00000	−0.0397464
$634$	0	0
$635$	16.0000	0.634941
$636$	0	0
$637$	7.00000	0.277350
$638$	0	0
$639$	12.0000	0.474713
$640$	0	0
$641$	38.0000	1.50091	0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000	1.50091	0.750455	+	0.660922i	$0.229834\pi$
$642$	0	0
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	0	0
$645$	−1.00000	−0.0393750
$646$	0	0
$647$	2.00000	0.0786281	0.0393141	−	0.999227i	$-0.487483\pi$
$647$	2.00000	0.0786281	0.0393141	+	0.999227i	$0.487483\pi$
$648$	0	0
$649$	−70.0000	−2.74774
$650$	0	0
$651$	0	0
$652$	0	0
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	0	0
$655$	4.00000	0.156293
$656$	0	0
$657$	8.00000	0.312110
$658$	0	0
$659$	3.00000	0.116863	0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000	0.116863	0.0584317	+	0.998291i	$0.481390\pi$
$660$	0	0
$661$	−26.0000	−1.01128	−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000	−1.01128	−0.505641	+	0.862744i	$0.668744\pi$
$662$	0	0
$663$	−6.00000	−0.233021
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.00000	−0.232321
$668$	0	0
$669$	2.00000	0.0773245
$670$	0	0
$671$	−50.0000	−1.93023
$672$	0	0
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	0	0
$675$	−20.0000	−0.769800
$676$	0	0
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−22.0000	−0.843042
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	0	0
$685$	8.00000	0.305664
$686$	0	0
$687$	16.0000	0.610438
$688$	0	0
$689$	−9.00000	−0.342873
$690$	0	0
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	14.0000	0.531050
$696$	0	0
$697$	48.0000	1.81813
$698$	0	0
$699$	−15.0000	−0.567352
$700$	0	0
$701$	23.0000	0.868698	0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000	0.868698	0.434349	+	0.900745i	$0.356978\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−9.00000	−0.338960
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−49.0000	−1.84023	−0.920117	−	0.391644i	$-0.871906\pi$
$709$	−49.0000	−1.84023	−0.920117	+	0.391644i	$0.871906\pi$
$710$	0	0
$711$	34.0000	1.27510
$712$	0	0
$713$	−54.0000	−2.02232
$714$	0	0
$715$	−5.00000	−0.186989
$716$	0	0
$717$	−22.0000	−0.821605
$718$	0	0
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−1.00000	−0.0371904
$724$	0	0
$725$	−4.00000	−0.148556
$726$	0	0
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−6.00000	−0.221918
$732$	0	0
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	0	0
$735$	7.00000	0.258199
$736$	0	0
$737$	20.0000	0.736709
$738$	0	0
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	0	0
$741$	−4.00000	−0.146944
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	−5.00000	−0.183186
$746$	0	0
$747$	12.0000	0.439057
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	0	0
$753$	13.0000	0.473746
$754$	0	0
$755$	−12.0000	−0.436725
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	0	0
$759$	30.0000	1.08893
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	12.0000	0.433861
$766$	0	0
$767$	14.0000	0.505511
$768$	0	0
$769$	22.0000	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$770$	0	0
$771$	3.00000	0.108042
$772$	0	0
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	0	0
$775$	−36.0000	−1.29316
$776$	0	0
$777$	0	0
$778$	0	0
$779$	32.0000	1.14652
$780$	0	0
$781$	−30.0000	−1.07348
$782$	0	0
$783$	5.00000	0.178685
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−38.0000	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$788$	0	0
$789$	−5.00000	−0.178005
$790$	0	0
$791$	0	0
$792$	0	0
$793$	10.0000	0.355110
$794$	0	0
$795$	−9.00000	−0.319197
$796$	0	0
$797$	−26.0000	−0.920967	−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000	−0.920967	−0.460484	+	0.887668i	$0.652324\pi$
$798$	0	0
$799$	−54.0000	−1.91038
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−20.0000	−0.705785
$804$	0	0
$805$	0	0
$806$	0	0
$807$	6.00000	0.211210
$808$	0	0
$809$	−44.0000	−1.54696	−0.773479	−	0.633822i	$-0.781485\pi$
$809$	−44.0000	−1.54696	−0.773479	+	0.633822i	$0.781485\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	−11.0000	−0.385787
$814$	0	0
$815$	5.00000	0.175142
$816$	0	0
$817$	−4.00000	−0.139942
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−33.0000	−1.15171	−0.575854	−	0.817553i	$-0.695330\pi$
$821$	−33.0000	−1.15171	−0.575854	+	0.817553i	$0.695330\pi$
$822$	0	0
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	0	0
$825$	20.0000	0.696311
$826$	0	0
$827$	33.0000	1.14752	0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000	1.14752	0.573761	+	0.819023i	$0.305484\pi$
$828$	0	0
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	0	0
$833$	42.0000	1.45521
$834$	0	0
$835$	10.0000	0.346064
$836$	0	0
$837$	45.0000	1.55543
$838$	0	0
$839$	−47.0000	−1.62262	−0.811310	−	0.584616i	$-0.801245\pi$
$839$	−47.0000	−1.62262	−0.811310	+	0.584616i	$0.801245\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−15.0000	−0.516627
$844$	0	0
$845$	−12.0000	−0.412813
$846$	0	0
$847$	0	0
$848$	0	0
$849$	6.00000	0.205919
$850$	0	0
$851$	0	0
$852$	0	0
$853$	50.0000	1.71197	0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000	1.71197	0.855984	+	0.517003i	$0.172952\pi$
$854$	0	0
$855$	8.00000	0.273594
$856$	0	0
$857$	17.0000	0.580709	0.290354	−	0.956919i	$-0.406227\pi$
$857$	17.0000	0.580709	0.290354	+	0.956919i	$0.406227\pi$
$858$	0	0
$859$	11.0000	0.375315	0.187658	−	0.982235i	$-0.439910\pi$
$859$	11.0000	0.375315	0.187658	+	0.982235i	$0.439910\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	46.0000	1.56586	0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000	1.56586	0.782929	+	0.622111i	$0.213725\pi$
$864$	0	0
$865$	−14.0000	−0.476014
$866$	0	0
$867$	−19.0000	−0.645274
$868$	0	0
$869$	−85.0000	−2.88343
$870$	0	0
$871$	−4.00000	−0.135535
$872$	0	0
$873$	8.00000	0.270759
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−39.0000	−1.31694	−0.658468	−	0.752609i	$-0.728795\pi$
$877$	−39.0000	−1.31694	−0.658468	+	0.752609i	$0.728795\pi$
$878$	0	0
$879$	−18.0000	−0.607125
$880$	0	0
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	0	0
$885$	14.0000	0.470605
$886$	0	0
$887$	33.0000	1.10803	0.554016	−	0.832506i	$-0.313095\pi$
$887$	33.0000	1.10803	0.554016	+	0.832506i	$0.313095\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	5.00000	0.167506
$892$	0	0
$893$	−36.0000	−1.20469
$894$	0	0
$895$	−10.0000	−0.334263
$896$	0	0
$897$	−6.00000	−0.200334
$898$	0	0
$899$	9.00000	0.300167
$900$	0	0
$901$	−54.0000	−1.79900
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−21.0000	−0.698064
$906$	0	0
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	0	0
$913$	−30.0000	−0.992855
$914$	0	0
$915$	10.0000	0.330590
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−6.00000	−0.197922	−0.0989609	−	0.995091i	$-0.531552\pi$
$919$	−6.00000	−0.197922	−0.0989609	+	0.995091i	$0.531552\pi$
$920$	0	0
$921$	11.0000	0.362462
$922$	0	0
$923$	6.00000	0.197492
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−4.00000	−0.131377
$928$	0	0
$929$	−38.0000	−1.24674	−0.623370	−	0.781927i	$-0.714237\pi$
$929$	−38.0000	−1.24674	−0.623370	+	0.781927i	$0.714237\pi$
$930$	0	0
$931$	28.0000	0.917663
$932$	0	0
$933$	−24.0000	−0.785725
$934$	0	0
$935$	−30.0000	−0.981105
$936$	0	0
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	−17.0000	−0.554774
$940$	0	0
$941$	−47.0000	−1.53216	−0.766078	−	0.642747i	$-0.777794\pi$
$941$	−47.0000	−1.53216	−0.766078	+	0.642747i	$0.777794\pi$
$942$	0	0
$943$	48.0000	1.56310
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−7.00000	−0.227469	−0.113735	−	0.993511i	$-0.536281\pi$
$947$	−7.00000	−0.227469	−0.113735	+	0.993511i	$0.536281\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	0	0
$951$	−18.0000	−0.583690
$952$	0	0
$953$	27.0000	0.874616	0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000	0.874616	0.437308	+	0.899312i	$0.355932\pi$
$954$	0	0
$955$	−24.0000	−0.776622
$956$	0	0
$957$	−5.00000	−0.161627
$958$	0	0
$959$	0	0
$960$	0	0
$961$	50.0000	1.61290
$962$	0	0
$963$	24.0000	0.773389
$964$	0	0
$965$	12.0000	0.386294
$966$	0	0
$967$	−39.0000	−1.25416	−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000	−1.25416	−0.627078	+	0.778957i	$0.715749\pi$
$968$	0	0
$969$	−24.0000	−0.770991
$970$	0	0
$971$	52.0000	1.66876	0.834380	−	0.551190i	$-0.185826\pi$
$971$	52.0000	1.66876	0.834380	+	0.551190i	$0.185826\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−4.00000	−0.128103
$976$	0	0
$977$	−7.00000	−0.223950	−0.111975	−	0.993711i	$-0.535718\pi$
$977$	−7.00000	−0.223950	−0.111975	+	0.993711i	$0.535718\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	0	0
$983$	5.00000	0.159475	0.0797376	−	0.996816i	$-0.474592\pi$
$983$	5.00000	0.159475	0.0797376	+	0.996816i	$0.474592\pi$
$984$	0	0
$985$	22.0000	0.700978
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	54.0000	1.71537	0.857683	−	0.514178i	$-0.171903\pi$
$991$	54.0000	1.71537	0.857683	+	0.514178i	$0.171903\pi$
$992$	0	0
$993$	7.00000	0.222138
$994$	0	0
$995$	−20.0000	−0.634043
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1856.2.a.g.1.1		1
4.3	odd	2		1856.2.a.l.1.1		1
8.3	odd	2		928.2.a.a.1.1	✓	1
8.5	even	2		928.2.a.b.1.1	yes	1
24.5	odd	2		8352.2.a.h.1.1		1
24.11	even	2		8352.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
928.2.a.a.1.1	✓	1	8.3	odd	2
928.2.a.b.1.1	yes	1	8.5	even	2
1856.2.a.g.1.1		1	1.1	even	1	trivial
1856.2.a.l.1.1		1	4.3	odd	2
8352.2.a.g.1.1		1	24.11	even	2
8352.2.a.h.1.1		1	24.5	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:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1856.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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