LMFDB - Embedded newform 1650.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1650,2,Mod(1,1650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.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:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +8.00000 q^{19} +1.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000 q^{27} +2.00000 q^{29} +8.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} +8.00000 q^{38} -2.00000 q^{39} +6.00000 q^{41} -8.00000 q^{43} +1.00000 q^{44} -4.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} +2.00000 q^{51} -2.00000 q^{52} -2.00000 q^{53} +1.00000 q^{54} +8.00000 q^{57} +2.00000 q^{58} +4.00000 q^{59} -6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +1.00000 q^{66} +12.0000 q^{67} +2.00000 q^{68} -4.00000 q^{69} -12.0000 q^{71} +1.00000 q^{72} -2.00000 q^{73} +2.00000 q^{74} +8.00000 q^{76} -2.00000 q^{78} +1.00000 q^{81} +6.00000 q^{82} -4.00000 q^{83} -8.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} -4.00000 q^{92} +8.00000 q^{93} +4.00000 q^{94} +1.00000 q^{96} +14.0000 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$3$	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
$7$	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
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	0	0
$22$	1.00000	0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	2.00000	0.342997
$35$	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	$0.447432\pi$
$38$	8.00000	1.29777
$39$	−2.00000	−0.320256
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−4.00000	−0.589768
$47$	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
$49$	−7.00000	−1.00000
$50$	0	0
$51$	2.00000	0.280056
$52$	−2.00000	−0.277350
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0	0
$57$	8.00000	1.05963
$58$	2.00000	0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	2.00000	0.242536
$69$	−4.00000	−0.481543
$70$	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
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	8.00000	0.917663
$77$	0	0
$78$	−2.00000	−0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	−8.00000	−0.862662
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	0	0
$92$	−4.00000	−0.417029
$93$	8.00000	0.829561
$94$	4.00000	0.412568
$95$	0	0
$96$	1.00000	0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−7.00000	−0.707107
$99$	1.00000	0.100504
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.00000	0.198030
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−2.00000	−0.194257
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	1.00000	0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	2.00000	0.185695
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−6.00000	−0.543214
$123$	6.00000	0.541002
$124$	8.00000	0.718421
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	2.00000	0.171499
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−4.00000	−0.340503
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−12.0000	−1.00702
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	−2.00000	−0.165521
$147$	−7.00000	−0.577350
$148$	2.00000	0.164399
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	8.00000	0.648886
$153$	2.00000	0.161690
$154$	0	0
$155$	0	0
$156$	−2.00000	−0.160128
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	0	0
$159$	−2.00000	−0.158610
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	8.00000	0.611775
$172$	−8.00000	−0.609994
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	1.00000	0.0753778
$177$	4.00000	0.300658
$178$	−6.00000	−0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	−4.00000	−0.294884
$185$	0	0
$186$	8.00000	0.586588
$187$	2.00000	0.146254
$188$	4.00000	0.291730
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	1.00000	0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	−7.00000	−0.500000
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	1.00000	0.0710669
$199$	−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
$201$	12.0000	0.846415
$202$	−6.00000	−0.422159
$203$	0	0
$204$	2.00000	0.140028
$205$	0	0
$206$	−16.0000	−1.11477
$207$	−4.00000	−0.278019
$208$	−2.00000	−0.138675
$209$	8.00000	0.553372
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−2.00000	−0.137361
$213$	−12.0000	−0.822226
$214$	−20.0000	−1.36717
$215$	0	0
$216$	1.00000	0.0680414
$217$	0	0
$218$	−6.00000	−0.406371
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−4.00000	−0.269069
$222$	2.00000	0.134231
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	0	0
$226$	−2.00000	−0.133038
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	8.00000	0.529813
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	2.00000	0.131306
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	4.00000	0.260378
$237$	0	0
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−6.00000	−0.384111
$245$	0	0
$246$	6.00000	0.382546
$247$	−16.0000	−1.01806
$248$	8.00000	0.508001
$249$	−4.00000	−0.253490
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−26.0000	−1.62184	−0.810918	−	0.585160i	$-0.801032\pi$
$257$	−26.0000	−1.62184	−0.810918	+	0.585160i	$0.801032\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	0	0
$261$	2.00000	0.123797
$262$	12.0000	0.741362
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	0	0
$267$	−6.00000	−0.367194
$268$	12.0000	0.733017
$269$	−22.0000	−1.34136	−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000	−1.34136	−0.670682	+	0.741745i	$0.733998\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−2.00000	−0.120824
$275$	0	0
$276$	−4.00000	−0.240772
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	16.0000	0.959616
$279$	8.00000	0.478947
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	4.00000	0.238197
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−2.00000	−0.118262
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	14.0000	0.820695
$292$	−2.00000	−0.117041
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−7.00000	−0.408248
$295$	0	0
$296$	2.00000	0.116248
$297$	1.00000	0.0580259
$298$	10.0000	0.579284
$299$	8.00000	0.462652
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	−6.00000	−0.344691
$304$	8.00000	0.458831
$305$	0	0
$306$	2.00000	0.114332
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	0	0
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	−2.00000	−0.113228
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	0	0
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−2.00000	−0.112154
$319$	2.00000	0.111979
$320$	0	0
$321$	−20.0000	−1.11629
$322$	0	0
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	0	0
$326$	−20.0000	−1.10770
$327$	−6.00000	−0.331801
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−4.00000	−0.219529
$333$	2.00000	0.109599
$334$	−16.0000	−0.875481
$335$	0	0
$336$	0	0
$337$	−10.0000	−0.544735	−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000	−0.544735	−0.272367	+	0.962193i	$0.587807\pi$
$338$	−9.00000	−0.489535
$339$	−2.00000	−0.108625
$340$	0	0
$341$	8.00000	0.433224
$342$	8.00000	0.432590
$343$	0	0
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−18.0000	−0.967686
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	2.00000	0.107211
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	1.00000	0.0533002
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−2.00000	−0.105118
$363$	1.00000	0.0524864
$364$	0	0
$365$	0	0
$366$	−6.00000	−0.313625
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	−4.00000	−0.208514
$369$	6.00000	0.312348
$370$	0	0
$371$	0	0
$372$	8.00000	0.414781
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	4.00000	0.206284
$377$	−4.00000	−0.206010
$378$	0	0
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	−12.0000	−0.613973
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−8.00000	−0.406663
$388$	14.0000	0.710742
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	−7.00000	−0.353553
$393$	12.0000	0.605320
$394$	−10.0000	−0.503793
$395$	0	0
$396$	1.00000	0.0502519
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−24.0000	−1.20301
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	12.0000	0.598506
$403$	−16.0000	−0.797017
$404$	−6.00000	−0.298511
$405$	0	0
$406$	0	0
$407$	2.00000	0.0991363
$408$	2.00000	0.0990148
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	0	0
$411$	−2.00000	−0.0986527
$412$	−16.0000	−0.788263
$413$	0	0
$414$	−4.00000	−0.196589
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	16.0000	0.783523
$418$	8.00000	0.391293
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	38.0000	1.85201	0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000	1.85201	0.926003	+	0.377515i	$0.123221\pi$
$422$	0	0
$423$	4.00000	0.194487
$424$	−2.00000	−0.0971286
$425$	0	0
$426$	−12.0000	−0.581402
$427$	0	0
$428$	−20.0000	−0.966736
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−32.0000	−1.53077
$438$	−2.00000	−0.0955637
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	−4.00000	−0.190261
$443$	28.0000	1.33032	0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000	1.33032	0.665160	+	0.746701i	$0.268363\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	16.0000	0.757622
$447$	10.0000	0.472984
$448$	0	0
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	0	0
$451$	6.00000	0.282529
$452$	−2.00000	−0.0940721
$453$	−8.00000	−0.375873
$454$	−12.0000	−0.563188
$455$	0	0
$456$	8.00000	0.374634
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	14.0000	0.654177
$459$	2.00000	0.0933520
$460$	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
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	18.0000	0.833834
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	0	0
$471$	2.00000	0.0921551
$472$	4.00000	0.184115
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−2.00000	−0.0915737
$478$	16.0000	0.731823
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	18.0000	0.819878
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−6.00000	−0.271607
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	6.00000	0.270501
$493$	4.00000	0.180151
$494$	−16.0000	−0.719874
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	−4.00000	−0.179244
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	−16.0000	−0.714827
$502$	−20.0000	−0.892644
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	−4.00000	−0.177822
$507$	−9.00000	−0.399704
$508$	16.0000	0.709885
$509$	−22.0000	−0.975133	−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000	−0.975133	−0.487566	+	0.873086i	$0.662115\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	8.00000	0.353209
$514$	−26.0000	−1.14681
$515$	0	0
$516$	−8.00000	−0.352180
$517$	4.00000	0.175920
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	2.00000	0.0875376
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	24.0000	1.04645
$527$	16.0000	0.696971
$528$	1.00000	0.0435194
$529$	−7.00000	−0.304348
$530$	0	0
$531$	4.00000	0.173585
$532$	0	0
$533$	−12.0000	−0.519778
$534$	−6.00000	−0.259645
$535$	0	0
$536$	12.0000	0.518321
$537$	−12.0000	−0.517838
$538$	−22.0000	−0.948487
$539$	−7.00000	−0.301511
$540$	0	0
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	0	0
$543$	−2.00000	−0.0858282
$544$	2.00000	0.0857493
$545$	0	0
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−2.00000	−0.0854358
$549$	−6.00000	−0.256074
$550$	0	0
$551$	16.0000	0.681623
$552$	−4.00000	−0.170251
$553$	0	0
$554$	14.0000	0.594803
$555$	0	0
$556$	16.0000	0.678551
$557$	46.0000	1.94908	0.974541	−	0.224208i	$-0.0719796\pi$
$557$	46.0000	1.94908	0.974541	+	0.224208i	$0.0719796\pi$
$558$	8.00000	0.338667
$559$	16.0000	0.676728
$560$	0	0
$561$	2.00000	0.0844401
$562$	−10.0000	−0.421825
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	4.00000	0.168430
$565$	0	0
$566$	8.00000	0.336265
$567$	0	0
$568$	−12.0000	−0.503509
$569$	14.0000	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$570$	0	0
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	−2.00000	−0.0836242
$573$	−12.0000	−0.501307
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−13.0000	−0.540729
$579$	22.0000	0.914289
$580$	0	0
$581$	0	0
$582$	14.0000	0.580319
$583$	−2.00000	−0.0828315
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	6.00000	0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−7.00000	−0.288675
$589$	64.0000	2.63707
$590$	0	0
$591$	−10.0000	−0.411345
$592$	2.00000	0.0821995
$593$	26.0000	1.06769	0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000	1.06769	0.533846	+	0.845582i	$0.320746\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	10.0000	0.409616
$597$	−24.0000	−0.982255
$598$	8.00000	0.327144
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	−8.00000	−0.325515
$605$	0	0
$606$	−6.00000	−0.243733
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	8.00000	0.324443
$609$	0	0
$610$	0	0
$611$	−8.00000	−0.323645
$612$	2.00000	0.0808452
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	−16.0000	−0.643614
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	−20.0000	−0.801927
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	6.00000	0.239808
$627$	8.00000	0.319489
$628$	2.00000	0.0798087
$629$	4.00000	0.159490
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	6.00000	0.238290
$635$	0	0
$636$	−2.00000	−0.0793052
$637$	14.0000	0.554700
$638$	2.00000	0.0791808
$639$	−12.0000	−0.474713
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	−20.0000	−0.789337
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	0	0
$646$	16.0000	0.629512
$647$	44.0000	1.72982	0.864909	−	0.501928i	$-0.167376\pi$
$647$	44.0000	1.72982	0.864909	+	0.501928i	$0.167376\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	0	0
$651$	0	0
$652$	−20.0000	−0.783260
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	6.00000	0.234261
$657$	−2.00000	−0.0780274
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−12.0000	−0.466393
$663$	−4.00000	−0.155347
$664$	−4.00000	−0.155230
$665$	0	0
$666$	2.00000	0.0774984
$667$	−8.00000	−0.309761
$668$	−16.0000	−0.619059
$669$	16.0000	0.618596
$670$	0	0
$671$	−6.00000	−0.231627
$672$	0	0
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	−9.00000	−0.346154
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	0	0
$681$	−12.0000	−0.459841
$682$	8.00000	0.306336
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	0	0
$687$	14.0000	0.534133
$688$	−8.00000	−0.304997
$689$	4.00000	0.152388
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	20.0000	0.759190
$695$	0	0
$696$	2.00000	0.0758098
$697$	12.0000	0.454532
$698$	−30.0000	−1.13552
$699$	18.0000	0.680823
$700$	0	0
$701$	−46.0000	−1.73740	−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000	−1.73740	−0.868698	+	0.495342i	$0.835043\pi$
$702$	−2.00000	−0.0754851
$703$	16.0000	0.603451
$704$	1.00000	0.0376889
$705$	0	0
$706$	−26.0000	−0.978523
$707$	0	0
$708$	4.00000	0.150329
$709$	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
$711$	0	0
$712$	−6.00000	−0.224860
$713$	−32.0000	−1.19841
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	16.0000	0.597531
$718$	−32.0000	−1.19423
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	0	0
$722$	45.0000	1.67473
$723$	18.0000	0.669427
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	1.00000	0.0371135
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−16.0000	−0.591781
$732$	−6.00000	−0.221766
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−16.0000	−0.590571
$735$	0	0
$736$	−4.00000	−0.147442
$737$	12.0000	0.442026
$738$	6.00000	0.220863
$739$	24.0000	0.882854	0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000	0.882854	0.441427	+	0.897297i	$0.354472\pi$
$740$	0	0
$741$	−16.0000	−0.587775
$742$	0	0
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	8.00000	0.293294
$745$	0	0
$746$	−2.00000	−0.0732252
$747$	−4.00000	−0.146352
$748$	2.00000	0.0731272
$749$	0	0
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	4.00000	0.145865
$753$	−20.0000	−0.728841
$754$	−4.00000	−0.145671
$755$	0	0
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	36.0000	1.30758
$759$	−4.00000	−0.145191
$760$	0	0
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	16.0000	0.579619
$763$	0	0
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−12.0000	−0.433578
$767$	−8.00000	−0.288863
$768$	1.00000	0.0360844
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	−26.0000	−0.936367
$772$	22.0000	0.791797
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	−22.0000	−0.788738
$779$	48.0000	1.71978
$780$	0	0
$781$	−12.0000	−0.429394
$782$	−8.00000	−0.286079
$783$	2.00000	0.0714742
$784$	−7.00000	−0.250000
$785$	0	0
$786$	12.0000	0.428026
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	−10.0000	−0.356235
$789$	24.0000	0.854423
$790$	0	0
$791$	0	0
$792$	1.00000	0.0355335
$793$	12.0000	0.426132
$794$	2.00000	0.0709773
$795$	0	0
$796$	−24.0000	−0.850657
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	0	0
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	−2.00000	−0.0705785
$804$	12.0000	0.423207
$805$	0	0
$806$	−16.0000	−0.563576
$807$	−22.0000	−0.774437
$808$	−6.00000	−0.211079
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	−8.00000	−0.280918	−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000	−0.280918	−0.140459	+	0.990086i	$0.544858\pi$
$812$	0	0
$813$	0	0
$814$	2.00000	0.0701000
$815$	0	0
$816$	2.00000	0.0700140
$817$	−64.0000	−2.23908
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	−2.00000	−0.0697580
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−4.00000	−0.139010
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	14.0000	0.485655
$832$	−2.00000	−0.0693375
$833$	−14.0000	−0.485071
$834$	16.0000	0.554035
$835$	0	0
$836$	8.00000	0.276686
$837$	8.00000	0.276520
$838$	4.00000	0.138178
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	38.0000	1.30957
$843$	−10.0000	−0.344418
$844$	0	0
$845$	0	0
$846$	4.00000	0.137523
$847$	0	0
$848$	−2.00000	−0.0686803
$849$	8.00000	0.274559
$850$	0	0
$851$	−8.00000	−0.274236
$852$	−12.0000	−0.411113
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	0	0
$856$	−20.0000	−0.683586
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	−2.00000	−0.0682789
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	0	0
$862$	−24.0000	−0.817443
$863$	−4.00000	−0.136162	−0.0680808	−	0.997680i	$-0.521688\pi$
$863$	−4.00000	−0.136162	−0.0680808	+	0.997680i	$0.521688\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−13.0000	−0.441503
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−24.0000	−0.813209
$872$	−6.00000	−0.203186
$873$	14.0000	0.473828
$874$	−32.0000	−1.08242
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−16.0000	−0.539974
$879$	6.00000	0.202375
$880$	0	0
$881$	58.0000	1.95407	0.977035	−	0.213080i	$-0.0683494\pi$
$881$	58.0000	1.95407	0.977035	+	0.213080i	$0.0683494\pi$
$882$	−7.00000	−0.235702
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	28.0000	0.940678
$887$	−40.0000	−1.34307	−0.671534	−	0.740973i	$-0.734364\pi$
$887$	−40.0000	−1.34307	−0.671534	+	0.740973i	$0.734364\pi$
$888$	2.00000	0.0671156
$889$	0	0
$890$	0	0
$891$	1.00000	0.0335013
$892$	16.0000	0.535720
$893$	32.0000	1.07084
$894$	10.0000	0.334450
$895$	0	0
$896$	0	0
$897$	8.00000	0.267112
$898$	10.0000	0.333704
$899$	16.0000	0.533630
$900$	0	0
$901$	−4.00000	−0.133259
$902$	6.00000	0.199778
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	0	0
$906$	−8.00000	−0.265782
$907$	−52.0000	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$908$	−12.0000	−0.398234
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	8.00000	0.264906
$913$	−4.00000	−0.132381
$914$	38.0000	1.25693
$915$	0	0
$916$	14.0000	0.462573
$917$	0	0
$918$	2.00000	0.0660098
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	0	0
$921$	0	0
$922$	18.0000	0.592798
$923$	24.0000	0.789970
$924$	0	0
$925$	0	0
$926$	−8.00000	−0.262896
$927$	−16.0000	−0.525509
$928$	2.00000	0.0656532
$929$	50.0000	1.64045	0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000	1.64045	0.820223	+	0.572043i	$0.193849\pi$
$930$	0	0
$931$	−56.0000	−1.83533
$932$	18.0000	0.589610
$933$	−20.0000	−0.654771
$934$	−36.0000	−1.17796
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	54.0000	1.76410	0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000	1.76410	0.882052	+	0.471153i	$0.156162\pi$
$938$	0	0
$939$	6.00000	0.195803
$940$	0	0
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	2.00000	0.0651635
$943$	−24.0000	−0.781548
$944$	4.00000	0.130189
$945$	0	0
$946$	−8.00000	−0.260102
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	−38.0000	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$954$	−2.00000	−0.0647524
$955$	0	0
$956$	16.0000	0.517477
$957$	2.00000	0.0646508
$958$	24.0000	0.775405
$959$	0	0
$960$	0	0
$961$	33.0000	1.06452
$962$	−4.00000	−0.128965
$963$	−20.0000	−0.644491
$964$	18.0000	0.579741
$965$	0	0
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	1.00000	0.0321412
$969$	16.0000	0.513994
$970$	0	0
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−6.00000	−0.192055
$977$	38.0000	1.21573	0.607864	−	0.794041i	$-0.292027\pi$
$977$	38.0000	1.21573	0.607864	+	0.794041i	$0.292027\pi$
$978$	−20.0000	−0.639529
$979$	−6.00000	−0.191761
$980$	0	0
$981$	−6.00000	−0.191565
$982$	−12.0000	−0.382935
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	4.00000	0.127386
$987$	0	0
$988$	−16.0000	−0.509028
$989$	32.0000	1.01754
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	8.00000	0.254000
$993$	−12.0000	−0.380808
$994$	0	0
$995$	0	0
$996$	−4.00000	−0.126745
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	4.00000	0.126618
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.a.r.1.1		1
3.2	odd	2		4950.2.a.k.1.1		1
5.2	odd	4		1650.2.c.l.199.2		2
5.3	odd	4		1650.2.c.l.199.1		2
5.4	even	2		330.2.a.a.1.1	✓	1
15.2	even	4		4950.2.c.g.199.1		2
15.8	even	4		4950.2.c.g.199.2		2
15.14	odd	2		990.2.a.j.1.1		1
20.19	odd	2		2640.2.a.n.1.1		1
55.54	odd	2		3630.2.a.n.1.1		1
60.59	even	2		7920.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.a.a.1.1	✓	1	5.4	even	2
990.2.a.j.1.1		1	15.14	odd	2
1650.2.a.r.1.1		1	1.1	even	1	trivial
1650.2.c.l.199.1		2	5.3	odd	4
1650.2.c.l.199.2		2	5.2	odd	4
2640.2.a.n.1.1		1	20.19	odd	2
3630.2.a.n.1.1		1	55.54	odd	2
4950.2.a.k.1.1		1	3.2	odd	2
4950.2.c.g.199.1		2	15.2	even	4
4950.2.c.g.199.2		2	15.8	even	4
7920.2.a.bb.1.1		1	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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