LMFDB - Embedded newform 8954.2.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8954,2,Mod(1,8954)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8954.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8954, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8954 = 2 \cdot 11^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8954.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,2,1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$71.4980499699$
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	$\chi$	$=$	8954.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{10} +2.00000 q^{12} +6.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +3.00000 q^{20} -6.00000 q^{23} -2.00000 q^{24} +4.00000 q^{25} -4.00000 q^{27} -6.00000 q^{29} -6.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} +6.00000 q^{38} -3.00000 q^{40} -6.00000 q^{43} +3.00000 q^{45} +6.00000 q^{46} -3.00000 q^{47} +2.00000 q^{48} -7.00000 q^{49} -4.00000 q^{50} -6.00000 q^{51} +6.00000 q^{53} +4.00000 q^{54} -12.0000 q^{57} +6.00000 q^{58} +6.00000 q^{60} +6.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} -3.00000 q^{68} -12.0000 q^{69} -9.00000 q^{71} -1.00000 q^{72} -6.00000 q^{73} +1.00000 q^{74} +8.00000 q^{75} -6.00000 q^{76} -9.00000 q^{79} +3.00000 q^{80} -11.0000 q^{81} -3.00000 q^{83} -9.00000 q^{85} +6.00000 q^{86} -12.0000 q^{87} +6.00000 q^{89} -3.00000 q^{90} -6.00000 q^{92} +8.00000 q^{93} +3.00000 q^{94} -18.0000 q^{95} -2.00000 q^{96} -10.0000 q^{97} +7.00000 q^{98} +O(q^{100})\)

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
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	−2.00000	−0.816497
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.00000	−0.948683
$11$	0	0
$11$	0	0
$12$	2.00000	0.577350
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	6.00000	1.54919
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−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	$0.741620\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	−2.00000	−0.408248
$25$	4.00000	0.800000
$26$	0	0
$27$	−4.00000	−0.769800
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−6.00000	−1.09545
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	6.00000	0.973329
$39$	0	0
$40$	−3.00000	−0.474342
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	3.00000	0.447214
$46$	6.00000	0.884652
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	2.00000	0.288675
$49$	−7.00000	−1.00000
$50$	−4.00000	−0.565685
$51$	−6.00000	−0.840168
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	0	0
$57$	−12.0000	−1.58944
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	6.00000	0.774597
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−3.00000	−0.363803
$69$	−12.0000	−1.44463
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.00000	0.116248
$75$	8.00000	0.923760
$76$	−6.00000	−0.688247
$77$	0	0
$78$	0	0
$79$	−9.00000	−1.01258	−0.506290	−	0.862364i	$-0.668983\pi$
$79$	−9.00000	−1.01258	−0.506290	+	0.862364i	$0.668983\pi$
$80$	3.00000	0.335410
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	6.00000	0.646997
$87$	−12.0000	−1.28654
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−3.00000	−0.316228
$91$	0	0
$92$	−6.00000	−0.625543
$93$	8.00000	0.829561
$94$	3.00000	0.309426
$95$	−18.0000	−1.84676
$96$	−2.00000	−0.204124
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	4.00000	0.400000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	6.00000	0.594089
$103$	−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
$106$	−6.00000	−0.582772
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	−4.00000	−0.384900
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	12.0000	1.12390
$115$	−18.0000	−1.67851
$116$	−6.00000	−0.557086
$117$	0	0
$118$	0	0
$119$	0	0
$120$	−6.00000	−0.547723
$121$	0	0
$122$	−6.00000	−0.543214
$123$	0	0
$124$	4.00000	0.359211
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0000	−1.05654
$130$	0	0
$131$	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
$134$	−4.00000	−0.345547
$135$	−12.0000	−1.03280
$136$	3.00000	0.257248
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	12.0000	1.02151
$139$	−15.0000	−1.27228	−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000	−1.27228	−0.636142	+	0.771572i	$0.719471\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	9.00000	0.755263
$143$	0	0
$144$	1.00000	0.0833333
$145$	−18.0000	−1.49482
$146$	6.00000	0.496564
$147$	−14.0000	−1.15470
$148$	−1.00000	−0.0821995
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	−8.00000	−0.653197
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	6.00000	0.486664
$153$	−3.00000	−0.242536
$154$	0	0
$155$	12.0000	0.963863
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	9.00000	0.716002
$159$	12.0000	0.951662
$160$	−3.00000	−0.237171
$161$	0	0
$162$	11.0000	0.864242
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	0	0
$165$	0	0
$166$	3.00000	0.232845
$167$	−9.00000	−0.696441	−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000	−0.696441	−0.348220	+	0.937413i	$0.613214\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	9.00000	0.690268
$171$	−6.00000	−0.458831
$172$	−6.00000	−0.457496
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	12.0000	0.909718
$175$	0	0
$176$	0	0
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	3.00000	0.223607
$181$	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
$183$	12.0000	0.887066
$184$	6.00000	0.442326
$185$	−3.00000	−0.220564
$186$	−8.00000	−0.586588
$187$	0	0
$188$	−3.00000	−0.218797
$189$	0	0
$190$	18.0000	1.30586
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	2.00000	0.144338
$193$	−3.00000	−0.215945	−0.107972	−	0.994154i	$-0.534436\pi$
$193$	−3.00000	−0.215945	−0.107972	+	0.994154i	$0.534436\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	−7.00000	−0.500000
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	−4.00000	−0.282843
$201$	8.00000	0.564276
$202$	−3.00000	−0.211079
$203$	0	0
$204$	−6.00000	−0.420084
$205$	0	0
$206$	4.00000	0.278693
$207$	−6.00000	−0.417029
$208$	0	0
$209$	0	0
$210$	0	0
$211$	27.0000	1.85876	0.929378	−	0.369129i	$-0.120344\pi$
$211$	27.0000	1.85876	0.929378	+	0.369129i	$0.120344\pi$
$212$	6.00000	0.412082
$213$	−18.0000	−1.23334
$214$	−15.0000	−1.02538
$215$	−18.0000	−1.22759
$216$	4.00000	0.272166
$217$	0	0
$218$	−6.00000	−0.406371
$219$	−12.0000	−0.810885
$220$	0	0
$221$	0	0
$222$	2.00000	0.134231
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	0	0
$225$	4.00000	0.266667
$226$	0	0
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	−12.0000	−0.794719
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	18.0000	1.18688
$231$	0	0
$232$	6.00000	0.393919
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	0	0
$235$	−9.00000	−0.587095
$236$	0	0
$237$	−18.0000	−1.16923
$238$	0	0
$239$	9.00000	0.582162	0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000	0.582162	0.291081	+	0.956698i	$0.405985\pi$
$240$	6.00000	0.387298
$241$	−9.00000	−0.579741	−0.289870	−	0.957066i	$-0.593612\pi$
$241$	−9.00000	−0.579741	−0.289870	+	0.957066i	$0.593612\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	6.00000	0.384111
$245$	−21.0000	−1.34164
$246$	0	0
$247$	0	0
$248$	−4.00000	−0.254000
$249$	−6.00000	−0.380235
$250$	3.00000	0.189737
$251$	3.00000	0.189358	0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000	0.189358	0.0946792	+	0.995508i	$0.469817\pi$
$252$	0	0
$253$	0	0
$254$	6.00000	0.376473
$255$	−18.0000	−1.12720
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	12.0000	0.747087
$259$	0	0
$260$	0	0
$261$	−6.00000	−0.371391
$262$	−18.0000	−1.11204
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	18.0000	1.10573
$266$	0	0
$267$	12.0000	0.734388
$268$	4.00000	0.244339
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	12.0000	0.730297
$271$	−18.0000	−1.09342	−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000	−1.09342	−0.546711	+	0.837321i	$0.684120\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	−9.00000	−0.543710
$275$	0	0
$276$	−12.0000	−0.722315
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	15.0000	0.899640
$279$	4.00000	0.239474
$280$	0	0
$281$	−9.00000	−0.536895	−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$282$	6.00000	0.357295
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−9.00000	−0.534052
$285$	−36.0000	−2.13246
$286$	0	0
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	18.0000	1.05700
$291$	−20.0000	−1.17242
$292$	−6.00000	−0.351123
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	14.0000	0.816497
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	9.00000	0.521356
$299$	0	0
$300$	8.00000	0.461880
$301$	0	0
$302$	0	0
$303$	6.00000	0.344691
$304$	−6.00000	−0.344124
$305$	18.0000	1.03068
$306$	3.00000	0.171499
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−12.0000	−0.681554
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	0	0
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−9.00000	−0.506290
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	−12.0000	−0.672927
$319$	0	0
$320$	3.00000	0.167705
$321$	30.0000	1.67444
$322$	0	0
$323$	18.0000	1.00155
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−11.0000	−0.609234
$327$	12.0000	0.663602
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−1.00000	−0.0549650	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000	−0.0549650	−0.0274825	+	0.999622i	$0.508749\pi$
$332$	−3.00000	−0.164646
$333$	−1.00000	−0.0547997
$334$	9.00000	0.492458
$335$	12.0000	0.655630
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	13.0000	0.707107
$339$	0	0
$340$	−9.00000	−0.488094
$341$	0	0
$342$	6.00000	0.324443
$343$	0	0
$344$	6.00000	0.323498
$345$	−36.0000	−1.93817
$346$	6.00000	0.322562
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−12.0000	−0.643268
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−27.0000	−1.43301
$356$	6.00000	0.317999
$357$	0	0
$358$	3.00000	0.158555
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	−3.00000	−0.158114
$361$	17.0000	0.894737
$362$	−20.0000	−1.05118
$363$	0	0
$364$	0	0
$365$	−18.0000	−0.942163
$366$	−12.0000	−0.627250
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	3.00000	0.155963
$371$	0	0
$372$	8.00000	0.414781
$373$	−15.0000	−0.776671	−0.388335	−	0.921518i	$-0.626950\pi$
$373$	−15.0000	−0.776671	−0.388335	+	0.921518i	$0.626950\pi$
$374$	0	0
$375$	−6.00000	−0.309839
$376$	3.00000	0.154713
$377$	0	0
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−18.0000	−0.923381
$381$	−12.0000	−0.614779
$382$	12.0000	0.613973
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	3.00000	0.152696
$387$	−6.00000	−0.304997
$388$	−10.0000	−0.507673
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	7.00000	0.353553
$393$	36.0000	1.81596
$394$	−15.0000	−0.755689
$395$	−27.0000	−1.35852
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	4.00000	0.200000
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	−8.00000	−0.399004
$403$	0	0
$404$	3.00000	0.149256
$405$	−33.0000	−1.63978
$406$	0	0
$407$	0	0
$408$	6.00000	0.297044
$409$	−18.0000	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$410$	0	0
$411$	18.0000	0.887875
$412$	−4.00000	−0.197066
$413$	0	0
$414$	6.00000	0.294884
$415$	−9.00000	−0.441793
$416$	0	0
$417$	−30.0000	−1.46911
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	−27.0000	−1.31434
$423$	−3.00000	−0.145865
$424$	−6.00000	−0.291386
$425$	−12.0000	−0.582086
$426$	18.0000	0.872103
$427$	0	0
$428$	15.0000	0.725052
$429$	0	0
$430$	18.0000	0.868037
$431$	3.00000	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$432$	−4.00000	−0.192450
$433$	−7.00000	−0.336399	−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000	−0.336399	−0.168199	+	0.985753i	$0.553795\pi$
$434$	0	0
$435$	−36.0000	−1.72607
$436$	6.00000	0.287348
$437$	36.0000	1.72211
$438$	12.0000	0.573382
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	0	0
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	−2.00000	−0.0949158
$445$	18.0000	0.853282
$446$	1.00000	0.0473514
$447$	−18.0000	−0.851371
$448$	0	0
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	−4.00000	−0.188562
$451$	0	0
$452$	0	0
$453$	0	0
$454$	24.0000	1.12638
$455$	0	0
$456$	12.0000	0.561951
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	−22.0000	−1.02799
$459$	12.0000	0.560112
$460$	−18.0000	−0.839254
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−6.00000	−0.278543
$465$	24.0000	1.11297
$466$	−24.0000	−1.11178
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	0	0
$469$	0	0
$470$	9.00000	0.415139
$471$	8.00000	0.368621
$472$	0	0
$473$	0	0
$474$	18.0000	0.826767
$475$	−24.0000	−1.10120
$476$	0	0
$477$	6.00000	0.274721
$478$	−9.00000	−0.411650
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	−6.00000	−0.273861
$481$	0	0
$482$	9.00000	0.409939
$483$	0	0
$484$	0	0
$485$	−30.0000	−1.36223
$486$	10.0000	0.453609
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	−6.00000	−0.271607
$489$	22.0000	0.994874
$490$	21.0000	0.948683
$491$	21.0000	0.947717	0.473858	−	0.880601i	$-0.342861\pi$
$491$	21.0000	0.947717	0.473858	+	0.880601i	$0.342861\pi$
$492$	0	0
$493$	18.0000	0.810679
$494$	0	0
$495$	0	0
$496$	4.00000	0.179605
$497$	0	0
$498$	6.00000	0.268866
$499$	13.0000	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$499$	13.0000	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$500$	−3.00000	−0.134164
$501$	−18.0000	−0.804181
$502$	−3.00000	−0.133897
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	0	0
$505$	9.00000	0.400495
$506$	0	0
$507$	−26.0000	−1.15470
$508$	−6.00000	−0.266207
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	18.0000	0.797053
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	24.0000	1.05963
$514$	18.0000	0.793946
$515$	−12.0000	−0.528783
$516$	−12.0000	−0.528271
$517$	0	0
$518$	0	0
$519$	−12.0000	−0.526742
$520$	0	0
$521$	−9.00000	−0.394297	−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000	−0.394297	−0.197149	+	0.980374i	$0.563168\pi$
$522$	6.00000	0.262613
$523$	−18.0000	−0.787085	−0.393543	−	0.919306i	$-0.628751\pi$
$523$	−18.0000	−0.787085	−0.393543	+	0.919306i	$0.628751\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	6.00000	0.261612
$527$	−12.0000	−0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	−18.0000	−0.781870
$531$	0	0
$532$	0	0
$533$	0	0
$534$	−12.0000	−0.519291
$535$	45.0000	1.94552
$536$	−4.00000	−0.172774
$537$	−6.00000	−0.258919
$538$	6.00000	0.258678
$539$	0	0
$540$	−12.0000	−0.516398
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	18.0000	0.773166
$543$	40.0000	1.71656
$544$	3.00000	0.128624
$545$	18.0000	0.771035
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	9.00000	0.384461
$549$	6.00000	0.256074
$550$	0	0
$551$	36.0000	1.53365
$552$	12.0000	0.510754
$553$	0	0
$554$	18.0000	0.764747
$555$	−6.00000	−0.254686
$556$	−15.0000	−0.636142
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−4.00000	−0.169334
$559$	0	0
$560$	0	0
$561$	0	0
$562$	9.00000	0.379642
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	−24.0000	−1.00880
$567$	0	0
$568$	9.00000	0.377632
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	36.0000	1.50787
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	0	0
$573$	−24.0000	−1.00261
$574$	0	0
$575$	−24.0000	−1.00087
$576$	1.00000	0.0416667
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	8.00000	0.332756
$579$	−6.00000	−0.249351
$580$	−18.0000	−0.747409
$581$	0	0
$582$	20.0000	0.829027
$583$	0	0
$584$	6.00000	0.248282
$585$	0	0
$586$	21.0000	0.867502
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	−14.0000	−0.577350
$589$	−24.0000	−0.988903
$590$	0	0
$591$	30.0000	1.23404
$592$	−1.00000	−0.0410997
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	0	0
$595$	0	0
$596$	−9.00000	−0.368654
$597$	−40.0000	−1.63709
$598$	0	0
$599$	9.00000	0.367730	0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000	0.367730	0.183865	+	0.982952i	$0.441139\pi$
$600$	−8.00000	−0.326599
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	0	0
$605$	0	0
$606$	−6.00000	−0.243733
$607$	12.0000	0.487065	0.243532	−	0.969893i	$-0.421694\pi$
$607$	12.0000	0.487065	0.243532	+	0.969893i	$0.421694\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	−18.0000	−0.728799
$611$	0	0
$612$	−3.00000	−0.121268
$613$	30.0000	1.21169	0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000	1.21169	0.605844	+	0.795583i	$0.292835\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	0	0
$617$	3.00000	0.120775	0.0603877	−	0.998175i	$-0.480766\pi$
$617$	3.00000	0.120775	0.0603877	+	0.998175i	$0.480766\pi$
$618$	8.00000	0.321807
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	12.0000	0.481932
$621$	24.0000	0.963087
$622$	30.0000	1.20289
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	−28.0000	−1.11911
$627$	0	0
$628$	4.00000	0.159617
$629$	3.00000	0.119618
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	9.00000	0.358001
$633$	54.0000	2.14631
$634$	−12.0000	−0.476581
$635$	−18.0000	−0.714308
$636$	12.0000	0.475831
$637$	0	0
$638$	0	0
$639$	−9.00000	−0.356034
$640$	−3.00000	−0.118585
$641$	33.0000	1.30342	0.651711	−	0.758468i	$-0.274052\pi$
$641$	33.0000	1.30342	0.651711	+	0.758468i	$0.274052\pi$
$642$	−30.0000	−1.18401
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	0	0
$645$	−36.0000	−1.41750
$646$	−18.0000	−0.708201
$647$	−30.0000	−1.17942	−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000	−1.17942	−0.589711	+	0.807614i	$0.700758\pi$
$648$	11.0000	0.432121
$649$	0	0
$650$	0	0
$651$	0	0
$652$	11.0000	0.430793
$653$	27.0000	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	−12.0000	−0.469237
$655$	54.0000	2.10995
$656$	0	0
$657$	−6.00000	−0.234082
$658$	0	0
$659$	−9.00000	−0.350590	−0.175295	−	0.984516i	$-0.556088\pi$
$659$	−9.00000	−0.350590	−0.175295	+	0.984516i	$0.556088\pi$
$660$	0	0
$661$	−41.0000	−1.59472	−0.797358	−	0.603507i	$-0.793769\pi$
$661$	−41.0000	−1.59472	−0.797358	+	0.603507i	$0.793769\pi$
$662$	1.00000	0.0388661
$663$	0	0
$664$	3.00000	0.116423
$665$	0	0
$666$	1.00000	0.0387492
$667$	36.0000	1.39393
$668$	−9.00000	−0.348220
$669$	−2.00000	−0.0773245
$670$	−12.0000	−0.463600
$671$	0	0
$672$	0	0
$673$	−24.0000	−0.925132	−0.462566	−	0.886585i	$-0.653071\pi$
$673$	−24.0000	−0.925132	−0.462566	+	0.886585i	$0.653071\pi$
$674$	−18.0000	−0.693334
$675$	−16.0000	−0.615840
$676$	−13.0000	−0.500000
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	0	0
$680$	9.00000	0.345134
$681$	−48.0000	−1.83936
$682$	0	0
$683$	33.0000	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$684$	−6.00000	−0.229416
$685$	27.0000	1.03162
$686$	0	0
$687$	44.0000	1.67870
$688$	−6.00000	−0.228748
$689$	0	0
$690$	36.0000	1.37050
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	0	0
$695$	−45.0000	−1.70695
$696$	12.0000	0.454859
$697$	0	0
$698$	−30.0000	−1.13552
$699$	48.0000	1.81553
$700$	0	0
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	0	0
$703$	6.00000	0.226294
$704$	0	0
$705$	−18.0000	−0.677919
$706$	6.00000	0.225813
$707$	0	0
$708$	0	0
$709$	19.0000	0.713560	0.356780	−	0.934188i	$-0.383875\pi$
$709$	19.0000	0.713560	0.356780	+	0.934188i	$0.383875\pi$
$710$	27.0000	1.01329
$711$	−9.00000	−0.337526
$712$	−6.00000	−0.224860
$713$	−24.0000	−0.898807
$714$	0	0
$715$	0	0
$716$	−3.00000	−0.112115
$717$	18.0000	0.672222
$718$	6.00000	0.223918
$719$	39.0000	1.45445	0.727227	−	0.686397i	$-0.240809\pi$
$719$	39.0000	1.45445	0.727227	+	0.686397i	$0.240809\pi$
$720$	3.00000	0.111803
$721$	0	0
$722$	−17.0000	−0.632674
$723$	−18.0000	−0.669427
$724$	20.0000	0.743294
$725$	−24.0000	−0.891338
$726$	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
$729$	13.0000	0.481481
$730$	18.0000	0.666210
$731$	18.0000	0.665754
$732$	12.0000	0.443533
$733$	−51.0000	−1.88373	−0.941864	−	0.335994i	$-0.890928\pi$
$733$	−51.0000	−1.88373	−0.941864	+	0.335994i	$0.890928\pi$
$734$	−17.0000	−0.627481
$735$	−42.0000	−1.54919
$736$	6.00000	0.221163
$737$	0	0
$738$	0	0
$739$	−45.0000	−1.65535	−0.827676	−	0.561206i	$-0.810337\pi$
$739$	−45.0000	−1.65535	−0.827676	+	0.561206i	$0.810337\pi$
$740$	−3.00000	−0.110282
$741$	0	0
$742$	0	0
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	−8.00000	−0.293294
$745$	−27.0000	−0.989203
$746$	15.0000	0.549189
$747$	−3.00000	−0.109764
$748$	0	0
$749$	0	0
$750$	6.00000	0.219089
$751$	−23.0000	−0.839282	−0.419641	−	0.907690i	$-0.637844\pi$
$751$	−23.0000	−0.839282	−0.419641	+	0.907690i	$0.637844\pi$
$752$	−3.00000	−0.109399
$753$	6.00000	0.218652
$754$	0	0
$755$	0	0
$756$	0	0
$757$	43.0000	1.56286	0.781431	−	0.623992i	$-0.214490\pi$
$757$	43.0000	1.56286	0.781431	+	0.623992i	$0.214490\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	18.0000	0.652929
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	12.0000	0.434714
$763$	0	0
$764$	−12.0000	−0.434145
$765$	−9.00000	−0.325396
$766$	−6.00000	−0.216789
$767$	0	0
$768$	2.00000	0.0721688
$769$	−39.0000	−1.40638	−0.703188	−	0.711004i	$-0.748241\pi$
$769$	−39.0000	−1.40638	−0.703188	+	0.711004i	$0.748241\pi$
$770$	0	0
$771$	−36.0000	−1.29651
$772$	−3.00000	−0.107972
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	6.00000	0.215666
$775$	16.0000	0.574737
$776$	10.0000	0.358979
$777$	0	0
$778$	18.0000	0.645331
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−18.0000	−0.643679
$783$	24.0000	0.857690
$784$	−7.00000	−0.250000
$785$	12.0000	0.428298
$786$	−36.0000	−1.28408
$787$	27.0000	0.962446	0.481223	−	0.876598i	$-0.340193\pi$
$787$	27.0000	0.962446	0.481223	+	0.876598i	$0.340193\pi$
$788$	15.0000	0.534353
$789$	−12.0000	−0.427211
$790$	27.0000	0.960617
$791$	0	0
$792$	0	0
$793$	0	0
$794$	−2.00000	−0.0709773
$795$	36.0000	1.27679
$796$	−20.0000	−0.708881
$797$	−45.0000	−1.59398	−0.796991	−	0.603991i	$-0.793576\pi$
$797$	−45.0000	−1.59398	−0.796991	+	0.603991i	$0.793576\pi$
$798$	0	0
$799$	9.00000	0.318397
$800$	−4.00000	−0.141421
$801$	6.00000	0.212000
$802$	−12.0000	−0.423735
$803$	0	0
$804$	8.00000	0.282138
$805$	0	0
$806$	0	0
$807$	−12.0000	−0.422420
$808$	−3.00000	−0.105540
$809$	−27.0000	−0.949269	−0.474635	−	0.880183i	$-0.657420\pi$
$809$	−27.0000	−0.949269	−0.474635	+	0.880183i	$0.657420\pi$
$810$	33.0000	1.15950
$811$	−27.0000	−0.948098	−0.474049	−	0.880498i	$-0.657208\pi$
$811$	−27.0000	−0.948098	−0.474049	+	0.880498i	$0.657208\pi$
$812$	0	0
$813$	−36.0000	−1.26258
$814$	0	0
$815$	33.0000	1.15594
$816$	−6.00000	−0.210042
$817$	36.0000	1.25948
$818$	18.0000	0.629355
$819$	0	0
$820$	0	0
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	−18.0000	−0.627822
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	−6.00000	−0.208514
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	9.00000	0.312395
$831$	−36.0000	−1.24883
$832$	0	0
$833$	21.0000	0.727607
$834$	30.0000	1.03882
$835$	−27.0000	−0.934374
$836$	0	0
$837$	−16.0000	−0.553041
$838$	−24.0000	−0.829066
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	−18.0000	−0.619953
$844$	27.0000	0.929378
$845$	−39.0000	−1.34164
$846$	3.00000	0.103142
$847$	0	0
$848$	6.00000	0.206041
$849$	48.0000	1.64736
$850$	12.0000	0.411597
$851$	6.00000	0.205677
$852$	−18.0000	−0.616670
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	0	0
$855$	−18.0000	−0.615587
$856$	−15.0000	−0.512689
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	−31.0000	−1.05771	−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000	−1.05771	−0.528853	+	0.848713i	$0.677378\pi$
$860$	−18.0000	−0.613795
$861$	0	0
$862$	−3.00000	−0.102180
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	4.00000	0.136083
$865$	−18.0000	−0.612018
$866$	7.00000	0.237870
$867$	−16.0000	−0.543388
$868$	0	0
$869$	0	0
$870$	36.0000	1.22051
$871$	0	0
$872$	−6.00000	−0.203186
$873$	−10.0000	−0.338449
$874$	−36.0000	−1.21772
$875$	0	0
$876$	−12.0000	−0.405442
$877$	−9.00000	−0.303908	−0.151954	−	0.988388i	$-0.548557\pi$
$877$	−9.00000	−0.303908	−0.151954	+	0.988388i	$0.548557\pi$
$878$	−24.0000	−0.809961
$879$	−42.0000	−1.41662
$880$	0	0
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	7.00000	0.235702
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	0	0
$886$	36.0000	1.20944
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	2.00000	0.0671156
$889$	0	0
$890$	−18.0000	−0.603361
$891$	0	0
$892$	−1.00000	−0.0334825
$893$	18.0000	0.602347
$894$	18.0000	0.602010
$895$	−9.00000	−0.300837
$896$	0	0
$897$	0	0
$898$	18.0000	0.600668
$899$	−24.0000	−0.800445
$900$	4.00000	0.133333
$901$	−18.0000	−0.599667
$902$	0	0
$903$	0	0
$904$	0	0
$905$	60.0000	1.99447
$906$	0	0
$907$	−19.0000	−0.630885	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	−19.0000	−0.630885	−0.315442	+	0.948945i	$0.602153\pi$
$908$	−24.0000	−0.796468
$909$	3.00000	0.0995037
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	−12.0000	−0.397360
$913$	0	0
$914$	−18.0000	−0.595387
$915$	36.0000	1.19012
$916$	22.0000	0.726900
$917$	0	0
$918$	−12.0000	−0.396059
$919$	48.0000	1.58337	0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000	1.58337	0.791687	+	0.610927i	$0.209203\pi$
$920$	18.0000	0.593442
$921$	24.0000	0.790827
$922$	−30.0000	−0.987997
$923$	0	0
$924$	0	0
$925$	−4.00000	−0.131519
$926$	4.00000	0.131448
$927$	−4.00000	−0.131377
$928$	6.00000	0.196960
$929$	3.00000	0.0984268	0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000	0.0984268	0.0492134	+	0.998788i	$0.484329\pi$
$930$	−24.0000	−0.786991
$931$	42.0000	1.37649
$932$	24.0000	0.786146
$933$	−60.0000	−1.96431
$934$	−21.0000	−0.687141
$935$	0	0
$936$	0	0
$937$	12.0000	0.392023	0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000	0.392023	0.196011	+	0.980602i	$0.437201\pi$
$938$	0	0
$939$	56.0000	1.82749
$940$	−9.00000	−0.293548
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	−8.00000	−0.260654
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−18.0000	−0.584613
$949$	0	0
$950$	24.0000	0.778663
$951$	24.0000	0.778253
$952$	0	0
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	−6.00000	−0.194257
$955$	−36.0000	−1.16493
$956$	9.00000	0.291081
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	6.00000	0.193649
$961$	−15.0000	−0.483871
$962$	0	0
$963$	15.0000	0.483368
$964$	−9.00000	−0.289870
$965$	−9.00000	−0.289720
$966$	0	0
$967$	−51.0000	−1.64005	−0.820025	−	0.572328i	$-0.806040\pi$
$967$	−51.0000	−1.64005	−0.820025	+	0.572328i	$0.806040\pi$
$968$	0	0
$969$	36.0000	1.15649
$970$	30.0000	0.963242
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	−10.0000	−0.320750
$973$	0	0
$974$	20.0000	0.640841
$975$	0	0
$976$	6.00000	0.192055
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	−22.0000	−0.703482
$979$	0	0
$980$	−21.0000	−0.670820
$981$	6.00000	0.191565
$982$	−21.0000	−0.670137
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	0	0
$985$	45.0000	1.43382
$986$	−18.0000	−0.573237
$987$	0	0
$988$	0	0
$989$	36.0000	1.14473
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	−4.00000	−0.127000
$993$	−2.00000	−0.0634681
$994$	0	0
$995$	−60.0000	−1.90213
$996$	−6.00000	−0.190117
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	−13.0000	−0.411508
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8954.2.a.d.1.1	✓	1
11.10	odd	2		8954.2.a.h.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8954.2.a.d.1.1	✓	1	1.1	even	1	trivial
8954.2.a.h.1.1	yes	1	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8954 = 2 \cdot 11^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8954.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more