LMFDB - Embedded newform 605.4.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,4,Mod(1,605)] 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("605.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$35.6961555535$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} +3.00000 q^{6} +9.00000 q^{7} +15.0000 q^{8} -18.0000 q^{9} +5.00000 q^{10} +21.0000 q^{12} -2.00000 q^{13} -9.00000 q^{14} +15.0000 q^{15} +41.0000 q^{16} -21.0000 q^{17} +18.0000 q^{18} +85.0000 q^{19} +35.0000 q^{20} -27.0000 q^{21} +22.0000 q^{23} -45.0000 q^{24} +25.0000 q^{25} +2.00000 q^{26} +135.000 q^{27} -63.0000 q^{28} +165.000 q^{29} -15.0000 q^{30} -83.0000 q^{31} -161.000 q^{32} +21.0000 q^{34} -45.0000 q^{35} +126.000 q^{36} +1.00000 q^{37} -85.0000 q^{38} +6.00000 q^{39} -75.0000 q^{40} +478.000 q^{41} +27.0000 q^{42} +8.00000 q^{43} +90.0000 q^{45} -22.0000 q^{46} +126.000 q^{47} -123.000 q^{48} -262.000 q^{49} -25.0000 q^{50} +63.0000 q^{51} +14.0000 q^{52} -683.000 q^{53} -135.000 q^{54} +135.000 q^{56} -255.000 q^{57} -165.000 q^{58} -290.000 q^{59} -105.000 q^{60} -257.000 q^{61} +83.0000 q^{62} -162.000 q^{63} -167.000 q^{64} +10.0000 q^{65} +776.000 q^{67} +147.000 q^{68} -66.0000 q^{69} +45.0000 q^{70} -313.000 q^{71} -270.000 q^{72} -902.000 q^{73} -1.00000 q^{74} -75.0000 q^{75} -595.000 q^{76} -6.00000 q^{78} -830.000 q^{79} -205.000 q^{80} +81.0000 q^{81} -478.000 q^{82} -842.000 q^{83} +189.000 q^{84} +105.000 q^{85} -8.00000 q^{86} -495.000 q^{87} +25.0000 q^{89} -90.0000 q^{90} -18.0000 q^{91} -154.000 q^{92} +249.000 q^{93} -126.000 q^{94} -425.000 q^{95} +483.000 q^{96} -1784.00 q^{97} +262.000 q^{98} +O(q^{100})\)

Coefficient data

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

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

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

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	−3.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−3.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−7.00000	−0.875000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	3.00000	0.204124
$7$	9.00000	0.485954	0.242977	−	0.970032i	$-0.421876\pi$
$7$	9.00000	0.485954	0.242977	+	0.970032i	$0.421876\pi$
$8$	15.0000	0.662913
$9$	−18.0000	−0.666667
$10$	5.00000	0.158114
$11$	0	0
$11$	0	0
$12$	21.0000	0.505181
$13$	−2.00000	−0.0426692	−0.0213346	−	0.999772i	$-0.506792\pi$
$13$	−2.00000	−0.0426692	−0.0213346	+	0.999772i	$0.506792\pi$
$14$	−9.00000	−0.171811
$15$	15.0000	0.258199
$16$	41.0000	0.640625
$17$	−21.0000	−0.299603	−0.149801	−	0.988716i	$-0.547863\pi$
$17$	−21.0000	−0.299603	−0.149801	+	0.988716i	$0.547863\pi$
$18$	18.0000	0.235702
$19$	85.0000	1.02633	0.513167	−	0.858289i	$-0.328472\pi$
$19$	85.0000	1.02633	0.513167	+	0.858289i	$0.328472\pi$
$20$	35.0000	0.391312
$21$	−27.0000	−0.280566
$22$	0	0
$23$	22.0000	0.199449	0.0997243	−	0.995015i	$-0.468204\pi$
$23$	22.0000	0.199449	0.0997243	+	0.995015i	$0.468204\pi$
$24$	−45.0000	−0.382733
$25$	25.0000	0.200000
$26$	2.00000	0.0150859
$27$	135.000	0.962250
$28$	−63.0000	−0.425210
$29$	165.000	1.05654	0.528271	−	0.849076i	$-0.322840\pi$
$29$	165.000	1.05654	0.528271	+	0.849076i	$0.322840\pi$
$30$	−15.0000	−0.0912871
$31$	−83.0000	−0.480879	−0.240439	−	0.970664i	$-0.577292\pi$
$31$	−83.0000	−0.480879	−0.240439	+	0.970664i	$0.577292\pi$
$32$	−161.000	−0.889408
$33$	0	0
$34$	21.0000	0.105926
$35$	−45.0000	−0.217325
$36$	126.000	0.583333
$37$	1.00000	0.00444322	0.00222161	−	0.999998i	$-0.499293\pi$
$37$	1.00000	0.00444322	0.00222161	+	0.999998i	$0.499293\pi$
$38$	−85.0000	−0.362864
$39$	6.00000	0.0246351
$40$	−75.0000	−0.296464
$41$	478.000	1.82076	0.910379	−	0.413776i	$-0.135790\pi$
$41$	478.000	1.82076	0.910379	+	0.413776i	$0.135790\pi$
$42$	27.0000	0.0991950
$43$	8.00000	0.0283718	0.0141859	−	0.999899i	$-0.495484\pi$
$43$	8.00000	0.0283718	0.0141859	+	0.999899i	$0.495484\pi$
$44$	0	0
$45$	90.0000	0.298142
$46$	−22.0000	−0.0705157
$47$	126.000	0.391042	0.195521	−	0.980699i	$-0.437360\pi$
$47$	126.000	0.391042	0.195521	+	0.980699i	$0.437360\pi$
$48$	−123.000	−0.369865
$49$	−262.000	−0.763848
$50$	−25.0000	−0.0707107
$51$	63.0000	0.172976
$52$	14.0000	0.0373356
$53$	−683.000	−1.77014	−0.885069	−	0.465461i	$-0.845889\pi$
$53$	−683.000	−1.77014	−0.885069	+	0.465461i	$0.845889\pi$
$54$	−135.000	−0.340207
$55$	0	0
$56$	135.000	0.322145
$57$	−255.000	−0.592554
$58$	−165.000	−0.373544
$59$	−290.000	−0.639912	−0.319956	−	0.947432i	$-0.603668\pi$
$59$	−290.000	−0.639912	−0.319956	+	0.947432i	$0.603668\pi$
$60$	−105.000	−0.225924
$61$	−257.000	−0.539434	−0.269717	−	0.962940i	$-0.586930\pi$
$61$	−257.000	−0.539434	−0.269717	+	0.962940i	$0.586930\pi$
$62$	83.0000	0.170016
$63$	−162.000	−0.323970
$64$	−167.000	−0.326172
$65$	10.0000	0.0190823
$66$	0	0
$67$	776.000	1.41498	0.707489	−	0.706725i	$-0.249828\pi$
$67$	776.000	1.41498	0.707489	+	0.706725i	$0.249828\pi$
$68$	147.000	0.262152
$69$	−66.0000	−0.115152
$70$	45.0000	0.0768361
$71$	−313.000	−0.523187	−0.261593	−	0.965178i	$-0.584248\pi$
$71$	−313.000	−0.523187	−0.261593	+	0.965178i	$0.584248\pi$
$72$	−270.000	−0.441942
$73$	−902.000	−1.44618	−0.723090	−	0.690754i	$-0.757279\pi$
$73$	−902.000	−1.44618	−0.723090	+	0.690754i	$0.757279\pi$
$74$	−1.00000	−0.00157091
$75$	−75.0000	−0.115470
$76$	−595.000	−0.898042
$77$	0	0
$78$	−6.00000	−0.00870982
$79$	−830.000	−1.18205	−0.591027	−	0.806652i	$-0.701277\pi$
$79$	−830.000	−1.18205	−0.591027	+	0.806652i	$0.701277\pi$
$80$	−205.000	−0.286496
$81$	81.0000	0.111111
$82$	−478.000	−0.643735
$83$	−842.000	−1.11351	−0.556756	−	0.830676i	$-0.687954\pi$
$83$	−842.000	−1.11351	−0.556756	+	0.830676i	$0.687954\pi$
$84$	189.000	0.245495
$85$	105.000	0.133986
$86$	−8.00000	−0.0100310
$87$	−495.000	−0.609995
$88$	0	0
$89$	25.0000	0.0297752	0.0148876	−	0.999889i	$-0.495261\pi$
$89$	25.0000	0.0297752	0.0148876	+	0.999889i	$0.495261\pi$
$90$	−90.0000	−0.105409
$91$	−18.0000	−0.0207353
$92$	−154.000	−0.174517
$93$	249.000	0.277635
$94$	−126.000	−0.138254
$95$	−425.000	−0.458990
$96$	483.000	0.513500
$97$	−1784.00	−1.86740	−0.933700	−	0.358057i	$-0.883439\pi$
$97$	−1784.00	−1.86740	−0.933700	+	0.358057i	$0.883439\pi$
$98$	262.000	0.270061
$99$	0	0
$100$	−175.000	−0.175000
$101$	298.000	0.293585	0.146793	−	0.989167i	$-0.453105\pi$
$101$	298.000	0.293585	0.146793	+	0.989167i	$0.453105\pi$
$102$	−63.0000	−0.0611562
$103$	1832.00	1.75255	0.876273	−	0.481814i	$-0.160022\pi$
$103$	1832.00	1.75255	0.876273	+	0.481814i	$0.160022\pi$
$104$	−30.0000	−0.0282860
$105$	135.000	0.125473
$106$	683.000	0.625838
$107$	1404.00	1.26850	0.634251	−	0.773127i	$-0.281308\pi$
$107$	1404.00	1.26850	0.634251	+	0.773127i	$0.281308\pi$
$108$	−945.000	−0.841969
$109$	−1050.00	−0.922677	−0.461338	−	0.887224i	$-0.652631\pi$
$109$	−1050.00	−0.922677	−0.461338	+	0.887224i	$0.652631\pi$
$110$	0	0
$111$	−3.00000	−0.00256529
$112$	369.000	0.311314
$113$	−1668.00	−1.38860	−0.694302	−	0.719684i	$-0.744287\pi$
$113$	−1668.00	−1.38860	−0.694302	+	0.719684i	$0.744287\pi$
$114$	255.000	0.209499
$115$	−110.000	−0.0891961
$116$	−1155.00	−0.924475
$117$	36.0000	0.0284462
$118$	290.000	0.226243
$119$	−189.000	−0.145593
$120$	225.000	0.171163
$121$	0	0
$122$	257.000	0.190719
$123$	−1434.00	−1.05121
$124$	581.000	0.420769
$125$	−125.000	−0.0894427
$126$	162.000	0.114541
$127$	2384.00	1.66571	0.832857	−	0.553488i	$-0.186703\pi$
$127$	2384.00	1.66571	0.832857	+	0.553488i	$0.186703\pi$
$128$	1455.00	1.00473
$129$	−24.0000	−0.0163805
$130$	−10.0000	−0.00674660
$131$	−1167.00	−0.778330	−0.389165	−	0.921168i	$-0.627236\pi$
$131$	−1167.00	−0.778330	−0.389165	+	0.921168i	$0.627236\pi$
$132$	0	0
$133$	765.000	0.498751
$134$	−776.000	−0.500270
$135$	−675.000	−0.430331
$136$	−315.000	−0.198610
$137$	−1164.00	−0.725892	−0.362946	−	0.931810i	$-0.618229\pi$
$137$	−1164.00	−0.725892	−0.362946	+	0.931810i	$0.618229\pi$
$138$	66.0000	0.0407123
$139$	−1260.00	−0.768862	−0.384431	−	0.923154i	$-0.625602\pi$
$139$	−1260.00	−0.768862	−0.384431	+	0.923154i	$0.625602\pi$
$140$	315.000	0.190160
$141$	−378.000	−0.225768
$142$	313.000	0.184974
$143$	0	0
$144$	−738.000	−0.427083
$145$	−825.000	−0.472500
$146$	902.000	0.511302
$147$	786.000	0.441008
$148$	−7.00000	−0.00388781
$149$	55.0000	0.0302401	0.0151201	−	0.999886i	$-0.495187\pi$
$149$	55.0000	0.0302401	0.0151201	+	0.999886i	$0.495187\pi$
$150$	75.0000	0.0408248
$151$	598.000	0.322282	0.161141	−	0.986931i	$-0.448483\pi$
$151$	598.000	0.322282	0.161141	+	0.986931i	$0.448483\pi$
$152$	1275.00	0.680369
$153$	378.000	0.199735
$154$	0	0
$155$	415.000	0.215055
$156$	−42.0000	−0.0215557
$157$	1321.00	0.671511	0.335756	−	0.941949i	$-0.391008\pi$
$157$	1321.00	0.671511	0.335756	+	0.941949i	$0.391008\pi$
$158$	830.000	0.417919
$159$	2049.00	1.02199
$160$	805.000	0.397755
$161$	198.000	0.0969229
$162$	−81.0000	−0.0392837
$163$	577.000	0.277265	0.138632	−	0.990344i	$-0.455729\pi$
$163$	577.000	0.277265	0.138632	+	0.990344i	$0.455729\pi$
$164$	−3346.00	−1.59316
$165$	0	0
$166$	842.000	0.393686
$167$	1169.00	0.541676	0.270838	−	0.962625i	$-0.412699\pi$
$167$	1169.00	0.541676	0.270838	+	0.962625i	$0.412699\pi$
$168$	−405.000	−0.185991
$169$	−2193.00	−0.998179
$170$	−105.000	−0.0473714
$171$	−1530.00	−0.684222
$172$	−56.0000	−0.0248253
$173$	−1542.00	−0.677665	−0.338833	−	0.940847i	$-0.610032\pi$
$173$	−1542.00	−0.677665	−0.338833	+	0.940847i	$0.610032\pi$
$174$	495.000	0.215666
$175$	225.000	0.0971909
$176$	0	0
$177$	870.000	0.369453
$178$	−25.0000	−0.0105271
$179$	−560.000	−0.233834	−0.116917	−	0.993142i	$-0.537301\pi$
$179$	−560.000	−0.233834	−0.116917	+	0.993142i	$0.537301\pi$
$180$	−630.000	−0.260875
$181$	−3058.00	−1.25580	−0.627899	−	0.778295i	$-0.716085\pi$
$181$	−3058.00	−1.25580	−0.627899	+	0.778295i	$0.716085\pi$
$182$	18.0000	0.00733104
$183$	771.000	0.311442
$184$	330.000	0.132217
$185$	−5.00000	−0.00198707
$186$	−249.000	−0.0981590
$187$	0	0
$188$	−882.000	−0.342162
$189$	1215.00	0.467610
$190$	425.000	0.162278
$191$	−1828.00	−0.692510	−0.346255	−	0.938140i	$-0.612547\pi$
$191$	−1828.00	−0.692510	−0.346255	+	0.938140i	$0.612547\pi$
$192$	501.000	0.188315
$193$	−577.000	−0.215199	−0.107599	−	0.994194i	$-0.534316\pi$
$193$	−577.000	−0.215199	−0.107599	+	0.994194i	$0.534316\pi$
$194$	1784.00	0.660225
$195$	−30.0000	−0.0110172
$196$	1834.00	0.668367
$197$	2164.00	0.782633	0.391316	−	0.920256i	$-0.372020\pi$
$197$	2164.00	0.782633	0.391316	+	0.920256i	$0.372020\pi$
$198$	0	0
$199$	−4425.00	−1.57628	−0.788141	−	0.615495i	$-0.788956\pi$
$199$	−4425.00	−1.57628	−0.788141	+	0.615495i	$0.788956\pi$
$200$	375.000	0.132583
$201$	−2328.00	−0.816938
$202$	−298.000	−0.103798
$203$	1485.00	0.513431
$204$	−441.000	−0.151354
$205$	−2390.00	−0.814268
$206$	−1832.00	−0.619619
$207$	−396.000	−0.132966
$208$	−82.0000	−0.0273350
$209$	0	0
$210$	−135.000	−0.0443614
$211$	1793.00	0.585001	0.292500	−	0.956265i	$-0.405513\pi$
$211$	1793.00	0.585001	0.292500	+	0.956265i	$0.405513\pi$
$212$	4781.00	1.54887
$213$	939.000	0.302062
$214$	−1404.00	−0.448483
$215$	−40.0000	−0.0126883
$216$	2025.00	0.637888
$217$	−747.000	−0.233685
$218$	1050.00	0.326215
$219$	2706.00	0.834952
$220$	0	0
$221$	42.0000	0.0127838
$222$	3.00000	0.000906968 0
$223$	1142.00	0.342933	0.171466	−	0.985190i	$-0.445150\pi$
$223$	1142.00	0.342933	0.171466	+	0.985190i	$0.445150\pi$
$224$	−1449.00	−0.432212
$225$	−450.000	−0.133333
$226$	1668.00	0.490946
$227$	−4906.00	−1.43446	−0.717231	−	0.696836i	$-0.754591\pi$
$227$	−4906.00	−1.43446	−0.717231	+	0.696836i	$0.754591\pi$
$228$	1785.00	0.518485
$229$	1130.00	0.326081	0.163040	−	0.986619i	$-0.447870\pi$
$229$	1130.00	0.326081	0.163040	+	0.986619i	$0.447870\pi$
$230$	110.000	0.0315356
$231$	0	0
$232$	2475.00	0.700395
$233$	5403.00	1.51915	0.759576	−	0.650419i	$-0.225407\pi$
$233$	5403.00	1.51915	0.759576	+	0.650419i	$0.225407\pi$
$234$	−36.0000	−0.0100572
$235$	−630.000	−0.174879
$236$	2030.00	0.559923
$237$	2490.00	0.682459
$238$	189.000	0.0514750
$239$	−5090.00	−1.37759	−0.688797	−	0.724955i	$-0.741861\pi$
$239$	−5090.00	−1.37759	−0.688797	+	0.724955i	$0.741861\pi$
$240$	615.000	0.165409
$241$	6578.00	1.75820	0.879100	−	0.476637i	$-0.158144\pi$
$241$	6578.00	1.75820	0.879100	+	0.476637i	$0.158144\pi$
$242$	0	0
$243$	−3888.00	−1.02640
$244$	1799.00	0.472005
$245$	1310.00	0.341603
$246$	1434.00	0.371661
$247$	−170.000	−0.0437929
$248$	−1245.00	−0.318781
$249$	2526.00	0.642887
$250$	125.000	0.0316228
$251$	3102.00	0.780066	0.390033	−	0.920801i	$-0.372464\pi$
$251$	3102.00	0.780066	0.390033	+	0.920801i	$0.372464\pi$
$252$	1134.00	0.283473
$253$	0	0
$254$	−2384.00	−0.588919
$255$	−315.000	−0.0773571
$256$	−119.000	−0.0290527
$257$	4866.00	1.18106	0.590531	−	0.807015i	$-0.298918\pi$
$257$	4866.00	1.18106	0.590531	+	0.807015i	$0.298918\pi$
$258$	24.0000	0.00579137
$259$	9.00000	0.00215920
$260$	−70.0000	−0.0166970
$261$	−2970.00	−0.704362
$262$	1167.00	0.275181
$263$	2163.00	0.507134	0.253567	−	0.967318i	$-0.418396\pi$
$263$	2163.00	0.507134	0.253567	+	0.967318i	$0.418396\pi$
$264$	0	0
$265$	3415.00	0.791629
$266$	−765.000	−0.176335
$267$	−75.0000	−0.0171907
$268$	−5432.00	−1.23811
$269$	7020.00	1.59114	0.795571	−	0.605861i	$-0.207171\pi$
$269$	7020.00	1.59114	0.795571	+	0.605861i	$0.207171\pi$
$270$	675.000	0.152145
$271$	−4812.00	−1.07863	−0.539314	−	0.842105i	$-0.681316\pi$
$271$	−4812.00	−1.07863	−0.539314	+	0.842105i	$0.681316\pi$
$272$	−861.000	−0.191933
$273$	54.0000	0.0119715
$274$	1164.00	0.256642
$275$	0	0
$276$	462.000	0.100758
$277$	−5176.00	−1.12273	−0.561364	−	0.827569i	$-0.689723\pi$
$277$	−5176.00	−1.12273	−0.561364	+	0.827569i	$0.689723\pi$
$278$	1260.00	0.271834
$279$	1494.00	0.320586
$280$	−675.000	−0.144068
$281$	−1242.00	−0.263671	−0.131835	−	0.991272i	$-0.542087\pi$
$281$	−1242.00	−0.263671	−0.131835	+	0.991272i	$0.542087\pi$
$282$	378.000	0.0798212
$283$	−7402.00	−1.55478	−0.777391	−	0.629018i	$-0.783457\pi$
$283$	−7402.00	−1.55478	−0.777391	+	0.629018i	$0.783457\pi$
$284$	2191.00	0.457788
$285$	1275.00	0.264998
$286$	0	0
$287$	4302.00	0.884805
$288$	2898.00	0.592938
$289$	−4472.00	−0.910238
$290$	825.000	0.167054
$291$	5352.00	1.07814
$292$	6314.00	1.26541
$293$	3578.00	0.713410	0.356705	−	0.934217i	$-0.383900\pi$
$293$	3578.00	0.713410	0.356705	+	0.934217i	$0.383900\pi$
$294$	−786.000	−0.155920
$295$	1450.00	0.286177
$296$	15.0000	0.00294546
$297$	0	0
$298$	−55.0000	−0.0106915
$299$	−44.0000	−0.00851032
$300$	525.000	0.101036
$301$	72.0000	0.0137874
$302$	−598.000	−0.113944
$303$	−894.000	−0.169502
$304$	3485.00	0.657495
$305$	1285.00	0.241242
$306$	−378.000	−0.0706171
$307$	9094.00	1.69063	0.845313	−	0.534272i	$-0.179414\pi$
$307$	9094.00	1.69063	0.845313	+	0.534272i	$0.179414\pi$
$308$	0	0
$309$	−5496.00	−1.01183
$310$	−415.000	−0.0760336
$311$	−7443.00	−1.35709	−0.678543	−	0.734561i	$-0.737388\pi$
$311$	−7443.00	−1.35709	−0.678543	+	0.734561i	$0.737388\pi$
$312$	90.0000	0.0163309
$313$	2822.00	0.509613	0.254807	−	0.966992i	$-0.417988\pi$
$313$	2822.00	0.509613	0.254807	+	0.966992i	$0.417988\pi$
$314$	−1321.00	−0.237415
$315$	810.000	0.144884
$316$	5810.00	1.03430
$317$	−1869.00	−0.331147	−0.165573	−	0.986197i	$-0.552947\pi$
$317$	−1869.00	−0.331147	−0.165573	+	0.986197i	$0.552947\pi$
$318$	−2049.00	−0.361328
$319$	0	0
$320$	835.000	0.145868
$321$	−4212.00	−0.732370
$322$	−198.000	−0.0342674
$323$	−1785.00	−0.307492
$324$	−567.000	−0.0972222
$325$	−50.0000	−0.00853385
$326$	−577.000	−0.0980278
$327$	3150.00	0.532708
$328$	7170.00	1.20700
$329$	1134.00	0.190029
$330$	0	0
$331$	−11408.0	−1.89438	−0.947191	−	0.320670i	$-0.896092\pi$
$331$	−11408.0	−1.89438	−0.947191	+	0.320670i	$0.896092\pi$
$332$	5894.00	0.974323
$333$	−18.0000	−0.00296214
$334$	−1169.00	−0.191511
$335$	−3880.00	−0.632797
$336$	−1107.00	−0.179738
$337$	−10251.0	−1.65700	−0.828498	−	0.559992i	$-0.810804\pi$
$337$	−10251.0	−1.65700	−0.828498	+	0.559992i	$0.810804\pi$
$338$	2193.00	0.352910
$339$	5004.00	0.801711
$340$	−735.000	−0.117238
$341$	0	0
$342$	1530.00	0.241909
$343$	−5445.00	−0.857150
$344$	120.000	0.0188080
$345$	330.000	0.0514974
$346$	1542.00	0.239591
$347$	11494.0	1.77819	0.889093	−	0.457727i	$-0.151336\pi$
$347$	11494.0	1.77819	0.889093	+	0.457727i	$0.151336\pi$
$348$	3465.00	0.533746
$349$	−5690.00	−0.872718	−0.436359	−	0.899773i	$-0.643732\pi$
$349$	−5690.00	−0.872718	−0.436359	+	0.899773i	$0.643732\pi$
$350$	−225.000	−0.0343622
$351$	−270.000	−0.0410585
$352$	0	0
$353$	−4398.00	−0.663122	−0.331561	−	0.943434i	$-0.607575\pi$
$353$	−4398.00	−0.663122	−0.331561	+	0.943434i	$0.607575\pi$
$354$	−870.000	−0.130621
$355$	1565.00	0.233976
$356$	−175.000	−0.0260533
$357$	567.000	0.0840583
$358$	560.000	0.0826730
$359$	8840.00	1.29960	0.649801	−	0.760104i	$-0.274852\pi$
$359$	8840.00	1.29960	0.649801	+	0.760104i	$0.274852\pi$
$360$	1350.00	0.197642
$361$	366.000	0.0533605
$362$	3058.00	0.443991
$363$	0	0
$364$	126.000	0.0181434
$365$	4510.00	0.646751
$366$	−771.000	−0.110112
$367$	−5564.00	−0.791385	−0.395693	−	0.918383i	$-0.629495\pi$
$367$	−5564.00	−0.791385	−0.395693	+	0.918383i	$0.629495\pi$
$368$	902.000	0.127772
$369$	−8604.00	−1.21384
$370$	5.00000	0.000702534 0
$371$	−6147.00	−0.860206
$372$	−1743.00	−0.242931
$373$	−9222.00	−1.28015	−0.640076	−	0.768311i	$-0.721097\pi$
$373$	−9222.00	−1.28015	−0.640076	+	0.768311i	$0.721097\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	1890.00	0.259227
$377$	−330.000	−0.0450819
$378$	−1215.00	−0.165325
$379$	4670.00	0.632933	0.316467	−	0.948604i	$-0.397503\pi$
$379$	4670.00	0.632933	0.316467	+	0.948604i	$0.397503\pi$
$380$	2975.00	0.401617
$381$	−7152.00	−0.961701
$382$	1828.00	0.244839
$383$	−378.000	−0.0504305	−0.0252153	−	0.999682i	$-0.508027\pi$
$383$	−378.000	−0.0504305	−0.0252153	+	0.999682i	$0.508027\pi$
$384$	−4365.00	−0.580079
$385$	0	0
$386$	577.000	0.0760843
$387$	−144.000	−0.0189146
$388$	12488.0	1.63397
$389$	10110.0	1.31773	0.658865	−	0.752261i	$-0.271037\pi$
$389$	10110.0	1.31773	0.658865	+	0.752261i	$0.271037\pi$
$390$	30.0000	0.00389515
$391$	−462.000	−0.0597554
$392$	−3930.00	−0.506365
$393$	3501.00	0.449369
$394$	−2164.00	−0.276702
$395$	4150.00	0.528631
$396$	0	0
$397$	12186.0	1.54055	0.770274	−	0.637713i	$-0.220119\pi$
$397$	12186.0	1.54055	0.770274	+	0.637713i	$0.220119\pi$
$398$	4425.00	0.557300
$399$	−2295.00	−0.287954
$400$	1025.00	0.128125
$401$	−4573.00	−0.569488	−0.284744	−	0.958604i	$-0.591909\pi$
$401$	−4573.00	−0.569488	−0.284744	+	0.958604i	$0.591909\pi$
$402$	2328.00	0.288831
$403$	166.000	0.0205187
$404$	−2086.00	−0.256887
$405$	−405.000	−0.0496904
$406$	−1485.00	−0.181525
$407$	0	0
$408$	945.000	0.114668
$409$	−2280.00	−0.275645	−0.137822	−	0.990457i	$-0.544010\pi$
$409$	−2280.00	−0.275645	−0.137822	+	0.990457i	$0.544010\pi$
$410$	2390.00	0.287887
$411$	3492.00	0.419094
$412$	−12824.0	−1.53348
$413$	−2610.00	−0.310968
$414$	396.000	0.0470105
$415$	4210.00	0.497978
$416$	322.000	0.0379504
$417$	3780.00	0.443903
$418$	0	0
$419$	−3700.00	−0.431401	−0.215700	−	0.976460i	$-0.569203\pi$
$419$	−3700.00	−0.431401	−0.215700	+	0.976460i	$0.569203\pi$
$420$	−945.000	−0.109789
$421$	3612.00	0.418143	0.209071	−	0.977900i	$-0.432956\pi$
$421$	3612.00	0.418143	0.209071	+	0.977900i	$0.432956\pi$
$422$	−1793.00	−0.206829
$423$	−2268.00	−0.260695
$424$	−10245.0	−1.17345
$425$	−525.000	−0.0599206
$426$	−939.000	−0.106795
$427$	−2313.00	−0.262140
$428$	−9828.00	−1.10994
$429$	0	0
$430$	40.0000	0.00448598
$431$	−792.000	−0.0885135	−0.0442567	−	0.999020i	$-0.514092\pi$
$431$	−792.000	−0.0885135	−0.0442567	+	0.999020i	$0.514092\pi$
$432$	5535.00	0.616442
$433$	−4888.00	−0.542500	−0.271250	−	0.962509i	$-0.587437\pi$
$433$	−4888.00	−0.542500	−0.271250	+	0.962509i	$0.587437\pi$
$434$	747.000	0.0826202
$435$	2475.00	0.272798
$436$	7350.00	0.807342
$437$	1870.00	0.204701
$438$	−2706.00	−0.295200
$439$	−15100.0	−1.64165	−0.820824	−	0.571181i	$-0.806485\pi$
$439$	−15100.0	−1.64165	−0.820824	+	0.571181i	$0.806485\pi$
$440$	0	0
$441$	4716.00	0.509232
$442$	−42.0000	−0.00451977
$443$	−11188.0	−1.19991	−0.599953	−	0.800036i	$-0.704814\pi$
$443$	−11188.0	−1.19991	−0.599953	+	0.800036i	$0.704814\pi$
$444$	21.0000	0.00224463
$445$	−125.000	−0.0133159
$446$	−1142.00	−0.121245
$447$	−165.000	−0.0174591
$448$	−1503.00	−0.158505
$449$	−12070.0	−1.26864	−0.634319	−	0.773071i	$-0.718719\pi$
$449$	−12070.0	−1.26864	−0.634319	+	0.773071i	$0.718719\pi$
$450$	450.000	0.0471405
$451$	0	0
$452$	11676.0	1.21503
$453$	−1794.00	−0.186069
$454$	4906.00	0.507159
$455$	90.0000	0.00927311
$456$	−3825.00	−0.392811
$457$	12449.0	1.27427	0.637133	−	0.770754i	$-0.280120\pi$
$457$	12449.0	1.27427	0.637133	+	0.770754i	$0.280120\pi$
$458$	−1130.00	−0.115287
$459$	−2835.00	−0.288293
$460$	770.000	0.0780466
$461$	−2957.00	−0.298745	−0.149372	−	0.988781i	$-0.547725\pi$
$461$	−2957.00	−0.298745	−0.149372	+	0.988781i	$0.547725\pi$
$462$	0	0
$463$	−9738.00	−0.977458	−0.488729	−	0.872436i	$-0.662539\pi$
$463$	−9738.00	−0.977458	−0.488729	+	0.872436i	$0.662539\pi$
$464$	6765.00	0.676848
$465$	−1245.00	−0.124162
$466$	−5403.00	−0.537101
$467$	−13779.0	−1.36534	−0.682672	−	0.730725i	$-0.739182\pi$
$467$	−13779.0	−1.36534	−0.682672	+	0.730725i	$0.739182\pi$
$468$	−252.000	−0.0248904
$469$	6984.00	0.687614
$470$	630.000	0.0618292
$471$	−3963.00	−0.387697
$472$	−4350.00	−0.424205
$473$	0	0
$474$	−2490.00	−0.241286
$475$	2125.00	0.205267
$476$	1323.00	0.127394
$477$	12294.0	1.18009
$478$	5090.00	0.487053
$479$	−16320.0	−1.55674	−0.778371	−	0.627804i	$-0.783954\pi$
$479$	−16320.0	−1.55674	−0.778371	+	0.627804i	$0.783954\pi$
$480$	−2415.00	−0.229644
$481$	−2.00000	−0.000189589 0
$482$	−6578.00	−0.621618
$483$	−594.000	−0.0559585
$484$	0	0
$485$	8920.00	0.835126
$486$	3888.00	0.362887
$487$	−2744.00	−0.255323	−0.127662	−	0.991818i	$-0.540747\pi$
$487$	−2744.00	−0.255323	−0.127662	+	0.991818i	$0.540747\pi$
$488$	−3855.00	−0.357598
$489$	−1731.00	−0.160079
$490$	−1310.00	−0.120775
$491$	853.000	0.0784019	0.0392010	−	0.999231i	$-0.487519\pi$
$491$	853.000	0.0784019	0.0392010	+	0.999231i	$0.487519\pi$
$492$	10038.0	0.919813
$493$	−3465.00	−0.316543
$494$	170.000	0.0154831
$495$	0	0
$496$	−3403.00	−0.308063
$497$	−2817.00	−0.254245
$498$	−2526.00	−0.227295
$499$	−6840.00	−0.613628	−0.306814	−	0.951769i	$-0.599263\pi$
$499$	−6840.00	−0.613628	−0.306814	+	0.951769i	$0.599263\pi$
$500$	875.000	0.0782624
$501$	−3507.00	−0.312737
$502$	−3102.00	−0.275795
$503$	5128.00	0.454565	0.227283	−	0.973829i	$-0.427016\pi$
$503$	5128.00	0.454565	0.227283	+	0.973829i	$0.427016\pi$
$504$	−2430.00	−0.214763
$505$	−1490.00	−0.131295
$506$	0	0
$507$	6579.00	0.576299
$508$	−16688.0	−1.45750
$509$	−18160.0	−1.58139	−0.790695	−	0.612210i	$-0.790281\pi$
$509$	−18160.0	−1.58139	−0.790695	+	0.612210i	$0.790281\pi$
$510$	315.000	0.0273499
$511$	−8118.00	−0.702777
$512$	−11521.0	−0.994455
$513$	11475.0	0.987590
$514$	−4866.00	−0.417568
$515$	−9160.00	−0.783763
$516$	168.000	0.0143329
$517$	0	0
$518$	−9.00000	−0.000763392 0
$519$	4626.00	0.391250
$520$	150.000	0.0126499
$521$	6462.00	0.543388	0.271694	−	0.962384i	$-0.412416\pi$
$521$	6462.00	0.543388	0.271694	+	0.962384i	$0.412416\pi$
$522$	2970.00	0.249029
$523$	−5932.00	−0.495962	−0.247981	−	0.968765i	$-0.579767\pi$
$523$	−5932.00	−0.495962	−0.247981	+	0.968765i	$0.579767\pi$
$524$	8169.00	0.681039
$525$	−675.000	−0.0561132
$526$	−2163.00	−0.179299
$527$	1743.00	0.144073
$528$	0	0
$529$	−11683.0	−0.960220
$530$	−3415.00	−0.279883
$531$	5220.00	0.426608
$532$	−5355.00	−0.436407
$533$	−956.000	−0.0776904
$534$	75.0000	0.00607784
$535$	−7020.00	−0.567292
$536$	11640.0	0.938006
$537$	1680.00	0.135004
$538$	−7020.00	−0.562553
$539$	0	0
$540$	4725.00	0.376540
$541$	−12647.0	−1.00506	−0.502530	−	0.864560i	$-0.667597\pi$
$541$	−12647.0	−1.00506	−0.502530	+	0.864560i	$0.667597\pi$
$542$	4812.00	0.381353
$543$	9174.00	0.725035
$544$	3381.00	0.266469
$545$	5250.00	0.412634
$546$	−54.0000	−0.00423258
$547$	13524.0	1.05712	0.528560	−	0.848896i	$-0.322732\pi$
$547$	13524.0	1.05712	0.528560	+	0.848896i	$0.322732\pi$
$548$	8148.00	0.635156
$549$	4626.00	0.359623
$550$	0	0
$551$	14025.0	1.08436
$552$	−990.000	−0.0763355
$553$	−7470.00	−0.574424
$554$	5176.00	0.396944
$555$	15.0000	0.00114723
$556$	8820.00	0.672754
$557$	−25066.0	−1.90679	−0.953394	−	0.301729i	$-0.902436\pi$
$557$	−25066.0	−1.90679	−0.953394	+	0.301729i	$0.902436\pi$
$558$	−1494.00	−0.113344
$559$	−16.0000	−0.00121060
$560$	−1845.00	−0.139224
$561$	0	0
$562$	1242.00	0.0932217
$563$	−12102.0	−0.905930	−0.452965	−	0.891528i	$-0.649634\pi$
$563$	−12102.0	−0.905930	−0.452965	+	0.891528i	$0.649634\pi$
$564$	2646.00	0.197547
$565$	8340.00	0.621003
$566$	7402.00	0.549698
$567$	729.000	0.0539949
$568$	−4695.00	−0.346827
$569$	20860.0	1.53690	0.768451	−	0.639909i	$-0.221028\pi$
$569$	20860.0	1.53690	0.768451	+	0.639909i	$0.221028\pi$
$570$	−1275.00	−0.0936910
$571$	−20637.0	−1.51249	−0.756245	−	0.654289i	$-0.772968\pi$
$571$	−20637.0	−1.51249	−0.756245	+	0.654289i	$0.772968\pi$
$572$	0	0
$573$	5484.00	0.399821
$574$	−4302.00	−0.312826
$575$	550.000	0.0398897
$576$	3006.00	0.217448
$577$	3266.00	0.235642	0.117821	−	0.993035i	$-0.462409\pi$
$577$	3266.00	0.235642	0.117821	+	0.993035i	$0.462409\pi$
$578$	4472.00	0.321818
$579$	1731.00	0.124245
$580$	5775.00	0.413438
$581$	−7578.00	−0.541116
$582$	−5352.00	−0.381181
$583$	0	0
$584$	−13530.0	−0.958691
$585$	−180.000	−0.0127215
$586$	−3578.00	−0.252228
$587$	3351.00	0.235623	0.117811	−	0.993036i	$-0.462412\pi$
$587$	3351.00	0.235623	0.117811	+	0.993036i	$0.462412\pi$
$588$	−5502.00	−0.385882
$589$	−7055.00	−0.493542
$590$	−1450.00	−0.101179
$591$	−6492.00	−0.451853
$592$	41.0000	0.00284644
$593$	20258.0	1.40286	0.701430	−	0.712738i	$-0.252545\pi$
$593$	20258.0	1.40286	0.701430	+	0.712738i	$0.252545\pi$
$594$	0	0
$595$	945.000	0.0651113
$596$	−385.000	−0.0264601
$597$	13275.0	0.910066
$598$	44.0000	0.00300885
$599$	20445.0	1.39459	0.697296	−	0.716784i	$-0.254387\pi$
$599$	20445.0	1.39459	0.697296	+	0.716784i	$0.254387\pi$
$600$	−1125.00	−0.0765466
$601$	1498.00	0.101672	0.0508359	−	0.998707i	$-0.483811\pi$
$601$	1498.00	0.101672	0.0508359	+	0.998707i	$0.483811\pi$
$602$	−72.0000	−0.00487459
$603$	−13968.0	−0.943318
$604$	−4186.00	−0.281997
$605$	0	0
$606$	894.000	0.0599278
$607$	−23461.0	−1.56879	−0.784393	−	0.620265i	$-0.787025\pi$
$607$	−23461.0	−1.56879	−0.784393	+	0.620265i	$0.787025\pi$
$608$	−13685.0	−0.912829
$609$	−4455.00	−0.296430
$610$	−1285.00	−0.0852920
$611$	−252.000	−0.0166855
$612$	−2646.00	−0.174768
$613$	1718.00	0.113196	0.0565982	−	0.998397i	$-0.481975\pi$
$613$	1718.00	0.113196	0.0565982	+	0.998397i	$0.481975\pi$
$614$	−9094.00	−0.597726
$615$	7170.00	0.470118
$616$	0	0
$617$	26276.0	1.71448	0.857238	−	0.514920i	$-0.172178\pi$
$617$	26276.0	1.71448	0.857238	+	0.514920i	$0.172178\pi$
$618$	5496.00	0.357737
$619$	−15560.0	−1.01035	−0.505177	−	0.863016i	$-0.668573\pi$
$619$	−15560.0	−1.01035	−0.505177	+	0.863016i	$0.668573\pi$
$620$	−2905.00	−0.188174
$621$	2970.00	0.191919
$622$	7443.00	0.479802
$623$	225.000	0.0144694
$624$	246.000	0.0157819
$625$	625.000	0.0400000
$626$	−2822.00	−0.180175
$627$	0	0
$628$	−9247.00	−0.587572
$629$	−21.0000	−0.00133120
$630$	−810.000	−0.0512241
$631$	−28433.0	−1.79382	−0.896910	−	0.442214i	$-0.854193\pi$
$631$	−28433.0	−1.79382	−0.896910	+	0.442214i	$0.854193\pi$
$632$	−12450.0	−0.783599
$633$	−5379.00	−0.337750
$634$	1869.00	0.117078
$635$	−11920.0	−0.744930
$636$	−14343.0	−0.894240
$637$	524.000	0.0325928
$638$	0	0
$639$	5634.00	0.348791
$640$	−7275.00	−0.449328
$641$	9847.00	0.606760	0.303380	−	0.952870i	$-0.401885\pi$
$641$	9847.00	0.606760	0.303380	+	0.952870i	$0.401885\pi$
$642$	4212.00	0.258932
$643$	2177.00	0.133519	0.0667593	−	0.997769i	$-0.478734\pi$
$643$	2177.00	0.133519	0.0667593	+	0.997769i	$0.478734\pi$
$644$	−1386.00	−0.0848075
$645$	120.000	0.00732557
$646$	1785.00	0.108715
$647$	4466.00	0.271370	0.135685	−	0.990752i	$-0.456676\pi$
$647$	4466.00	0.271370	0.135685	+	0.990752i	$0.456676\pi$
$648$	1215.00	0.0736570
$649$	0	0
$650$	50.0000	0.00301717
$651$	2241.00	0.134918
$652$	−4039.00	−0.242607
$653$	11507.0	0.689592	0.344796	−	0.938678i	$-0.387948\pi$
$653$	11507.0	0.689592	0.344796	+	0.938678i	$0.387948\pi$
$654$	−3150.00	−0.188341
$655$	5835.00	0.348080
$656$	19598.0	1.16642
$657$	16236.0	0.964120
$658$	−1134.00	−0.0671853
$659$	−12825.0	−0.758105	−0.379052	−	0.925375i	$-0.623750\pi$
$659$	−12825.0	−0.758105	−0.379052	+	0.925375i	$0.623750\pi$
$660$	0	0
$661$	−8818.00	−0.518881	−0.259441	−	0.965759i	$-0.583538\pi$
$661$	−8818.00	−0.518881	−0.259441	+	0.965759i	$0.583538\pi$
$662$	11408.0	0.669765
$663$	−126.000	−0.00738075
$664$	−12630.0	−0.738161
$665$	−3825.00	−0.223048
$666$	18.0000	0.00104728
$667$	3630.00	0.210726
$668$	−8183.00	−0.473967
$669$	−3426.00	−0.197992
$670$	3880.00	0.223728
$671$	0	0
$672$	4347.00	0.249537
$673$	9263.00	0.530553	0.265277	−	0.964172i	$-0.414537\pi$
$673$	9263.00	0.530553	0.265277	+	0.964172i	$0.414537\pi$
$674$	10251.0	0.585836
$675$	3375.00	0.192450
$676$	15351.0	0.873407
$677$	1184.00	0.0672154	0.0336077	−	0.999435i	$-0.489300\pi$
$677$	1184.00	0.0672154	0.0336077	+	0.999435i	$0.489300\pi$
$678$	−5004.00	−0.283448
$679$	−16056.0	−0.907471
$680$	1575.00	0.0888213
$681$	14718.0	0.828186
$682$	0	0
$683$	−1693.00	−0.0948475	−0.0474238	−	0.998875i	$-0.515101\pi$
$683$	−1693.00	−0.0948475	−0.0474238	+	0.998875i	$0.515101\pi$
$684$	10710.0	0.598695
$685$	5820.00	0.324629
$686$	5445.00	0.303048
$687$	−3390.00	−0.188263
$688$	328.000	0.0181757
$689$	1366.00	0.0755304
$690$	−330.000	−0.0182071
$691$	13022.0	0.716903	0.358452	−	0.933548i	$-0.383305\pi$
$691$	13022.0	0.716903	0.358452	+	0.933548i	$0.383305\pi$
$692$	10794.0	0.592957
$693$	0	0
$694$	−11494.0	−0.628683
$695$	6300.00	0.343845
$696$	−7425.00	−0.404373
$697$	−10038.0	−0.545504
$698$	5690.00	0.308553
$699$	−16209.0	−0.877083
$700$	−1575.00	−0.0850420
$701$	−1177.00	−0.0634161	−0.0317080	−	0.999497i	$-0.510095\pi$
$701$	−1177.00	−0.0634161	−0.0317080	+	0.999497i	$0.510095\pi$
$702$	270.000	0.0145164
$703$	85.0000	0.00456022
$704$	0	0
$705$	1890.00	0.100967
$706$	4398.00	0.234449
$707$	2682.00	0.142669
$708$	−6090.00	−0.323271
$709$	−24130.0	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$709$	−24130.0	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$710$	−1565.00	−0.0827231
$711$	14940.0	0.788036
$712$	375.000	0.0197384
$713$	−1826.00	−0.0959106
$714$	−567.000	−0.0297191
$715$	0	0
$716$	3920.00	0.204605
$717$	15270.0	0.795354
$718$	−8840.00	−0.459479
$719$	13785.0	0.715012	0.357506	−	0.933911i	$-0.383627\pi$
$719$	13785.0	0.715012	0.357506	+	0.933911i	$0.383627\pi$
$720$	3690.00	0.190997
$721$	16488.0	0.851658
$722$	−366.000	−0.0188658
$723$	−19734.0	−1.01510
$724$	21406.0	1.09882
$725$	4125.00	0.211308
$726$	0	0
$727$	−17654.0	−0.900620	−0.450310	−	0.892872i	$-0.648686\pi$
$727$	−17654.0	−0.900620	−0.450310	+	0.892872i	$0.648686\pi$
$728$	−270.000	−0.0137457
$729$	9477.00	0.481481
$730$	−4510.00	−0.228661
$731$	−168.000	−0.00850028
$732$	−5397.00	−0.272512
$733$	−14412.0	−0.726220	−0.363110	−	0.931746i	$-0.618285\pi$
$733$	−14412.0	−0.726220	−0.363110	+	0.931746i	$0.618285\pi$
$734$	5564.00	0.279797
$735$	−3930.00	−0.197225
$736$	−3542.00	−0.177391
$737$	0	0
$738$	8604.00	0.429157
$739$	−16480.0	−0.820334	−0.410167	−	0.912011i	$-0.634530\pi$
$739$	−16480.0	−0.820334	−0.410167	+	0.912011i	$0.634530\pi$
$740$	35.0000	0.00173868
$741$	510.000	0.0252838
$742$	6147.00	0.304129
$743$	−30127.0	−1.48755	−0.743777	−	0.668428i	$-0.766967\pi$
$743$	−30127.0	−1.48755	−0.743777	+	0.668428i	$0.766967\pi$
$744$	3735.00	0.184048
$745$	−275.000	−0.0135238
$746$	9222.00	0.452602
$747$	15156.0	0.742341
$748$	0	0
$749$	12636.0	0.616434
$750$	−375.000	−0.0182574
$751$	36577.0	1.77725	0.888624	−	0.458636i	$-0.151662\pi$
$751$	36577.0	1.77725	0.888624	+	0.458636i	$0.151662\pi$
$752$	5166.00	0.250511
$753$	−9306.00	−0.450371
$754$	330.000	0.0159388
$755$	−2990.00	−0.144129
$756$	−8505.00	−0.409159
$757$	19386.0	0.930774	0.465387	−	0.885107i	$-0.345915\pi$
$757$	19386.0	0.930774	0.465387	+	0.885107i	$0.345915\pi$
$758$	−4670.00	−0.223776
$759$	0	0
$760$	−6375.00	−0.304270
$761$	18218.0	0.867808	0.433904	−	0.900959i	$-0.357136\pi$
$761$	18218.0	0.867808	0.433904	+	0.900959i	$0.357136\pi$
$762$	7152.00	0.340013
$763$	−9450.00	−0.448379
$764$	12796.0	0.605946
$765$	−1890.00	−0.0893243
$766$	378.000	0.0178299
$767$	580.000	0.0273045
$768$	357.000	0.0167736
$769$	−9650.00	−0.452520	−0.226260	−	0.974067i	$-0.572650\pi$
$769$	−9650.00	−0.452520	−0.226260	+	0.974067i	$0.572650\pi$
$770$	0	0
$771$	−14598.0	−0.681886
$772$	4039.00	0.188299
$773$	12617.0	0.587066	0.293533	−	0.955949i	$-0.405169\pi$
$773$	12617.0	0.587066	0.293533	+	0.955949i	$0.405169\pi$
$774$	144.000	0.00668730
$775$	−2075.00	−0.0961757
$776$	−26760.0	−1.23792
$777$	−27.0000	−0.00124661
$778$	−10110.0	−0.465888
$779$	40630.0	1.86870
$780$	210.000	0.00964001
$781$	0	0
$782$	462.000	0.0211267
$783$	22275.0	1.01666
$784$	−10742.0	−0.489340
$785$	−6605.00	−0.300309
$786$	−3501.00	−0.158876
$787$	22364.0	1.01295	0.506474	−	0.862255i	$-0.330949\pi$
$787$	22364.0	1.01295	0.506474	+	0.862255i	$0.330949\pi$
$788$	−15148.0	−0.684803
$789$	−6489.00	−0.292794
$790$	−4150.00	−0.186899
$791$	−15012.0	−0.674798
$792$	0	0
$793$	514.000	0.0230172
$794$	−12186.0	−0.544666
$795$	−10245.0	−0.457047
$796$	30975.0	1.37925
$797$	−17594.0	−0.781947	−0.390973	−	0.920402i	$-0.627862\pi$
$797$	−17594.0	−0.781947	−0.390973	+	0.920402i	$0.627862\pi$
$798$	2295.00	0.101807
$799$	−2646.00	−0.117157
$800$	−4025.00	−0.177882
$801$	−450.000	−0.0198501
$802$	4573.00	0.201344
$803$	0	0
$804$	16296.0	0.714820
$805$	−990.000	−0.0433452
$806$	−166.000	−0.00725447
$807$	−21060.0	−0.918646
$808$	4470.00	0.194621
$809$	45030.0	1.95695	0.978474	−	0.206371i	$-0.0661655\pi$
$809$	45030.0	1.95695	0.978474	+	0.206371i	$0.0661655\pi$
$810$	405.000	0.0175682
$811$	2943.00	0.127426	0.0637131	−	0.997968i	$-0.479706\pi$
$811$	2943.00	0.127426	0.0637131	+	0.997968i	$0.479706\pi$
$812$	−10395.0	−0.449252
$813$	14436.0	0.622746
$814$	0	0
$815$	−2885.00	−0.123996
$816$	2583.00	0.110813
$817$	680.000	0.0291190
$818$	2280.00	0.0974552
$819$	324.000	0.0138235
$820$	16730.0	0.712484
$821$	4038.00	0.171653	0.0858265	−	0.996310i	$-0.472647\pi$
$821$	4038.00	0.171653	0.0858265	+	0.996310i	$0.472647\pi$
$822$	−3492.00	−0.148172
$823$	−5688.00	−0.240913	−0.120456	−	0.992719i	$-0.538436\pi$
$823$	−5688.00	−0.240913	−0.120456	+	0.992719i	$0.538436\pi$
$824$	27480.0	1.16179
$825$	0	0
$826$	2610.00	0.109944
$827$	16824.0	0.707410	0.353705	−	0.935357i	$-0.384922\pi$
$827$	16824.0	0.707410	0.353705	+	0.935357i	$0.384922\pi$
$828$	2772.00	0.116345
$829$	−22940.0	−0.961085	−0.480542	−	0.876972i	$-0.659560\pi$
$829$	−22940.0	−0.961085	−0.480542	+	0.876972i	$0.659560\pi$
$830$	−4210.00	−0.176062
$831$	15528.0	0.648207
$832$	334.000	0.0139175
$833$	5502.00	0.228851
$834$	−3780.00	−0.156943
$835$	−5845.00	−0.242245
$836$	0	0
$837$	−11205.0	−0.462726
$838$	3700.00	0.152523
$839$	12040.0	0.495431	0.247716	−	0.968833i	$-0.420320\pi$
$839$	12040.0	0.495431	0.247716	+	0.968833i	$0.420320\pi$
$840$	2025.00	0.0831775
$841$	2836.00	0.116282
$842$	−3612.00	−0.147836
$843$	3726.00	0.152230
$844$	−12551.0	−0.511876
$845$	10965.0	0.446399
$846$	2268.00	0.0921696
$847$	0	0
$848$	−28003.0	−1.13399
$849$	22206.0	0.897654
$850$	525.000	0.0211851
$851$	22.0000	0.000886193 0
$852$	−6573.00	−0.264304
$853$	14338.0	0.575526	0.287763	−	0.957702i	$-0.407088\pi$
$853$	14338.0	0.575526	0.287763	+	0.957702i	$0.407088\pi$
$854$	2313.00	0.0926806
$855$	7650.00	0.305994
$856$	21060.0	0.840907
$857$	17619.0	0.702280	0.351140	−	0.936323i	$-0.385794\pi$
$857$	17619.0	0.702280	0.351140	+	0.936323i	$0.385794\pi$
$858$	0	0
$859$	−25550.0	−1.01485	−0.507424	−	0.861696i	$-0.669402\pi$
$859$	−25550.0	−1.01485	−0.507424	+	0.861696i	$0.669402\pi$
$860$	280.000	0.0111022
$861$	−12906.0	−0.510842
$862$	792.000	0.0312942
$863$	36922.0	1.45636	0.728180	−	0.685385i	$-0.240366\pi$
$863$	36922.0	1.45636	0.728180	+	0.685385i	$0.240366\pi$
$864$	−21735.0	−0.855833
$865$	7710.00	0.303061
$866$	4888.00	0.191803
$867$	13416.0	0.525526
$868$	5229.00	0.204474
$869$	0	0
$870$	−2475.00	−0.0964487
$871$	−1552.00	−0.0603760
$872$	−15750.0	−0.611654
$873$	32112.0	1.24493
$874$	−1870.00	−0.0723726
$875$	−1125.00	−0.0434651
$876$	−18942.0	−0.730583
$877$	−11486.0	−0.442252	−0.221126	−	0.975245i	$-0.570973\pi$
$877$	−11486.0	−0.442252	−0.221126	+	0.975245i	$0.570973\pi$
$878$	15100.0	0.580410
$879$	−10734.0	−0.411887
$880$	0	0
$881$	−2958.00	−0.113119	−0.0565593	−	0.998399i	$-0.518013\pi$
$881$	−2958.00	−0.113119	−0.0565593	+	0.998399i	$0.518013\pi$
$882$	−4716.00	−0.180041
$883$	−5173.00	−0.197152	−0.0985761	−	0.995130i	$-0.531429\pi$
$883$	−5173.00	−0.197152	−0.0985761	+	0.995130i	$0.531429\pi$
$884$	−294.000	−0.0111858
$885$	−4350.00	−0.165224
$886$	11188.0	0.424230
$887$	33424.0	1.26524	0.632620	−	0.774462i	$-0.281979\pi$
$887$	33424.0	1.26524	0.632620	+	0.774462i	$0.281979\pi$
$888$	−45.0000	−0.00170056
$889$	21456.0	0.809461
$890$	125.000	0.00470788
$891$	0	0
$892$	−7994.00	−0.300066
$893$	10710.0	0.401340
$894$	165.000	0.00617274
$895$	2800.00	0.104574
$896$	13095.0	0.488251
$897$	132.000	0.00491344
$898$	12070.0	0.448531
$899$	−13695.0	−0.508069
$900$	3150.00	0.116667
$901$	14343.0	0.530338
$902$	0	0
$903$	−216.000	−0.00796017
$904$	−25020.0	−0.920523
$905$	15290.0	0.561610
$906$	1794.00	0.0657855
$907$	27101.0	0.992143	0.496072	−	0.868282i	$-0.334775\pi$
$907$	27101.0	0.992143	0.496072	+	0.868282i	$0.334775\pi$
$908$	34342.0	1.25515
$909$	−5364.00	−0.195723
$910$	−90.0000	−0.00327854
$911$	−23893.0	−0.868947	−0.434473	−	0.900685i	$-0.643065\pi$
$911$	−23893.0	−0.868947	−0.434473	+	0.900685i	$0.643065\pi$
$912$	−10455.0	−0.379605
$913$	0	0
$914$	−12449.0	−0.450521
$915$	−3855.00	−0.139281
$916$	−7910.00	−0.285321
$917$	−10503.0	−0.378233
$918$	2835.00	0.101927
$919$	34980.0	1.25559	0.627793	−	0.778380i	$-0.283958\pi$
$919$	34980.0	1.25559	0.627793	+	0.778380i	$0.283958\pi$
$920$	−1650.00	−0.0591292
$921$	−27282.0	−0.976083
$922$	2957.00	0.105622
$923$	626.000	0.0223240
$924$	0	0
$925$	25.0000	0.000888643 0
$926$	9738.00	0.345584
$927$	−32976.0	−1.16836
$928$	−26565.0	−0.939697
$929$	21595.0	0.762658	0.381329	−	0.924439i	$-0.375467\pi$
$929$	21595.0	0.762658	0.381329	+	0.924439i	$0.375467\pi$
$930$	1245.00	0.0438980
$931$	−22270.0	−0.783963
$932$	−37821.0	−1.32926
$933$	22329.0	0.783514
$934$	13779.0	0.482722
$935$	0	0
$936$	540.000	0.0188573
$937$	−31446.0	−1.09637	−0.548184	−	0.836358i	$-0.684680\pi$
$937$	−31446.0	−1.09637	−0.548184	+	0.836358i	$0.684680\pi$
$938$	−6984.00	−0.243108
$939$	−8466.00	−0.294225
$940$	4410.00	0.153020
$941$	24353.0	0.843661	0.421831	−	0.906675i	$-0.361388\pi$
$941$	24353.0	0.843661	0.421831	+	0.906675i	$0.361388\pi$
$942$	3963.00	0.137072
$943$	10516.0	0.363147
$944$	−11890.0	−0.409943
$945$	−6075.00	−0.209121
$946$	0	0
$947$	−22089.0	−0.757968	−0.378984	−	0.925403i	$-0.623727\pi$
$947$	−22089.0	−0.757968	−0.378984	+	0.925403i	$0.623727\pi$
$948$	−17430.0	−0.597152
$949$	1804.00	0.0617074
$950$	−2125.00	−0.0725727
$951$	5607.00	0.191188
$952$	−2835.00	−0.0965156
$953$	37893.0	1.28801	0.644006	−	0.765021i	$-0.277271\pi$
$953$	37893.0	1.28801	0.644006	+	0.765021i	$0.277271\pi$
$954$	−12294.0	−0.417225
$955$	9140.00	0.309700
$956$	35630.0	1.20539
$957$	0	0
$958$	16320.0	0.550392
$959$	−10476.0	−0.352750
$960$	−2505.00	−0.0842172
$961$	−22902.0	−0.768756
$962$	2.00000	6.70297e−5 0
$963$	−25272.0	−0.845669
$964$	−46046.0	−1.53843
$965$	2885.00	0.0962398
$966$	594.000	0.0197843
$967$	−40601.0	−1.35020	−0.675098	−	0.737728i	$-0.735899\pi$
$967$	−40601.0	−1.35020	−0.675098	+	0.737728i	$0.735899\pi$
$968$	0	0
$969$	5355.00	0.177531
$970$	−8920.00	−0.295262
$971$	−1188.00	−0.0392634	−0.0196317	−	0.999807i	$-0.506249\pi$
$971$	−1188.00	−0.0392634	−0.0196317	+	0.999807i	$0.506249\pi$
$972$	27216.0	0.898100
$973$	−11340.0	−0.373632
$974$	2744.00	0.0902705
$975$	150.000	0.00492702
$976$	−10537.0	−0.345575
$977$	−17024.0	−0.557468	−0.278734	−	0.960368i	$-0.589915\pi$
$977$	−17024.0	−0.557468	−0.278734	+	0.960368i	$0.589915\pi$
$978$	1731.00	0.0565964
$979$	0	0
$980$	−9170.00	−0.298903
$981$	18900.0	0.615118
$982$	−853.000	−0.0277193
$983$	43262.0	1.40371	0.701853	−	0.712322i	$-0.252356\pi$
$983$	43262.0	1.40371	0.701853	+	0.712322i	$0.252356\pi$
$984$	−21510.0	−0.696864
$985$	−10820.0	−0.350004
$986$	3465.00	0.111915
$987$	−3402.00	−0.109713
$988$	1190.00	0.0383188
$989$	176.000	0.00565872
$990$	0	0
$991$	−18328.0	−0.587496	−0.293748	−	0.955883i	$-0.594903\pi$
$991$	−18328.0	−0.587496	−0.293748	+	0.955883i	$0.594903\pi$
$992$	13363.0	0.427697
$993$	34224.0	1.09372
$994$	2817.00	0.0898891
$995$	22125.0	0.704934
$996$	−17682.0	−0.562526
$997$	−34196.0	−1.08626	−0.543128	−	0.839650i	$-0.682760\pi$
$997$	−34196.0	−1.08626	−0.543128	+	0.839650i	$0.682760\pi$
$998$	6840.00	0.216950
$999$	135.000	0.00427549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.4.a.b.1.1		1
11.10	odd	2		55.4.a.a.1.1	✓	1
33.32	even	2		495.4.a.a.1.1		1
44.43	even	2		880.4.a.j.1.1		1
55.32	even	4		275.4.b.a.199.2		2
55.43	even	4		275.4.b.a.199.1		2
55.54	odd	2		275.4.a.a.1.1		1
165.164	even	2		2475.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.4.a.a.1.1	✓	1	11.10	odd	2
275.4.a.a.1.1		1	55.54	odd	2
275.4.b.a.199.1		2	55.43	even	4
275.4.b.a.199.2		2	55.32	even	4
495.4.a.a.1.1		1	33.32	even	2
605.4.a.b.1.1		1	1.1	even	1	trivial
880.4.a.j.1.1		1	44.43	even	2
2475.4.a.h.1.1		1	165.164	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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