LMFDB - Embedded newform 2601.2.a.y.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 867)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.53209$ of defining polynomial
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)

$f(q)$	$=$	$q+2.53209 q^{2} +4.41147 q^{4} +0.879385 q^{5} +4.41147 q^{7} +6.10607 q^{8} +O(q^{10})$	$q+2.53209 q^{2} +4.41147 q^{4} +0.879385 q^{5} +4.41147 q^{7} +6.10607 q^{8} +2.22668 q^{10} +3.71688 q^{11} -3.12061 q^{13} +11.1702 q^{14} +6.63816 q^{16} -2.04189 q^{19} +3.87939 q^{20} +9.41147 q^{22} +0.162504 q^{23} -4.22668 q^{25} -7.90167 q^{26} +19.4611 q^{28} -8.33275 q^{29} +1.77332 q^{31} +4.59627 q^{32} +3.87939 q^{35} -2.73648 q^{37} -5.17024 q^{38} +5.36959 q^{40} +2.58853 q^{41} -11.7588 q^{43} +16.3969 q^{44} +0.411474 q^{46} -3.26857 q^{47} +12.4611 q^{49} -10.7023 q^{50} -13.7665 q^{52} +6.46791 q^{53} +3.26857 q^{55} +26.9368 q^{56} -21.0993 q^{58} -7.23442 q^{59} +2.50980 q^{61} +4.49020 q^{62} -1.63816 q^{64} -2.74422 q^{65} -4.61081 q^{67} +9.82295 q^{70} +1.12836 q^{71} -2.77332 q^{73} -6.92902 q^{74} -9.00774 q^{76} +16.3969 q^{77} -3.45336 q^{79} +5.83750 q^{80} +6.55438 q^{82} +14.8307 q^{83} -29.7743 q^{86} +22.6955 q^{88} +11.4192 q^{89} -13.7665 q^{91} +0.716881 q^{92} -8.27631 q^{94} -1.79561 q^{95} +4.30541 q^{97} +31.5526 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} + 3 q^{11} - 15 q^{13} + 12 q^{14} + 3 q^{16} - 3 q^{19} + 6 q^{20} + 18 q^{22} + 3 q^{23} - 6 q^{25} - 12 q^{26} + 21 q^{28} - 6 q^{29} + 12 q^{31} + 6 q^{35} - 3 q^{37} + 6 q^{38} + 9 q^{40} + 18 q^{41} - 24 q^{43} + 21 q^{44} - 9 q^{46} - 6 q^{50} - 6 q^{52} + 24 q^{53} + 24 q^{56} - 9 q^{58} + 9 q^{59} + 9 q^{61} + 12 q^{62} + 12 q^{64} + 21 q^{65} - 18 q^{67} + 9 q^{70} - 15 q^{71} - 15 q^{73} + 12 q^{74} - 3 q^{76} + 21 q^{77} + 3 q^{79} + 15 q^{80} + 9 q^{82} - 30 q^{86} - 6 q^{91} - 6 q^{92} + 9 q^{94} - 6 q^{95} + 15 q^{97} + 27 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8 + 3 * q^11 - 15 * q^13 + 12 * q^14 + 3 * q^16 - 3 * q^19 + 6 * q^20 + 18 * q^22 + 3 * q^23 - 6 * q^25 - 12 * q^26 + 21 * q^28 - 6 * q^29 + 12 * q^31 + 6 * q^35 - 3 * q^37 + 6 * q^38 + 9 * q^40 + 18 * q^41 - 24 * q^43 + 21 * q^44 - 9 * q^46 - 6 * q^50 - 6 * q^52 + 24 * q^53 + 24 * q^56 - 9 * q^58 + 9 * q^59 + 9 * q^61 + 12 * q^62 + 12 * q^64 + 21 * q^65 - 18 * q^67 + 9 * q^70 - 15 * q^71 - 15 * q^73 + 12 * q^74 - 3 * q^76 + 21 * q^77 + 3 * q^79 + 15 * q^80 + 9 * q^82 - 30 * q^86 - 6 * q^91 - 6 * q^92 + 9 * q^94 - 6 * q^95 + 15 * q^97 + 27 * q^98

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 $

$2$	2.53209	1.79046	0.895229	−	0.445607i	$-0.147012\pi$
$2$	2.53209	1.79046	0.895229	+	0.445607i	$0.147012\pi$
$3$	0	0
$3$	0	0
$4$	4.41147	2.20574
$5$	0.879385	0.393273	0.196637	−	0.980476i	$-0.436998\pi$
$5$	0.879385	0.393273	0.196637	+	0.980476i	$0.436998\pi$
$6$	0	0
$7$	4.41147	1.66738	0.833690	−	0.552232i	$-0.186224\pi$
$7$	4.41147	1.66738	0.833690	+	0.552232i	$0.186224\pi$
$8$	6.10607	2.15882
$9$	0	0
$10$	2.22668	0.704139
$11$	3.71688	1.12068	0.560341	−	0.828262i	$-0.310670\pi$
$11$	3.71688	1.12068	0.560341	+	0.828262i	$0.310670\pi$
$12$	0	0
$13$	−3.12061	−0.865503	−0.432751	−	0.901513i	$-0.642457\pi$
$13$	−3.12061	−0.865503	−0.432751	+	0.901513i	$0.642457\pi$
$14$	11.1702	2.98537
$15$	0	0
$16$	6.63816	1.65954
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−2.04189	−0.468441	−0.234221	−	0.972183i	$-0.575254\pi$
$19$	−2.04189	−0.468441	−0.234221	+	0.972183i	$0.575254\pi$
$20$	3.87939	0.867457
$21$	0	0
$22$	9.41147	2.00653
$23$	0.162504	0.0338844	0.0169422	−	0.999856i	$-0.494607\pi$
$23$	0.162504	0.0338844	0.0169422	+	0.999856i	$0.494607\pi$
$24$	0	0
$25$	−4.22668	−0.845336
$26$	−7.90167	−1.54965
$27$	0	0
$28$	19.4611	3.67780
$29$	−8.33275	−1.54735	−0.773676	−	0.633581i	$-0.781584\pi$
$29$	−8.33275	−1.54735	−0.773676	+	0.633581i	$0.781584\pi$
$30$	0	0
$31$	1.77332	0.318497	0.159249	−	0.987238i	$-0.449093\pi$
$31$	1.77332	0.318497	0.159249	+	0.987238i	$0.449093\pi$
$32$	4.59627	0.812513
$33$	0	0
$34$	0	0
$35$	3.87939	0.655736
$36$	0	0
$37$	−2.73648	−0.449875	−0.224937	−	0.974373i	$-0.572218\pi$
$37$	−2.73648	−0.449875	−0.224937	+	0.974373i	$0.572218\pi$
$38$	−5.17024	−0.838724
$39$	0	0
$40$	5.36959	0.849006
$41$	2.58853	0.404260	0.202130	−	0.979359i	$-0.435214\pi$
$41$	2.58853	0.404260	0.202130	+	0.979359i	$0.435214\pi$
$42$	0	0
$43$	−11.7588	−1.79320	−0.896598	−	0.442846i	$-0.853969\pi$
$43$	−11.7588	−1.79320	−0.896598	+	0.442846i	$0.853969\pi$
$44$	16.3969	2.47193
$45$	0	0
$46$	0.411474	0.0606686
$47$	−3.26857	−0.476770	−0.238385	−	0.971171i	$-0.576618\pi$
$47$	−3.26857	−0.476770	−0.238385	+	0.971171i	$0.576618\pi$
$48$	0	0
$49$	12.4611	1.78016
$50$	−10.7023	−1.51354
$51$	0	0
$52$	−13.7665	−1.90907
$53$	6.46791	0.888436	0.444218	−	0.895919i	$-0.353482\pi$
$53$	6.46791	0.888436	0.444218	+	0.895919i	$0.353482\pi$
$54$	0	0
$55$	3.26857	0.440734
$56$	26.9368	3.59958
$57$	0	0
$58$	−21.0993	−2.77047
$59$	−7.23442	−0.941842	−0.470921	−	0.882176i	$-0.656078\pi$
$59$	−7.23442	−0.941842	−0.470921	+	0.882176i	$0.656078\pi$
$60$	0	0
$61$	2.50980	0.321347	0.160673	−	0.987008i	$-0.448633\pi$
$61$	2.50980	0.321347	0.160673	+	0.987008i	$0.448633\pi$
$62$	4.49020	0.570256
$63$	0	0
$64$	−1.63816	−0.204769
$65$	−2.74422	−0.340379
$66$	0	0
$67$	−4.61081	−0.563301	−0.281650	−	0.959517i	$-0.590882\pi$
$67$	−4.61081	−0.563301	−0.281650	+	0.959517i	$0.590882\pi$
$68$	0	0
$69$	0	0
$70$	9.82295	1.17407
$71$	1.12836	0.133911	0.0669556	−	0.997756i	$-0.478671\pi$
$71$	1.12836	0.133911	0.0669556	+	0.997756i	$0.478671\pi$
$72$	0	0
$73$	−2.77332	−0.324592	−0.162296	−	0.986742i	$-0.551890\pi$
$73$	−2.77332	−0.324592	−0.162296	+	0.986742i	$0.551890\pi$
$74$	−6.92902	−0.805482
$75$	0	0
$76$	−9.00774	−1.03326
$77$	16.3969	1.86860
$78$	0	0
$79$	−3.45336	−0.388534	−0.194267	−	0.980949i	$-0.562233\pi$
$79$	−3.45336	−0.388534	−0.194267	+	0.980949i	$0.562233\pi$
$80$	5.83750	0.652652
$81$	0	0
$82$	6.55438	0.723810
$83$	14.8307	1.62788	0.813940	−	0.580949i	$-0.197319\pi$
$83$	14.8307	1.62788	0.813940	+	0.580949i	$0.197319\pi$
$84$	0	0
$85$	0	0
$86$	−29.7743	−3.21064
$87$	0	0
$88$	22.6955	2.41935
$89$	11.4192	1.21043	0.605217	−	0.796060i	$-0.293086\pi$
$89$	11.4192	1.21043	0.605217	+	0.796060i	$0.293086\pi$
$90$	0	0
$91$	−13.7665	−1.44312
$92$	0.716881	0.0747401
$93$	0	0
$94$	−8.27631	−0.853636
$95$	−1.79561	−0.184225
$96$	0	0
$97$	4.30541	0.437148	0.218574	−	0.975820i	$-0.429860\pi$
$97$	4.30541	0.437148	0.218574	+	0.975820i	$0.429860\pi$
$98$	31.5526	3.18730
$99$	0	0
$100$	−18.6459	−1.86459
$101$	9.08647	0.904137	0.452069	−	0.891983i	$-0.350686\pi$
$101$	9.08647	0.904137	0.452069	+	0.891983i	$0.350686\pi$
$102$	0	0
$103$	−15.5253	−1.52975	−0.764876	−	0.644178i	$-0.777200\pi$
$103$	−15.5253	−1.52975	−0.764876	+	0.644178i	$0.777200\pi$
$104$	−19.0547	−1.86847
$105$	0	0
$106$	16.3773	1.59071
$107$	−10.2344	−0.989399	−0.494699	−	0.869064i	$-0.664722\pi$
$107$	−10.2344	−0.989399	−0.494699	+	0.869064i	$0.664722\pi$
$108$	0	0
$109$	6.63816	0.635820	0.317910	−	0.948121i	$-0.397019\pi$
$109$	6.63816	0.635820	0.317910	+	0.948121i	$0.397019\pi$
$110$	8.27631	0.789115
$111$	0	0
$112$	29.2841	2.76708
$113$	12.5740	1.18286	0.591430	−	0.806356i	$-0.298564\pi$
$113$	12.5740	1.18286	0.591430	+	0.806356i	$0.298564\pi$
$114$	0	0
$115$	0.142903	0.0133258
$116$	−36.7597	−3.41305
$117$	0	0
$118$	−18.3182	−1.68633
$119$	0	0
$120$	0	0
$121$	2.81521	0.255928
$122$	6.35504	0.575358
$123$	0	0
$124$	7.82295	0.702521
$125$	−8.11381	−0.725721
$126$	0	0
$127$	12.5594	1.11447	0.557235	−	0.830355i	$-0.311862\pi$
$127$	12.5594	1.11447	0.557235	+	0.830355i	$0.311862\pi$
$128$	−13.3405	−1.17914
$129$	0	0
$130$	−6.94862	−0.609434
$131$	19.9709	1.74487	0.872433	−	0.488734i	$-0.162541\pi$
$131$	19.9709	1.74487	0.872433	+	0.488734i	$0.162541\pi$
$132$	0	0
$133$	−9.00774	−0.781070
$134$	−11.6750	−1.00857
$135$	0	0
$136$	0	0
$137$	17.2267	1.47177	0.735887	−	0.677104i	$-0.236765\pi$
$137$	17.2267	1.47177	0.735887	+	0.677104i	$0.236765\pi$
$138$	0	0
$139$	−3.37733	−0.286461	−0.143231	−	0.989689i	$-0.545749\pi$
$139$	−3.37733	−0.286461	−0.143231	+	0.989689i	$0.545749\pi$
$140$	17.1138	1.44638
$141$	0	0
$142$	2.85710	0.239762
$143$	−11.5990	−0.969953
$144$	0	0
$145$	−7.32770	−0.608532
$146$	−7.02229	−0.581169
$147$	0	0
$148$	−12.0719	−0.992306
$149$	1.38413	0.113393	0.0566963	−	0.998391i	$-0.481943\pi$
$149$	1.38413	0.113393	0.0566963	+	0.998391i	$0.481943\pi$
$150$	0	0
$151$	6.12836	0.498719	0.249359	−	0.968411i	$-0.419780\pi$
$151$	6.12836	0.498719	0.249359	+	0.968411i	$0.419780\pi$
$152$	−12.4679	−1.01128
$153$	0	0
$154$	41.5185	3.34565
$155$	1.55943	0.125256
$156$	0	0
$157$	−13.0496	−1.04147	−0.520737	−	0.853717i	$-0.674343\pi$
$157$	−13.0496	−1.04147	−0.520737	+	0.853717i	$0.674343\pi$
$158$	−8.74422	−0.695653
$159$	0	0
$160$	4.04189	0.319539
$161$	0.716881	0.0564982
$162$	0	0
$163$	−20.8726	−1.63487	−0.817433	−	0.576023i	$-0.804604\pi$
$163$	−20.8726	−1.63487	−0.817433	+	0.576023i	$0.804604\pi$
$164$	11.4192	0.891691
$165$	0	0
$166$	37.5526	2.91465
$167$	−11.7074	−0.905945	−0.452972	−	0.891525i	$-0.649636\pi$
$167$	−11.7074	−0.905945	−0.452972	+	0.891525i	$0.649636\pi$
$168$	0	0
$169$	−3.26176	−0.250905
$170$	0	0
$171$	0	0
$172$	−51.8735	−3.95532
$173$	16.6827	1.26836	0.634182	−	0.773184i	$-0.281337\pi$
$173$	16.6827	1.26836	0.634182	+	0.773184i	$0.281337\pi$
$174$	0	0
$175$	−18.6459	−1.40950
$176$	24.6732	1.85982
$177$	0	0
$178$	28.9145	2.16723
$179$	−4.29767	−0.321223	−0.160611	−	0.987018i	$-0.551347\pi$
$179$	−4.29767	−0.321223	−0.160611	+	0.987018i	$0.551347\pi$
$180$	0	0
$181$	22.2618	1.65470	0.827352	−	0.561684i	$-0.189846\pi$
$181$	22.2618	1.65470	0.827352	+	0.561684i	$0.189846\pi$
$182$	−34.8580	−2.58385
$183$	0	0
$184$	0.992259	0.0731503
$185$	−2.40642	−0.176924
$186$	0	0
$187$	0	0
$188$	−14.4192	−1.05163
$189$	0	0
$190$	−4.54664	−0.329848
$191$	−11.2567	−0.814507	−0.407254	−	0.913315i	$-0.633513\pi$
$191$	−11.2567	−0.814507	−0.407254	+	0.913315i	$0.633513\pi$
$192$	0	0
$193$	−6.68273	−0.481034	−0.240517	−	0.970645i	$-0.577317\pi$
$193$	−6.68273	−0.481034	−0.240517	+	0.970645i	$0.577317\pi$
$194$	10.9017	0.782695
$195$	0	0
$196$	54.9718	3.92656
$197$	−12.7101	−0.905555	−0.452778	−	0.891623i	$-0.649567\pi$
$197$	−12.7101	−0.905555	−0.452778	+	0.891623i	$0.649567\pi$
$198$	0	0
$199$	27.2003	1.92818	0.964088	−	0.265582i	$-0.0855642\pi$
$199$	27.2003	1.92818	0.964088	+	0.265582i	$0.0855642\pi$
$200$	−25.8084	−1.82493
$201$	0	0
$202$	23.0077	1.61882
$203$	−36.7597	−2.58003
$204$	0	0
$205$	2.27631	0.158984
$206$	−39.3114	−2.73895
$207$	0	0
$208$	−20.7151	−1.43634
$209$	−7.58946	−0.524974
$210$	0	0
$211$	4.63041	0.318771	0.159385	−	0.987216i	$-0.449049\pi$
$211$	4.63041	0.318771	0.159385	+	0.987216i	$0.449049\pi$
$212$	28.5330	1.95966
$213$	0	0
$214$	−25.9145	−1.77148
$215$	−10.3405	−0.705216
$216$	0	0
$217$	7.82295	0.531056
$218$	16.8084	1.13841
$219$	0	0
$220$	14.4192	0.972143
$221$	0	0
$222$	0	0
$223$	18.2344	1.22107	0.610534	−	0.791990i	$-0.290955\pi$
$223$	18.2344	1.22107	0.610534	+	0.791990i	$0.290955\pi$
$224$	20.2763	1.35477
$225$	0	0
$226$	31.8384	2.11786
$227$	25.6955	1.70547	0.852736	−	0.522342i	$-0.174942\pi$
$227$	25.6955	1.70547	0.852736	+	0.522342i	$0.174942\pi$
$228$	0	0
$229$	−17.5790	−1.16166	−0.580828	−	0.814027i	$-0.697271\pi$
$229$	−17.5790	−1.16166	−0.580828	+	0.814027i	$0.697271\pi$
$230$	0.361844	0.0238593
$231$	0	0
$232$	−50.8803	−3.34046
$233$	4.25402	0.278690	0.139345	−	0.990244i	$-0.455500\pi$
$233$	4.25402	0.278690	0.139345	+	0.990244i	$0.455500\pi$
$234$	0	0
$235$	−2.87433	−0.187501
$236$	−31.9145	−2.07745
$237$	0	0
$238$	0	0
$239$	−5.87433	−0.379979	−0.189990	−	0.981786i	$-0.560845\pi$
$239$	−5.87433	−0.379979	−0.189990	+	0.981786i	$0.560845\pi$
$240$	0	0
$241$	−13.6878	−0.881708	−0.440854	−	0.897579i	$-0.645324\pi$
$241$	−13.6878	−0.881708	−0.440854	+	0.897579i	$0.645324\pi$
$242$	7.12836	0.458228
$243$	0	0
$244$	11.0719	0.708807
$245$	10.9581	0.700088
$246$	0	0
$247$	6.37195	0.405437
$248$	10.8280	0.687579
$249$	0	0
$250$	−20.5449	−1.29937
$251$	−15.2986	−0.965639	−0.482820	−	0.875720i	$-0.660387\pi$
$251$	−15.2986	−0.965639	−0.482820	+	0.875720i	$0.660387\pi$
$252$	0	0
$253$	0.604007	0.0379736
$254$	31.8016	1.99541
$255$	0	0
$256$	−30.5030	−1.90644
$257$	26.2199	1.63555	0.817775	−	0.575537i	$-0.195207\pi$
$257$	26.2199	1.63555	0.817775	+	0.575537i	$0.195207\pi$
$258$	0	0
$259$	−12.0719	−0.750113
$260$	−12.1061	−0.750786
$261$	0	0
$262$	50.5681	3.12411
$263$	20.5449	1.26685	0.633426	−	0.773803i	$-0.281648\pi$
$263$	20.5449	1.26685	0.633426	+	0.773803i	$0.281648\pi$
$264$	0	0
$265$	5.68779	0.349398
$266$	−22.8084	−1.39847
$267$	0	0
$268$	−20.3405	−1.24249
$269$	−0.342244	−0.0208670	−0.0104335	−	0.999946i	$-0.503321\pi$
$269$	−0.342244	−0.0208670	−0.0104335	+	0.999946i	$0.503321\pi$
$270$	0	0
$271$	−7.73648	−0.469958	−0.234979	−	0.972000i	$-0.575502\pi$
$271$	−7.73648	−0.469958	−0.234979	+	0.972000i	$0.575502\pi$
$272$	0	0
$273$	0	0
$274$	43.6195	2.63515
$275$	−15.7101	−0.947353
$276$	0	0
$277$	−28.4320	−1.70831	−0.854157	−	0.520015i	$-0.825926\pi$
$277$	−28.4320	−1.70831	−0.854157	+	0.520015i	$0.825926\pi$
$278$	−8.55169	−0.512896
$279$	0	0
$280$	23.6878	1.41562
$281$	−15.7297	−0.938354	−0.469177	−	0.883104i	$-0.655449\pi$
$281$	−15.7297	−0.938354	−0.469177	+	0.883104i	$0.655449\pi$
$282$	0	0
$283$	−8.12330	−0.482880	−0.241440	−	0.970416i	$-0.577620\pi$
$283$	−8.12330	−0.482880	−0.241440	+	0.970416i	$0.577620\pi$
$284$	4.97771	0.295373
$285$	0	0
$286$	−29.3696	−1.73666
$287$	11.4192	0.674055
$288$	0	0
$289$	0	0
$290$	−18.5544	−1.08955
$291$	0	0
$292$	−12.2344	−0.715965
$293$	−21.0797	−1.23149	−0.615743	−	0.787947i	$-0.711144\pi$
$293$	−21.0797	−1.23149	−0.615743	+	0.787947i	$0.711144\pi$
$294$	0	0
$295$	−6.36184	−0.370401
$296$	−16.7091	−0.971199
$297$	0	0
$298$	3.50475	0.203025
$299$	−0.507112	−0.0293270
$300$	0	0
$301$	−51.8735	−2.98994
$302$	15.5175	0.892934
$303$	0	0
$304$	−13.5544	−0.777397
$305$	2.20708	0.126377
$306$	0	0
$307$	15.0915	0.861318	0.430659	−	0.902515i	$-0.358281\pi$
$307$	15.0915	0.861318	0.430659	+	0.902515i	$0.358281\pi$
$308$	72.3346	4.12165
$309$	0	0
$310$	3.94862	0.224266
$311$	26.9368	1.52744	0.763722	−	0.645546i	$-0.223370\pi$
$311$	26.9368	1.52744	0.763722	+	0.645546i	$0.223370\pi$
$312$	0	0
$313$	3.99319	0.225709	0.112854	−	0.993612i	$-0.464001\pi$
$313$	3.99319	0.225709	0.112854	+	0.993612i	$0.464001\pi$
$314$	−33.0428	−1.86471
$315$	0	0
$316$	−15.2344	−0.857003
$317$	2.13341	0.119824	0.0599121	−	0.998204i	$-0.480918\pi$
$317$	2.13341	0.119824	0.0599121	+	0.998204i	$0.480918\pi$
$318$	0	0
$319$	−30.9718	−1.73409
$320$	−1.44057	−0.0805303
$321$	0	0
$322$	1.81521	0.101158
$323$	0	0
$324$	0	0
$325$	13.1898	0.731641
$326$	−52.8512	−2.92716
$327$	0	0
$328$	15.8057	0.872724
$329$	−14.4192	−0.794957
$330$	0	0
$331$	7.76382	0.426738	0.213369	−	0.976972i	$-0.431556\pi$
$331$	7.76382	0.426738	0.213369	+	0.976972i	$0.431556\pi$
$332$	65.4252	3.59067
$333$	0	0
$334$	−29.6441	−1.62206
$335$	−4.05468	−0.221531
$336$	0	0
$337$	−14.8990	−0.811599	−0.405800	−	0.913962i	$-0.633007\pi$
$337$	−14.8990	−0.811599	−0.405800	+	0.913962i	$0.633007\pi$
$338$	−8.25908	−0.449234
$339$	0	0
$340$	0	0
$341$	6.59121	0.356934
$342$	0	0
$343$	24.0915	1.30082
$344$	−71.7998	−3.87119
$345$	0	0
$346$	42.2422	2.27095
$347$	−6.14290	−0.329768	−0.164884	−	0.986313i	$-0.552725\pi$
$347$	−6.14290	−0.329768	−0.164884	+	0.986313i	$0.552725\pi$
$348$	0	0
$349$	1.79830	0.0962605	0.0481303	−	0.998841i	$-0.484674\pi$
$349$	1.79830	0.0962605	0.0481303	+	0.998841i	$0.484674\pi$
$350$	−47.2131	−2.52364
$351$	0	0
$352$	17.0838	0.910568
$353$	−35.2199	−1.87456	−0.937282	−	0.348571i	$-0.886667\pi$
$353$	−35.2199	−1.87456	−0.937282	+	0.348571i	$0.886667\pi$
$354$	0	0
$355$	0.992259	0.0526637
$356$	50.3756	2.66990
$357$	0	0
$358$	−10.8821	−0.575135
$359$	−16.7888	−0.886079	−0.443039	−	0.896502i	$-0.646100\pi$
$359$	−16.7888	−0.886079	−0.443039	+	0.896502i	$0.646100\pi$
$360$	0	0
$361$	−14.8307	−0.780563
$362$	56.3688	2.96268
$363$	0	0
$364$	−60.7306	−3.18315
$365$	−2.43882	−0.127653
$366$	0	0
$367$	19.2490	1.00479	0.502394	−	0.864639i	$-0.332453\pi$
$367$	19.2490	1.00479	0.502394	+	0.864639i	$0.332453\pi$
$368$	1.07873	0.0562325
$369$	0	0
$370$	−6.09327	−0.316774
$371$	28.5330	1.48136
$372$	0	0
$373$	−33.4953	−1.73432	−0.867159	−	0.498031i	$-0.834057\pi$
$373$	−33.4953	−1.73432	−0.867159	+	0.498031i	$0.834057\pi$
$374$	0	0
$375$	0	0
$376$	−19.9581	−1.02926
$377$	26.0033	1.33924
$378$	0	0
$379$	−15.1043	−0.775856	−0.387928	−	0.921690i	$-0.626809\pi$
$379$	−15.1043	−0.775856	−0.387928	+	0.921690i	$0.626809\pi$
$380$	−7.92127	−0.406353
$381$	0	0
$382$	−28.5030	−1.45834
$383$	−23.7811	−1.21516	−0.607578	−	0.794260i	$-0.707859\pi$
$383$	−23.7811	−1.21516	−0.607578	+	0.794260i	$0.707859\pi$
$384$	0	0
$385$	14.4192	0.734871
$386$	−16.9213	−0.861270
$387$	0	0
$388$	18.9932	0.964233
$389$	24.3378	1.23398	0.616988	−	0.786973i	$-0.288353\pi$
$389$	24.3378	1.23398	0.616988	+	0.786973i	$0.288353\pi$
$390$	0	0
$391$	0	0
$392$	76.0883	3.84304
$393$	0	0
$394$	−32.1830	−1.62136
$395$	−3.03684	−0.152800
$396$	0	0
$397$	1.09926	0.0551703	0.0275851	−	0.999619i	$-0.491218\pi$
$397$	1.09926	0.0551703	0.0275851	+	0.999619i	$0.491218\pi$
$398$	68.8735	3.45232
$399$	0	0
$400$	−28.0574	−1.40287
$401$	23.3236	1.16472	0.582362	−	0.812930i	$-0.302129\pi$
$401$	23.3236	1.16472	0.582362	+	0.812930i	$0.302129\pi$
$402$	0	0
$403$	−5.53384	−0.275660
$404$	40.0847	1.99429
$405$	0	0
$406$	−93.0788	−4.61943
$407$	−10.1712	−0.504167
$408$	0	0
$409$	20.1233	0.995033	0.497517	−	0.867454i	$-0.334245\pi$
$409$	20.1233	0.995033	0.497517	+	0.867454i	$0.334245\pi$
$410$	5.76382	0.284655
$411$	0	0
$412$	−68.4894	−3.37423
$413$	−31.9145	−1.57041
$414$	0	0
$415$	13.0419	0.640201
$416$	−14.3432	−0.703232
$417$	0	0
$418$	−19.2172	−0.939943
$419$	−1.22163	−0.0596805	−0.0298402	−	0.999555i	$-0.509500\pi$
$419$	−1.22163	−0.0596805	−0.0298402	+	0.999555i	$0.509500\pi$
$420$	0	0
$421$	9.21482	0.449103	0.224551	−	0.974462i	$-0.427908\pi$
$421$	9.21482	0.449103	0.224551	+	0.974462i	$0.427908\pi$
$422$	11.7246	0.570746
$423$	0	0
$424$	39.4935	1.91797
$425$	0	0
$426$	0	0
$427$	11.0719	0.535808
$428$	−45.1489	−2.18235
$429$	0	0
$430$	−26.1830	−1.26266
$431$	5.46522	0.263251	0.131625	−	0.991300i	$-0.457980\pi$
$431$	5.46522	0.263251	0.131625	+	0.991300i	$0.457980\pi$
$432$	0	0
$433$	13.5125	0.649369	0.324684	−	0.945822i	$-0.394742\pi$
$433$	13.5125	0.649369	0.324684	+	0.945822i	$0.394742\pi$
$434$	19.8084	0.950834
$435$	0	0
$436$	29.2841	1.40245
$437$	−0.331815	−0.0158729
$438$	0	0
$439$	14.0983	0.672876	0.336438	−	0.941706i	$-0.390778\pi$
$439$	14.0983	0.672876	0.336438	+	0.941706i	$0.390778\pi$
$440$	19.9581	0.951466
$441$	0	0
$442$	0	0
$443$	−7.18716	−0.341472	−0.170736	−	0.985317i	$-0.554615\pi$
$443$	−7.18716	−0.341472	−0.170736	+	0.985317i	$0.554615\pi$
$444$	0	0
$445$	10.0419	0.476031
$446$	46.1712	2.18627
$447$	0	0
$448$	−7.22668	−0.341429
$449$	13.7324	0.648070	0.324035	−	0.946045i	$-0.394960\pi$
$449$	13.7324	0.648070	0.324035	+	0.946045i	$0.394960\pi$
$450$	0	0
$451$	9.62124	0.453047
$452$	55.4698	2.60908
$453$	0	0
$454$	65.0634	3.05357
$455$	−12.1061	−0.567541
$456$	0	0
$457$	−15.8479	−0.741335	−0.370667	−	0.928766i	$-0.620871\pi$
$457$	−15.8479	−0.741335	−0.370667	+	0.928766i	$0.620871\pi$
$458$	−44.5117	−2.07989
$459$	0	0
$460$	0.630415	0.0293932
$461$	−7.69553	−0.358416	−0.179208	−	0.983811i	$-0.557354\pi$
$461$	−7.69553	−0.358416	−0.179208	+	0.983811i	$0.557354\pi$
$462$	0	0
$463$	32.7597	1.52247	0.761236	−	0.648475i	$-0.224593\pi$
$463$	32.7597	1.52247	0.761236	+	0.648475i	$0.224593\pi$
$464$	−55.3141	−2.56789
$465$	0	0
$466$	10.7716	0.498983
$467$	−17.1726	−0.794654	−0.397327	−	0.917677i	$-0.630062\pi$
$467$	−17.1726	−0.794654	−0.397327	+	0.917677i	$0.630062\pi$
$468$	0	0
$469$	−20.3405	−0.939237
$470$	−7.27807	−0.335712
$471$	0	0
$472$	−44.1739	−2.03327
$473$	−43.7060	−2.00960
$474$	0	0
$475$	8.63041	0.395991
$476$	0	0
$477$	0	0
$478$	−14.8743	−0.680336
$479$	−22.1343	−1.01134	−0.505672	−	0.862726i	$-0.668755\pi$
$479$	−22.1343	−1.01134	−0.505672	+	0.862726i	$0.668755\pi$
$480$	0	0
$481$	8.53951	0.389368
$482$	−34.6587	−1.57866
$483$	0	0
$484$	12.4192	0.564510
$485$	3.78611	0.171918
$486$	0	0
$487$	31.3874	1.42230	0.711150	−	0.703040i	$-0.248175\pi$
$487$	31.3874	1.42230	0.711150	+	0.703040i	$0.248175\pi$
$488$	15.3250	0.693731
$489$	0	0
$490$	27.7469	1.25348
$491$	0.206148	0.00930331	0.00465166	−	0.999989i	$-0.498519\pi$
$491$	0.206148	0.00930331	0.00465166	+	0.999989i	$0.498519\pi$
$492$	0	0
$493$	0	0
$494$	16.1343	0.725918
$495$	0	0
$496$	11.7716	0.528559
$497$	4.97771	0.223281
$498$	0	0
$499$	5.50063	0.246242	0.123121	−	0.992392i	$-0.460710\pi$
$499$	5.50063	0.246242	0.123121	+	0.992392i	$0.460710\pi$
$500$	−35.7939	−1.60075
$501$	0	0
$502$	−38.7374	−1.72894
$503$	−5.63135	−0.251089	−0.125545	−	0.992088i	$-0.540068\pi$
$503$	−5.63135	−0.251089	−0.125545	+	0.992088i	$0.540068\pi$
$504$	0	0
$505$	7.99050	0.355573
$506$	1.52940	0.0679901
$507$	0	0
$508$	55.4056	2.45823
$509$	15.8530	0.702671	0.351335	−	0.936250i	$-0.385728\pi$
$509$	15.8530	0.702671	0.351335	+	0.936250i	$0.385728\pi$
$510$	0	0
$511$	−12.2344	−0.541219
$512$	−50.5553	−2.23425
$513$	0	0
$514$	66.3911	2.92838
$515$	−13.6527	−0.601610
$516$	0	0
$517$	−12.1489	−0.534308
$518$	−30.5672	−1.34304
$519$	0	0
$520$	−16.7564	−0.734817
$521$	−35.5749	−1.55857	−0.779283	−	0.626673i	$-0.784416\pi$
$521$	−35.5749	−1.55857	−0.779283	+	0.626673i	$0.784416\pi$
$522$	0	0
$523$	6.32770	0.276691	0.138345	−	0.990384i	$-0.455822\pi$
$523$	6.32770	0.276691	0.138345	+	0.990384i	$0.455822\pi$
$524$	88.1011	3.84872
$525$	0	0
$526$	52.0215	2.26824
$527$	0	0
$528$	0	0
$529$	−22.9736	−0.998852
$530$	14.4020	0.625582
$531$	0	0
$532$	−39.7374	−1.72284
$533$	−8.07779	−0.349888
$534$	0	0
$535$	−9.00000	−0.389104
$536$	−28.1539	−1.21607
$537$	0	0
$538$	−0.866592	−0.0373614
$539$	46.3164	1.99499
$540$	0	0
$541$	9.51249	0.408974	0.204487	−	0.978869i	$-0.434447\pi$
$541$	9.51249	0.408974	0.204487	+	0.978869i	$0.434447\pi$
$542$	−19.5895	−0.841439
$543$	0	0
$544$	0	0
$545$	5.83750	0.250051
$546$	0	0
$547$	25.9522	1.10964	0.554819	−	0.831971i	$-0.312788\pi$
$547$	25.9522	1.10964	0.554819	+	0.831971i	$0.312788\pi$
$548$	75.9951	3.24635
$549$	0	0
$550$	−39.7793	−1.69620
$551$	17.0145	0.724844
$552$	0	0
$553$	−15.2344	−0.647834
$554$	−71.9924	−3.05866
$555$	0	0
$556$	−14.8990	−0.631858
$557$	3.03684	0.128675	0.0643374	−	0.997928i	$-0.479507\pi$
$557$	3.03684	0.128675	0.0643374	+	0.997928i	$0.479507\pi$
$558$	0	0
$559$	36.6946	1.55202
$560$	25.7520	1.08822
$561$	0	0
$562$	−39.8289	−1.68008
$563$	−32.7050	−1.37835	−0.689176	−	0.724594i	$-0.742027\pi$
$563$	−32.7050	−1.37835	−0.689176	+	0.724594i	$0.742027\pi$
$564$	0	0
$565$	11.0574	0.465187
$566$	−20.5689	−0.864576
$567$	0	0
$568$	6.88981	0.289090
$569$	10.7980	0.452675	0.226337	−	0.974049i	$-0.427325\pi$
$569$	10.7980	0.452675	0.226337	+	0.974049i	$0.427325\pi$
$570$	0	0
$571$	4.22937	0.176994	0.0884968	−	0.996076i	$-0.471794\pi$
$571$	4.22937	0.176994	0.0884968	+	0.996076i	$0.471794\pi$
$572$	−51.1685	−2.13946
$573$	0	0
$574$	28.9145	1.20687
$575$	−0.686852	−0.0286437
$576$	0	0
$577$	11.4311	0.475882	0.237941	−	0.971280i	$-0.423528\pi$
$577$	11.4311	0.475882	0.237941	+	0.971280i	$0.423528\pi$
$578$	0	0
$579$	0	0
$580$	−32.3259	−1.34226
$581$	65.4252	2.71429
$582$	0	0
$583$	24.0405	0.995654
$584$	−16.9341	−0.700737
$585$	0	0
$586$	−53.3756	−2.20492
$587$	19.8256	0.818292	0.409146	−	0.912469i	$-0.365827\pi$
$587$	19.8256	0.818292	0.409146	+	0.912469i	$0.365827\pi$
$588$	0	0
$589$	−3.62092	−0.149197
$590$	−16.1088	−0.663187
$591$	0	0
$592$	−18.1652	−0.746585
$593$	15.0933	0.619806	0.309903	−	0.950768i	$-0.399703\pi$
$593$	15.0933	0.619806	0.309903	+	0.950768i	$0.399703\pi$
$594$	0	0
$595$	0	0
$596$	6.10607	0.250114
$597$	0	0
$598$	−1.28405	−0.0525088
$599$	−37.8776	−1.54764	−0.773819	−	0.633407i	$-0.781656\pi$
$599$	−37.8776	−1.54764	−0.773819	+	0.633407i	$0.781656\pi$
$600$	0	0
$601$	33.9436	1.38459	0.692293	−	0.721616i	$-0.256600\pi$
$601$	33.9436	1.38459	0.692293	+	0.721616i	$0.256600\pi$
$602$	−131.348	−5.35336
$603$	0	0
$604$	27.0351	1.10004
$605$	2.47565	0.100650
$606$	0	0
$607$	18.7811	0.762300	0.381150	−	0.924513i	$-0.375528\pi$
$607$	18.7811	0.762300	0.381150	+	0.924513i	$0.375528\pi$
$608$	−9.38507	−0.380615
$609$	0	0
$610$	5.58853	0.226273
$611$	10.1999	0.412646
$612$	0	0
$613$	17.9590	0.725359	0.362679	−	0.931914i	$-0.381862\pi$
$613$	17.9590	0.725359	0.362679	+	0.931914i	$0.381862\pi$
$614$	38.2131	1.54215
$615$	0	0
$616$	100.121	4.03398
$617$	2.13104	0.0857926	0.0428963	−	0.999080i	$-0.486341\pi$
$617$	2.13104	0.0857926	0.0428963	+	0.999080i	$0.486341\pi$
$618$	0	0
$619$	−2.94263	−0.118274	−0.0591371	−	0.998250i	$-0.518835\pi$
$619$	−2.94263	−0.118274	−0.0591371	+	0.998250i	$0.518835\pi$
$620$	6.87939	0.276283
$621$	0	0
$622$	68.2063	2.73482
$623$	50.3756	2.01825
$624$	0	0
$625$	13.9982	0.559930
$626$	10.1111	0.404122
$627$	0	0
$628$	−57.5681	−2.29722
$629$	0	0
$630$	0	0
$631$	9.05913	0.360638	0.180319	−	0.983608i	$-0.442287\pi$
$631$	9.05913	0.360638	0.180319	+	0.983608i	$0.442287\pi$
$632$	−21.0865	−0.838775
$633$	0	0
$634$	5.40198	0.214540
$635$	11.0446	0.438291
$636$	0	0
$637$	−38.8863	−1.54073
$638$	−78.4234	−3.10481
$639$	0	0
$640$	−11.7314	−0.463725
$641$	−3.29498	−0.130144	−0.0650719	−	0.997881i	$-0.520728\pi$
$641$	−3.29498	−0.130144	−0.0650719	+	0.997881i	$0.520728\pi$
$642$	0	0
$643$	−20.3874	−0.804002	−0.402001	−	0.915639i	$-0.631685\pi$
$643$	−20.3874	−0.804002	−0.402001	+	0.915639i	$0.631685\pi$
$644$	3.16250	0.124620
$645$	0	0
$646$	0	0
$647$	6.14290	0.241502	0.120751	−	0.992683i	$-0.461470\pi$
$647$	6.14290	0.241502	0.120751	+	0.992683i	$0.461470\pi$
$648$	0	0
$649$	−26.8895	−1.05550
$650$	33.3979	1.30997
$651$	0	0
$652$	−92.0788	−3.60609
$653$	−34.2736	−1.34123	−0.670615	−	0.741805i	$-0.733970\pi$
$653$	−34.2736	−1.34123	−0.670615	+	0.741805i	$0.733970\pi$
$654$	0	0
$655$	17.5621	0.686209
$656$	17.1830	0.670885
$657$	0	0
$658$	−36.5107	−1.42334
$659$	32.3884	1.26167	0.630836	−	0.775916i	$-0.282712\pi$
$659$	32.3884	1.26167	0.630836	+	0.775916i	$0.282712\pi$
$660$	0	0
$661$	4.49970	0.175018	0.0875089	−	0.996164i	$-0.472109\pi$
$661$	4.49970	0.175018	0.0875089	+	0.996164i	$0.472109\pi$
$662$	19.6587	0.764057
$663$	0	0
$664$	90.5572	3.51430
$665$	−7.92127	−0.307174
$666$	0	0
$667$	−1.35410	−0.0524311
$668$	−51.6468	−1.99828
$669$	0	0
$670$	−10.2668	−0.396642
$671$	9.32863	0.360128
$672$	0	0
$673$	−11.7793	−0.454059	−0.227029	−	0.973888i	$-0.572901\pi$
$673$	−11.7793	−0.454059	−0.227029	+	0.973888i	$0.572901\pi$
$674$	−37.7256	−1.45313
$675$	0	0
$676$	−14.3892	−0.553430
$677$	14.7178	0.565652	0.282826	−	0.959171i	$-0.408728\pi$
$677$	14.7178	0.565652	0.282826	+	0.959171i	$0.408728\pi$
$678$	0	0
$679$	18.9932	0.728892
$680$	0	0
$681$	0	0
$682$	16.6895	0.639076
$683$	−41.7998	−1.59943	−0.799713	−	0.600382i	$-0.795015\pi$
$683$	−41.7998	−1.59943	−0.799713	+	0.600382i	$0.795015\pi$
$684$	0	0
$685$	15.1489	0.578809
$686$	61.0019	2.32906
$687$	0	0
$688$	−78.0565	−2.97588
$689$	−20.1839	−0.768944
$690$	0	0
$691$	−33.2380	−1.26443	−0.632217	−	0.774791i	$-0.717855\pi$
$691$	−33.2380	−1.26443	−0.632217	+	0.774791i	$0.717855\pi$
$692$	73.5954	2.79768
$693$	0	0
$694$	−15.5544	−0.590436
$695$	−2.96997	−0.112657
$696$	0	0
$697$	0	0
$698$	4.55344	0.172350
$699$	0	0
$700$	−82.2559	−3.10898
$701$	9.91859	0.374620	0.187310	−	0.982301i	$-0.440023\pi$
$701$	9.91859	0.374620	0.187310	+	0.982301i	$0.440023\pi$
$702$	0	0
$703$	5.58759	0.210740
$704$	−6.08883	−0.229481
$705$	0	0
$706$	−89.1799	−3.35633
$707$	40.0847	1.50754
$708$	0	0
$709$	19.0669	0.716071	0.358036	−	0.933708i	$-0.383447\pi$
$709$	19.0669	0.716071	0.358036	+	0.933708i	$0.383447\pi$
$710$	2.51249	0.0942920
$711$	0	0
$712$	69.7265	2.61311
$713$	0.288171	0.0107921
$714$	0	0
$715$	−10.1999	−0.381456
$716$	−18.9590	−0.708533
$717$	0	0
$718$	−42.5107	−1.58649
$719$	−42.5235	−1.58586	−0.792930	−	0.609313i	$-0.791445\pi$
$719$	−42.5235	−1.58586	−0.792930	+	0.609313i	$0.791445\pi$
$720$	0	0
$721$	−68.4894	−2.55068
$722$	−37.5526	−1.39756
$723$	0	0
$724$	98.2072	3.64984
$725$	35.2199	1.30803
$726$	0	0
$727$	8.13610	0.301751	0.150876	−	0.988553i	$-0.451791\pi$
$727$	8.13610	0.301751	0.150876	+	0.988553i	$0.451791\pi$
$728$	−84.0592	−3.11544
$729$	0	0
$730$	−6.17530	−0.228558
$731$	0	0
$732$	0	0
$733$	−19.7965	−0.731202	−0.365601	−	0.930772i	$-0.619137\pi$
$733$	−19.7965	−0.731202	−0.365601	+	0.930772i	$0.619137\pi$
$734$	48.7401	1.79903
$735$	0	0
$736$	0.746911	0.0275315
$737$	−17.1379	−0.631281
$738$	0	0
$739$	6.52940	0.240188	0.120094	−	0.992763i	$-0.461680\pi$
$739$	6.52940	0.240188	0.120094	+	0.992763i	$0.461680\pi$
$740$	−10.6159	−0.390247
$741$	0	0
$742$	72.2481	2.65231
$743$	−15.4935	−0.568401	−0.284201	−	0.958765i	$-0.591728\pi$
$743$	−15.4935	−0.568401	−0.284201	+	0.958765i	$0.591728\pi$
$744$	0	0
$745$	1.21719	0.0445942
$746$	−84.8130	−3.10522
$747$	0	0
$748$	0	0
$749$	−45.1489	−1.64970
$750$	0	0
$751$	−27.8188	−1.01512	−0.507562	−	0.861615i	$-0.669453\pi$
$751$	−27.8188	−1.01512	−0.507562	+	0.861615i	$0.669453\pi$
$752$	−21.6973	−0.791218
$753$	0	0
$754$	65.8427	2.39785
$755$	5.38919	0.196133
$756$	0	0
$757$	9.35328	0.339951	0.169975	−	0.985448i	$-0.445631\pi$
$757$	9.35328	0.339951	0.169975	+	0.985448i	$0.445631\pi$
$758$	−38.2455	−1.38914
$759$	0	0
$760$	−10.9641	−0.397710
$761$	37.5458	1.36103	0.680517	−	0.732732i	$-0.261755\pi$
$761$	37.5458	1.36103	0.680517	+	0.732732i	$0.261755\pi$
$762$	0	0
$763$	29.2841	1.06015
$764$	−49.6587	−1.79659
$765$	0	0
$766$	−60.2158	−2.17568
$767$	22.5758	0.815167
$768$	0	0
$769$	−26.2253	−0.945707	−0.472853	−	0.881141i	$-0.656776\pi$
$769$	−26.2253	−0.945707	−0.472853	+	0.881141i	$0.656776\pi$
$770$	36.5107	1.31576
$771$	0	0
$772$	−29.4807	−1.06103
$773$	−33.4567	−1.20335	−0.601676	−	0.798740i	$-0.705500\pi$
$773$	−33.4567	−1.20335	−0.601676	+	0.798740i	$0.705500\pi$
$774$	0	0
$775$	−7.49525	−0.269237
$776$	26.2891	0.943724
$777$	0	0
$778$	61.6255	2.20938
$779$	−5.28548	−0.189372
$780$	0	0
$781$	4.19396	0.150072
$782$	0	0
$783$	0	0
$784$	82.7187	2.95424
$785$	−11.4757	−0.409584
$786$	0	0
$787$	8.79561	0.313530	0.156765	−	0.987636i	$-0.449894\pi$
$787$	8.79561	0.313530	0.156765	+	0.987636i	$0.449894\pi$
$788$	−56.0702	−1.99742
$789$	0	0
$790$	−7.68954	−0.273582
$791$	55.4698	1.97228
$792$	0	0
$793$	−7.83212	−0.278127
$794$	2.78342	0.0987800
$795$	0	0
$796$	119.993	4.25305
$797$	13.8972	0.492265	0.246133	−	0.969236i	$-0.420840\pi$
$797$	13.8972	0.492265	0.246133	+	0.969236i	$0.420840\pi$
$798$	0	0
$799$	0	0
$800$	−19.4270	−0.686847
$801$	0	0
$802$	59.0574	2.08539
$803$	−10.3081	−0.363765
$804$	0	0
$805$	0.630415	0.0222192
$806$	−14.0122	−0.493558
$807$	0	0
$808$	55.4826	1.95187
$809$	36.1857	1.27222	0.636111	−	0.771597i	$-0.280542\pi$
$809$	36.1857	1.27222	0.636111	+	0.771597i	$0.280542\pi$
$810$	0	0
$811$	29.1320	1.02296	0.511481	−	0.859295i	$-0.329097\pi$
$811$	29.1320	1.02296	0.511481	+	0.859295i	$0.329097\pi$
$812$	−162.164	−5.69086
$813$	0	0
$814$	−25.7543	−0.902689
$815$	−18.3550	−0.642949
$816$	0	0
$817$	24.0101	0.840007
$818$	50.9540	1.78156
$819$	0	0
$820$	10.0419	0.350678
$821$	41.5149	1.44888	0.724439	−	0.689339i	$-0.242099\pi$
$821$	41.5149	1.44888	0.724439	+	0.689339i	$0.242099\pi$
$822$	0	0
$823$	16.5416	0.576603	0.288302	−	0.957540i	$-0.406909\pi$
$823$	16.5416	0.576603	0.288302	+	0.957540i	$0.406909\pi$
$824$	−94.7984	−3.30246
$825$	0	0
$826$	−80.8103	−2.81175
$827$	19.5422	0.679549	0.339774	−	0.940507i	$-0.389649\pi$
$827$	19.5422	0.679549	0.339774	+	0.940507i	$0.389649\pi$
$828$	0	0
$829$	−40.3519	−1.40148	−0.700739	−	0.713418i	$-0.747146\pi$
$829$	−40.3519	−1.40148	−0.700739	+	0.713418i	$0.747146\pi$
$830$	33.0232	1.14625
$831$	0	0
$832$	5.11205	0.177229
$833$	0	0
$834$	0	0
$835$	−10.2953	−0.356284
$836$	−33.4807	−1.15795
$837$	0	0
$838$	−3.09327	−0.106855
$839$	26.2635	0.906717	0.453359	−	0.891328i	$-0.350226\pi$
$839$	26.2635	0.906717	0.453359	+	0.891328i	$0.350226\pi$
$840$	0	0
$841$	40.4347	1.39430
$842$	23.3327	0.804100
$843$	0	0
$844$	20.4270	0.703125
$845$	−2.86835	−0.0986741
$846$	0	0
$847$	12.4192	0.426729
$848$	42.9350	1.47439
$849$	0	0
$850$	0	0
$851$	−0.444689	−0.0152437
$852$	0	0
$853$	45.5140	1.55837	0.779185	−	0.626794i	$-0.215633\pi$
$853$	45.5140	1.55837	0.779185	+	0.626794i	$0.215633\pi$
$854$	28.0351	0.959341
$855$	0	0
$856$	−62.4921	−2.13593
$857$	30.8530	1.05392	0.526959	−	0.849891i	$-0.323332\pi$
$857$	30.8530	1.05392	0.526959	+	0.849891i	$0.323332\pi$
$858$	0	0
$859$	25.4284	0.867605	0.433803	−	0.901008i	$-0.357171\pi$
$859$	25.4284	0.867605	0.433803	+	0.901008i	$0.357171\pi$
$860$	−45.6168	−1.55552
$861$	0	0
$862$	13.8384	0.471339
$863$	0.238541	0.00812004	0.00406002	−	0.999992i	$-0.498708\pi$
$863$	0.238541	0.00812004	0.00406002	+	0.999992i	$0.498708\pi$
$864$	0	0
$865$	14.6705	0.498814
$866$	34.2148	1.16267
$867$	0	0
$868$	34.5107	1.17137
$869$	−12.8357	−0.435423
$870$	0	0
$871$	14.3886	0.487538
$872$	40.5330	1.37262
$873$	0	0
$874$	−0.840185	−0.0284197
$875$	−35.7939	−1.21005
$876$	0	0
$877$	41.1816	1.39060	0.695302	−	0.718718i	$-0.255271\pi$
$877$	41.1816	1.39060	0.695302	+	0.718718i	$0.255271\pi$
$878$	35.6982	1.20476
$879$	0	0
$880$	21.6973	0.731415
$881$	−14.0746	−0.474186	−0.237093	−	0.971487i	$-0.576195\pi$
$881$	−14.0746	−0.474186	−0.237093	+	0.971487i	$0.576195\pi$
$882$	0	0
$883$	32.0496	1.07856	0.539278	−	0.842128i	$-0.318697\pi$
$883$	32.0496	1.07856	0.539278	+	0.842128i	$0.318697\pi$
$884$	0	0
$885$	0	0
$886$	−18.1985	−0.611391
$887$	15.0300	0.504659	0.252330	−	0.967641i	$-0.418803\pi$
$887$	15.0300	0.504659	0.252330	+	0.967641i	$0.418803\pi$
$888$	0	0
$889$	55.4056	1.85824
$890$	25.4270	0.852313
$891$	0	0
$892$	80.4407	2.69335
$893$	6.67406	0.223339
$894$	0	0
$895$	−3.77930	−0.126328
$896$	−58.8512	−1.96608
$897$	0	0
$898$	34.7716	1.16034
$899$	−14.7766	−0.492828
$900$	0	0
$901$	0	0
$902$	24.3618	0.811161
$903$	0	0
$904$	76.7775	2.55358
$905$	19.5767	0.650750
$906$	0	0
$907$	−2.51155	−0.0833948	−0.0416974	−	0.999130i	$-0.513277\pi$
$907$	−2.51155	−0.0833948	−0.0416974	+	0.999130i	$0.513277\pi$
$908$	113.355	3.76182
$909$	0	0
$910$	−30.6536	−1.01616
$911$	20.9956	0.695614	0.347807	−	0.937566i	$-0.386926\pi$
$911$	20.9956	0.695614	0.347807	+	0.937566i	$0.386926\pi$
$912$	0	0
$913$	55.1239	1.82434
$914$	−40.1284	−1.32733
$915$	0	0
$916$	−77.5494	−2.56231
$917$	88.1011	2.90936
$918$	0	0
$919$	−43.9050	−1.44829	−0.724146	−	0.689647i	$-0.757766\pi$
$919$	−43.9050	−1.44829	−0.724146	+	0.689647i	$0.757766\pi$
$920$	0.872578	0.0287680
$921$	0	0
$922$	−19.4858	−0.641729
$923$	−3.52116	−0.115900
$924$	0	0
$925$	11.5662	0.380296
$926$	82.9505	2.72592
$927$	0	0
$928$	−38.2995	−1.25724
$929$	−47.9368	−1.57275	−0.786377	−	0.617747i	$-0.788046\pi$
$929$	−47.9368	−1.57275	−0.786377	+	0.617747i	$0.788046\pi$
$930$	0	0
$931$	−25.4442	−0.833900
$932$	18.7665	0.614718
$933$	0	0
$934$	−43.4826	−1.42279
$935$	0	0
$936$	0	0
$937$	−2.39094	−0.0781086	−0.0390543	−	0.999237i	$-0.512435\pi$
$937$	−2.39094	−0.0781086	−0.0390543	+	0.999237i	$0.512435\pi$
$938$	−51.5039	−1.68166
$939$	0	0
$940$	−12.6800	−0.413577
$941$	−21.9614	−0.715921	−0.357961	−	0.933737i	$-0.616528\pi$
$941$	−21.9614	−0.715921	−0.357961	+	0.933737i	$0.616528\pi$
$942$	0	0
$943$	0.420645	0.0136981
$944$	−48.0232	−1.56302
$945$	0	0
$946$	−110.667	−3.59811
$947$	−6.05199	−0.196663	−0.0983317	−	0.995154i	$-0.531351\pi$
$947$	−6.05199	−0.196663	−0.0983317	+	0.995154i	$0.531351\pi$
$948$	0	0
$949$	8.65446	0.280936
$950$	21.8530	0.709004
$951$	0	0
$952$	0	0
$953$	53.8955	1.74585	0.872923	−	0.487858i	$-0.162222\pi$
$953$	53.8955	1.74585	0.872923	+	0.487858i	$0.162222\pi$
$954$	0	0
$955$	−9.89899	−0.320324
$956$	−25.9145	−0.838134
$957$	0	0
$958$	−56.0461	−1.81077
$959$	75.9951	2.45401
$960$	0	0
$961$	−27.8553	−0.898559
$962$	21.6228	0.697147
$963$	0	0
$964$	−60.3833	−1.94482
$965$	−5.87670	−0.189178
$966$	0	0
$967$	−55.4175	−1.78211	−0.891053	−	0.453900i	$-0.850032\pi$
$967$	−55.4175	−1.78211	−0.891053	+	0.453900i	$0.850032\pi$
$968$	17.1898	0.552503
$969$	0	0
$970$	9.58677	0.307813
$971$	28.4201	0.912046	0.456023	−	0.889968i	$-0.349273\pi$
$971$	28.4201	0.912046	0.456023	+	0.889968i	$0.349273\pi$
$972$	0	0
$973$	−14.8990	−0.477640
$974$	79.4758	2.54657
$975$	0	0
$976$	16.6604	0.533288
$977$	56.3492	1.80277	0.901385	−	0.433019i	$-0.142552\pi$
$977$	56.3492	1.80277	0.901385	+	0.433019i	$0.142552\pi$
$978$	0	0
$979$	42.4439	1.35651
$980$	48.3414	1.54421
$981$	0	0
$982$	0.521984	0.0166572
$983$	10.5362	0.336053	0.168026	−	0.985782i	$-0.446261\pi$
$983$	10.5362	0.336053	0.168026	+	0.985782i	$0.446261\pi$
$984$	0	0
$985$	−11.1771	−0.356130
$986$	0	0
$987$	0	0
$988$	28.1097	0.894288
$989$	−1.91085	−0.0607613
$990$	0	0
$991$	36.4344	1.15738	0.578688	−	0.815549i	$-0.303565\pi$
$991$	36.4344	1.15738	0.578688	+	0.815549i	$0.303565\pi$
$992$	8.15064	0.258783
$993$	0	0
$994$	12.6040	0.399775
$995$	23.9195	0.758300
$996$	0	0
$997$	−0.861215	−0.0272750	−0.0136375	−	0.999907i	$-0.504341\pi$
$997$	−0.861215	−0.0272750	−0.0136375	+	0.999907i	$0.504341\pi$
$998$	13.9281	0.440886
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.y.1.3		3
3.2	odd	2		867.2.a.i.1.1	✓	3
17.16	even	2		2601.2.a.z.1.3		3
51.2	odd	8		867.2.e.j.616.1		12
51.5	even	16		867.2.h.l.688.6		24
51.8	odd	8		867.2.e.j.829.6		12
51.11	even	16		867.2.h.l.733.2		24
51.14	even	16		867.2.h.l.757.2		24
51.20	even	16		867.2.h.l.757.1		24
51.23	even	16		867.2.h.l.733.1		24
51.26	odd	8		867.2.e.j.829.5		12
51.29	even	16		867.2.h.l.688.5		24
51.32	odd	8		867.2.e.j.616.2		12
51.38	odd	4		867.2.d.d.577.6		6
51.41	even	16		867.2.h.l.712.6		24
51.44	even	16		867.2.h.l.712.5		24
51.47	odd	4		867.2.d.d.577.5		6
51.50	odd	2		867.2.a.j.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.1	✓	3	3.2	odd	2
867.2.a.j.1.1	yes	3	51.50	odd	2
867.2.d.d.577.5		6	51.47	odd	4
867.2.d.d.577.6		6	51.38	odd	4
867.2.e.j.616.1		12	51.2	odd	8
867.2.e.j.616.2		12	51.32	odd	8
867.2.e.j.829.5		12	51.26	odd	8
867.2.e.j.829.6		12	51.8	odd	8
867.2.h.l.688.5		24	51.29	even	16
867.2.h.l.688.6		24	51.5	even	16
867.2.h.l.712.5		24	51.44	even	16
867.2.h.l.712.6		24	51.41	even	16
867.2.h.l.733.1		24	51.23	even	16
867.2.h.l.733.2		24	51.11	even	16
867.2.h.l.757.1		24	51.20	even	16
867.2.h.l.757.2		24	51.14	even	16
2601.2.a.y.1.3		3	1.1	even	1	trivial
2601.2.a.z.1.3		3	17.16	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q+2.53209 q^{2} +4.41147 q^{4} +0.879385 q^{5} +4.41147 q^{7} +6.10607 q^{8} +O(q^{10})\)	\(q+2.53209 q^{2} +4.41147 q^{4} +0.879385 q^{5} +4.41147 q^{7} +6.10607 q^{8} +2.22668 q^{10} +3.71688 q^{11} -3.12061 q^{13} +11.1702 q^{14} +6.63816 q^{16} -2.04189 q^{19} +3.87939 q^{20} +9.41147 q^{22} +0.162504 q^{23} -4.22668 q^{25} -7.90167 q^{26} +19.4611 q^{28} -8.33275 q^{29} +1.77332 q^{31} +4.59627 q^{32} +3.87939 q^{35} -2.73648 q^{37} -5.17024 q^{38} +5.36959 q^{40} +2.58853 q^{41} -11.7588 q^{43} +16.3969 q^{44} +0.411474 q^{46} -3.26857 q^{47} +12.4611 q^{49} -10.7023 q^{50} -13.7665 q^{52} +6.46791 q^{53} +3.26857 q^{55} +26.9368 q^{56} -21.0993 q^{58} -7.23442 q^{59} +2.50980 q^{61} +4.49020 q^{62} -1.63816 q^{64} -2.74422 q^{65} -4.61081 q^{67} +9.82295 q^{70} +1.12836 q^{71} -2.77332 q^{73} -6.92902 q^{74} -9.00774 q^{76} +16.3969 q^{77} -3.45336 q^{79} +5.83750 q^{80} +6.55438 q^{82} +14.8307 q^{83} -29.7743 q^{86} +22.6955 q^{88} +11.4192 q^{89} -13.7665 q^{91} +0.716881 q^{92} -8.27631 q^{94} -1.79561 q^{95} +4.30541 q^{97} +31.5526 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} + 3 q^{11} - 15 q^{13} + 12 q^{14} + 3 q^{16} - 3 q^{19} + 6 q^{20} + 18 q^{22} + 3 q^{23} - 6 q^{25} - 12 q^{26} + 21 q^{28} - 6 q^{29} + 12 q^{31} + 6 q^{35} - 3 q^{37} + 6 q^{38} + 9 q^{40} + 18 q^{41} - 24 q^{43} + 21 q^{44} - 9 q^{46} - 6 q^{50} - 6 q^{52} + 24 q^{53} + 24 q^{56} - 9 q^{58} + 9 q^{59} + 9 q^{61} + 12 q^{62} + 12 q^{64} + 21 q^{65} - 18 q^{67} + 9 q^{70} - 15 q^{71} - 15 q^{73} + 12 q^{74} - 3 q^{76} + 21 q^{77} + 3 q^{79} + 15 q^{80} + 9 q^{82} - 30 q^{86} - 6 q^{91} - 6 q^{92} + 9 q^{94} - 6 q^{95} + 15 q^{97} + 27 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8 + 3 * q^11 - 15 * q^13 + 12 * q^14 + 3 * q^16 - 3 * q^19 + 6 * q^20 + 18 * q^22 + 3 * q^23 - 6 * q^25 - 12 * q^26 + 21 * q^28 - 6 * q^29 + 12 * q^31 + 6 * q^35 - 3 * q^37 + 6 * q^38 + 9 * q^40 + 18 * q^41 - 24 * q^43 + 21 * q^44 - 9 * q^46 - 6 * q^50 - 6 * q^52 + 24 * q^53 + 24 * q^56 - 9 * q^58 + 9 * q^59 + 9 * q^61 + 12 * q^62 + 12 * q^64 + 21 * q^65 - 18 * q^67 + 9 * q^70 - 15 * q^71 - 15 * q^73 + 12 * q^74 - 3 * q^76 + 21 * q^77 + 3 * q^79 + 15 * q^80 + 9 * q^82 - 30 * q^86 - 6 * q^91 - 6 * q^92 + 9 * q^94 - 6 * q^95 + 15 * q^97 + 27 * q^98

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