LMFDB - Embedded newform 6566.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6566,2,Mod(1,6566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6566, 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("6566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6566 = 2 \cdot 7^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6566.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:	$52.4297739672$
Analytic rank:	$1$
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	$\chi$	$=$	6566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -4.00000 q^{11} +2.00000 q^{12} +2.00000 q^{13} -4.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} -2.00000 q^{20} -4.00000 q^{22} +2.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} -4.00000 q^{27} +2.00000 q^{29} -4.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -8.00000 q^{33} +4.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} -6.00000 q^{38} +4.00000 q^{39} -2.00000 q^{40} -8.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} -2.00000 q^{45} -4.00000 q^{47} +2.00000 q^{48} -1.00000 q^{50} +8.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} -4.00000 q^{54} +8.00000 q^{55} -12.0000 q^{57} +2.00000 q^{58} +10.0000 q^{59} -4.00000 q^{60} -2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -8.00000 q^{66} -1.00000 q^{67} +4.00000 q^{68} -12.0000 q^{71} +1.00000 q^{72} +8.00000 q^{73} +2.00000 q^{74} -2.00000 q^{75} -6.00000 q^{76} +4.00000 q^{78} -16.0000 q^{79} -2.00000 q^{80} -11.0000 q^{81} -8.00000 q^{82} +2.00000 q^{83} -8.00000 q^{85} -4.00000 q^{86} +4.00000 q^{87} -4.00000 q^{88} -2.00000 q^{90} -8.00000 q^{93} -4.00000 q^{94} +12.0000 q^{95} +2.00000 q^{96} +8.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	2.00000	0.816497
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	2.00000	0.577350
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	−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
$22$	−4.00000	−0.852803
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	2.00000	0.408248
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	−4.00000	−0.769800
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−4.00000	−0.730297
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	−8.00000	−1.39262
$34$	4.00000	0.685994
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−6.00000	−0.973329
$39$	4.00000	0.640513
$40$	−2.00000	−0.316228
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−4.00000	−0.603023
$45$	−2.00000	−0.298142
$46$	0	0
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	2.00000	0.288675
$49$	0	0
$50$	−1.00000	−0.141421
$51$	8.00000	1.12022
$52$	2.00000	0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−4.00000	−0.544331
$55$	8.00000	1.07872
$56$	0	0
$57$	−12.0000	−1.58944
$58$	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	$0.274373\pi$
$60$	−4.00000	−0.516398
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	−8.00000	−0.984732
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	2.00000	0.232495
$75$	−2.00000	−0.230940
$76$	−6.00000	−0.688247
$77$	0	0
$78$	4.00000	0.452911
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−2.00000	−0.223607
$81$	−11.0000	−1.22222
$82$	−8.00000	−0.883452
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	−8.00000	−0.867722
$86$	−4.00000	−0.431331
$87$	4.00000	0.428845
$88$	−4.00000	−0.426401
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	0	0
$93$	−8.00000	−0.829561
$94$	−4.00000	−0.412568
$95$	12.0000	1.23117
$96$	2.00000	0.204124
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	−1.00000	−0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	8.00000	0.792118
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	−4.00000	−0.384900
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	8.00000	0.762770
$111$	4.00000	0.379663
$112$	0	0
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	−12.0000	−1.12390
$115$	0	0
$116$	2.00000	0.185695
$117$	2.00000	0.184900
$118$	10.0000	0.920575
$119$	0	0
$120$	−4.00000	−0.365148
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	−16.0000	−1.44267
$124$	−4.00000	−0.359211
$125$	12.0000	1.07331
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	−4.00000	−0.350823
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−8.00000	−0.696311
$133$	0	0
$134$	−1.00000	−0.0863868
$135$	8.00000	0.688530
$136$	4.00000	0.342997
$137$	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
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−12.0000	−1.00702
$143$	−8.00000	−0.668994
$144$	1.00000	0.0833333
$145$	−4.00000	−0.332182
$146$	8.00000	0.662085
$147$	0	0
$148$	2.00000	0.164399
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	−2.00000	−0.163299
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−6.00000	−0.486664
$153$	4.00000	0.323381
$154$	0	0
$155$	8.00000	0.642575
$156$	4.00000	0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−16.0000	−1.27289
$159$	−12.0000	−0.951662
$160$	−2.00000	−0.158114
$161$	0	0
$162$	−11.0000	−0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−8.00000	−0.624695
$165$	16.0000	1.24560
$166$	2.00000	0.155230
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−8.00000	−0.613572
$171$	−6.00000	−0.458831
$172$	−4.00000	−0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	4.00000	0.303239
$175$	0	0
$176$	−4.00000	−0.301511
$177$	20.0000	1.50329
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−2.00000	−0.149071
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	0	0
$185$	−4.00000	−0.294086
$186$	−8.00000	−0.586588
$187$	−16.0000	−1.17004
$188$	−4.00000	−0.291730
$189$	0	0
$190$	12.0000	0.870572
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	2.00000	0.144338
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	8.00000	0.574367
$195$	−8.00000	−0.572892
$196$	0	0
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−4.00000	−0.284268
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.00000	−0.0707107
$201$	−2.00000	−0.141069
$202$	6.00000	0.422159
$203$	0	0
$204$	8.00000	0.560112
$205$	16.0000	1.11749
$206$	−4.00000	−0.278693
$207$	0	0
$208$	2.00000	0.138675
$209$	24.0000	1.66011
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−6.00000	−0.412082
$213$	−24.0000	−1.64445
$214$	−20.0000	−1.36717
$215$	8.00000	0.545595
$216$	−4.00000	−0.272166
$217$	0	0
$218$	−2.00000	−0.135457
$219$	16.0000	1.08118
$220$	8.00000	0.539360
$221$	8.00000	0.538138
$222$	4.00000	0.268462
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	14.0000	0.931266
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	−12.0000	−0.794719
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	0	0
$232$	2.00000	0.131306
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	2.00000	0.130744
$235$	8.00000	0.521862
$236$	10.0000	0.650945
$237$	−32.0000	−2.07862
$238$	0	0
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	−4.00000	−0.258199
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	5.00000	0.321412
$243$	−10.0000	−0.641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−16.0000	−1.02012
$247$	−12.0000	−0.763542
$248$	−4.00000	−0.254000
$249$	4.00000	0.253490
$250$	12.0000	0.758947
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	0	0
$253$	0	0
$254$	−8.00000	−0.501965
$255$	−16.0000	−1.00196
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	−4.00000	−0.248069
$261$	2.00000	0.123797
$262$	−6.00000	−0.370681
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	−8.00000	−0.492366
$265$	12.0000	0.737154
$266$	0	0
$267$	0	0
$268$	−1.00000	−0.0610847
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	8.00000	0.486864
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	14.0000	0.845771
$275$	4.00000	0.241209
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	10.0000	0.599760
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	−8.00000	−0.476393
$283$	18.0000	1.06999	0.534994	−	0.844856i	$-0.320314\pi$
$283$	18.0000	1.06999	0.534994	+	0.844856i	$0.320314\pi$
$284$	−12.0000	−0.712069
$285$	24.0000	1.42164
$286$	−8.00000	−0.473050
$287$	0	0
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	−4.00000	−0.234888
$291$	16.0000	0.937937
$292$	8.00000	0.468165
$293$	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
$295$	−20.0000	−1.16445
$296$	2.00000	0.116248
$297$	16.0000	0.928414
$298$	14.0000	0.810998
$299$	0	0
$300$	−2.00000	−0.115470
$301$	0	0
$302$	−8.00000	−0.460348
$303$	12.0000	0.689382
$304$	−6.00000	−0.344124
$305$	4.00000	0.229039
$306$	4.00000	0.228665
$307$	−22.0000	−1.25561	−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000	−1.25561	−0.627803	+	0.778372i	$0.716046\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	8.00000	0.454369
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	4.00000	0.226455
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−16.0000	−0.900070
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	−12.0000	−0.672927
$319$	−8.00000	−0.447914
$320$	−2.00000	−0.111803
$321$	−40.0000	−2.23258
$322$	0	0
$323$	−24.0000	−1.33540
$324$	−11.0000	−0.611111
$325$	−2.00000	−0.110940
$326$	−4.00000	−0.221540
$327$	−4.00000	−0.221201
$328$	−8.00000	−0.441726
$329$	0	0
$330$	16.0000	0.880771
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	2.00000	0.109764
$333$	2.00000	0.109599
$334$	−12.0000	−0.656611
$335$	2.00000	0.109272
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−9.00000	−0.489535
$339$	28.0000	1.52075
$340$	−8.00000	−0.433861
$341$	16.0000	0.866449
$342$	−6.00000	−0.324443
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−6.00000	−0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	4.00000	0.214423
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	−8.00000	−0.427008
$352$	−4.00000	−0.213201
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	20.0000	1.06299
$355$	24.0000	1.27379
$356$	0	0
$357$	0	0
$358$	−12.0000	−0.634220
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−2.00000	−0.105409
$361$	17.0000	0.894737
$362$	10.0000	0.525588
$363$	10.0000	0.524864
$364$	0	0
$365$	−16.0000	−0.837478
$366$	−4.00000	−0.209083
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	0	0
$369$	−8.00000	−0.416463
$370$	−4.00000	−0.207950
$371$	0	0
$372$	−8.00000	−0.414781
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−16.0000	−0.827340
$375$	24.0000	1.23935
$376$	−4.00000	−0.206284
$377$	4.00000	0.206010
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	12.0000	0.615587
$381$	−16.0000	−0.819705
$382$	−24.0000	−1.22795
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	14.0000	0.712581
$387$	−4.00000	−0.203331
$388$	8.00000	0.406138
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	−8.00000	−0.405096
$391$	0	0
$392$	0	0
$393$	−12.0000	−0.605320
$394$	2.00000	0.100759
$395$	32.0000	1.61009
$396$	−4.00000	−0.201008
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−2.00000	−0.0997509
$403$	−8.00000	−0.398508
$404$	6.00000	0.298511
$405$	22.0000	1.09319
$406$	0	0
$407$	−8.00000	−0.396545
$408$	8.00000	0.396059
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	16.0000	0.790184
$411$	28.0000	1.38114
$412$	−4.00000	−0.197066
$413$	0	0
$414$	0	0
$415$	−4.00000	−0.196352
$416$	2.00000	0.0980581
$417$	20.0000	0.979404
$418$	24.0000	1.17388
$419$	−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
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−20.0000	−0.973585
$423$	−4.00000	−0.194487
$424$	−6.00000	−0.291386
$425$	−4.00000	−0.194029
$426$	−24.0000	−1.16280
$427$	0	0
$428$	−20.0000	−0.966736
$429$	−16.0000	−0.772487
$430$	8.00000	0.385794
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	−4.00000	−0.192450
$433$	−24.0000	−1.15337	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−24.0000	−1.15337	−0.576683	+	0.816968i	$0.695653\pi$
$434$	0	0
$435$	−8.00000	−0.383571
$436$	−2.00000	−0.0957826
$437$	0	0
$438$	16.0000	0.764510
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	8.00000	0.381385
$441$	0	0
$442$	8.00000	0.380521
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	8.00000	0.378811
$447$	28.0000	1.32435
$448$	0	0
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−1.00000	−0.0471405
$451$	32.0000	1.50682
$452$	14.0000	0.658505
$453$	−16.0000	−0.751746
$454$	10.0000	0.469323
$455$	0	0
$456$	−12.0000	−0.561951
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	2.00000	0.0934539
$459$	−16.0000	−0.746816
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	2.00000	0.0928477
$465$	16.0000	0.741982
$466$	−10.0000	−0.463241
$467$	34.0000	1.57333	0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000	1.57333	0.786666	+	0.617379i	$0.211805\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	8.00000	0.369012
$471$	−28.0000	−1.29017
$472$	10.0000	0.460287
$473$	16.0000	0.735681
$474$	−32.0000	−1.46981
$475$	6.00000	0.275299
$476$	0	0
$477$	−6.00000	−0.274721
$478$	−20.0000	−0.914779
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	−4.00000	−0.182574
$481$	4.00000	0.182384
$482$	20.0000	0.910975
$483$	0	0
$484$	5.00000	0.227273
$485$	−16.0000	−0.726523
$486$	−10.0000	−0.453609
$487$	−28.0000	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$488$	−2.00000	−0.0905357
$489$	−8.00000	−0.361773
$490$	0	0
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	−16.0000	−0.721336
$493$	8.00000	0.360302
$494$	−12.0000	−0.539906
$495$	8.00000	0.359573
$496$	−4.00000	−0.179605
$497$	0	0
$498$	4.00000	0.179244
$499$	12.0000	0.537194	0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000	0.537194	0.268597	+	0.963253i	$0.413440\pi$
$500$	12.0000	0.536656
$501$	−24.0000	−1.07224
$502$	−6.00000	−0.267793
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	0	0
$507$	−18.0000	−0.799408
$508$	−8.00000	−0.354943
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	−16.0000	−0.708492
$511$	0	0
$512$	1.00000	0.0441942
$513$	24.0000	1.05963
$514$	0	0
$515$	8.00000	0.352522
$516$	−8.00000	−0.352180
$517$	16.0000	0.703679
$518$	0	0
$519$	−12.0000	−0.526742
$520$	−4.00000	−0.175412
$521$	8.00000	0.350486	0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000	0.350486	0.175243	+	0.984525i	$0.443929\pi$
$522$	2.00000	0.0875376
$523$	−30.0000	−1.31181	−0.655904	−	0.754844i	$-0.727712\pi$
$523$	−30.0000	−1.31181	−0.655904	+	0.754844i	$0.727712\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	28.0000	1.22086
$527$	−16.0000	−0.696971
$528$	−8.00000	−0.348155
$529$	−23.0000	−1.00000
$530$	12.0000	0.521247
$531$	10.0000	0.433963
$532$	0	0
$533$	−16.0000	−0.693037
$534$	0	0
$535$	40.0000	1.72935
$536$	−1.00000	−0.0431934
$537$	−24.0000	−1.03568
$538$	−6.00000	−0.258678
$539$	0	0
$540$	8.00000	0.344265
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	32.0000	1.37452
$543$	20.0000	0.858282
$544$	4.00000	0.171499
$545$	4.00000	0.171341
$546$	0	0
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	14.0000	0.598050
$549$	−2.00000	−0.0853579
$550$	4.00000	0.170561
$551$	−12.0000	−0.511217
$552$	0	0
$553$	0	0
$554$	−2.00000	−0.0849719
$555$	−8.00000	−0.339581
$556$	10.0000	0.424094
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	−4.00000	−0.169334
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−32.0000	−1.35104
$562$	−10.0000	−0.421825
$563$	42.0000	1.77009	0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000	1.77009	0.885044	+	0.465506i	$0.154128\pi$
$564$	−8.00000	−0.336861
$565$	−28.0000	−1.17797
$566$	18.0000	0.756596
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	24.0000	1.00525
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−8.00000	−0.334497
$573$	−48.0000	−2.00523
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−4.00000	−0.166522	−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000	−0.166522	−0.0832611	+	0.996528i	$0.526534\pi$
$578$	−1.00000	−0.0415945
$579$	28.0000	1.16364
$580$	−4.00000	−0.166091
$581$	0	0
$582$	16.0000	0.663221
$583$	24.0000	0.993978
$584$	8.00000	0.331042
$585$	−4.00000	−0.165380
$586$	6.00000	0.247858
$587$	42.0000	1.73353	0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000	1.73353	0.866763	+	0.498721i	$0.166197\pi$
$588$	0	0
$589$	24.0000	0.988903
$590$	−20.0000	−0.823387
$591$	4.00000	0.164538
$592$	2.00000	0.0821995
$593$	−20.0000	−0.821302	−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000	−0.821302	−0.410651	+	0.911793i	$0.634698\pi$
$594$	16.0000	0.656488
$595$	0	0
$596$	14.0000	0.573462
$597$	8.00000	0.327418
$598$	0	0
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	−2.00000	−0.0816497
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	0	0
$603$	−1.00000	−0.0407231
$604$	−8.00000	−0.325515
$605$	−10.0000	−0.406558
$606$	12.0000	0.487467
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	4.00000	0.161955
$611$	−8.00000	−0.323645
$612$	4.00000	0.161690
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	−22.0000	−0.887848
$615$	32.0000	1.29036
$616$	0	0
$617$	2.00000	0.0805170	0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000	0.0805170	0.0402585	+	0.999189i	$0.487182\pi$
$618$	−8.00000	−0.321807
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	−16.0000	−0.641542
$623$	0	0
$624$	4.00000	0.160128
$625$	−19.0000	−0.760000
$626$	0	0
$627$	48.0000	1.91694
$628$	−14.0000	−0.558661
$629$	8.00000	0.318981
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	−16.0000	−0.636446
$633$	−40.0000	−1.58986
$634$	−2.00000	−0.0794301
$635$	16.0000	0.634941
$636$	−12.0000	−0.475831
$637$	0	0
$638$	−8.00000	−0.316723
$639$	−12.0000	−0.474713
$640$	−2.00000	−0.0790569
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	−40.0000	−1.57867
$643$	−42.0000	−1.65632	−0.828159	−	0.560493i	$-0.810612\pi$
$643$	−42.0000	−1.65632	−0.828159	+	0.560493i	$0.810612\pi$
$644$	0	0
$645$	16.0000	0.629999
$646$	−24.0000	−0.944267
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	−11.0000	−0.432121
$649$	−40.0000	−1.57014
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	−4.00000	−0.156412
$655$	12.0000	0.468879
$656$	−8.00000	−0.312348
$657$	8.00000	0.312110
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	16.0000	0.622799
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−20.0000	−0.777322
$663$	16.0000	0.621389
$664$	2.00000	0.0776151
$665$	0	0
$666$	2.00000	0.0774984
$667$	0	0
$668$	−12.0000	−0.464294
$669$	16.0000	0.618596
$670$	2.00000	0.0772667
$671$	8.00000	0.308837
$672$	0	0
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	2.00000	0.0770371
$675$	4.00000	0.153960
$676$	−9.00000	−0.346154
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	28.0000	1.07533
$679$	0	0
$680$	−8.00000	−0.306786
$681$	20.0000	0.766402
$682$	16.0000	0.612672
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−6.00000	−0.229416
$685$	−28.0000	−1.06983
$686$	0	0
$687$	4.00000	0.152610
$688$	−4.00000	−0.152499
$689$	−12.0000	−0.457164
$690$	0	0
$691$	42.0000	1.59776	0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000	1.59776	0.798878	+	0.601494i	$0.205427\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	−20.0000	−0.758643
$696$	4.00000	0.151620
$697$	−32.0000	−1.21209
$698$	2.00000	0.0757011
$699$	−20.0000	−0.756469
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−8.00000	−0.301941
$703$	−12.0000	−0.452589
$704$	−4.00000	−0.150756
$705$	16.0000	0.602595
$706$	−4.00000	−0.150542
$707$	0	0
$708$	20.0000	0.751646
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	24.0000	0.900704
$711$	−16.0000	−0.600047
$712$	0	0
$713$	0	0
$714$	0	0
$715$	16.0000	0.598366
$716$	−12.0000	−0.448461
$717$	−40.0000	−1.49383
$718$	24.0000	0.895672
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	−2.00000	−0.0745356
$721$	0	0
$722$	17.0000	0.632674
$723$	40.0000	1.48762
$724$	10.0000	0.371647
$725$	−2.00000	−0.0742781
$726$	10.0000	0.371135
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−16.0000	−0.592187
$731$	−16.0000	−0.591781
$732$	−4.00000	−0.147844
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	24.0000	0.885856
$735$	0	0
$736$	0	0
$737$	4.00000	0.147342
$738$	−8.00000	−0.294484
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	−4.00000	−0.147043
$741$	−24.0000	−0.881662
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−8.00000	−0.293294
$745$	−28.0000	−1.02584
$746$	10.0000	0.366126
$747$	2.00000	0.0731762
$748$	−16.0000	−0.585018
$749$	0	0
$750$	24.0000	0.876356
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	−4.00000	−0.145865
$753$	−12.0000	−0.437304
$754$	4.00000	0.145671
$755$	16.0000	0.582300
$756$	0	0
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	12.0000	0.435286
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	−16.0000	−0.579619
$763$	0	0
$764$	−24.0000	−0.868290
$765$	−8.00000	−0.289241
$766$	4.00000	0.144526
$767$	20.0000	0.722158
$768$	2.00000	0.0721688
$769$	16.0000	0.576975	0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000	0.576975	0.288487	+	0.957484i	$0.406848\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	−4.00000	−0.143777
$775$	4.00000	0.143684
$776$	8.00000	0.287183
$777$	0	0
$778$	10.0000	0.358517
$779$	48.0000	1.71978
$780$	−8.00000	−0.286446
$781$	48.0000	1.71758
$782$	0	0
$783$	−8.00000	−0.285897
$784$	0	0
$785$	28.0000	0.999363
$786$	−12.0000	−0.428026
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	2.00000	0.0712470
$789$	56.0000	1.99365
$790$	32.0000	1.13851
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−4.00000	−0.142044
$794$	−14.0000	−0.496841
$795$	24.0000	0.851192
$796$	4.00000	0.141776
$797$	−6.00000	−0.212531	−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000	−0.212531	−0.106265	+	0.994338i	$0.533889\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	18.0000	0.635602
$803$	−32.0000	−1.12926
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	−8.00000	−0.281788
$807$	−12.0000	−0.422420
$808$	6.00000	0.211079
$809$	−26.0000	−0.914111	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000	−0.914111	−0.457056	+	0.889438i	$0.651096\pi$
$810$	22.0000	0.773001
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	0	0
$813$	64.0000	2.24458
$814$	−8.00000	−0.280400
$815$	8.00000	0.280228
$816$	8.00000	0.280056
$817$	24.0000	0.839654
$818$	−32.0000	−1.11885
$819$	0	0
$820$	16.0000	0.558744
$821$	38.0000	1.32621	0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000	1.32621	0.663105	+	0.748527i	$0.269238\pi$
$822$	28.0000	0.976612
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	−4.00000	−0.139347
$825$	8.00000	0.278524
$826$	0	0
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	0	0
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	−4.00000	−0.138842
$831$	−4.00000	−0.138758
$832$	2.00000	0.0693375
$833$	0	0
$834$	20.0000	0.692543
$835$	24.0000	0.830554
$836$	24.0000	0.830057
$837$	16.0000	0.553041
$838$	−26.0000	−0.898155
$839$	−20.0000	−0.690477	−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000	−0.690477	−0.345238	+	0.938515i	$0.612202\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−10.0000	−0.344623
$843$	−20.0000	−0.688837
$844$	−20.0000	−0.688428
$845$	18.0000	0.619219
$846$	−4.00000	−0.137523
$847$	0	0
$848$	−6.00000	−0.206041
$849$	36.0000	1.23552
$850$	−4.00000	−0.137199
$851$	0	0
$852$	−24.0000	−0.822226
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	0	0
$855$	12.0000	0.410391
$856$	−20.0000	−0.683586
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	−16.0000	−0.546231
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	16.0000	0.544962
$863$	−12.0000	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$864$	−4.00000	−0.136083
$865$	12.0000	0.408012
$866$	−24.0000	−0.815553
$867$	−2.00000	−0.0679236
$868$	0	0
$869$	64.0000	2.17105
$870$	−8.00000	−0.271225
$871$	−2.00000	−0.0677674
$872$	−2.00000	−0.0677285
$873$	8.00000	0.270759
$874$	0	0
$875$	0	0
$876$	16.0000	0.540590
$877$	2.00000	0.0675352	0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000	0.0675352	0.0337676	+	0.999430i	$0.489249\pi$
$878$	32.0000	1.07995
$879$	12.0000	0.404750
$880$	8.00000	0.269680
$881$	48.0000	1.61716	0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000	1.61716	0.808581	+	0.588386i	$0.200236\pi$
$882$	0	0
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	8.00000	0.269069
$885$	−40.0000	−1.34459
$886$	−4.00000	−0.134383
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	4.00000	0.134231
$889$	0	0
$890$	0	0
$891$	44.0000	1.47406
$892$	8.00000	0.267860
$893$	24.0000	0.803129
$894$	28.0000	0.936460
$895$	24.0000	0.802232
$896$	0	0
$897$	0	0
$898$	18.0000	0.600668
$899$	−8.00000	−0.266815
$900$	−1.00000	−0.0333333
$901$	−24.0000	−0.799556
$902$	32.0000	1.06548
$903$	0	0
$904$	14.0000	0.465633
$905$	−20.0000	−0.664822
$906$	−16.0000	−0.531564
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	10.0000	0.331862
$909$	6.00000	0.199007
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	−12.0000	−0.397360
$913$	−8.00000	−0.264761
$914$	−26.0000	−0.860004
$915$	8.00000	0.264472
$916$	2.00000	0.0660819
$917$	0	0
$918$	−16.0000	−0.528079
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−44.0000	−1.44985
$922$	18.0000	0.592798
$923$	−24.0000	−0.789970
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	24.0000	0.788689
$927$	−4.00000	−0.131377
$928$	2.00000	0.0656532
$929$	−32.0000	−1.04989	−0.524943	−	0.851137i	$-0.675913\pi$
$929$	−32.0000	−1.04989	−0.524943	+	0.851137i	$0.675913\pi$
$930$	16.0000	0.524661
$931$	0	0
$932$	−10.0000	−0.327561
$933$	−32.0000	−1.04763
$934$	34.0000	1.11251
$935$	32.0000	1.04651
$936$	2.00000	0.0653720
$937$	4.00000	0.130674	0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000	0.130674	0.0653372	+	0.997863i	$0.479188\pi$
$938$	0	0
$939$	0	0
$940$	8.00000	0.260931
$941$	54.0000	1.76035	0.880175	−	0.474650i	$-0.157425\pi$
$941$	54.0000	1.76035	0.880175	+	0.474650i	$0.157425\pi$
$942$	−28.0000	−0.912289
$943$	0	0
$944$	10.0000	0.325472
$945$	0	0
$946$	16.0000	0.520205
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	−32.0000	−1.03931
$949$	16.0000	0.519382
$950$	6.00000	0.194666
$951$	−4.00000	−0.129709
$952$	0	0
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−6.00000	−0.194257
$955$	48.0000	1.55324
$956$	−20.0000	−0.646846
$957$	−16.0000	−0.517207
$958$	−12.0000	−0.387702
$959$	0	0
$960$	−4.00000	−0.129099
$961$	−15.0000	−0.483871
$962$	4.00000	0.128965
$963$	−20.0000	−0.644491
$964$	20.0000	0.644157
$965$	−28.0000	−0.901352
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	5.00000	0.160706
$969$	−48.0000	−1.54198
$970$	−16.0000	−0.513729
$971$	−30.0000	−0.962746	−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000	−0.962746	−0.481373	+	0.876516i	$0.659862\pi$
$972$	−10.0000	−0.320750
$973$	0	0
$974$	−28.0000	−0.897178
$975$	−4.00000	−0.128103
$976$	−2.00000	−0.0640184
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−8.00000	−0.255812
$979$	0	0
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	28.0000	0.893516
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	−16.0000	−0.510061
$985$	−4.00000	−0.127451
$986$	8.00000	0.254772
$987$	0	0
$988$	−12.0000	−0.381771
$989$	0	0
$990$	8.00000	0.254257
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	−4.00000	−0.127000
$993$	−40.0000	−1.26936
$994$	0	0
$995$	−8.00000	−0.253617
$996$	4.00000	0.126745
$997$	6.00000	0.190022	0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000	0.190022	0.0950110	+	0.995476i	$0.469711\pi$
$998$	12.0000	0.379853
$999$	−8.00000	−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6566.2.a.o.1.1	yes	1
7.6	odd	2		6566.2.a.j.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6566.2.a.j.1.1	✓	1	7.6	odd	2
6566.2.a.o.1.1	yes	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6566 = 2 \cdot 7^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6566.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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