LMFDB - Embedded newform 975.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} -1.00000 q^{11} -2.00000 q^{12} -1.00000 q^{13} +4.00000 q^{16} -1.00000 q^{17} -4.00000 q^{19} -1.00000 q^{21} -3.00000 q^{23} +1.00000 q^{27} +2.00000 q^{28} -8.00000 q^{29} -4.00000 q^{31} -1.00000 q^{33} -2.00000 q^{36} +3.00000 q^{37} -1.00000 q^{39} -9.00000 q^{41} -8.00000 q^{43} +2.00000 q^{44} +10.0000 q^{47} +4.00000 q^{48} -6.00000 q^{49} -1.00000 q^{51} +2.00000 q^{52} -1.00000 q^{53} -4.00000 q^{57} +4.00000 q^{59} -11.0000 q^{61} -1.00000 q^{63} -8.00000 q^{64} -4.00000 q^{67} +2.00000 q^{68} -3.00000 q^{69} -1.00000 q^{71} +14.0000 q^{73} +8.00000 q^{76} +1.00000 q^{77} +1.00000 q^{79} +1.00000 q^{81} +6.00000 q^{83} +2.00000 q^{84} -8.00000 q^{87} -15.0000 q^{89} +1.00000 q^{91} +6.00000 q^{92} -4.00000 q^{93} -15.0000 q^{97} -1.00000 q^{99} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−2.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−2.00000	−0.577350
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	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
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	0	0
$33$	−1.00000	−0.174078
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	0	0
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	4.00000	0.577350
$49$	−6.00000	−0.857143
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	0	0
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	2.00000	0.242536
$69$	−3.00000	−0.361158
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	0	0
$75$	0	0
$76$	8.00000	0.917663
$77$	1.00000	0.113961
$78$	0	0
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	0	0
$87$	−8.00000	−0.857690
$88$	0	0
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	6.00000	0.625543
$93$	−4.00000	−0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−15.0000	−1.52302	−0.761510	−	0.648154i	$-0.775541\pi$
$97$	−15.0000	−1.52302	−0.761510	+	0.648154i	$0.775541\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	17.0000	1.64345	0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000	1.64345	0.821726	+	0.569883i	$0.193011\pi$
$108$	−2.00000	−0.192450
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	−4.00000	−0.377964
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	0	0
$116$	16.0000	1.48556
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	1.00000	0.0916698
$120$	0	0
$121$	−10.0000	−0.909091
$122$	0	0
$123$	−9.00000	−0.811503
$124$	8.00000	0.718421
$125$	0	0
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	0	0
$129$	−8.00000	−0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	2.00000	0.174078
$133$	4.00000	0.346844
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	19.0000	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$139$	19.0000	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	0	0
$143$	1.00000	0.0836242
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	−6.00000	−0.494872
$148$	−6.00000	−0.493197
$149$	9.00000	0.737309	0.368654	−	0.929567i	$-0.379819\pi$
$149$	9.00000	0.737309	0.368654	+	0.929567i	$0.379819\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	0	0
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	−20.0000	−1.59617	−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000	−1.59617	−0.798087	+	0.602542i	$0.794154\pi$
$158$	0	0
$159$	−1.00000	−0.0793052
$160$	0	0
$161$	3.00000	0.236433
$162$	0	0
$163$	−17.0000	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$164$	18.0000	1.40556
$165$	0	0
$166$	0	0
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−4.00000	−0.305888
$172$	16.0000	1.21999
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	0	0
$175$	0	0
$176$	−4.00000	−0.301511
$177$	4.00000	0.300658
$178$	0	0
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−3.00000	−0.222988	−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000	−0.222988	−0.111494	+	0.993765i	$0.535564\pi$
$182$	0	0
$183$	−11.0000	−0.813143
$184$	0	0
$185$	0	0
$186$	0	0
$187$	1.00000	0.0731272
$188$	−20.0000	−1.45865
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	−8.00000	−0.577350
$193$	−9.00000	−0.647834	−0.323917	−	0.946085i	$-0.605000\pi$
$193$	−9.00000	−0.647834	−0.323917	+	0.946085i	$0.605000\pi$
$194$	0	0
$195$	0	0
$196$	12.0000	0.857143
$197$	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
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	0	0
$203$	8.00000	0.561490
$204$	2.00000	0.140028
$205$	0	0
$206$	0	0
$207$	−3.00000	−0.208514
$208$	−4.00000	−0.277350
$209$	4.00000	0.276686
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.00000	0.137361
$213$	−1.00000	−0.0685189
$214$	0	0
$215$	0	0
$216$	0	0
$217$	4.00000	0.271538
$218$	0	0
$219$	14.0000	0.946032
$220$	0	0
$221$	1.00000	0.0672673
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	8.00000	0.529813
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	1.00000	0.0657952
$232$	0	0
$233$	13.0000	0.851658	0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000	0.851658	0.425829	+	0.904804i	$0.359982\pi$
$234$	0	0
$235$	0	0
$236$	−8.00000	−0.520756
$237$	1.00000	0.0649570
$238$	0	0
$239$	27.0000	1.74648	0.873242	−	0.487286i	$-0.162013\pi$
$239$	27.0000	1.74648	0.873242	+	0.487286i	$0.162013\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	22.0000	1.40841
$245$	0	0
$246$	0	0
$247$	4.00000	0.254514
$248$	0	0
$249$	6.00000	0.380235
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	2.00000	0.125988
$253$	3.00000	0.188608
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−3.00000	−0.186411
$260$	0	0
$261$	−8.00000	−0.495188
$262$	0	0
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−15.0000	−0.917985
$268$	8.00000	0.488678
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−4.00000	−0.242536
$273$	1.00000	0.0605228
$274$	0	0
$275$	0	0
$276$	6.00000	0.361158
$277$	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
$279$	−4.00000	−0.239474
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	0	0
$287$	9.00000	0.531253
$288$	0	0
$289$	−16.0000	−0.941176
$290$	0	0
$291$	−15.0000	−0.879316
$292$	−28.0000	−1.63858
$293$	−4.00000	−0.233682	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000	−0.233682	−0.116841	+	0.993151i	$0.537277\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1.00000	−0.0580259
$298$	0	0
$299$	3.00000	0.173494
$300$	0	0
$301$	8.00000	0.461112
$302$	0	0
$303$	10.0000	0.574485
$304$	−16.0000	−0.917663
$305$	0	0
$306$	0	0
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	−2.00000	−0.113961
$309$	−6.00000	−0.341328
$310$	0	0
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	0	0
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	0	0
$315$	0	0
$316$	−2.00000	−0.112509
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	8.00000	0.447914
$320$	0	0
$321$	17.0000	0.948847
$322$	0	0
$323$	4.00000	0.222566
$324$	−2.00000	−0.111111
$325$	0	0
$326$	0	0
$327$	12.0000	0.663602
$328$	0	0
$329$	−10.0000	−0.551318
$330$	0	0
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−12.0000	−0.658586
$333$	3.00000	0.164399
$334$	0	0
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−28.0000	−1.52526	−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000	−1.52526	−0.762629	+	0.646837i	$0.776092\pi$
$338$	0	0
$339$	18.0000	0.977626
$340$	0	0
$341$	4.00000	0.216612
$342$	0	0
$343$	13.0000	0.701934
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−27.0000	−1.44944	−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000	−1.44944	−0.724718	+	0.689046i	$0.758030\pi$
$348$	16.0000	0.857690
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	0	0
$355$	0	0
$356$	30.0000	1.59000
$357$	1.00000	0.0529256
$358$	0	0
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	−10.0000	−0.524864
$364$	−2.00000	−0.104828
$365$	0	0
$366$	0	0
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	−12.0000	−0.625543
$369$	−9.00000	−0.468521
$370$	0	0
$371$	1.00000	0.0519174
$372$	8.00000	0.414781
$373$	−34.0000	−1.76045	−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000	−1.76045	−0.880227	+	0.474554i	$0.842610\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	8.00000	0.412021
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	−6.00000	−0.307389
$382$	0	0
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.00000	−0.406663
$388$	30.0000	1.52302
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	0	0
$391$	3.00000	0.151717
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	2.00000	0.100504
$397$	39.0000	1.95735	0.978677	−	0.205406i	$-0.0658513\pi$
$397$	39.0000	1.95735	0.978677	+	0.205406i	$0.0658513\pi$
$398$	0	0
$399$	4.00000	0.200250
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	−20.0000	−0.995037
$405$	0	0
$406$	0	0
$407$	−3.00000	−0.148704
$408$	0	0
$409$	−8.00000	−0.395575	−0.197787	−	0.980245i	$-0.563376\pi$
$409$	−8.00000	−0.395575	−0.197787	+	0.980245i	$0.563376\pi$
$410$	0	0
$411$	−2.00000	−0.0986527
$412$	12.0000	0.591198
$413$	−4.00000	−0.196827
$414$	0	0
$415$	0	0
$416$	0	0
$417$	19.0000	0.930434
$418$	0	0
$419$	28.0000	1.36789	0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000	1.36789	0.683945	+	0.729534i	$0.260263\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	0	0
$423$	10.0000	0.486217
$424$	0	0
$425$	0	0
$426$	0	0
$427$	11.0000	0.532327
$428$	−34.0000	−1.64345
$429$	1.00000	0.0482805
$430$	0	0
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	4.00000	0.192450
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	0	0
$435$	0	0
$436$	−24.0000	−1.14939
$437$	12.0000	0.574038
$438$	0	0
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	0	0
$443$	−23.0000	−1.09276	−0.546381	−	0.837536i	$-0.683995\pi$
$443$	−23.0000	−1.09276	−0.546381	+	0.837536i	$0.683995\pi$
$444$	−6.00000	−0.284747
$445$	0	0
$446$	0	0
$447$	9.00000	0.425685
$448$	8.00000	0.377964
$449$	−21.0000	−0.991051	−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000	−0.991051	−0.495526	+	0.868593i	$0.665025\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	−36.0000	−1.69330
$453$	2.00000	0.0939682
$454$	0	0
$455$	0	0
$456$	0	0
$457$	17.0000	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$458$	0	0
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−25.0000	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$461$	−25.0000	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$462$	0	0
$463$	−21.0000	−0.975953	−0.487976	−	0.872857i	$-0.662265\pi$
$463$	−21.0000	−0.975953	−0.487976	+	0.872857i	$0.662265\pi$
$464$	−32.0000	−1.48556
$465$	0	0
$466$	0	0
$467$	−35.0000	−1.61961	−0.809803	−	0.586701i	$-0.800426\pi$
$467$	−35.0000	−1.61961	−0.809803	+	0.586701i	$0.800426\pi$
$468$	2.00000	0.0924500
$469$	4.00000	0.184703
$470$	0	0
$471$	−20.0000	−0.921551
$472$	0	0
$473$	8.00000	0.367840
$474$	0	0
$475$	0	0
$476$	−2.00000	−0.0916698
$477$	−1.00000	−0.0457869
$478$	0	0
$479$	−27.0000	−1.23366	−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000	−1.23366	−0.616831	+	0.787096i	$0.711584\pi$
$480$	0	0
$481$	−3.00000	−0.136788
$482$	0	0
$483$	3.00000	0.136505
$484$	20.0000	0.909091
$485$	0	0
$486$	0	0
$487$	−35.0000	−1.58600	−0.793001	−	0.609221i	$-0.791482\pi$
$487$	−35.0000	−1.58600	−0.793001	+	0.609221i	$0.791482\pi$
$488$	0	0
$489$	−17.0000	−0.768767
$490$	0	0
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	18.0000	0.811503
$493$	8.00000	0.360302
$494$	0	0
$495$	0	0
$496$	−16.0000	−0.718421
$497$	1.00000	0.0448561
$498$	0	0
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	0	0
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	1.00000	0.0444116
$508$	12.0000	0.532414
$509$	−19.0000	−0.842160	−0.421080	−	0.907023i	$-0.638349\pi$
$509$	−19.0000	−0.842160	−0.421080	+	0.907023i	$0.638349\pi$
$510$	0	0
$511$	−14.0000	−0.619324
$512$	0	0
$513$	−4.00000	−0.176604
$514$	0	0
$515$	0	0
$516$	16.0000	0.704361
$517$	−10.0000	−0.439799
$518$	0	0
$519$	2.00000	0.0877903
$520$	0	0
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	0	0
$523$	10.0000	0.437269	0.218635	−	0.975807i	$-0.429840\pi$
$523$	10.0000	0.437269	0.218635	+	0.975807i	$0.429840\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	4.00000	0.174243
$528$	−4.00000	−0.174078
$529$	−14.0000	−0.608696
$530$	0	0
$531$	4.00000	0.173585
$532$	−8.00000	−0.346844
$533$	9.00000	0.389833
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−6.00000	−0.258919
$538$	0	0
$539$	6.00000	0.258438
$540$	0	0
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	0	0
$543$	−3.00000	−0.128742
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	4.00000	0.170872
$549$	−11.0000	−0.469469
$550$	0	0
$551$	32.0000	1.36325
$552$	0	0
$553$	−1.00000	−0.0425243
$554$	0	0
$555$	0	0
$556$	−38.0000	−1.61156
$557$	−20.0000	−0.847427	−0.423714	−	0.905796i	$-0.639274\pi$
$557$	−20.0000	−0.847427	−0.423714	+	0.905796i	$0.639274\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	0	0
$561$	1.00000	0.0422200
$562$	0	0
$563$	37.0000	1.55936	0.779682	−	0.626176i	$-0.215381\pi$
$563$	37.0000	1.55936	0.779682	+	0.626176i	$0.215381\pi$
$564$	−20.0000	−0.842152
$565$	0	0
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	−12.0000	−0.503066	−0.251533	−	0.967849i	$-0.580935\pi$
$569$	−12.0000	−0.503066	−0.251533	+	0.967849i	$0.580935\pi$
$570$	0	0
$571$	−3.00000	−0.125546	−0.0627730	−	0.998028i	$-0.519994\pi$
$571$	−3.00000	−0.125546	−0.0627730	+	0.998028i	$0.519994\pi$
$572$	−2.00000	−0.0836242
$573$	−18.0000	−0.751961
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	1.00000	0.0416305	0.0208153	−	0.999783i	$-0.493374\pi$
$577$	1.00000	0.0416305	0.0208153	+	0.999783i	$0.493374\pi$
$578$	0	0
$579$	−9.00000	−0.374027
$580$	0	0
$581$	−6.00000	−0.248922
$582$	0	0
$583$	1.00000	0.0414158
$584$	0	0
$585$	0	0
$586$	0	0
$587$	42.0000	1.73353	0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000	1.73353	0.866763	+	0.498721i	$0.166197\pi$
$588$	12.0000	0.494872
$589$	16.0000	0.659269
$590$	0	0
$591$	22.0000	0.904959
$592$	12.0000	0.493197
$593$	−8.00000	−0.328521	−0.164260	−	0.986417i	$-0.552524\pi$
$593$	−8.00000	−0.328521	−0.164260	+	0.986417i	$0.552524\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	0	0
$599$	−10.0000	−0.408589	−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000	−0.408589	−0.204294	+	0.978909i	$0.565490\pi$
$600$	0	0
$601$	−25.0000	−1.01977	−0.509886	−	0.860242i	$-0.670312\pi$
$601$	−25.0000	−1.01977	−0.509886	+	0.860242i	$0.670312\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	−4.00000	−0.162758
$605$	0	0
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	0	0
$609$	8.00000	0.324176
$610$	0	0
$611$	−10.0000	−0.404557
$612$	2.00000	0.0808452
$613$	25.0000	1.00974	0.504870	−	0.863195i	$-0.331540\pi$
$613$	25.0000	1.00974	0.504870	+	0.863195i	$0.331540\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−44.0000	−1.77137	−0.885687	−	0.464283i	$-0.846312\pi$
$617$	−44.0000	−1.77137	−0.885687	+	0.464283i	$0.846312\pi$
$618$	0	0
$619$	−6.00000	−0.241160	−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000	−0.241160	−0.120580	+	0.992704i	$0.538475\pi$
$620$	0	0
$621$	−3.00000	−0.120386
$622$	0	0
$623$	15.0000	0.600962
$624$	−4.00000	−0.160128
$625$	0	0
$626$	0	0
$627$	4.00000	0.159745
$628$	40.0000	1.59617
$629$	−3.00000	−0.119618
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	0	0
$633$	−4.00000	−0.158986
$634$	0	0
$635$	0	0
$636$	2.00000	0.0793052
$637$	6.00000	0.237729
$638$	0	0
$639$	−1.00000	−0.0395594
$640$	0	0
$641$	40.0000	1.57991	0.789953	−	0.613168i	$-0.210105\pi$
$641$	40.0000	1.57991	0.789953	+	0.613168i	$0.210105\pi$
$642$	0	0
$643$	−1.00000	−0.0394362	−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000	−0.0394362	−0.0197181	+	0.999806i	$0.506277\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	0	0
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	0	0
$649$	−4.00000	−0.157014
$650$	0	0
$651$	4.00000	0.156772
$652$	34.0000	1.33154
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	0	0
$656$	−36.0000	−1.40556
$657$	14.0000	0.546192
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	0	0
$663$	1.00000	0.0388368
$664$	0	0
$665$	0	0
$666$	0	0
$667$	24.0000	0.929284
$668$	−36.0000	−1.39288
$669$	16.0000	0.618596
$670$	0	0
$671$	11.0000	0.424650
$672$	0	0
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	0	0
$675$	0	0
$676$	−2.00000	−0.0769231
$677$	−25.0000	−0.960828	−0.480414	−	0.877042i	$-0.659514\pi$
$677$	−25.0000	−0.960828	−0.480414	+	0.877042i	$0.659514\pi$
$678$	0	0
$679$	15.0000	0.575647
$680$	0	0
$681$	−12.0000	−0.459841
$682$	0	0
$683$	42.0000	1.60709	0.803543	−	0.595247i	$-0.202946\pi$
$683$	42.0000	1.60709	0.803543	+	0.595247i	$0.202946\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	0	0
$687$	−10.0000	−0.381524
$688$	−32.0000	−1.21999
$689$	1.00000	0.0380970
$690$	0	0
$691$	50.0000	1.90209	0.951045	−	0.309053i	$-0.100012\pi$
$691$	50.0000	1.90209	0.951045	+	0.309053i	$0.100012\pi$
$692$	−4.00000	−0.152057
$693$	1.00000	0.0379869
$694$	0	0
$695$	0	0
$696$	0	0
$697$	9.00000	0.340899
$698$	0	0
$699$	13.0000	0.491705
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	0	0
$703$	−12.0000	−0.452589
$704$	8.00000	0.301511
$705$	0	0
$706$	0	0
$707$	−10.0000	−0.376089
$708$	−8.00000	−0.300658
$709$	−20.0000	−0.751116	−0.375558	−	0.926799i	$-0.622549\pi$
$709$	−20.0000	−0.751116	−0.375558	+	0.926799i	$0.622549\pi$
$710$	0	0
$711$	1.00000	0.0375029
$712$	0	0
$713$	12.0000	0.449404
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	27.0000	1.00833
$718$	0	0
$719$	42.0000	1.56634	0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000	1.56634	0.783168	+	0.621810i	$0.213603\pi$
$720$	0	0
$721$	6.00000	0.223452
$722$	0	0
$723$	0	0
$724$	6.00000	0.222988
$725$	0	0
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	8.00000	0.295891
$732$	22.0000	0.813143
$733$	−25.0000	−0.923396	−0.461698	−	0.887037i	$-0.652760\pi$
$733$	−25.0000	−0.923396	−0.461698	+	0.887037i	$0.652760\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	4.00000	0.147342
$738$	0	0
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	0	0
$741$	4.00000	0.146944
$742$	0	0
$743$	28.0000	1.02722	0.513610	−	0.858024i	$-0.328308\pi$
$743$	28.0000	1.02722	0.513610	+	0.858024i	$0.328308\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	6.00000	0.219529
$748$	−2.00000	−0.0731272
$749$	−17.0000	−0.621166
$750$	0	0
$751$	3.00000	0.109472	0.0547358	−	0.998501i	$-0.482568\pi$
$751$	3.00000	0.109472	0.0547358	+	0.998501i	$0.482568\pi$
$752$	40.0000	1.45865
$753$	18.0000	0.655956
$754$	0	0
$755$	0	0
$756$	2.00000	0.0727393
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	0	0
$759$	3.00000	0.108893
$760$	0	0
$761$	2.00000	0.0724999	0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000	0.0724999	0.0362500	+	0.999343i	$0.488459\pi$
$762$	0	0
$763$	−12.0000	−0.434429
$764$	36.0000	1.30243
$765$	0	0
$766$	0	0
$767$	−4.00000	−0.144432
$768$	16.0000	0.577350
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	18.0000	0.647834
$773$	−2.00000	−0.0719350	−0.0359675	−	0.999353i	$-0.511451\pi$
$773$	−2.00000	−0.0719350	−0.0359675	+	0.999353i	$0.511451\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−3.00000	−0.107624
$778$	0	0
$779$	36.0000	1.28983
$780$	0	0
$781$	1.00000	0.0357828
$782$	0	0
$783$	−8.00000	−0.285897
$784$	−24.0000	−0.857143
$785$	0	0
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−44.0000	−1.56744
$789$	16.0000	0.569615
$790$	0	0
$791$	−18.0000	−0.640006
$792$	0	0
$793$	11.0000	0.390621
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−19.0000	−0.673015	−0.336507	−	0.941681i	$-0.609246\pi$
$797$	−19.0000	−0.673015	−0.336507	+	0.941681i	$0.609246\pi$
$798$	0	0
$799$	−10.0000	−0.353775
$800$	0	0
$801$	−15.0000	−0.529999
$802$	0	0
$803$	−14.0000	−0.494049
$804$	8.00000	0.282138
$805$	0	0
$806$	0	0
$807$	−14.0000	−0.492823
$808$	0	0
$809$	8.00000	0.281265	0.140633	−	0.990062i	$-0.455086\pi$
$809$	8.00000	0.281265	0.140633	+	0.990062i	$0.455086\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	−16.0000	−0.561490
$813$	−2.00000	−0.0701431
$814$	0	0
$815$	0	0
$816$	−4.00000	−0.140028
$817$	32.0000	1.11954
$818$	0	0
$819$	1.00000	0.0349428
$820$	0	0
$821$	−21.0000	−0.732905	−0.366453	−	0.930437i	$-0.619428\pi$
$821$	−21.0000	−0.732905	−0.366453	+	0.930437i	$0.619428\pi$
$822$	0	0
$823$	−14.0000	−0.488009	−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000	−0.488009	−0.244005	+	0.969774i	$0.578461\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	6.00000	0.208514
$829$	−6.00000	−0.208389	−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000	−0.208389	−0.104194	+	0.994557i	$0.533226\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	8.00000	0.277350
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	−8.00000	−0.276686
$837$	−4.00000	−0.138260
$838$	0	0
$839$	19.0000	0.655953	0.327976	−	0.944686i	$-0.393633\pi$
$839$	19.0000	0.655953	0.327976	+	0.944686i	$0.393633\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	0	0
$843$	6.00000	0.206651
$844$	8.00000	0.275371
$845$	0	0
$846$	0	0
$847$	10.0000	0.343604
$848$	−4.00000	−0.137361
$849$	−26.0000	−0.892318
$850$	0	0
$851$	−9.00000	−0.308516
$852$	2.00000	0.0685189
$853$	21.0000	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$853$	21.0000	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−23.0000	−0.785665	−0.392833	−	0.919610i	$-0.628505\pi$
$857$	−23.0000	−0.785665	−0.392833	+	0.919610i	$0.628505\pi$
$858$	0	0
$859$	−25.0000	−0.852989	−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000	−0.852989	−0.426494	+	0.904490i	$0.640252\pi$
$860$	0	0
$861$	9.00000	0.306719
$862$	0	0
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−16.0000	−0.543388
$868$	−8.00000	−0.271538
$869$	−1.00000	−0.0339227
$870$	0	0
$871$	4.00000	0.135535
$872$	0	0
$873$	−15.0000	−0.507673
$874$	0	0
$875$	0	0
$876$	−28.0000	−0.946032
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	0	0
$879$	−4.00000	−0.134917
$880$	0	0
$881$	38.0000	1.28025	0.640126	−	0.768270i	$-0.278882\pi$
$881$	38.0000	1.28025	0.640126	+	0.768270i	$0.278882\pi$
$882$	0	0
$883$	6.00000	0.201916	0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000	0.201916	0.100958	+	0.994891i	$0.467809\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	0	0
$887$	39.0000	1.30949	0.654746	−	0.755849i	$-0.272776\pi$
$887$	39.0000	1.30949	0.654746	+	0.755849i	$0.272776\pi$
$888$	0	0
$889$	6.00000	0.201234
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	−32.0000	−1.07144
$893$	−40.0000	−1.33855
$894$	0	0
$895$	0	0
$896$	0	0
$897$	3.00000	0.100167
$898$	0	0
$899$	32.0000	1.06726
$900$	0	0
$901$	1.00000	0.0333148
$902$	0	0
$903$	8.00000	0.266223
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−46.0000	−1.52740	−0.763702	−	0.645568i	$-0.776621\pi$
$907$	−46.0000	−1.52740	−0.763702	+	0.645568i	$0.776621\pi$
$908$	24.0000	0.796468
$909$	10.0000	0.331679
$910$	0	0
$911$	34.0000	1.12647	0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000	1.12647	0.563235	+	0.826297i	$0.309557\pi$
$912$	−16.0000	−0.529813
$913$	−6.00000	−0.198571
$914$	0	0
$915$	0	0
$916$	20.0000	0.660819
$917$	0	0
$918$	0	0
$919$	33.0000	1.08857	0.544285	−	0.838901i	$-0.316801\pi$
$919$	33.0000	1.08857	0.544285	+	0.838901i	$0.316801\pi$
$920$	0	0
$921$	23.0000	0.757876
$922$	0	0
$923$	1.00000	0.0329154
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	0	0
$927$	−6.00000	−0.197066
$928$	0	0
$929$	−11.0000	−0.360898	−0.180449	−	0.983584i	$-0.557755\pi$
$929$	−11.0000	−0.360898	−0.180449	+	0.983584i	$0.557755\pi$
$930$	0	0
$931$	24.0000	0.786568
$932$	−26.0000	−0.851658
$933$	−28.0000	−0.916679
$934$	0	0
$935$	0	0
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	0	0
$939$	28.0000	0.913745
$940$	0	0
$941$	49.0000	1.59735	0.798677	−	0.601760i	$-0.205534\pi$
$941$	49.0000	1.59735	0.798677	+	0.601760i	$0.205534\pi$
$942$	0	0
$943$	27.0000	0.879241
$944$	16.0000	0.520756
$945$	0	0
$946$	0	0
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	−2.00000	−0.0649570
$949$	−14.0000	−0.454459
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	−9.00000	−0.291539	−0.145769	−	0.989319i	$-0.546566\pi$
$953$	−9.00000	−0.291539	−0.145769	+	0.989319i	$0.546566\pi$
$954$	0	0
$955$	0	0
$956$	−54.0000	−1.74648
$957$	8.00000	0.258603
$958$	0	0
$959$	2.00000	0.0645834
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	17.0000	0.547817
$964$	0	0
$965$	0	0
$966$	0	0
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	0	0
$969$	4.00000	0.128499
$970$	0	0
$971$	−58.0000	−1.86131	−0.930654	−	0.365900i	$-0.880761\pi$
$971$	−58.0000	−1.86131	−0.930654	+	0.365900i	$0.880761\pi$
$972$	−2.00000	−0.0641500
$973$	−19.0000	−0.609112
$974$	0	0
$975$	0	0
$976$	−44.0000	−1.40841
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	15.0000	0.479402
$980$	0	0
$981$	12.0000	0.383131
$982$	0	0
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−10.0000	−0.318304
$988$	−8.00000	−0.254514
$989$	24.0000	0.763156
$990$	0	0
$991$	11.0000	0.349427	0.174713	−	0.984619i	$-0.444100\pi$
$991$	11.0000	0.349427	0.174713	+	0.984619i	$0.444100\pi$
$992$	0	0
$993$	24.0000	0.761617
$994$	0	0
$995$	0	0
$996$	−12.0000	−0.380235
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	0	0
$999$	3.00000	0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.a.h.1.1		1
3.2	odd	2		2925.2.a.h.1.1		1
5.2	odd	4		195.2.c.a.79.1	✓	2
5.3	odd	4		195.2.c.a.79.2	yes	2
5.4	even	2		975.2.a.g.1.1		1
15.2	even	4		585.2.c.a.469.2		2
15.8	even	4		585.2.c.a.469.1		2
15.14	odd	2		2925.2.a.j.1.1		1
20.3	even	4		3120.2.l.c.1249.1		2
20.7	even	4		3120.2.l.c.1249.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.a.79.1	✓	2	5.2	odd	4
195.2.c.a.79.2	yes	2	5.3	odd	4
585.2.c.a.469.1		2	15.8	even	4
585.2.c.a.469.2		2	15.2	even	4
975.2.a.g.1.1		1	5.4	even	2
975.2.a.h.1.1		1	1.1	even	1	trivial
2925.2.a.h.1.1		1	3.2	odd	2
2925.2.a.j.1.1		1	15.14	odd	2
3120.2.l.c.1249.1		2	20.3	even	4
3120.2.l.c.1249.2		2	20.7	even	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

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