LMFDB - Embedded newform 2601.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} -3.00000 q^{5} -2.00000 q^{7} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} -3.00000 q^{5} -2.00000 q^{7} +6.00000 q^{10} -5.00000 q^{11} -1.00000 q^{13} +4.00000 q^{14} -4.00000 q^{16} -5.00000 q^{19} -6.00000 q^{20} +10.0000 q^{22} -1.00000 q^{23} +4.00000 q^{25} +2.00000 q^{26} -4.00000 q^{28} -6.00000 q^{29} -10.0000 q^{31} +8.00000 q^{32} +6.00000 q^{35} +2.00000 q^{37} +10.0000 q^{38} -5.00000 q^{41} +1.00000 q^{43} -10.0000 q^{44} +2.00000 q^{46} +2.00000 q^{47} -3.00000 q^{49} -8.00000 q^{50} -2.00000 q^{52} -6.00000 q^{53} +15.0000 q^{55} +12.0000 q^{58} -10.0000 q^{61} +20.0000 q^{62} -8.00000 q^{64} +3.00000 q^{65} -12.0000 q^{67} -12.0000 q^{70} -6.00000 q^{73} -4.00000 q^{74} -10.0000 q^{76} +10.0000 q^{77} +4.00000 q^{79} +12.0000 q^{80} +10.0000 q^{82} -6.00000 q^{83} -2.00000 q^{86} +10.0000 q^{89} +2.00000 q^{91} -2.00000 q^{92} -4.00000 q^{94} +15.0000 q^{95} -8.00000 q^{97} +6.00000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	0	0
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	0	0
$9$	0	0
$10$	6.00000	1.89737
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	−4.00000	−1.00000
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−6.00000	−1.34164
$21$	0	0
$22$	10.0000	2.13201
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	2.00000	0.392232
$27$	0	0
$28$	−4.00000	−0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	0	0
$35$	6.00000	1.01419
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	10.0000	1.62221
$39$	0	0
$40$	0	0
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−10.0000	−1.50756
$45$	0	0
$46$	2.00000	0.294884
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	−8.00000	−1.13137
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	15.0000	2.02260
$56$	0	0
$57$	0	0
$58$	12.0000	1.57568
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	20.0000	2.54000
$63$	0	0
$64$	−8.00000	−1.00000
$65$	3.00000	0.372104
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	0	0
$69$	0	0
$70$	−12.0000	−1.43427
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−10.0000	−1.14708
$77$	10.0000	1.13961
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	12.0000	1.34164
$81$	0	0
$82$	10.0000	1.10432
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	0	0
$86$	−2.00000	−0.215666
$87$	0	0
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	−2.00000	−0.208514
$93$	0	0
$94$	−4.00000	−0.412568
$95$	15.0000	1.53897
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	8.00000	0.800000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	9.00000	0.886796	0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000	0.886796	0.443398	+	0.896325i	$0.353773\pi$
$104$	0	0
$105$	0	0
$106$	12.0000	1.16554
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	−30.0000	−2.86039
$111$	0	0
$112$	8.00000	0.755929
$113$	−11.0000	−1.03479	−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000	−1.03479	−0.517396	+	0.855746i	$0.673099\pi$
$114$	0	0
$115$	3.00000	0.279751
$116$	−12.0000	−1.11417
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	20.0000	1.81071
$123$	0	0
$124$	−20.0000	−1.79605
$125$	3.00000	0.268328
$126$	0	0
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	0	0
$129$	0	0
$130$	−6.00000	−0.526235
$131$	5.00000	0.436852	0.218426	−	0.975854i	$-0.429908\pi$
$131$	5.00000	0.436852	0.218426	+	0.975854i	$0.429908\pi$
$132$	0	0
$133$	10.0000	0.867110
$134$	24.0000	2.07328
$135$	0	0
$136$	0	0
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	0	0
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	12.0000	1.01419
$141$	0	0
$142$	0	0
$143$	5.00000	0.418121
$144$	0	0
$145$	18.0000	1.49482
$146$	12.0000	0.993127
$147$	0	0
$148$	4.00000	0.328798
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	0	0
$153$	0	0
$154$	−20.0000	−1.61165
$155$	30.0000	2.40966
$156$	0	0
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	−24.0000	−1.89737
$161$	2.00000	0.157622
$162$	0	0
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	12.0000	0.931381
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	2.00000	0.152499
$173$	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
$175$	−8.00000	−0.604743
$176$	20.0000	1.50756
$177$	0	0
$178$	−20.0000	−1.49906
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	0	0
$185$	−6.00000	−0.441129
$186$	0	0
$187$	0	0
$188$	4.00000	0.291730
$189$	0	0
$190$	−30.0000	−2.17643
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	16.0000	1.14873
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−23.0000	−1.63868	−0.819341	−	0.573306i	$-0.805660\pi$
$197$	−23.0000	−1.63868	−0.819341	+	0.573306i	$0.805660\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	0	0
$202$	24.0000	1.68863
$203$	12.0000	0.842235
$204$	0	0
$205$	15.0000	1.04765
$206$	−18.0000	−1.25412
$207$	0	0
$208$	4.00000	0.277350
$209$	25.0000	1.72929
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	−12.0000	−0.824163
$213$	0	0
$214$	−6.00000	−0.410152
$215$	−3.00000	−0.204598
$216$	0	0
$217$	20.0000	1.35769
$218$	−8.00000	−0.541828
$219$	0	0
$220$	30.0000	2.02260
$221$	0	0
$222$	0	0
$223$	11.0000	0.736614	0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000	0.736614	0.368307	+	0.929704i	$0.379937\pi$
$224$	−16.0000	−1.06904
$225$	0	0
$226$	22.0000	1.46342
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	0	0
$233$	−29.0000	−1.89985	−0.949927	−	0.312473i	$-0.898843\pi$
$233$	−29.0000	−1.89985	−0.949927	+	0.312473i	$0.898843\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	0	0
$237$	0	0
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−28.0000	−1.79991
$243$	0	0
$244$	−20.0000	−1.28037
$245$	9.00000	0.574989
$246$	0	0
$247$	5.00000	0.318142
$248$	0	0
$249$	0	0
$250$	−6.00000	−0.379473
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	5.00000	0.314347
$254$	−14.0000	−0.878438
$255$	0	0
$256$	16.0000	1.00000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	6.00000	0.372104
$261$	0	0
$262$	−10.0000	−0.617802
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	18.0000	1.10573
$266$	−20.0000	−1.22628
$267$	0	0
$268$	−24.0000	−1.46603
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	0	0
$271$	27.0000	1.64013	0.820067	−	0.572268i	$-0.193936\pi$
$271$	27.0000	1.64013	0.820067	+	0.572268i	$0.193936\pi$
$272$	0	0
$273$	0	0
$274$	16.0000	0.966595
$275$	−20.0000	−1.20605
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−32.0000	−1.91923
$279$	0	0
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	−10.0000	−0.591312
$287$	10.0000	0.590281
$288$	0	0
$289$	0	0
$290$	−36.0000	−2.11399
$291$	0	0
$292$	−12.0000	−0.702247
$293$	−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
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	1.00000	0.0578315
$300$	0	0
$301$	−2.00000	−0.115278
$302$	24.0000	1.38104
$303$	0	0
$304$	20.0000	1.14708
$305$	30.0000	1.71780
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	20.0000	1.13961
$309$	0	0
$310$	−60.0000	−3.40777
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	34.0000	1.91873
$315$	0	0
$316$	8.00000	0.450035
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	0	0
$319$	30.0000	1.67968
$320$	24.0000	1.34164
$321$	0	0
$322$	−4.00000	−0.222911
$323$	0	0
$324$	0	0
$325$	−4.00000	−0.221880
$326$	28.0000	1.55078
$327$	0	0
$328$	0	0
$329$	−4.00000	−0.220527
$330$	0	0
$331$	23.0000	1.26419	0.632097	−	0.774889i	$-0.282194\pi$
$331$	23.0000	1.26419	0.632097	+	0.774889i	$0.282194\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	−6.00000	−0.328305
$335$	36.0000	1.96689
$336$	0	0
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	24.0000	1.30543
$339$	0	0
$340$	0	0
$341$	50.0000	2.70765
$342$	0	0
$343$	20.0000	1.07990
$344$	0	0
$345$	0	0
$346$	−2.00000	−0.107521
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	16.0000	0.855236
$351$	0	0
$352$	−40.0000	−2.13201
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	0	0
$355$	0	0
$356$	20.0000	1.06000
$357$	0	0
$358$	−20.0000	−1.05703
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−40.0000	−2.10235
$363$	0	0
$364$	4.00000	0.209657
$365$	18.0000	0.942163
$366$	0	0
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	12.0000	0.623850
$371$	12.0000	0.623009
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	−34.0000	−1.74646	−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000	−1.74646	−0.873231	+	0.487306i	$0.837980\pi$
$380$	30.0000	1.53897
$381$	0	0
$382$	−16.0000	−0.818631
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	−30.0000	−1.52894
$386$	−12.0000	−0.610784
$387$	0	0
$388$	−16.0000	−0.812277
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	46.0000	2.31745
$395$	−12.0000	−0.603786
$396$	0	0
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	−32.0000	−1.60402
$399$	0	0
$400$	−16.0000	−0.800000
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	0	0
$403$	10.0000	0.498135
$404$	−24.0000	−1.19404
$405$	0	0
$406$	−24.0000	−1.19110
$407$	−10.0000	−0.495682
$408$	0	0
$409$	25.0000	1.23617	0.618085	−	0.786111i	$-0.287909\pi$
$409$	25.0000	1.23617	0.618085	+	0.786111i	$0.287909\pi$
$410$	−30.0000	−1.48159
$411$	0	0
$412$	18.0000	0.886796
$413$	0	0
$414$	0	0
$415$	18.0000	0.883585
$416$	−8.00000	−0.392232
$417$	0	0
$418$	−50.0000	−2.44558
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	20.0000	0.973585
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	20.0000	0.967868
$428$	6.00000	0.290021
$429$	0	0
$430$	6.00000	0.289346
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	0	0
$433$	11.0000	0.528626	0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000	0.528626	0.264313	+	0.964437i	$0.414855\pi$
$434$	−40.0000	−1.92006
$435$	0	0
$436$	8.00000	0.383131
$437$	5.00000	0.239182
$438$	0	0
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−34.0000	−1.61539	−0.807694	−	0.589601i	$-0.799285\pi$
$443$	−34.0000	−1.61539	−0.807694	+	0.589601i	$0.799285\pi$
$444$	0	0
$445$	−30.0000	−1.42214
$446$	−22.0000	−1.04173
$447$	0	0
$448$	16.0000	0.755929
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	0	0
$451$	25.0000	1.17720
$452$	−22.0000	−1.03479
$453$	0	0
$454$	6.00000	0.281594
$455$	−6.00000	−0.281284
$456$	0	0
$457$	−23.0000	−1.07589	−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000	−1.07589	−0.537947	+	0.842978i	$0.680800\pi$
$458$	20.0000	0.934539
$459$	0	0
$460$	6.00000	0.279751
$461$	32.0000	1.49039	0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000	1.49039	0.745194	+	0.666847i	$0.232357\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	24.0000	1.11417
$465$	0	0
$466$	58.0000	2.68680
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	24.0000	1.10822
$470$	12.0000	0.553519
$471$	0	0
$472$	0	0
$473$	−5.00000	−0.229900
$474$	0	0
$475$	−20.0000	−0.917663
$476$	0	0
$477$	0	0
$478$	−40.0000	−1.82956
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	20.0000	0.910975
$483$	0	0
$484$	28.0000	1.27273
$485$	24.0000	1.08978
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	0	0
$489$	0	0
$490$	−18.0000	−0.813157
$491$	−38.0000	−1.71492	−0.857458	−	0.514554i	$-0.827958\pi$
$491$	−38.0000	−1.71492	−0.857458	+	0.514554i	$0.827958\pi$
$492$	0	0
$493$	0	0
$494$	−10.0000	−0.449921
$495$	0	0
$496$	40.0000	1.79605
$497$	0	0
$498$	0	0
$499$	−6.00000	−0.268597	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000	−0.268597	−0.134298	+	0.990941i	$0.542878\pi$
$500$	6.00000	0.268328
$501$	0	0
$502$	−36.0000	−1.60676
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	0	0
$505$	36.0000	1.60198
$506$	−10.0000	−0.444554
$507$	0	0
$508$	14.0000	0.621150
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	−32.0000	−1.41421
$513$	0	0
$514$	4.00000	0.176432
$515$	−27.0000	−1.18976
$516$	0	0
$517$	−10.0000	−0.439799
$518$	8.00000	0.351500
$519$	0	0
$520$	0	0
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	0	0
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	12.0000	0.523225
$527$	0	0
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−36.0000	−1.56374
$531$	0	0
$532$	20.0000	0.867110
$533$	5.00000	0.216574
$534$	0	0
$535$	−9.00000	−0.389104
$536$	0	0
$537$	0	0
$538$	42.0000	1.81075
$539$	15.0000	0.646096
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	−54.0000	−2.31950
$543$	0	0
$544$	0	0
$545$	−12.0000	−0.514024
$546$	0	0
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	−16.0000	−0.683486
$549$	0	0
$550$	40.0000	1.70561
$551$	30.0000	1.27804
$552$	0	0
$553$	−8.00000	−0.340195
$554$	−44.0000	−1.86938
$555$	0	0
$556$	32.0000	1.35710
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	−1.00000	−0.0422955
$560$	−24.0000	−1.01419
$561$	0	0
$562$	−44.0000	−1.85603
$563$	14.0000	0.590030	0.295015	−	0.955493i	$-0.404675\pi$
$563$	14.0000	0.590030	0.295015	+	0.955493i	$0.404675\pi$
$564$	0	0
$565$	33.0000	1.38832
$566$	8.00000	0.336265
$567$	0	0
$568$	0	0
$569$	−40.0000	−1.67689	−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000	−1.67689	−0.838444	+	0.544988i	$0.816534\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	10.0000	0.418121
$573$	0	0
$574$	−20.0000	−0.834784
$575$	−4.00000	−0.166812
$576$	0	0
$577$	−27.0000	−1.12402	−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000	−1.12402	−0.562012	+	0.827129i	$0.689973\pi$
$578$	0	0
$579$	0	0
$580$	36.0000	1.49482
$581$	12.0000	0.497844
$582$	0	0
$583$	30.0000	1.24247
$584$	0	0
$585$	0	0
$586$	28.0000	1.15667
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	50.0000	2.06021
$590$	0	0
$591$	0	0
$592$	−8.00000	−0.328798
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−2.00000	−0.0817861
$599$	20.0000	0.817178	0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000	0.817178	0.408589	+	0.912719i	$0.366021\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	4.00000	0.163028
$603$	0	0
$604$	−24.0000	−0.976546
$605$	−42.0000	−1.70754
$606$	0	0
$607$	−28.0000	−1.13648	−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000	−1.13648	−0.568242	+	0.822861i	$0.692376\pi$
$608$	−40.0000	−1.62221
$609$	0	0
$610$	−60.0000	−2.42933
$611$	−2.00000	−0.0809113
$612$	0	0
$613$	−21.0000	−0.848182	−0.424091	−	0.905620i	$-0.639406\pi$
$613$	−21.0000	−0.848182	−0.424091	+	0.905620i	$0.639406\pi$
$614$	24.0000	0.968561
$615$	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	$0.820655\pi$
$618$	0	0
$619$	−36.0000	−1.44696	−0.723481	−	0.690344i	$-0.757459\pi$
$619$	−36.0000	−1.44696	−0.723481	+	0.690344i	$0.757459\pi$
$620$	60.0000	2.40966
$621$	0	0
$622$	0	0
$623$	−20.0000	−0.801283
$624$	0	0
$625$	−29.0000	−1.16000
$626$	−32.0000	−1.27898
$627$	0	0
$628$	−34.0000	−1.35675
$629$	0	0
$630$	0	0
$631$	23.0000	0.915616	0.457808	−	0.889051i	$-0.348635\pi$
$631$	23.0000	0.915616	0.457808	+	0.889051i	$0.348635\pi$
$632$	0	0
$633$	0	0
$634$	−44.0000	−1.74746
$635$	−21.0000	−0.833360
$636$	0	0
$637$	3.00000	0.118864
$638$	−60.0000	−2.37542
$639$	0	0
$640$	0	0
$641$	−35.0000	−1.38242	−0.691208	−	0.722655i	$-0.742921\pi$
$641$	−35.0000	−1.38242	−0.691208	+	0.722655i	$0.742921\pi$
$642$	0	0
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	0	0
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	0	0
$649$	0	0
$650$	8.00000	0.313786
$651$	0	0
$652$	−28.0000	−1.09656
$653$	−11.0000	−0.430463	−0.215232	−	0.976563i	$-0.569051\pi$
$653$	−11.0000	−0.430463	−0.215232	+	0.976563i	$0.569051\pi$
$654$	0	0
$655$	−15.0000	−0.586098
$656$	20.0000	0.780869
$657$	0	0
$658$	8.00000	0.311872
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	−27.0000	−1.05018	−0.525089	−	0.851047i	$-0.675968\pi$
$661$	−27.0000	−1.05018	−0.525089	+	0.851047i	$0.675968\pi$
$662$	−46.0000	−1.78784
$663$	0	0
$664$	0	0
$665$	−30.0000	−1.16335
$666$	0	0
$667$	6.00000	0.232321
$668$	6.00000	0.232147
$669$	0	0
$670$	−72.0000	−2.78160
$671$	50.0000	1.93023
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	−64.0000	−2.46519
$675$	0	0
$676$	−24.0000	−0.923077
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	0	0
$679$	16.0000	0.614024
$680$	0	0
$681$	0	0
$682$	−100.000	−3.82920
$683$	21.0000	0.803543	0.401771	−	0.915740i	$-0.368395\pi$
$683$	21.0000	0.803543	0.401771	+	0.915740i	$0.368395\pi$
$684$	0	0
$685$	24.0000	0.916993
$686$	−40.0000	−1.52721
$687$	0	0
$688$	−4.00000	−0.152499
$689$	6.00000	0.228582
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	16.0000	0.607352
$695$	−48.0000	−1.82074
$696$	0	0
$697$	0	0
$698$	−10.0000	−0.378506
$699$	0	0
$700$	−16.0000	−0.604743
$701$	8.00000	0.302156	0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000	0.302156	0.151078	+	0.988522i	$0.451726\pi$
$702$	0	0
$703$	−10.0000	−0.377157
$704$	40.0000	1.50756
$705$	0	0
$706$	48.0000	1.80650
$707$	24.0000	0.902613
$708$	0	0
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	10.0000	0.374503
$714$	0	0
$715$	−15.0000	−0.560968
$716$	20.0000	0.747435
$717$	0	0
$718$	20.0000	0.746393
$719$	9.00000	0.335643	0.167822	−	0.985817i	$-0.446327\pi$
$719$	9.00000	0.335643	0.167822	+	0.985817i	$0.446327\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	−12.0000	−0.446594
$723$	0	0
$724$	40.0000	1.48659
$725$	−24.0000	−0.891338
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	0	0
$729$	0	0
$730$	−36.0000	−1.33242
$731$	0	0
$732$	0	0
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	−36.0000	−1.32878
$735$	0	0
$736$	−8.00000	−0.294884
$737$	60.0000	2.21013
$738$	0	0
$739$	−5.00000	−0.183928	−0.0919640	−	0.995762i	$-0.529314\pi$
$739$	−5.00000	−0.183928	−0.0919640	+	0.995762i	$0.529314\pi$
$740$	−12.0000	−0.441129
$741$	0	0
$742$	−24.0000	−0.881068
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	0	0
$746$	−28.0000	−1.02515
$747$	0	0
$748$	0	0
$749$	−6.00000	−0.219235
$750$	0	0
$751$	10.0000	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$752$	−8.00000	−0.291730
$753$	0	0
$754$	−12.0000	−0.437014
$755$	36.0000	1.31017
$756$	0	0
$757$	−43.0000	−1.56286	−0.781431	−	0.623992i	$-0.785510\pi$
$757$	−43.0000	−1.56286	−0.781431	+	0.623992i	$0.785510\pi$
$758$	68.0000	2.46987
$759$	0	0
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	−8.00000	−0.289619
$764$	16.0000	0.578860
$765$	0	0
$766$	32.0000	1.15621
$767$	0	0
$768$	0	0
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	60.0000	2.16225
$771$	0	0
$772$	12.0000	0.431889
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	0	0
$775$	−40.0000	−1.43684
$776$	0	0
$777$	0	0
$778$	60.0000	2.15110
$779$	25.0000	0.895718
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	12.0000	0.428571
$785$	51.0000	1.82027
$786$	0	0
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	−46.0000	−1.63868
$789$	0	0
$790$	24.0000	0.853882
$791$	22.0000	0.782230
$792$	0	0
$793$	10.0000	0.355110
$794$	−16.0000	−0.567819
$795$	0	0
$796$	32.0000	1.13421
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	0	0
$800$	32.0000	1.13137
$801$	0	0
$802$	−30.0000	−1.05934
$803$	30.0000	1.05868
$804$	0	0
$805$	−6.00000	−0.211472
$806$	−20.0000	−0.704470
$807$	0	0
$808$	0	0
$809$	11.0000	0.386739	0.193370	−	0.981126i	$-0.438058\pi$
$809$	11.0000	0.386739	0.193370	+	0.981126i	$0.438058\pi$
$810$	0	0
$811$	−50.0000	−1.75574	−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000	−1.75574	−0.877869	+	0.478901i	$0.841035\pi$
$812$	24.0000	0.842235
$813$	0	0
$814$	20.0000	0.701000
$815$	42.0000	1.47120
$816$	0	0
$817$	−5.00000	−0.174928
$818$	−50.0000	−1.74821
$819$	0	0
$820$	30.0000	1.04765
$821$	25.0000	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$822$	0	0
$823$	46.0000	1.60346	0.801730	−	0.597687i	$-0.203913\pi$
$823$	46.0000	1.60346	0.801730	+	0.597687i	$0.203913\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	0	0
$829$	−50.0000	−1.73657	−0.868286	−	0.496064i	$-0.834778\pi$
$829$	−50.0000	−1.73657	−0.868286	+	0.496064i	$0.834778\pi$
$830$	−36.0000	−1.24958
$831$	0	0
$832$	8.00000	0.277350
$833$	0	0
$834$	0	0
$835$	−9.00000	−0.311458
$836$	50.0000	1.72929
$837$	0	0
$838$	−32.0000	−1.10542
$839$	41.0000	1.41548	0.707739	−	0.706474i	$-0.249715\pi$
$839$	41.0000	1.41548	0.707739	+	0.706474i	$0.249715\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	26.0000	0.896019
$843$	0	0
$844$	−20.0000	−0.688428
$845$	36.0000	1.23844
$846$	0	0
$847$	−28.0000	−0.962091
$848$	24.0000	0.824163
$849$	0	0
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	0	0
$853$	−36.0000	−1.23262	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	−36.0000	−1.23262	−0.616308	+	0.787505i	$0.711372\pi$
$854$	−40.0000	−1.36877
$855$	0	0
$856$	0	0
$857$	2.00000	0.0683187	0.0341593	−	0.999416i	$-0.489125\pi$
$857$	2.00000	0.0683187	0.0341593	+	0.999416i	$0.489125\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−6.00000	−0.204598
$861$	0	0
$862$	40.0000	1.36241
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	0	0
$865$	−3.00000	−0.102003
$866$	−22.0000	−0.747590
$867$	0	0
$868$	40.0000	1.35769
$869$	−20.0000	−0.678454
$870$	0	0
$871$	12.0000	0.406604
$872$	0	0
$873$	0	0
$874$	−10.0000	−0.338255
$875$	−6.00000	−0.202837
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	48.0000	1.61992
$879$	0	0
$880$	−60.0000	−2.02260
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	0	0
$883$	19.0000	0.639401	0.319700	−	0.947519i	$-0.396418\pi$
$883$	19.0000	0.639401	0.319700	+	0.947519i	$0.396418\pi$
$884$	0	0
$885$	0	0
$886$	68.0000	2.28450
$887$	13.0000	0.436497	0.218249	−	0.975893i	$-0.429966\pi$
$887$	13.0000	0.436497	0.218249	+	0.975893i	$0.429966\pi$
$888$	0	0
$889$	−14.0000	−0.469545
$890$	60.0000	2.01120
$891$	0	0
$892$	22.0000	0.736614
$893$	−10.0000	−0.334637
$894$	0	0
$895$	−30.0000	−1.00279
$896$	0	0
$897$	0	0
$898$	68.0000	2.26919
$899$	60.0000	2.00111
$900$	0	0
$901$	0	0
$902$	−50.0000	−1.66482
$903$	0	0
$904$	0	0
$905$	−60.0000	−1.99447
$906$	0	0
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	−6.00000	−0.199117
$909$	0	0
$910$	12.0000	0.397796
$911$	−5.00000	−0.165657	−0.0828287	−	0.996564i	$-0.526395\pi$
$911$	−5.00000	−0.165657	−0.0828287	+	0.996564i	$0.526395\pi$
$912$	0	0
$913$	30.0000	0.992855
$914$	46.0000	1.52154
$915$	0	0
$916$	−20.0000	−0.660819
$917$	−10.0000	−0.330229
$918$	0	0
$919$	15.0000	0.494804	0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000	0.494804	0.247402	+	0.968913i	$0.420423\pi$
$920$	0	0
$921$	0	0
$922$	−64.0000	−2.10773
$923$	0	0
$924$	0	0
$925$	8.00000	0.263038
$926$	32.0000	1.05159
$927$	0	0
$928$	−48.0000	−1.57568
$929$	21.0000	0.688988	0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000	0.688988	0.344494	+	0.938789i	$0.388051\pi$
$930$	0	0
$931$	15.0000	0.491605
$932$	−58.0000	−1.89985
$933$	0	0
$934$	−56.0000	−1.83238
$935$	0	0
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−48.0000	−1.56726
$939$	0	0
$940$	−12.0000	−0.391397
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	5.00000	0.162822
$944$	0	0
$945$	0	0
$946$	10.0000	0.325128
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	0	0
$949$	6.00000	0.194768
$950$	40.0000	1.29777
$951$	0	0
$952$	0	0
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	0	0
$955$	−24.0000	−0.776622
$956$	40.0000	1.29369
$957$	0	0
$958$	42.0000	1.35696
$959$	16.0000	0.516667
$960$	0	0
$961$	69.0000	2.22581
$962$	4.00000	0.128965
$963$	0	0
$964$	−20.0000	−0.644157
$965$	−18.0000	−0.579441
$966$	0	0
$967$	57.0000	1.83300	0.916498	−	0.400039i	$-0.131003\pi$
$967$	57.0000	1.83300	0.916498	+	0.400039i	$0.131003\pi$
$968$	0	0
$969$	0	0
$970$	−48.0000	−1.54119
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	0	0
$973$	−32.0000	−1.02587
$974$	64.0000	2.05069
$975$	0	0
$976$	40.0000	1.28037
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	0	0
$979$	−50.0000	−1.59801
$980$	18.0000	0.574989
$981$	0	0
$982$	76.0000	2.42526
$983$	−19.0000	−0.606006	−0.303003	−	0.952990i	$-0.597989\pi$
$983$	−19.0000	−0.606006	−0.303003	+	0.952990i	$0.597989\pi$
$984$	0	0
$985$	69.0000	2.19852
$986$	0	0
$987$	0	0
$988$	10.0000	0.318142
$989$	−1.00000	−0.0317982
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	−80.0000	−2.54000
$993$	0	0
$994$	0	0
$995$	−48.0000	−1.52170
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	12.0000	0.379853
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.a.1.1		1
3.2	odd	2		867.2.a.e.1.1		1
17.4	even	4		153.2.d.c.118.2		2
17.13	even	4		153.2.d.c.118.1		2
17.16	even	2		2601.2.a.c.1.1		1
51.2	odd	8		867.2.e.a.616.2		4
51.5	even	16		867.2.h.e.688.1		8
51.8	odd	8		867.2.e.a.829.1		4
51.11	even	16		867.2.h.e.733.1		8
51.14	even	16		867.2.h.e.757.1		8
51.20	even	16		867.2.h.e.757.2		8
51.23	even	16		867.2.h.e.733.2		8
51.26	odd	8		867.2.e.a.829.2		4
51.29	even	16		867.2.h.e.688.2		8
51.32	odd	8		867.2.e.a.616.1		4
51.38	odd	4		51.2.d.a.16.1	✓	2
51.41	even	16		867.2.h.e.712.1		8
51.44	even	16		867.2.h.e.712.2		8
51.47	odd	4		51.2.d.a.16.2	yes	2
51.50	odd	2		867.2.a.d.1.1		1
68.47	odd	4		2448.2.c.f.577.1		2
68.55	odd	4		2448.2.c.f.577.2		2
204.47	even	4		816.2.c.b.577.1		2
204.191	even	4		816.2.c.b.577.2		2
255.38	even	4		1275.2.d.c.424.2		2
255.47	even	4		1275.2.d.c.424.1		2
255.89	odd	4		1275.2.g.b.526.2		2
255.98	even	4		1275.2.d.a.424.2		2
255.149	odd	4		1275.2.g.b.526.1		2
255.242	even	4		1275.2.d.a.424.1		2
408.149	odd	4		3264.2.c.g.577.1		2
408.251	even	4		3264.2.c.h.577.2		2
408.293	odd	4		3264.2.c.g.577.2		2
408.395	even	4		3264.2.c.h.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.d.a.16.1	✓	2	51.38	odd	4
51.2.d.a.16.2	yes	2	51.47	odd	4
153.2.d.c.118.1		2	17.13	even	4
153.2.d.c.118.2		2	17.4	even	4
816.2.c.b.577.1		2	204.47	even	4
816.2.c.b.577.2		2	204.191	even	4
867.2.a.d.1.1		1	51.50	odd	2
867.2.a.e.1.1		1	3.2	odd	2
867.2.e.a.616.1		4	51.32	odd	8
867.2.e.a.616.2		4	51.2	odd	8
867.2.e.a.829.1		4	51.8	odd	8
867.2.e.a.829.2		4	51.26	odd	8
867.2.h.e.688.1		8	51.5	even	16
867.2.h.e.688.2		8	51.29	even	16
867.2.h.e.712.1		8	51.41	even	16
867.2.h.e.712.2		8	51.44	even	16
867.2.h.e.733.1		8	51.11	even	16
867.2.h.e.733.2		8	51.23	even	16
867.2.h.e.757.1		8	51.14	even	16
867.2.h.e.757.2		8	51.20	even	16
1275.2.d.a.424.1		2	255.242	even	4
1275.2.d.a.424.2		2	255.98	even	4
1275.2.d.c.424.1		2	255.47	even	4
1275.2.d.c.424.2		2	255.38	even	4
1275.2.g.b.526.1		2	255.149	odd	4
1275.2.g.b.526.2		2	255.89	odd	4
2448.2.c.f.577.1		2	68.47	odd	4
2448.2.c.f.577.2		2	68.55	odd	4
2601.2.a.a.1.1		1	1.1	even	1	trivial
2601.2.a.c.1.1		1	17.16	even	2
3264.2.c.g.577.1		2	408.149	odd	4
3264.2.c.g.577.2		2	408.293	odd	4
3264.2.c.h.577.1		2	408.395	even	4
3264.2.c.h.577.2		2	408.251	even	4

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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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