LMFDB - Embedded newform 585.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
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	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{10} -5.00000 q^{11} -1.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} +7.00000 q^{17} -6.00000 q^{19} +2.00000 q^{20} +10.0000 q^{22} -3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -2.00000 q^{28} -2.00000 q^{29} +2.00000 q^{31} +8.00000 q^{32} -14.0000 q^{34} -1.00000 q^{35} +7.00000 q^{37} +12.0000 q^{38} -9.00000 q^{41} -8.00000 q^{43} -10.0000 q^{44} +6.00000 q^{46} -10.0000 q^{47} -6.00000 q^{49} -2.00000 q^{50} -2.00000 q^{52} -5.00000 q^{53} -5.00000 q^{55} +4.00000 q^{58} +5.00000 q^{61} -4.00000 q^{62} -8.00000 q^{64} -1.00000 q^{65} -4.00000 q^{67} +14.0000 q^{68} +2.00000 q^{70} -9.00000 q^{71} -6.00000 q^{73} -14.0000 q^{74} -12.0000 q^{76} +5.00000 q^{77} -3.00000 q^{79} -4.00000 q^{80} +18.0000 q^{82} +4.00000 q^{83} +7.00000 q^{85} +16.0000 q^{86} -11.0000 q^{89} +1.00000 q^{91} -6.00000 q^{92} +20.0000 q^{94} -6.00000 q^{95} -11.0000 q^{97} +12.0000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	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
$9$	0	0
$10$	−2.00000	−0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.00000	0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	10.0000	2.13201
$23$	−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
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	−2.00000	−0.377964
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	−14.0000	−2.40098
$35$	−1.00000	−0.169031
$36$	0	0
$37$	7.00000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	12.0000	1.94666
$39$	0	0
$40$	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	$0.708828\pi$
$44$	−10.0000	−1.50756
$45$	0	0
$46$	6.00000	0.884652
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−2.00000	−0.282843
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	0	0
$57$	0	0
$58$	4.00000	0.525226
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	−8.00000	−1.00000
$65$	−1.00000	−0.124035
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	14.0000	1.69775
$69$	0	0
$70$	2.00000	0.239046
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−14.0000	−1.62747
$75$	0	0
$76$	−12.0000	−1.37649
$77$	5.00000	0.569803
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	18.0000	1.98777
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	7.00000	0.759257
$86$	16.0000	1.72532
$87$	0	0
$88$	0	0
$89$	−11.0000	−1.16600	−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000	−1.16600	−0.582999	+	0.812473i	$0.698121\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−6.00000	−0.625543
$93$	0	0
$94$	20.0000	2.06284
$95$	−6.00000	−0.615587
$96$	0	0
$97$	−11.0000	−1.11688	−0.558440	−	0.829545i	$-0.688600\pi$
$97$	−11.0000	−1.11688	−0.558440	+	0.829545i	$0.688600\pi$
$98$	12.0000	1.21218
$99$	0	0
$100$	2.00000	0.200000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	0	0
$106$	10.0000	0.971286
$107$	17.0000	1.64345	0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000	1.64345	0.821726	+	0.569883i	$0.193011\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	10.0000	0.953463
$111$	0	0
$112$	4.00000	0.377964
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	−3.00000	−0.279751
$116$	−4.00000	−0.371391
$117$	0	0
$118$	0	0
$119$	−7.00000	−0.641689
$120$	0	0
$121$	14.0000	1.27273
$122$	−10.0000	−0.905357
$123$	0	0
$124$	4.00000	0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	0	0
$130$	2.00000	0.175412
$131$	22.0000	1.92215	0.961074	−	0.276289i	$-0.0891049\pi$
$131$	22.0000	1.92215	0.961074	+	0.276289i	$0.0891049\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	8.00000	0.691095
$135$	0	0
$136$	0	0
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	0	0
$139$	15.0000	1.27228	0.636142	−	0.771572i	$-0.280529\pi$
$139$	15.0000	1.27228	0.636142	+	0.771572i	$0.280529\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	18.0000	1.51053
$143$	5.00000	0.418121
$144$	0	0
$145$	−2.00000	−0.166091
$146$	12.0000	0.993127
$147$	0	0
$148$	14.0000	1.15079
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	0	0
$154$	−10.0000	−0.805823
$155$	2.00000	0.160644
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	8.00000	0.632456
$161$	3.00000	0.236433
$162$	0	0
$163$	15.0000	1.17489	0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000	1.17489	0.587445	+	0.809264i	$0.300134\pi$
$164$	−18.0000	−1.40556
$165$	0	0
$166$	−8.00000	−0.620920
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−14.0000	−1.07375
$171$	0	0
$172$	−16.0000	−1.21999
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	20.0000	1.50756
$177$	0	0
$178$	22.0000	1.64897
$179$	−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
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	0	0
$185$	7.00000	0.514650
$186$	0	0
$187$	−35.0000	−2.55945
$188$	−20.0000	−1.45865
$189$	0	0
$190$	12.0000	0.870572
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	0	0
$193$	−17.0000	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$194$	22.0000	1.57951
$195$	0	0
$196$	−12.0000	−0.857143
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	0	0
$199$	−28.0000	−1.98487	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−28.0000	−1.98487	−0.992434	+	0.122782i	$0.960818\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	2.00000	0.140372
$204$	0	0
$205$	−9.00000	−0.628587
$206$	8.00000	0.557386
$207$	0	0
$208$	4.00000	0.277350
$209$	30.0000	2.07514
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	−34.0000	−2.32419
$215$	−8.00000	−0.545595
$216$	0	0
$217$	−2.00000	−0.135769
$218$	−8.00000	−0.541828
$219$	0	0
$220$	−10.0000	−0.674200
$221$	−7.00000	−0.470871
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	−8.00000	−0.534522
$225$	0	0
$226$	20.0000	1.33038
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	0	0
$233$	−19.0000	−1.24473	−0.622366	−	0.782727i	$-0.713828\pi$
$233$	−19.0000	−1.24473	−0.622366	+	0.782727i	$0.713828\pi$
$234$	0	0
$235$	−10.0000	−0.652328
$236$	0	0
$237$	0	0
$238$	14.0000	0.907485
$239$	−9.00000	−0.582162	−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000	−0.582162	−0.291081	+	0.956698i	$0.594015\pi$
$240$	0	0
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	−28.0000	−1.79991
$243$	0	0
$244$	10.0000	0.640184
$245$	−6.00000	−0.383326
$246$	0	0
$247$	6.00000	0.381771
$248$	0	0
$249$	0	0
$250$	−2.00000	−0.126491
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	15.0000	0.943042
$254$	4.00000	0.250982
$255$	0	0
$256$	16.0000	1.00000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	−7.00000	−0.434959
$260$	−2.00000	−0.124035
$261$	0	0
$262$	−44.0000	−2.71833
$263$	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
$265$	−5.00000	−0.307148
$266$	−12.0000	−0.735767
$267$	0	0
$268$	−8.00000	−0.488678
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	0	0
$271$	−22.0000	−1.33640	−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000	−1.33640	−0.668202	+	0.743980i	$0.732936\pi$
$272$	−28.0000	−1.69775
$273$	0	0
$274$	−28.0000	−1.69154
$275$	−5.00000	−0.301511
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−30.0000	−1.79928
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	−18.0000	−1.06810
$285$	0	0
$286$	−10.0000	−0.591312
$287$	9.00000	0.531253
$288$	0	0
$289$	32.0000	1.88235
$290$	4.00000	0.234888
$291$	0	0
$292$	−12.0000	−0.702247
$293$	−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
$297$	0	0
$298$	30.0000	1.73785
$299$	3.00000	0.173494
$300$	0	0
$301$	8.00000	0.461112
$302$	16.0000	0.920697
$303$	0	0
$304$	24.0000	1.37649
$305$	5.00000	0.286299
$306$	0	0
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	10.0000	0.569803
$309$	0	0
$310$	−4.00000	−0.227185
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−36.0000	−2.03160
$315$	0	0
$316$	−6.00000	−0.337526
$317$	24.0000	1.34797	0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000	1.34797	0.673987	+	0.738743i	$0.264580\pi$
$318$	0	0
$319$	10.0000	0.559893
$320$	−8.00000	−0.447214
$321$	0	0
$322$	−6.00000	−0.334367
$323$	−42.0000	−2.33694
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	−30.0000	−1.66155
$327$	0	0
$328$	0	0
$329$	10.0000	0.551318
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	8.00000	0.439057
$333$	0	0
$334$	−48.0000	−2.62644
$335$	−4.00000	−0.218543
$336$	0	0
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	−2.00000	−0.108786
$339$	0	0
$340$	14.0000	0.759257
$341$	−10.0000	−0.541530
$342$	0	0
$343$	13.0000	0.701934
$344$	0	0
$345$	0	0
$346$	−36.0000	−1.93537
$347$	−11.0000	−0.590511	−0.295255	−	0.955418i	$-0.595405\pi$
$347$	−11.0000	−0.590511	−0.295255	+	0.955418i	$0.595405\pi$
$348$	0	0
$349$	24.0000	1.28469	0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000	1.28469	0.642345	+	0.766415i	$0.277962\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	−40.0000	−2.13201
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	−9.00000	−0.477670
$356$	−22.0000	−1.16600
$357$	0	0
$358$	12.0000	0.634220
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	14.0000	0.735824
$363$	0	0
$364$	2.00000	0.104828
$365$	−6.00000	−0.314054
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	12.0000	0.625543
$369$	0	0
$370$	−14.0000	−0.727825
$371$	5.00000	0.259587
$372$	0	0
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	70.0000	3.61961
$375$	0	0
$376$	0	0
$377$	2.00000	0.103005
$378$	0	0
$379$	10.0000	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	−12.0000	−0.615587
$381$	0	0
$382$	−24.0000	−1.22795
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	5.00000	0.254824
$386$	34.0000	1.73055
$387$	0	0
$388$	−22.0000	−1.11688
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	0	0
$391$	−21.0000	−1.06202
$392$	0	0
$393$	0	0
$394$	48.0000	2.41821
$395$	−3.00000	−0.150946
$396$	0	0
$397$	15.0000	0.752828	0.376414	−	0.926451i	$-0.377157\pi$
$397$	15.0000	0.752828	0.376414	+	0.926451i	$0.377157\pi$
$398$	56.0000	2.80703
$399$	0	0
$400$	−4.00000	−0.200000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	0	0
$405$	0	0
$406$	−4.00000	−0.198517
$407$	−35.0000	−1.73489
$408$	0	0
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	18.0000	0.888957
$411$	0	0
$412$	−8.00000	−0.394132
$413$	0	0
$414$	0	0
$415$	4.00000	0.196352
$416$	−8.00000	−0.392232
$417$	0	0
$418$	−60.0000	−2.93470
$419$	−26.0000	−1.27018	−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000	−1.27018	−0.635092	+	0.772437i	$0.719038\pi$
$420$	0	0
$421$	−20.0000	−0.974740	−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000	−0.974740	−0.487370	+	0.873195i	$0.662044\pi$
$422$	24.0000	1.16830
$423$	0	0
$424$	0	0
$425$	7.00000	0.339550
$426$	0	0
$427$	−5.00000	−0.241967
$428$	34.0000	1.64345
$429$	0	0
$430$	16.0000	0.771589
$431$	40.0000	1.92673	0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000	1.92673	0.963366	+	0.268190i	$0.0864254\pi$
$432$	0	0
$433$	−20.0000	−0.961139	−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000	−0.961139	−0.480569	+	0.876957i	$0.659570\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	8.00000	0.383131
$437$	18.0000	0.861057
$438$	0	0
$439$	15.0000	0.715911	0.357955	−	0.933739i	$-0.383474\pi$
$439$	15.0000	0.715911	0.357955	+	0.933739i	$0.383474\pi$
$440$	0	0
$441$	0	0
$442$	14.0000	0.665912
$443$	1.00000	0.0475114	0.0237557	−	0.999718i	$-0.492438\pi$
$443$	1.00000	0.0475114	0.0237557	+	0.999718i	$0.492438\pi$
$444$	0	0
$445$	−11.0000	−0.521450
$446$	16.0000	0.757622
$447$	0	0
$448$	8.00000	0.377964
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	0	0
$451$	45.0000	2.11897
$452$	−20.0000	−0.940721
$453$	0	0
$454$	−4.00000	−0.187729
$455$	1.00000	0.0468807
$456$	0	0
$457$	−7.00000	−0.327446	−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000	−0.327446	−0.163723	+	0.986506i	$0.552350\pi$
$458$	−28.0000	−1.30835
$459$	0	0
$460$	−6.00000	−0.279751
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	0	0
$463$	15.0000	0.697109	0.348555	−	0.937288i	$-0.386673\pi$
$463$	15.0000	0.697109	0.348555	+	0.937288i	$0.386673\pi$
$464$	8.00000	0.371391
$465$	0	0
$466$	38.0000	1.76032
$467$	1.00000	0.0462745	0.0231372	−	0.999732i	$-0.492635\pi$
$467$	1.00000	0.0462745	0.0231372	+	0.999732i	$0.492635\pi$
$468$	0	0
$469$	4.00000	0.184703
$470$	20.0000	0.922531
$471$	0	0
$472$	0	0
$473$	40.0000	1.83920
$474$	0	0
$475$	−6.00000	−0.275299
$476$	−14.0000	−0.641689
$477$	0	0
$478$	18.0000	0.823301
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	0	0
$481$	−7.00000	−0.319173
$482$	−44.0000	−2.00415
$483$	0	0
$484$	28.0000	1.27273
$485$	−11.0000	−0.499484
$486$	0	0
$487$	5.00000	0.226572	0.113286	−	0.993562i	$-0.463862\pi$
$487$	5.00000	0.226572	0.113286	+	0.993562i	$0.463862\pi$
$488$	0	0
$489$	0	0
$490$	12.0000	0.542105
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	−14.0000	−0.630528
$494$	−12.0000	−0.539906
$495$	0	0
$496$	−8.00000	−0.359211
$497$	9.00000	0.403705
$498$	0	0
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	2.00000	0.0894427
$501$	0	0
$502$	0	0
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	0	0
$506$	−30.0000	−1.33366
$507$	0	0
$508$	−4.00000	−0.177471
$509$	−27.0000	−1.19675	−0.598377	−	0.801215i	$-0.704187\pi$
$509$	−27.0000	−1.19675	−0.598377	+	0.801215i	$0.704187\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	−32.0000	−1.41421
$513$	0	0
$514$	4.00000	0.176432
$515$	−4.00000	−0.176261
$516$	0	0
$517$	50.0000	2.19900
$518$	14.0000	0.615125
$519$	0	0
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	44.0000	1.92215
$525$	0	0
$526$	−32.0000	−1.39527
$527$	14.0000	0.609850
$528$	0	0
$529$	−14.0000	−0.608696
$530$	10.0000	0.434372
$531$	0	0
$532$	12.0000	0.520266
$533$	9.00000	0.389833
$534$	0	0
$535$	17.0000	0.734974
$536$	0	0
$537$	0	0
$538$	−48.0000	−2.06943
$539$	30.0000	1.29219
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	44.0000	1.88996
$543$	0	0
$544$	56.0000	2.40098
$545$	4.00000	0.171341
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	28.0000	1.19610
$549$	0	0
$550$	10.0000	0.426401
$551$	12.0000	0.511217
$552$	0	0
$553$	3.00000	0.127573
$554$	4.00000	0.169944
$555$	0	0
$556$	30.0000	1.27228
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	4.00000	0.169031
$561$	0	0
$562$	36.0000	1.51857
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	0	0
$565$	−10.0000	−0.420703
$566$	−40.0000	−1.68133
$567$	0	0
$568$	0	0
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	0	0
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	10.0000	0.418121
$573$	0	0
$574$	−18.0000	−0.751305
$575$	−3.00000	−0.125109
$576$	0	0
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	−64.0000	−2.66205
$579$	0	0
$580$	−4.00000	−0.166091
$581$	−4.00000	−0.165948
$582$	0	0
$583$	25.0000	1.03539
$584$	0	0
$585$	0	0
$586$	8.00000	0.330477
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	0	0
$591$	0	0
$592$	−28.0000	−1.15079
$593$	16.0000	0.657041	0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000	0.657041	0.328521	+	0.944497i	$0.393450\pi$
$594$	0	0
$595$	−7.00000	−0.286972
$596$	−30.0000	−1.22885
$597$	0	0
$598$	−6.00000	−0.245358
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	0	0
$601$	−5.00000	−0.203954	−0.101977	−	0.994787i	$-0.532517\pi$
$601$	−5.00000	−0.203954	−0.101977	+	0.994787i	$0.532517\pi$
$602$	−16.0000	−0.652111
$603$	0	0
$604$	−16.0000	−0.651031
$605$	14.0000	0.569181
$606$	0	0
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−48.0000	−1.94666
$609$	0	0
$610$	−10.0000	−0.404888
$611$	10.0000	0.404557
$612$	0	0
$613$	9.00000	0.363507	0.181753	−	0.983344i	$-0.441823\pi$
$613$	9.00000	0.363507	0.181753	+	0.983344i	$0.441823\pi$
$614$	−46.0000	−1.85641
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	−38.0000	−1.52735	−0.763674	−	0.645601i	$-0.776607\pi$
$619$	−38.0000	−1.52735	−0.763674	+	0.645601i	$0.776607\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	40.0000	1.60385
$623$	11.0000	0.440706
$624$	0	0
$625$	1.00000	0.0400000
$626$	44.0000	1.75859
$627$	0	0
$628$	36.0000	1.43656
$629$	49.0000	1.95376
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	0	0
$633$	0	0
$634$	−48.0000	−1.90632
$635$	−2.00000	−0.0793676
$636$	0	0
$637$	6.00000	0.237729
$638$	−20.0000	−0.791808
$639$	0	0
$640$	0	0
$641$	−20.0000	−0.789953	−0.394976	−	0.918691i	$-0.629247\pi$
$641$	−20.0000	−0.789953	−0.394976	+	0.918691i	$0.629247\pi$
$642$	0	0
$643$	−37.0000	−1.45914	−0.729569	−	0.683907i	$-0.760279\pi$
$643$	−37.0000	−1.45914	−0.729569	+	0.683907i	$0.760279\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	84.0000	3.30494
$647$	−17.0000	−0.668339	−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000	−0.668339	−0.334169	+	0.942513i	$0.608456\pi$
$648$	0	0
$649$	0	0
$650$	2.00000	0.0784465
$651$	0	0
$652$	30.0000	1.17489
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	22.0000	0.859611
$656$	36.0000	1.40556
$657$	0	0
$658$	−20.0000	−0.779681
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	6.00000	0.232670
$666$	0	0
$667$	6.00000	0.232321
$668$	48.0000	1.85718
$669$	0	0
$670$	8.00000	0.309067
$671$	−25.0000	−0.965114
$672$	0	0
$673$	42.0000	1.61898	0.809491	−	0.587133i	$-0.199743\pi$
$673$	42.0000	1.61898	0.809491	+	0.587133i	$0.199743\pi$
$674$	−16.0000	−0.616297
$675$	0	0
$676$	2.00000	0.0769231
$677$	−21.0000	−0.807096	−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000	−0.807096	−0.403548	+	0.914959i	$0.632223\pi$
$678$	0	0
$679$	11.0000	0.422141
$680$	0	0
$681$	0	0
$682$	20.0000	0.765840
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	0	0
$685$	14.0000	0.534913
$686$	−26.0000	−0.992685
$687$	0	0
$688$	32.0000	1.21999
$689$	5.00000	0.190485
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	36.0000	1.36851
$693$	0	0
$694$	22.0000	0.835109
$695$	15.0000	0.568982
$696$	0	0
$697$	−63.0000	−2.38630
$698$	−48.0000	−1.81683
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	−28.0000	−1.05755	−0.528773	−	0.848763i	$-0.677348\pi$
$701$	−28.0000	−1.05755	−0.528773	+	0.848763i	$0.677348\pi$
$702$	0	0
$703$	−42.0000	−1.58406
$704$	40.0000	1.50756
$705$	0	0
$706$	−12.0000	−0.451626
$707$	0	0
$708$	0	0
$709$	−44.0000	−1.65245	−0.826227	−	0.563337i	$-0.809517\pi$
$709$	−44.0000	−1.65245	−0.826227	+	0.563337i	$0.809517\pi$
$710$	18.0000	0.675528
$711$	0	0
$712$	0	0
$713$	−6.00000	−0.224702
$714$	0	0
$715$	5.00000	0.186989
$716$	−12.0000	−0.448461
$717$	0	0
$718$	−32.0000	−1.19423
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	0	0
$721$	4.00000	0.148968
$722$	−34.0000	−1.26535
$723$	0	0
$724$	−14.0000	−0.520306
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	0	0
$729$	0	0
$730$	12.0000	0.444140
$731$	−56.0000	−2.07123
$732$	0	0
$733$	43.0000	1.58824	0.794121	−	0.607760i	$-0.207932\pi$
$733$	43.0000	1.58824	0.794121	+	0.607760i	$0.207932\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	−24.0000	−0.884652
$737$	20.0000	0.736709
$738$	0	0
$739$	−6.00000	−0.220714	−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000	−0.220714	−0.110357	+	0.993892i	$0.535199\pi$
$740$	14.0000	0.514650
$741$	0	0
$742$	−10.0000	−0.367112
$743$	−30.0000	−1.10059	−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000	−1.10059	−0.550297	+	0.834969i	$0.685485\pi$
$744$	0	0
$745$	−15.0000	−0.549557
$746$	64.0000	2.34321
$747$	0	0
$748$	−70.0000	−2.55945
$749$	−17.0000	−0.621166
$750$	0	0
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	40.0000	1.45865
$753$	0	0
$754$	−4.00000	−0.145671
$755$	−8.00000	−0.291150
$756$	0	0
$757$	20.0000	0.726912	0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000	0.726912	0.363456	+	0.931611i	$0.381597\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	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
$763$	−4.00000	−0.144810
$764$	24.0000	0.868290
$765$	0	0
$766$	−12.0000	−0.433578
$767$	0	0
$768$	0	0
$769$	−28.0000	−1.00971	−0.504853	−	0.863205i	$-0.668453\pi$
$769$	−28.0000	−1.00971	−0.504853	+	0.863205i	$0.668453\pi$
$770$	−10.0000	−0.360375
$771$	0	0
$772$	−34.0000	−1.22369
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	0	0
$775$	2.00000	0.0718421
$776$	0	0
$777$	0	0
$778$	−8.00000	−0.286814
$779$	54.0000	1.93475
$780$	0	0
$781$	45.0000	1.61023
$782$	42.0000	1.50192
$783$	0	0
$784$	24.0000	0.857143
$785$	18.0000	0.642448
$786$	0	0
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	−48.0000	−1.70993
$789$	0	0
$790$	6.00000	0.213470
$791$	10.0000	0.355559
$792$	0	0
$793$	−5.00000	−0.177555
$794$	−30.0000	−1.06466
$795$	0	0
$796$	−56.0000	−1.98487
$797$	−39.0000	−1.38145	−0.690725	−	0.723117i	$-0.742709\pi$
$797$	−39.0000	−1.38145	−0.690725	+	0.723117i	$0.742709\pi$
$798$	0	0
$799$	−70.0000	−2.47642
$800$	8.00000	0.282843
$801$	0	0
$802$	−28.0000	−0.988714
$803$	30.0000	1.05868
$804$	0	0
$805$	3.00000	0.105736
$806$	4.00000	0.140894
$807$	0	0
$808$	0	0
$809$	50.0000	1.75791	0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000	1.75791	0.878953	+	0.476908i	$0.158243\pi$
$810$	0	0
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	4.00000	0.140372
$813$	0	0
$814$	70.0000	2.45350
$815$	15.0000	0.525427
$816$	0	0
$817$	48.0000	1.67931
$818$	−60.0000	−2.09785
$819$	0	0
$820$	−18.0000	−0.628587
$821$	−17.0000	−0.593304	−0.296652	−	0.954986i	$-0.595870\pi$
$821$	−17.0000	−0.593304	−0.296652	+	0.954986i	$0.595870\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	26.0000	0.904109	0.452054	−	0.891990i	$-0.350691\pi$
$827$	26.0000	0.904109	0.452054	+	0.891990i	$0.350691\pi$
$828$	0	0
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−8.00000	−0.277684
$831$	0	0
$832$	8.00000	0.277350
$833$	−42.0000	−1.45521
$834$	0	0
$835$	24.0000	0.830554
$836$	60.0000	2.07514
$837$	0	0
$838$	52.0000	1.79631
$839$	−17.0000	−0.586905	−0.293453	−	0.955974i	$-0.594804\pi$
$839$	−17.0000	−0.586905	−0.293453	+	0.955974i	$0.594804\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	40.0000	1.37849
$843$	0	0
$844$	−24.0000	−0.826114
$845$	1.00000	0.0344010
$846$	0	0
$847$	−14.0000	−0.481046
$848$	20.0000	0.686803
$849$	0	0
$850$	−14.0000	−0.480196
$851$	−21.0000	−0.719871
$852$	0	0
$853$	−39.0000	−1.33533	−0.667667	−	0.744460i	$-0.732707\pi$
$853$	−39.0000	−1.33533	−0.667667	+	0.744460i	$0.732707\pi$
$854$	10.0000	0.342193
$855$	0	0
$856$	0	0
$857$	45.0000	1.53717	0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000	1.53717	0.768585	+	0.639747i	$0.220961\pi$
$858$	0	0
$859$	19.0000	0.648272	0.324136	−	0.946011i	$-0.394927\pi$
$859$	19.0000	0.648272	0.324136	+	0.946011i	$0.394927\pi$
$860$	−16.0000	−0.545595
$861$	0	0
$862$	−80.0000	−2.72481
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	18.0000	0.612018
$866$	40.0000	1.35926
$867$	0	0
$868$	−4.00000	−0.135769
$869$	15.0000	0.508840
$870$	0	0
$871$	4.00000	0.135535
$872$	0	0
$873$	0	0
$874$	−36.0000	−1.21772
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−30.0000	−1.01245
$879$	0	0
$880$	20.0000	0.674200
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	−14.0000	−0.470871
$885$	0	0
$886$	−2.00000	−0.0671913
$887$	−13.0000	−0.436497	−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000	−0.436497	−0.218249	+	0.975893i	$0.570034\pi$
$888$	0	0
$889$	2.00000	0.0670778
$890$	22.0000	0.737442
$891$	0	0
$892$	−16.0000	−0.535720
$893$	60.0000	2.00782
$894$	0	0
$895$	−6.00000	−0.200558
$896$	0	0
$897$	0	0
$898$	18.0000	0.600668
$899$	−4.00000	−0.133407
$900$	0	0
$901$	−35.0000	−1.16602
$902$	−90.0000	−2.99667
$903$	0	0
$904$	0	0
$905$	−7.00000	−0.232688
$906$	0	0
$907$	38.0000	1.26177	0.630885	−	0.775877i	$-0.282692\pi$
$907$	38.0000	1.26177	0.630885	+	0.775877i	$0.282692\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	−2.00000	−0.0662994
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	−20.0000	−0.661903
$914$	14.0000	0.463079
$915$	0	0
$916$	28.0000	0.925146
$917$	−22.0000	−0.726504
$918$	0	0
$919$	−19.0000	−0.626752	−0.313376	−	0.949629i	$-0.601460\pi$
$919$	−19.0000	−0.626752	−0.313376	+	0.949629i	$0.601460\pi$
$920$	0	0
$921$	0	0
$922$	74.0000	2.43706
$923$	9.00000	0.296239
$924$	0	0
$925$	7.00000	0.230159
$926$	−30.0000	−0.985861
$927$	0	0
$928$	−16.0000	−0.525226
$929$	29.0000	0.951459	0.475730	−	0.879592i	$-0.342184\pi$
$929$	29.0000	0.951459	0.475730	+	0.879592i	$0.342184\pi$
$930$	0	0
$931$	36.0000	1.17985
$932$	−38.0000	−1.24473
$933$	0	0
$934$	−2.00000	−0.0654420
$935$	−35.0000	−1.14462
$936$	0	0
$937$	−6.00000	−0.196011	−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000	−0.196011	−0.0980057	+	0.995186i	$0.531246\pi$
$938$	−8.00000	−0.261209
$939$	0	0
$940$	−20.0000	−0.652328
$941$	−15.0000	−0.488986	−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000	−0.488986	−0.244493	+	0.969651i	$0.578622\pi$
$942$	0	0
$943$	27.0000	0.879241
$944$	0	0
$945$	0	0
$946$	−80.0000	−2.60102
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	0	0
$949$	6.00000	0.194768
$950$	12.0000	0.389331
$951$	0	0
$952$	0	0
$953$	15.0000	0.485898	0.242949	−	0.970039i	$-0.421885\pi$
$953$	15.0000	0.485898	0.242949	+	0.970039i	$0.421885\pi$
$954$	0	0
$955$	12.0000	0.388311
$956$	−18.0000	−0.582162
$957$	0	0
$958$	6.00000	0.193851
$959$	−14.0000	−0.452084
$960$	0	0
$961$	−27.0000	−0.870968
$962$	14.0000	0.451378
$963$	0	0
$964$	44.0000	1.41714
$965$	−17.0000	−0.547249
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	0	0
$969$	0	0
$970$	22.0000	0.706377
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	−15.0000	−0.480878
$974$	−10.0000	−0.320421
$975$	0	0
$976$	−20.0000	−0.640184
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	0	0
$979$	55.0000	1.75781
$980$	−12.0000	−0.383326
$981$	0	0
$982$	0	0
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	28.0000	0.891702
$987$	0	0
$988$	12.0000	0.381771
$989$	24.0000	0.763156
$990$	0	0
$991$	−57.0000	−1.81066	−0.905332	−	0.424704i	$-0.860378\pi$
$991$	−57.0000	−1.81066	−0.905332	+	0.424704i	$0.860378\pi$
$992$	16.0000	0.508001
$993$	0	0
$994$	−18.0000	−0.570925
$995$	−28.0000	−0.887660
$996$	0	0
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	28.0000	0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.a.c.1.1		1
3.2	odd	2		195.2.a.c.1.1	✓	1
4.3	odd	2		9360.2.a.bv.1.1		1
5.2	odd	4		2925.2.c.a.2224.1		2
5.3	odd	4		2925.2.c.a.2224.2		2
5.4	even	2		2925.2.a.s.1.1		1
12.11	even	2		3120.2.a.d.1.1		1
13.12	even	2		7605.2.a.t.1.1		1
15.2	even	4		975.2.c.c.274.2		2
15.8	even	4		975.2.c.c.274.1		2
15.14	odd	2		975.2.a.a.1.1		1
21.20	even	2		9555.2.a.u.1.1		1
39.38	odd	2		2535.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.c.1.1	✓	1	3.2	odd	2
585.2.a.c.1.1		1	1.1	even	1	trivial
975.2.a.a.1.1		1	15.14	odd	2
975.2.c.c.274.1		2	15.8	even	4
975.2.c.c.274.2		2	15.2	even	4
2535.2.a.d.1.1		1	39.38	odd	2
2925.2.a.s.1.1		1	5.4	even	2
2925.2.c.a.2224.1		2	5.2	odd	4
2925.2.c.a.2224.2		2	5.3	odd	4
3120.2.a.d.1.1		1	12.11	even	2
7605.2.a.t.1.1		1	13.12	even	2
9360.2.a.bv.1.1		1	4.3	odd	2
9555.2.a.u.1.1		1	21.20	even	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

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