LMFDB - Embedded newform 605.4.a.c.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,-5,-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:	yes
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)

$f(q)$

$=$

\(q+1.00000 q^{2} -5.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} -5.00000 q^{6} +29.0000 q^{7} -15.0000 q^{8} -2.00000 q^{9} +5.00000 q^{10} +35.0000 q^{12} -88.0000 q^{13} +29.0000 q^{14} -25.0000 q^{15} +41.0000 q^{16} +21.0000 q^{17} -2.00000 q^{18} +105.000 q^{19} -35.0000 q^{20} -145.000 q^{21} +160.000 q^{23} +75.0000 q^{24} +25.0000 q^{25} -88.0000 q^{26} +145.000 q^{27} -203.000 q^{28} -165.000 q^{29} -25.0000 q^{30} -85.0000 q^{31} +161.000 q^{32} +21.0000 q^{34} +145.000 q^{35} +14.0000 q^{36} -15.0000 q^{37} +105.000 q^{38} +440.000 q^{39} -75.0000 q^{40} -270.000 q^{41} -145.000 q^{42} +12.0000 q^{43} -10.0000 q^{45} +160.000 q^{46} -370.000 q^{47} -205.000 q^{48} +498.000 q^{49} +25.0000 q^{50} -105.000 q^{51} +616.000 q^{52} -615.000 q^{53} +145.000 q^{54} -435.000 q^{56} -525.000 q^{57} -165.000 q^{58} +396.000 q^{59} +175.000 q^{60} -835.000 q^{61} -85.0000 q^{62} -58.0000 q^{63} -167.000 q^{64} -440.000 q^{65} -540.000 q^{67} -147.000 q^{68} -800.000 q^{69} +145.000 q^{70} -187.000 q^{71} +30.0000 q^{72} -58.0000 q^{73} -15.0000 q^{74} -125.000 q^{75} -735.000 q^{76} +440.000 q^{78} -620.000 q^{79} +205.000 q^{80} -671.000 q^{81} -270.000 q^{82} +828.000 q^{83} +1015.00 q^{84} +105.000 q^{85} +12.0000 q^{86} +825.000 q^{87} -1535.00 q^{89} -10.0000 q^{90} -2552.00 q^{91} -1120.00 q^{92} +425.000 q^{93} -370.000 q^{94} +525.000 q^{95} -805.000 q^{96} -90.0000 q^{97} +498.000 q^{98} +O(q^{100})\)

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	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−5.00000	−0.340207
$7$	29.0000	1.56585	0.782926	−	0.622114i	$-0.213726\pi$
$7$	29.0000	1.56585	0.782926	+	0.622114i	$0.213726\pi$
$8$	−15.0000	−0.662913
$9$	−2.00000	−0.0740741
$10$	5.00000	0.158114
$11$	0	0
$11$	0	0
$12$	35.0000	0.841969
$13$	−88.0000	−1.87745	−0.938723	−	0.344671i	$-0.887990\pi$
$13$	−88.0000	−1.87745	−0.938723	+	0.344671i	$0.887990\pi$
$14$	29.0000	0.553613
$15$	−25.0000	−0.430331
$16$	41.0000	0.640625
$17$	21.0000	0.299603	0.149801	−	0.988716i	$-0.452137\pi$
$17$	21.0000	0.299603	0.149801	+	0.988716i	$0.452137\pi$
$18$	−2.00000	−0.0261891
$19$	105.000	1.26782	0.633912	−	0.773405i	$-0.281448\pi$
$19$	105.000	1.26782	0.633912	+	0.773405i	$0.281448\pi$
$20$	−35.0000	−0.391312
$21$	−145.000	−1.50674
$22$	0	0
$23$	160.000	1.45054	0.725268	−	0.688467i	$-0.241716\pi$
$23$	160.000	1.45054	0.725268	+	0.688467i	$0.241716\pi$
$24$	75.0000	0.637888
$25$	25.0000	0.200000
$26$	−88.0000	−0.663778
$27$	145.000	1.03353
$28$	−203.000	−1.37012
$29$	−165.000	−1.05654	−0.528271	−	0.849076i	$-0.677160\pi$
$29$	−165.000	−1.05654	−0.528271	+	0.849076i	$0.677160\pi$
$30$	−25.0000	−0.152145
$31$	−85.0000	−0.492466	−0.246233	−	0.969211i	$-0.579193\pi$
$31$	−85.0000	−0.492466	−0.246233	+	0.969211i	$0.579193\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	21.0000	0.105926
$35$	145.000	0.700271
$36$	14.0000	0.0648148
$37$	−15.0000	−0.0666482	−0.0333241	−	0.999445i	$-0.510609\pi$
$37$	−15.0000	−0.0666482	−0.0333241	+	0.999445i	$0.510609\pi$
$38$	105.000	0.448243
$39$	440.000	1.80657
$40$	−75.0000	−0.296464
$41$	−270.000	−1.02846	−0.514231	−	0.857652i	$-0.671922\pi$
$41$	−270.000	−1.02846	−0.514231	+	0.857652i	$0.671922\pi$
$42$	−145.000	−0.532714
$43$	12.0000	0.0425577	0.0212789	−	0.999774i	$-0.493226\pi$
$43$	12.0000	0.0425577	0.0212789	+	0.999774i	$0.493226\pi$
$44$	0	0
$45$	−10.0000	−0.0331269
$46$	160.000	0.512842
$47$	−370.000	−1.14830	−0.574149	−	0.818751i	$-0.694667\pi$
$47$	−370.000	−1.14830	−0.574149	+	0.818751i	$0.694667\pi$
$48$	−205.000	−0.616442
$49$	498.000	1.45190
$50$	25.0000	0.0707107
$51$	−105.000	−0.288293
$52$	616.000	1.64277
$53$	−615.000	−1.59390	−0.796950	−	0.604045i	$-0.793555\pi$
$53$	−615.000	−1.59390	−0.796950	+	0.604045i	$0.793555\pi$
$54$	145.000	0.365407
$55$	0	0
$56$	−435.000	−1.03802
$57$	−525.000	−1.21996
$58$	−165.000	−0.373544
$59$	396.000	0.873810	0.436905	−	0.899508i	$-0.356075\pi$
$59$	396.000	0.873810	0.436905	+	0.899508i	$0.356075\pi$
$60$	175.000	0.376540
$61$	−835.000	−1.75264	−0.876318	−	0.481733i	$-0.840007\pi$
$61$	−835.000	−1.75264	−0.876318	+	0.481733i	$0.840007\pi$
$62$	−85.0000	−0.174113
$63$	−58.0000	−0.115989
$64$	−167.000	−0.326172
$65$	−440.000	−0.839620
$66$	0	0
$67$	−540.000	−0.984649	−0.492325	−	0.870412i	$-0.663853\pi$
$67$	−540.000	−0.984649	−0.492325	+	0.870412i	$0.663853\pi$
$68$	−147.000	−0.262152
$69$	−800.000	−1.39578
$70$	145.000	0.247583
$71$	−187.000	−0.312575	−0.156287	−	0.987712i	$-0.549953\pi$
$71$	−187.000	−0.312575	−0.156287	+	0.987712i	$0.549953\pi$
$72$	30.0000	0.0491046
$73$	−58.0000	−0.0929916	−0.0464958	−	0.998918i	$-0.514805\pi$
$73$	−58.0000	−0.0929916	−0.0464958	+	0.998918i	$0.514805\pi$
$74$	−15.0000	−0.0235637
$75$	−125.000	−0.192450
$76$	−735.000	−1.10935
$77$	0	0
$78$	440.000	0.638720
$79$	−620.000	−0.882980	−0.441490	−	0.897266i	$-0.645550\pi$
$79$	−620.000	−0.882980	−0.441490	+	0.897266i	$0.645550\pi$
$80$	205.000	0.286496
$81$	−671.000	−0.920439
$82$	−270.000	−0.363616
$83$	828.000	1.09500	0.547499	−	0.836806i	$-0.315580\pi$
$83$	828.000	1.09500	0.547499	+	0.836806i	$0.315580\pi$
$84$	1015.00	1.31840
$85$	105.000	0.133986
$86$	12.0000	0.0150464
$87$	825.000	1.01666
$88$	0	0
$89$	−1535.00	−1.82820	−0.914099	−	0.405490i	$-0.867101\pi$
$89$	−1535.00	−1.82820	−0.914099	+	0.405490i	$0.867101\pi$
$90$	−10.0000	−0.0117121
$91$	−2552.00	−2.93981
$92$	−1120.00	−1.26922
$93$	425.000	0.473876
$94$	−370.000	−0.405985
$95$	525.000	0.566988
$96$	−805.000	−0.855833
$97$	−90.0000	−0.0942074	−0.0471037	−	0.998890i	$-0.514999\pi$
$97$	−90.0000	−0.0942074	−0.0471037	+	0.998890i	$0.514999\pi$
$98$	498.000	0.513322
$99$	0	0
$100$	−175.000	−0.175000
$101$	910.000	0.896519	0.448259	−	0.893904i	$-0.352044\pi$
$101$	910.000	0.896519	0.448259	+	0.893904i	$0.352044\pi$
$102$	−105.000	−0.101927
$103$	−410.000	−0.392218	−0.196109	−	0.980582i	$-0.562831\pi$
$103$	−410.000	−0.392218	−0.196109	+	0.980582i	$0.562831\pi$
$104$	1320.00	1.24458
$105$	−725.000	−0.673836
$106$	−615.000	−0.563529
$107$	−206.000	−0.186119	−0.0930597	−	0.995661i	$-0.529665\pi$
$107$	−206.000	−0.186119	−0.0930597	+	0.995661i	$0.529665\pi$
$108$	−1015.00	−0.904337
$109$	−750.000	−0.659055	−0.329527	−	0.944146i	$-0.606889\pi$
$109$	−750.000	−0.659055	−0.329527	+	0.944146i	$0.606889\pi$
$110$	0	0
$111$	75.0000	0.0641323
$112$	1189.00	1.00312
$113$	−1500.00	−1.24874	−0.624372	−	0.781127i	$-0.714645\pi$
$113$	−1500.00	−1.24874	−0.624372	+	0.781127i	$0.714645\pi$
$114$	−525.000	−0.431322
$115$	800.000	0.648699
$116$	1155.00	0.924475
$117$	176.000	0.139070
$118$	396.000	0.308939
$119$	609.000	0.469134
$120$	375.000	0.285272
$121$	0	0
$122$	−835.000	−0.619650
$123$	1350.00	0.989637
$124$	595.000	0.430908
$125$	125.000	0.0894427
$126$	−58.0000	−0.0410083
$127$	1184.00	0.827268	0.413634	−	0.910443i	$-0.364259\pi$
$127$	1184.00	0.827268	0.413634	+	0.910443i	$0.364259\pi$
$128$	−1455.00	−1.00473
$129$	−60.0000	−0.0409512
$130$	−440.000	−0.296850
$131$	845.000	0.563572	0.281786	−	0.959477i	$-0.409073\pi$
$131$	845.000	0.563572	0.281786	+	0.959477i	$0.409073\pi$
$132$	0	0
$133$	3045.00	1.98523
$134$	−540.000	−0.348126
$135$	725.000	0.462208
$136$	−315.000	−0.198610
$137$	140.000	0.0873066	0.0436533	−	0.999047i	$-0.486100\pi$
$137$	140.000	0.0873066	0.0436533	+	0.999047i	$0.486100\pi$
$138$	−800.000	−0.493482
$139$	−1820.00	−1.11058	−0.555289	−	0.831657i	$-0.687392\pi$
$139$	−1820.00	−1.11058	−0.555289	+	0.831657i	$0.687392\pi$
$140$	−1015.00	−0.612737
$141$	1850.00	1.10495
$142$	−187.000	−0.110512
$143$	0	0
$144$	−82.0000	−0.0474537
$145$	−825.000	−0.472500
$146$	−58.0000	−0.0328775
$147$	−2490.00	−1.39709
$148$	105.000	0.0583172
$149$	−615.000	−0.338139	−0.169070	−	0.985604i	$-0.554076\pi$
$149$	−615.000	−0.338139	−0.169070	+	0.985604i	$0.554076\pi$
$150$	−125.000	−0.0680414
$151$	2260.00	1.21799	0.608994	−	0.793175i	$-0.291573\pi$
$151$	2260.00	1.21799	0.608994	+	0.793175i	$0.291573\pi$
$152$	−1575.00	−0.840456
$153$	−42.0000	−0.0221928
$154$	0	0
$155$	−425.000	−0.220238
$156$	−3080.00	−1.58075
$157$	225.000	0.114376	0.0571878	−	0.998363i	$-0.481787\pi$
$157$	225.000	0.114376	0.0571878	+	0.998363i	$0.481787\pi$
$158$	−620.000	−0.312181
$159$	3075.00	1.53373
$160$	805.000	0.397755
$161$	4640.00	2.27132
$162$	−671.000	−0.325424
$163$	−1225.00	−0.588647	−0.294323	−	0.955706i	$-0.595094\pi$
$163$	−1225.00	−0.588647	−0.294323	+	0.955706i	$0.595094\pi$
$164$	1890.00	0.899904
$165$	0	0
$166$	828.000	0.387140
$167$	1689.00	0.782627	0.391314	−	0.920257i	$-0.372021\pi$
$167$	1689.00	0.782627	0.391314	+	0.920257i	$0.372021\pi$
$168$	2175.00	0.998839
$169$	5547.00	2.52481
$170$	105.000	0.0473714
$171$	−210.000	−0.0939129
$172$	−84.0000	−0.0372380
$173$	−1518.00	−0.667118	−0.333559	−	0.942729i	$-0.608250\pi$
$173$	−1518.00	−0.667118	−0.333559	+	0.942729i	$0.608250\pi$
$174$	825.000	0.359443
$175$	725.000	0.313171
$176$	0	0
$177$	−1980.00	−0.840824
$178$	−1535.00	−0.646366
$179$	−630.000	−0.263064	−0.131532	−	0.991312i	$-0.541990\pi$
$179$	−630.000	−0.263064	−0.131532	+	0.991312i	$0.541990\pi$
$180$	70.0000	0.0289861
$181$	−920.000	−0.377807	−0.188903	−	0.981996i	$-0.560493\pi$
$181$	−920.000	−0.377807	−0.188903	+	0.981996i	$0.560493\pi$
$182$	−2552.00	−1.03938
$183$	4175.00	1.68647
$184$	−2400.00	−0.961578
$185$	−75.0000	−0.0298060
$186$	425.000	0.167540
$187$	0	0
$188$	2590.00	1.00476
$189$	4205.00	1.61835
$190$	525.000	0.200461
$191$	−180.000	−0.0681903	−0.0340951	−	0.999419i	$-0.510855\pi$
$191$	−180.000	−0.0681903	−0.0340951	+	0.999419i	$0.510855\pi$
$192$	835.000	0.313859
$193$	373.000	0.139115	0.0695573	−	0.997578i	$-0.477841\pi$
$193$	373.000	0.139115	0.0695573	+	0.997578i	$0.477841\pi$
$194$	−90.0000	−0.0333073
$195$	2200.00	0.807924
$196$	−3486.00	−1.27041
$197$	−4026.00	−1.45604	−0.728022	−	0.685554i	$-0.759560\pi$
$197$	−4026.00	−1.45604	−0.728022	+	0.685554i	$0.759560\pi$
$198$	0	0
$199$	1489.00	0.530414	0.265207	−	0.964191i	$-0.414560\pi$
$199$	1489.00	0.530414	0.265207	+	0.964191i	$0.414560\pi$
$200$	−375.000	−0.132583
$201$	2700.00	0.947479
$202$	910.000	0.316967
$203$	−4785.00	−1.65439
$204$	735.000	0.252256
$205$	−1350.00	−0.459942
$206$	−410.000	−0.138670
$207$	−320.000	−0.107447
$208$	−3608.00	−1.20274
$209$	0	0
$210$	−725.000	−0.238237
$211$	−5435.00	−1.77327	−0.886637	−	0.462466i	$-0.846965\pi$
$211$	−5435.00	−1.77327	−0.886637	+	0.462466i	$0.846965\pi$
$212$	4305.00	1.39466
$213$	935.000	0.300775
$214$	−206.000	−0.0658031
$215$	60.0000	0.0190324
$216$	−2175.00	−0.685139
$217$	−2465.00	−0.771130
$218$	−750.000	−0.233011
$219$	290.000	0.0894812
$220$	0	0
$221$	−1848.00	−0.562488
$222$	75.0000	0.0226742
$223$	−3610.00	−1.08405	−0.542026	−	0.840362i	$-0.682342\pi$
$223$	−3610.00	−1.08405	−0.542026	+	0.840362i	$0.682342\pi$
$224$	4669.00	1.39268
$225$	−50.0000	−0.0148148
$226$	−1500.00	−0.441498
$227$	−6274.00	−1.83445	−0.917225	−	0.398370i	$-0.869576\pi$
$227$	−6274.00	−1.83445	−0.917225	+	0.398370i	$0.869576\pi$
$228$	3675.00	1.06747
$229$	4316.00	1.24546	0.622728	−	0.782439i	$-0.286024\pi$
$229$	4316.00	1.24546	0.622728	+	0.782439i	$0.286024\pi$
$230$	800.000	0.229350
$231$	0	0
$232$	2475.00	0.700395
$233$	213.000	0.0598888	0.0299444	−	0.999552i	$-0.490467\pi$
$233$	213.000	0.0598888	0.0299444	+	0.999552i	$0.490467\pi$
$234$	176.000	0.0491687
$235$	−1850.00	−0.513535
$236$	−2772.00	−0.764584
$237$	3100.00	0.849648
$238$	609.000	0.165864
$239$	4890.00	1.32346	0.661732	−	0.749741i	$-0.269822\pi$
$239$	4890.00	1.32346	0.661732	+	0.749741i	$0.269822\pi$
$240$	−1025.00	−0.275681
$241$	1810.00	0.483786	0.241893	−	0.970303i	$-0.422232\pi$
$241$	1810.00	0.483786	0.241893	+	0.970303i	$0.422232\pi$
$242$	0	0
$243$	−560.000	−0.147835
$244$	5845.00	1.53356
$245$	2490.00	0.649307
$246$	1350.00	0.349890
$247$	−9240.00	−2.38027
$248$	1275.00	0.326462
$249$	−4140.00	−1.05366
$250$	125.000	0.0316228
$251$	3848.00	0.967664	0.483832	−	0.875161i	$-0.339245\pi$
$251$	3848.00	0.967664	0.483832	+	0.875161i	$0.339245\pi$
$252$	406.000	0.101490
$253$	0	0
$254$	1184.00	0.292483
$255$	−525.000	−0.128929
$256$	−119.000	−0.0290527
$257$	−2400.00	−0.582521	−0.291260	−	0.956644i	$-0.594075\pi$
$257$	−2400.00	−0.582521	−0.291260	+	0.956644i	$0.594075\pi$
$258$	−60.0000	−0.0144784
$259$	−435.000	−0.104361
$260$	3080.00	0.734667
$261$	330.000	0.0782624
$262$	845.000	0.199253
$263$	1803.00	0.422729	0.211365	−	0.977407i	$-0.432209\pi$
$263$	1803.00	0.422729	0.211365	+	0.977407i	$0.432209\pi$
$264$	0	0
$265$	−3075.00	−0.712814
$266$	3045.00	0.701883
$267$	7675.00	1.75918
$268$	3780.00	0.861568
$269$	−4044.00	−0.916606	−0.458303	−	0.888796i	$-0.651543\pi$
$269$	−4044.00	−0.916606	−0.458303	+	0.888796i	$0.651543\pi$
$270$	725.000	0.163415
$271$	2500.00	0.560384	0.280192	−	0.959944i	$-0.409602\pi$
$271$	2500.00	0.560384	0.280192	+	0.959944i	$0.409602\pi$
$272$	861.000	0.191933
$273$	12760.0	2.82883
$274$	140.000	0.0308676
$275$	0	0
$276$	5600.00	1.22131
$277$	3074.00	0.666783	0.333391	−	0.942789i	$-0.391807\pi$
$277$	3074.00	0.666783	0.333391	+	0.942789i	$0.391807\pi$
$278$	−1820.00	−0.392649
$279$	170.000	0.0364790
$280$	−2175.00	−0.464218
$281$	670.000	0.142238	0.0711189	−	0.997468i	$-0.477343\pi$
$281$	670.000	0.142238	0.0711189	+	0.997468i	$0.477343\pi$
$282$	1850.00	0.390659
$283$	−4432.00	−0.930937	−0.465468	−	0.885065i	$-0.654114\pi$
$283$	−4432.00	−0.930937	−0.465468	+	0.885065i	$0.654114\pi$
$284$	1309.00	0.273503
$285$	−2625.00	−0.545584
$286$	0	0
$287$	−7830.00	−1.61042
$288$	−322.000	−0.0658821
$289$	−4472.00	−0.910238
$290$	−825.000	−0.167054
$291$	450.000	0.0906511
$292$	406.000	0.0813676
$293$	−7122.00	−1.42004	−0.710020	−	0.704182i	$-0.751314\pi$
$293$	−7122.00	−1.42004	−0.710020	+	0.704182i	$0.751314\pi$
$294$	−2490.00	−0.493945
$295$	1980.00	0.390780
$296$	225.000	0.0441820
$297$	0	0
$298$	−615.000	−0.119550
$299$	−14080.0	−2.72330
$300$	875.000	0.168394
$301$	348.000	0.0666392
$302$	2260.00	0.430624
$303$	−4550.00	−0.862675
$304$	4305.00	0.812200
$305$	−4175.00	−0.783803
$306$	−42.0000	−0.00784634
$307$	7426.00	1.38053	0.690267	−	0.723554i	$-0.257493\pi$
$307$	7426.00	1.38053	0.690267	+	0.723554i	$0.257493\pi$
$308$	0	0
$309$	2050.00	0.377412
$310$	−425.000	−0.0778657
$311$	3107.00	0.566501	0.283250	−	0.959046i	$-0.408587\pi$
$311$	3107.00	0.566501	0.283250	+	0.959046i	$0.408587\pi$
$312$	−6600.00	−1.19760
$313$	−2030.00	−0.366589	−0.183295	−	0.983058i	$-0.558676\pi$
$313$	−2030.00	−0.366589	−0.183295	+	0.983058i	$0.558676\pi$
$314$	225.000	0.0404378
$315$	−290.000	−0.0518719
$316$	4340.00	0.772608
$317$	−3165.00	−0.560770	−0.280385	−	0.959888i	$-0.590462\pi$
$317$	−3165.00	−0.560770	−0.280385	+	0.959888i	$0.590462\pi$
$318$	3075.00	0.542256
$319$	0	0
$320$	−835.000	−0.145868
$321$	1030.00	0.179093
$322$	4640.00	0.803034
$323$	2205.00	0.379844
$324$	4697.00	0.805384
$325$	−2200.00	−0.375489
$326$	−1225.00	−0.208118
$327$	3750.00	0.634176
$328$	4050.00	0.681780
$329$	−10730.0	−1.79807
$330$	0	0
$331$	4760.00	0.790433	0.395216	−	0.918588i	$-0.370670\pi$
$331$	4760.00	0.790433	0.395216	+	0.918588i	$0.370670\pi$
$332$	−5796.00	−0.958123
$333$	30.0000	0.00493691
$334$	1689.00	0.276701
$335$	−2700.00	−0.440349
$336$	−5945.00	−0.965257
$337$	6899.00	1.11517	0.557585	−	0.830120i	$-0.311728\pi$
$337$	6899.00	1.11517	0.557585	+	0.830120i	$0.311728\pi$
$338$	5547.00	0.892654
$339$	7500.00	1.20160
$340$	−735.000	−0.117238
$341$	0	0
$342$	−210.000	−0.0332032
$343$	4495.00	0.707601
$344$	−180.000	−0.0282121
$345$	−4000.00	−0.624211
$346$	−1518.00	−0.235862
$347$	3386.00	0.523833	0.261916	−	0.965091i	$-0.415646\pi$
$347$	3386.00	0.523833	0.261916	+	0.965091i	$0.415646\pi$
$348$	−5775.00	−0.889576
$349$	5490.00	0.842043	0.421021	−	0.907051i	$-0.361672\pi$
$349$	5490.00	0.842043	0.421021	+	0.907051i	$0.361672\pi$
$350$	725.000	0.110723
$351$	−12760.0	−1.94039
$352$	0	0
$353$	−10500.0	−1.58317	−0.791584	−	0.611060i	$-0.790743\pi$
$353$	−10500.0	−1.58317	−0.791584	+	0.611060i	$0.790743\pi$
$354$	−1980.00	−0.297276
$355$	−935.000	−0.139788
$356$	10745.0	1.59967
$357$	−3045.00	−0.451424
$358$	−630.000	−0.0930071
$359$	9610.00	1.41280	0.706402	−	0.707811i	$-0.250317\pi$
$359$	9610.00	1.41280	0.706402	+	0.707811i	$0.250317\pi$
$360$	150.000	0.0219603
$361$	4166.00	0.607377
$362$	−920.000	−0.133575
$363$	0	0
$364$	17864.0	2.57233
$365$	−290.000	−0.0415871
$366$	4175.00	0.596259
$367$	−12180.0	−1.73240	−0.866200	−	0.499697i	$-0.833445\pi$
$367$	−12180.0	−1.73240	−0.866200	+	0.499697i	$0.833445\pi$
$368$	6560.00	0.929249
$369$	540.000	0.0761823
$370$	−75.0000	−0.0105380
$371$	−17835.0	−2.49581
$372$	−2975.00	−0.414641
$373$	7362.00	1.02196	0.510978	−	0.859594i	$-0.329283\pi$
$373$	7362.00	1.02196	0.510978	+	0.859594i	$0.329283\pi$
$374$	0	0
$375$	−625.000	−0.0860663
$376$	5550.00	0.761222
$377$	14520.0	1.98360
$378$	4205.00	0.572174
$379$	−8816.00	−1.19485	−0.597424	−	0.801925i	$-0.703809\pi$
$379$	−8816.00	−1.19485	−0.597424	+	0.801925i	$0.703809\pi$
$380$	−3675.00	−0.496115
$381$	−5920.00	−0.796039
$382$	−180.000	−0.0241089
$383$	690.000	0.0920558	0.0460279	−	0.998940i	$-0.485344\pi$
$383$	690.000	0.0920558	0.0460279	+	0.998940i	$0.485344\pi$
$384$	7275.00	0.966799
$385$	0	0
$386$	373.000	0.0491845
$387$	−24.0000	−0.00315243
$388$	630.000	0.0824315
$389$	13224.0	1.72361	0.861804	−	0.507242i	$-0.169335\pi$
$389$	13224.0	1.72361	0.861804	+	0.507242i	$0.169335\pi$
$390$	2200.00	0.285644
$391$	3360.00	0.434584
$392$	−7470.00	−0.962480
$393$	−4225.00	−0.542298
$394$	−4026.00	−0.514789
$395$	−3100.00	−0.394881
$396$	0	0
$397$	−14950.0	−1.88997	−0.944986	−	0.327110i	$-0.893925\pi$
$397$	−14950.0	−1.88997	−0.944986	+	0.327110i	$0.893925\pi$
$398$	1489.00	0.187530
$399$	−15225.0	−1.91028
$400$	1025.00	0.128125
$401$	13055.0	1.62577	0.812887	−	0.582421i	$-0.197894\pi$
$401$	13055.0	1.62577	0.812887	+	0.582421i	$0.197894\pi$
$402$	2700.00	0.334984
$403$	7480.00	0.924579
$404$	−6370.00	−0.784454
$405$	−3355.00	−0.411633
$406$	−4785.00	−0.584915
$407$	0	0
$408$	1575.00	0.191113
$409$	12310.0	1.48824	0.744120	−	0.668046i	$-0.232869\pi$
$409$	12310.0	1.48824	0.744120	+	0.668046i	$0.232869\pi$
$410$	−1350.00	−0.162614
$411$	−700.000	−0.0840108
$412$	2870.00	0.343191
$413$	11484.0	1.36826
$414$	−320.000	−0.0379883
$415$	4140.00	0.489698
$416$	−14168.0	−1.66982
$417$	9100.00	1.06865
$418$	0	0
$419$	8810.00	1.02720	0.513600	−	0.858030i	$-0.328312\pi$
$419$	8810.00	1.02720	0.513600	+	0.858030i	$0.328312\pi$
$420$	5075.00	0.589606
$421$	−3510.00	−0.406335	−0.203167	−	0.979144i	$-0.565124\pi$
$421$	−3510.00	−0.406335	−0.203167	+	0.979144i	$0.565124\pi$
$422$	−5435.00	−0.626947
$423$	740.000	0.0850592
$424$	9225.00	1.05662
$425$	525.000	0.0599206
$426$	935.000	0.106340
$427$	−24215.0	−2.74437
$428$	1442.00	0.162854
$429$	0	0
$430$	60.0000	0.00672897
$431$	6660.00	0.744318	0.372159	−	0.928169i	$-0.378618\pi$
$431$	6660.00	0.744318	0.372159	+	0.928169i	$0.378618\pi$
$432$	5945.00	0.662104
$433$	3450.00	0.382902	0.191451	−	0.981502i	$-0.438681\pi$
$433$	3450.00	0.382902	0.191451	+	0.981502i	$0.438681\pi$
$434$	−2465.00	−0.272635
$435$	4125.00	0.454663
$436$	5250.00	0.576673
$437$	16800.0	1.83902
$438$	290.000	0.0316364
$439$	16430.0	1.78624	0.893122	−	0.449815i	$-0.148510\pi$
$439$	16430.0	1.78624	0.893122	+	0.449815i	$0.148510\pi$
$440$	0	0
$441$	−996.000	−0.107548
$442$	−1848.00	−0.198870
$443$	−8840.00	−0.948084	−0.474042	−	0.880502i	$-0.657205\pi$
$443$	−8840.00	−0.948084	−0.474042	+	0.880502i	$0.657205\pi$
$444$	−525.000	−0.0561158
$445$	−7675.00	−0.817595
$446$	−3610.00	−0.383270
$447$	3075.00	0.325375
$448$	−4843.00	−0.510737
$449$	−3030.00	−0.318473	−0.159237	−	0.987240i	$-0.550903\pi$
$449$	−3030.00	−0.318473	−0.159237	+	0.987240i	$0.550903\pi$
$450$	−50.0000	−0.00523783
$451$	0	0
$452$	10500.0	1.09265
$453$	−11300.0	−1.17201
$454$	−6274.00	−0.648576
$455$	−12760.0	−1.31472
$456$	7875.00	0.808730
$457$	−12581.0	−1.28778	−0.643889	−	0.765119i	$-0.722680\pi$
$457$	−12581.0	−1.28778	−0.643889	+	0.765119i	$0.722680\pi$
$458$	4316.00	0.440335
$459$	3045.00	0.309648
$460$	−5600.00	−0.567612
$461$	13945.0	1.40886	0.704429	−	0.709775i	$-0.251203\pi$
$461$	13945.0	1.40886	0.704429	+	0.709775i	$0.251203\pi$
$462$	0	0
$463$	2500.00	0.250939	0.125470	−	0.992097i	$-0.459956\pi$
$463$	2500.00	0.250939	0.125470	+	0.992097i	$0.459956\pi$
$464$	−6765.00	−0.676848
$465$	2125.00	0.211924
$466$	213.000	0.0211739
$467$	3115.00	0.308662	0.154331	−	0.988019i	$-0.450678\pi$
$467$	3115.00	0.308662	0.154331	+	0.988019i	$0.450678\pi$
$468$	−1232.00	−0.121686
$469$	−15660.0	−1.54182
$470$	−1850.00	−0.181562
$471$	−1125.00	−0.110058
$472$	−5940.00	−0.579260
$473$	0	0
$474$	3100.00	0.300396
$475$	2625.00	0.253565
$476$	−4263.00	−0.410492
$477$	1230.00	0.118067
$478$	4890.00	0.467915
$479$	−6130.00	−0.584732	−0.292366	−	0.956306i	$-0.594443\pi$
$479$	−6130.00	−0.584732	−0.292366	+	0.956306i	$0.594443\pi$
$480$	−4025.00	−0.382740
$481$	1320.00	0.125129
$482$	1810.00	0.171044
$483$	−23200.0	−2.18558
$484$	0	0
$485$	−450.000	−0.0421308
$486$	−560.000	−0.0522677
$487$	−1780.00	−0.165625	−0.0828126	−	0.996565i	$-0.526390\pi$
$487$	−1780.00	−0.165625	−0.0828126	+	0.996565i	$0.526390\pi$
$488$	12525.0	1.16184
$489$	6125.00	0.566426
$490$	2490.00	0.229565
$491$	−3855.00	−0.354325	−0.177163	−	0.984182i	$-0.556692\pi$
$491$	−3855.00	−0.354325	−0.177163	+	0.984182i	$0.556692\pi$
$492$	−9450.00	−0.865933
$493$	−3465.00	−0.316543
$494$	−9240.00	−0.841553
$495$	0	0
$496$	−3485.00	−0.315486
$497$	−5423.00	−0.489446
$498$	−4140.00	−0.372526
$499$	−13114.0	−1.17648	−0.588240	−	0.808687i	$-0.700179\pi$
$499$	−13114.0	−1.17648	−0.588240	+	0.808687i	$0.700179\pi$
$500$	−875.000	−0.0782624
$501$	−8445.00	−0.753083
$502$	3848.00	0.342121
$503$	4228.00	0.374786	0.187393	−	0.982285i	$-0.439996\pi$
$503$	4228.00	0.374786	0.187393	+	0.982285i	$0.439996\pi$
$504$	870.000	0.0768906
$505$	4550.00	0.400935
$506$	0	0
$507$	−27735.0	−2.42950
$508$	−8288.00	−0.723859
$509$	−21454.0	−1.86824	−0.934118	−	0.356965i	$-0.883811\pi$
$509$	−21454.0	−1.86824	−0.934118	+	0.356965i	$0.883811\pi$
$510$	−525.000	−0.0455831
$511$	−1682.00	−0.145611
$512$	11521.0	0.994455
$513$	15225.0	1.31033
$514$	−2400.00	−0.205952
$515$	−2050.00	−0.175405
$516$	420.000	0.0358323
$517$	0	0
$518$	−435.000	−0.0368973
$519$	7590.00	0.641935
$520$	6600.00	0.556595
$521$	−4150.00	−0.348973	−0.174486	−	0.984660i	$-0.555826\pi$
$521$	−4150.00	−0.348973	−0.174486	+	0.984660i	$0.555826\pi$
$522$	330.000	0.0276699
$523$	−14518.0	−1.21382	−0.606910	−	0.794771i	$-0.707591\pi$
$523$	−14518.0	−1.21382	−0.606910	+	0.794771i	$0.707591\pi$
$524$	−5915.00	−0.493126
$525$	−3625.00	−0.301349
$526$	1803.00	0.149457
$527$	−1785.00	−0.147544
$528$	0	0
$529$	13433.0	1.10405
$530$	−3075.00	−0.252018
$531$	−792.000	−0.0647267
$532$	−21315.0	−1.73707
$533$	23760.0	1.93088
$534$	7675.00	0.621966
$535$	−1030.00	−0.0832351
$536$	8100.00	0.652736
$537$	3150.00	0.253133
$538$	−4044.00	−0.324069
$539$	0	0
$540$	−5075.00	−0.404432
$541$	−20765.0	−1.65020	−0.825099	−	0.564988i	$-0.808881\pi$
$541$	−20765.0	−1.65020	−0.825099	+	0.564988i	$0.808881\pi$
$542$	2500.00	0.198126
$543$	4600.00	0.363545
$544$	3381.00	0.266469
$545$	−3750.00	−0.294738
$546$	12760.0	1.00014
$547$	−21454.0	−1.67698	−0.838489	−	0.544919i	$-0.816560\pi$
$547$	−21454.0	−1.67698	−0.838489	+	0.544919i	$0.816560\pi$
$548$	−980.000	−0.0763933
$549$	1670.00	0.129825
$550$	0	0
$551$	−17325.0	−1.33951
$552$	12000.0	0.925279
$553$	−17980.0	−1.38262
$554$	3074.00	0.235743
$555$	375.000	0.0286808
$556$	12740.0	0.971756
$557$	10724.0	0.815782	0.407891	−	0.913031i	$-0.366264\pi$
$557$	10724.0	0.815782	0.407891	+	0.913031i	$0.366264\pi$
$558$	170.000	0.0128973
$559$	−1056.00	−0.0798999
$560$	5945.00	0.448611
$561$	0	0
$562$	670.000	0.0502887
$563$	17682.0	1.32364	0.661818	−	0.749664i	$-0.269785\pi$
$563$	17682.0	1.32364	0.661818	+	0.749664i	$0.269785\pi$
$564$	−12950.0	−0.966832
$565$	−7500.00	−0.558456
$566$	−4432.00	−0.329136
$567$	−19459.0	−1.44127
$568$	2805.00	0.207210
$569$	−14910.0	−1.09852	−0.549262	−	0.835650i	$-0.685091\pi$
$569$	−14910.0	−1.09852	−0.549262	+	0.835650i	$0.685091\pi$
$570$	−2625.00	−0.192893
$571$	1235.00	0.0905134	0.0452567	−	0.998975i	$-0.485589\pi$
$571$	1235.00	0.0905134	0.0452567	+	0.998975i	$0.485589\pi$
$572$	0	0
$573$	900.000	0.0656161
$574$	−7830.00	−0.569369
$575$	4000.00	0.290107
$576$	334.000	0.0241609
$577$	−4300.00	−0.310245	−0.155122	−	0.987895i	$-0.549577\pi$
$577$	−4300.00	−0.310245	−0.155122	+	0.987895i	$0.549577\pi$
$578$	−4472.00	−0.321818
$579$	−1865.00	−0.133863
$580$	5775.00	0.413438
$581$	24012.0	1.71461
$582$	450.000	0.0320500
$583$	0	0
$584$	870.000	0.0616453
$585$	880.000	0.0621941
$586$	−7122.00	−0.502060
$587$	−18435.0	−1.29624	−0.648121	−	0.761537i	$-0.724445\pi$
$587$	−18435.0	−1.29624	−0.648121	+	0.761537i	$0.724445\pi$
$588$	17430.0	1.22245
$589$	−8925.00	−0.624360
$590$	1980.00	0.138162
$591$	20130.0	1.40108
$592$	−615.000	−0.0426965
$593$	14742.0	1.02088	0.510440	−	0.859914i	$-0.329483\pi$
$593$	14742.0	1.02088	0.510440	+	0.859914i	$0.329483\pi$
$594$	0	0
$595$	3045.00	0.209803
$596$	4305.00	0.295872
$597$	−7445.00	−0.510391
$598$	−14080.0	−0.962833
$599$	5675.00	0.387102	0.193551	−	0.981090i	$-0.437999\pi$
$599$	5675.00	0.387102	0.193551	+	0.981090i	$0.437999\pi$
$600$	1875.00	0.127578
$601$	−10350.0	−0.702471	−0.351236	−	0.936287i	$-0.614238\pi$
$601$	−10350.0	−0.702471	−0.351236	+	0.936287i	$0.614238\pi$
$602$	348.000	0.0235605
$603$	1080.00	0.0729370
$604$	−15820.0	−1.06574
$605$	0	0
$606$	−4550.00	−0.305002
$607$	6411.00	0.428689	0.214345	−	0.976758i	$-0.431238\pi$
$607$	6411.00	0.428689	0.214345	+	0.976758i	$0.431238\pi$
$608$	16905.0	1.12761
$609$	23925.0	1.59194
$610$	−4175.00	−0.277116
$611$	32560.0	2.15587
$612$	294.000	0.0194187
$613$	12208.0	0.804366	0.402183	−	0.915559i	$-0.368252\pi$
$613$	12208.0	0.804366	0.402183	+	0.915559i	$0.368252\pi$
$614$	7426.00	0.488093
$615$	6750.00	0.442579
$616$	0	0
$617$	−12270.0	−0.800602	−0.400301	−	0.916384i	$-0.631094\pi$
$617$	−12270.0	−0.800602	−0.400301	+	0.916384i	$0.631094\pi$
$618$	2050.00	0.133435
$619$	−23030.0	−1.49540	−0.747701	−	0.664036i	$-0.768842\pi$
$619$	−23030.0	−1.49540	−0.747701	+	0.664036i	$0.768842\pi$
$620$	2975.00	0.192708
$621$	23200.0	1.49917
$622$	3107.00	0.200288
$623$	−44515.0	−2.86269
$624$	18040.0	1.15734
$625$	625.000	0.0400000
$626$	−2030.00	−0.129609
$627$	0	0
$628$	−1575.00	−0.100079
$629$	−315.000	−0.0199680
$630$	−290.000	−0.0183395
$631$	−24983.0	−1.57616	−0.788080	−	0.615572i	$-0.788925\pi$
$631$	−24983.0	−1.57616	−0.788080	+	0.615572i	$0.788925\pi$
$632$	9300.00	0.585339
$633$	27175.0	1.70633
$634$	−3165.00	−0.198262
$635$	5920.00	0.369965
$636$	−21525.0	−1.34202
$637$	−43824.0	−2.72586
$638$	0	0
$639$	374.000	0.0231537
$640$	−7275.00	−0.449328
$641$	−18485.0	−1.13902	−0.569511	−	0.821983i	$-0.692868\pi$
$641$	−18485.0	−1.13902	−0.569511	+	0.821983i	$0.692868\pi$
$642$	1030.00	0.0633191
$643$	−14445.0	−0.885933	−0.442967	−	0.896538i	$-0.646074\pi$
$643$	−14445.0	−0.885933	−0.442967	+	0.896538i	$0.646074\pi$
$644$	−32480.0	−1.98741
$645$	−300.000	−0.0183139
$646$	2205.00	0.134295
$647$	1000.00	0.0607636	0.0303818	−	0.999538i	$-0.490328\pi$
$647$	1000.00	0.0607636	0.0303818	+	0.999538i	$0.490328\pi$
$648$	10065.0	0.610171
$649$	0	0
$650$	−2200.00	−0.132756
$651$	12325.0	0.742020
$652$	8575.00	0.515066
$653$	14375.0	0.861466	0.430733	−	0.902479i	$-0.358255\pi$
$653$	14375.0	0.861466	0.430733	+	0.902479i	$0.358255\pi$
$654$	3750.00	0.224215
$655$	4225.00	0.252037
$656$	−11070.0	−0.658858
$657$	116.000	0.00688827
$658$	−10730.0	−0.635713
$659$	1955.00	0.115563	0.0577815	−	0.998329i	$-0.481597\pi$
$659$	1955.00	0.115563	0.0577815	+	0.998329i	$0.481597\pi$
$660$	0	0
$661$	418.000	0.0245965	0.0122983	−	0.999924i	$-0.496085\pi$
$661$	418.000	0.0245965	0.0122983	+	0.999924i	$0.496085\pi$
$662$	4760.00	0.279460
$663$	9240.00	0.541255
$664$	−12420.0	−0.725888
$665$	15225.0	0.887820
$666$	30.0000	0.00174546
$667$	−26400.0	−1.53255
$668$	−11823.0	−0.684799
$669$	18050.0	1.04313
$670$	−2700.00	−0.155687
$671$	0	0
$672$	−23345.0	−1.34011
$673$	−14947.0	−0.856114	−0.428057	−	0.903752i	$-0.640802\pi$
$673$	−14947.0	−0.856114	−0.428057	+	0.903752i	$0.640802\pi$
$674$	6899.00	0.394272
$675$	3625.00	0.206706
$676$	−38829.0	−2.20921
$677$	11614.0	0.659324	0.329662	−	0.944099i	$-0.393065\pi$
$677$	11614.0	0.659324	0.329662	+	0.944099i	$0.393065\pi$
$678$	7500.00	0.424832
$679$	−2610.00	−0.147515
$680$	−1575.00	−0.0888213
$681$	31370.0	1.76520
$682$	0	0
$683$	21925.0	1.22831	0.614156	−	0.789185i	$-0.289497\pi$
$683$	21925.0	1.22831	0.614156	+	0.789185i	$0.289497\pi$
$684$	1470.00	0.0821738
$685$	700.000	0.0390447
$686$	4495.00	0.250175
$687$	−21580.0	−1.19844
$688$	492.000	0.0272636
$689$	54120.0	2.99246
$690$	−4000.00	−0.220692
$691$	15778.0	0.868630	0.434315	−	0.900761i	$-0.356990\pi$
$691$	15778.0	0.868630	0.434315	+	0.900761i	$0.356990\pi$
$692$	10626.0	0.583728
$693$	0	0
$694$	3386.00	0.185203
$695$	−9100.00	−0.496666
$696$	−12375.0	−0.673956
$697$	−5670.00	−0.308130
$698$	5490.00	0.297707
$699$	−1065.00	−0.0576280
$700$	−5075.00	−0.274024
$701$	11345.0	0.611262	0.305631	−	0.952150i	$-0.401133\pi$
$701$	11345.0	0.611262	0.305631	+	0.952150i	$0.401133\pi$
$702$	−12760.0	−0.686033
$703$	−1575.00	−0.0844982
$704$	0	0
$705$	9250.00	0.494149
$706$	−10500.0	−0.559735
$707$	26390.0	1.40382
$708$	13860.0	0.735721
$709$	−7170.00	−0.379795	−0.189898	−	0.981804i	$-0.560816\pi$
$709$	−7170.00	−0.379795	−0.189898	+	0.981804i	$0.560816\pi$
$710$	−935.000	−0.0494224
$711$	1240.00	0.0654060
$712$	23025.0	1.21194
$713$	−13600.0	−0.714339
$714$	−3045.00	−0.159603
$715$	0	0
$716$	4410.00	0.230181
$717$	−24450.0	−1.27350
$718$	9610.00	0.499501
$719$	31295.0	1.62324	0.811618	−	0.584189i	$-0.198587\pi$
$719$	31295.0	1.62324	0.811618	+	0.584189i	$0.198587\pi$
$720$	−410.000	−0.0212219
$721$	−11890.0	−0.614156
$722$	4166.00	0.214740
$723$	−9050.00	−0.465523
$724$	6440.00	0.330581
$725$	−4125.00	−0.211308
$726$	0	0
$727$	18460.0	0.941738	0.470869	−	0.882203i	$-0.343940\pi$
$727$	18460.0	0.941738	0.470869	+	0.882203i	$0.343940\pi$
$728$	38280.0	1.94883
$729$	20917.0	1.06269
$730$	−290.000	−0.0147033
$731$	252.000	0.0127504
$732$	−29225.0	−1.47567
$733$	5108.00	0.257392	0.128696	−	0.991684i	$-0.458921\pi$
$733$	5108.00	0.257392	0.128696	+	0.991684i	$0.458921\pi$
$734$	−12180.0	−0.612496
$735$	−12450.0	−0.624796
$736$	25760.0	1.29012
$737$	0	0
$738$	540.000	0.0269345
$739$	−7040.00	−0.350434	−0.175217	−	0.984530i	$-0.556063\pi$
$739$	−7040.00	−0.350434	−0.175217	+	0.984530i	$0.556063\pi$
$740$	525.000	0.0260802
$741$	46200.0	2.29042
$742$	−17835.0	−0.882404
$743$	−12343.0	−0.609449	−0.304725	−	0.952441i	$-0.598564\pi$
$743$	−12343.0	−0.609449	−0.304725	+	0.952441i	$0.598564\pi$
$744$	−6375.00	−0.314138
$745$	−3075.00	−0.151221
$746$	7362.00	0.361316
$747$	−1656.00	−0.0811109
$748$	0	0
$749$	−5974.00	−0.291436
$750$	−625.000	−0.0304290
$751$	8727.00	0.424038	0.212019	−	0.977266i	$-0.431996\pi$
$751$	8727.00	0.424038	0.212019	+	0.977266i	$0.431996\pi$
$752$	−15170.0	−0.735629
$753$	−19240.0	−0.931135
$754$	14520.0	0.701309
$755$	11300.0	0.544701
$756$	−29435.0	−1.41606
$757$	−29630.0	−1.42262	−0.711308	−	0.702880i	$-0.751897\pi$
$757$	−29630.0	−1.42262	−0.711308	+	0.702880i	$0.751897\pi$
$758$	−8816.00	−0.422443
$759$	0	0
$760$	−7875.00	−0.375864
$761$	9710.00	0.462532	0.231266	−	0.972890i	$-0.425713\pi$
$761$	9710.00	0.462532	0.231266	+	0.972890i	$0.425713\pi$
$762$	−5920.00	−0.281442
$763$	−21750.0	−1.03198
$764$	1260.00	0.0596665
$765$	−210.000	−0.00992492
$766$	690.000	0.0325466
$767$	−34848.0	−1.64053
$768$	595.000	0.0279560
$769$	−18250.0	−0.855802	−0.427901	−	0.903826i	$-0.640747\pi$
$769$	−18250.0	−0.855802	−0.427901	+	0.903826i	$0.640747\pi$
$770$	0	0
$771$	12000.0	0.560531
$772$	−2611.00	−0.121725
$773$	−16155.0	−0.751688	−0.375844	−	0.926683i	$-0.622647\pi$
$773$	−16155.0	−0.751688	−0.375844	+	0.926683i	$0.622647\pi$
$774$	−24.0000	−0.00111455
$775$	−2125.00	−0.0984932
$776$	1350.00	0.0624513
$777$	2175.00	0.100422
$778$	13224.0	0.609387
$779$	−28350.0	−1.30391
$780$	−15400.0	−0.706934
$781$	0	0
$782$	3360.00	0.153649
$783$	−23925.0	−1.09197
$784$	20418.0	0.930120
$785$	1125.00	0.0511503
$786$	−4225.00	−0.191731
$787$	4894.00	0.221667	0.110834	−	0.993839i	$-0.464648\pi$
$787$	4894.00	0.221667	0.110834	+	0.993839i	$0.464648\pi$
$788$	28182.0	1.27404
$789$	−9015.00	−0.406771
$790$	−3100.00	−0.139611
$791$	−43500.0	−1.95535
$792$	0	0
$793$	73480.0	3.29048
$794$	−14950.0	−0.668206
$795$	15375.0	0.685906
$796$	−10423.0	−0.464112
$797$	20810.0	0.924878	0.462439	−	0.886651i	$-0.346974\pi$
$797$	20810.0	0.924878	0.462439	+	0.886651i	$0.346974\pi$
$798$	−15225.0	−0.675387
$799$	−7770.00	−0.344034
$800$	4025.00	0.177882
$801$	3070.00	0.135422
$802$	13055.0	0.574798
$803$	0	0
$804$	−18900.0	−0.829044
$805$	23200.0	1.01577
$806$	7480.00	0.326888
$807$	20220.0	0.882005
$808$	−13650.0	−0.594314
$809$	13400.0	0.582347	0.291174	−	0.956670i	$-0.405954\pi$
$809$	13400.0	0.582347	0.291174	+	0.956670i	$0.405954\pi$
$810$	−3355.00	−0.145534
$811$	4555.00	0.197223	0.0986114	−	0.995126i	$-0.468560\pi$
$811$	4555.00	0.197223	0.0986114	+	0.995126i	$0.468560\pi$
$812$	33495.0	1.44759
$813$	−12500.0	−0.539230
$814$	0	0
$815$	−6125.00	−0.263251
$816$	−4305.00	−0.184688
$817$	1260.00	0.0539557
$818$	12310.0	0.526172
$819$	5104.00	0.217763
$820$	9450.00	0.402449
$821$	−32130.0	−1.36583	−0.682914	−	0.730499i	$-0.739288\pi$
$821$	−32130.0	−1.36583	−0.682914	+	0.730499i	$0.739288\pi$
$822$	−700.000	−0.0297023
$823$	3710.00	0.157135	0.0785677	−	0.996909i	$-0.474965\pi$
$823$	3710.00	0.157135	0.0785677	+	0.996909i	$0.474965\pi$
$824$	6150.00	0.260007
$825$	0	0
$826$	11484.0	0.483752
$827$	−17786.0	−0.747860	−0.373930	−	0.927457i	$-0.621990\pi$
$827$	−17786.0	−0.747860	−0.373930	+	0.927457i	$0.621990\pi$
$828$	2240.00	0.0940162
$829$	7300.00	0.305838	0.152919	−	0.988239i	$-0.451133\pi$
$829$	7300.00	0.305838	0.152919	+	0.988239i	$0.451133\pi$
$830$	4140.00	0.173134
$831$	−15370.0	−0.641612
$832$	14696.0	0.612370
$833$	10458.0	0.434992
$834$	9100.00	0.377826
$835$	8445.00	0.350002
$836$	0	0
$837$	−12325.0	−0.508978
$838$	8810.00	0.363170
$839$	36924.0	1.51938	0.759689	−	0.650287i	$-0.225351\pi$
$839$	36924.0	1.51938	0.759689	+	0.650287i	$0.225351\pi$
$840$	10875.0	0.446694
$841$	2836.00	0.116282
$842$	−3510.00	−0.143661
$843$	−3350.00	−0.136868
$844$	38045.0	1.55161
$845$	27735.0	1.12913
$846$	740.000	0.0300730
$847$	0	0
$848$	−25215.0	−1.02109
$849$	22160.0	0.895794
$850$	525.000	0.0211851
$851$	−2400.00	−0.0966756
$852$	−6545.00	−0.263178
$853$	−28572.0	−1.14688	−0.573439	−	0.819248i	$-0.694391\pi$
$853$	−28572.0	−1.14688	−0.573439	+	0.819248i	$0.694391\pi$
$854$	−24215.0	−0.970281
$855$	−1050.00	−0.0419991
$856$	3090.00	0.123381
$857$	45721.0	1.82240	0.911202	−	0.411961i	$-0.135156\pi$
$857$	45721.0	1.82240	0.911202	+	0.411961i	$0.135156\pi$
$858$	0	0
$859$	−10740.0	−0.426594	−0.213297	−	0.976987i	$-0.568420\pi$
$859$	−10740.0	−0.426594	−0.213297	+	0.976987i	$0.568420\pi$
$860$	−420.000	−0.0166534
$861$	39150.0	1.54963
$862$	6660.00	0.263156
$863$	−34590.0	−1.36438	−0.682188	−	0.731176i	$-0.738972\pi$
$863$	−34590.0	−1.36438	−0.682188	+	0.731176i	$0.738972\pi$
$864$	23345.0	0.919228
$865$	−7590.00	−0.298344
$866$	3450.00	0.135376
$867$	22360.0	0.875877
$868$	17255.0	0.674738
$869$	0	0
$870$	4125.00	0.160748
$871$	47520.0	1.84863
$872$	11250.0	0.436896
$873$	180.000	0.00697832
$874$	16800.0	0.650193
$875$	3625.00	0.140054
$876$	−2030.00	−0.0782961
$877$	11834.0	0.455651	0.227825	−	0.973702i	$-0.426838\pi$
$877$	11834.0	0.455651	0.227825	+	0.973702i	$0.426838\pi$
$878$	16430.0	0.631533
$879$	35610.0	1.36643
$880$	0	0
$881$	4942.00	0.188990	0.0944950	−	0.995525i	$-0.469876\pi$
$881$	4942.00	0.188990	0.0944950	+	0.995525i	$0.469876\pi$
$882$	−996.000	−0.0380239
$883$	27965.0	1.06580	0.532898	−	0.846180i	$-0.321103\pi$
$883$	27965.0	1.06580	0.532898	+	0.846180i	$0.321103\pi$
$884$	12936.0	0.492177
$885$	−9900.00	−0.376028
$886$	−8840.00	−0.335198
$887$	36936.0	1.39818	0.699092	−	0.715032i	$-0.253588\pi$
$887$	36936.0	1.39818	0.699092	+	0.715032i	$0.253588\pi$
$888$	−1125.00	−0.0425141
$889$	34336.0	1.29538
$890$	−7675.00	−0.289064
$891$	0	0
$892$	25270.0	0.948545
$893$	−38850.0	−1.45584
$894$	3075.00	0.115037
$895$	−3150.00	−0.117646
$896$	−42195.0	−1.57325
$897$	70400.0	2.62050
$898$	−3030.00	−0.112597
$899$	14025.0	0.520311
$900$	350.000	0.0129630
$901$	−12915.0	−0.477537
$902$	0	0
$903$	−1740.00	−0.0641236
$904$	22500.0	0.827808
$905$	−4600.00	−0.168960
$906$	−11300.0	−0.414368
$907$	−22585.0	−0.826817	−0.413408	−	0.910546i	$-0.635662\pi$
$907$	−22585.0	−0.826817	−0.413408	+	0.910546i	$0.635662\pi$
$908$	43918.0	1.60514
$909$	−1820.00	−0.0664088
$910$	−12760.0	−0.464824
$911$	21665.0	0.787918	0.393959	−	0.919128i	$-0.371105\pi$
$911$	21665.0	0.787918	0.393959	+	0.919128i	$0.371105\pi$
$912$	−21525.0	−0.781539
$913$	0	0
$914$	−12581.0	−0.455298
$915$	20875.0	0.754214
$916$	−30212.0	−1.08977
$917$	24505.0	0.882472
$918$	3045.00	0.109477
$919$	11900.0	0.427143	0.213572	−	0.976927i	$-0.431490\pi$
$919$	11900.0	0.427143	0.213572	+	0.976927i	$0.431490\pi$
$920$	−12000.0	−0.430031
$921$	−37130.0	−1.32842
$922$	13945.0	0.498106
$923$	16456.0	0.586843
$924$	0	0
$925$	−375.000	−0.0133296
$926$	2500.00	0.0887204
$927$	820.000	0.0290532
$928$	−26565.0	−0.939697
$929$	28691.0	1.01326	0.506631	−	0.862163i	$-0.330891\pi$
$929$	28691.0	1.01326	0.506631	+	0.862163i	$0.330891\pi$
$930$	2125.00	0.0749263
$931$	52290.0	1.84075
$932$	−1491.00	−0.0524027
$933$	−15535.0	−0.545116
$934$	3115.00	0.109128
$935$	0	0
$936$	−2640.00	−0.0921913
$937$	10694.0	0.372847	0.186424	−	0.982469i	$-0.440310\pi$
$937$	10694.0	0.372847	0.186424	+	0.982469i	$0.440310\pi$
$938$	−15660.0	−0.545114
$939$	10150.0	0.352751
$940$	12950.0	0.449343
$941$	−33365.0	−1.15586	−0.577932	−	0.816085i	$-0.696140\pi$
$941$	−33365.0	−1.15586	−0.577932	+	0.816085i	$0.696140\pi$
$942$	−1125.00	−0.0389113
$943$	−43200.0	−1.49182
$944$	16236.0	0.559785
$945$	21025.0	0.723750
$946$	0	0
$947$	28825.0	0.989109	0.494555	−	0.869146i	$-0.335331\pi$
$947$	28825.0	0.989109	0.494555	+	0.869146i	$0.335331\pi$
$948$	−21700.0	−0.743442
$949$	5104.00	0.174587
$950$	2625.00	0.0896487
$951$	15825.0	0.539601
$952$	−9135.00	−0.310995
$953$	−14373.0	−0.488549	−0.244274	−	0.969706i	$-0.578550\pi$
$953$	−14373.0	−0.488549	−0.244274	+	0.969706i	$0.578550\pi$
$954$	1230.00	0.0417429
$955$	−900.000	−0.0304956
$956$	−34230.0	−1.15803
$957$	0	0
$958$	−6130.00	−0.206734
$959$	4060.00	0.136709
$960$	4175.00	0.140362
$961$	−22566.0	−0.757477
$962$	1320.00	0.0442396
$963$	412.000	0.0137866
$964$	−12670.0	−0.423312
$965$	1865.00	0.0622140
$966$	−23200.0	−0.772720
$967$	25799.0	0.857952	0.428976	−	0.903316i	$-0.358874\pi$
$967$	25799.0	0.857952	0.428976	+	0.903316i	$0.358874\pi$
$968$	0	0
$969$	−11025.0	−0.365505
$970$	−450.000	−0.0148955
$971$	52470.0	1.73413	0.867066	−	0.498193i	$-0.166003\pi$
$971$	52470.0	1.73413	0.867066	+	0.498193i	$0.166003\pi$
$972$	3920.00	0.129356
$973$	−52780.0	−1.73900
$974$	−1780.00	−0.0585574
$975$	11000.0	0.361315
$976$	−34235.0	−1.12278
$977$	37770.0	1.23682	0.618408	−	0.785857i	$-0.287778\pi$
$977$	37770.0	1.23682	0.618408	+	0.785857i	$0.287778\pi$
$978$	6125.00	0.200262
$979$	0	0
$980$	−17430.0	−0.568144
$981$	1500.00	0.0488189
$982$	−3855.00	−0.125273
$983$	−50740.0	−1.64634	−0.823171	−	0.567793i	$-0.807797\pi$
$983$	−50740.0	−1.64634	−0.823171	+	0.567793i	$0.807797\pi$
$984$	−20250.0	−0.656043
$985$	−20130.0	−0.651163
$986$	−3465.00	−0.111915
$987$	53650.0	1.73019
$988$	64680.0	2.08274
$989$	1920.00	0.0617315
$990$	0	0
$991$	−2480.00	−0.0794953	−0.0397476	−	0.999210i	$-0.512655\pi$
$991$	−2480.00	−0.0794953	−0.0397476	+	0.999210i	$0.512655\pi$
$992$	−13685.0	−0.438003
$993$	−23800.0	−0.760594
$994$	−5423.00	−0.173045
$995$	7445.00	0.237208
$996$	28980.0	0.921954
$997$	−13644.0	−0.433410	−0.216705	−	0.976237i	$-0.569531\pi$
$997$	−13644.0	−0.433410	−0.216705	+	0.976237i	$0.569531\pi$
$998$	−13114.0	−0.415948
$999$	−2175.00	−0.0688828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.4.a.c.1.1	yes	1
11.10	odd	2		605.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.4.a.a.1.1	✓	1	11.10	odd	2
605.4.a.c.1.1	yes	1	1.1	even	1	trivial

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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