LMFDB - Embedded newform 5166.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5166,2,Mod(1,5166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5166, 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("5166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5166.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:	$41.2507176842$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} +4.00000 q^{23} -4.00000 q^{25} +1.00000 q^{28} +5.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +10.0000 q^{37} +8.00000 q^{38} -1.00000 q^{40} +1.00000 q^{41} -5.00000 q^{43} +2.00000 q^{44} -4.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} +4.00000 q^{50} +9.00000 q^{53} +2.00000 q^{55} -1.00000 q^{56} -5.00000 q^{58} +10.0000 q^{59} +13.0000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +3.00000 q^{68} -1.00000 q^{70} -9.00000 q^{71} +4.00000 q^{73} -10.0000 q^{74} -8.00000 q^{76} +2.00000 q^{77} -11.0000 q^{79} +1.00000 q^{80} -1.00000 q^{82} +14.0000 q^{83} +3.00000 q^{85} +5.00000 q^{86} -2.00000 q^{88} +1.00000 q^{89} +4.00000 q^{92} +6.00000 q^{94} -8.00000 q^{95} +7.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	0	0
$28$	1.00000	0.188982
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	1.00000	0.169031
$36$	0	0
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	8.00000	1.29777
$39$	0	0
$40$	−1.00000	−0.158114
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−4.00000	−0.589768
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	0	0
$52$	0	0
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	2.00000	0.269680
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−5.00000	−0.656532
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	3.00000	0.381000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	3.00000	0.363803
$69$	0	0
$70$	−1.00000	−0.119523
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	0	0
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−8.00000	−0.917663
$77$	2.00000	0.227921
$78$	0	0
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	−1.00000	−0.110432
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	0	0
$85$	3.00000	0.325396
$86$	5.00000	0.539164
$87$	0	0
$88$	−2.00000	−0.213201
$89$	1.00000	0.106000	0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000	0.106000	0.0529999	+	0.998595i	$0.483122\pi$
$90$	0	0
$91$	0	0
$92$	4.00000	0.417029
$93$	0	0
$94$	6.00000	0.618853
$95$	−8.00000	−0.820783
$96$	0	0
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−4.00000	−0.400000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	0	0
$105$	0	0
$106$	−9.00000	−0.874157
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	5.00000	0.464238
$117$	0	0
$118$	−10.0000	−0.920575
$119$	3.00000	0.275010
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−13.0000	−1.17696
$123$	0	0
$124$	−3.00000	−0.269408
$125$	−9.00000	−0.804984
$126$	0	0
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	0	0
$133$	−8.00000	−0.693688
$134$	2.00000	0.172774
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	9.00000	0.755263
$143$	0	0
$144$	0	0
$145$	5.00000	0.415227
$146$	−4.00000	−0.331042
$147$	0	0
$148$	10.0000	0.821995
$149$	−3.00000	−0.245770	−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000	−0.245770	−0.122885	+	0.992421i	$0.539215\pi$
$150$	0	0
$151$	19.0000	1.54620	0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000	1.54620	0.773099	+	0.634285i	$0.218706\pi$
$152$	8.00000	0.648886
$153$	0	0
$154$	−2.00000	−0.161165
$155$	−3.00000	−0.240966
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	11.0000	0.875113
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	4.00000	0.315244
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	1.00000	0.0780869
$165$	0	0
$166$	−14.0000	−1.08661
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	−3.00000	−0.230089
$171$	0	0
$172$	−5.00000	−0.381246
$173$	1.00000	0.0760286	0.0380143	−	0.999277i	$-0.487897\pi$
$173$	1.00000	0.0760286	0.0380143	+	0.999277i	$0.487897\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	2.00000	0.150756
$177$	0	0
$178$	−1.00000	−0.0749532
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	0	0
$183$	0	0
$184$	−4.00000	−0.294884
$185$	10.0000	0.735215
$186$	0	0
$187$	6.00000	0.438763
$188$	−6.00000	−0.437595
$189$	0	0
$190$	8.00000	0.580381
$191$	11.0000	0.795932	0.397966	−	0.917400i	$-0.369716\pi$
$191$	11.0000	0.795932	0.397966	+	0.917400i	$0.369716\pi$
$192$	0	0
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	−7.00000	−0.502571
$195$	0	0
$196$	1.00000	0.0714286
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−24.0000	−1.70131	−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000	−1.70131	−0.850657	+	0.525720i	$0.823796\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	−10.0000	−0.703598
$203$	5.00000	0.350931
$204$	0	0
$205$	1.00000	0.0698430
$206$	−13.0000	−0.905753
$207$	0	0
$208$	0	0
$209$	−16.0000	−1.10674
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	9.00000	0.618123
$213$	0	0
$214$	3.00000	0.205076
$215$	−5.00000	−0.340997
$216$	0	0
$217$	−3.00000	−0.203653
$218$	2.00000	0.135457
$219$	0	0
$220$	2.00000	0.134840
$221$	0	0
$222$	0	0
$223$	21.0000	1.40626	0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000	1.40626	0.703132	+	0.711059i	$0.251784\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	9.00000	0.598671
$227$	−25.0000	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$227$	−25.0000	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	10.0000	0.650945
$237$	0	0
$238$	−3.00000	−0.194461
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	13.0000	0.832240
$245$	1.00000	0.0638877
$246$	0	0
$247$	0	0
$248$	3.00000	0.190500
$249$	0	0
$250$	9.00000	0.569210
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	−8.00000	−0.494242
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	8.00000	0.490511
$267$	0	0
$268$	−2.00000	−0.122169
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	12.0000	0.724947
$275$	−8.00000	−0.482418
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−14.0000	−0.839664
$279$	0	0
$280$	−1.00000	−0.0597614
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	0	0
$283$	18.0000	1.06999	0.534994	−	0.844856i	$-0.320314\pi$
$283$	18.0000	1.06999	0.534994	+	0.844856i	$0.320314\pi$
$284$	−9.00000	−0.534052
$285$	0	0
$286$	0	0
$287$	1.00000	0.0590281
$288$	0	0
$289$	−8.00000	−0.470588
$290$	−5.00000	−0.293610
$291$	0	0
$292$	4.00000	0.234082
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	−10.0000	−0.581238
$297$	0	0
$298$	3.00000	0.173785
$299$	0	0
$300$	0	0
$301$	−5.00000	−0.288195
$302$	−19.0000	−1.09333
$303$	0	0
$304$	−8.00000	−0.458831
$305$	13.0000	0.744378
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	3.00000	0.170389
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−11.0000	−0.618798
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	10.0000	0.559893
$320$	1.00000	0.0559017
$321$	0	0
$322$	−4.00000	−0.222911
$323$	−24.0000	−1.33540
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	−1.00000	−0.0552158
$329$	−6.00000	−0.330791
$330$	0	0
$331$	−32.0000	−1.75888	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000	−1.75888	−0.879440	+	0.476011i	$0.842082\pi$
$332$	14.0000	0.768350
$333$	0	0
$334$	0	0
$335$	−2.00000	−0.109272
$336$	0	0
$337$	−19.0000	−1.03500	−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000	−1.03500	−0.517498	+	0.855684i	$0.673136\pi$
$338$	13.0000	0.707107
$339$	0	0
$340$	3.00000	0.162698
$341$	−6.00000	−0.324918
$342$	0	0
$343$	1.00000	0.0539949
$344$	5.00000	0.269582
$345$	0	0
$346$	−1.00000	−0.0537603
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	−2.00000	−0.106600
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	0	0
$355$	−9.00000	−0.477670
$356$	1.00000	0.0529999
$357$	0	0
$358$	−16.0000	−0.845626
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	14.0000	0.735824
$363$	0	0
$364$	0	0
$365$	4.00000	0.209370
$366$	0	0
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	−10.0000	−0.519875
$371$	9.00000	0.467257
$372$	0	0
$373$	−18.0000	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$374$	−6.00000	−0.310253
$375$	0	0
$376$	6.00000	0.309426
$377$	0	0
$378$	0	0
$379$	37.0000	1.90056	0.950281	−	0.311393i	$-0.100796\pi$
$379$	37.0000	1.90056	0.950281	+	0.311393i	$0.100796\pi$
$380$	−8.00000	−0.410391
$381$	0	0
$382$	−11.0000	−0.562809
$383$	22.0000	1.12415	0.562074	−	0.827087i	$-0.310004\pi$
$383$	22.0000	1.12415	0.562074	+	0.827087i	$0.310004\pi$
$384$	0	0
$385$	2.00000	0.101929
$386$	−12.0000	−0.610784
$387$	0	0
$388$	7.00000	0.355371
$389$	2.00000	0.101404	0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000	0.101404	0.0507020	+	0.998714i	$0.483854\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−12.0000	−0.604551
$395$	−11.0000	−0.553470
$396$	0	0
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	24.0000	1.20301
$399$	0	0
$400$	−4.00000	−0.200000
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	0	0
$403$	0	0
$404$	10.0000	0.497519
$405$	0	0
$406$	−5.00000	−0.248146
$407$	20.0000	0.991363
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	−1.00000	−0.0493865
$411$	0	0
$412$	13.0000	0.640464
$413$	10.0000	0.492068
$414$	0	0
$415$	14.0000	0.687233
$416$	0	0
$417$	0	0
$418$	16.0000	0.782586
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	−19.0000	−0.926003	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000	−0.926003	−0.463002	+	0.886357i	$0.653228\pi$
$422$	12.0000	0.584151
$423$	0	0
$424$	−9.00000	−0.437079
$425$	−12.0000	−0.582086
$426$	0	0
$427$	13.0000	0.629114
$428$	−3.00000	−0.145010
$429$	0	0
$430$	5.00000	0.241121
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	3.00000	0.144005
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−32.0000	−1.53077
$438$	0	0
$439$	34.0000	1.62273	0.811366	−	0.584539i	$-0.198725\pi$
$439$	34.0000	1.62273	0.811366	+	0.584539i	$0.198725\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	0	0
$443$	25.0000	1.18779	0.593893	−	0.804544i	$-0.297590\pi$
$443$	25.0000	1.18779	0.593893	+	0.804544i	$0.297590\pi$
$444$	0	0
$445$	1.00000	0.0474045
$446$	−21.0000	−0.994379
$447$	0	0
$448$	1.00000	0.0472456
$449$	33.0000	1.55737	0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000	1.55737	0.778683	+	0.627417i	$0.215888\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−9.00000	−0.423324
$453$	0	0
$454$	25.0000	1.17331
$455$	0	0
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−20.0000	−0.934539
$459$	0	0
$460$	4.00000	0.186501
$461$	21.0000	0.978068	0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000	0.978068	0.489034	+	0.872265i	$0.337349\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	10.0000	0.463241
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	0	0
$469$	−2.00000	−0.0923514
$470$	6.00000	0.276759
$471$	0	0
$472$	−10.0000	−0.460287
$473$	−10.0000	−0.459800
$474$	0	0
$475$	32.0000	1.46826
$476$	3.00000	0.137505
$477$	0	0
$478$	−12.0000	−0.548867
$479$	10.0000	0.456912	0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000	0.456912	0.228456	+	0.973554i	$0.426632\pi$
$480$	0	0
$481$	0	0
$482$	10.0000	0.455488
$483$	0	0
$484$	−7.00000	−0.318182
$485$	7.00000	0.317854
$486$	0	0
$487$	12.0000	0.543772	0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000	0.543772	0.271886	+	0.962329i	$0.412353\pi$
$488$	−13.0000	−0.588482
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	−37.0000	−1.66979	−0.834893	−	0.550412i	$-0.814471\pi$
$491$	−37.0000	−1.66979	−0.834893	+	0.550412i	$0.814471\pi$
$492$	0	0
$493$	15.0000	0.675566
$494$	0	0
$495$	0	0
$496$	−3.00000	−0.134704
$497$	−9.00000	−0.403705
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	−9.00000	−0.402492
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	−8.00000	−0.355643
$507$	0	0
$508$	2.00000	0.0887357
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−15.0000	−0.661622
$515$	13.0000	0.572848
$516$	0	0
$517$	−12.0000	−0.527759
$518$	−10.0000	−0.439375
$519$	0	0
$520$	0	0
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	−16.0000	−0.697633
$527$	−9.00000	−0.392046
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−9.00000	−0.390935
$531$	0	0
$532$	−8.00000	−0.346844
$533$	0	0
$534$	0	0
$535$	−3.00000	−0.129701
$536$	2.00000	0.0863868
$537$	0	0
$538$	−10.0000	−0.431131
$539$	2.00000	0.0861461
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	−20.0000	−0.859074
$543$	0	0
$544$	−3.00000	−0.128624
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−12.0000	−0.512615
$549$	0	0
$550$	8.00000	0.341121
$551$	−40.0000	−1.70406
$552$	0	0
$553$	−11.0000	−0.467768
$554$	−26.0000	−1.10463
$555$	0	0
$556$	14.0000	0.593732
$557$	−33.0000	−1.39825	−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000	−1.39825	−0.699127	+	0.714997i	$0.746428\pi$
$558$	0	0
$559$	0	0
$560$	1.00000	0.0422577
$561$	0	0
$562$	2.00000	0.0843649
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−9.00000	−0.378633
$566$	−18.0000	−0.756596
$567$	0	0
$568$	9.00000	0.377632
$569$	25.0000	1.04805	0.524027	−	0.851701i	$-0.324429\pi$
$569$	25.0000	1.04805	0.524027	+	0.851701i	$0.324429\pi$
$570$	0	0
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	0	0
$573$	0	0
$574$	−1.00000	−0.0417392
$575$	−16.0000	−0.667246
$576$	0	0
$577$	46.0000	1.91501	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000	1.91501	0.957503	+	0.288425i	$0.0931316\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	5.00000	0.207614
$581$	14.0000	0.580818
$582$	0	0
$583$	18.0000	0.745484
$584$	−4.00000	−0.165521
$585$	0	0
$586$	14.0000	0.578335
$587$	21.0000	0.866763	0.433381	−	0.901211i	$-0.357320\pi$
$587$	21.0000	0.866763	0.433381	+	0.901211i	$0.357320\pi$
$588$	0	0
$589$	24.0000	0.988903
$590$	−10.0000	−0.411693
$591$	0	0
$592$	10.0000	0.410997
$593$	43.0000	1.76580	0.882899	−	0.469563i	$-0.155588\pi$
$593$	43.0000	1.76580	0.882899	+	0.469563i	$0.155588\pi$
$594$	0	0
$595$	3.00000	0.122988
$596$	−3.00000	−0.122885
$597$	0	0
$598$	0	0
$599$	44.0000	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$600$	0	0
$601$	21.0000	0.856608	0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000	0.856608	0.428304	+	0.903635i	$0.359111\pi$
$602$	5.00000	0.203785
$603$	0	0
$604$	19.0000	0.773099
$605$	−7.00000	−0.284590
$606$	0	0
$607$	−43.0000	−1.74532	−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000	−1.74532	−0.872658	+	0.488332i	$0.837606\pi$
$608$	8.00000	0.324443
$609$	0	0
$610$	−13.0000	−0.526355
$611$	0	0
$612$	0	0
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	0	0
$619$	−24.0000	−0.964641	−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000	−0.964641	−0.482321	+	0.875995i	$0.660206\pi$
$620$	−3.00000	−0.120483
$621$	0	0
$622$	18.0000	0.721734
$623$	1.00000	0.0400642
$624$	0	0
$625$	11.0000	0.440000
$626$	22.0000	0.879297
$627$	0	0
$628$	4.00000	0.159617
$629$	30.0000	1.19618
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	11.0000	0.437557
$633$	0	0
$634$	−18.0000	−0.714871
$635$	2.00000	0.0793676
$636$	0	0
$637$	0	0
$638$	−10.0000	−0.395904
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	−7.00000	−0.276053	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000	−0.276053	−0.138027	+	0.990429i	$0.544076\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	24.0000	0.944267
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	0	0
$649$	20.0000	0.785069
$650$	0	0
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−3.00000	−0.117399	−0.0586995	−	0.998276i	$-0.518695\pi$
$653$	−3.00000	−0.117399	−0.0586995	+	0.998276i	$0.518695\pi$
$654$	0	0
$655$	8.00000	0.312586
$656$	1.00000	0.0390434
$657$	0	0
$658$	6.00000	0.233904
$659$	−44.0000	−1.71400	−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000	−1.71400	−0.856998	+	0.515319i	$0.827673\pi$
$660$	0	0
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	32.0000	1.24372
$663$	0	0
$664$	−14.0000	−0.543305
$665$	−8.00000	−0.310227
$666$	0	0
$667$	20.0000	0.774403
$668$	0	0
$669$	0	0
$670$	2.00000	0.0772667
$671$	26.0000	1.00372
$672$	0	0
$673$	30.0000	1.15642	0.578208	−	0.815890i	$-0.303752\pi$
$673$	30.0000	1.15642	0.578208	+	0.815890i	$0.303752\pi$
$674$	19.0000	0.731853
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	7.00000	0.268635
$680$	−3.00000	−0.115045
$681$	0	0
$682$	6.00000	0.229752
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−5.00000	−0.190623
$689$	0	0
$690$	0	0
$691$	13.0000	0.494543	0.247272	−	0.968946i	$-0.420466\pi$
$691$	13.0000	0.494543	0.247272	+	0.968946i	$0.420466\pi$
$692$	1.00000	0.0380143
$693$	0	0
$694$	12.0000	0.455514
$695$	14.0000	0.531050
$696$	0	0
$697$	3.00000	0.113633
$698$	−14.0000	−0.529908
$699$	0	0
$700$	−4.00000	−0.151186
$701$	−16.0000	−0.604312	−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000	−0.604312	−0.302156	+	0.953259i	$0.597706\pi$
$702$	0	0
$703$	−80.0000	−3.01726
$704$	2.00000	0.0753778
$705$	0	0
$706$	−24.0000	−0.903252
$707$	10.0000	0.376089
$708$	0	0
$709$	3.00000	0.112667	0.0563337	−	0.998412i	$-0.482059\pi$
$709$	3.00000	0.112667	0.0563337	+	0.998412i	$0.482059\pi$
$710$	9.00000	0.337764
$711$	0	0
$712$	−1.00000	−0.0374766
$713$	−12.0000	−0.449404
$714$	0	0
$715$	0	0
$716$	16.0000	0.597948
$717$	0	0
$718$	24.0000	0.895672
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	13.0000	0.484145
$722$	−45.0000	−1.67473
$723$	0	0
$724$	−14.0000	−0.520306
$725$	−20.0000	−0.742781
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	0	0
$729$	0	0
$730$	−4.00000	−0.148047
$731$	−15.0000	−0.554795
$732$	0	0
$733$	13.0000	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−4.00000	−0.147342
$738$	0	0
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	10.0000	0.367607
$741$	0	0
$742$	−9.00000	−0.330400
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	0	0
$745$	−3.00000	−0.109911
$746$	18.0000	0.659027
$747$	0	0
$748$	6.00000	0.219382
$749$	−3.00000	−0.109618
$750$	0	0
$751$	24.0000	0.875772	0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000	0.875772	0.437886	+	0.899030i	$0.355727\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	0	0
$755$	19.0000	0.691481
$756$	0	0
$757$	−5.00000	−0.181728	−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000	−0.181728	−0.0908640	+	0.995863i	$0.528963\pi$
$758$	−37.0000	−1.34390
$759$	0	0
$760$	8.00000	0.290191
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	−2.00000	−0.0724049
$764$	11.0000	0.397966
$765$	0	0
$766$	−22.0000	−0.794892
$767$	0	0
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	−2.00000	−0.0720750
$771$	0	0
$772$	12.0000	0.431889
$773$	38.0000	1.36677	0.683383	−	0.730061i	$-0.260508\pi$
$773$	38.0000	1.36677	0.683383	+	0.730061i	$0.260508\pi$
$774$	0	0
$775$	12.0000	0.431053
$776$	−7.00000	−0.251285
$777$	0	0
$778$	−2.00000	−0.0717035
$779$	−8.00000	−0.286630
$780$	0	0
$781$	−18.0000	−0.644091
$782$	−12.0000	−0.429119
$783$	0	0
$784$	1.00000	0.0357143
$785$	4.00000	0.142766
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	12.0000	0.427482
$789$	0	0
$790$	11.0000	0.391362
$791$	−9.00000	−0.320003
$792$	0	0
$793$	0	0
$794$	−20.0000	−0.709773
$795$	0	0
$796$	−24.0000	−0.850657
$797$	−21.0000	−0.743858	−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000	−0.743858	−0.371929	+	0.928261i	$0.621304\pi$
$798$	0	0
$799$	−18.0000	−0.636794
$800$	4.00000	0.141421
$801$	0	0
$802$	−25.0000	−0.882781
$803$	8.00000	0.282314
$804$	0	0
$805$	4.00000	0.140981
$806$	0	0
$807$	0	0
$808$	−10.0000	−0.351799
$809$	−54.0000	−1.89854	−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000	−1.89854	−0.949269	+	0.314464i	$0.898175\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	5.00000	0.175466
$813$	0	0
$814$	−20.0000	−0.701000
$815$	−4.00000	−0.140114
$816$	0	0
$817$	40.0000	1.39942
$818$	10.0000	0.349642
$819$	0	0
$820$	1.00000	0.0349215
$821$	4.00000	0.139601	0.0698005	−	0.997561i	$-0.477764\pi$
$821$	4.00000	0.139601	0.0698005	+	0.997561i	$0.477764\pi$
$822$	0	0
$823$	−51.0000	−1.77775	−0.888874	−	0.458151i	$-0.848512\pi$
$823$	−51.0000	−1.77775	−0.888874	+	0.458151i	$0.848512\pi$
$824$	−13.0000	−0.452876
$825$	0	0
$826$	−10.0000	−0.347945
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	−14.0000	−0.485947
$831$	0	0
$832$	0	0
$833$	3.00000	0.103944
$834$	0	0
$835$	0	0
$836$	−16.0000	−0.553372
$837$	0	0
$838$	28.0000	0.967244
$839$	−14.0000	−0.483334	−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000	−0.483334	−0.241667	+	0.970359i	$0.577694\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	19.0000	0.654783
$843$	0	0
$844$	−12.0000	−0.413057
$845$	−13.0000	−0.447214
$846$	0	0
$847$	−7.00000	−0.240523
$848$	9.00000	0.309061
$849$	0	0
$850$	12.0000	0.411597
$851$	40.0000	1.37118
$852$	0	0
$853$	−21.0000	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$854$	−13.0000	−0.444851
$855$	0	0
$856$	3.00000	0.102538
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	0	0
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−5.00000	−0.170499
$861$	0	0
$862$	−16.0000	−0.544962
$863$	32.0000	1.08929	0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000	1.08929	0.544646	+	0.838666i	$0.316664\pi$
$864$	0	0
$865$	1.00000	0.0340010
$866$	0	0
$867$	0	0
$868$	−3.00000	−0.101827
$869$	−22.0000	−0.746299
$870$	0	0
$871$	0	0
$872$	2.00000	0.0677285
$873$	0	0
$874$	32.0000	1.08242
$875$	−9.00000	−0.304256
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	−34.0000	−1.14744
$879$	0	0
$880$	2.00000	0.0674200
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	−26.0000	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$884$	0	0
$885$	0	0
$886$	−25.0000	−0.839891
$887$	−20.0000	−0.671534	−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000	−0.671534	−0.335767	+	0.941945i	$0.608996\pi$
$888$	0	0
$889$	2.00000	0.0670778
$890$	−1.00000	−0.0335201
$891$	0	0
$892$	21.0000	0.703132
$893$	48.0000	1.60626
$894$	0	0
$895$	16.0000	0.534821
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−33.0000	−1.10122
$899$	−15.0000	−0.500278
$900$	0	0
$901$	27.0000	0.899500
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	9.00000	0.299336
$905$	−14.0000	−0.465376
$906$	0	0
$907$	19.0000	0.630885	0.315442	−	0.948945i	$-0.397847\pi$
$907$	19.0000	0.630885	0.315442	+	0.948945i	$0.397847\pi$
$908$	−25.0000	−0.829654
$909$	0	0
$910$	0	0
$911$	−2.00000	−0.0662630	−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000	−0.0662630	−0.0331315	+	0.999451i	$0.510548\pi$
$912$	0	0
$913$	28.0000	0.926665
$914$	18.0000	0.595387
$915$	0	0
$916$	20.0000	0.660819
$917$	8.00000	0.264183
$918$	0	0
$919$	3.00000	0.0989609	0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000	0.0989609	0.0494804	+	0.998775i	$0.484243\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	−21.0000	−0.691598
$923$	0	0
$924$	0	0
$925$	−40.0000	−1.31519
$926$	−16.0000	−0.525793
$927$	0	0
$928$	−5.00000	−0.164133
$929$	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
$931$	−8.00000	−0.262189
$932$	−10.0000	−0.327561
$933$	0	0
$934$	6.00000	0.196326
$935$	6.00000	0.196221
$936$	0	0
$937$	7.00000	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	−6.00000	−0.195698
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	4.00000	0.130258
$944$	10.0000	0.325472
$945$	0	0
$946$	10.0000	0.325128
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	0	0
$950$	−32.0000	−1.03822
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	0	0
$955$	11.0000	0.355952
$956$	12.0000	0.388108
$957$	0	0
$958$	−10.0000	−0.323085
$959$	−12.0000	−0.387500
$960$	0	0
$961$	−22.0000	−0.709677
$962$	0	0
$963$	0	0
$964$	−10.0000	−0.322078
$965$	12.0000	0.386294
$966$	0	0
$967$	−47.0000	−1.51142	−0.755709	−	0.654907i	$-0.772708\pi$
$967$	−47.0000	−1.51142	−0.755709	+	0.654907i	$0.772708\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−7.00000	−0.224756
$971$	−13.0000	−0.417190	−0.208595	−	0.978002i	$-0.566889\pi$
$971$	−13.0000	−0.417190	−0.208595	+	0.978002i	$0.566889\pi$
$972$	0	0
$973$	14.0000	0.448819
$974$	−12.0000	−0.384505
$975$	0	0
$976$	13.0000	0.416120
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	0	0
$979$	2.00000	0.0639203
$980$	1.00000	0.0319438
$981$	0	0
$982$	37.0000	1.18072
$983$	3.00000	0.0956851	0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000	0.0956851	0.0478426	+	0.998855i	$0.484765\pi$
$984$	0	0
$985$	12.0000	0.382352
$986$	−15.0000	−0.477697
$987$	0	0
$988$	0	0
$989$	−20.0000	−0.635963
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	3.00000	0.0952501
$993$	0	0
$994$	9.00000	0.285463
$995$	−24.0000	−0.760851
$996$	0	0
$997$	4.00000	0.126681	0.0633406	−	0.997992i	$-0.479825\pi$
$997$	4.00000	0.126681	0.0633406	+	0.997992i	$0.479825\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5166.2.a.o.1.1		1
3.2	odd	2		574.2.a.g.1.1	✓	1
12.11	even	2		4592.2.a.l.1.1		1
21.20	even	2		4018.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.g.1.1	✓	1	3.2	odd	2
4018.2.a.s.1.1		1	21.20	even	2
4592.2.a.l.1.1		1	12.11	even	2
5166.2.a.o.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5166.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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