LMFDB - Embedded newform 529.2.a.j.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,2,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$529 = 23^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,2,2,4,7,-8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1$ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.830830$ of defining polynomial
Character	$\chi$	$=$	529.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20362 q^{2} -2.51334 q^{3} +2.85592 q^{4} +1.23648 q^{5} -5.53843 q^{6} +2.37279 q^{7} +1.88612 q^{8} +3.31686 q^{9} +2.72472 q^{10} +1.91184 q^{11} -7.17789 q^{12} +0.196474 q^{13} +5.22871 q^{14} -3.10769 q^{15} -1.55555 q^{16} +1.55991 q^{17} +7.30909 q^{18} +7.98446 q^{19} +3.53129 q^{20} -5.96361 q^{21} +4.21297 q^{22} -4.74046 q^{24} -3.47112 q^{25} +0.432953 q^{26} -0.796384 q^{27} +6.77649 q^{28} +4.97732 q^{29} -6.84815 q^{30} +1.78268 q^{31} -7.20009 q^{32} -4.80511 q^{33} +3.43743 q^{34} +2.93390 q^{35} +9.47270 q^{36} -3.88323 q^{37} +17.5947 q^{38} -0.493805 q^{39} +2.33215 q^{40} +0.426496 q^{41} -13.1415 q^{42} -4.45317 q^{43} +5.46008 q^{44} +4.10123 q^{45} -2.58842 q^{47} +3.90963 q^{48} -1.36989 q^{49} -7.64901 q^{50} -3.92057 q^{51} +0.561114 q^{52} -9.81939 q^{53} -1.75493 q^{54} +2.36395 q^{55} +4.47536 q^{56} -20.0676 q^{57} +10.9681 q^{58} -7.21890 q^{59} -8.87531 q^{60} -7.42966 q^{61} +3.92834 q^{62} +7.87021 q^{63} -12.7551 q^{64} +0.242936 q^{65} -10.5886 q^{66} -7.26650 q^{67} +4.45497 q^{68} +6.46519 q^{70} -0.730284 q^{71} +6.25601 q^{72} -6.44434 q^{73} -8.55714 q^{74} +8.72409 q^{75} +22.8030 q^{76} +4.53640 q^{77} -1.08816 q^{78} +5.67808 q^{79} -1.92341 q^{80} -7.94901 q^{81} +0.939833 q^{82} +12.8897 q^{83} -17.0316 q^{84} +1.92879 q^{85} -9.81308 q^{86} -12.5097 q^{87} +3.60597 q^{88} +13.9002 q^{89} +9.03754 q^{90} +0.466190 q^{91} -4.48047 q^{93} -5.70388 q^{94} +9.87261 q^{95} +18.0963 q^{96} -4.32377 q^{97} -3.01871 q^{98} +6.34133 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$5 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 7 q^{5} - 8 q^{6} + 8 q^{7} - 9 q^{8} - q^{9} + 5 q^{10} + 13 q^{11} - 5 q^{12} + 4 q^{13} + 12 q^{14} + 5 q^{15} + 6 q^{16} + 16 q^{17} + 4 q^{18} + 10 q^{19} + 10 q^{20}+ \cdots - 18 q^{99}+O(q^{100})$ 5 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 7 * q^5 - 8 * q^6 + 8 * q^7 - 9 * q^8 - q^9 + 5 * q^10 + 13 * q^11 - 5 * q^12 + 4 * q^13 + 12 * q^14 + 5 * q^15 + 6 * q^16 + 16 * q^17 + 4 * q^18 + 10 * q^19 + 10 * q^20 + q^21 + 3 * q^22 - 19 * q^24 - 2 * q^25 + 6 * q^26 - 13 * q^27 - 9 * q^28 + 7 * q^29 - 9 * q^30 + 5 * q^31 - 6 * q^32 + 3 * q^33 - 9 * q^34 + 9 * q^35 + 8 * q^36 - 7 * q^37 + 4 * q^38 - 5 * q^39 - 17 * q^40 + 9 * q^41 - 4 * q^42 + 17 * q^44 + 3 * q^45 - 9 * q^47 + 20 * q^48 - 9 * q^49 + 8 * q^50 + 13 * q^51 + q^52 + 2 * q^53 + 8 * q^54 + 16 * q^55 + q^56 - 18 * q^57 - 6 * q^58 - 16 * q^59 - 7 * q^60 + 4 * q^61 + 2 * q^62 + 5 * q^63 - 21 * q^64 - q^65 - 23 * q^66 - 17 * q^67 + 15 * q^68 + 19 * q^70 - 7 * q^71 + 15 * q^72 - 18 * q^73 - 5 * q^74 + 8 * q^75 + 30 * q^76 + 12 * q^77 - 2 * q^78 + 13 * q^79 - 7 * q^80 - 11 * q^81 - 3 * q^82 + 13 * q^83 - 41 * q^84 + 7 * q^85 - 11 * q^86 - 17 * q^87 - 30 * q^88 + 15 * q^89 - q^90 + 2 * q^91 + 2 * q^93 - 19 * q^94 - 8 * q^95 + 24 * q^96 - 16 * q^97 + 3 * q^98 - 18 * q^99

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

)

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

$2$	2.20362	1.55819	0.779096	−	0.626905i	$-0.215679\pi$
$2$	2.20362	1.55819	0.779096	+	0.626905i	$0.215679\pi$
$3$	−2.51334	−1.45108	−0.725538	−	0.688182i	$-0.758409\pi$
$3$	−2.51334	−1.45108	−0.725538	+	0.688182i	$0.758409\pi$
$4$	2.85592	1.42796
$5$	1.23648	0.552970	0.276485	−	0.961018i	$-0.410830\pi$
$5$	1.23648	0.552970	0.276485	+	0.961018i	$0.410830\pi$
$6$	−5.53843	−2.26105
$7$	2.37279	0.896829	0.448414	−	0.893826i	$-0.351989\pi$
$7$	2.37279	0.896829	0.448414	+	0.893826i	$0.351989\pi$
$8$	1.88612	0.666845
$9$	3.31686	1.10562
$10$	2.72472	0.861633
$11$	1.91184	0.576443	0.288221	−	0.957564i	$-0.406936\pi$
$11$	1.91184	0.576443	0.288221	+	0.957564i	$0.406936\pi$
$12$	−7.17789	−2.07208
$13$	0.196474	0.0544920	0.0272460	−	0.999629i	$-0.491326\pi$
$13$	0.196474	0.0544920	0.0272460	+	0.999629i	$0.491326\pi$
$14$	5.22871	1.39743
$15$	−3.10769	−0.802402
$16$	−1.55555	−0.388889
$17$	1.55991	0.378333	0.189166	−	0.981945i	$-0.439421\pi$
$17$	1.55991	0.378333	0.189166	+	0.981945i	$0.439421\pi$
$18$	7.30909	1.72277
$19$	7.98446	1.83176	0.915880	−	0.401452i	$-0.131494\pi$
$19$	7.98446	1.83176	0.915880	+	0.401452i	$0.131494\pi$
$20$	3.53129	0.789620
$21$	−5.96361	−1.30137
$22$	4.21297	0.898208
$23$	0	0
$23$	0	0
$24$	−4.74046	−0.967643
$25$	−3.47112	−0.694224
$26$	0.432953	0.0849090
$27$	−0.796384	−0.153264
$28$	6.77649	1.28064
$29$	4.97732	0.924264	0.462132	−	0.886811i	$-0.347085\pi$
$29$	4.97732	0.924264	0.462132	+	0.886811i	$0.347085\pi$
$30$	−6.84815	−1.25030
$31$	1.78268	0.320179	0.160089	−	0.987103i	$-0.448822\pi$
$31$	1.78268	0.320179	0.160089	+	0.987103i	$0.448822\pi$
$32$	−7.20009	−1.27281
$33$	−4.80511	−0.836462
$34$	3.43743	0.589515
$35$	2.93390	0.495919
$36$	9.47270	1.57878
$37$	−3.88323	−0.638398	−0.319199	−	0.947688i	$-0.603414\pi$
$37$	−3.88323	−0.638398	−0.319199	+	0.947688i	$0.603414\pi$
$38$	17.5947	2.85423
$39$	−0.493805	−0.0790720
$40$	2.33215	0.368745
$41$	0.426496	0.0666075	0.0333037	−	0.999445i	$-0.489397\pi$
$41$	0.426496	0.0666075	0.0333037	+	0.999445i	$0.489397\pi$
$42$	−13.1415	−2.02778
$43$	−4.45317	−0.679102	−0.339551	−	0.940588i	$-0.610275\pi$
$43$	−4.45317	−0.679102	−0.339551	+	0.940588i	$0.610275\pi$
$44$	5.46008	0.823138
$45$	4.10123	0.611375
$46$	0	0
$47$	−2.58842	−0.377559	−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842	−0.377559	−0.188780	+	0.982019i	$0.560453\pi$
$48$	3.90963	0.564307
$49$	−1.36989	−0.195698
$50$	−7.64901	−1.08173
$51$	−3.92057	−0.548989
$52$	0.561114	0.0778125
$53$	−9.81939	−1.34880	−0.674399	−	0.738367i	$-0.735597\pi$
$53$	−9.81939	−1.34880	−0.674399	+	0.738367i	$0.735597\pi$
$54$	−1.75493	−0.238815
$55$	2.36395	0.318756
$56$	4.47536	0.598046
$57$	−20.0676	−2.65802
$58$	10.9681	1.44018
$59$	−7.21890	−0.939821	−0.469911	−	0.882714i	$-0.655714\pi$
$59$	−7.21890	−0.939821	−0.469911	+	0.882714i	$0.655714\pi$
$60$	−8.87531	−1.14580
$61$	−7.42966	−0.951271	−0.475635	−	0.879643i	$-0.657782\pi$
$61$	−7.42966	−0.951271	−0.475635	+	0.879643i	$0.657782\pi$
$62$	3.92834	0.498900
$63$	7.87021	0.991553
$64$	−12.7551	−1.59439
$65$	0.242936	0.0301325
$66$	−10.5886	−1.30337
$67$	−7.26650	−0.887744	−0.443872	−	0.896090i	$-0.646396\pi$
$67$	−7.26650	−0.887744	−0.443872	+	0.896090i	$0.646396\pi$
$68$	4.45497	0.540244
$69$	0	0
$70$	6.46519	0.772738
$71$	−0.730284	−0.0866687	−0.0433344	−	0.999061i	$-0.513798\pi$
$71$	−0.730284	−0.0866687	−0.0433344	+	0.999061i	$0.513798\pi$
$72$	6.25601	0.737278
$73$	−6.44434	−0.754253	−0.377126	−	0.926162i	$-0.623088\pi$
$73$	−6.44434	−0.754253	−0.377126	+	0.926162i	$0.623088\pi$
$74$	−8.55714	−0.994747
$75$	8.72409	1.00737
$76$	22.8030	2.61568
$77$	4.53640	0.516970
$78$	−1.08816	−0.123209
$79$	5.67808	0.638834	0.319417	−	0.947614i	$-0.396513\pi$
$79$	5.67808	0.638834	0.319417	+	0.947614i	$0.396513\pi$
$80$	−1.92341	−0.215044
$81$	−7.94901	−0.883223
$82$	0.939833	0.103787
$83$	12.8897	1.41483	0.707416	−	0.706797i	$-0.249861\pi$
$83$	12.8897	1.41483	0.707416	+	0.706797i	$0.249861\pi$
$84$	−17.0316	−1.85830
$85$	1.92879	0.209207
$86$	−9.81308	−1.05817
$87$	−12.5097	−1.34118
$88$	3.60597	0.384398
$89$	13.9002	1.47342	0.736711	−	0.676208i	$-0.236378\pi$
$89$	13.9002	1.47342	0.736711	+	0.676208i	$0.236378\pi$
$90$	9.03754	0.952640
$91$	0.466190	0.0488700
$92$	0	0
$93$	−4.48047	−0.464603
$94$	−5.70388	−0.588310
$95$	9.87261	1.01291
$96$	18.0963	1.84694
$97$	−4.32377	−0.439012	−0.219506	−	0.975611i	$-0.570445\pi$
$97$	−4.32377	−0.439012	−0.219506	+	0.975611i	$0.570445\pi$
$98$	−3.01871	−0.304936
$99$	6.34133	0.637327
$100$	−9.91325	−0.991325
$101$	−1.82028	−0.181124	−0.0905622	−	0.995891i	$-0.528866\pi$
$101$	−1.82028	−0.181124	−0.0905622	+	0.995891i	$0.528866\pi$
$102$	−8.63943	−0.855431
$103$	15.3132	1.50886	0.754429	−	0.656382i	$-0.227914\pi$
$103$	15.3132	1.50886	0.754429	+	0.656382i	$0.227914\pi$
$104$	0.370574	0.0363377
$105$	−7.37388	−0.719617
$106$	−21.6382	−2.10168
$107$	−1.98833	−0.192219	−0.0961094	−	0.995371i	$-0.530640\pi$
$107$	−1.98833	−0.192219	−0.0961094	+	0.995371i	$0.530640\pi$
$108$	−2.27441	−0.218855
$109$	−15.5948	−1.49371	−0.746855	−	0.664987i	$-0.768437\pi$
$109$	−15.5948	−1.49371	−0.746855	+	0.664987i	$0.768437\pi$
$110$	5.20925	0.496682
$111$	9.75985	0.926364
$112$	−3.69100	−0.348766
$113$	1.48825	0.140002	0.0700012	−	0.997547i	$-0.477700\pi$
$113$	1.48825	0.140002	0.0700012	+	0.997547i	$0.477700\pi$
$114$	−44.2213	−4.14171
$115$	0	0
$116$	14.2148	1.31981
$117$	0.651677	0.0602475
$118$	−15.9077	−1.46442
$119$	3.70132	0.339300
$120$	−5.86148	−0.535078
$121$	−7.34485	−0.667714
$122$	−16.3721	−1.48226
$123$	−1.07193	−0.0966525
$124$	5.09119	0.457203
$125$	−10.4744	−0.936855
$126$	17.3429	1.54503
$127$	5.99437	0.531914	0.265957	−	0.963985i	$-0.414312\pi$
$127$	5.99437	0.531914	0.265957	+	0.963985i	$0.414312\pi$
$128$	−13.7072	−1.21156
$129$	11.1923	0.985429
$130$	0.535337	0.0469521
$131$	−12.7688	−1.11562	−0.557809	−	0.829970i	$-0.688358\pi$
$131$	−12.7688	−1.11562	−0.557809	+	0.829970i	$0.688358\pi$
$132$	−13.7230	−1.19444
$133$	18.9454	1.64277
$134$	−16.0126	−1.38328
$135$	−0.984712	−0.0847506
$136$	2.94217	0.252289
$137$	−0.697560	−0.0595966	−0.0297983	−	0.999556i	$-0.509486\pi$
$137$	−0.697560	−0.0595966	−0.0297983	+	0.999556i	$0.509486\pi$
$138$	0	0
$139$	13.9559	1.18372	0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559	1.18372	0.591862	+	0.806039i	$0.298393\pi$
$140$	8.37899	0.708154
$141$	6.50557	0.547867
$142$	−1.60926	−0.135046
$143$	0.375627	0.0314115
$144$	−5.15956	−0.429963
$145$	6.15435	0.511091
$146$	−14.2008	−1.17527
$147$	3.44299	0.283973
$148$	−11.0902	−0.911608
$149$	16.6390	1.36312	0.681561	−	0.731761i	$-0.261301\pi$
$149$	16.6390	1.36312	0.681561	+	0.731761i	$0.261301\pi$
$150$	19.2246	1.56968
$151$	13.1900	1.07338	0.536692	−	0.843778i	$-0.319674\pi$
$151$	13.1900	1.07338	0.536692	+	0.843778i	$0.319674\pi$
$152$	15.0597	1.22150
$153$	5.17399	0.418293
$154$	9.99647	0.805539
$155$	2.20425	0.177049
$156$	−1.41027	−0.112912
$157$	−4.12867	−0.329504	−0.164752	−	0.986335i	$-0.552682\pi$
$157$	−4.12867	−0.329504	−0.164752	+	0.986335i	$0.552682\pi$
$158$	12.5123	0.995426
$159$	24.6794	1.95721
$160$	−8.90276	−0.703825
$161$	0	0
$162$	−17.5166	−1.37623
$163$	−14.7893	−1.15839	−0.579194	−	0.815190i	$-0.696633\pi$
$163$	−14.7893	−1.15839	−0.579194	+	0.815190i	$0.696633\pi$
$164$	1.21804	0.0951129
$165$	−5.94142	−0.462539
$166$	28.4040	2.20458
$167$	1.32974	0.102899	0.0514493	−	0.998676i	$-0.483616\pi$
$167$	1.32974	0.102899	0.0514493	+	0.998676i	$0.483616\pi$
$168$	−11.2481	−0.867810
$169$	−12.9614	−0.997031
$170$	4.25031	0.325984
$171$	26.4834	2.02523
$172$	−12.7179	−0.969731
$173$	−16.9361	−1.28762	−0.643812	−	0.765184i	$-0.722648\pi$
$173$	−16.9361	−1.28762	−0.643812	+	0.765184i	$0.722648\pi$
$174$	−27.5665	−2.08981
$175$	−8.23622	−0.622600
$176$	−2.97398	−0.224172
$177$	18.1435	1.36375
$178$	30.6308	2.29587
$179$	−1.43135	−0.106984	−0.0534920	−	0.998568i	$-0.517035\pi$
$179$	−1.43135	−0.106984	−0.0534920	+	0.998568i	$0.517035\pi$
$180$	11.7128	0.873020
$181$	16.1314	1.19903	0.599517	−	0.800362i	$-0.295359\pi$
$181$	16.1314	1.19903	0.599517	+	0.800362i	$0.295359\pi$
$182$	1.02730	0.0761488
$183$	18.6732	1.38037
$184$	0	0
$185$	−4.80153	−0.353015
$186$	−9.87324	−0.723941
$187$	2.98230	0.218087
$188$	−7.39232	−0.539140
$189$	−1.88965	−0.137452
$190$	21.7554	1.57831
$191$	20.7445	1.50102	0.750509	−	0.660860i	$-0.229808\pi$
$191$	20.7445	1.50102	0.750509	+	0.660860i	$0.229808\pi$
$192$	32.0579	2.31358
$193$	14.6523	1.05469	0.527346	−	0.849651i	$-0.323187\pi$
$193$	14.6523	1.05469	0.527346	+	0.849651i	$0.323187\pi$
$194$	−9.52793	−0.684065
$195$	−0.610579	−0.0437245
$196$	−3.91229	−0.279450
$197$	11.6779	0.832016	0.416008	−	0.909361i	$-0.363429\pi$
$197$	11.6779	0.832016	0.416008	+	0.909361i	$0.363429\pi$
$198$	13.9738	0.993078
$199$	5.72341	0.405722	0.202861	−	0.979208i	$-0.434976\pi$
$199$	5.72341	0.405722	0.202861	+	0.979208i	$0.434976\pi$
$200$	−6.54696	−0.462940
$201$	18.2632	1.28818
$202$	−4.01119	−0.282226
$203$	11.8101	0.828907
$204$	−11.1968	−0.783935
$205$	0.527353	0.0368319
$206$	33.7445	2.35109
$207$	0	0
$208$	−0.305626	−0.0211913
$209$	15.2650	1.05590
$210$	−16.2492	−1.12130
$211$	−14.0677	−0.968463	−0.484232	−	0.874940i	$-0.660901\pi$
$211$	−14.0677	−0.968463	−0.484232	+	0.874940i	$0.660901\pi$
$212$	−28.0434	−1.92603
$213$	1.83545	0.125763
$214$	−4.38151	−0.299514
$215$	−5.50625	−0.375523
$216$	−1.50208	−0.102204
$217$	4.22992	0.287145
$218$	−34.3649	−2.32748
$219$	16.1968	1.09448
$220$	6.75127	0.455171
$221$	0.306480	0.0206161
$222$	21.5070	1.44345
$223$	−4.20359	−0.281493	−0.140746	−	0.990046i	$-0.544950\pi$
$223$	−4.20359	−0.281493	−0.140746	+	0.990046i	$0.544950\pi$
$224$	−17.0843	−1.14149
$225$	−11.5132	−0.767549
$226$	3.27952	0.218150
$227$	−18.4308	−1.22329	−0.611647	−	0.791131i	$-0.709493\pi$
$227$	−18.4308	−1.22329	−0.611647	+	0.791131i	$0.709493\pi$
$228$	−57.3116	−3.79555
$229$	−10.9247	−0.721923	−0.360961	−	0.932581i	$-0.617551\pi$
$229$	−10.9247	−0.721923	−0.360961	+	0.932581i	$0.617551\pi$
$230$	0	0
$231$	−11.4015	−0.750163
$232$	9.38783	0.616341
$233$	4.16483	0.272847	0.136423	−	0.990651i	$-0.456439\pi$
$233$	4.16483	0.272847	0.136423	+	0.990651i	$0.456439\pi$
$234$	1.43604	0.0938772
$235$	−3.20052	−0.208779
$236$	−20.6166	−1.34203
$237$	−14.2709	−0.926997
$238$	8.15629	0.528694
$239$	−22.5171	−1.45651	−0.728257	−	0.685305i	$-0.759669\pi$
$239$	−22.5171	−1.45651	−0.728257	+	0.685305i	$0.759669\pi$
$240$	4.83418	0.312045
$241$	−5.92913	−0.381929	−0.190965	−	0.981597i	$-0.561162\pi$
$241$	−5.92913	−0.381929	−0.190965	+	0.981597i	$0.561162\pi$
$242$	−16.1852	−1.04043
$243$	22.3677	1.43489
$244$	−21.2185	−1.35838
$245$	−1.69384	−0.108215
$246$	−2.36212	−0.150603
$247$	1.56874	0.0998163
$248$	3.36235	0.213510
$249$	−32.3963	−2.05303
$250$	−23.0815	−1.45980
$251$	1.55061	0.0978738	0.0489369	−	0.998802i	$-0.484417\pi$
$251$	1.55061	0.0978738	0.0489369	+	0.998802i	$0.484417\pi$
$252$	22.4767	1.41590
$253$	0	0
$254$	13.2093	0.828824
$255$	−4.84770	−0.303575
$256$	−4.69517	−0.293448
$257$	27.4579	1.71278	0.856388	−	0.516333i	$-0.172703\pi$
$257$	27.4579	1.71278	0.856388	+	0.516333i	$0.172703\pi$
$258$	24.6636	1.53549
$259$	−9.21406	−0.572534
$260$	0.693805	0.0430280
$261$	16.5091	1.02189
$262$	−28.1376	−1.73835
$263$	12.9407	0.797958	0.398979	−	0.916960i	$-0.369365\pi$
$263$	12.9407	0.797958	0.398979	+	0.916960i	$0.369365\pi$
$264$	−9.06302	−0.557791
$265$	−12.1415	−0.745845
$266$	41.7484	2.55976
$267$	−34.9360	−2.13805
$268$	−20.7526	−1.26766
$269$	−9.99766	−0.609568	−0.304784	−	0.952421i	$-0.598584\pi$
$269$	−9.99766	−0.609568	−0.304784	+	0.952421i	$0.598584\pi$
$270$	−2.16993	−0.132058
$271$	4.41139	0.267973	0.133986	−	0.990983i	$-0.457222\pi$
$271$	4.41139	0.267973	0.133986	+	0.990983i	$0.457222\pi$
$272$	−2.42652	−0.147129
$273$	−1.17169	−0.0709141
$274$	−1.53715	−0.0928629
$275$	−6.63624	−0.400180
$276$	0	0
$277$	−30.8042	−1.85085	−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042	−1.85085	−0.925423	+	0.378935i	$0.876290\pi$
$278$	30.7535	1.84447
$279$	5.91290	0.353996
$280$	5.53369	0.330701
$281$	3.57931	0.213524	0.106762	−	0.994285i	$-0.465952\pi$
$281$	3.57931	0.213524	0.106762	+	0.994285i	$0.465952\pi$
$282$	14.3358	0.853682
$283$	−14.7804	−0.878604	−0.439302	−	0.898339i	$-0.644774\pi$
$283$	−14.7804	−0.878604	−0.439302	+	0.898339i	$0.644774\pi$
$284$	−2.08563	−0.123760
$285$	−24.8132	−1.46981
$286$	0.827738	0.0489452
$287$	1.01198	0.0597355
$288$	−23.8817	−1.40724
$289$	−14.5667	−0.856864
$290$	13.5618	0.796377
$291$	10.8671	0.637040
$292$	−18.4045	−1.07704
$293$	−21.5135	−1.25683	−0.628415	−	0.777878i	$-0.716296\pi$
$293$	−21.5135	−1.25683	−0.628415	+	0.777878i	$0.716296\pi$
$294$	7.58703	0.442485
$295$	−8.92602	−0.519693
$296$	−7.32424	−0.425713
$297$	−1.52256	−0.0883481
$298$	36.6660	2.12401
$299$	0	0
$300$	24.9153	1.43849
$301$	−10.5664	−0.609038
$302$	29.0656	1.67254
$303$	4.57497	0.262825
$304$	−12.4203	−0.712351
$305$	−9.18662	−0.526024
$306$	11.4015	0.651780
$307$	14.1449	0.807294	0.403647	−	0.914915i	$-0.367742\pi$
$307$	14.1449	0.807294	0.403647	+	0.914915i	$0.367742\pi$
$308$	12.9556	0.738213
$309$	−38.4873	−2.18947
$310$	4.85731	0.275877
$311$	0.570139	0.0323296	0.0161648	−	0.999869i	$-0.494854\pi$
$311$	0.570139	0.0323296	0.0161648	+	0.999869i	$0.494854\pi$
$312$	−0.931376	−0.0527288
$313$	21.1327	1.19449	0.597247	−	0.802058i	$-0.296261\pi$
$313$	21.1327	1.19449	0.597247	+	0.802058i	$0.296261\pi$
$314$	−9.09801	−0.513431
$315$	9.73134	0.548299
$316$	16.2162	0.912230
$317$	−8.81213	−0.494939	−0.247469	−	0.968896i	$-0.579599\pi$
$317$	−8.81213	−0.494939	−0.247469	+	0.968896i	$0.579599\pi$
$318$	54.3840	3.04970
$319$	9.51585	0.532785
$320$	−15.7714	−0.881650
$321$	4.99734	0.278924
$322$	0	0
$323$	12.4550	0.693015
$324$	−22.7017	−1.26121
$325$	−0.681984	−0.0378297
$326$	−32.5900	−1.80499
$327$	39.1949	2.16749
$328$	0.804424	0.0444169
$329$	−6.14176	−0.338606
$330$	−13.0926	−0.720724
$331$	30.1875	1.65925	0.829627	−	0.558317i	$-0.188553\pi$
$331$	30.1875	1.65925	0.829627	+	0.558317i	$0.188553\pi$
$332$	36.8121	2.02033
$333$	−12.8801	−0.705827
$334$	2.93024	0.160336
$335$	−8.98487	−0.490896
$336$	9.27672	0.506086
$337$	4.95577	0.269958	0.134979	−	0.990848i	$-0.456903\pi$
$337$	4.95577	0.269958	0.134979	+	0.990848i	$0.456903\pi$
$338$	−28.5619	−1.55356
$339$	−3.74046	−0.203154
$340$	5.50847	0.298739
$341$	3.40820	0.184565
$342$	58.3591	3.15570
$343$	−19.8600	−1.07234
$344$	−8.39923	−0.452856
$345$	0	0
$346$	−37.3205	−2.00636
$347$	−6.76696	−0.363269	−0.181635	−	0.983366i	$-0.558139\pi$
$347$	−6.76696	−0.363269	−0.181635	+	0.983366i	$0.558139\pi$
$348$	−35.7266	−1.91515
$349$	10.0918	0.540204	0.270102	−	0.962832i	$-0.412943\pi$
$349$	10.0918	0.540204	0.270102	+	0.962832i	$0.412943\pi$
$350$	−18.1495	−0.970130
$351$	−0.156469	−0.00835168
$352$	−13.7654	−0.733701
$353$	24.4693	1.30237	0.651184	−	0.758920i	$-0.274273\pi$
$353$	24.4693	1.30237	0.651184	+	0.758920i	$0.274273\pi$
$354$	39.9814	2.12499
$355$	−0.902980	−0.0479252
$356$	39.6980	2.10399
$357$	−9.30267	−0.492349
$358$	−3.15414	−0.166702
$359$	−0.418813	−0.0221041	−0.0110520	−	0.999939i	$-0.503518\pi$
$359$	−0.418813	−0.0221041	−0.0110520	+	0.999939i	$0.503518\pi$
$360$	7.73543	0.407693
$361$	44.7516	2.35534
$362$	35.5473	1.86833
$363$	18.4601	0.968903
$364$	1.33140	0.0697845
$365$	−7.96829	−0.417079
$366$	41.1486	2.15087
$367$	−28.5682	−1.49125	−0.745624	−	0.666367i	$-0.767849\pi$
$367$	−28.5682	−1.49125	−0.745624	+	0.666367i	$0.767849\pi$
$368$	0	0
$369$	1.41463	0.0736426
$370$	−10.5807	−0.550065
$371$	−23.2993	−1.20964
$372$	−12.7959	−0.663436
$373$	−14.4078	−0.746006	−0.373003	−	0.927830i	$-0.621672\pi$
$373$	−14.4078	−0.746006	−0.373003	+	0.927830i	$0.621672\pi$
$374$	6.57183	0.339821
$375$	26.3256	1.35945
$376$	−4.88207	−0.251774
$377$	0.977912	0.0503650
$378$	−4.16406	−0.214176
$379$	5.62712	0.289046	0.144523	−	0.989501i	$-0.453835\pi$
$379$	5.62712	0.289046	0.144523	+	0.989501i	$0.453835\pi$
$380$	28.1954	1.44639
$381$	−15.0659	−0.771848
$382$	45.7129	2.33887
$383$	−0.231660	−0.0118373	−0.00591864	−	0.999982i	$-0.501884\pi$
$383$	−0.231660	−0.0118373	−0.00591864	+	0.999982i	$0.501884\pi$
$384$	34.4508	1.75806
$385$	5.60916	0.285869
$386$	32.2879	1.64341
$387$	−14.7706	−0.750830
$388$	−12.3484	−0.626893
$389$	30.1698	1.52967	0.764835	−	0.644226i	$-0.222820\pi$
$389$	30.1698	1.52967	0.764835	+	0.644226i	$0.222820\pi$
$390$	−1.34548	−0.0681311
$391$	0	0
$392$	−2.58378	−0.130500
$393$	32.0924	1.61885
$394$	25.7336	1.29644
$395$	7.02083	0.353256
$396$	18.1103	0.910078
$397$	−13.0453	−0.654723	−0.327362	−	0.944899i	$-0.606160\pi$
$397$	−13.0453	−0.654723	−0.327362	+	0.944899i	$0.606160\pi$
$398$	12.6122	0.632192
$399$	−47.6162	−2.38379
$400$	5.39952	0.269976
$401$	21.3257	1.06496	0.532479	−	0.846444i	$-0.321261\pi$
$401$	21.3257	1.06496	0.532479	+	0.846444i	$0.321261\pi$
$402$	40.2450	2.00724
$403$	0.350250	0.0174472
$404$	−5.19857	−0.258639
$405$	−9.82878	−0.488396
$406$	26.0249	1.29160
$407$	−7.42412	−0.368000
$408$	−7.39467	−0.366091
$409$	−9.14902	−0.452390	−0.226195	−	0.974082i	$-0.572629\pi$
$409$	−9.14902	−0.452390	−0.226195	+	0.974082i	$0.572629\pi$
$410$	1.16208	0.0573912
$411$	1.75320	0.0864791
$412$	43.7334	2.15459
$413$	−17.1289	−0.842859
$414$	0	0
$415$	15.9379	0.782360
$416$	−1.41463	−0.0693579
$417$	−35.0759	−1.71767
$418$	33.6383	1.64530
$419$	8.97420	0.438418	0.219209	−	0.975678i	$-0.429652\pi$
$419$	8.97420	0.438418	0.219209	+	0.975678i	$0.429652\pi$
$420$	−21.0592	−1.02758
$421$	−31.4723	−1.53387	−0.766933	−	0.641728i	$-0.778218\pi$
$421$	−31.4723	−1.53387	−0.766933	+	0.641728i	$0.778218\pi$
$422$	−30.9999	−1.50905
$423$	−8.58543	−0.417438
$424$	−18.5206	−0.899439
$425$	−5.41462	−0.262648
$426$	4.04462	0.195963
$427$	−17.6290	−0.853127
$428$	−5.67851	−0.274481
$429$	−0.944078	−0.0455805
$430$	−12.1337	−0.585137
$431$	22.1024	1.06464	0.532318	−	0.846545i	$-0.321321\pi$
$431$	22.1024	1.06464	0.532318	+	0.846545i	$0.321321\pi$
$432$	1.23882	0.0596027
$433$	−12.6952	−0.610095	−0.305047	−	0.952337i	$-0.598672\pi$
$433$	−12.6952	−0.610095	−0.305047	+	0.952337i	$0.598672\pi$
$434$	9.32111	0.447428
$435$	−15.4679	−0.741631
$436$	−44.5375	−2.13296
$437$	0	0
$438$	35.6915	1.70541
$439$	18.4210	0.879187	0.439593	−	0.898197i	$-0.355123\pi$
$439$	18.4210	0.879187	0.439593	+	0.898197i	$0.355123\pi$
$440$	4.45871	0.212561
$441$	−4.54373	−0.216368
$442$	0.675365	0.0321238
$443$	−13.9128	−0.661016	−0.330508	−	0.943803i	$-0.607220\pi$
$443$	−13.9128	−0.661016	−0.330508	+	0.943803i	$0.607220\pi$
$444$	27.8734	1.32281
$445$	17.1873	0.814758
$446$	−9.26309	−0.438620
$447$	−41.8195	−1.97799
$448$	−30.2652	−1.42989
$449$	30.0925	1.42015	0.710076	−	0.704125i	$-0.248661\pi$
$449$	30.0925	1.42015	0.710076	+	0.704125i	$0.248661\pi$
$450$	−25.3707	−1.19599
$451$	0.815394	0.0383954
$452$	4.25031	0.199918
$453$	−33.1508	−1.55756
$454$	−40.6143	−1.90612
$455$	0.576434	0.0270237
$456$	−37.8500	−1.77249
$457$	−38.0475	−1.77979	−0.889894	−	0.456166i	$-0.849222\pi$
$457$	−38.0475	−1.77979	−0.889894	+	0.456166i	$0.849222\pi$
$458$	−24.0738	−1.12489
$459$	−1.24228	−0.0579849
$460$	0	0
$461$	8.76016	0.408001	0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016	0.408001	0.204001	+	0.978971i	$0.434606\pi$
$462$	−25.1245	−1.16890
$463$	−27.8367	−1.29368	−0.646841	−	0.762625i	$-0.723910\pi$
$463$	−27.8367	−1.29368	−0.646841	+	0.762625i	$0.723910\pi$
$464$	−7.74248	−0.359436
$465$	−5.54001	−0.256912
$466$	9.17768	0.425148
$467$	17.3663	0.803619	0.401809	−	0.915723i	$-0.368381\pi$
$467$	17.3663	0.803619	0.401809	+	0.915723i	$0.368381\pi$
$468$	1.86114	0.0860311
$469$	−17.2418	−0.796155
$470$	−7.05272	−0.325318
$471$	10.3768	0.478135
$472$	−13.6157	−0.626715
$473$	−8.51377	−0.391463
$474$	−31.4477	−1.44444
$475$	−27.7150	−1.27165
$476$	10.5707	0.484507
$477$	−32.5696	−1.49126
$478$	−49.6191	−2.26953
$479$	25.4778	1.16411	0.582055	−	0.813150i	$-0.302249\pi$
$479$	25.4778	1.16411	0.582055	+	0.813150i	$0.302249\pi$
$480$	22.3756	1.02130
$481$	−0.762952	−0.0347876
$482$	−13.0655	−0.595119
$483$	0	0
$484$	−20.9763	−0.953469
$485$	−5.34625	−0.242761
$486$	49.2898	2.23583
$487$	−6.16107	−0.279185	−0.139592	−	0.990209i	$-0.544579\pi$
$487$	−6.16107	−0.279185	−0.139592	+	0.990209i	$0.544579\pi$
$488$	−14.0133	−0.634350
$489$	37.1705	1.68091
$490$	−3.73257	−0.168620
$491$	−32.6476	−1.47337	−0.736683	−	0.676238i	$-0.763609\pi$
$491$	−32.6476	−1.47337	−0.736683	+	0.676238i	$0.763609\pi$
$492$	−3.06134	−0.138016
$493$	7.76414	0.349679
$494$	3.45689	0.155533
$495$	7.84092	0.352423
$496$	−2.77305	−0.124514
$497$	−1.73281	−0.0777270
$498$	−71.3889	−3.19901
$499$	−8.57369	−0.383811	−0.191906	−	0.981413i	$-0.561467\pi$
$499$	−8.57369	−0.383811	−0.191906	+	0.981413i	$0.561467\pi$
$500$	−29.9140	−1.33779
$501$	−3.34209	−0.149314
$502$	3.41695	0.152506
$503$	−6.75554	−0.301214	−0.150607	−	0.988594i	$-0.548123\pi$
$503$	−6.75554	−0.301214	−0.150607	+	0.988594i	$0.548123\pi$
$504$	14.8442	0.661212
$505$	−2.25073	−0.100156
$506$	0	0
$507$	32.5764	1.44677
$508$	17.1194	0.759553
$509$	40.9726	1.81608	0.908038	−	0.418887i	$-0.137580\pi$
$509$	40.9726	1.81608	0.908038	+	0.418887i	$0.137580\pi$
$510$	−10.6825	−0.473028
$511$	−15.2910	−0.676436
$512$	17.0681	0.754309
$513$	−6.35870	−0.280743
$514$	60.5066	2.66883
$515$	18.9345	0.834353
$516$	31.9644	1.40715
$517$	−4.94865	−0.217641
$518$	−20.3043	−0.892118
$519$	42.5660	1.86844
$520$	0.458206	0.0200937
$521$	18.7268	0.820438	0.410219	−	0.911987i	$-0.365452\pi$
$521$	18.7268	0.820438	0.410219	+	0.911987i	$0.365452\pi$
$522$	36.3797	1.59229
$523$	−23.5640	−1.03038	−0.515191	−	0.857075i	$-0.672279\pi$
$523$	−23.5640	−1.03038	−0.515191	+	0.857075i	$0.672279\pi$
$524$	−36.4668	−1.59306
$525$	20.7004	0.903440
$526$	28.5163	1.24337
$527$	2.78081	0.121134
$528$	7.47461	0.325291
$529$	0	0
$530$	−26.7551	−1.16217
$531$	−23.9441	−1.03909
$532$	54.1066	2.34582
$533$	0.0837952	0.00362957
$534$	−76.9854	−3.33148
$535$	−2.45853	−0.106291
$536$	−13.7055	−0.591988
$537$	3.59746	0.155242
$538$	−22.0310	−0.949824
$539$	−2.61901	−0.112809
$540$	−2.81226	−0.121020
$541$	0.953288	0.0409850	0.0204925	−	0.999790i	$-0.493477\pi$
$541$	0.953288	0.0409850	0.0204925	+	0.999790i	$0.493477\pi$
$542$	9.72101	0.417553
$543$	−40.5435	−1.73989
$544$	−11.2315	−0.481545
$545$	−19.2826	−0.825977
$546$	−2.58196	−0.110498
$547$	29.7860	1.27356	0.636779	−	0.771046i	$-0.280266\pi$
$547$	29.7860	1.27356	0.636779	+	0.771046i	$0.280266\pi$
$548$	−1.99218	−0.0851016
$549$	−24.6432	−1.05174
$550$	−14.6237	−0.623558
$551$	39.7412	1.69303
$552$	0	0
$553$	13.4729	0.572925
$554$	−67.8807	−2.88397
$555$	12.0679	0.512252
$556$	39.8570	1.69031
$557$	6.00871	0.254597	0.127299	−	0.991864i	$-0.459369\pi$
$557$	6.00871	0.254597	0.127299	+	0.991864i	$0.459369\pi$
$558$	13.0298	0.551594
$559$	−0.874931	−0.0370056
$560$	−4.56384	−0.192857
$561$	−7.49552	−0.316461
$562$	7.88742	0.332711
$563$	−0.0891900	−0.00375891	−0.00187946	−	0.999998i	$-0.500598\pi$
$563$	−0.0891900	−0.00375891	−0.00187946	+	0.999998i	$0.500598\pi$
$564$	18.5794	0.782333
$565$	1.84018	0.0774171
$566$	−32.5703	−1.36903
$567$	−18.8613	−0.792100
$568$	−1.37740	−0.0577946
$569$	41.3596	1.73388	0.866942	−	0.498410i	$-0.166082\pi$
$569$	41.3596	1.73388	0.866942	+	0.498410i	$0.166082\pi$
$570$	−54.6788	−2.29024
$571$	−25.7905	−1.07930	−0.539649	−	0.841890i	$-0.681443\pi$
$571$	−25.7905	−1.07930	−0.539649	+	0.841890i	$0.681443\pi$
$572$	1.07276	0.0448544
$573$	−52.1379	−2.17809
$574$	2.23002	0.0930793
$575$	0	0
$576$	−42.3070	−1.76279
$577$	27.1442	1.13003	0.565014	−	0.825081i	$-0.308871\pi$
$577$	27.1442	1.13003	0.565014	+	0.825081i	$0.308871\pi$
$578$	−32.0994	−1.33516
$579$	−36.8261	−1.53044
$580$	17.5763	0.729817
$581$	30.5846	1.26886
$582$	23.9469	0.992631
$583$	−18.7731	−0.777504
$584$	−12.1548	−0.502970
$585$	0.805784	0.0333151
$586$	−47.4074	−1.95838
$587$	31.6348	1.30571	0.652854	−	0.757484i	$-0.273572\pi$
$587$	31.6348	1.30571	0.652854	+	0.757484i	$0.273572\pi$
$588$	9.83291	0.405503
$589$	14.2337	0.586490
$590$	−19.6695	−0.809781
$591$	−29.3505	−1.20732
$592$	6.04057	0.248266
$593$	−25.7460	−1.05726	−0.528630	−	0.848852i	$-0.677294\pi$
$593$	−25.7460	−1.05726	−0.528630	+	0.848852i	$0.677294\pi$
$594$	−3.35514	−0.137663
$595$	4.57661	0.187623
$596$	47.5198	1.94649
$597$	−14.3849	−0.588733
$598$	0	0
$599$	16.9434	0.692289	0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434	0.692289	0.346144	+	0.938181i	$0.387491\pi$
$600$	16.4547	0.671761
$601$	−9.65496	−0.393834	−0.196917	−	0.980420i	$-0.563093\pi$
$601$	−9.65496	−0.393834	−0.196917	+	0.980420i	$0.563093\pi$
$602$	−23.2843	−0.948998
$603$	−24.1020	−0.981509
$604$	37.6695	1.53275
$605$	−9.08175	−0.369226
$606$	10.0815	0.409532
$607$	3.24527	0.131721	0.0658607	−	0.997829i	$-0.479021\pi$
$607$	3.24527	0.131721	0.0658607	+	0.997829i	$0.479021\pi$
$608$	−57.4888	−2.33148
$609$	−29.6828	−1.20281
$610$	−20.2438	−0.819647
$611$	−0.508556	−0.0205740
$612$	14.7765	0.597305
$613$	32.9143	1.32940	0.664698	−	0.747112i	$-0.268560\pi$
$613$	32.9143	1.32940	0.664698	+	0.747112i	$0.268560\pi$
$614$	31.1700	1.25792
$615$	−1.32542	−0.0534459
$616$	8.55620	0.344739
$617$	−3.02442	−0.121759	−0.0608794	−	0.998145i	$-0.519390\pi$
$617$	−3.02442	−0.121759	−0.0608794	+	0.998145i	$0.519390\pi$
$618$	−84.8112	−3.41161
$619$	−10.4224	−0.418911	−0.209455	−	0.977818i	$-0.567169\pi$
$619$	−10.4224	−0.418911	−0.209455	+	0.977818i	$0.567169\pi$
$620$	6.29515	0.252819
$621$	0	0
$622$	1.25637	0.0503758
$623$	32.9823	1.32141
$624$	0.768140	0.0307502
$625$	4.40427	0.176171
$626$	46.5684	1.86125
$627$	−38.3662	−1.53220
$628$	−11.7912	−0.470519
$629$	−6.05746	−0.241527
$630$	21.4441	0.854355
$631$	−34.1013	−1.35755	−0.678776	−	0.734346i	$-0.737489\pi$
$631$	−34.1013	−1.35755	−0.678776	+	0.734346i	$0.737489\pi$
$632$	10.7096	0.426003
$633$	35.3570	1.40531
$634$	−19.4186	−0.771209
$635$	7.41191	0.294133
$636$	70.4826	2.79482
$637$	−0.269147	−0.0106640
$638$	20.9693	0.830182
$639$	−2.42225	−0.0958228
$640$	−16.9487	−0.669955
$641$	9.00567	0.355702	0.177851	−	0.984057i	$-0.443085\pi$
$641$	9.00567	0.355702	0.177851	+	0.984057i	$0.443085\pi$
$642$	11.0122	0.434617
$643$	22.9522	0.905146	0.452573	−	0.891727i	$-0.350506\pi$
$643$	22.9522	0.905146	0.452573	+	0.891727i	$0.350506\pi$
$644$	0	0
$645$	13.8391	0.544913
$646$	27.4460	1.07985
$647$	−44.9543	−1.76734	−0.883669	−	0.468113i	$-0.844934\pi$
$647$	−44.9543	−1.76734	−0.883669	+	0.468113i	$0.844934\pi$
$648$	−14.9928	−0.588973
$649$	−13.8014	−0.541753
$650$	−1.50283	−0.0589459
$651$	−10.6312	−0.416670
$652$	−42.2371	−1.65413
$653$	−29.3634	−1.14908	−0.574539	−	0.818477i	$-0.694819\pi$
$653$	−29.3634	−1.14908	−0.574539	+	0.818477i	$0.694819\pi$
$654$	86.3706	3.37736
$655$	−15.7884	−0.616903
$656$	−0.663437	−0.0259029
$657$	−21.3750	−0.833918
$658$	−13.5341	−0.527613
$659$	40.1537	1.56417	0.782083	−	0.623174i	$-0.214157\pi$
$659$	40.1537	1.56417	0.782083	+	0.623174i	$0.214157\pi$
$660$	−16.9682	−0.660487
$661$	−9.96660	−0.387656	−0.193828	−	0.981036i	$-0.562090\pi$
$661$	−9.96660	−0.387656	−0.193828	+	0.981036i	$0.562090\pi$
$662$	66.5216	2.58544
$663$	−0.770289	−0.0299155
$664$	24.3116	0.943474
$665$	23.4256	0.908406
$666$	−28.3829	−1.09981
$667$	0	0
$668$	3.79764	0.146935
$669$	10.5650	0.408468
$670$	−19.7992	−0.764910
$671$	−14.2044	−0.548353
$672$	42.9385	1.65639
$673$	−34.0567	−1.31279	−0.656395	−	0.754417i	$-0.727920\pi$
$673$	−34.0567	−1.31279	−0.656395	+	0.754417i	$0.727920\pi$
$674$	10.9206	0.420646
$675$	2.76435	0.106400
$676$	−37.0167	−1.42372
$677$	24.9911	0.960486	0.480243	−	0.877135i	$-0.340548\pi$
$677$	24.9911	0.960486	0.480243	+	0.877135i	$0.340548\pi$
$678$	−8.24254	−0.316553
$679$	−10.2594	−0.393719
$680$	3.63793	0.139508
$681$	46.3227	1.77509
$682$	7.51037	0.287587
$683$	34.4762	1.31919	0.659597	−	0.751619i	$-0.270727\pi$
$683$	34.4762	1.31919	0.659597	+	0.751619i	$0.270727\pi$
$684$	75.6344	2.89195
$685$	−0.862518	−0.0329551
$686$	−43.7637	−1.67091
$687$	27.4574	1.04756
$688$	6.92715	0.264095
$689$	−1.92925	−0.0734987
$690$	0	0
$691$	−21.2259	−0.807470	−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259	−0.807470	−0.403735	+	0.914876i	$0.632288\pi$
$692$	−48.3680	−1.83868
$693$	15.0466	0.571573
$694$	−14.9118	−0.566043
$695$	17.2562	0.654565
$696$	−23.5948	−0.894358
$697$	0.665293	0.0251998
$698$	22.2386	0.841742
$699$	−10.4676	−0.395922
$700$	−23.5220	−0.889048
$701$	24.1261	0.911232	0.455616	−	0.890176i	$-0.349419\pi$
$701$	24.1261	0.911232	0.455616	+	0.890176i	$0.349419\pi$
$702$	−0.344797	−0.0130135
$703$	−31.0054	−1.16939
$704$	−24.3858	−0.919074
$705$	8.04399	0.302954
$706$	53.9208	2.02934
$707$	−4.31913	−0.162438
$708$	51.8165	1.94738
$709$	−7.03693	−0.264277	−0.132139	−	0.991231i	$-0.542184\pi$
$709$	−7.03693	−0.264277	−0.132139	+	0.991231i	$0.542184\pi$
$710$	−1.98982	−0.0746767
$711$	18.8334	0.706309
$712$	26.2175	0.982544
$713$	0	0
$714$	−20.4995	−0.767175
$715$	0.464455	0.0173696
$716$	−4.08782	−0.152769
$717$	56.5932	2.11351
$718$	−0.922903	−0.0344424
$719$	26.5682	0.990829	0.495414	−	0.868657i	$-0.335016\pi$
$719$	26.5682	0.990829	0.495414	+	0.868657i	$0.335016\pi$
$720$	−6.37969	−0.237757
$721$	36.3350	1.35319
$722$	98.6152	3.67008
$723$	14.9019	0.554208
$724$	46.0699	1.71217
$725$	−17.2769	−0.641646
$726$	40.6789	1.50974
$727$	5.22756	0.193879	0.0969397	−	0.995290i	$-0.469095\pi$
$727$	5.22756	0.193879	0.0969397	+	0.995290i	$0.469095\pi$
$728$	0.879292	0.0325887
$729$	−32.3705	−1.19891
$730$	−17.5590	−0.649889
$731$	−6.94652	−0.256926
$732$	53.3293	1.97111
$733$	26.6889	0.985776	0.492888	−	0.870093i	$-0.335941\pi$
$733$	26.6889	0.985776	0.492888	+	0.870093i	$0.335941\pi$
$734$	−62.9533	−2.32365
$735$	4.25719	0.157029
$736$	0	0
$737$	−13.8924	−0.511734
$738$	3.11730	0.114749
$739$	−2.23955	−0.0823831	−0.0411916	−	0.999151i	$-0.513115\pi$
$739$	−2.23955	−0.0823831	−0.0411916	+	0.999151i	$0.513115\pi$
$740$	−13.7128	−0.504092
$741$	−3.94276	−0.144841
$742$	−51.3427	−1.88485
$743$	−18.1401	−0.665497	−0.332748	−	0.943016i	$-0.607976\pi$
$743$	−18.1401	−0.665497	−0.332748	+	0.943016i	$0.607976\pi$
$744$	−8.45072	−0.309819
$745$	20.5738	0.753766
$746$	−31.7492	−1.16242
$747$	42.7535	1.56427
$748$	8.51720	0.311420
$749$	−4.71788	−0.172387
$750$	58.0115	2.11828
$751$	−28.2267	−1.03001	−0.515003	−	0.857188i	$-0.672209\pi$
$751$	−28.2267	−1.03001	−0.515003	+	0.857188i	$0.672209\pi$
$752$	4.02642	0.146829
$753$	−3.89721	−0.142022
$754$	2.15494	0.0784783
$755$	16.3091	0.593549
$756$	−5.39669	−0.196276
$757$	−0.122014	−0.00443466	−0.00221733	−	0.999998i	$-0.500706\pi$
$757$	−0.122014	−0.00443466	−0.00221733	+	0.999998i	$0.500706\pi$
$758$	12.4000	0.450389
$759$	0	0
$760$	18.6210	0.675453
$761$	−26.7054	−0.968070	−0.484035	−	0.875049i	$-0.660829\pi$
$761$	−26.7054	−0.968070	−0.484035	+	0.875049i	$0.660829\pi$
$762$	−33.1994	−1.20269
$763$	−37.0031	−1.33960
$764$	59.2446	2.14340
$765$	6.39753	0.231303
$766$	−0.510490	−0.0184447
$767$	−1.41833	−0.0512127
$768$	11.8005	0.425815
$769$	7.85104	0.283116	0.141558	−	0.989930i	$-0.454789\pi$
$769$	7.85104	0.283116	0.141558	+	0.989930i	$0.454789\pi$
$770$	12.3604	0.445439
$771$	−69.0109	−2.48537
$772$	41.8457	1.50606
$773$	34.2817	1.23303	0.616513	−	0.787345i	$-0.288545\pi$
$773$	34.2817	1.23303	0.616513	+	0.787345i	$0.288545\pi$
$774$	−32.5486	−1.16994
$775$	−6.18789	−0.222276
$776$	−8.15516	−0.292753
$777$	23.1580	0.830790
$778$	66.4827	2.38352
$779$	3.40534	0.122009
$780$	−1.74377	−0.0624369
$781$	−1.39619	−0.0499596
$782$	0	0
$783$	−3.96386	−0.141657
$784$	2.13094	0.0761049
$785$	−5.10502	−0.182206
$786$	70.7192	2.52247
$787$	−16.0125	−0.570785	−0.285392	−	0.958411i	$-0.592124\pi$
$787$	−16.0125	−0.570785	−0.285392	+	0.958411i	$0.592124\pi$
$788$	33.3512	1.18809
$789$	−32.5243	−1.15790
$790$	15.4712	0.550441
$791$	3.53129	0.125558
$792$	11.9605	0.424998
$793$	−1.45973	−0.0518367
$794$	−28.7468	−1.02018
$795$	30.5156	1.08228
$796$	16.3456	0.579355
$797$	−21.5237	−0.762409	−0.381205	−	0.924491i	$-0.624491\pi$
$797$	−21.5237	−0.762409	−0.381205	+	0.924491i	$0.624491\pi$
$798$	−104.928	−3.71440
$799$	−4.03769	−0.142843
$800$	24.9924	0.883614
$801$	46.1052	1.62905
$802$	46.9938	1.65941
$803$	−12.3206	−0.434784
$804$	52.1582	1.83948
$805$	0	0
$806$	0.771816	0.0271860
$807$	25.1275	0.884530
$808$	−3.43327	−0.120782
$809$	24.1251	0.848194	0.424097	−	0.905617i	$-0.360592\pi$
$809$	24.1251	0.848194	0.424097	+	0.905617i	$0.360592\pi$
$810$	−21.6589	−0.761015
$811$	14.3383	0.503486	0.251743	−	0.967794i	$-0.418996\pi$
$811$	14.3383	0.503486	0.251743	+	0.967794i	$0.418996\pi$
$812$	33.7287	1.18365
$813$	−11.0873	−0.388849
$814$	−16.3599	−0.573415
$815$	−18.2867	−0.640554
$816$	6.09866	0.213496
$817$	−35.5561	−1.24395
$818$	−20.1609	−0.704910
$819$	1.54629	0.0540317
$820$	1.50608	0.0525946
$821$	14.2085	0.495879	0.247939	−	0.968776i	$-0.420247\pi$
$821$	14.2085	0.495879	0.247939	+	0.968776i	$0.420247\pi$
$822$	3.86339	0.134751
$823$	16.0231	0.558530	0.279265	−	0.960214i	$-0.409909\pi$
$823$	16.0231	0.558530	0.279265	+	0.960214i	$0.409909\pi$
$824$	28.8826	1.00617
$825$	16.6791	0.580692
$826$	−37.7455	−1.31334
$827$	−35.1240	−1.22138	−0.610690	−	0.791870i	$-0.709108\pi$
$827$	−35.1240	−1.22138	−0.610690	+	0.791870i	$0.709108\pi$
$828$	0	0
$829$	−2.29604	−0.0797447	−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604	−0.0797447	−0.0398723	+	0.999205i	$0.512695\pi$
$830$	35.1210	1.21907
$831$	77.4214	2.68572
$832$	−2.50605	−0.0868815
$833$	−2.13690	−0.0740391
$834$	−77.2938	−2.67647
$835$	1.64420	0.0568999
$836$	43.5958	1.50779
$837$	−1.41970	−0.0490719
$838$	19.7757	0.683140
$839$	−38.6117	−1.33302	−0.666511	−	0.745495i	$-0.732213\pi$
$839$	−38.6117	−1.33302	−0.666511	+	0.745495i	$0.732213\pi$
$840$	−13.9080	−0.479873
$841$	−4.22633	−0.145736
$842$	−69.3528	−2.39006
$843$	−8.99601	−0.309839
$844$	−40.1764	−1.38293
$845$	−16.0265	−0.551328
$846$	−18.9190	−0.650448
$847$	−17.4278	−0.598825
$848$	15.2746	0.524532
$849$	37.1481	1.27492
$850$	−11.9317	−0.409255
$851$	0	0
$852$	5.24190	0.179584
$853$	−38.4294	−1.31580	−0.657898	−	0.753107i	$-0.728554\pi$
$853$	−38.4294	−1.31580	−0.657898	+	0.753107i	$0.728554\pi$
$854$	−38.8475	−1.32933
$855$	32.7461	1.11989
$856$	−3.75023	−0.128180
$857$	−50.8895	−1.73835	−0.869176	−	0.494504i	$-0.835350\pi$
$857$	−50.8895	−1.73835	−0.869176	+	0.494504i	$0.835350\pi$
$858$	−2.08038	−0.0710232
$859$	9.14711	0.312095	0.156048	−	0.987750i	$-0.450125\pi$
$859$	9.14711	0.312095	0.156048	+	0.987750i	$0.450125\pi$
$860$	−15.7254	−0.536232
$861$	−2.54346	−0.0866807
$862$	48.7052	1.65891
$863$	12.3389	0.420019	0.210010	−	0.977699i	$-0.432650\pi$
$863$	12.3389	0.420019	0.210010	+	0.977699i	$0.432650\pi$
$864$	5.73404	0.195076
$865$	−20.9411	−0.712018
$866$	−27.9754	−0.950644
$867$	36.6110	1.24338
$868$	12.0803	0.410032
$869$	10.8556	0.368251
$870$	−34.0854	−1.15560
$871$	−1.42768	−0.0483750
$872$	−29.4137	−0.996073
$873$	−14.3414	−0.485381
$874$	0	0
$875$	−24.8534	−0.840199
$876$	46.2568	1.56287
$877$	2.30720	0.0779086	0.0389543	−	0.999241i	$-0.487597\pi$
$877$	2.30720	0.0779086	0.0389543	+	0.999241i	$0.487597\pi$
$878$	40.5928	1.36994
$879$	54.0706	1.82376
$880$	−3.67726	−0.123960
$881$	35.6004	1.19941	0.599703	−	0.800222i	$-0.295285\pi$
$881$	35.6004	1.19941	0.599703	+	0.800222i	$0.295285\pi$
$882$	−10.0126	−0.337143
$883$	30.4745	1.02555	0.512775	−	0.858523i	$-0.328618\pi$
$883$	30.4745	1.02555	0.512775	+	0.858523i	$0.328618\pi$
$884$	0.875284	0.0294390
$885$	22.4341	0.754114
$886$	−30.6584	−1.02999
$887$	20.7912	0.698099	0.349049	−	0.937104i	$-0.386505\pi$
$887$	20.7912	0.698099	0.349049	+	0.937104i	$0.386505\pi$
$888$	18.4083	0.617742
$889$	14.2233	0.477036
$890$	37.8743	1.26955
$891$	−15.1973	−0.509127
$892$	−12.0051	−0.401961
$893$	−20.6671	−0.691598
$894$	−92.1541	−3.08209
$895$	−1.76983	−0.0591590
$896$	−32.5243	−1.08656
$897$	0	0
$898$	66.3122	2.21287
$899$	8.87296	0.295930
$900$	−32.8809	−1.09603
$901$	−15.3173	−0.510294
$902$	1.79681	0.0598274
$903$	26.5570	0.883761
$904$	2.80701	0.0933599
$905$	19.9461	0.663030
$906$	−73.0517	−2.42698
$907$	22.7118	0.754133	0.377067	−	0.926186i	$-0.376933\pi$
$907$	22.7118	0.754133	0.377067	+	0.926186i	$0.376933\pi$
$908$	−52.6368	−1.74681
$909$	−6.03761	−0.200255
$910$	1.27024	0.0421080
$911$	−0.834044	−0.0276331	−0.0138165	−	0.999905i	$-0.504398\pi$
$911$	−0.834044	−0.0276331	−0.0138165	+	0.999905i	$0.504398\pi$
$912$	31.2163	1.03367
$913$	24.6432	0.815570
$914$	−83.8422	−2.77325
$915$	23.0891	0.763301
$916$	−31.2000	−1.03088
$917$	−30.2977	−1.00052
$918$	−2.73752	−0.0903515
$919$	45.3320	1.49537	0.747683	−	0.664056i	$-0.231166\pi$
$919$	45.3320	1.49537	0.747683	+	0.664056i	$0.231166\pi$
$920$	0	0
$921$	−35.5510	−1.17145
$922$	19.3040	0.635744
$923$	−0.143482	−0.00472275
$924$	−32.5618	−1.07120
$925$	13.4791	0.443191
$926$	−61.3414	−2.01580
$927$	50.7919	1.66822
$928$	−35.8371	−1.17641
$929$	−17.7072	−0.580955	−0.290477	−	0.956882i	$-0.593814\pi$
$929$	−17.7072	−0.580955	−0.290477	+	0.956882i	$0.593814\pi$
$930$	−12.2081	−0.400318
$931$	−10.9378	−0.358472
$932$	11.8944	0.389615
$933$	−1.43295	−0.0469128
$934$	38.2687	1.25219
$935$	3.68755	0.120596
$936$	1.22914	0.0401758
$937$	23.3260	0.762028	0.381014	−	0.924569i	$-0.375575\pi$
$937$	23.3260	0.762028	0.381014	+	0.924569i	$0.375575\pi$
$938$	−37.9944	−1.24056
$939$	−53.1137	−1.73330
$940$	−9.14044	−0.298128
$941$	−11.6148	−0.378630	−0.189315	−	0.981916i	$-0.560627\pi$
$941$	−11.6148	−0.378630	−0.189315	+	0.981916i	$0.560627\pi$
$942$	22.8664	0.745027
$943$	0	0
$944$	11.2294	0.365486
$945$	−2.33651	−0.0760067
$946$	−18.7611	−0.609975
$947$	5.99794	0.194907	0.0974534	−	0.995240i	$-0.468930\pi$
$947$	5.99794	0.194907	0.0974534	+	0.995240i	$0.468930\pi$
$948$	−40.7567	−1.32372
$949$	−1.26614	−0.0411008
$950$	−61.0732	−1.98148
$951$	22.1479	0.718194
$952$	6.98115	0.226260
$953$	17.9067	0.580054	0.290027	−	0.957018i	$-0.406336\pi$
$953$	17.9067	0.580054	0.290027	+	0.957018i	$0.406336\pi$
$954$	−71.7708	−2.32367
$955$	25.6501	0.830019
$956$	−64.3072	−2.07984
$957$	−23.9165	−0.773112
$958$	56.1432	1.81391
$959$	−1.65516	−0.0534479
$960$	39.6389	1.27934
$961$	−27.8221	−0.897486
$962$	−1.68125	−0.0542058
$963$	−6.59501	−0.212521
$964$	−16.9331	−0.545380
$965$	18.1172	0.583213
$966$	0	0
$967$	33.5068	1.07751	0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068	1.07751	0.538753	+	0.842464i	$0.318896\pi$
$968$	−13.8533	−0.445262
$969$	−31.3036	−1.00562
$970$	−11.7811	−0.378268
$971$	−59.2860	−1.90258	−0.951289	−	0.308300i	$-0.900240\pi$
$971$	−59.2860	−1.90258	−0.951289	+	0.308300i	$0.900240\pi$
$972$	63.8804	2.04896
$973$	33.1144	1.06160
$974$	−13.5766	−0.435024
$975$	1.71406	0.0548937
$976$	11.5572	0.369938
$977$	12.6420	0.404452	0.202226	−	0.979339i	$-0.435182\pi$
$977$	12.6420	0.404452	0.202226	+	0.979339i	$0.435182\pi$
$978$	81.9095	2.61918
$979$	26.5751	0.849343
$980$	−4.83747	−0.154527
$981$	−51.7258	−1.65148
$982$	−71.9428	−2.29579
$983$	58.3650	1.86156	0.930778	−	0.365586i	$-0.119131\pi$
$983$	58.3650	1.86156	0.930778	+	0.365586i	$0.119131\pi$
$984$	−2.02179	−0.0644522
$985$	14.4395	0.460080
$986$	17.1092	0.544867
$987$	15.4363	0.491343
$988$	4.48019	0.142534
$989$	0	0
$990$	17.2784	0.549142
$991$	−45.7911	−1.45460	−0.727301	−	0.686319i	$-0.759225\pi$
$991$	−45.7911	−1.45460	−0.727301	+	0.686319i	$0.759225\pi$
$992$	−12.8354	−0.407526
$993$	−75.8714	−2.40770
$994$	−3.81844	−0.121114
$995$	7.07687	0.224352
$996$	−92.5212	−2.93165
$997$	−39.3521	−1.24629	−0.623147	−	0.782105i	$-0.714146\pi$
$997$	−39.3521	−1.24629	−0.623147	+	0.782105i	$0.714146\pi$
$998$	−18.8931	−0.598051
$999$	3.09254	0.0978436

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.a.j.1.5		5
3.2	odd	2		4761.2.a.bn.1.1		5
4.3	odd	2		8464.2.a.bt.1.5		5
23.2	even	11		529.2.c.f.487.1		10
23.3	even	11		529.2.c.c.170.1		10
23.4	even	11		529.2.c.e.177.1		10
23.5	odd	22		529.2.c.i.255.1		10
23.6	even	11		529.2.c.e.266.1		10
23.7	odd	22		23.2.c.a.3.1	✓	10
23.8	even	11		529.2.c.c.501.1		10
23.9	even	11		529.2.c.h.334.1		10
23.10	odd	22		23.2.c.a.8.1	yes	10
23.11	odd	22		529.2.c.g.466.1		10
23.12	even	11		529.2.c.f.466.1		10
23.13	even	11		529.2.c.a.399.1		10
23.14	odd	22		529.2.c.i.334.1		10
23.15	odd	22		529.2.c.b.501.1		10
23.16	even	11		529.2.c.a.118.1		10
23.17	odd	22		529.2.c.d.266.1		10
23.18	even	11		529.2.c.h.255.1		10
23.19	odd	22		529.2.c.d.177.1		10
23.20	odd	22		529.2.c.b.170.1		10
23.21	odd	22		529.2.c.g.487.1		10
23.22	odd	2		529.2.a.i.1.5		5
69.53	even	22		207.2.i.c.118.1		10
69.56	even	22		207.2.i.c.100.1		10
69.68	even	2		4761.2.a.bo.1.1		5
92.7	even	22		368.2.m.c.49.1		10
92.79	even	22		368.2.m.c.353.1		10
92.91	even	2		8464.2.a.bs.1.5		5
115.7	even	44		575.2.p.b.49.2		20
115.33	even	44		575.2.p.b.399.2		20
115.53	even	44		575.2.p.b.49.1		20
115.79	odd	22		575.2.k.b.376.1		10
115.99	odd	22		575.2.k.b.26.1		10
115.102	even	44		575.2.p.b.399.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.7	odd	22
23.2.c.a.8.1	yes	10	23.10	odd	22
207.2.i.c.100.1		10	69.56	even	22
207.2.i.c.118.1		10	69.53	even	22
368.2.m.c.49.1		10	92.7	even	22
368.2.m.c.353.1		10	92.79	even	22
529.2.a.i.1.5		5	23.22	odd	2
529.2.a.j.1.5		5	1.1	even	1	trivial
529.2.c.a.118.1		10	23.16	even	11
529.2.c.a.399.1		10	23.13	even	11
529.2.c.b.170.1		10	23.20	odd	22
529.2.c.b.501.1		10	23.15	odd	22
529.2.c.c.170.1		10	23.3	even	11
529.2.c.c.501.1		10	23.8	even	11
529.2.c.d.177.1		10	23.19	odd	22
529.2.c.d.266.1		10	23.17	odd	22
529.2.c.e.177.1		10	23.4	even	11
529.2.c.e.266.1		10	23.6	even	11
529.2.c.f.466.1		10	23.12	even	11
529.2.c.f.487.1		10	23.2	even	11
529.2.c.g.466.1		10	23.11	odd	22
529.2.c.g.487.1		10	23.21	odd	22
529.2.c.h.255.1		10	23.18	even	11
529.2.c.h.334.1		10	23.9	even	11
529.2.c.i.255.1		10	23.5	odd	22
529.2.c.i.334.1		10	23.14	odd	22
575.2.k.b.26.1		10	115.99	odd	22
575.2.k.b.376.1		10	115.79	odd	22
575.2.p.b.49.1		20	115.53	even	44
575.2.p.b.49.2		20	115.7	even	44
575.2.p.b.399.1		20	115.102	even	44
575.2.p.b.399.2		20	115.33	even	44
4761.2.a.bn.1.1		5	3.2	odd	2
4761.2.a.bo.1.1		5	69.68	even	2
8464.2.a.bs.1.5		5	92.91	even	2
8464.2.a.bt.1.5		5	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	529.2.a.j.1.5

Level	$529$
Weight	$2$
Character	529.1
Self dual	yes
Analytic conductor	$4.224$
Analytic rank	$0$
Dimension	$5$
CM	no
Inner twists	$1$