LMFDB - Embedded newform 4650.2.a.t.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4650,2,Mod(1,4650)] 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("4650.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,1,1,0,-1,2,-1,1,0,0,1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.1304369399$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 930)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4650.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{21} -1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +8.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} -4.00000 q^{39} +10.0000 q^{41} -2.00000 q^{42} -8.00000 q^{43} +4.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -6.00000 q^{51} -4.00000 q^{52} +14.0000 q^{53} -1.00000 q^{54} -2.00000 q^{56} -8.00000 q^{58} +14.0000 q^{59} -6.00000 q^{61} +1.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +10.0000 q^{67} -6.00000 q^{68} +6.00000 q^{71} -1.00000 q^{72} +8.00000 q^{73} +4.00000 q^{74} +4.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} -10.0000 q^{82} +12.0000 q^{83} +2.00000 q^{84} +8.00000 q^{86} +8.00000 q^{87} +16.0000 q^{89} -8.00000 q^{91} -1.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} +10.0000 q^{97} +3.00000 q^{98} +O(q^{100})$

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	0	0
$39$	−4.00000	−0.640513
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−2.00000	−0.308607
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−6.00000	−0.840168
$52$	−4.00000	−0.554700
$53$	14.0000	1.92305	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000	1.92305	0.961524	+	0.274721i	$0.0885855\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	0	0
$58$	−8.00000	−1.05045
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	1.00000	0.127000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	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
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−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	$0.344915\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	0	0
$77$	0	0
$78$	4.00000	0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	8.00000	0.862662
$87$	8.00000	0.857690
$88$	0	0
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	0	0
$93$	−1.00000	−0.103695
$94$	−4.00000	−0.412568
$95$	0	0
$96$	−1.00000	−0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	6.00000	0.594089
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−14.0000	−1.35980
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	1.00000	0.0962250
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	2.00000	0.188982
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	0	0
$116$	8.00000	0.742781
$117$	−4.00000	−0.369800
$118$	−14.0000	−1.28880
$119$	−12.0000	−1.10004
$120$	0	0
$121$	−11.0000	−1.00000
$122$	6.00000	0.543214
$123$	10.0000	0.901670
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	−2.00000	−0.178174
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	0	0
$134$	−10.0000	−0.863868
$135$	0	0
$136$	6.00000	0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−6.00000	−0.503509
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	−8.00000	−0.662085
$147$	−3.00000	−0.247436
$148$	−4.00000	−0.328798
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	−8.00000	−0.636446
$159$	14.0000	1.11027
$160$	0	0
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−6.00000	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−12.0000	−0.931381
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−2.00000	−0.154303
$169$	3.00000	0.230769
$170$	0	0
$171$	0	0
$172$	−8.00000	−0.609994
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−8.00000	−0.606478
$175$	0	0
$176$	0	0
$177$	14.0000	1.05230
$178$	−16.0000	−1.19925
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	8.00000	0.592999
$183$	−6.00000	−0.443533
$184$	0	0
$185$	0	0
$186$	1.00000	0.0733236
$187$	0	0
$188$	4.00000	0.291730
$189$	2.00000	0.145479
$190$	0	0
$191$	−14.0000	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$192$	1.00000	0.0721688
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−3.00000	−0.214286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	−24.0000	−1.70131	−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000	−1.70131	−0.850657	+	0.525720i	$0.823796\pi$
$200$	0	0
$201$	10.0000	0.705346
$202$	6.00000	0.422159
$203$	16.0000	1.12298
$204$	−6.00000	−0.420084
$205$	0	0
$206$	−6.00000	−0.418040
$207$	0	0
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	14.0000	0.961524
$213$	6.00000	0.411113
$214$	8.00000	0.546869
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−2.00000	−0.135769
$218$	−18.0000	−1.21911
$219$	8.00000	0.540590
$220$	0	0
$221$	24.0000	1.61441
$222$	4.00000	0.268462
$223$	20.0000	1.33930	0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000	1.33930	0.669650	+	0.742677i	$0.266444\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	14.0000	0.931266
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−8.00000	−0.525226
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	14.0000	0.911322
$237$	8.00000	0.519656
$238$	12.0000	0.777844
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	11.0000	0.707107
$243$	1.00000	0.0641500
$244$	−6.00000	−0.384111
$245$	0	0
$246$	−10.0000	−0.637577
$247$	0	0
$248$	1.00000	0.0635001
$249$	12.0000	0.760469
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	8.00000	0.498058
$259$	−8.00000	−0.497096
$260$	0	0
$261$	8.00000	0.495188
$262$	18.0000	1.11204
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	16.0000	0.979184
$268$	10.0000	0.610847
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−6.00000	−0.363803
$273$	−8.00000	−0.484182
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	−4.00000	−0.239904
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	−4.00000	−0.238197
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	0	0
$287$	20.0000	1.18056
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	10.0000	0.586210
$292$	8.00000	0.468165
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	4.00000	0.232495
$297$	0	0
$298$	−18.0000	−1.04271
$299$	0	0
$300$	0	0
$301$	−16.0000	−0.922225
$302$	8.00000	0.460348
$303$	−6.00000	−0.344691
$304$	0	0
$305$	0	0
$306$	6.00000	0.342997
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	0	0
$309$	6.00000	0.341328
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	4.00000	0.226455
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	8.00000	0.450035
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	−14.0000	−0.785081
$319$	0	0
$320$	0	0
$321$	−8.00000	−0.446516
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	0	0
$326$	6.00000	0.332309
$327$	18.0000	0.995402
$328$	−10.0000	−0.552158
$329$	8.00000	0.441054
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	12.0000	0.658586
$333$	−4.00000	−0.219199
$334$	−8.00000	−0.437741
$335$	0	0
$336$	2.00000	0.109109
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	−3.00000	−0.163178
$339$	−14.0000	−0.760376
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−20.0000	−1.07990
$344$	8.00000	0.431331
$345$	0	0
$346$	10.0000	0.537603
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	8.00000	0.428845
$349$	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
$351$	−4.00000	−0.213504
$352$	0	0
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	−14.0000	−0.744092
$355$	0	0
$356$	16.0000	0.847998
$357$	−12.0000	−0.635107
$358$	0	0
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	6.00000	0.315353
$363$	−11.0000	−0.577350
$364$	−8.00000	−0.419314
$365$	0	0
$366$	6.00000	0.313625
$367$	36.0000	1.87918	0.939592	−	0.342296i	$-0.111204\pi$
$367$	36.0000	1.87918	0.939592	+	0.342296i	$0.111204\pi$
$368$	0	0
$369$	10.0000	0.520579
$370$	0	0
$371$	28.0000	1.45369
$372$	−1.00000	−0.0518476
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	0	0
$376$	−4.00000	−0.206284
$377$	−32.0000	−1.64808
$378$	−2.00000	−0.102869
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	0	0
$381$	0	0
$382$	14.0000	0.716302
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−2.00000	−0.101797
$387$	−8.00000	−0.406663
$388$	10.0000	0.507673
$389$	−32.0000	−1.62246	−0.811232	−	0.584724i	$-0.801203\pi$
$389$	−32.0000	−1.62246	−0.811232	+	0.584724i	$0.801203\pi$
$390$	0	0
$391$	0	0
$392$	3.00000	0.151523
$393$	−18.0000	−0.907980
$394$	−2.00000	−0.100759
$395$	0	0
$396$	0	0
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	24.0000	1.20301
$399$	0	0
$400$	0	0
$401$	4.00000	0.199750	0.0998752	−	0.995000i	$-0.468156\pi$
$401$	4.00000	0.199750	0.0998752	+	0.995000i	$0.468156\pi$
$402$	−10.0000	−0.498755
$403$	4.00000	0.199254
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−16.0000	−0.794067
$407$	0	0
$408$	6.00000	0.297044
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	6.00000	0.295599
$413$	28.0000	1.37779
$414$	0	0
$415$	0	0
$416$	4.00000	0.196116
$417$	4.00000	0.195881
$418$	0	0
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−16.0000	−0.778868
$423$	4.00000	0.194487
$424$	−14.0000	−0.679900
$425$	0	0
$426$	−6.00000	−0.290701
$427$	−12.0000	−0.580721
$428$	−8.00000	−0.386695
$429$	0	0
$430$	0	0
$431$	−6.00000	−0.289010	−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000	−0.289010	−0.144505	+	0.989504i	$0.546159\pi$
$432$	1.00000	0.0481125
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	18.0000	0.862044
$437$	0	0
$438$	−8.00000	−0.382255
$439$	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
$441$	−3.00000	−0.142857
$442$	−24.0000	−1.14156
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	−20.0000	−0.947027
$447$	18.0000	0.851371
$448$	2.00000	0.0944911
$449$	−20.0000	−0.943858	−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000	−0.943858	−0.471929	+	0.881636i	$0.656442\pi$
$450$	0	0
$451$	0	0
$452$	−14.0000	−0.658505
$453$	−8.00000	−0.375873
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	10.0000	0.467269
$459$	−6.00000	−0.280056
$460$	0	0
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	8.00000	0.371391
$465$	0	0
$466$	−14.0000	−0.648537
$467$	32.0000	1.48078	0.740392	−	0.672176i	$-0.234640\pi$
$467$	32.0000	1.48078	0.740392	+	0.672176i	$0.234640\pi$
$468$	−4.00000	−0.184900
$469$	20.0000	0.923514
$470$	0	0
$471$	18.0000	0.829396
$472$	−14.0000	−0.644402
$473$	0	0
$474$	−8.00000	−0.367452
$475$	0	0
$476$	−12.0000	−0.550019
$477$	14.0000	0.641016
$478$	12.0000	0.548867
$479$	−42.0000	−1.91903	−0.959514	−	0.281659i	$-0.909115\pi$
$479$	−42.0000	−1.91903	−0.959514	+	0.281659i	$0.909115\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	14.0000	0.637683
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	6.00000	0.271607
$489$	−6.00000	−0.271329
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	10.0000	0.450835
$493$	−48.0000	−2.16181
$494$	0	0
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	12.0000	0.538274
$498$	−12.0000	−0.537733
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	8.00000	0.357414
$502$	0	0
$503$	20.0000	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	0	0
$507$	3.00000	0.133235
$508$	0	0
$509$	4.00000	0.177297	0.0886484	−	0.996063i	$-0.471745\pi$
$509$	4.00000	0.177297	0.0886484	+	0.996063i	$0.471745\pi$
$510$	0	0
$511$	16.0000	0.707798
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	2.00000	0.0882162
$515$	0	0
$516$	−8.00000	−0.352180
$517$	0	0
$518$	8.00000	0.351500
$519$	−10.0000	−0.438951
$520$	0	0
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	−8.00000	−0.350150
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	16.0000	0.697633
$527$	6.00000	0.261364
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	14.0000	0.607548
$532$	0	0
$533$	−40.0000	−1.73259
$534$	−16.0000	−0.692388
$535$	0	0
$536$	−10.0000	−0.431934
$537$	0	0
$538$	−24.0000	−1.03471
$539$	0	0
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	16.0000	0.687259
$543$	−6.00000	−0.257485
$544$	6.00000	0.257248
$545$	0	0
$546$	8.00000	0.342368
$547$	−6.00000	−0.256541	−0.128271	−	0.991739i	$-0.540943\pi$
$547$	−6.00000	−0.256541	−0.128271	+	0.991739i	$0.540943\pi$
$548$	6.00000	0.256307
$549$	−6.00000	−0.256074
$550$	0	0
$551$	0	0
$552$	0	0
$553$	16.0000	0.680389
$554$	16.0000	0.679775
$555$	0	0
$556$	4.00000	0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	1.00000	0.0423334
$559$	32.0000	1.35346
$560$	0	0
$561$	0	0
$562$	−30.0000	−1.26547
$563$	32.0000	1.34864	0.674320	−	0.738440i	$-0.264437\pi$
$563$	32.0000	1.34864	0.674320	+	0.738440i	$0.264437\pi$
$564$	4.00000	0.168430
$565$	0	0
$566$	14.0000	0.588464
$567$	2.00000	0.0839921
$568$	−6.00000	−0.251754
$569$	4.00000	0.167689	0.0838444	−	0.996479i	$-0.473280\pi$
$569$	4.00000	0.167689	0.0838444	+	0.996479i	$0.473280\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	−14.0000	−0.584858
$574$	−20.0000	−0.834784
$575$	0	0
$576$	1.00000	0.0416667
$577$	6.00000	0.249783	0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000	0.249783	0.124892	+	0.992170i	$0.460142\pi$
$578$	−19.0000	−0.790296
$579$	2.00000	0.0831172
$580$	0	0
$581$	24.0000	0.995688
$582$	−10.0000	−0.414513
$583$	0	0
$584$	−8.00000	−0.331042
$585$	0	0
$586$	6.00000	0.247858
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−3.00000	−0.123718
$589$	0	0
$590$	0	0
$591$	2.00000	0.0822690
$592$	−4.00000	−0.164399
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	0	0
$596$	18.0000	0.737309
$597$	−24.0000	−0.982255
$598$	0	0
$599$	42.0000	1.71607	0.858037	−	0.513588i	$-0.171684\pi$
$599$	42.0000	1.71607	0.858037	+	0.513588i	$0.171684\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	16.0000	0.652111
$603$	10.0000	0.407231
$604$	−8.00000	−0.325515
$605$	0	0
$606$	6.00000	0.243733
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	0	0
$609$	16.0000	0.648353
$610$	0	0
$611$	−16.0000	−0.647291
$612$	−6.00000	−0.242536
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	0	0
$617$	−38.0000	−1.52982	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000	−1.52982	−0.764911	+	0.644136i	$0.777217\pi$
$618$	−6.00000	−0.241355
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	0	0
$622$	−18.0000	−0.721734
$623$	32.0000	1.28205
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−16.0000	−0.639489
$627$	0	0
$628$	18.0000	0.718278
$629$	24.0000	0.956943
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−8.00000	−0.318223
$633$	16.0000	0.635943
$634$	−10.0000	−0.397151
$635$	0	0
$636$	14.0000	0.555136
$637$	12.0000	0.475457
$638$	0	0
$639$	6.00000	0.237356
$640$	0	0
$641$	−44.0000	−1.73790	−0.868948	−	0.494904i	$-0.835203\pi$
$641$	−44.0000	−1.73790	−0.868948	+	0.494904i	$0.835203\pi$
$642$	8.00000	0.315735
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	16.0000	0.629025	0.314512	−	0.949253i	$-0.398159\pi$
$647$	16.0000	0.629025	0.314512	+	0.949253i	$0.398159\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	−6.00000	−0.234978
$653$	10.0000	0.391330	0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000	0.391330	0.195665	+	0.980671i	$0.437313\pi$
$654$	−18.0000	−0.703856
$655$	0	0
$656$	10.0000	0.390434
$657$	8.00000	0.312110
$658$	−8.00000	−0.311872
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	0	0
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	12.0000	0.466393
$663$	24.0000	0.932083
$664$	−12.0000	−0.465690
$665$	0	0
$666$	4.00000	0.154997
$667$	0	0
$668$	8.00000	0.309529
$669$	20.0000	0.773245
$670$	0	0
$671$	0	0
$672$	−2.00000	−0.0771517
$673$	20.0000	0.770943	0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000	0.770943	0.385472	+	0.922720i	$0.374039\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	3.00000	0.115385
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	14.0000	0.537667
$679$	20.0000	0.767530
$680$	0	0
$681$	−12.0000	−0.459841
$682$	0	0
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	0	0
$685$	0	0
$686$	20.0000	0.763604
$687$	−10.0000	−0.381524
$688$	−8.00000	−0.304997
$689$	−56.0000	−2.13343
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	−10.0000	−0.380143
$693$	0	0
$694$	20.0000	0.759190
$695$	0	0
$696$	−8.00000	−0.303239
$697$	−60.0000	−2.27266
$698$	−2.00000	−0.0757011
$699$	14.0000	0.529529
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	4.00000	0.150970
$703$	0	0
$704$	0	0
$705$	0	0
$706$	14.0000	0.526897
$707$	−12.0000	−0.451306
$708$	14.0000	0.526152
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−16.0000	−0.599625
$713$	0	0
$714$	12.0000	0.449089
$715$	0	0
$716$	0	0
$717$	−12.0000	−0.448148
$718$	−18.0000	−0.671754
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	0	0
$721$	12.0000	0.446903
$722$	19.0000	0.707107
$723$	−14.0000	−0.520666
$724$	−6.00000	−0.222988
$725$	0	0
$726$	11.0000	0.408248
$727$	10.0000	0.370879	0.185440	−	0.982656i	$-0.440629\pi$
$727$	10.0000	0.370879	0.185440	+	0.982656i	$0.440629\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	0	0
$731$	48.0000	1.77534
$732$	−6.00000	−0.221766
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−36.0000	−1.32878
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−10.0000	−0.368105
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	0	0
$742$	−28.0000	−1.02791
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	6.00000	0.219676
$747$	12.0000	0.439057
$748$	0	0
$749$	−16.0000	−0.584627
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	32.0000	1.16537
$755$	0	0
$756$	2.00000	0.0727393
$757$	12.0000	0.436147	0.218074	−	0.975932i	$-0.430023\pi$
$757$	12.0000	0.436147	0.218074	+	0.975932i	$0.430023\pi$
$758$	−8.00000	−0.290573
$759$	0	0
$760$	0	0
$761$	−20.0000	−0.724999	−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000	−0.724999	−0.362500	+	0.931984i	$0.618077\pi$
$762$	0	0
$763$	36.0000	1.30329
$764$	−14.0000	−0.506502
$765$	0	0
$766$	0	0
$767$	−56.0000	−2.02204
$768$	1.00000	0.0360844
$769$	30.0000	1.08183	0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000	1.08183	0.540914	+	0.841078i	$0.318079\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	2.00000	0.0719816
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	−10.0000	−0.358979
$777$	−8.00000	−0.286998
$778$	32.0000	1.14726
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	8.00000	0.285897
$784$	−3.00000	−0.107143
$785$	0	0
$786$	18.0000	0.642039
$787$	−44.0000	−1.56843	−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000	−1.56843	−0.784215	+	0.620489i	$0.786934\pi$
$788$	2.00000	0.0712470
$789$	−16.0000	−0.569615
$790$	0	0
$791$	−28.0000	−0.995565
$792$	0	0
$793$	24.0000	0.852265
$794$	18.0000	0.638796
$795$	0	0
$796$	−24.0000	−0.850657
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	0	0
$801$	16.0000	0.565332
$802$	−4.00000	−0.141245
$803$	0	0
$804$	10.0000	0.352673
$805$	0	0
$806$	−4.00000	−0.140894
$807$	24.0000	0.844840
$808$	6.00000	0.211079
$809$	4.00000	0.140633	0.0703163	−	0.997525i	$-0.477599\pi$
$809$	4.00000	0.140633	0.0703163	+	0.997525i	$0.477599\pi$
$810$	0	0
$811$	56.0000	1.96643	0.983213	−	0.182462i	$-0.0584065\pi$
$811$	56.0000	1.96643	0.983213	+	0.182462i	$0.0584065\pi$
$812$	16.0000	0.561490
$813$	−16.0000	−0.561144
$814$	0	0
$815$	0	0
$816$	−6.00000	−0.210042
$817$	0	0
$818$	−30.0000	−1.04893
$819$	−8.00000	−0.279543
$820$	0	0
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	−6.00000	−0.209274
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	−28.0000	−0.974245
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	−16.0000	−0.555034
$832$	−4.00000	−0.138675
$833$	18.0000	0.623663
$834$	−4.00000	−0.138509
$835$	0	0
$836$	0	0
$837$	−1.00000	−0.0345651
$838$	6.00000	0.207267
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	6.00000	0.206774
$843$	30.0000	1.03325
$844$	16.0000	0.550743
$845$	0	0
$846$	−4.00000	−0.137523
$847$	−22.0000	−0.755929
$848$	14.0000	0.480762
$849$	−14.0000	−0.480479
$850$	0	0
$851$	0	0
$852$	6.00000	0.205557
$853$	−18.0000	−0.616308	−0.308154	−	0.951336i	$-0.599711\pi$
$853$	−18.0000	−0.616308	−0.308154	+	0.951336i	$0.599711\pi$
$854$	12.0000	0.410632
$855$	0	0
$856$	8.00000	0.273434
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	20.0000	0.681598
$862$	6.00000	0.204361
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−16.0000	−0.543702
$867$	19.0000	0.645274
$868$	−2.00000	−0.0678844
$869$	0	0
$870$	0	0
$871$	−40.0000	−1.35535
$872$	−18.0000	−0.609557
$873$	10.0000	0.338449
$874$	0	0
$875$	0	0
$876$	8.00000	0.270295
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	−24.0000	−0.809961
$879$	−6.00000	−0.202375
$880$	0	0
$881$	−48.0000	−1.61716	−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000	−1.61716	−0.808581	+	0.588386i	$0.799764\pi$
$882$	3.00000	0.101015
$883$	12.0000	0.403832	0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000	0.403832	0.201916	+	0.979403i	$0.435283\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−36.0000	−1.20944
$887$	56.0000	1.88030	0.940148	−	0.340766i	$-0.110687\pi$
$887$	56.0000	1.88030	0.940148	+	0.340766i	$0.110687\pi$
$888$	4.00000	0.134231
$889$	0	0
$890$	0	0
$891$	0	0
$892$	20.0000	0.669650
$893$	0	0
$894$	−18.0000	−0.602010
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	0	0
$898$	20.0000	0.667409
$899$	−8.00000	−0.266815
$900$	0	0
$901$	−84.0000	−2.79845
$902$	0	0
$903$	−16.0000	−0.532447
$904$	14.0000	0.465633
$905$	0	0
$906$	8.00000	0.265782
$907$	−2.00000	−0.0664089	−0.0332045	−	0.999449i	$-0.510571\pi$
$907$	−2.00000	−0.0664089	−0.0332045	+	0.999449i	$0.510571\pi$
$908$	−12.0000	−0.398234
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	0	0
$913$	0	0
$914$	8.00000	0.264616
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−36.0000	−1.18882
$918$	6.00000	0.198030
$919$	−60.0000	−1.97922	−0.989609	−	0.143787i	$-0.954072\pi$
$919$	−60.0000	−1.97922	−0.989609	+	0.143787i	$0.954072\pi$
$920$	0	0
$921$	−10.0000	−0.329511
$922$	12.0000	0.395199
$923$	−24.0000	−0.789970
$924$	0	0
$925$	0	0
$926$	0	0
$927$	6.00000	0.197066
$928$	−8.00000	−0.262613
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	14.0000	0.458585
$933$	18.0000	0.589294
$934$	−32.0000	−1.04707
$935$	0	0
$936$	4.00000	0.130744
$937$	42.0000	1.37208	0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000	1.37208	0.686040	+	0.727564i	$0.259347\pi$
$938$	−20.0000	−0.653023
$939$	16.0000	0.522140
$940$	0	0
$941$	−8.00000	−0.260793	−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000	−0.260793	−0.130396	+	0.991462i	$0.541625\pi$
$942$	−18.0000	−0.586472
$943$	0	0
$944$	14.0000	0.455661
$945$	0	0
$946$	0	0
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	8.00000	0.259828
$949$	−32.0000	−1.03876
$950$	0	0
$951$	10.0000	0.324272
$952$	12.0000	0.388922
$953$	46.0000	1.49009	0.745043	−	0.667016i	$-0.232429\pi$
$953$	46.0000	1.49009	0.745043	+	0.667016i	$0.232429\pi$
$954$	−14.0000	−0.453267
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	42.0000	1.35696
$959$	12.0000	0.387500
$960$	0	0
$961$	1.00000	0.0322581
$962$	−16.0000	−0.515861
$963$	−8.00000	−0.257796
$964$	−14.0000	−0.450910
$965$	0	0
$966$	0	0
$967$	−52.0000	−1.67221	−0.836104	−	0.548572i	$-0.815172\pi$
$967$	−52.0000	−1.67221	−0.836104	+	0.548572i	$0.815172\pi$
$968$	11.0000	0.353553
$969$	0	0
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	1.00000	0.0320750
$973$	8.00000	0.256468
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−6.00000	−0.192055
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	6.00000	0.191859
$979$	0	0
$980$	0	0
$981$	18.0000	0.574696
$982$	−36.0000	−1.14881
$983$	40.0000	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$983$	40.0000	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$984$	−10.0000	−0.318788
$985$	0	0
$986$	48.0000	1.52863
$987$	8.00000	0.254643
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	1.00000	0.0317500
$993$	−12.0000	−0.380808
$994$	−12.0000	−0.380617
$995$	0	0
$996$	12.0000	0.380235
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	−20.0000	−0.633089
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.t.1.1		1
5.2	odd	4		4650.2.d.g.3349.1		2
5.3	odd	4		4650.2.d.g.3349.2		2
5.4	even	2		930.2.a.k.1.1	✓	1
15.14	odd	2		2790.2.a.f.1.1		1
20.19	odd	2		7440.2.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.k.1.1	✓	1	5.4	even	2
2790.2.a.f.1.1		1	15.14	odd	2
4650.2.a.t.1.1		1	1.1	even	1	trivial
4650.2.d.g.3349.1		2	5.2	odd	4
4650.2.d.g.3349.2		2	5.3	odd	4
7440.2.a.u.1.1		1	20.19	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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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