LMFDB - Embedded newform 665.2.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [665,2,Mod(1,665)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("665.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$665 = 5 \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	665.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$5.31005173442$
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	$\chi$	$=$	665.1

$q$ -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} -1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -4.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} -3.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{23} +3.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +5.00000 q^{27} -1.00000 q^{28} -10.0000 q^{29} -1.00000 q^{30} -8.00000 q^{31} +5.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +2.00000 q^{36} +3.00000 q^{37} -1.00000 q^{38} +4.00000 q^{39} -3.00000 q^{40} +1.00000 q^{41} -1.00000 q^{42} -11.0000 q^{43} -2.00000 q^{45} +1.00000 q^{46} -4.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.00000 q^{51} +4.00000 q^{52} -5.00000 q^{53} +5.00000 q^{54} -3.00000 q^{56} +1.00000 q^{57} -10.0000 q^{58} +14.0000 q^{59} +1.00000 q^{60} +8.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} -4.00000 q^{65} -6.00000 q^{67} +3.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} -5.00000 q^{71} +6.00000 q^{72} +15.0000 q^{73} +3.00000 q^{74} -1.00000 q^{75} +1.00000 q^{76} +4.00000 q^{78} -12.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +4.00000 q^{83} +1.00000 q^{84} -3.00000 q^{85} -11.0000 q^{86} +10.0000 q^{87} -14.0000 q^{89} -2.00000 q^{90} -4.00000 q^{91} -1.00000 q^{92} +8.00000 q^{93} -4.00000 q^{94} -1.00000 q^{95} -5.00000 q^{96} +14.0000 q^{97} +1.00000 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	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	−1.00000	−0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−2.00000	−0.471405
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	0	0
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	3.00000	0.612372
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	−1.00000	−0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	−3.00000	−0.514496
$35$	1.00000	0.169031
$36$	2.00000	0.333333
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−1.00000	−0.162221
$39$	4.00000	0.640513
$40$	−3.00000	−0.474342
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	−1.00000	−0.154303
$43$	−11.0000	−1.67748	−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000	−1.67748	−0.838742	+	0.544529i	$0.816708\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	1.00000	0.147442
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	3.00000	0.420084
$52$	4.00000	0.554700
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	−3.00000	−0.400892
$57$	1.00000	0.132453
$58$	−10.0000	−1.31306
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	1.00000	0.129099
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	3.00000	0.363803
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	−5.00000	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$72$	6.00000	0.707107
$73$	15.0000	1.75562	0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000	1.75562	0.877809	+	0.479012i	$0.159005\pi$
$74$	3.00000	0.348743
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	0	0
$78$	4.00000	0.452911
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	1.00000	0.109109
$85$	−3.00000	−0.325396
$86$	−11.0000	−1.18616
$87$	10.0000	1.07211
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−2.00000	−0.210819
$91$	−4.00000	−0.419314
$92$	−1.00000	−0.104257
$93$	8.00000	0.829561
$94$	−4.00000	−0.412568
$95$	−1.00000	−0.102598
$96$	−5.00000	−0.510310
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	3.00000	0.297044
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	12.0000	1.17670
$105$	−1.00000	−0.0975900
$106$	−5.00000	−0.485643
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	−5.00000	−0.481125
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	−1.00000	−0.0944911
$113$	1.00000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	1.00000	0.0936586
$115$	1.00000	0.0932505
$116$	10.0000	0.928477
$117$	8.00000	0.739600
$118$	14.0000	1.28880
$119$	−3.00000	−0.275010
$120$	3.00000	0.273861
$121$	−11.0000	−1.00000
$122$	8.00000	0.724286
$123$	−1.00000	−0.0901670
$124$	8.00000	0.718421
$125$	1.00000	0.0894427
$126$	−2.00000	−0.178174
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−3.00000	−0.265165
$129$	11.0000	0.968496
$130$	−4.00000	−0.350823
$131$	−21.0000	−1.83478	−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000	−1.83478	−0.917389	+	0.397991i	$0.869707\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	−6.00000	−0.518321
$135$	5.00000	0.430331
$136$	9.00000	0.771744
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	−1.00000	−0.0851257
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	−1.00000	−0.0845154
$141$	4.00000	0.336861
$142$	−5.00000	−0.419591
$143$	0	0
$144$	2.00000	0.166667
$145$	−10.0000	−0.830455
$146$	15.0000	1.24141
$147$	−1.00000	−0.0824786
$148$	−3.00000	−0.246598
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	−1.00000	−0.0816497
$151$	−11.0000	−0.895167	−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000	−0.895167	−0.447584	+	0.894242i	$0.647715\pi$
$152$	3.00000	0.243332
$153$	6.00000	0.485071
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−4.00000	−0.320256
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	−12.0000	−0.954669
$159$	5.00000	0.396526
$160$	5.00000	0.395285
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	3.00000	0.234978	0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000	0.234978	0.117489	+	0.993074i	$0.462515\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	4.00000	0.310460
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	3.00000	0.231455
$169$	3.00000	0.230769
$170$	−3.00000	−0.230089
$171$	2.00000	0.152944
$172$	11.0000	0.838742
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	10.0000	0.758098
$175$	1.00000	0.0755929
$176$	0	0
$177$	−14.0000	−1.05230
$178$	−14.0000	−1.04934
$179$	−13.0000	−0.971666	−0.485833	−	0.874052i	$-0.661484\pi$
$179$	−13.0000	−0.971666	−0.485833	+	0.874052i	$0.661484\pi$
$180$	2.00000	0.149071
$181$	−21.0000	−1.56092	−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000	−1.56092	−0.780459	+	0.625207i	$0.785014\pi$
$182$	−4.00000	−0.296500
$183$	−8.00000	−0.591377
$184$	−3.00000	−0.221163
$185$	3.00000	0.220564
$186$	8.00000	0.586588
$187$	0	0
$188$	4.00000	0.291730
$189$	5.00000	0.363696
$190$	−1.00000	−0.0725476
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−7.00000	−0.505181
$193$	−11.0000	−0.791797	−0.395899	−	0.918294i	$-0.629567\pi$
$193$	−11.0000	−0.791797	−0.395899	+	0.918294i	$0.629567\pi$
$194$	14.0000	1.00514
$195$	4.00000	0.286446
$196$	−1.00000	−0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	−3.00000	−0.212132
$201$	6.00000	0.423207
$202$	14.0000	0.985037
$203$	−10.0000	−0.701862
$204$	−3.00000	−0.210042
$205$	1.00000	0.0698430
$206$	8.00000	0.557386
$207$	−2.00000	−0.139010
$208$	4.00000	0.277350
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	−11.0000	−0.757271	−0.378636	−	0.925546i	$-0.623607\pi$
$211$	−11.0000	−0.757271	−0.378636	+	0.925546i	$0.623607\pi$
$212$	5.00000	0.343401
$213$	5.00000	0.342594
$214$	18.0000	1.23045
$215$	−11.0000	−0.750194
$216$	−15.0000	−1.02062
$217$	−8.00000	−0.543075
$218$	16.0000	1.08366
$219$	−15.0000	−1.01361
$220$	0	0
$221$	12.0000	0.807207
$222$	−3.00000	−0.201347
$223$	15.0000	1.00447	0.502237	−	0.864730i	$-0.332510\pi$
$223$	15.0000	1.00447	0.502237	+	0.864730i	$0.332510\pi$
$224$	5.00000	0.334077
$225$	−2.00000	−0.133333
$226$	1.00000	0.0665190
$227$	−15.0000	−0.995585	−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000	−0.995585	−0.497792	+	0.867296i	$0.665856\pi$
$228$	−1.00000	−0.0662266
$229$	24.0000	1.58596	0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000	1.58596	0.792982	+	0.609245i	$0.208527\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	30.0000	1.96960
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	8.00000	0.522976
$235$	−4.00000	−0.260931
$236$	−14.0000	−0.911322
$237$	12.0000	0.779484
$238$	−3.00000	−0.194461
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	1.00000	0.0645497
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−11.0000	−0.707107
$243$	−16.0000	−1.02640
$244$	−8.00000	−0.512148
$245$	1.00000	0.0638877
$246$	−1.00000	−0.0637577
$247$	4.00000	0.254514
$248$	24.0000	1.52400
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−16.0000	−1.00393
$255$	3.00000	0.187867
$256$	−17.0000	−1.06250
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	11.0000	0.684830
$259$	3.00000	0.186411
$260$	4.00000	0.248069
$261$	20.0000	1.23797
$262$	−21.0000	−1.29738
$263$	19.0000	1.17159	0.585795	−	0.810459i	$-0.300782\pi$
$263$	19.0000	1.17159	0.585795	+	0.810459i	$0.300782\pi$
$264$	0	0
$265$	−5.00000	−0.307148
$266$	−1.00000	−0.0613139
$267$	14.0000	0.856786
$268$	6.00000	0.366508
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	5.00000	0.304290
$271$	−15.0000	−0.911185	−0.455593	−	0.890188i	$-0.650573\pi$
$271$	−15.0000	−0.911185	−0.455593	+	0.890188i	$0.650573\pi$
$272$	3.00000	0.181902
$273$	4.00000	0.242091
$274$	12.0000	0.724947
$275$	0	0
$276$	1.00000	0.0601929
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−7.00000	−0.419832
$279$	16.0000	0.957895
$280$	−3.00000	−0.179284
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	4.00000	0.238197
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	5.00000	0.296695
$285$	1.00000	0.0592349
$286$	0	0
$287$	1.00000	0.0590281
$288$	−10.0000	−0.589256
$289$	−8.00000	−0.470588
$290$	−10.0000	−0.587220
$291$	−14.0000	−0.820695
$292$	−15.0000	−0.877809
$293$	−8.00000	−0.467365	−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000	−0.467365	−0.233682	+	0.972313i	$0.575078\pi$
$294$	−1.00000	−0.0583212
$295$	14.0000	0.815112
$296$	−9.00000	−0.523114
$297$	0	0
$298$	−5.00000	−0.289642
$299$	−4.00000	−0.231326
$300$	1.00000	0.0577350
$301$	−11.0000	−0.634029
$302$	−11.0000	−0.632979
$303$	−14.0000	−0.804279
$304$	1.00000	0.0573539
$305$	8.00000	0.458079
$306$	6.00000	0.342997
$307$	−7.00000	−0.399511	−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−8.00000	−0.454369
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−12.0000	−0.679366
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	13.0000	0.733632
$315$	−2.00000	−0.112687
$316$	12.0000	0.675053
$317$	33.0000	1.85346	0.926732	−	0.375722i	$-0.122605\pi$
$317$	33.0000	1.85346	0.926732	+	0.375722i	$0.122605\pi$
$318$	5.00000	0.280386
$319$	0	0
$320$	7.00000	0.391312
$321$	−18.0000	−1.00466
$322$	1.00000	0.0557278
$323$	3.00000	0.166924
$324$	−1.00000	−0.0555556
$325$	−4.00000	−0.221880
$326$	3.00000	0.166155
$327$	−16.0000	−0.884802
$328$	−3.00000	−0.165647
$329$	−4.00000	−0.220527
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−4.00000	−0.219529
$333$	−6.00000	−0.328798
$334$	8.00000	0.437741
$335$	−6.00000	−0.327815
$336$	1.00000	0.0545545
$337$	−34.0000	−1.85210	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000	−1.85210	−0.926049	+	0.377403i	$0.876817\pi$
$338$	3.00000	0.163178
$339$	−1.00000	−0.0543125
$340$	3.00000	0.162698
$341$	0	0
$342$	2.00000	0.108148
$343$	1.00000	0.0539949
$344$	33.0000	1.77924
$345$	−1.00000	−0.0538382
$346$	−6.00000	−0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−10.0000	−0.536056
$349$	4.00000	0.214115	0.107058	−	0.994253i	$-0.465857\pi$
$349$	4.00000	0.214115	0.107058	+	0.994253i	$0.465857\pi$
$350$	1.00000	0.0534522
$351$	−20.0000	−1.06752
$352$	0	0
$353$	13.0000	0.691920	0.345960	−	0.938249i	$-0.387553\pi$
$353$	13.0000	0.691920	0.345960	+	0.938249i	$0.387553\pi$
$354$	−14.0000	−0.744092
$355$	−5.00000	−0.265372
$356$	14.0000	0.741999
$357$	3.00000	0.158777
$358$	−13.0000	−0.687071
$359$	−18.0000	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$360$	6.00000	0.316228
$361$	1.00000	0.0526316
$362$	−21.0000	−1.10374
$363$	11.0000	0.577350
$364$	4.00000	0.209657
$365$	15.0000	0.785136
$366$	−8.00000	−0.418167
$367$	−38.0000	−1.98358	−0.991792	−	0.127862i	$-0.959188\pi$
$367$	−38.0000	−1.98358	−0.991792	+	0.127862i	$0.959188\pi$
$368$	−1.00000	−0.0521286
$369$	−2.00000	−0.104116
$370$	3.00000	0.155963
$371$	−5.00000	−0.259587
$372$	−8.00000	−0.414781
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	12.0000	0.618853
$377$	40.0000	2.06010
$378$	5.00000	0.257172
$379$	−25.0000	−1.28416	−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000	−1.28416	−0.642082	+	0.766636i	$0.721929\pi$
$380$	1.00000	0.0512989
$381$	16.0000	0.819705
$382$	−6.00000	−0.306987
$383$	27.0000	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−11.0000	−0.559885
$387$	22.0000	1.11832
$388$	−14.0000	−0.710742
$389$	27.0000	1.36895	0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000	1.36895	0.684477	+	0.729034i	$0.260031\pi$
$390$	4.00000	0.202548
$391$	−3.00000	−0.151717
$392$	−3.00000	−0.151523
$393$	21.0000	1.05931
$394$	−18.0000	−0.906827
$395$	−12.0000	−0.603786
$396$	0	0
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−17.0000	−0.852133
$399$	1.00000	0.0500626
$400$	−1.00000	−0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	6.00000	0.299253
$403$	32.0000	1.59403
$404$	−14.0000	−0.696526
$405$	1.00000	0.0496904
$406$	−10.0000	−0.496292
$407$	0	0
$408$	−9.00000	−0.445566
$409$	−17.0000	−0.840596	−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000	−0.840596	−0.420298	+	0.907386i	$0.638074\pi$
$410$	1.00000	0.0493865
$411$	−12.0000	−0.591916
$412$	−8.00000	−0.394132
$413$	14.0000	0.688895
$414$	−2.00000	−0.0982946
$415$	4.00000	0.196352
$416$	−20.0000	−0.980581
$417$	7.00000	0.342791
$418$	0	0
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	1.00000	0.0487950
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−11.0000	−0.535472
$423$	8.00000	0.388973
$424$	15.0000	0.728464
$425$	−3.00000	−0.145521
$426$	5.00000	0.242251
$427$	8.00000	0.387147
$428$	−18.0000	−0.870063
$429$	0	0
$430$	−11.0000	−0.530467
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	−5.00000	−0.240563
$433$	−4.00000	−0.192228	−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000	−0.192228	−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−8.00000	−0.384012
$435$	10.0000	0.479463
$436$	−16.0000	−0.766261
$437$	−1.00000	−0.0478365
$438$	−15.0000	−0.716728
$439$	2.00000	0.0954548	0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000	0.0954548	0.0477274	+	0.998860i	$0.484802\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	12.0000	0.570782
$443$	−16.0000	−0.760183	−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000	−0.760183	−0.380091	+	0.924949i	$0.624107\pi$
$444$	3.00000	0.142374
$445$	−14.0000	−0.663664
$446$	15.0000	0.710271
$447$	5.00000	0.236492
$448$	7.00000	0.330719
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	−2.00000	−0.0942809
$451$	0	0
$452$	−1.00000	−0.0470360
$453$	11.0000	0.516825
$454$	−15.0000	−0.703985
$455$	−4.00000	−0.187523
$456$	−3.00000	−0.140488
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	24.0000	1.12145
$459$	−15.0000	−0.700140
$460$	−1.00000	−0.0466252
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−31.0000	−1.44069	−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000	−1.44069	−0.720346	+	0.693615i	$0.756017\pi$
$464$	10.0000	0.464238
$465$	8.00000	0.370991
$466$	14.0000	0.648537
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	−8.00000	−0.369800
$469$	−6.00000	−0.277054
$470$	−4.00000	−0.184506
$471$	−13.0000	−0.599008
$472$	−42.0000	−1.93321
$473$	0	0
$474$	12.0000	0.551178
$475$	−1.00000	−0.0458831
$476$	3.00000	0.137505
$477$	10.0000	0.457869
$478$	−10.0000	−0.457389
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	−5.00000	−0.228218
$481$	−12.0000	−0.547153
$482$	−17.0000	−0.774329
$483$	−1.00000	−0.0455016
$484$	11.0000	0.500000
$485$	14.0000	0.635707
$486$	−16.0000	−0.725775
$487$	−42.0000	−1.90320	−0.951601	−	0.307337i	$-0.900562\pi$
$487$	−42.0000	−1.90320	−0.951601	+	0.307337i	$0.900562\pi$
$488$	−24.0000	−1.08643
$489$	−3.00000	−0.135665
$490$	1.00000	0.0451754
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	1.00000	0.0450835
$493$	30.0000	1.35113
$494$	4.00000	0.179969
$495$	0	0
$496$	8.00000	0.359211
$497$	−5.00000	−0.224281
$498$	−4.00000	−0.179244
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	−1.00000	−0.0447214
$501$	−8.00000	−0.357414
$502$	5.00000	0.223161
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	6.00000	0.267261
$505$	14.0000	0.622992
$506$	0	0
$507$	−3.00000	−0.133235
$508$	16.0000	0.709885
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	3.00000	0.132842
$511$	15.0000	0.663561
$512$	−11.0000	−0.486136
$513$	−5.00000	−0.220755
$514$	2.00000	0.0882162
$515$	8.00000	0.352522
$516$	−11.0000	−0.484248
$517$	0	0
$518$	3.00000	0.131812
$519$	6.00000	0.263371
$520$	12.0000	0.526235
$521$	−11.0000	−0.481919	−0.240959	−	0.970535i	$-0.577462\pi$
$521$	−11.0000	−0.481919	−0.240959	+	0.970535i	$0.577462\pi$
$522$	20.0000	0.875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	21.0000	0.917389
$525$	−1.00000	−0.0436436
$526$	19.0000	0.828439
$527$	24.0000	1.04546
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−5.00000	−0.217186
$531$	−28.0000	−1.21510
$532$	1.00000	0.0433555
$533$	−4.00000	−0.173259
$534$	14.0000	0.605839
$535$	18.0000	0.778208
$536$	18.0000	0.777482
$537$	13.0000	0.560991
$538$	−18.0000	−0.776035
$539$	0	0
$540$	−5.00000	−0.215166
$541$	−3.00000	−0.128980	−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000	−0.128980	−0.0644900	+	0.997918i	$0.520542\pi$
$542$	−15.0000	−0.644305
$543$	21.0000	0.901196
$544$	−15.0000	−0.643120
$545$	16.0000	0.685365
$546$	4.00000	0.171184
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−12.0000	−0.512615
$549$	−16.0000	−0.682863
$550$	0	0
$551$	10.0000	0.426014
$552$	3.00000	0.127688
$553$	−12.0000	−0.510292
$554$	−10.0000	−0.424859
$555$	−3.00000	−0.127343
$556$	7.00000	0.296866
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	16.0000	0.677334
$559$	44.0000	1.86100
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	22.0000	0.928014
$563$	9.00000	0.379305	0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000	0.379305	0.189652	+	0.981851i	$0.439264\pi$
$564$	−4.00000	−0.168430
$565$	1.00000	0.0420703
$566$	2.00000	0.0840663
$567$	1.00000	0.0419961
$568$	15.0000	0.629386
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	1.00000	0.0418854
$571$	24.0000	1.00437	0.502184	−	0.864761i	$-0.332530\pi$
$571$	24.0000	1.00437	0.502184	+	0.864761i	$0.332530\pi$
$572$	0	0
$573$	6.00000	0.250654
$574$	1.00000	0.0417392
$575$	1.00000	0.0417029
$576$	−14.0000	−0.583333
$577$	−6.00000	−0.249783	−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000	−0.249783	−0.124892	+	0.992170i	$0.539858\pi$
$578$	−8.00000	−0.332756
$579$	11.0000	0.457144
$580$	10.0000	0.415227
$581$	4.00000	0.165948
$582$	−14.0000	−0.580319
$583$	0	0
$584$	−45.0000	−1.86211
$585$	8.00000	0.330759
$586$	−8.00000	−0.330477
$587$	34.0000	1.40333	0.701665	−	0.712507i	$-0.252440\pi$
$587$	34.0000	1.40333	0.701665	+	0.712507i	$0.252440\pi$
$588$	1.00000	0.0412393
$589$	8.00000	0.329634
$590$	14.0000	0.576371
$591$	18.0000	0.740421
$592$	−3.00000	−0.123299
$593$	29.0000	1.19089	0.595444	−	0.803397i	$-0.296976\pi$
$593$	29.0000	1.19089	0.595444	+	0.803397i	$0.296976\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	5.00000	0.204808
$597$	17.0000	0.695764
$598$	−4.00000	−0.163572
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	3.00000	0.122474
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	−11.0000	−0.448327
$603$	12.0000	0.488678
$604$	11.0000	0.447584
$605$	−11.0000	−0.447214
$606$	−14.0000	−0.568711
$607$	3.00000	0.121766	0.0608831	−	0.998145i	$-0.480608\pi$
$607$	3.00000	0.121766	0.0608831	+	0.998145i	$0.480608\pi$
$608$	−5.00000	−0.202777
$609$	10.0000	0.405220
$610$	8.00000	0.323911
$611$	16.0000	0.647291
$612$	−6.00000	−0.242536
$613$	−24.0000	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$614$	−7.00000	−0.282497
$615$	−1.00000	−0.0403239
$616$	0	0
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	−8.00000	−0.321807
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	8.00000	0.321288
$621$	5.00000	0.200643
$622$	12.0000	0.481156
$623$	−14.0000	−0.560898
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	0	0
$628$	−13.0000	−0.518756
$629$	−9.00000	−0.358854
$630$	−2.00000	−0.0796819
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	36.0000	1.43200
$633$	11.0000	0.437211
$634$	33.0000	1.31060
$635$	−16.0000	−0.634941
$636$	−5.00000	−0.198263
$637$	−4.00000	−0.158486
$638$	0	0
$639$	10.0000	0.395594
$640$	−3.00000	−0.118585
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	−18.0000	−0.710403
$643$	−2.00000	−0.0788723	−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000	−0.0788723	−0.0394362	+	0.999222i	$0.512556\pi$
$644$	−1.00000	−0.0394055
$645$	11.0000	0.433125
$646$	3.00000	0.118033
$647$	38.0000	1.49393	0.746967	−	0.664861i	$-0.231509\pi$
$647$	38.0000	1.49393	0.746967	+	0.664861i	$0.231509\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	−4.00000	−0.156893
$651$	8.00000	0.313545
$652$	−3.00000	−0.117489
$653$	4.00000	0.156532	0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000	0.156532	0.0782660	+	0.996933i	$0.475062\pi$
$654$	−16.0000	−0.625650
$655$	−21.0000	−0.820538
$656$	−1.00000	−0.0390434
$657$	−30.0000	−1.17041
$658$	−4.00000	−0.155936
$659$	−27.0000	−1.05177	−0.525885	−	0.850555i	$-0.676266\pi$
$659$	−27.0000	−1.05177	−0.525885	+	0.850555i	$0.676266\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	8.00000	0.310929
$663$	−12.0000	−0.466041
$664$	−12.0000	−0.465690
$665$	−1.00000	−0.0387783
$666$	−6.00000	−0.232495
$667$	−10.0000	−0.387202
$668$	−8.00000	−0.309529
$669$	−15.0000	−0.579934
$670$	−6.00000	−0.231800
$671$	0	0
$672$	−5.00000	−0.192879
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	−34.0000	−1.30963
$675$	5.00000	0.192450
$676$	−3.00000	−0.115385
$677$	−8.00000	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$678$	−1.00000	−0.0384048
$679$	14.0000	0.537271
$680$	9.00000	0.345134
$681$	15.0000	0.574801
$682$	0	0
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	−2.00000	−0.0764719
$685$	12.0000	0.458496
$686$	1.00000	0.0381802
$687$	−24.0000	−0.915657
$688$	11.0000	0.419371
$689$	20.0000	0.761939
$690$	−1.00000	−0.0380693
$691$	31.0000	1.17930	0.589648	−	0.807661i	$-0.299267\pi$
$691$	31.0000	1.17930	0.589648	+	0.807661i	$0.299267\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	−7.00000	−0.265525
$696$	−30.0000	−1.13715
$697$	−3.00000	−0.113633
$698$	4.00000	0.151402
$699$	−14.0000	−0.529529
$700$	−1.00000	−0.0377964
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−20.0000	−0.754851
$703$	−3.00000	−0.113147
$704$	0	0
$705$	4.00000	0.150649
$706$	13.0000	0.489261
$707$	14.0000	0.526524
$708$	14.0000	0.526152
$709$	−21.0000	−0.788672	−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000	−0.788672	−0.394336	+	0.918966i	$0.629025\pi$
$710$	−5.00000	−0.187647
$711$	24.0000	0.900070
$712$	42.0000	1.57402
$713$	−8.00000	−0.299602
$714$	3.00000	0.112272
$715$	0	0
$716$	13.0000	0.485833
$717$	10.0000	0.373457
$718$	−18.0000	−0.671754
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	2.00000	0.0745356
$721$	8.00000	0.297936
$722$	1.00000	0.0372161
$723$	17.0000	0.632237
$724$	21.0000	0.780459
$725$	−10.0000	−0.371391
$726$	11.0000	0.408248
$727$	−2.00000	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$728$	12.0000	0.444750
$729$	13.0000	0.481481
$730$	15.0000	0.555175
$731$	33.0000	1.22055
$732$	8.00000	0.295689
$733$	31.0000	1.14501	0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000	1.14501	0.572506	+	0.819901i	$0.305971\pi$
$734$	−38.0000	−1.40261
$735$	−1.00000	−0.0368856
$736$	5.00000	0.184302
$737$	0	0
$738$	−2.00000	−0.0736210
$739$	6.00000	0.220714	0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000	0.220714	0.110357	+	0.993892i	$0.464801\pi$
$740$	−3.00000	−0.110282
$741$	−4.00000	−0.146944
$742$	−5.00000	−0.183556
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	−24.0000	−0.879883
$745$	−5.00000	−0.183186
$746$	−14.0000	−0.512576
$747$	−8.00000	−0.292705
$748$	0	0
$749$	18.0000	0.657706
$750$	−1.00000	−0.0365148
$751$	−35.0000	−1.27717	−0.638584	−	0.769552i	$-0.720480\pi$
$751$	−35.0000	−1.27717	−0.638584	+	0.769552i	$0.720480\pi$
$752$	4.00000	0.145865
$753$	−5.00000	−0.182210
$754$	40.0000	1.45671
$755$	−11.0000	−0.400331
$756$	−5.00000	−0.181848
$757$	40.0000	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$757$	40.0000	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$758$	−25.0000	−0.908041
$759$	0	0
$760$	3.00000	0.108821
$761$	2.00000	0.0724999	0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000	0.0724999	0.0362500	+	0.999343i	$0.488459\pi$
$762$	16.0000	0.579619
$763$	16.0000	0.579239
$764$	6.00000	0.217072
$765$	6.00000	0.216930
$766$	27.0000	0.975550
$767$	−56.0000	−2.02204
$768$	17.0000	0.613435
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	11.0000	0.395899
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	22.0000	0.790774
$775$	−8.00000	−0.287368
$776$	−42.0000	−1.50771
$777$	−3.00000	−0.107624
$778$	27.0000	0.967997
$779$	−1.00000	−0.0358287
$780$	−4.00000	−0.143223
$781$	0	0
$782$	−3.00000	−0.107280
$783$	−50.0000	−1.78685
$784$	−1.00000	−0.0357143
$785$	13.0000	0.463990
$786$	21.0000	0.749045
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	18.0000	0.641223
$789$	−19.0000	−0.676418
$790$	−12.0000	−0.426941
$791$	1.00000	0.0355559
$792$	0	0
$793$	−32.0000	−1.13635
$794$	−1.00000	−0.0354887
$795$	5.00000	0.177332
$796$	17.0000	0.602549
$797$	−8.00000	−0.283375	−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000	−0.283375	−0.141687	+	0.989911i	$0.545253\pi$
$798$	1.00000	0.0353996
$799$	12.0000	0.424529
$800$	5.00000	0.176777
$801$	28.0000	0.989331
$802$	10.0000	0.353112
$803$	0	0
$804$	−6.00000	−0.211604
$805$	1.00000	0.0352454
$806$	32.0000	1.12715
$807$	18.0000	0.633630
$808$	−42.0000	−1.47755
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	1.00000	0.0351364
$811$	14.0000	0.491606	0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000	0.491606	0.245803	+	0.969320i	$0.420948\pi$
$812$	10.0000	0.350931
$813$	15.0000	0.526073
$814$	0	0
$815$	3.00000	0.105085
$816$	−3.00000	−0.105021
$817$	11.0000	0.384841
$818$	−17.0000	−0.594391
$819$	8.00000	0.279543
$820$	−1.00000	−0.0349215
$821$	41.0000	1.43091	0.715455	−	0.698659i	$-0.246219\pi$
$821$	41.0000	1.43091	0.715455	+	0.698659i	$0.246219\pi$
$822$	−12.0000	−0.418548
$823$	5.00000	0.174289	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000	0.174289	0.0871445	+	0.996196i	$0.472226\pi$
$824$	−24.0000	−0.836080
$825$	0	0
$826$	14.0000	0.487122
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	2.00000	0.0695048
$829$	−15.0000	−0.520972	−0.260486	−	0.965478i	$-0.583883\pi$
$829$	−15.0000	−0.520972	−0.260486	+	0.965478i	$0.583883\pi$
$830$	4.00000	0.138842
$831$	10.0000	0.346896
$832$	−28.0000	−0.970725
$833$	−3.00000	−0.103944
$834$	7.00000	0.242390
$835$	8.00000	0.276851
$836$	0	0
$837$	−40.0000	−1.38260
$838$	−15.0000	−0.518166
$839$	−42.0000	−1.45000	−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000	−1.45000	−0.725001	+	0.688748i	$0.758161\pi$
$840$	3.00000	0.103510
$841$	71.0000	2.44828
$842$	−2.00000	−0.0689246
$843$	−22.0000	−0.757720
$844$	11.0000	0.378636
$845$	3.00000	0.103203
$846$	8.00000	0.275046
$847$	−11.0000	−0.377964
$848$	5.00000	0.171701
$849$	−2.00000	−0.0686398
$850$	−3.00000	−0.102899
$851$	3.00000	0.102839
$852$	−5.00000	−0.171297
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	8.00000	0.273754
$855$	2.00000	0.0683986
$856$	−54.0000	−1.84568
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	−5.00000	−0.170598	−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000	−0.170598	−0.0852989	+	0.996355i	$0.527185\pi$
$860$	11.0000	0.375097
$861$	−1.00000	−0.0340799
$862$	12.0000	0.408722
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	25.0000	0.850517
$865$	−6.00000	−0.204006
$866$	−4.00000	−0.135926
$867$	8.00000	0.271694
$868$	8.00000	0.271538
$869$	0	0
$870$	10.0000	0.339032
$871$	24.0000	0.813209
$872$	−48.0000	−1.62549
$873$	−28.0000	−0.947656
$874$	−1.00000	−0.0338255
$875$	1.00000	0.0338062
$876$	15.0000	0.506803
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	2.00000	0.0674967
$879$	8.00000	0.269833
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	−2.00000	−0.0673435
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	−12.0000	−0.403604
$885$	−14.0000	−0.470605
$886$	−16.0000	−0.537531
$887$	−5.00000	−0.167884	−0.0839418	−	0.996471i	$-0.526751\pi$
$887$	−5.00000	−0.167884	−0.0839418	+	0.996471i	$0.526751\pi$
$888$	9.00000	0.302020
$889$	−16.0000	−0.536623
$890$	−14.0000	−0.469281
$891$	0	0
$892$	−15.0000	−0.502237
$893$	4.00000	0.133855
$894$	5.00000	0.167225
$895$	−13.0000	−0.434542
$896$	−3.00000	−0.100223
$897$	4.00000	0.133556
$898$	−24.0000	−0.800890
$899$	80.0000	2.66815
$900$	2.00000	0.0666667
$901$	15.0000	0.499722
$902$	0	0
$903$	11.0000	0.366057
$904$	−3.00000	−0.0997785
$905$	−21.0000	−0.698064
$906$	11.0000	0.365451
$907$	−20.0000	−0.664089	−0.332045	−	0.943264i	$-0.607738\pi$
$907$	−20.0000	−0.664089	−0.332045	+	0.943264i	$0.607738\pi$
$908$	15.0000	0.497792
$909$	−28.0000	−0.928701
$910$	−4.00000	−0.132599
$911$	−57.0000	−1.88849	−0.944247	−	0.329238i	$-0.893208\pi$
$911$	−57.0000	−1.88849	−0.944247	+	0.329238i	$0.893208\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	−16.0000	−0.529233
$915$	−8.00000	−0.264472
$916$	−24.0000	−0.792982
$917$	−21.0000	−0.693481
$918$	−15.0000	−0.495074
$919$	28.0000	0.923635	0.461817	−	0.886975i	$-0.347198\pi$
$919$	28.0000	0.923635	0.461817	+	0.886975i	$0.347198\pi$
$920$	−3.00000	−0.0989071
$921$	7.00000	0.230658
$922$	−6.00000	−0.197599
$923$	20.0000	0.658308
$924$	0	0
$925$	3.00000	0.0986394
$926$	−31.0000	−1.01872
$927$	−16.0000	−0.525509
$928$	−50.0000	−1.64133
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	8.00000	0.262330
$931$	−1.00000	−0.0327737
$932$	−14.0000	−0.458585
$933$	−12.0000	−0.392862
$934$	6.00000	0.196326
$935$	0	0
$936$	−24.0000	−0.784465
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−6.00000	−0.195907
$939$	−6.00000	−0.195803
$940$	4.00000	0.130466
$941$	−17.0000	−0.554184	−0.277092	−	0.960843i	$-0.589371\pi$
$941$	−17.0000	−0.554184	−0.277092	+	0.960843i	$0.589371\pi$
$942$	−13.0000	−0.423563
$943$	1.00000	0.0325645
$944$	−14.0000	−0.455661
$945$	5.00000	0.162650
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	−12.0000	−0.389742
$949$	−60.0000	−1.94768
$950$	−1.00000	−0.0324443
$951$	−33.0000	−1.07010
$952$	9.00000	0.291692
$953$	−21.0000	−0.680257	−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000	−0.680257	−0.340128	+	0.940379i	$0.610471\pi$
$954$	10.0000	0.323762
$955$	−6.00000	−0.194155
$956$	10.0000	0.323423
$957$	0	0
$958$	21.0000	0.678479
$959$	12.0000	0.387500
$960$	−7.00000	−0.225924
$961$	33.0000	1.06452
$962$	−12.0000	−0.386896
$963$	−36.0000	−1.16008
$964$	17.0000	0.547533
$965$	−11.0000	−0.354103
$966$	−1.00000	−0.0321745
$967$	−20.0000	−0.643157	−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000	−0.643157	−0.321578	+	0.946883i	$0.604213\pi$
$968$	33.0000	1.06066
$969$	−3.00000	−0.0963739
$970$	14.0000	0.449513
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	16.0000	0.513200
$973$	−7.00000	−0.224410
$974$	−42.0000	−1.34577
$975$	4.00000	0.128103
$976$	−8.00000	−0.256074
$977$	−27.0000	−0.863807	−0.431903	−	0.901920i	$-0.642158\pi$
$977$	−27.0000	−0.863807	−0.431903	+	0.901920i	$0.642158\pi$
$978$	−3.00000	−0.0959294
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−32.0000	−1.02168
$982$	20.0000	0.638226
$983$	23.0000	0.733586	0.366793	−	0.930303i	$-0.380456\pi$
$983$	23.0000	0.733586	0.366793	+	0.930303i	$0.380456\pi$
$984$	3.00000	0.0956365
$985$	−18.0000	−0.573528
$986$	30.0000	0.955395
$987$	4.00000	0.127321
$988$	−4.00000	−0.127257
$989$	−11.0000	−0.349780
$990$	0	0
$991$	−53.0000	−1.68360	−0.841800	−	0.539789i	$-0.818504\pi$
$991$	−53.0000	−1.68360	−0.841800	+	0.539789i	$0.818504\pi$
$992$	−40.0000	−1.27000
$993$	−8.00000	−0.253872
$994$	−5.00000	−0.158590
$995$	−17.0000	−0.538936
$996$	4.00000	0.126745
$997$	−57.0000	−1.80521	−0.902604	−	0.430472i	$-0.858347\pi$
$997$	−57.0000	−1.80521	−0.902604	+	0.430472i	$0.858347\pi$
$998$	36.0000	1.13956
$999$	15.0000	0.474579

Display

a_p

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p

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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

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a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.a.d.1.1	✓	1
3.2	odd	2		5985.2.a.d.1.1		1
5.4	even	2		3325.2.a.e.1.1		1
7.6	odd	2		4655.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.a.d.1.1	✓	1	1.1	even	1	trivial
3325.2.a.e.1.1		1	5.4	even	2
4655.2.a.q.1.1		1	7.6	odd	2
5985.2.a.d.1.1		1	3.2	odd	2

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

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

Label	665.2.a.d.1.1

Level	$665$
Weight	$2$
Character	665.1
Self dual	yes
Analytic conductor	$5.310$
Analytic rank	$1$
Dimension	$1$
CM	no
Inner twists	$1$