LMFDB - Embedded newform 2646.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2646.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2646.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} -1.00000 q^{10} -1.00000 q^{11} -2.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} -5.00000 q^{19} +1.00000 q^{20} +1.00000 q^{22} +3.00000 q^{23} -4.00000 q^{25} +2.00000 q^{26} +2.00000 q^{29} +5.00000 q^{31} -1.00000 q^{32} -6.00000 q^{34} +3.00000 q^{37} +5.00000 q^{38} -1.00000 q^{40} -3.00000 q^{41} -2.00000 q^{43} -1.00000 q^{44} -3.00000 q^{46} +10.0000 q^{47} +4.00000 q^{50} -2.00000 q^{52} +8.00000 q^{53} -1.00000 q^{55} -2.00000 q^{58} +10.0000 q^{59} -4.00000 q^{61} -5.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} +10.0000 q^{67} +6.00000 q^{68} -13.0000 q^{71} +14.0000 q^{73} -3.00000 q^{74} -5.00000 q^{76} -2.00000 q^{79} +1.00000 q^{80} +3.00000 q^{82} -6.00000 q^{83} +6.00000 q^{85} +2.00000 q^{86} +1.00000 q^{88} +17.0000 q^{89} +3.00000 q^{92} -10.0000 q^{94} -5.00000 q^{95} -4.00000 q^{97} +O(q^{100})$

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	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
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	0	0
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	5.00000	0.811107
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−3.00000	−0.442326
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	0	0
$49$	0	0
$50$	4.00000	0.565685
$51$	0	0
$52$	−2.00000	−0.277350
$53$	8.00000	1.09888	0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000	1.09888	0.549442	+	0.835532i	$0.314840\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	−2.00000	−0.262613
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	−13.0000	−1.54282	−0.771408	−	0.636341i	$-0.780447\pi$
$71$	−13.0000	−1.54282	−0.771408	+	0.636341i	$0.780447\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−3.00000	−0.348743
$75$	0	0
$76$	−5.00000	−0.573539
$77$	0	0
$78$	0	0
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	3.00000	0.331295
$83$	−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
$86$	2.00000	0.215666
$87$	0	0
$88$	1.00000	0.106600
$89$	17.0000	1.80200	0.900998	−	0.433823i	$-0.142836\pi$
$89$	17.0000	1.80200	0.900998	+	0.433823i	$0.142836\pi$
$90$	0	0
$91$	0	0
$92$	3.00000	0.312772
$93$	0	0
$94$	−10.0000	−1.03142
$95$	−5.00000	−0.512989
$96$	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
$99$	0	0
$100$	−4.00000	−0.400000
$101$	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
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−8.00000	−0.777029
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	0	0
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	1.00000	0.0953463
$111$	0	0
$112$	0	0
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	0	0
$115$	3.00000	0.279751
$116$	2.00000	0.185695
$117$	0	0
$118$	−10.0000	−0.920575
$119$	0	0
$120$	0	0
$121$	−10.0000	−0.909091
$122$	4.00000	0.362143
$123$	0	0
$124$	5.00000	0.449013
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	2.00000	0.175412
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	0	0
$134$	−10.0000	−0.863868
$135$	0	0
$136$	−6.00000	−0.514496
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	0	0
$142$	13.0000	1.09094
$143$	2.00000	0.167248
$144$	0	0
$145$	2.00000	0.166091
$146$	−14.0000	−1.15865
$147$	0	0
$148$	3.00000	0.246598
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	5.00000	0.405554
$153$	0	0
$154$	0	0
$155$	5.00000	0.401610
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	2.00000	0.159111
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	0	0
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	6.00000	0.465690
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−6.00000	−0.460179
$171$	0	0
$172$	−2.00000	−0.152499
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−17.0000	−1.27420
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	0	0
$183$	0	0
$184$	−3.00000	−0.221163
$185$	3.00000	0.220564
$186$	0	0
$187$	−6.00000	−0.438763
$188$	10.0000	0.729325
$189$	0	0
$190$	5.00000	0.362738
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	0	0
$197$	−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
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	−10.0000	−0.703598
$203$	0	0
$204$	0	0
$205$	−3.00000	−0.209529
$206$	11.0000	0.766406
$207$	0	0
$208$	−2.00000	−0.138675
$209$	5.00000	0.345857
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	8.00000	0.549442
$213$	0	0
$214$	8.00000	0.546869
$215$	−2.00000	−0.136399
$216$	0	0
$217$	0	0
$218$	−1.00000	−0.0677285
$219$	0	0
$220$	−1.00000	−0.0674200
$221$	−12.0000	−0.807207
$222$	0	0
$223$	23.0000	1.54019	0.770097	−	0.637927i	$-0.220208\pi$
$223$	23.0000	1.54019	0.770097	+	0.637927i	$0.220208\pi$
$224$	0	0
$225$	0	0
$226$	−16.0000	−1.06430
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	0	0
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	−3.00000	−0.197814
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−28.0000	−1.83434	−0.917170	−	0.398495i	$-0.869533\pi$
$233$	−28.0000	−1.83434	−0.917170	+	0.398495i	$0.869533\pi$
$234$	0	0
$235$	10.0000	0.652328
$236$	10.0000	0.650945
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	26.0000	1.67481	0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000	1.67481	0.837404	+	0.546585i	$0.184072\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	−4.00000	−0.256074
$245$	0	0
$246$	0	0
$247$	10.0000	0.636285
$248$	−5.00000	−0.317500
$249$	0	0
$250$	9.00000	0.569210
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	−3.00000	−0.188608
$254$	10.0000	0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	0	0
$259$	0	0
$260$	−2.00000	−0.124035
$261$	0	0
$262$	−18.0000	−1.11204
$263$	11.0000	0.678289	0.339145	−	0.940734i	$-0.389862\pi$
$263$	11.0000	0.678289	0.339145	+	0.940734i	$0.389862\pi$
$264$	0	0
$265$	8.00000	0.491436
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	1.00000	0.0609711	0.0304855	−	0.999535i	$-0.490295\pi$
$269$	1.00000	0.0609711	0.0304855	+	0.999535i	$0.490295\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	10.0000	0.604122
$275$	4.00000	0.241209
$276$	0	0
$277$	−17.0000	−1.02143	−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000	−1.02143	−0.510716	+	0.859750i	$0.670619\pi$
$278$	−12.0000	−0.719712
$279$	0	0
$280$	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
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−13.0000	−0.771408
$285$	0	0
$286$	−2.00000	−0.118262
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	−2.00000	−0.117444
$291$	0	0
$292$	14.0000	0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	−3.00000	−0.174371
$297$	0	0
$298$	−20.0000	−1.15857
$299$	−6.00000	−0.346989
$300$	0	0
$301$	0	0
$302$	20.0000	1.15087
$303$	0	0
$304$	−5.00000	−0.286770
$305$	−4.00000	−0.229039
$306$	0	0
$307$	11.0000	0.627803	0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000	0.627803	0.313902	+	0.949456i	$0.398364\pi$
$308$	0	0
$309$	0	0
$310$	−5.00000	−0.283981
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−2.00000	−0.112509
$317$	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
$319$	−2.00000	−0.111979
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	−30.0000	−1.66924
$324$	0	0
$325$	8.00000	0.443760
$326$	−6.00000	−0.332309
$327$	0	0
$328$	3.00000	0.165647
$329$	0	0
$330$	0	0
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	16.0000	0.875481
$335$	10.0000	0.546358
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	6.00000	0.325396
$341$	−5.00000	−0.270765
$342$	0	0
$343$	0	0
$344$	2.00000	0.107833
$345$	0	0
$346$	−11.0000	−0.591364
$347$	−9.00000	−0.483145	−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000	−0.483145	−0.241573	+	0.970383i	$0.577663\pi$
$348$	0	0
$349$	12.0000	0.642345	0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000	0.642345	0.321173	+	0.947021i	$0.395923\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−9.00000	−0.479022	−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000	−0.479022	−0.239511	+	0.970894i	$0.576987\pi$
$354$	0	0
$355$	−13.0000	−0.689968
$356$	17.0000	0.900998
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−20.0000	−1.05118
$363$	0	0
$364$	0	0
$365$	14.0000	0.732793
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	3.00000	0.156386
$369$	0	0
$370$	−3.00000	−0.155963
$371$	0	0
$372$	0	0
$373$	1.00000	0.0517780	0.0258890	−	0.999665i	$-0.491758\pi$
$373$	1.00000	0.0517780	0.0258890	+	0.999665i	$0.491758\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	−10.0000	−0.515711
$377$	−4.00000	−0.206010
$378$	0	0
$379$	−6.00000	−0.308199	−0.154100	−	0.988055i	$-0.549248\pi$
$379$	−6.00000	−0.308199	−0.154100	+	0.988055i	$0.549248\pi$
$380$	−5.00000	−0.256495
$381$	0	0
$382$	3.00000	0.153493
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	0	0
$388$	−4.00000	−0.203069
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	0	0
$393$	0	0
$394$	24.0000	1.20910
$395$	−2.00000	−0.100631
$396$	0	0
$397$	28.0000	1.40528	0.702640	−	0.711546i	$-0.252005\pi$
$397$	28.0000	1.40528	0.702640	+	0.711546i	$0.252005\pi$
$398$	7.00000	0.350878
$399$	0	0
$400$	−4.00000	−0.200000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	−10.0000	−0.498135
$404$	10.0000	0.497519
$405$	0	0
$406$	0	0
$407$	−3.00000	−0.148704
$408$	0	0
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	3.00000	0.148159
$411$	0	0
$412$	−11.0000	−0.541931
$413$	0	0
$414$	0	0
$415$	−6.00000	−0.294528
$416$	2.00000	0.0980581
$417$	0	0
$418$	−5.00000	−0.244558
$419$	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
$421$	15.0000	0.731055	0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000	0.731055	0.365528	+	0.930800i	$0.380889\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−8.00000	−0.388514
$425$	−24.0000	−1.16417
$426$	0	0
$427$	0	0
$428$	−8.00000	−0.386695
$429$	0	0
$430$	2.00000	0.0964486
$431$	13.0000	0.626188	0.313094	−	0.949722i	$-0.398635\pi$
$431$	13.0000	0.626188	0.313094	+	0.949722i	$0.398635\pi$
$432$	0	0
$433$	−26.0000	−1.24948	−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000	−1.24948	−0.624740	+	0.780833i	$0.714795\pi$
$434$	0	0
$435$	0	0
$436$	1.00000	0.0478913
$437$	−15.0000	−0.717547
$438$	0	0
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	1.00000	0.0476731
$441$	0	0
$442$	12.0000	0.570782
$443$	21.0000	0.997740	0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000	0.997740	0.498870	+	0.866677i	$0.333748\pi$
$444$	0	0
$445$	17.0000	0.805877
$446$	−23.0000	−1.08908
$447$	0	0
$448$	0	0
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	3.00000	0.141264
$452$	16.0000	0.752577
$453$	0	0
$454$	−8.00000	−0.375459
$455$	0	0
$456$	0	0
$457$	−31.0000	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−16.0000	−0.747631
$459$	0	0
$460$	3.00000	0.139876
$461$	3.00000	0.139724	0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000	0.139724	0.0698620	+	0.997557i	$0.477744\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	28.0000	1.29707
$467$	−22.0000	−1.01804	−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000	−1.01804	−0.509019	+	0.860755i	$0.669992\pi$
$468$	0	0
$469$	0	0
$470$	−10.0000	−0.461266
$471$	0	0
$472$	−10.0000	−0.460287
$473$	2.00000	0.0919601
$474$	0	0
$475$	20.0000	0.917663
$476$	0	0
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−26.0000	−1.18427
$483$	0	0
$484$	−10.0000	−0.454545
$485$	−4.00000	−0.181631
$486$	0	0
$487$	22.0000	0.996915	0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000	0.996915	0.498458	+	0.866914i	$0.333900\pi$
$488$	4.00000	0.181071
$489$	0	0
$490$	0	0
$491$	27.0000	1.21849	0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000	1.21849	0.609246	+	0.792981i	$0.291472\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	−10.0000	−0.449921
$495$	0	0
$496$	5.00000	0.224507
$497$	0	0
$498$	0	0
$499$	−6.00000	−0.268597	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000	−0.268597	−0.134298	+	0.990941i	$0.542878\pi$
$500$	−9.00000	−0.402492
$501$	0	0
$502$	−4.00000	−0.178529
$503$	26.0000	1.15928	0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000	1.15928	0.579641	+	0.814872i	$0.303193\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	3.00000	0.133366
$507$	0	0
$508$	−10.0000	−0.443678
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	7.00000	0.308757
$515$	−11.0000	−0.484718
$516$	0	0
$517$	−10.0000	−0.439799
$518$	0	0
$519$	0	0
$520$	2.00000	0.0877058
$521$	−25.0000	−1.09527	−0.547635	−	0.836717i	$-0.684472\pi$
$521$	−25.0000	−1.09527	−0.547635	+	0.836717i	$0.684472\pi$
$522$	0	0
$523$	−29.0000	−1.26808	−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000	−1.26808	−0.634041	+	0.773300i	$0.718605\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	−11.0000	−0.479623
$527$	30.0000	1.30682
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−8.00000	−0.347498
$531$	0	0
$532$	0	0
$533$	6.00000	0.259889
$534$	0	0
$535$	−8.00000	−0.345870
$536$	−10.0000	−0.431934
$537$	0	0
$538$	−1.00000	−0.0431131
$539$	0	0
$540$	0	0
$541$	43.0000	1.84871	0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000	1.84871	0.924357	+	0.381528i	$0.124602\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	−6.00000	−0.257248
$545$	1.00000	0.0428353
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−10.0000	−0.427179
$549$	0	0
$550$	−4.00000	−0.170561
$551$	−10.0000	−0.426014
$552$	0	0
$553$	0	0
$554$	17.0000	0.722261
$555$	0	0
$556$	12.0000	0.508913
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−34.0000	−1.43293	−0.716465	−	0.697623i	$-0.754241\pi$
$563$	−34.0000	−1.43293	−0.716465	+	0.697623i	$0.754241\pi$
$564$	0	0
$565$	16.0000	0.673125
$566$	4.00000	0.168133
$567$	0	0
$568$	13.0000	0.545468
$569$	−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
$571$	−24.0000	−1.00437	−0.502184	−	0.864761i	$-0.667470\pi$
$571$	−24.0000	−1.00437	−0.502184	+	0.864761i	$0.667470\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	−12.0000	−0.500435
$576$	0	0
$577$	8.00000	0.333044	0.166522	−	0.986038i	$-0.446746\pi$
$577$	8.00000	0.333044	0.166522	+	0.986038i	$0.446746\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	2.00000	0.0830455
$581$	0	0
$582$	0	0
$583$	−8.00000	−0.331326
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−6.00000	−0.247858
$587$	−32.0000	−1.32078	−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000	−1.32078	−0.660391	+	0.750922i	$0.729609\pi$
$588$	0	0
$589$	−25.0000	−1.03011
$590$	−10.0000	−0.411693
$591$	0	0
$592$	3.00000	0.123299
$593$	−33.0000	−1.35515	−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000	−1.35515	−0.677574	+	0.735455i	$0.736969\pi$
$594$	0	0
$595$	0	0
$596$	20.0000	0.819232
$597$	0	0
$598$	6.00000	0.245358
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	0	0
$603$	0	0
$604$	−20.0000	−0.813788
$605$	−10.0000	−0.406558
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	5.00000	0.202777
$609$	0	0
$610$	4.00000	0.161955
$611$	−20.0000	−0.809113
$612$	0	0
$613$	−1.00000	−0.0403896	−0.0201948	−	0.999796i	$-0.506429\pi$
$613$	−1.00000	−0.0403896	−0.0201948	+	0.999796i	$0.506429\pi$
$614$	−11.0000	−0.443924
$615$	0	0
$616$	0	0
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	0	0
$619$	−31.0000	−1.24600	−0.622998	−	0.782224i	$-0.714085\pi$
$619$	−31.0000	−1.24600	−0.622998	+	0.782224i	$0.714085\pi$
$620$	5.00000	0.200805
$621$	0	0
$622$	−2.00000	−0.0801927
$623$	0	0
$624$	0	0
$625$	11.0000	0.440000
$626$	−18.0000	−0.719425
$627$	0	0
$628$	10.0000	0.399043
$629$	18.0000	0.717707
$630$	0	0
$631$	−42.0000	−1.67199	−0.835997	−	0.548734i	$-0.815110\pi$
$631$	−42.0000	−1.67199	−0.835997	+	0.548734i	$0.815110\pi$
$632$	2.00000	0.0795557
$633$	0	0
$634$	−18.0000	−0.714871
$635$	−10.0000	−0.396838
$636$	0	0
$637$	0	0
$638$	2.00000	0.0791808
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	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
$643$	−33.0000	−1.30139	−0.650696	−	0.759338i	$-0.725523\pi$
$643$	−33.0000	−1.30139	−0.650696	+	0.759338i	$0.725523\pi$
$644$	0	0
$645$	0	0
$646$	30.0000	1.18033
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	0	0
$649$	−10.0000	−0.392534
$650$	−8.00000	−0.313786
$651$	0	0
$652$	6.00000	0.234978
$653$	−22.0000	−0.860927	−0.430463	−	0.902608i	$-0.641650\pi$
$653$	−22.0000	−0.860927	−0.430463	+	0.902608i	$0.641650\pi$
$654$	0	0
$655$	18.0000	0.703318
$656$	−3.00000	−0.117130
$657$	0	0
$658$	0	0
$659$	−17.0000	−0.662226	−0.331113	−	0.943591i	$-0.607424\pi$
$659$	−17.0000	−0.662226	−0.331113	+	0.943591i	$0.607424\pi$
$660$	0	0
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	16.0000	0.621858
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	6.00000	0.232321
$668$	−16.0000	−0.619059
$669$	0	0
$670$	−10.0000	−0.386334
$671$	4.00000	0.154418
$672$	0	0
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−33.0000	−1.26829	−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000	−1.26829	−0.634147	+	0.773213i	$0.718648\pi$
$678$	0	0
$679$	0	0
$680$	−6.00000	−0.230089
$681$	0	0
$682$	5.00000	0.191460
$683$	−11.0000	−0.420903	−0.210452	−	0.977604i	$-0.567493\pi$
$683$	−11.0000	−0.420903	−0.210452	+	0.977604i	$0.567493\pi$
$684$	0	0
$685$	−10.0000	−0.382080
$686$	0	0
$687$	0	0
$688$	−2.00000	−0.0762493
$689$	−16.0000	−0.609551
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	11.0000	0.418157
$693$	0	0
$694$	9.00000	0.341635
$695$	12.0000	0.455186
$696$	0	0
$697$	−18.0000	−0.681799
$698$	−12.0000	−0.454207
$699$	0	0
$700$	0	0
$701$	−26.0000	−0.982006	−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000	−0.982006	−0.491003	+	0.871158i	$0.663370\pi$
$702$	0	0
$703$	−15.0000	−0.565736
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	9.00000	0.338719
$707$	0	0
$708$	0	0
$709$	−35.0000	−1.31445	−0.657226	−	0.753693i	$-0.728270\pi$
$709$	−35.0000	−1.31445	−0.657226	+	0.753693i	$0.728270\pi$
$710$	13.0000	0.487881
$711$	0	0
$712$	−17.0000	−0.637102
$713$	15.0000	0.561754
$714$	0	0
$715$	2.00000	0.0747958
$716$	12.0000	0.448461
$717$	0	0
$718$	32.0000	1.19423
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	0	0
$721$	0	0
$722$	−6.00000	−0.223297
$723$	0	0
$724$	20.0000	0.743294
$725$	−8.00000	−0.297113
$726$	0	0
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	0	0
$729$	0	0
$730$	−14.0000	−0.518163
$731$	−12.0000	−0.443836
$732$	0	0
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	7.00000	0.258375
$735$	0	0
$736$	−3.00000	−0.110581
$737$	−10.0000	−0.368355
$738$	0	0
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	3.00000	0.110282
$741$	0	0
$742$	0	0
$743$	−21.0000	−0.770415	−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000	−0.770415	−0.385208	+	0.922830i	$0.625870\pi$
$744$	0	0
$745$	20.0000	0.732743
$746$	−1.00000	−0.0366126
$747$	0	0
$748$	−6.00000	−0.219382
$749$	0	0
$750$	0	0
$751$	30.0000	1.09472	0.547358	−	0.836899i	$-0.315634\pi$
$751$	30.0000	1.09472	0.547358	+	0.836899i	$0.315634\pi$
$752$	10.0000	0.364662
$753$	0	0
$754$	4.00000	0.145671
$755$	−20.0000	−0.727875
$756$	0	0
$757$	46.0000	1.67190	0.835949	−	0.548807i	$-0.184918\pi$
$757$	46.0000	1.67190	0.835949	+	0.548807i	$0.184918\pi$
$758$	6.00000	0.217930
$759$	0	0
$760$	5.00000	0.181369
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	0	0
$764$	−3.00000	−0.108536
$765$	0	0
$766$	24.0000	0.867155
$767$	−20.0000	−0.722158
$768$	0	0
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	−45.0000	−1.61854	−0.809269	−	0.587439i	$-0.800136\pi$
$773$	−45.0000	−1.61854	−0.809269	+	0.587439i	$0.800136\pi$
$774$	0	0
$775$	−20.0000	−0.718421
$776$	4.00000	0.143592
$777$	0	0
$778$	0	0
$779$	15.0000	0.537431
$780$	0	0
$781$	13.0000	0.465177
$782$	−18.0000	−0.643679
$783$	0	0
$784$	0	0
$785$	10.0000	0.356915
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−24.0000	−0.854965
$789$	0	0
$790$	2.00000	0.0711568
$791$	0	0
$792$	0	0
$793$	8.00000	0.284088
$794$	−28.0000	−0.993683
$795$	0	0
$796$	−7.00000	−0.248108
$797$	−9.00000	−0.318796	−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000	−0.318796	−0.159398	+	0.987214i	$0.550955\pi$
$798$	0	0
$799$	60.0000	2.12265
$800$	4.00000	0.141421
$801$	0	0
$802$	−18.0000	−0.635602
$803$	−14.0000	−0.494049
$804$	0	0
$805$	0	0
$806$	10.0000	0.352235
$807$	0	0
$808$	−10.0000	−0.351799
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	25.0000	0.877869	0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000	0.877869	0.438934	+	0.898519i	$0.355356\pi$
$812$	0	0
$813$	0	0
$814$	3.00000	0.105150
$815$	6.00000	0.210171
$816$	0	0
$817$	10.0000	0.349856
$818$	−6.00000	−0.209785
$819$	0	0
$820$	−3.00000	−0.104765
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	0	0
$823$	−20.0000	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$824$	11.0000	0.383203
$825$	0	0
$826$	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
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	6.00000	0.208263
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	0	0
$835$	−16.0000	−0.553703
$836$	5.00000	0.172929
$837$	0	0
$838$	−28.0000	−0.967244
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−15.0000	−0.516934
$843$	0	0
$844$	20.0000	0.688428
$845$	−9.00000	−0.309609
$846$	0	0
$847$	0	0
$848$	8.00000	0.274721
$849$	0	0
$850$	24.0000	0.823193
$851$	9.00000	0.308516
$852$	0	0
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	0	0
$855$	0	0
$856$	8.00000	0.273434
$857$	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
$859$	−21.0000	−0.716511	−0.358255	−	0.933624i	$-0.616628\pi$
$859$	−21.0000	−0.716511	−0.358255	+	0.933624i	$0.616628\pi$
$860$	−2.00000	−0.0681994
$861$	0	0
$862$	−13.0000	−0.442782
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	0	0
$865$	11.0000	0.374011
$866$	26.0000	0.883516
$867$	0	0
$868$	0	0
$869$	2.00000	0.0678454
$870$	0	0
$871$	−20.0000	−0.677674
$872$	−1.00000	−0.0338643
$873$	0	0
$874$	15.0000	0.507383
$875$	0	0
$876$	0	0
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	24.0000	0.809961
$879$	0	0
$880$	−1.00000	−0.0337100
$881$	−5.00000	−0.168454	−0.0842271	−	0.996447i	$-0.526842\pi$
$881$	−5.00000	−0.168454	−0.0842271	+	0.996447i	$0.526842\pi$
$882$	0	0
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	−21.0000	−0.705509
$887$	−42.0000	−1.41022	−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000	−1.41022	−0.705111	+	0.709097i	$0.749103\pi$
$888$	0	0
$889$	0	0
$890$	−17.0000	−0.569841
$891$	0	0
$892$	23.0000	0.770097
$893$	−50.0000	−1.67319
$894$	0	0
$895$	12.0000	0.401116
$896$	0	0
$897$	0	0
$898$	12.0000	0.400445
$899$	10.0000	0.333519
$900$	0	0
$901$	48.0000	1.59911
$902$	−3.00000	−0.0998891
$903$	0	0
$904$	−16.0000	−0.532152
$905$	20.0000	0.664822
$906$	0	0
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	8.00000	0.265489
$909$	0	0
$910$	0	0
$911$	28.0000	0.927681	0.463841	−	0.885919i	$-0.346471\pi$
$911$	28.0000	0.927681	0.463841	+	0.885919i	$0.346471\pi$
$912$	0	0
$913$	6.00000	0.198571
$914$	31.0000	1.02539
$915$	0	0
$916$	16.0000	0.528655
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	−3.00000	−0.0989071
$921$	0	0
$922$	−3.00000	−0.0987997
$923$	26.0000	0.855800
$924$	0	0
$925$	−12.0000	−0.394558
$926$	4.00000	0.131448
$927$	0	0
$928$	−2.00000	−0.0656532
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	0	0
$932$	−28.0000	−0.917170
$933$	0	0
$934$	22.0000	0.719862
$935$	−6.00000	−0.196221
$936$	0	0
$937$	−48.0000	−1.56809	−0.784046	−	0.620703i	$-0.786847\pi$
$937$	−48.0000	−1.56809	−0.784046	+	0.620703i	$0.786847\pi$
$938$	0	0
$939$	0	0
$940$	10.0000	0.326164
$941$	33.0000	1.07577	0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000	1.07577	0.537885	+	0.843018i	$0.319224\pi$
$942$	0	0
$943$	−9.00000	−0.293080
$944$	10.0000	0.325472
$945$	0	0
$946$	−2.00000	−0.0650256
$947$	−43.0000	−1.39731	−0.698656	−	0.715458i	$-0.746218\pi$
$947$	−43.0000	−1.39731	−0.698656	+	0.715458i	$0.746218\pi$
$948$	0	0
$949$	−28.0000	−0.908918
$950$	−20.0000	−0.648886
$951$	0	0
$952$	0	0
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	0	0
$955$	−3.00000	−0.0970777
$956$	24.0000	0.776215
$957$	0	0
$958$	36.0000	1.16311
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	6.00000	0.193448
$963$	0	0
$964$	26.0000	0.837404
$965$	14.0000	0.450676
$966$	0	0
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	10.0000	0.321412
$969$	0	0
$970$	4.00000	0.128432
$971$	22.0000	0.706014	0.353007	−	0.935621i	$-0.385159\pi$
$971$	22.0000	0.706014	0.353007	+	0.935621i	$0.385159\pi$
$972$	0	0
$973$	0	0
$974$	−22.0000	−0.704925
$975$	0	0
$976$	−4.00000	−0.128037
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	0	0
$979$	−17.0000	−0.543322
$980$	0	0
$981$	0	0
$982$	−27.0000	−0.861605
$983$	10.0000	0.318950	0.159475	−	0.987202i	$-0.449020\pi$
$983$	10.0000	0.318950	0.159475	+	0.987202i	$0.449020\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	−12.0000	−0.382158
$987$	0	0
$988$	10.0000	0.318142
$989$	−6.00000	−0.190789
$990$	0	0
$991$	50.0000	1.58830	0.794151	−	0.607720i	$-0.207916\pi$
$991$	50.0000	1.58830	0.794151	+	0.607720i	$0.207916\pi$
$992$	−5.00000	−0.158750
$993$	0	0
$994$	0	0
$995$	−7.00000	−0.221915
$996$	0	0
$997$	−44.0000	−1.39349	−0.696747	−	0.717317i	$-0.745370\pi$
$997$	−44.0000	−1.39349	−0.696747	+	0.717317i	$0.745370\pi$
$998$	6.00000	0.189927
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.a.j.1.1	yes	1
3.2	odd	2		2646.2.a.u.1.1	yes	1
7.6	odd	2		2646.2.a.e.1.1	✓	1
21.20	even	2		2646.2.a.z.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2646.2.a.e.1.1	✓	1	7.6	odd	2
2646.2.a.j.1.1	yes	1	1.1	even	1	trivial
2646.2.a.u.1.1	yes	1	3.2	odd	2
2646.2.a.z.1.1	yes	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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