LMFDB - Embedded newform 560.6.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,6,Mod(1,560)] 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("560.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	560.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,-1,0,25,0,-49,0,-242] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$89.8149390953$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	560.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} +25.0000 q^{5} -49.0000 q^{7} -242.000 q^{9} +453.000 q^{11} -969.000 q^{13} -25.0000 q^{15} +1637.00 q^{17} +1550.00 q^{19} +49.0000 q^{21} +1654.00 q^{23} +625.000 q^{25} +485.000 q^{27} -4985.00 q^{29} -1192.00 q^{31} -453.000 q^{33} -1225.00 q^{35} -11018.0 q^{37} +969.000 q^{39} -1728.00 q^{41} +10814.0 q^{43} -6050.00 q^{45} -26237.0 q^{47} +2401.00 q^{49} -1637.00 q^{51} +25936.0 q^{53} +11325.0 q^{55} -1550.00 q^{57} +4580.00 q^{59} -12488.0 q^{61} +11858.0 q^{63} -24225.0 q^{65} +15848.0 q^{67} -1654.00 q^{69} -51792.0 q^{71} +4846.00 q^{73} -625.000 q^{75} -22197.0 q^{77} -62765.0 q^{79} +58321.0 q^{81} +23644.0 q^{83} +40925.0 q^{85} +4985.00 q^{87} -147300. q^{89} +47481.0 q^{91} +1192.00 q^{93} +38750.0 q^{95} -8343.00 q^{97} -109626. q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.0641500	−0.0320750	−	0.999485i	$-0.510212\pi$
$3$	−1.00000	−0.0641500	−0.0320750	+	0.999485i	$0.510212\pi$
$4$	0	0
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	0	0
$9$	−242.000	−0.995885
$10$	0	0
$11$	453.000	1.12880	0.564399	−	0.825502i	$-0.309108\pi$
$11$	453.000	1.12880	0.564399	+	0.825502i	$0.309108\pi$
$12$	0	0
$13$	−969.000	−1.59025	−0.795125	−	0.606446i	$-0.792595\pi$
$13$	−969.000	−1.59025	−0.795125	+	0.606446i	$0.792595\pi$
$14$	0	0
$15$	−25.0000	−0.0286888
$16$	0	0
$17$	1637.00	1.37381	0.686905	−	0.726748i	$-0.258969\pi$
$17$	1637.00	1.37381	0.686905	+	0.726748i	$0.258969\pi$
$18$	0	0
$19$	1550.00	0.985026	0.492513	−	0.870305i	$-0.336078\pi$
$19$	1550.00	0.985026	0.492513	+	0.870305i	$0.336078\pi$
$20$	0	0
$21$	49.0000	0.0242464
$22$	0	0
$23$	1654.00	0.651952	0.325976	−	0.945378i	$-0.394307\pi$
$23$	1654.00	0.651952	0.325976	+	0.945378i	$0.394307\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	485.000	0.128036
$28$	0	0
$29$	−4985.00	−1.10070	−0.550352	−	0.834933i	$-0.685506\pi$
$29$	−4985.00	−1.10070	−0.550352	+	0.834933i	$0.685506\pi$
$30$	0	0
$31$	−1192.00	−0.222778	−0.111389	−	0.993777i	$-0.535530\pi$
$31$	−1192.00	−0.222778	−0.111389	+	0.993777i	$0.535530\pi$
$32$	0	0
$33$	−453.000	−0.0724125
$34$	0	0
$35$	−1225.00	−0.169031
$36$	0	0
$37$	−11018.0	−1.32312	−0.661559	−	0.749893i	$-0.730105\pi$
$37$	−11018.0	−1.32312	−0.661559	+	0.749893i	$0.730105\pi$
$38$	0	0
$39$	969.000	0.102015
$40$	0	0
$41$	−1728.00	−0.160540	−0.0802702	−	0.996773i	$-0.525578\pi$
$41$	−1728.00	−0.160540	−0.0802702	+	0.996773i	$0.525578\pi$
$42$	0	0
$43$	10814.0	0.891898	0.445949	−	0.895058i	$-0.352866\pi$
$43$	10814.0	0.891898	0.445949	+	0.895058i	$0.352866\pi$
$44$	0	0
$45$	−6050.00	−0.445373
$46$	0	0
$47$	−26237.0	−1.73249	−0.866243	−	0.499624i	$-0.833472\pi$
$47$	−26237.0	−1.73249	−0.866243	+	0.499624i	$0.833472\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	−1637.00	−0.0881299
$52$	0	0
$53$	25936.0	1.26827	0.634137	−	0.773220i	$-0.281355\pi$
$53$	25936.0	1.26827	0.634137	+	0.773220i	$0.281355\pi$
$54$	0	0
$55$	11325.0	0.504814
$56$	0	0
$57$	−1550.00	−0.0631894
$58$	0	0
$59$	4580.00	0.171291	0.0856457	−	0.996326i	$-0.472705\pi$
$59$	4580.00	0.171291	0.0856457	+	0.996326i	$0.472705\pi$
$60$	0	0
$61$	−12488.0	−0.429703	−0.214851	−	0.976647i	$-0.568927\pi$
$61$	−12488.0	−0.429703	−0.214851	+	0.976647i	$0.568927\pi$
$62$	0	0
$63$	11858.0	0.376409
$64$	0	0
$65$	−24225.0	−0.711181
$66$	0	0
$67$	15848.0	0.431308	0.215654	−	0.976470i	$-0.430812\pi$
$67$	15848.0	0.431308	0.215654	+	0.976470i	$0.430812\pi$
$68$	0	0
$69$	−1654.00	−0.0418228
$70$	0	0
$71$	−51792.0	−1.21932	−0.609659	−	0.792664i	$-0.708694\pi$
$71$	−51792.0	−1.21932	−0.609659	+	0.792664i	$0.708694\pi$
$72$	0	0
$73$	4846.00	0.106433	0.0532165	−	0.998583i	$-0.483053\pi$
$73$	4846.00	0.106433	0.0532165	+	0.998583i	$0.483053\pi$
$74$	0	0
$75$	−625.000	−0.0128300
$76$	0	0
$77$	−22197.0	−0.426646
$78$	0	0
$79$	−62765.0	−1.13149	−0.565744	−	0.824581i	$-0.691411\pi$
$79$	−62765.0	−1.13149	−0.565744	+	0.824581i	$0.691411\pi$
$80$	0	0
$81$	58321.0	0.987671
$82$	0	0
$83$	23644.0	0.376726	0.188363	−	0.982099i	$-0.439682\pi$
$83$	23644.0	0.376726	0.188363	+	0.982099i	$0.439682\pi$
$84$	0	0
$85$	40925.0	0.614386
$86$	0	0
$87$	4985.00	0.0706101
$88$	0	0
$89$	−147300.	−1.97119	−0.985593	−	0.169133i	$-0.945903\pi$
$89$	−147300.	−1.97119	−0.985593	+	0.169133i	$0.945903\pi$
$90$	0	0
$91$	47481.0	0.601058
$92$	0	0
$93$	1192.00	0.0142912
$94$	0	0
$95$	38750.0	0.440517
$96$	0	0
$97$	−8343.00	−0.0900312	−0.0450156	−	0.998986i	$-0.514334\pi$
$97$	−8343.00	−0.0900312	−0.0450156	+	0.998986i	$0.514334\pi$
$98$	0	0
$99$	−109626.	−1.12415
$100$	0	0
$101$	−11878.0	−0.115862	−0.0579308	−	0.998321i	$-0.518450\pi$
$101$	−11878.0	−0.115862	−0.0579308	+	0.998321i	$0.518450\pi$
$102$	0	0
$103$	132439.	1.23005	0.615025	−	0.788508i	$-0.289146\pi$
$103$	132439.	1.23005	0.615025	+	0.788508i	$0.289146\pi$
$104$	0	0
$105$	1225.00	0.0108433
$106$	0	0
$107$	−136842.	−1.15547	−0.577737	−	0.816223i	$-0.696064\pi$
$107$	−136842.	−1.15547	−0.577737	+	0.816223i	$0.696064\pi$
$108$	0	0
$109$	109485.	0.882650	0.441325	−	0.897347i	$-0.354509\pi$
$109$	109485.	0.882650	0.441325	+	0.897347i	$0.354509\pi$
$110$	0	0
$111$	11018.0	0.0848780
$112$	0	0
$113$	−200934.	−1.48033	−0.740163	−	0.672428i	$-0.765252\pi$
$113$	−200934.	−1.48033	−0.740163	+	0.672428i	$0.765252\pi$
$114$	0	0
$115$	41350.0	0.291562
$116$	0	0
$117$	234498.	1.58371
$118$	0	0
$119$	−80213.0	−0.519251
$120$	0	0
$121$	44158.0	0.274186
$122$	0	0
$123$	1728.00	0.0102987
$124$	0	0
$125$	15625.0	0.0894427
$126$	0	0
$127$	−330692.	−1.81934	−0.909671	−	0.415329i	$-0.863666\pi$
$127$	−330692.	−1.81934	−0.909671	+	0.415329i	$0.863666\pi$
$128$	0	0
$129$	−10814.0	−0.0572153
$130$	0	0
$131$	−43982.0	−0.223922	−0.111961	−	0.993713i	$-0.535713\pi$
$131$	−43982.0	−0.223922	−0.111961	+	0.993713i	$0.535713\pi$
$132$	0	0
$133$	−75950.0	−0.372305
$134$	0	0
$135$	12125.0	0.0572595
$136$	0	0
$137$	−99748.0	−0.454049	−0.227025	−	0.973889i	$-0.572900\pi$
$137$	−99748.0	−0.454049	−0.227025	+	0.973889i	$0.572900\pi$
$138$	0	0
$139$	−258930.	−1.13670	−0.568349	−	0.822787i	$-0.692418\pi$
$139$	−258930.	−1.13670	−0.568349	+	0.822787i	$0.692418\pi$
$140$	0	0
$141$	26237.0	0.111139
$142$	0	0
$143$	−438957.	−1.79507
$144$	0	0
$145$	−124625.	−0.492249
$146$	0	0
$147$	−2401.00	−0.00916429
$148$	0	0
$149$	−498430.	−1.83924	−0.919620	−	0.392809i	$-0.871503\pi$
$149$	−498430.	−1.83924	−0.919620	+	0.392809i	$0.871503\pi$
$150$	0	0
$151$	245803.	0.877293	0.438647	−	0.898660i	$-0.355458\pi$
$151$	245803.	0.877293	0.438647	+	0.898660i	$0.355458\pi$
$152$	0	0
$153$	−396154.	−1.36816
$154$	0	0
$155$	−29800.0	−0.0996293
$156$	0	0
$157$	−85478.0	−0.276761	−0.138381	−	0.990379i	$-0.544190\pi$
$157$	−85478.0	−0.276761	−0.138381	+	0.990379i	$0.544190\pi$
$158$	0	0
$159$	−25936.0	−0.0813599
$160$	0	0
$161$	−81046.0	−0.246415
$162$	0	0
$163$	−193026.	−0.569045	−0.284523	−	0.958669i	$-0.591835\pi$
$163$	−193026.	−0.569045	−0.284523	+	0.958669i	$0.591835\pi$
$164$	0	0
$165$	−11325.0	−0.0323838
$166$	0	0
$167$	157783.	0.437793	0.218897	−	0.975748i	$-0.429754\pi$
$167$	157783.	0.437793	0.218897	+	0.975748i	$0.429754\pi$
$168$	0	0
$169$	567668.	1.52889
$170$	0	0
$171$	−375100.	−0.980972
$172$	0	0
$173$	−265659.	−0.674853	−0.337427	−	0.941352i	$-0.609556\pi$
$173$	−265659.	−0.674853	−0.337427	+	0.941352i	$0.609556\pi$
$174$	0	0
$175$	−30625.0	−0.0755929
$176$	0	0
$177$	−4580.00	−0.0109883
$178$	0	0
$179$	−183660.	−0.428432	−0.214216	−	0.976786i	$-0.568720\pi$
$179$	−183660.	−0.428432	−0.214216	+	0.976786i	$0.568720\pi$
$180$	0	0
$181$	−635048.	−1.44082	−0.720411	−	0.693548i	$-0.756047\pi$
$181$	−635048.	−1.44082	−0.720411	+	0.693548i	$0.756047\pi$
$182$	0	0
$183$	12488.0	0.0275655
$184$	0	0
$185$	−275450.	−0.591716
$186$	0	0
$187$	741561.	1.55075
$188$	0	0
$189$	−23765.0	−0.0483931
$190$	0	0
$191$	226613.	0.449471	0.224735	−	0.974420i	$-0.427848\pi$
$191$	226613.	0.449471	0.224735	+	0.974420i	$0.427848\pi$
$192$	0	0
$193$	46476.0	0.0898122	0.0449061	−	0.998991i	$-0.485701\pi$
$193$	46476.0	0.0898122	0.0449061	+	0.998991i	$0.485701\pi$
$194$	0	0
$195$	24225.0	0.0456223
$196$	0	0
$197$	204972.	0.376295	0.188148	−	0.982141i	$-0.439752\pi$
$197$	204972.	0.376295	0.188148	+	0.982141i	$0.439752\pi$
$198$	0	0
$199$	953020.	1.70596	0.852981	−	0.521942i	$-0.174792\pi$
$199$	953020.	1.70596	0.852981	+	0.521942i	$0.174792\pi$
$200$	0	0
$201$	−15848.0	−0.0276684
$202$	0	0
$203$	244265.	0.416027
$204$	0	0
$205$	−43200.0	−0.0717958
$206$	0	0
$207$	−400268.	−0.649270
$208$	0	0
$209$	702150.	1.11190
$210$	0	0
$211$	223523.	0.345634	0.172817	−	0.984954i	$-0.444713\pi$
$211$	223523.	0.345634	0.172817	+	0.984954i	$0.444713\pi$
$212$	0	0
$213$	51792.0	0.0782193
$214$	0	0
$215$	270350.	0.398869
$216$	0	0
$217$	58408.0	0.0842021
$218$	0	0
$219$	−4846.00	−0.00682768
$220$	0	0
$221$	−1.58625e6	−2.18470
$222$	0	0
$223$	−1.01480e6	−1.36653	−0.683264	−	0.730171i	$-0.739440\pi$
$223$	−1.01480e6	−1.36653	−0.683264	+	0.730171i	$0.739440\pi$
$224$	0	0
$225$	−151250.	−0.199177
$226$	0	0
$227$	−999797.	−1.28780	−0.643898	−	0.765111i	$-0.722684\pi$
$227$	−999797.	−1.28780	−0.643898	+	0.765111i	$0.722684\pi$
$228$	0	0
$229$	−851120.	−1.07251	−0.536256	−	0.844055i	$-0.680162\pi$
$229$	−851120.	−1.07251	−0.536256	+	0.844055i	$0.680162\pi$
$230$	0	0
$231$	22197.0	0.0273693
$232$	0	0
$233$	1.09270e6	1.31859	0.659295	−	0.751885i	$-0.270855\pi$
$233$	1.09270e6	1.31859	0.659295	+	0.751885i	$0.270855\pi$
$234$	0	0
$235$	−655925.	−0.774791
$236$	0	0
$237$	62765.0	0.0725850
$238$	0	0
$239$	−765905.	−0.867322	−0.433661	−	0.901076i	$-0.642778\pi$
$239$	−765905.	−0.867322	−0.433661	+	0.901076i	$0.642778\pi$
$240$	0	0
$241$	−1.21094e6	−1.34301	−0.671505	−	0.741000i	$-0.734352\pi$
$241$	−1.21094e6	−1.34301	−0.671505	+	0.741000i	$0.734352\pi$
$242$	0	0
$243$	−176176.	−0.191395
$244$	0	0
$245$	60025.0	0.0638877
$246$	0	0
$247$	−1.50195e6	−1.56644
$248$	0	0
$249$	−23644.0	−0.0241670
$250$	0	0
$251$	−278262.	−0.278785	−0.139393	−	0.990237i	$-0.544515\pi$
$251$	−278262.	−0.278785	−0.139393	+	0.990237i	$0.544515\pi$
$252$	0	0
$253$	749262.	0.735923
$254$	0	0
$255$	−40925.0	−0.0394129
$256$	0	0
$257$	−352998.	−0.333380	−0.166690	−	0.986009i	$-0.553308\pi$
$257$	−352998.	−0.333380	−0.166690	+	0.986009i	$0.553308\pi$
$258$	0	0
$259$	539882.	0.500091
$260$	0	0
$261$	1.20637e6	1.09617
$262$	0	0
$263$	1.55809e6	1.38901	0.694503	−	0.719490i	$-0.255624\pi$
$263$	1.55809e6	1.38901	0.694503	+	0.719490i	$0.255624\pi$
$264$	0	0
$265$	648400.	0.567190
$266$	0	0
$267$	147300.	0.126452
$268$	0	0
$269$	−1.21963e6	−1.02766	−0.513828	−	0.857893i	$-0.671773\pi$
$269$	−1.21963e6	−1.02766	−0.513828	+	0.857893i	$0.671773\pi$
$270$	0	0
$271$	−405792.	−0.335645	−0.167823	−	0.985817i	$-0.553674\pi$
$271$	−405792.	−0.335645	−0.167823	+	0.985817i	$0.553674\pi$
$272$	0	0
$273$	−47481.0	−0.0385579
$274$	0	0
$275$	283125.	0.225760
$276$	0	0
$277$	652442.	0.510908	0.255454	−	0.966821i	$-0.417775\pi$
$277$	652442.	0.510908	0.255454	+	0.966821i	$0.417775\pi$
$278$	0	0
$279$	288464.	0.221861
$280$	0	0
$281$	118827.	0.0897737	0.0448869	−	0.998992i	$-0.485707\pi$
$281$	118827.	0.0897737	0.0448869	+	0.998992i	$0.485707\pi$
$282$	0	0
$283$	−1.48801e6	−1.10443	−0.552217	−	0.833700i	$-0.686218\pi$
$283$	−1.48801e6	−1.10443	−0.552217	+	0.833700i	$0.686218\pi$
$284$	0	0
$285$	−38750.0	−0.0282592
$286$	0	0
$287$	84672.0	0.0606785
$288$	0	0
$289$	1.25991e6	0.887351
$290$	0	0
$291$	8343.00	0.00577550
$292$	0	0
$293$	1.89580e6	1.29010	0.645050	−	0.764140i	$-0.276836\pi$
$293$	1.89580e6	1.29010	0.645050	+	0.764140i	$0.276836\pi$
$294$	0	0
$295$	114500.	0.0766038
$296$	0	0
$297$	219705.	0.144527
$298$	0	0
$299$	−1.60273e6	−1.03677
$300$	0	0
$301$	−529886.	−0.337106
$302$	0	0
$303$	11878.0	0.00743253
$304$	0	0
$305$	−312200.	−0.192169
$306$	0	0
$307$	821853.	0.497678	0.248839	−	0.968545i	$-0.419951\pi$
$307$	821853.	0.497678	0.248839	+	0.968545i	$0.419951\pi$
$308$	0	0
$309$	−132439.	−0.0789078
$310$	0	0
$311$	2.09600e6	1.22882	0.614412	−	0.788985i	$-0.289393\pi$
$311$	2.09600e6	1.22882	0.614412	+	0.788985i	$0.289393\pi$
$312$	0	0
$313$	394571.	0.227648	0.113824	−	0.993501i	$-0.463690\pi$
$313$	394571.	0.227648	0.113824	+	0.993501i	$0.463690\pi$
$314$	0	0
$315$	296450.	0.168335
$316$	0	0
$317$	321422.	0.179650	0.0898250	−	0.995958i	$-0.471369\pi$
$317$	321422.	0.179650	0.0898250	+	0.995958i	$0.471369\pi$
$318$	0	0
$319$	−2.25820e6	−1.24247
$320$	0	0
$321$	136842.	0.0741237
$322$	0	0
$323$	2.53735e6	1.35324
$324$	0	0
$325$	−605625.	−0.318050
$326$	0	0
$327$	−109485.	−0.0566220
$328$	0	0
$329$	1.28561e6	0.654818
$330$	0	0
$331$	2.23259e6	1.12005	0.560027	−	0.828475i	$-0.310791\pi$
$331$	2.23259e6	1.12005	0.560027	+	0.828475i	$0.310791\pi$
$332$	0	0
$333$	2.66636e6	1.31767
$334$	0	0
$335$	396200.	0.192887
$336$	0	0
$337$	−3.65656e6	−1.75387	−0.876936	−	0.480608i	$-0.840416\pi$
$337$	−3.65656e6	−1.75387	−0.876936	+	0.480608i	$0.840416\pi$
$338$	0	0
$339$	200934.	0.0949629
$340$	0	0
$341$	−539976.	−0.251471
$342$	0	0
$343$	−117649.	−0.0539949
$344$	0	0
$345$	−41350.0	−0.0187037
$346$	0	0
$347$	1.88962e6	0.842462	0.421231	−	0.906953i	$-0.361598\pi$
$347$	1.88962e6	0.842462	0.421231	+	0.906953i	$0.361598\pi$
$348$	0	0
$349$	−2.69329e6	−1.18364	−0.591820	−	0.806070i	$-0.701590\pi$
$349$	−2.69329e6	−1.18364	−0.591820	+	0.806070i	$0.701590\pi$
$350$	0	0
$351$	−469965.	−0.203609
$352$	0	0
$353$	−1.57468e6	−0.672598	−0.336299	−	0.941755i	$-0.609175\pi$
$353$	−1.57468e6	−0.672598	−0.336299	+	0.941755i	$0.609175\pi$
$354$	0	0
$355$	−1.29480e6	−0.545295
$356$	0	0
$357$	80213.0	0.0333100
$358$	0	0
$359$	−4.05576e6	−1.66087	−0.830436	−	0.557114i	$-0.811909\pi$
$359$	−4.05576e6	−1.66087	−0.830436	+	0.557114i	$0.811909\pi$
$360$	0	0
$361$	−73599.0	−0.0297238
$362$	0	0
$363$	−44158.0	−0.0175891
$364$	0	0
$365$	121150.	0.0475983
$366$	0	0
$367$	4.90628e6	1.90146	0.950731	−	0.310018i	$-0.100335\pi$
$367$	4.90628e6	1.90146	0.950731	+	0.310018i	$0.100335\pi$
$368$	0	0
$369$	418176.	0.159880
$370$	0	0
$371$	−1.27086e6	−0.479363
$372$	0	0
$373$	−3.45336e6	−1.28520	−0.642599	−	0.766202i	$-0.722144\pi$
$373$	−3.45336e6	−1.28520	−0.642599	+	0.766202i	$0.722144\pi$
$374$	0	0
$375$	−15625.0	−0.00573775
$376$	0	0
$377$	4.83046e6	1.75039
$378$	0	0
$379$	4.23466e6	1.51433	0.757165	−	0.653224i	$-0.226584\pi$
$379$	4.23466e6	1.51433	0.757165	+	0.653224i	$0.226584\pi$
$380$	0	0
$381$	330692.	0.116711
$382$	0	0
$383$	1.86460e6	0.649516	0.324758	−	0.945797i	$-0.394717\pi$
$383$	1.86460e6	0.649516	0.324758	+	0.945797i	$0.394717\pi$
$384$	0	0
$385$	−554925.	−0.190802
$386$	0	0
$387$	−2.61699e6	−0.888228
$388$	0	0
$389$	−4.81502e6	−1.61333	−0.806666	−	0.591008i	$-0.798730\pi$
$389$	−4.81502e6	−1.61333	−0.806666	+	0.591008i	$0.798730\pi$
$390$	0	0
$391$	2.70760e6	0.895658
$392$	0	0
$393$	43982.0	0.0143646
$394$	0	0
$395$	−1.56912e6	−0.506017
$396$	0	0
$397$	1.21376e6	0.386505	0.193253	−	0.981149i	$-0.438096\pi$
$397$	1.21376e6	0.386505	0.193253	+	0.981149i	$0.438096\pi$
$398$	0	0
$399$	75950.0	0.0238834
$400$	0	0
$401$	5.90442e6	1.83365	0.916824	−	0.399291i	$-0.130744\pi$
$401$	5.90442e6	1.83365	0.916824	+	0.399291i	$0.130744\pi$
$402$	0	0
$403$	1.15505e6	0.354272
$404$	0	0
$405$	1.45802e6	0.441700
$406$	0	0
$407$	−4.99115e6	−1.49353
$408$	0	0
$409$	4.84289e6	1.43152	0.715758	−	0.698348i	$-0.246081\pi$
$409$	4.84289e6	1.43152	0.715758	+	0.698348i	$0.246081\pi$
$410$	0	0
$411$	99748.0	0.0291273
$412$	0	0
$413$	−224420.	−0.0647420
$414$	0	0
$415$	591100.	0.168477
$416$	0	0
$417$	258930.	0.0729193
$418$	0	0
$419$	−270360.	−0.0752328	−0.0376164	−	0.999292i	$-0.511977\pi$
$419$	−270360.	−0.0752328	−0.0376164	+	0.999292i	$0.511977\pi$
$420$	0	0
$421$	3.13648e6	0.862456	0.431228	−	0.902243i	$-0.358080\pi$
$421$	3.13648e6	0.862456	0.431228	+	0.902243i	$0.358080\pi$
$422$	0	0
$423$	6.34935e6	1.72536
$424$	0	0
$425$	1.02312e6	0.274762
$426$	0	0
$427$	611912.	0.162412
$428$	0	0
$429$	438957.	0.115154
$430$	0	0
$431$	1.87703e6	0.486719	0.243360	−	0.969936i	$-0.421750\pi$
$431$	1.87703e6	0.486719	0.243360	+	0.969936i	$0.421750\pi$
$432$	0	0
$433$	3.20357e6	0.821134	0.410567	−	0.911830i	$-0.365331\pi$
$433$	3.20357e6	0.821134	0.410567	+	0.911830i	$0.365331\pi$
$434$	0	0
$435$	124625.	0.0315778
$436$	0	0
$437$	2.56370e6	0.642190
$438$	0	0
$439$	6.27209e6	1.55328	0.776642	−	0.629942i	$-0.216921\pi$
$439$	6.27209e6	1.55328	0.776642	+	0.629942i	$0.216921\pi$
$440$	0	0
$441$	−581042.	−0.142269
$442$	0	0
$443$	−724986.	−0.175517	−0.0877587	−	0.996142i	$-0.527970\pi$
$443$	−724986.	−0.175517	−0.0877587	+	0.996142i	$0.527970\pi$
$444$	0	0
$445$	−3.68250e6	−0.881541
$446$	0	0
$447$	498430.	0.117987
$448$	0	0
$449$	−875985.	−0.205060	−0.102530	−	0.994730i	$-0.532694\pi$
$449$	−875985.	−0.205060	−0.102530	+	0.994730i	$0.532694\pi$
$450$	0	0
$451$	−782784.	−0.181218
$452$	0	0
$453$	−245803.	−0.0562784
$454$	0	0
$455$	1.18702e6	0.268801
$456$	0	0
$457$	−832668.	−0.186501	−0.0932505	−	0.995643i	$-0.529726\pi$
$457$	−832668.	−0.186501	−0.0932505	+	0.995643i	$0.529726\pi$
$458$	0	0
$459$	793945.	0.175897
$460$	0	0
$461$	5.92115e6	1.29764	0.648820	−	0.760942i	$-0.275263\pi$
$461$	5.92115e6	1.29764	0.648820	+	0.760942i	$0.275263\pi$
$462$	0	0
$463$	−682776.	−0.148022	−0.0740109	−	0.997257i	$-0.523580\pi$
$463$	−682776.	−0.148022	−0.0740109	+	0.997257i	$0.523580\pi$
$464$	0	0
$465$	29800.0	0.00639122
$466$	0	0
$467$	5.41667e6	1.14932	0.574659	−	0.818393i	$-0.305135\pi$
$467$	5.41667e6	1.14932	0.574659	+	0.818393i	$0.305135\pi$
$468$	0	0
$469$	−776552.	−0.163019
$470$	0	0
$471$	85478.0	0.0177542
$472$	0	0
$473$	4.89874e6	1.00677
$474$	0	0
$475$	968750.	0.197005
$476$	0	0
$477$	−6.27651e6	−1.26306
$478$	0	0
$479$	−1.98599e6	−0.395493	−0.197746	−	0.980253i	$-0.563362\pi$
$479$	−1.98599e6	−0.395493	−0.197746	+	0.980253i	$0.563362\pi$
$480$	0	0
$481$	1.06764e7	2.10409
$482$	0	0
$483$	81046.0	0.0158075
$484$	0	0
$485$	−208575.	−0.0402632
$486$	0	0
$487$	1.06974e6	0.204388	0.102194	−	0.994764i	$-0.467414\pi$
$487$	1.06974e6	0.204388	0.102194	+	0.994764i	$0.467414\pi$
$488$	0	0
$489$	193026.	0.0365043
$490$	0	0
$491$	−4.59246e6	−0.859689	−0.429844	−	0.902903i	$-0.641432\pi$
$491$	−4.59246e6	−0.859689	−0.429844	+	0.902903i	$0.641432\pi$
$492$	0	0
$493$	−8.16045e6	−1.51216
$494$	0	0
$495$	−2.74065e6	−0.502737
$496$	0	0
$497$	2.53781e6	0.460859
$498$	0	0
$499$	−1.96066e6	−0.352492	−0.176246	−	0.984346i	$-0.556395\pi$
$499$	−1.96066e6	−0.352492	−0.176246	+	0.984346i	$0.556395\pi$
$500$	0	0
$501$	−157783.	−0.0280844
$502$	0	0
$503$	−3.51483e6	−0.619419	−0.309709	−	0.950831i	$-0.600232\pi$
$503$	−3.51483e6	−0.619419	−0.309709	+	0.950831i	$0.600232\pi$
$504$	0	0
$505$	−296950.	−0.0518149
$506$	0	0
$507$	−567668.	−0.0980787
$508$	0	0
$509$	−1.45211e6	−0.248431	−0.124215	−	0.992255i	$-0.539641\pi$
$509$	−1.45211e6	−0.248431	−0.124215	+	0.992255i	$0.539641\pi$
$510$	0	0
$511$	−237454.	−0.0402279
$512$	0	0
$513$	751750.	0.126119
$514$	0	0
$515$	3.31098e6	0.550095
$516$	0	0
$517$	−1.18854e7	−1.95563
$518$	0	0
$519$	265659.	0.0432918
$520$	0	0
$521$	−4.24240e6	−0.684726	−0.342363	−	0.939568i	$-0.611227\pi$
$521$	−4.24240e6	−0.684726	−0.342363	+	0.939568i	$0.611227\pi$
$522$	0	0
$523$	7.56012e6	1.20858	0.604289	−	0.796765i	$-0.293457\pi$
$523$	7.56012e6	1.20858	0.604289	+	0.796765i	$0.293457\pi$
$524$	0	0
$525$	30625.0	0.00484929
$526$	0	0
$527$	−1.95130e6	−0.306054
$528$	0	0
$529$	−3.70063e6	−0.574958
$530$	0	0
$531$	−1.10836e6	−0.170586
$532$	0	0
$533$	1.67443e6	0.255299
$534$	0	0
$535$	−3.42105e6	−0.516743
$536$	0	0
$537$	183660.	0.0274839
$538$	0	0
$539$	1.08765e6	0.161257
$540$	0	0
$541$	1.24065e6	0.182245	0.0911224	−	0.995840i	$-0.470955\pi$
$541$	1.24065e6	0.182245	0.0911224	+	0.995840i	$0.470955\pi$
$542$	0	0
$543$	635048.	0.0924287
$544$	0	0
$545$	2.73712e6	0.394733
$546$	0	0
$547$	1.85057e6	0.264446	0.132223	−	0.991220i	$-0.457789\pi$
$547$	1.85057e6	0.264446	0.132223	+	0.991220i	$0.457789\pi$
$548$	0	0
$549$	3.02210e6	0.427935
$550$	0	0
$551$	−7.72675e6	−1.08422
$552$	0	0
$553$	3.07548e6	0.427662
$554$	0	0
$555$	275450.	0.0379586
$556$	0	0
$557$	7.77555e6	1.06192	0.530962	−	0.847396i	$-0.321831\pi$
$557$	7.77555e6	1.06192	0.530962	+	0.847396i	$0.321831\pi$
$558$	0	0
$559$	−1.04788e7	−1.41834
$560$	0	0
$561$	−741561.	−0.0994809
$562$	0	0
$563$	−8.37716e6	−1.11385	−0.556924	−	0.830564i	$-0.688018\pi$
$563$	−8.37716e6	−1.11385	−0.556924	+	0.830564i	$0.688018\pi$
$564$	0	0
$565$	−5.02335e6	−0.662022
$566$	0	0
$567$	−2.85773e6	−0.373305
$568$	0	0
$569$	−6.15591e6	−0.797098	−0.398549	−	0.917147i	$-0.630486\pi$
$569$	−6.15591e6	−0.797098	−0.398549	+	0.917147i	$0.630486\pi$
$570$	0	0
$571$	−7.21513e6	−0.926092	−0.463046	−	0.886334i	$-0.653243\pi$
$571$	−7.21513e6	−0.926092	−0.463046	+	0.886334i	$0.653243\pi$
$572$	0	0
$573$	−226613.	−0.0288336
$574$	0	0
$575$	1.03375e6	0.130390
$576$	0	0
$577$	1.36699e7	1.70933	0.854666	−	0.519177i	$-0.173762\pi$
$577$	1.36699e7	1.70933	0.854666	+	0.519177i	$0.173762\pi$
$578$	0	0
$579$	−46476.0	−0.00576146
$580$	0	0
$581$	−1.15856e6	−0.142389
$582$	0	0
$583$	1.17490e7	1.43163
$584$	0	0
$585$	5.86245e6	0.708255
$586$	0	0
$587$	1.00686e7	1.20608	0.603040	−	0.797711i	$-0.293956\pi$
$587$	1.00686e7	1.20608	0.603040	+	0.797711i	$0.293956\pi$
$588$	0	0
$589$	−1.84760e6	−0.219442
$590$	0	0
$591$	−204972.	−0.0241394
$592$	0	0
$593$	9.80615e6	1.14515	0.572574	−	0.819853i	$-0.305945\pi$
$593$	9.80615e6	1.14515	0.572574	+	0.819853i	$0.305945\pi$
$594$	0	0
$595$	−2.00532e6	−0.232216
$596$	0	0
$597$	−953020.	−0.109438
$598$	0	0
$599$	−8.26257e6	−0.940911	−0.470455	−	0.882424i	$-0.655910\pi$
$599$	−8.26257e6	−0.940911	−0.470455	+	0.882424i	$0.655910\pi$
$600$	0	0
$601$	−3.59492e6	−0.405978	−0.202989	−	0.979181i	$-0.565066\pi$
$601$	−3.59492e6	−0.405978	−0.202989	+	0.979181i	$0.565066\pi$
$602$	0	0
$603$	−3.83522e6	−0.429533
$604$	0	0
$605$	1.10395e6	0.122620
$606$	0	0
$607$	1.32969e7	1.46480	0.732401	−	0.680873i	$-0.238400\pi$
$607$	1.32969e7	1.46480	0.732401	+	0.680873i	$0.238400\pi$
$608$	0	0
$609$	−244265.	−0.0266881
$610$	0	0
$611$	2.54237e7	2.75508
$612$	0	0
$613$	2.50327e6	0.269064	0.134532	−	0.990909i	$-0.457047\pi$
$613$	2.50327e6	0.269064	0.134532	+	0.990909i	$0.457047\pi$
$614$	0	0
$615$	43200.0	0.00460570
$616$	0	0
$617$	1.88254e6	0.199082	0.0995409	−	0.995033i	$-0.468263\pi$
$617$	1.88254e6	0.199082	0.0995409	+	0.995033i	$0.468263\pi$
$618$	0	0
$619$	−8.21487e6	−0.861736	−0.430868	−	0.902415i	$-0.641792\pi$
$619$	−8.21487e6	−0.861736	−0.430868	+	0.902415i	$0.641792\pi$
$620$	0	0
$621$	802190.	0.0834734
$622$	0	0
$623$	7.21770e6	0.745038
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	−702150.	−0.0713282
$628$	0	0
$629$	−1.80365e7	−1.81771
$630$	0	0
$631$	−1.61155e7	−1.61128	−0.805638	−	0.592408i	$-0.798177\pi$
$631$	−1.61155e7	−1.61128	−0.805638	+	0.592408i	$0.798177\pi$
$632$	0	0
$633$	−223523.	−0.0221724
$634$	0	0
$635$	−8.26730e6	−0.813635
$636$	0	0
$637$	−2.32657e6	−0.227179
$638$	0	0
$639$	1.25337e7	1.21430
$640$	0	0
$641$	−8.50544e6	−0.817620	−0.408810	−	0.912619i	$-0.634056\pi$
$641$	−8.50544e6	−0.817620	−0.408810	+	0.912619i	$0.634056\pi$
$642$	0	0
$643$	1.32191e7	1.26088	0.630440	−	0.776238i	$-0.282874\pi$
$643$	1.32191e7	1.26088	0.630440	+	0.776238i	$0.282874\pi$
$644$	0	0
$645$	−270350.	−0.0255875
$646$	0	0
$647$	−1.89115e6	−0.177609	−0.0888047	−	0.996049i	$-0.528305\pi$
$647$	−1.89115e6	−0.177609	−0.0888047	+	0.996049i	$0.528305\pi$
$648$	0	0
$649$	2.07474e6	0.193353
$650$	0	0
$651$	−58408.0	−0.00540157
$652$	0	0
$653$	4.90587e6	0.450228	0.225114	−	0.974332i	$-0.427725\pi$
$653$	4.90587e6	0.450228	0.225114	+	0.974332i	$0.427725\pi$
$654$	0	0
$655$	−1.09955e6	−0.100141
$656$	0	0
$657$	−1.17273e6	−0.105995
$658$	0	0
$659$	−1.36367e7	−1.22319	−0.611597	−	0.791169i	$-0.709473\pi$
$659$	−1.36367e7	−1.22319	−0.611597	+	0.791169i	$0.709473\pi$
$660$	0	0
$661$	−2.22345e6	−0.197935	−0.0989677	−	0.995091i	$-0.531554\pi$
$661$	−2.22345e6	−0.197935	−0.0989677	+	0.995091i	$0.531554\pi$
$662$	0	0
$663$	1.58625e6	0.140149
$664$	0	0
$665$	−1.89875e6	−0.166500
$666$	0	0
$667$	−8.24519e6	−0.717606
$668$	0	0
$669$	1.01480e6	0.0876629
$670$	0	0
$671$	−5.65706e6	−0.485048
$672$	0	0
$673$	4.88484e6	0.415731	0.207865	−	0.978157i	$-0.433348\pi$
$673$	4.88484e6	0.415731	0.207865	+	0.978157i	$0.433348\pi$
$674$	0	0
$675$	303125.	0.0256072
$676$	0	0
$677$	−1.98785e7	−1.66691	−0.833453	−	0.552590i	$-0.813640\pi$
$677$	−1.98785e7	−1.66691	−0.833453	+	0.552590i	$0.813640\pi$
$678$	0	0
$679$	408807.	0.0340286
$680$	0	0
$681$	999797.	0.0826122
$682$	0	0
$683$	−4.27870e6	−0.350962	−0.175481	−	0.984483i	$-0.556148\pi$
$683$	−4.27870e6	−0.350962	−0.175481	+	0.984483i	$0.556148\pi$
$684$	0	0
$685$	−2.49370e6	−0.203057
$686$	0	0
$687$	851120.	0.0688017
$688$	0	0
$689$	−2.51320e7	−2.01687
$690$	0	0
$691$	−9.48925e6	−0.756026	−0.378013	−	0.925800i	$-0.623393\pi$
$691$	−9.48925e6	−0.756026	−0.378013	+	0.925800i	$0.623393\pi$
$692$	0	0
$693$	5.37167e6	0.424890
$694$	0	0
$695$	−6.47325e6	−0.508347
$696$	0	0
$697$	−2.82874e6	−0.220552
$698$	0	0
$699$	−1.09270e6	−0.0845875
$700$	0	0
$701$	−5.86385e6	−0.450700	−0.225350	−	0.974278i	$-0.572353\pi$
$701$	−5.86385e6	−0.450700	−0.225350	+	0.974278i	$0.572353\pi$
$702$	0	0
$703$	−1.70779e7	−1.30331
$704$	0	0
$705$	655925.	0.0497029
$706$	0	0
$707$	582022.	0.0437916
$708$	0	0
$709$	−2.66670e6	−0.199232	−0.0996161	−	0.995026i	$-0.531761\pi$
$709$	−2.66670e6	−0.199232	−0.0996161	+	0.995026i	$0.531761\pi$
$710$	0	0
$711$	1.51891e7	1.12683
$712$	0	0
$713$	−1.97157e6	−0.145241
$714$	0	0
$715$	−1.09739e7	−0.802781
$716$	0	0
$717$	765905.	0.0556387
$718$	0	0
$719$	4.46629e6	0.322199	0.161100	−	0.986938i	$-0.448496\pi$
$719$	4.46629e6	0.322199	0.161100	+	0.986938i	$0.448496\pi$
$720$	0	0
$721$	−6.48951e6	−0.464915
$722$	0	0
$723$	1.21094e6	0.0861541
$724$	0	0
$725$	−3.11562e6	−0.220141
$726$	0	0
$727$	7.47757e6	0.524716	0.262358	−	0.964971i	$-0.415500\pi$
$727$	7.47757e6	0.524716	0.262358	+	0.964971i	$0.415500\pi$
$728$	0	0
$729$	−1.39958e7	−0.975393
$730$	0	0
$731$	1.77025e7	1.22530
$732$	0	0
$733$	−4.39751e6	−0.302306	−0.151153	−	0.988510i	$-0.548299\pi$
$733$	−4.39751e6	−0.302306	−0.151153	+	0.988510i	$0.548299\pi$
$734$	0	0
$735$	−60025.0	−0.00409840
$736$	0	0
$737$	7.17914e6	0.486860
$738$	0	0
$739$	−2.84036e7	−1.91321	−0.956603	−	0.291395i	$-0.905880\pi$
$739$	−2.84036e7	−1.91321	−0.956603	+	0.291395i	$0.905880\pi$
$740$	0	0
$741$	1.50195e6	0.100487
$742$	0	0
$743$	1.96012e7	1.30260	0.651299	−	0.758821i	$-0.274224\pi$
$743$	1.96012e7	1.30260	0.651299	+	0.758821i	$0.274224\pi$
$744$	0	0
$745$	−1.24608e7	−0.822533
$746$	0	0
$747$	−5.72185e6	−0.375176
$748$	0	0
$749$	6.70526e6	0.436728
$750$	0	0
$751$	2.60344e6	0.168441	0.0842206	−	0.996447i	$-0.473160\pi$
$751$	2.60344e6	0.168441	0.0842206	+	0.996447i	$0.473160\pi$
$752$	0	0
$753$	278262.	0.0178841
$754$	0	0
$755$	6.14508e6	0.392337
$756$	0	0
$757$	−2.98869e7	−1.89558	−0.947789	−	0.318899i	$-0.896687\pi$
$757$	−2.98869e7	−1.89558	−0.947789	+	0.318899i	$0.896687\pi$
$758$	0	0
$759$	−749262.	−0.0472095
$760$	0	0
$761$	1.21470e7	0.760338	0.380169	−	0.924917i	$-0.375866\pi$
$761$	1.21470e7	0.760338	0.380169	+	0.924917i	$0.375866\pi$
$762$	0	0
$763$	−5.36476e6	−0.333610
$764$	0	0
$765$	−9.90385e6	−0.611858
$766$	0	0
$767$	−4.43802e6	−0.272396
$768$	0	0
$769$	4.53845e6	0.276753	0.138376	−	0.990380i	$-0.455812\pi$
$769$	4.53845e6	0.276753	0.138376	+	0.990380i	$0.455812\pi$
$770$	0	0
$771$	352998.	0.0213863
$772$	0	0
$773$	1.93330e7	1.16372	0.581861	−	0.813288i	$-0.302325\pi$
$773$	1.93330e7	1.16372	0.581861	+	0.813288i	$0.302325\pi$
$774$	0	0
$775$	−745000.	−0.0445556
$776$	0	0
$777$	−539882.	−0.0320809
$778$	0	0
$779$	−2.67840e6	−0.158136
$780$	0	0
$781$	−2.34618e7	−1.37636
$782$	0	0
$783$	−2.41772e6	−0.140930
$784$	0	0
$785$	−2.13695e6	−0.123771
$786$	0	0
$787$	−1.66392e7	−0.957627	−0.478814	−	0.877917i	$-0.658933\pi$
$787$	−1.66392e7	−0.957627	−0.478814	+	0.877917i	$0.658933\pi$
$788$	0	0
$789$	−1.55809e6	−0.0891048
$790$	0	0
$791$	9.84577e6	0.559511
$792$	0	0
$793$	1.21009e7	0.683335
$794$	0	0
$795$	−648400.	−0.0363852
$796$	0	0
$797$	1.80409e7	1.00603	0.503017	−	0.864276i	$-0.332223\pi$
$797$	1.80409e7	1.00603	0.503017	+	0.864276i	$0.332223\pi$
$798$	0	0
$799$	−4.29500e7	−2.38010
$800$	0	0
$801$	3.56466e7	1.96307
$802$	0	0
$803$	2.19524e6	0.120141
$804$	0	0
$805$	−2.02615e6	−0.110200
$806$	0	0
$807$	1.21963e6	0.0659241
$808$	0	0
$809$	2.33891e7	1.25644	0.628220	−	0.778036i	$-0.283784\pi$
$809$	2.33891e7	1.25644	0.628220	+	0.778036i	$0.283784\pi$
$810$	0	0
$811$	2.29037e7	1.22279	0.611397	−	0.791324i	$-0.290608\pi$
$811$	2.29037e7	1.22279	0.611397	+	0.791324i	$0.290608\pi$
$812$	0	0
$813$	405792.	0.0215316
$814$	0	0
$815$	−4.82565e6	−0.254485
$816$	0	0
$817$	1.67617e7	0.878543
$818$	0	0
$819$	−1.14904e7	−0.598585
$820$	0	0
$821$	−1.80745e7	−0.935853	−0.467926	−	0.883767i	$-0.654999\pi$
$821$	−1.80745e7	−0.935853	−0.467926	+	0.883767i	$0.654999\pi$
$822$	0	0
$823$	−1.17989e7	−0.607216	−0.303608	−	0.952797i	$-0.598191\pi$
$823$	−1.17989e7	−0.607216	−0.303608	+	0.952797i	$0.598191\pi$
$824$	0	0
$825$	−283125.	−0.0144825
$826$	0	0
$827$	−2.57650e6	−0.130999	−0.0654993	−	0.997853i	$-0.520864\pi$
$827$	−2.57650e6	−0.130999	−0.0654993	+	0.997853i	$0.520864\pi$
$828$	0	0
$829$	−3.84340e7	−1.94236	−0.971178	−	0.238356i	$-0.923392\pi$
$829$	−3.84340e7	−1.94236	−0.971178	+	0.238356i	$0.923392\pi$
$830$	0	0
$831$	−652442.	−0.0327747
$832$	0	0
$833$	3.93044e6	0.196258
$834$	0	0
$835$	3.94458e6	0.195787
$836$	0	0
$837$	−578120.	−0.0285236
$838$	0	0
$839$	1.24222e7	0.609247	0.304623	−	0.952473i	$-0.401469\pi$
$839$	1.24222e7	0.609247	0.304623	+	0.952473i	$0.401469\pi$
$840$	0	0
$841$	4.33908e6	0.211547
$842$	0	0
$843$	−118827.	−0.00575899
$844$	0	0
$845$	1.41917e7	0.683743
$846$	0	0
$847$	−2.16374e6	−0.103633
$848$	0	0
$849$	1.48801e6	0.0708495
$850$	0	0
$851$	−1.82238e7	−0.862610
$852$	0	0
$853$	7.92067e6	0.372726	0.186363	−	0.982481i	$-0.440330\pi$
$853$	7.92067e6	0.372726	0.186363	+	0.982481i	$0.440330\pi$
$854$	0	0
$855$	−9.37750e6	−0.438704
$856$	0	0
$857$	1.48983e7	0.692924	0.346462	−	0.938064i	$-0.387383\pi$
$857$	1.48983e7	0.692924	0.346462	+	0.938064i	$0.387383\pi$
$858$	0	0
$859$	1.38740e7	0.641534	0.320767	−	0.947158i	$-0.396059\pi$
$859$	1.38740e7	0.641534	0.320767	+	0.947158i	$0.396059\pi$
$860$	0	0
$861$	−84672.0	−0.00389253
$862$	0	0
$863$	−1.25500e7	−0.573610	−0.286805	−	0.957989i	$-0.592593\pi$
$863$	−1.25500e7	−0.573610	−0.286805	+	0.957989i	$0.592593\pi$
$864$	0	0
$865$	−6.64147e6	−0.301804
$866$	0	0
$867$	−1.25991e6	−0.0569236
$868$	0	0
$869$	−2.84325e7	−1.27722
$870$	0	0
$871$	−1.53567e7	−0.685887
$872$	0	0
$873$	2.01901e6	0.0896607
$874$	0	0
$875$	−765625.	−0.0338062
$876$	0	0
$877$	−2.86002e7	−1.25565	−0.627827	−	0.778353i	$-0.716056\pi$
$877$	−2.86002e7	−1.25565	−0.627827	+	0.778353i	$0.716056\pi$
$878$	0	0
$879$	−1.89580e6	−0.0827600
$880$	0	0
$881$	4.09608e7	1.77799	0.888993	−	0.457922i	$-0.151406\pi$
$881$	4.09608e7	1.77799	0.888993	+	0.457922i	$0.151406\pi$
$882$	0	0
$883$	−1.30504e7	−0.563279	−0.281639	−	0.959520i	$-0.590878\pi$
$883$	−1.30504e7	−0.563279	−0.281639	+	0.959520i	$0.590878\pi$
$884$	0	0
$885$	−114500.	−0.00491414
$886$	0	0
$887$	−2.53595e7	−1.08226	−0.541129	−	0.840939i	$-0.682003\pi$
$887$	−2.53595e7	−1.08226	−0.541129	+	0.840939i	$0.682003\pi$
$888$	0	0
$889$	1.62039e7	0.687647
$890$	0	0
$891$	2.64194e7	1.11488
$892$	0	0
$893$	−4.06674e7	−1.70654
$894$	0	0
$895$	−4.59150e6	−0.191601
$896$	0	0
$897$	1.60273e6	0.0665087
$898$	0	0
$899$	5.94212e6	0.245212
$900$	0	0
$901$	4.24572e7	1.74237
$902$	0	0
$903$	529886.	0.0216253
$904$	0	0
$905$	−1.58762e7	−0.644355
$906$	0	0
$907$	−1.98595e7	−0.801585	−0.400793	−	0.916169i	$-0.631265\pi$
$907$	−1.98595e7	−0.801585	−0.400793	+	0.916169i	$0.631265\pi$
$908$	0	0
$909$	2.87448e6	0.115385
$910$	0	0
$911$	1.99344e7	0.795808	0.397904	−	0.917427i	$-0.369738\pi$
$911$	1.99344e7	0.795808	0.397904	+	0.917427i	$0.369738\pi$
$912$	0	0
$913$	1.07107e7	0.425248
$914$	0	0
$915$	312200.	0.0123276
$916$	0	0
$917$	2.15512e6	0.0846346
$918$	0	0
$919$	1.10695e7	0.432355	0.216178	−	0.976354i	$-0.430641\pi$
$919$	1.10695e7	0.432355	0.216178	+	0.976354i	$0.430641\pi$
$920$	0	0
$921$	−821853.	−0.0319260
$922$	0	0
$923$	5.01864e7	1.93902
$924$	0	0
$925$	−6.88625e6	−0.264624
$926$	0	0
$927$	−3.20502e7	−1.22499
$928$	0	0
$929$	−3.25682e7	−1.23810	−0.619048	−	0.785353i	$-0.712481\pi$
$929$	−3.25682e7	−1.23810	−0.619048	+	0.785353i	$0.712481\pi$
$930$	0	0
$931$	3.72155e6	0.140718
$932$	0	0
$933$	−2.09600e6	−0.0788291
$934$	0	0
$935$	1.85390e7	0.693518
$936$	0	0
$937$	3.15690e7	1.17466	0.587329	−	0.809348i	$-0.300179\pi$
$937$	3.15690e7	1.17466	0.587329	+	0.809348i	$0.300179\pi$
$938$	0	0
$939$	−394571.	−0.0146036
$940$	0	0
$941$	−3.67997e7	−1.35479	−0.677393	−	0.735622i	$-0.736890\pi$
$941$	−3.67997e7	−1.35479	−0.677393	+	0.735622i	$0.736890\pi$
$942$	0	0
$943$	−2.85811e6	−0.104665
$944$	0	0
$945$	−594125.	−0.0216420
$946$	0	0
$947$	−1.88453e7	−0.682853	−0.341426	−	0.939909i	$-0.610910\pi$
$947$	−1.88453e7	−0.682853	−0.341426	+	0.939909i	$0.610910\pi$
$948$	0	0
$949$	−4.69577e6	−0.169255
$950$	0	0
$951$	−321422.	−0.0115246
$952$	0	0
$953$	−1.25120e7	−0.446265	−0.223133	−	0.974788i	$-0.571628\pi$
$953$	−1.25120e7	−0.446265	−0.223133	+	0.974788i	$0.571628\pi$
$954$	0	0
$955$	5.66532e6	0.201009
$956$	0	0
$957$	2.25820e6	0.0797046
$958$	0	0
$959$	4.88765e6	0.171614
$960$	0	0
$961$	−2.72083e7	−0.950370
$962$	0	0
$963$	3.31158e7	1.15072
$964$	0	0
$965$	1.16190e6	0.0401652
$966$	0	0
$967$	3.42344e7	1.17733	0.588663	−	0.808379i	$-0.299654\pi$
$967$	3.42344e7	1.17733	0.588663	+	0.808379i	$0.299654\pi$
$968$	0	0
$969$	−2.53735e6	−0.0868102
$970$	0	0
$971$	2.62027e7	0.891864	0.445932	−	0.895067i	$-0.352872\pi$
$971$	2.62027e7	0.891864	0.445932	+	0.895067i	$0.352872\pi$
$972$	0	0
$973$	1.26876e7	0.429632
$974$	0	0
$975$	605625.	0.0204029
$976$	0	0
$977$	−8.01114e6	−0.268508	−0.134254	−	0.990947i	$-0.542864\pi$
$977$	−8.01114e6	−0.268508	−0.134254	+	0.990947i	$0.542864\pi$
$978$	0	0
$979$	−6.67269e7	−2.22507
$980$	0	0
$981$	−2.64954e7	−0.879017
$982$	0	0
$983$	4.60126e7	1.51877	0.759387	−	0.650639i	$-0.225499\pi$
$983$	4.60126e7	1.51877	0.759387	+	0.650639i	$0.225499\pi$
$984$	0	0
$985$	5.12430e6	0.168284
$986$	0	0
$987$	−1.28561e6	−0.0420066
$988$	0	0
$989$	1.78864e7	0.581475
$990$	0	0
$991$	3.75828e7	1.21564	0.607821	−	0.794074i	$-0.292044\pi$
$991$	3.75828e7	1.21564	0.607821	+	0.794074i	$0.292044\pi$
$992$	0	0
$993$	−2.23259e6	−0.0718514
$994$	0	0
$995$	2.38255e7	0.762929
$996$	0	0
$997$	2.22066e7	0.707529	0.353765	−	0.935334i	$-0.384901\pi$
$997$	2.22066e7	0.707529	0.353765	+	0.935334i	$0.384901\pi$
$998$	0	0
$999$	−5.34373e6	−0.169407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.6.a.c.1.1		1
4.3	odd	2		35.6.a.a.1.1	✓	1
12.11	even	2		315.6.a.a.1.1		1
20.3	even	4		175.6.b.b.99.2		2
20.7	even	4		175.6.b.b.99.1		2
20.19	odd	2		175.6.a.a.1.1		1
28.27	even	2		245.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.a.1.1	✓	1	4.3	odd	2
175.6.a.a.1.1		1	20.19	odd	2
175.6.b.b.99.1		2	20.7	even	4
175.6.b.b.99.2		2	20.3	even	4
245.6.a.a.1.1		1	28.27	even	2
315.6.a.a.1.1		1	12.11	even	2
560.6.a.c.1.1		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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	560.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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