LMFDB - Embedded newform 5929.2.a.w.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5929,2,Mod(1,5929)] 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("5929.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5929, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,0,1,4,2,-1,0,9,0,-9,0,9,-11,0,-7,2,-3,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	yes
Analytic conductor:	$47.3433033584$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.713538$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.49086 q^{2} +0.713538 q^{3} +4.20440 q^{4} -2.20440 q^{5} +1.77733 q^{6} +5.49086 q^{8} -2.49086 q^{9} -5.49086 q^{10} +3.00000 q^{12} -3.28646 q^{13} -1.57292 q^{15} +5.26819 q^{16} +1.49086 q^{17} -6.20440 q^{18} -6.91794 q^{19} -9.26819 q^{20} +6.49086 q^{23} +3.91794 q^{24} -0.140614 q^{25} -8.18613 q^{26} -3.91794 q^{27} +1.64975 q^{29} -3.91794 q^{30} +2.35025 q^{31} +2.14061 q^{32} +3.71354 q^{34} -10.4726 q^{36} -5.55465 q^{37} -17.2316 q^{38} -2.34502 q^{39} -12.1041 q^{40} -11.2499 q^{41} -5.26819 q^{43} +5.49086 q^{45} +16.1679 q^{46} -1.49086 q^{47} +3.75905 q^{48} -0.350250 q^{50} +1.06379 q^{51} -13.8176 q^{52} +0.304735 q^{53} -9.75905 q^{54} -4.93621 q^{57} +4.10930 q^{58} +12.6587 q^{59} -6.61320 q^{60} -12.9817 q^{61} +5.85415 q^{62} -5.20440 q^{64} +7.24468 q^{65} -4.57292 q^{67} +6.26819 q^{68} +4.63148 q^{69} +11.3267 q^{71} -13.6770 q^{72} -8.56769 q^{73} -13.8359 q^{74} -0.100333 q^{75} -29.0858 q^{76} -5.84111 q^{78} -4.63148 q^{79} -11.6132 q^{80} +4.67699 q^{81} -28.0220 q^{82} -1.93621 q^{83} -3.28646 q^{85} -13.1223 q^{86} +1.17716 q^{87} -3.20440 q^{89} +13.6770 q^{90} +27.2902 q^{92} +1.67699 q^{93} -3.71354 q^{94} +15.2499 q^{95} +1.52741 q^{96} -1.85939 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} + 4 q^{4} + 2 q^{5} - q^{6} + 9 q^{8} - 9 q^{10} + 9 q^{12} - 11 q^{13} - 7 q^{15} + 2 q^{16} - 3 q^{17} - 10 q^{18} - 11 q^{19} - 14 q^{20} + 12 q^{23} + 2 q^{24} + 3 q^{25} - q^{26} - 2 q^{27}+ \cdots - 9 q^{97}+O(q^{100}) $ 3 * q + q^3 + 4 * q^4 + 2 * q^5 - q^6 + 9 * q^8 - 9 * q^10 + 9 * q^12 - 11 * q^13 - 7 * q^15 + 2 * q^16 - 3 * q^17 - 10 * q^18 - 11 * q^19 - 14 * q^20 + 12 * q^23 + 2 * q^24 + 3 * q^25 - q^26 - 2 * q^27 + 9 * q^29 - 2 * q^30 + 3 * q^31 + 3 * q^32 + 10 * q^34 - 9 * q^36 - 4 * q^37 - 8 * q^38 + 5 * q^39 - 3 * q^40 - 5 * q^41 - 2 * q^43 + 9 * q^45 + 10 * q^46 + 3 * q^47 - 10 * q^48 + 3 * q^50 - 2 * q^51 - 7 * q^52 + 17 * q^53 - 8 * q^54 - 20 * q^57 - 13 * q^58 - 8 * q^59 + 6 * q^60 - 24 * q^61 + 13 * q^62 - 7 * q^64 - 15 * q^65 - 16 * q^67 + 5 * q^68 + 3 * q^69 + 7 * q^71 - 10 * q^72 - 20 * q^73 - 22 * q^74 - 25 * q^75 - 39 * q^76 - 6 * q^78 - 3 * q^79 - 9 * q^80 - 17 * q^81 - 41 * q^82 - 11 * q^83 - 11 * q^85 - 21 * q^86 + 30 * q^87 - q^89 + 10 * q^90 + 25 * q^92 - 26 * q^93 - 10 * q^94 + 17 * q^95 + 27 * q^96 - 9 * q^97

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 $

$2$	2.49086	1.76131	0.880653	−	0.473761i	$-0.157104\pi$
$2$	2.49086	1.76131	0.880653	+	0.473761i	$0.157104\pi$
$3$	0.713538	0.411961	0.205981	−	0.978556i	$-0.433962\pi$
$3$	0.713538	0.411961	0.205981	+	0.978556i	$0.433962\pi$
$4$	4.20440	2.10220
$5$	−2.20440	−0.985838	−0.492919	−	0.870075i	$-0.664070\pi$
$5$	−2.20440	−0.985838	−0.492919	+	0.870075i	$0.664070\pi$
$6$	1.77733	0.725590
$7$	0	0
$7$	0	0
$8$	5.49086	1.94131
$9$	−2.49086	−0.830288
$10$	−5.49086	−1.73636
$11$	0	0
$11$	0	0
$12$	3.00000	0.866025
$13$	−3.28646	−0.911501	−0.455750	−	0.890108i	$-0.650629\pi$
$13$	−3.28646	−0.911501	−0.455750	+	0.890108i	$0.650629\pi$
$14$	0	0
$15$	−1.57292	−0.406127
$16$	5.26819	1.31705
$17$	1.49086	0.361588	0.180794	−	0.983521i	$-0.442133\pi$
$17$	1.49086	0.361588	0.180794	+	0.983521i	$0.442133\pi$
$18$	−6.20440	−1.46239
$19$	−6.91794	−1.58708	−0.793542	−	0.608515i	$-0.791765\pi$
$19$	−6.91794	−1.58708	−0.793542	+	0.608515i	$0.791765\pi$
$20$	−9.26819	−2.07243
$21$	0	0
$22$	0	0
$23$	6.49086	1.35344	0.676719	−	0.736241i	$-0.263401\pi$
$23$	6.49086	1.35344	0.676719	+	0.736241i	$0.263401\pi$
$24$	3.91794	0.799746
$25$	−0.140614	−0.0281228
$26$	−8.18613	−1.60543
$27$	−3.91794	−0.754008
$28$	0	0
$29$	1.64975	0.306351	0.153175	−	0.988199i	$-0.451050\pi$
$29$	1.64975	0.306351	0.153175	+	0.988199i	$0.451050\pi$
$30$	−3.91794	−0.715315
$31$	2.35025	0.422117	0.211059	−	0.977473i	$-0.432309\pi$
$31$	2.35025	0.422117	0.211059	+	0.977473i	$0.432309\pi$
$32$	2.14061	0.378411
$33$	0	0
$34$	3.71354	0.636867
$35$	0	0
$36$	−10.4726	−1.74543
$37$	−5.55465	−0.913179	−0.456590	−	0.889677i	$-0.650929\pi$
$37$	−5.55465	−0.913179	−0.456590	+	0.889677i	$0.650929\pi$
$38$	−17.2316	−2.79534
$39$	−2.34502	−0.375503
$40$	−12.1041	−1.91382
$41$	−11.2499	−1.75694	−0.878471	−	0.477796i	$-0.841436\pi$
$41$	−11.2499	−1.75694	−0.878471	+	0.477796i	$0.841436\pi$
$42$	0	0
$43$	−5.26819	−0.803391	−0.401696	−	0.915773i	$-0.631579\pi$
$43$	−5.26819	−0.803391	−0.401696	+	0.915773i	$0.631579\pi$
$44$	0	0
$45$	5.49086	0.818530
$46$	16.1679	2.38382
$47$	−1.49086	−0.217465	−0.108732	−	0.994071i	$-0.534679\pi$
$47$	−1.49086	−0.217465	−0.108732	+	0.994071i	$0.534679\pi$
$48$	3.75905	0.542573
$49$	0	0
$50$	−0.350250	−0.0495328
$51$	1.06379	0.148960
$52$	−13.8176	−1.91616
$53$	0.304735	0.0418585	0.0209293	−	0.999781i	$-0.493338\pi$
$53$	0.304735	0.0418585	0.0209293	+	0.999781i	$0.493338\pi$
$54$	−9.75905	−1.32804
$55$	0	0
$56$	0	0
$57$	−4.93621	−0.653817
$58$	4.10930	0.539578
$59$	12.6587	1.64802	0.824012	−	0.566572i	$-0.191731\pi$
$59$	12.6587	1.64802	0.824012	+	0.566572i	$0.191731\pi$
$60$	−6.61320	−0.853761
$61$	−12.9817	−1.66214	−0.831070	−	0.556168i	$-0.812271\pi$
$61$	−12.9817	−1.66214	−0.831070	+	0.556168i	$0.812271\pi$
$62$	5.85415	0.743478
$63$	0	0
$64$	−5.20440	−0.650550
$65$	7.24468	0.898592
$66$	0	0
$67$	−4.57292	−0.558672	−0.279336	−	0.960193i	$-0.590114\pi$
$67$	−4.57292	−0.558672	−0.279336	+	0.960193i	$0.590114\pi$
$68$	6.26819	0.760130
$69$	4.63148	0.557564
$70$	0	0
$71$	11.3267	1.34424	0.672119	−	0.740444i	$-0.265385\pi$
$71$	11.3267	1.34424	0.672119	+	0.740444i	$0.265385\pi$
$72$	−13.6770	−1.61185
$73$	−8.56769	−1.00277	−0.501386	−	0.865224i	$-0.667176\pi$
$73$	−8.56769	−1.00277	−0.501386	+	0.865224i	$0.667176\pi$
$74$	−13.8359	−1.60839
$75$	−0.100333	−0.0115855
$76$	−29.0858	−3.33637
$77$	0	0
$78$	−5.84111	−0.661376
$79$	−4.63148	−0.521082	−0.260541	−	0.965463i	$-0.583901\pi$
$79$	−4.63148	−0.521082	−0.260541	+	0.965463i	$0.583901\pi$
$80$	−11.6132	−1.29840
$81$	4.67699	0.519666
$82$	−28.0220	−3.09451
$83$	−1.93621	−0.212527	−0.106263	−	0.994338i	$-0.533889\pi$
$83$	−1.93621	−0.212527	−0.106263	+	0.994338i	$0.533889\pi$
$84$	0	0
$85$	−3.28646	−0.356467
$86$	−13.1223	−1.41502
$87$	1.17716	0.126205
$88$	0	0
$89$	−3.20440	−0.339666	−0.169833	−	0.985473i	$-0.554323\pi$
$89$	−3.20440	−0.339666	−0.169833	+	0.985473i	$0.554323\pi$
$90$	13.6770	1.44168
$91$	0	0
$92$	27.2902	2.84520
$93$	1.67699	0.173896
$94$	−3.71354	−0.383022
$95$	15.2499	1.56461
$96$	1.52741	0.155891
$97$	−1.85939	−0.188792	−0.0943960	−	0.995535i	$-0.530092\pi$
$97$	−1.85939	−0.188792	−0.0943960	+	0.995535i	$0.530092\pi$
$98$	0	0
$99$	0	0
$100$	−0.591197	−0.0591197
$101$	6.04551	0.601551	0.300776	−	0.953695i	$-0.402754\pi$
$101$	6.04551	0.601551	0.300776	+	0.953695i	$0.402754\pi$
$102$	2.64975	0.262364
$103$	1.06379	0.104818	0.0524091	−	0.998626i	$-0.483310\pi$
$103$	1.06379	0.104818	0.0524091	+	0.998626i	$0.483310\pi$
$104$	−18.0455	−1.76951
$105$	0	0
$106$	0.759053	0.0737257
$107$	6.33198	0.612135	0.306068	−	0.952010i	$-0.400987\pi$
$107$	6.33198	0.612135	0.306068	+	0.952010i	$0.400987\pi$
$108$	−16.4726	−1.58508
$109$	2.81387	0.269520	0.134760	−	0.990878i	$-0.456974\pi$
$109$	2.81387	0.269520	0.134760	+	0.990878i	$0.456974\pi$
$110$	0	0
$111$	−3.96345	−0.376194
$112$	0	0
$113$	−12.7538	−1.19978	−0.599889	−	0.800083i	$-0.704789\pi$
$113$	−12.7538	−1.19978	−0.599889	+	0.800083i	$0.704789\pi$
$114$	−12.2954	−1.15157
$115$	−14.3085	−1.33427
$116$	6.93621	0.644011
$117$	8.18613	0.756808
$118$	31.5311	2.90268
$119$	0	0
$120$	−8.63671	−0.788420
$121$	0	0
$122$	−32.3357	−2.92754
$123$	−8.02724	−0.723792
$124$	9.88139	0.887375
$125$	11.3320	1.01356
$126$	0	0
$127$	12.3775	1.09832	0.549162	−	0.835716i	$-0.314947\pi$
$127$	12.3775	1.09832	0.549162	+	0.835716i	$0.314947\pi$
$128$	−17.2447	−1.52423
$129$	−3.75905	−0.330966
$130$	18.0455	1.58270
$131$	0.759053	0.0663188	0.0331594	−	0.999450i	$-0.489443\pi$
$131$	0.759053	0.0663188	0.0331594	+	0.999450i	$0.489443\pi$
$132$	0	0
$133$	0	0
$134$	−11.3905	−0.983992
$135$	8.63671	0.743330
$136$	8.18613	0.701955
$137$	−5.84111	−0.499040	−0.249520	−	0.968370i	$-0.580273\pi$
$137$	−5.84111	−0.499040	−0.249520	+	0.968370i	$0.580273\pi$
$138$	11.5364	0.982042
$139$	−5.57292	−0.472689	−0.236345	−	0.971669i	$-0.575949\pi$
$139$	−5.57292	−0.472689	−0.236345	+	0.971669i	$0.575949\pi$
$140$	0	0
$141$	−1.06379	−0.0895871
$142$	28.2134	2.36761
$143$	0	0
$144$	−13.1223	−1.09353
$145$	−3.63671	−0.302012
$146$	−21.3409	−1.76619
$147$	0	0
$148$	−23.3540	−1.91969
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	−0.249917	−0.0204056
$151$	−14.8411	−1.20775	−0.603876	−	0.797078i	$-0.706378\pi$
$151$	−14.8411	−1.20775	−0.603876	+	0.797078i	$0.706378\pi$
$152$	−37.9855	−3.08103
$153$	−3.71354	−0.300222
$154$	0	0
$155$	−5.18089	−0.416139
$156$	−9.85939	−0.789383
$157$	−6.39053	−0.510020	−0.255010	−	0.966938i	$-0.582079\pi$
$157$	−6.39053	−0.510020	−0.255010	+	0.966938i	$0.582079\pi$
$158$	−11.5364	−0.917785
$159$	0.217440	0.0172441
$160$	−4.71877	−0.373052
$161$	0	0
$162$	11.6498	0.915291
$163$	9.94518	0.778967	0.389483	−	0.921033i	$-0.372654\pi$
$163$	9.94518	0.778967	0.389483	+	0.921033i	$0.372654\pi$
$164$	−47.2992	−3.69344
$165$	0	0
$166$	−4.82284	−0.374325
$167$	−1.94145	−0.150234	−0.0751168	−	0.997175i	$-0.523933\pi$
$167$	−1.94145	−0.150234	−0.0751168	+	0.997175i	$0.523933\pi$
$168$	0	0
$169$	−2.19917	−0.169167
$170$	−8.18613	−0.627847
$171$	17.2316	1.31774
$172$	−22.1496	−1.68889
$173$	6.43231	0.489039	0.244520	−	0.969644i	$-0.421370\pi$
$173$	6.43231	0.489039	0.244520	+	0.969644i	$0.421370\pi$
$174$	2.93214	0.222285
$175$	0	0
$176$	0	0
$177$	9.03248	0.678923
$178$	−7.98173	−0.598256
$179$	−3.58596	−0.268027	−0.134014	−	0.990979i	$-0.542787\pi$
$179$	−3.58596	−0.268027	−0.134014	+	0.990979i	$0.542787\pi$
$180$	23.0858	1.72071
$181$	−12.2134	−0.907813	−0.453906	−	0.891049i	$-0.649970\pi$
$181$	−12.2134	−0.907813	−0.453906	+	0.891049i	$0.649970\pi$
$182$	0	0
$183$	−9.26295	−0.684737
$184$	35.6404	2.62745
$185$	12.2447	0.900247
$186$	4.17716	0.306284
$187$	0	0
$188$	−6.26819	−0.457155
$189$	0	0
$190$	37.9855	2.75576
$191$	12.1093	0.876198	0.438099	−	0.898927i	$-0.355652\pi$
$191$	12.1093	0.876198	0.438099	+	0.898927i	$0.355652\pi$
$192$	−3.71354	−0.268002
$193$	11.9399	0.859456	0.429728	−	0.902958i	$-0.358609\pi$
$193$	11.9399	0.859456	0.429728	+	0.902958i	$0.358609\pi$
$194$	−4.63148	−0.332521
$195$	5.16936	0.370185
$196$	0	0
$197$	−12.1626	−0.866551	−0.433275	−	0.901262i	$-0.642642\pi$
$197$	−12.1626	−0.866551	−0.433275	+	0.901262i	$0.642642\pi$
$198$	0	0
$199$	−1.90490	−0.135035	−0.0675174	−	0.997718i	$-0.521508\pi$
$199$	−1.90490	−0.135035	−0.0675174	+	0.997718i	$0.521508\pi$
$200$	−0.772091	−0.0545951
$201$	−3.26295	−0.230151
$202$	15.0586	1.05952
$203$	0	0
$204$	4.47259	0.313144
$205$	24.7993	1.73206
$206$	2.64975	0.184617
$207$	−16.1679	−1.12374
$208$	−17.3137	−1.20049
$209$	0	0
$210$	0	0
$211$	16.2447	1.11833	0.559165	−	0.829056i	$-0.311122\pi$
$211$	16.2447	1.11833	0.559165	+	0.829056i	$0.311122\pi$
$212$	1.28123	0.0879951
$213$	8.08206	0.553774
$214$	15.7721	1.07816
$215$	11.6132	0.792014
$216$	−21.5129	−1.46377
$217$	0	0
$218$	7.00897	0.474707
$219$	−6.11337	−0.413103
$220$	0	0
$221$	−4.89967	−0.329587
$222$	−9.87242	−0.662594
$223$	−3.03655	−0.203342	−0.101671	−	0.994818i	$-0.532419\pi$
$223$	−3.03655	−0.203342	−0.101671	+	0.994818i	$0.532419\pi$
$224$	0	0
$225$	0.350250	0.0233500
$226$	−31.7680	−2.11318
$227$	18.4491	1.22451	0.612254	−	0.790661i	$-0.290263\pi$
$227$	18.4491	1.22451	0.612254	+	0.790661i	$0.290263\pi$
$228$	−20.7538	−1.37446
$229$	25.4998	1.68508	0.842538	−	0.538637i	$-0.181060\pi$
$229$	25.4998	1.68508	0.842538	+	0.538637i	$0.181060\pi$
$230$	−35.6404	−2.35006
$231$	0	0
$232$	9.05855	0.594723
$233$	−3.81761	−0.250100	−0.125050	−	0.992150i	$-0.539909\pi$
$233$	−3.81761	−0.250100	−0.125050	+	0.992150i	$0.539909\pi$
$234$	20.3905	1.33297
$235$	3.28646	0.214385
$236$	53.2223	3.46448
$237$	−3.30473	−0.214666
$238$	0	0
$239$	−13.0037	−0.841142	−0.420571	−	0.907260i	$-0.638170\pi$
$239$	−13.0037	−0.841142	−0.420571	+	0.907260i	$0.638170\pi$
$240$	−8.28646	−0.534889
$241$	−0.450583	−0.0290246	−0.0145123	−	0.999895i	$-0.504620\pi$
$241$	−0.450583	−0.0290246	−0.0145123	+	0.999895i	$0.504620\pi$
$242$	0	0
$243$	15.0910	0.968090
$244$	−54.5804	−3.49415
$245$	0	0
$246$	−19.9948	−1.27482
$247$	22.7355	1.44663
$248$	12.9049	0.819462
$249$	−1.38156	−0.0875529
$250$	28.2264	1.78519
$251$	−1.11861	−0.0706058	−0.0353029	−	0.999377i	$-0.511240\pi$
$251$	−1.11861	−0.0706058	−0.0353029	+	0.999377i	$0.511240\pi$
$252$	0	0
$253$	0	0
$254$	30.8306	1.93449
$255$	−2.34502	−0.146851
$256$	−32.5453	−2.03408
$257$	22.8396	1.42470	0.712348	−	0.701826i	$-0.247632\pi$
$257$	22.8396	1.42470	0.712348	+	0.701826i	$0.247632\pi$
$258$	−9.36329	−0.582933
$259$	0	0
$260$	30.4596	1.88902
$261$	−4.10930	−0.254359
$262$	1.89070	0.116808
$263$	9.19136	0.566764	0.283382	−	0.959007i	$-0.408544\pi$
$263$	9.19136	0.566764	0.283382	+	0.959007i	$0.408544\pi$
$264$	0	0
$265$	−0.671758	−0.0412658
$266$	0	0
$267$	−2.28646	−0.139929
$268$	−19.2264	−1.17444
$269$	15.6132	0.951954	0.475977	−	0.879458i	$-0.342095\pi$
$269$	15.6132	0.951954	0.475977	+	0.879458i	$0.342095\pi$
$270$	21.5129	1.30923
$271$	27.7445	1.68536	0.842680	−	0.538415i	$-0.180977\pi$
$271$	27.7445	1.68536	0.842680	+	0.538415i	$0.180977\pi$
$272$	7.85415	0.476228
$273$	0	0
$274$	−14.5494	−0.878962
$275$	0	0
$276$	19.4726	1.17211
$277$	−14.8124	−0.889989	−0.444995	−	0.895533i	$-0.646794\pi$
$277$	−14.8124	−0.889989	−0.444995	+	0.895533i	$0.646794\pi$
$278$	−13.8814	−0.832551
$279$	−5.85415	−0.350479
$280$	0	0
$281$	−15.2227	−0.908109	−0.454054	−	0.890974i	$-0.650023\pi$
$281$	−15.2227	−0.908109	−0.454054	+	0.890974i	$0.650023\pi$
$282$	−2.64975	−0.157790
$283$	21.7173	1.29096	0.645479	−	0.763778i	$-0.276658\pi$
$283$	21.7173	1.29096	0.645479	+	0.763778i	$0.276658\pi$
$284$	47.6222	2.82586
$285$	10.8814	0.644558
$286$	0	0
$287$	0	0
$288$	−5.33198	−0.314190
$289$	−14.7773	−0.869254
$290$	−9.05855	−0.531937
$291$	−1.32674	−0.0777750
$292$	−36.0220	−2.10803
$293$	11.1276	0.650080	0.325040	−	0.945700i	$-0.394622\pi$
$293$	11.1276	0.650080	0.325040	+	0.945700i	$0.394622\pi$
$294$	0	0
$295$	−27.9049	−1.62469
$296$	−30.4998	−1.77277
$297$	0	0
$298$	2.49086	0.144292
$299$	−21.3320	−1.23366
$300$	−0.421841	−0.0243550
$301$	0	0
$302$	−36.9672	−2.12722
$303$	4.31370	0.247816
$304$	−36.4450	−2.09026
$305$	28.6169	1.63860
$306$	−9.24992	−0.528783
$307$	24.9855	1.42600	0.712998	−	0.701166i	$-0.247337\pi$
$307$	24.9855	1.42600	0.712998	+	0.701166i	$0.247337\pi$
$308$	0	0
$309$	0.759053	0.0431810
$310$	−12.9049	−0.732949
$311$	−34.7408	−1.96997	−0.984984	−	0.172643i	$-0.944769\pi$
$311$	−34.7408	−1.96997	−0.984984	+	0.172643i	$0.944769\pi$
$312$	−12.8762	−0.728969
$313$	−23.7095	−1.34014	−0.670069	−	0.742299i	$-0.733736\pi$
$313$	−23.7095	−1.34014	−0.670069	+	0.742299i	$0.733736\pi$
$314$	−15.9179	−0.898301
$315$	0	0
$316$	−19.4726	−1.09542
$317$	19.6770	1.10517	0.552585	−	0.833457i	$-0.313641\pi$
$317$	19.6770	1.10517	0.552585	+	0.833457i	$0.313641\pi$
$318$	0.541613	0.0303722
$319$	0	0
$320$	11.4726	0.641337
$321$	4.51811	0.252176
$322$	0	0
$323$	−10.3137	−0.573870
$324$	19.6640	1.09244
$325$	0.462122	0.0256339
$326$	24.7721	1.37200
$327$	2.00780	0.111032
$328$	−61.7718	−3.41077
$329$	0	0
$330$	0	0
$331$	−28.1899	−1.54946	−0.774728	−	0.632295i	$-0.782113\pi$
$331$	−28.1899	−1.54946	−0.774728	+	0.632295i	$0.782113\pi$
$332$	−8.14061	−0.446774
$333$	13.8359	0.758201
$334$	−4.83588	−0.264608
$335$	10.0806	0.550760
$336$	0	0
$337$	−21.7460	−1.18458	−0.592290	−	0.805725i	$-0.701776\pi$
$337$	−21.7460	−1.18458	−0.592290	+	0.805725i	$0.701776\pi$
$338$	−5.47783	−0.297954
$339$	−9.10033	−0.494262
$340$	−13.8176	−0.749365
$341$	0	0
$342$	42.9217	2.32094
$343$	0	0
$344$	−28.9269	−1.55963
$345$	−10.2096	−0.549668
$346$	16.0220	0.861348
$347$	3.94145	0.211588	0.105794	−	0.994388i	$-0.466262\pi$
$347$	3.94145	0.211588	0.105794	+	0.994388i	$0.466262\pi$
$348$	4.94925	0.265308
$349$	−14.1093	−0.755254	−0.377627	−	0.925958i	$-0.623260\pi$
$349$	−14.1093	−0.755254	−0.377627	+	0.925958i	$0.623260\pi$
$350$	0	0
$351$	12.8762	0.687279
$352$	0	0
$353$	4.96869	0.264457	0.132228	−	0.991219i	$-0.457787\pi$
$353$	4.96869	0.264457	0.132228	+	0.991219i	$0.457787\pi$
$354$	22.4987	1.19579
$355$	−24.9687	−1.32520
$356$	−13.4726	−0.714046
$357$	0	0
$358$	−8.93214	−0.472078
$359$	4.07159	0.214890	0.107445	−	0.994211i	$-0.465733\pi$
$359$	4.07159	0.214890	0.107445	+	0.994211i	$0.465733\pi$
$360$	30.1496	1.58902
$361$	28.8579	1.51884
$362$	−30.4218	−1.59894
$363$	0	0
$364$	0	0
$365$	18.8866	0.988571
$366$	−23.0728	−1.20603
$367$	18.0220	0.940741	0.470371	−	0.882469i	$-0.344120\pi$
$367$	18.0220	0.940741	0.470371	+	0.882469i	$0.344120\pi$
$368$	34.1951	1.78254
$369$	28.0220	1.45877
$370$	30.4998	1.58561
$371$	0	0
$372$	7.05075	0.365564
$373$	−28.9164	−1.49724	−0.748618	−	0.663001i	$-0.769282\pi$
$373$	−28.9164	−1.49724	−0.748618	+	0.663001i	$0.769282\pi$
$374$	0	0
$375$	8.08580	0.417549
$376$	−8.18613	−0.422167
$377$	−5.42184	−0.279239
$378$	0	0
$379$	4.30847	0.221311	0.110656	−	0.993859i	$-0.464705\pi$
$379$	4.30847	0.221311	0.110656	+	0.993859i	$0.464705\pi$
$380$	64.1168	3.28912
$381$	8.83181	0.452467
$382$	30.1626	1.54325
$383$	12.3488	0.630992	0.315496	−	0.948927i	$-0.397829\pi$
$383$	12.3488	0.630992	0.315496	+	0.948927i	$0.397829\pi$
$384$	−12.3047	−0.627923
$385$	0	0
$386$	29.7408	1.51377
$387$	13.1223	0.667046
$388$	−7.81761	−0.396879
$389$	29.4230	1.49181	0.745903	−	0.666055i	$-0.232018\pi$
$389$	29.4230	1.49181	0.745903	+	0.666055i	$0.232018\pi$
$390$	12.8762	0.652010
$391$	9.67699	0.489387
$392$	0	0
$393$	0.541613	0.0273208
$394$	−30.2954	−1.52626
$395$	10.2096	0.513703
$396$	0	0
$397$	17.2995	0.868237	0.434119	−	0.900856i	$-0.357060\pi$
$397$	17.2995	0.868237	0.434119	+	0.900856i	$0.357060\pi$
$398$	−4.74485	−0.237838
$399$	0	0
$400$	−0.740780	−0.0370390
$401$	−24.9504	−1.24596	−0.622982	−	0.782236i	$-0.714079\pi$
$401$	−24.9504	−1.24596	−0.622982	+	0.782236i	$0.714079\pi$
$402$	−8.12758	−0.405367
$403$	−7.72401	−0.384760
$404$	25.4178	1.26458
$405$	−10.3100	−0.512306
$406$	0	0
$407$	0	0
$408$	5.84111	0.289178
$409$	−38.5584	−1.90659	−0.953295	−	0.302042i	$-0.902332\pi$
$409$	−38.5584	−1.90659	−0.953295	+	0.302042i	$0.902332\pi$
$410$	61.7718	3.05069
$411$	−4.16786	−0.205585
$412$	4.47259	0.220349
$413$	0	0
$414$	−40.2719	−1.97926
$415$	4.26819	0.209517
$416$	−7.03505	−0.344922
$417$	−3.97649	−0.194730
$418$	0	0
$419$	−0.908970	−0.0444061	−0.0222030	−	0.999753i	$-0.507068\pi$
$419$	−0.908970	−0.0444061	−0.0222030	+	0.999753i	$0.507068\pi$
$420$	0	0
$421$	15.5532	0.758014	0.379007	−	0.925394i	$-0.376266\pi$
$421$	15.5532	0.758014	0.379007	+	0.925394i	$0.376266\pi$
$422$	40.4633	1.96972
$423$	3.71354	0.180558
$424$	1.67326	0.0812606
$425$	−0.209636	−0.0101688
$426$	20.1313	0.975365
$427$	0	0
$428$	26.6222	1.28683
$429$	0	0
$430$	28.9269	1.39498
$431$	−3.53638	−0.170341	−0.0851707	−	0.996366i	$-0.527144\pi$
$431$	−3.53638	−0.170341	−0.0851707	+	0.996366i	$0.527144\pi$
$432$	−20.6404	−0.993064
$433$	−17.6457	−0.847997	−0.423999	−	0.905663i	$-0.639374\pi$
$433$	−17.6457	−0.847997	−0.423999	+	0.905663i	$0.639374\pi$
$434$	0	0
$435$	−2.59493	−0.124417
$436$	11.8306	0.566585
$437$	−44.9034	−2.14802
$438$	−15.2276	−0.727602
$439$	15.0272	0.717211	0.358606	−	0.933489i	$-0.383252\pi$
$439$	15.0272	0.717211	0.358606	+	0.933489i	$0.383252\pi$
$440$	0	0
$441$	0	0
$442$	−12.2044	−0.580504
$443$	13.2227	0.628228	0.314114	−	0.949385i	$-0.398293\pi$
$443$	13.2227	0.628228	0.314114	+	0.949385i	$0.398293\pi$
$444$	−16.6640	−0.790836
$445$	7.06379	0.334856
$446$	−7.56362	−0.358148
$447$	0.713538	0.0337492
$448$	0	0
$449$	−9.90864	−0.467617	−0.233809	−	0.972283i	$-0.575119\pi$
$449$	−9.90864	−0.467617	−0.233809	+	0.972283i	$0.575119\pi$
$450$	0.872425	0.0411265
$451$	0	0
$452$	−53.6222	−2.52217
$453$	−10.5897	−0.497547
$454$	45.9542	2.15674
$455$	0	0
$456$	−27.1041	−1.26926
$457$	−10.3450	−0.483919	−0.241960	−	0.970286i	$-0.577790\pi$
$457$	−10.3450	−0.483919	−0.241960	+	0.970286i	$0.577790\pi$
$458$	63.5166	2.96794
$459$	−5.84111	−0.272640
$460$	−60.1586	−2.80491
$461$	−15.3372	−0.714325	−0.357163	−	0.934042i	$-0.616256\pi$
$461$	−15.3372	−0.714325	−0.357163	+	0.934042i	$0.616256\pi$
$462$	0	0
$463$	−25.1313	−1.16795	−0.583976	−	0.811771i	$-0.698504\pi$
$463$	−25.1313	−1.16795	−0.583976	+	0.811771i	$0.698504\pi$
$464$	8.69120	0.403479
$465$	−3.69676	−0.171433
$466$	−9.50914	−0.440502
$467$	0.746015	0.0345214	0.0172607	−	0.999851i	$-0.494505\pi$
$467$	0.746015	0.0345214	0.0172607	+	0.999851i	$0.494505\pi$
$468$	34.4178	1.59096
$469$	0	0
$470$	8.18613	0.377598
$471$	−4.55989	−0.210108
$472$	69.5073	3.19933
$473$	0	0
$474$	−8.23164	−0.378092
$475$	0.972758	0.0446332
$476$	0	0
$477$	−0.759053	−0.0347546
$478$	−32.3905	−1.48151
$479$	−20.1130	−0.918988	−0.459494	−	0.888181i	$-0.651969\pi$
$479$	−20.1130	−0.918988	−0.459494	+	0.888181i	$0.651969\pi$
$480$	−3.36702	−0.153683
$481$	18.2552	0.832363
$482$	−1.12234	−0.0511212
$483$	0	0
$484$	0	0
$485$	4.09883	0.186118
$486$	37.5897	1.70510
$487$	−4.24992	−0.192582	−0.0962911	−	0.995353i	$-0.530698\pi$
$487$	−4.24992	−0.192582	−0.0962911	+	0.995353i	$0.530698\pi$
$488$	−71.2809	−3.22673
$489$	7.09626	0.320904
$490$	0	0
$491$	−30.3279	−1.36868	−0.684340	−	0.729163i	$-0.739909\pi$
$491$	−30.3279	−1.36868	−0.684340	+	0.729163i	$0.739909\pi$
$492$	−33.7497	−1.52156
$493$	2.45955	0.110773
$494$	56.6311	2.54796
$495$	0	0
$496$	12.3816	0.555948
$497$	0	0
$498$	−3.44128	−0.154207
$499$	14.4413	0.646480	0.323240	−	0.946317i	$-0.395228\pi$
$499$	14.4413	0.646480	0.323240	+	0.946317i	$0.395228\pi$
$500$	47.6442	2.13071
$501$	−1.38530	−0.0618905
$502$	−2.78630	−0.124358
$503$	−2.95822	−0.131901	−0.0659503	−	0.997823i	$-0.521008\pi$
$503$	−2.95822	−0.131901	−0.0659503	+	0.997823i	$0.521008\pi$
$504$	0	0
$505$	−13.3267	−0.593032
$506$	0	0
$507$	−1.56919	−0.0696901
$508$	52.0399	2.30890
$509$	24.9907	1.10769	0.553847	−	0.832619i	$-0.313159\pi$
$509$	24.9907	1.10769	0.553847	+	0.832619i	$0.313159\pi$
$510$	−5.84111	−0.258649
$511$	0	0
$512$	−46.5767	−2.05842
$513$	27.1041	1.19667
$514$	56.8904	2.50933
$515$	−2.34502	−0.103334
$516$	−15.8046	−0.695757
$517$	0	0
$518$	0	0
$519$	4.58970	0.201465
$520$	39.7796	1.74445
$521$	−28.8631	−1.26452	−0.632258	−	0.774758i	$-0.717872\pi$
$521$	−28.8631	−1.26452	−0.632258	+	0.774758i	$0.717872\pi$
$522$	−10.2357	−0.448005
$523$	0.472591	0.0206650	0.0103325	−	0.999947i	$-0.496711\pi$
$523$	0.472591	0.0206650	0.0103325	+	0.999947i	$0.496711\pi$
$524$	3.19136	0.139415
$525$	0	0
$526$	22.8944	0.998245
$527$	3.50390	0.152632
$528$	0	0
$529$	19.1313	0.831796
$530$	−1.67326	−0.0726817
$531$	−31.5311	−1.36834
$532$	0	0
$533$	36.9724	1.60145
$534$	−5.69527	−0.246458
$535$	−13.9582	−0.603466
$536$	−25.1093	−1.08456
$537$	−2.55872	−0.110417
$538$	38.8904	1.67668
$539$	0	0
$540$	36.3122	1.56263
$541$	−15.4596	−0.664658	−0.332329	−	0.943164i	$-0.607834\pi$
$541$	−15.4596	−0.664658	−0.332329	+	0.943164i	$0.607834\pi$
$542$	69.1078	2.96843
$543$	−8.71470	−0.373984
$544$	3.19136	0.136829
$545$	−6.20290	−0.265703
$546$	0	0
$547$	35.0440	1.49837	0.749187	−	0.662359i	$-0.230444\pi$
$547$	35.0440	1.49837	0.749187	+	0.662359i	$0.230444\pi$
$548$	−24.5584	−1.04908
$549$	32.3357	1.38005
$550$	0	0
$551$	−11.4129	−0.486205
$552$	25.4308	1.08241
$553$	0	0
$554$	−36.8956	−1.56754
$555$	8.73705	0.370867
$556$	−23.4308	−0.993688
$557$	−10.5326	−0.446282	−0.223141	−	0.974786i	$-0.571631\pi$
$557$	−10.5326	−0.446282	−0.223141	+	0.974786i	$0.571631\pi$
$558$	−14.5819	−0.617301
$559$	17.3137	0.732292
$560$	0	0
$561$	0	0
$562$	−37.9176	−1.59946
$563$	−30.7147	−1.29447	−0.647235	−	0.762290i	$-0.724075\pi$
$563$	−30.7147	−1.29447	−0.647235	+	0.762290i	$0.724075\pi$
$564$	−4.47259	−0.188330
$565$	28.1145	1.18279
$566$	54.0948	2.27377
$567$	0	0
$568$	62.1936	2.60959
$569$	30.7721	1.29003	0.645017	−	0.764169i	$-0.276850\pi$
$569$	30.7721	1.29003	0.645017	+	0.764169i	$0.276850\pi$
$570$	27.1041	1.13526
$571$	7.51694	0.314574	0.157287	−	0.987553i	$-0.449725\pi$
$571$	7.51694	0.314574	0.157287	+	0.987553i	$0.449725\pi$
$572$	0	0
$573$	8.64045	0.360960
$574$	0	0
$575$	−0.912705	−0.0380624
$576$	12.9635	0.540144
$577$	−27.6184	−1.14977	−0.574885	−	0.818234i	$-0.694953\pi$
$577$	−27.6184	−1.14977	−0.574885	+	0.818234i	$0.694953\pi$
$578$	−36.8083	−1.53102
$579$	8.51961	0.354063
$580$	−15.2902	−0.634891
$581$	0	0
$582$	−3.30473	−0.136986
$583$	0	0
$584$	−47.0440	−1.94670
$585$	−18.0455	−0.746090
$586$	27.7173	1.14499
$587$	29.9582	1.23651	0.618254	−	0.785978i	$-0.287840\pi$
$587$	29.9582	1.23651	0.618254	+	0.785978i	$0.287840\pi$
$588$	0	0
$589$	−16.2589	−0.669936
$590$	−69.5073	−2.86157
$591$	−8.67849	−0.356985
$592$	−29.2630	−1.20270
$593$	12.6680	0.520213	0.260107	−	0.965580i	$-0.416242\pi$
$593$	12.6680	0.520213	0.260107	+	0.965580i	$0.416242\pi$
$594$	0	0
$595$	0	0
$596$	4.20440	0.172219
$597$	−1.35922	−0.0556291
$598$	−53.1350	−2.17285
$599$	1.29427	0.0528823	0.0264411	−	0.999650i	$-0.491583\pi$
$599$	1.29427	0.0528823	0.0264411	+	0.999650i	$0.491583\pi$
$600$	−0.550916	−0.0224911
$601$	−41.0220	−1.67332	−0.836661	−	0.547721i	$-0.815496\pi$
$601$	−41.0220	−1.67332	−0.836661	+	0.547721i	$0.815496\pi$
$602$	0	0
$603$	11.3905	0.463858
$604$	−62.3980	−2.53894
$605$	0	0
$606$	10.7448	0.436480
$607$	−21.1768	−0.859541	−0.429770	−	0.902938i	$-0.641406\pi$
$607$	−21.1768	−0.859541	−0.429770	+	0.902938i	$0.641406\pi$
$608$	−14.8086	−0.600570
$609$	0	0
$610$	71.2809	2.88608
$611$	4.89967	0.198219
$612$	−15.6132	−0.631126
$613$	−6.76312	−0.273160	−0.136580	−	0.990629i	$-0.543611\pi$
$613$	−6.76312	−0.273160	−0.136580	+	0.990629i	$0.543611\pi$
$614$	62.2354	2.51162
$615$	17.6953	0.713542
$616$	0	0
$617$	−41.0728	−1.65353	−0.826763	−	0.562550i	$-0.809820\pi$
$617$	−41.0728	−1.65353	−0.826763	+	0.562550i	$0.809820\pi$
$618$	1.89070	0.0760550
$619$	30.4267	1.22295	0.611477	−	0.791262i	$-0.290576\pi$
$619$	30.4267	1.22295	0.611477	+	0.791262i	$0.290576\pi$
$620$	−21.7826	−0.874809
$621$	−25.4308	−1.02050
$622$	−86.5345	−3.46972
$623$	0	0
$624$	−12.3540	−0.494555
$625$	−24.2772	−0.971086
$626$	−59.0571	−2.36039
$627$	0	0
$628$	−26.8684	−1.07216
$629$	−8.28123	−0.330194
$630$	0	0
$631$	12.3670	0.492323	0.246162	−	0.969229i	$-0.420831\pi$
$631$	12.3670	0.492323	0.246162	+	0.969229i	$0.420831\pi$
$632$	−25.4308	−1.01158
$633$	11.5912	0.460709
$634$	49.0127	1.94654
$635$	−27.2850	−1.08277
$636$	0.914205	0.0362506
$637$	0	0
$638$	0	0
$639$	−28.2134	−1.11610
$640$	38.0142	1.50264
$641$	−47.1313	−1.86157	−0.930787	−	0.365561i	$-0.880877\pi$
$641$	−47.1313	−1.86157	−0.930787	+	0.365561i	$0.880877\pi$
$642$	11.2540	0.444159
$643$	−1.87242	−0.0738412	−0.0369206	−	0.999318i	$-0.511755\pi$
$643$	−1.87242	−0.0738412	−0.0369206	+	0.999318i	$0.511755\pi$
$644$	0	0
$645$	8.28646	0.326279
$646$	−25.6900	−1.01076
$647$	1.83588	0.0721758	0.0360879	−	0.999349i	$-0.488510\pi$
$647$	1.83588	0.0721758	0.0360879	+	0.999349i	$0.488510\pi$
$648$	25.6807	1.00883
$649$	0	0
$650$	1.15108	0.0451492
$651$	0	0
$652$	41.8135	1.63754
$653$	−18.1772	−0.711327	−0.355664	−	0.934614i	$-0.615745\pi$
$653$	−18.1772	−0.711327	−0.355664	+	0.934614i	$0.615745\pi$
$654$	5.00117	0.195561
$655$	−1.67326	−0.0653796
$656$	−59.2667	−2.31398
$657$	21.3409	0.832590
$658$	0	0
$659$	16.8997	0.658318	0.329159	−	0.944275i	$-0.393235\pi$
$659$	16.8997	0.658318	0.329159	+	0.944275i	$0.393235\pi$
$660$	0	0
$661$	45.3032	1.76209	0.881046	−	0.473031i	$-0.156840\pi$
$661$	45.3032	1.76209	0.881046	+	0.473031i	$0.156840\pi$
$662$	−70.2171	−2.72907
$663$	−3.49610	−0.135777
$664$	−10.6315	−0.412581
$665$	0	0
$666$	34.4633	1.33543
$667$	10.7083	0.414627
$668$	−8.16262	−0.315821
$669$	−2.16669	−0.0837691
$670$	25.1093	0.970057
$671$	0	0
$672$	0	0
$673$	−39.5076	−1.52291	−0.761454	−	0.648219i	$-0.775514\pi$
$673$	−39.5076	−1.52291	−0.761454	+	0.648219i	$0.775514\pi$
$674$	−54.1664	−2.08641
$675$	0.550916	0.0212048
$676$	−9.24618	−0.355622
$677$	−34.1339	−1.31187	−0.655936	−	0.754817i	$-0.727726\pi$
$677$	−34.1339	−1.31187	−0.655936	+	0.754817i	$0.727726\pi$
$678$	−22.6677	−0.870547
$679$	0	0
$680$	−18.0455	−0.692014
$681$	13.1641	0.504450
$682$	0	0
$683$	23.7863	0.910157	0.455079	−	0.890451i	$-0.349611\pi$
$683$	23.7863	0.910157	0.455079	+	0.890451i	$0.349611\pi$
$684$	72.4487	2.77015
$685$	12.8762	0.491973
$686$	0	0
$687$	18.1951	0.694186
$688$	−27.7538	−1.05810
$689$	−1.00150	−0.0381541
$690$	−25.4308	−0.968134
$691$	20.5625	0.782233	0.391116	−	0.920341i	$-0.372089\pi$
$691$	20.5625	0.782233	0.391116	+	0.920341i	$0.372089\pi$
$692$	27.0440	1.02806
$693$	0	0
$694$	9.81761	0.372671
$695$	12.2850	0.465995
$696$	6.46362	0.245003
$697$	−16.7721	−0.635288
$698$	−35.1443	−1.33023
$699$	−2.72401	−0.103031
$700$	0	0
$701$	23.9907	0.906116	0.453058	−	0.891481i	$-0.350333\pi$
$701$	23.9907	0.906116	0.453058	+	0.891481i	$0.350333\pi$
$702$	32.0728	1.21051
$703$	38.4267	1.44929
$704$	0	0
$705$	2.34502	0.0883184
$706$	12.3763	0.465789
$707$	0	0
$708$	37.9762	1.42723
$709$	−51.7117	−1.94207	−0.971037	−	0.238930i	$-0.923204\pi$
$709$	−51.7117	−1.94207	−0.971037	+	0.238930i	$0.923204\pi$
$710$	−62.1936	−2.33408
$711$	11.5364	0.432648
$712$	−17.5949	−0.659398
$713$	15.2552	0.571310
$714$	0	0
$715$	0	0
$716$	−15.0768	−0.563447
$717$	−9.27866	−0.346518
$718$	10.1418	0.378488
$719$	−25.7851	−0.961623	−0.480812	−	0.876824i	$-0.659658\pi$
$719$	−25.7851	−0.961623	−0.480812	+	0.876824i	$0.659658\pi$
$720$	28.9269	1.07804
$721$	0	0
$722$	71.8811	2.67514
$723$	−0.321508	−0.0119570
$724$	−51.3499	−1.90840
$725$	−0.231978	−0.00861543
$726$	0	0
$727$	−32.7330	−1.21400	−0.606999	−	0.794702i	$-0.707627\pi$
$727$	−32.7330	−1.21400	−0.606999	+	0.794702i	$0.707627\pi$
$728$	0	0
$729$	−3.26295	−0.120850
$730$	47.0440	1.74118
$731$	−7.85415	−0.290496
$732$	−38.9452	−1.43946
$733$	−9.28273	−0.342865	−0.171433	−	0.985196i	$-0.554840\pi$
$733$	−9.28273	−0.342865	−0.171433	+	0.985196i	$0.554840\pi$
$734$	44.8904	1.65693
$735$	0	0
$736$	13.8944	0.512156
$737$	0	0
$738$	69.7990	2.56934
$739$	50.0933	1.84271	0.921355	−	0.388722i	$-0.127083\pi$
$739$	50.0933	1.84271	0.921355	+	0.388722i	$0.127083\pi$
$740$	51.4816	1.89250
$741$	16.2227	0.595955
$742$	0	0
$743$	−13.1679	−0.483082	−0.241541	−	0.970391i	$-0.577653\pi$
$743$	−13.1679	−0.483082	−0.241541	+	0.970391i	$0.577653\pi$
$744$	9.20814	0.337587
$745$	−2.20440	−0.0807630
$746$	−72.0269	−2.63709
$747$	4.82284	0.176459
$748$	0	0
$749$	0	0
$750$	20.1406	0.735431
$751$	41.3137	1.50756	0.753779	−	0.657128i	$-0.228229\pi$
$751$	41.3137	1.50756	0.753779	+	0.657128i	$0.228229\pi$
$752$	−7.85415	−0.286411
$753$	−0.798168	−0.0290869
$754$	−13.5051	−0.491826
$755$	32.7158	1.19065
$756$	0	0
$757$	−45.5114	−1.65414	−0.827069	−	0.562100i	$-0.809994\pi$
$757$	−45.5114	−1.65414	−0.827069	+	0.562100i	$0.809994\pi$
$758$	10.7318	0.389797
$759$	0	0
$760$	83.7352	3.03740
$761$	31.2719	1.13361	0.566803	−	0.823853i	$-0.308180\pi$
$761$	31.2719	1.13361	0.566803	+	0.823853i	$0.308180\pi$
$762$	21.9988	0.796934
$763$	0	0
$764$	50.9124	1.84194
$765$	8.18613	0.295970
$766$	30.7591	1.11137
$767$	−41.6024	−1.50218
$768$	−23.2223	−0.837964
$769$	42.0467	1.51624	0.758121	−	0.652114i	$-0.226118\pi$
$769$	42.0467	1.51624	0.758121	+	0.652114i	$0.226118\pi$
$770$	0	0
$771$	16.2969	0.586920
$772$	50.2003	1.80675
$773$	−7.64452	−0.274954	−0.137477	−	0.990505i	$-0.543899\pi$
$773$	−7.64452	−0.274954	−0.137477	+	0.990505i	$0.543899\pi$
$774$	32.6860	1.17487
$775$	−0.330478	−0.0118711
$776$	−10.2096	−0.366505
$777$	0	0
$778$	73.2887	2.62753
$779$	77.8262	2.78841
$780$	21.7340	0.778204
$781$	0	0
$782$	24.1041	0.861960
$783$	−6.46362	−0.230991
$784$	0	0
$785$	14.0873	0.502797
$786$	1.34908	0.0481202
$787$	−27.9034	−0.994649	−0.497324	−	0.867565i	$-0.665684\pi$
$787$	−27.9034	−0.994649	−0.497324	+	0.867565i	$0.665684\pi$
$788$	−51.1365	−1.82166
$789$	6.55839	0.233485
$790$	25.4308	0.904788
$791$	0	0
$792$	0	0
$793$	42.6640	1.51504
$794$	43.0907	1.52923
$795$	−0.479325	−0.0169999
$796$	−8.00897	−0.283870
$797$	−10.0560	−0.356201	−0.178101	−	0.984012i	$-0.556995\pi$
$797$	−10.0560	−0.356201	−0.178101	+	0.984012i	$0.556995\pi$
$798$	0	0
$799$	−2.22267	−0.0786326
$800$	−0.301000	−0.0106420
$801$	7.98173	0.282020
$802$	−62.1481	−2.19453
$803$	0	0
$804$	−13.7188	−0.483824
$805$	0	0
$806$	−19.2394	−0.677681
$807$	11.1406	0.392168
$808$	33.1951	1.16780
$809$	−38.5726	−1.35614	−0.678070	−	0.734997i	$-0.737183\pi$
$809$	−38.5726	−1.35614	−0.678070	+	0.734997i	$0.737183\pi$
$810$	−25.6807	−0.902329
$811$	12.3760	0.434580	0.217290	−	0.976107i	$-0.430278\pi$
$811$	12.3760	0.434580	0.217290	+	0.976107i	$0.430278\pi$
$812$	0	0
$813$	19.7968	0.694303
$814$	0	0
$815$	−21.9232	−0.767935
$816$	5.60424	0.196187
$817$	36.4450	1.27505
$818$	−96.0437	−3.35809
$819$	0	0
$820$	104.266	3.64114
$821$	−29.7381	−1.03787	−0.518934	−	0.854814i	$-0.673671\pi$
$821$	−29.7381	−1.03787	−0.518934	+	0.854814i	$0.673671\pi$
$822$	−10.3816	−0.362099
$823$	40.7770	1.42140	0.710698	−	0.703497i	$-0.248379\pi$
$823$	40.7770	1.42140	0.710698	+	0.703497i	$0.248379\pi$
$824$	5.84111	0.203485
$825$	0	0
$826$	0	0
$827$	18.8411	0.655170	0.327585	−	0.944822i	$-0.393765\pi$
$827$	18.8411	0.655170	0.327585	+	0.944822i	$0.393765\pi$
$828$	−67.9762	−2.36233
$829$	31.1406	1.08156	0.540779	−	0.841165i	$-0.318129\pi$
$829$	31.1406	1.08156	0.540779	+	0.841165i	$0.318129\pi$
$830$	10.6315	0.369024
$831$	−10.5692	−0.366641
$832$	17.1041	0.592977
$833$	0	0
$834$	−9.90490	−0.342979
$835$	4.27973	0.148106
$836$	0	0
$837$	−9.20814	−0.318280
$838$	−2.26412	−0.0782127
$839$	−10.2589	−0.354176	−0.177088	−	0.984195i	$-0.556668\pi$
$839$	−10.2589	−0.354176	−0.177088	+	0.984195i	$0.556668\pi$
$840$	0	0
$841$	−26.2783	−0.906149
$842$	38.7408	1.33510
$843$	−10.8620	−0.374106
$844$	68.2992	2.35095
$845$	4.84785	0.166771
$846$	9.24992	0.318019
$847$	0	0
$848$	1.60540	0.0551297
$849$	15.4961	0.531825
$850$	−0.522175	−0.0179104
$851$	−36.0545	−1.23593
$852$	33.9802	1.16414
$853$	3.04435	0.104237	0.0521183	−	0.998641i	$-0.483403\pi$
$853$	3.04435	0.104237	0.0521183	+	0.998641i	$0.483403\pi$
$854$	0	0
$855$	−37.9855	−1.29908
$856$	34.7680	1.18835
$857$	49.5532	1.69270	0.846352	−	0.532624i	$-0.178794\pi$
$857$	49.5532	1.69270	0.846352	+	0.532624i	$0.178794\pi$
$858$	0	0
$859$	−36.8747	−1.25815	−0.629074	−	0.777346i	$-0.716566\pi$
$859$	−36.8747	−1.25815	−0.629074	+	0.777346i	$0.716566\pi$
$860$	48.8266	1.66497
$861$	0	0
$862$	−8.80864	−0.300023
$863$	−46.4230	−1.58026	−0.790129	−	0.612941i	$-0.789986\pi$
$863$	−46.4230	−1.58026	−0.790129	+	0.612941i	$0.789986\pi$
$864$	−8.38680	−0.285325
$865$	−14.1794	−0.482114
$866$	−43.9530	−1.49358
$867$	−10.5442	−0.358099
$868$	0	0
$869$	0	0
$870$	−6.46362	−0.219137
$871$	15.0287	0.509229
$872$	15.4506	0.523223
$873$	4.63148	0.156752
$874$	−111.848	−3.78332
$875$	0	0
$876$	−25.7031	−0.868426
$877$	−39.0310	−1.31798	−0.658991	−	0.752151i	$-0.729017\pi$
$877$	−39.0310	−1.31798	−0.658991	+	0.752151i	$0.729017\pi$
$878$	37.4308	1.26323
$879$	7.93995	0.267808
$880$	0	0
$881$	44.0049	1.48256	0.741281	−	0.671194i	$-0.234218\pi$
$881$	44.0049	1.48256	0.741281	+	0.671194i	$0.234218\pi$
$882$	0	0
$883$	−23.3596	−0.786112	−0.393056	−	0.919515i	$-0.628582\pi$
$883$	−23.3596	−0.786112	−0.393056	+	0.919515i	$0.628582\pi$
$884$	−20.6002	−0.692859
$885$	−19.9112	−0.669308
$886$	32.9359	1.10650
$887$	41.9176	1.40746	0.703728	−	0.710470i	$-0.251517\pi$
$887$	41.9176	1.40746	0.703728	+	0.710470i	$0.251517\pi$
$888$	−21.7628	−0.730311
$889$	0	0
$890$	17.5949	0.589783
$891$	0	0
$892$	−12.7669	−0.427466
$893$	10.3137	0.345135
$894$	1.77733	0.0594427
$895$	7.90490	0.264232
$896$	0	0
$897$	−15.2212	−0.508220
$898$	−24.6811	−0.823618
$899$	3.87733	0.129316
$900$	1.47259	0.0490864
$901$	0.454318	0.0151355
$902$	0	0
$903$	0	0
$904$	−70.0295	−2.32915
$905$	26.9232	0.894957
$906$	−26.3775	−0.876333
$907$	−20.5181	−0.681293	−0.340646	−	0.940192i	$-0.610646\pi$
$907$	−20.5181	−0.681293	−0.340646	+	0.940192i	$0.610646\pi$
$908$	77.5674	2.57416
$909$	−15.0586	−0.499461
$910$	0	0
$911$	27.6755	0.916930	0.458465	−	0.888712i	$-0.348399\pi$
$911$	27.6755	0.916930	0.458465	+	0.888712i	$0.348399\pi$
$912$	−26.0049	−0.861108
$913$	0	0
$914$	−25.7680	−0.852330
$915$	20.4193	0.675040
$916$	107.212	3.54237
$917$	0	0
$918$	−14.5494	−0.480202
$919$	−0.963454	−0.0317814	−0.0158907	−	0.999874i	$-0.505058\pi$
$919$	−0.963454	−0.0317814	−0.0158907	+	0.999874i	$0.505058\pi$
$920$	−78.5659	−2.59024
$921$	17.8281	0.587455
$922$	−38.2029	−1.25815
$923$	−37.2249	−1.22527
$924$	0	0
$925$	0.781061	0.0256811
$926$	−62.5987	−2.05712
$927$	−2.64975	−0.0870292
$928$	3.53148	0.115926
$929$	−26.3320	−0.863924	−0.431962	−	0.901892i	$-0.642179\pi$
$929$	−26.3320	−0.863924	−0.431962	+	0.901892i	$0.642179\pi$
$930$	−9.20814	−0.301947
$931$	0	0
$932$	−16.0507	−0.525760
$933$	−24.7889	−0.811551
$934$	1.85822	0.0608028
$935$	0	0
$936$	44.9489	1.46920
$937$	−21.3865	−0.698665	−0.349333	−	0.936999i	$-0.613592\pi$
$937$	−21.3865	−0.698665	−0.349333	+	0.936999i	$0.613592\pi$
$938$	0	0
$939$	−16.9176	−0.552085
$940$	13.8176	0.450681
$941$	14.8228	0.483211	0.241605	−	0.970375i	$-0.422326\pi$
$941$	14.8228	0.483211	0.241605	+	0.970375i	$0.422326\pi$
$942$	−11.3581	−0.370065
$943$	−73.0217	−2.37791
$944$	66.6885	2.17053
$945$	0	0
$946$	0	0
$947$	31.7120	1.03050	0.515251	−	0.857039i	$-0.327699\pi$
$947$	31.7120	1.03050	0.515251	+	0.857039i	$0.327699\pi$
$948$	−13.8944	−0.451270
$949$	28.1574	0.914027
$950$	2.42301	0.0786127
$951$	14.0403	0.455287
$952$	0	0
$953$	−49.9620	−1.61843	−0.809213	−	0.587515i	$-0.800106\pi$
$953$	−49.9620	−1.61843	−0.809213	+	0.587515i	$0.800106\pi$
$954$	−1.89070	−0.0612136
$955$	−26.6938	−0.863790
$956$	−54.6729	−1.76825
$957$	0	0
$958$	−50.0988	−1.61862
$959$	0	0
$960$	8.18613	0.264206
$961$	−25.4763	−0.821817
$962$	45.4711	1.46605
$963$	−15.7721	−0.508249
$964$	−1.89443	−0.0610156
$965$	−26.3204	−0.847285
$966$	0	0
$967$	52.4581	1.68694	0.843469	−	0.537178i	$-0.180510\pi$
$967$	52.4581	1.68694	0.843469	+	0.537178i	$0.180510\pi$
$968$	0	0
$969$	−7.35922	−0.236412
$970$	10.2096	0.327812
$971$	−30.8266	−0.989272	−0.494636	−	0.869100i	$-0.664699\pi$
$971$	−30.8266	−0.989272	−0.494636	+	0.869100i	$0.664699\pi$
$972$	63.4487	2.03512
$973$	0	0
$974$	−10.5860	−0.339196
$975$	0.329742	0.0105602
$976$	−68.3902	−2.18912
$977$	24.7355	0.791360	0.395680	−	0.918388i	$-0.370509\pi$
$977$	24.7355	0.791360	0.395680	+	0.918388i	$0.370509\pi$
$978$	17.6758	0.565211
$979$	0	0
$980$	0	0
$981$	−7.00897	−0.223779
$982$	−75.5427	−2.41066
$983$	−12.2238	−0.389880	−0.194940	−	0.980815i	$-0.562451\pi$
$983$	−12.2238	−0.389880	−0.194940	+	0.980815i	$0.562451\pi$
$984$	−44.0765	−1.40511
$985$	26.8113	0.854279
$986$	6.12641	0.195105
$987$	0	0
$988$	95.5894	3.04110
$989$	−34.1951	−1.08734
$990$	0	0
$991$	4.60017	0.146129	0.0730645	−	0.997327i	$-0.476722\pi$
$991$	4.60017	0.146129	0.0730645	+	0.997327i	$0.476722\pi$
$992$	5.03098	0.159734
$993$	−20.1145	−0.638316
$994$	0	0
$995$	4.19917	0.133123
$996$	−5.80864	−0.184054
$997$	−34.4763	−1.09188	−0.545938	−	0.837826i	$-0.683827\pi$
$997$	−34.4763	−1.09188	−0.545938	+	0.837826i	$0.683827\pi$
$998$	35.9713	1.13865
$999$	21.7628	0.688544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.w.1.3		3
7.3	odd	6		847.2.e.d.485.1		6
7.5	odd	6		847.2.e.d.606.1		6
7.6	odd	2		5929.2.a.v.1.3		3
11.10	odd	2		539.2.a.i.1.1		3
33.32	even	2		4851.2.a.bn.1.3		3
44.43	even	2		8624.2.a.ck.1.2		3
77.3	odd	30		847.2.n.d.9.3		24
77.5	odd	30		847.2.n.d.487.3		24
77.10	even	6		77.2.e.b.23.3	✓	6
77.17	even	30		847.2.n.e.366.3		24
77.19	even	30		847.2.n.e.130.3		24
77.24	even	30		847.2.n.e.807.1		24
77.26	odd	30		847.2.n.d.753.3		24
77.31	odd	30		847.2.n.d.807.3		24
77.32	odd	6		539.2.e.l.177.3		6
77.38	odd	30		847.2.n.d.366.1		24
77.40	even	30		847.2.n.e.753.1		24
77.47	odd	30		847.2.n.d.130.1		24
77.52	even	30		847.2.n.e.9.1		24
77.54	even	6		77.2.e.b.67.3	yes	6
77.59	odd	30		847.2.n.d.632.1		24
77.61	even	30		847.2.n.e.487.1		24
77.65	odd	6		539.2.e.l.67.3		6
77.68	even	30		847.2.n.e.81.3		24
77.73	even	30		847.2.n.e.632.3		24
77.75	odd	30		847.2.n.d.81.1		24
77.76	even	2		539.2.a.h.1.1		3
231.131	odd	6		693.2.i.g.298.1		6
231.164	odd	6		693.2.i.g.100.1		6
231.230	odd	2		4851.2.a.bo.1.3		3
308.87	odd	6		1232.2.q.k.177.2		6
308.131	odd	6		1232.2.q.k.529.2		6
308.307	odd	2		8624.2.a.cl.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.3	✓	6	77.10	even	6
77.2.e.b.67.3	yes	6	77.54	even	6
539.2.a.h.1.1		3	77.76	even	2
539.2.a.i.1.1		3	11.10	odd	2
539.2.e.l.67.3		6	77.65	odd	6
539.2.e.l.177.3		6	77.32	odd	6
693.2.i.g.100.1		6	231.164	odd	6
693.2.i.g.298.1		6	231.131	odd	6
847.2.e.d.485.1		6	7.3	odd	6
847.2.e.d.606.1		6	7.5	odd	6
847.2.n.d.9.3		24	77.3	odd	30
847.2.n.d.81.1		24	77.75	odd	30
847.2.n.d.130.1		24	77.47	odd	30
847.2.n.d.366.1		24	77.38	odd	30
847.2.n.d.487.3		24	77.5	odd	30
847.2.n.d.632.1		24	77.59	odd	30
847.2.n.d.753.3		24	77.26	odd	30
847.2.n.d.807.3		24	77.31	odd	30
847.2.n.e.9.1		24	77.52	even	30
847.2.n.e.81.3		24	77.68	even	30
847.2.n.e.130.3		24	77.19	even	30
847.2.n.e.366.3		24	77.17	even	30
847.2.n.e.487.1		24	77.61	even	30
847.2.n.e.632.3		24	77.73	even	30
847.2.n.e.753.1		24	77.40	even	30
847.2.n.e.807.1		24	77.24	even	30
1232.2.q.k.177.2		6	308.87	odd	6
1232.2.q.k.529.2		6	308.131	odd	6
4851.2.a.bn.1.3		3	33.32	even	2
4851.2.a.bo.1.3		3	231.230	odd	2
5929.2.a.v.1.3		3	7.6	odd	2
5929.2.a.w.1.3		3	1.1	even	1	trivial
8624.2.a.ck.1.2		3	44.43	even	2
8624.2.a.cl.1.2		3	308.307	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

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49086 q^{2} +0.713538 q^{3} +4.20440 q^{4} -2.20440 q^{5} +1.77733 q^{6} +5.49086 q^{8} -2.49086 q^{9} -5.49086 q^{10} +3.00000 q^{12} -3.28646 q^{13} -1.57292 q^{15} +5.26819 q^{16} +1.49086 q^{17} -6.20440 q^{18} -6.91794 q^{19} -9.26819 q^{20} +6.49086 q^{23} +3.91794 q^{24} -0.140614 q^{25} -8.18613 q^{26} -3.91794 q^{27} +1.64975 q^{29} -3.91794 q^{30} +2.35025 q^{31} +2.14061 q^{32} +3.71354 q^{34} -10.4726 q^{36} -5.55465 q^{37} -17.2316 q^{38} -2.34502 q^{39} -12.1041 q^{40} -11.2499 q^{41} -5.26819 q^{43} +5.49086 q^{45} +16.1679 q^{46} -1.49086 q^{47} +3.75905 q^{48} -0.350250 q^{50} +1.06379 q^{51} -13.8176 q^{52} +0.304735 q^{53} -9.75905 q^{54} -4.93621 q^{57} +4.10930 q^{58} +12.6587 q^{59} -6.61320 q^{60} -12.9817 q^{61} +5.85415 q^{62} -5.20440 q^{64} +7.24468 q^{65} -4.57292 q^{67} +6.26819 q^{68} +4.63148 q^{69} +11.3267 q^{71} -13.6770 q^{72} -8.56769 q^{73} -13.8359 q^{74} -0.100333 q^{75} -29.0858 q^{76} -5.84111 q^{78} -4.63148 q^{79} -11.6132 q^{80} +4.67699 q^{81} -28.0220 q^{82} -1.93621 q^{83} -3.28646 q^{85} -13.1223 q^{86} +1.17716 q^{87} -3.20440 q^{89} +13.6770 q^{90} +27.2902 q^{92} +1.67699 q^{93} -3.71354 q^{94} +15.2499 q^{95} +1.52741 q^{96} -1.85939 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} + 4 q^{4} + 2 q^{5} - q^{6} + 9 q^{8} - 9 q^{10} + 9 q^{12} - 11 q^{13} - 7 q^{15} + 2 q^{16} - 3 q^{17} - 10 q^{18} - 11 q^{19} - 14 q^{20} + 12 q^{23} + 2 q^{24} + 3 q^{25} - q^{26} - 2 q^{27}+ \cdots - 9 q^{97}+O(q^{100}) \) 3 * q + q^3 + 4 * q^4 + 2 * q^5 - q^6 + 9 * q^8 - 9 * q^10 + 9 * q^12 - 11 * q^13 - 7 * q^15 + 2 * q^16 - 3 * q^17 - 10 * q^18 - 11 * q^19 - 14 * q^20 + 12 * q^23 + 2 * q^24 + 3 * q^25 - q^26 - 2 * q^27 + 9 * q^29 - 2 * q^30 + 3 * q^31 + 3 * q^32 + 10 * q^34 - 9 * q^36 - 4 * q^37 - 8 * q^38 + 5 * q^39 - 3 * q^40 - 5 * q^41 - 2 * q^43 + 9 * q^45 + 10 * q^46 + 3 * q^47 - 10 * q^48 + 3 * q^50 - 2 * q^51 - 7 * q^52 + 17 * q^53 - 8 * q^54 - 20 * q^57 - 13 * q^58 - 8 * q^59 + 6 * q^60 - 24 * q^61 + 13 * q^62 - 7 * q^64 - 15 * q^65 - 16 * q^67 + 5 * q^68 + 3 * q^69 + 7 * q^71 - 10 * q^72 - 20 * q^73 - 22 * q^74 - 25 * q^75 - 39 * q^76 - 6 * q^78 - 3 * q^79 - 9 * q^80 - 17 * q^81 - 41 * q^82 - 11 * q^83 - 11 * q^85 - 21 * q^86 + 30 * q^87 - q^89 + 10 * q^90 + 25 * q^92 - 26 * q^93 - 10 * q^94 + 17 * q^95 + 27 * q^96 - 9 * q^97

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