LMFDB - Embedded newform 240.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,6,Mod(1,240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("240.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	240.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$38.4921167551$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	240.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} +25.0000 q^{5} +160.000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} +25.0000 q^{5} +160.000 q^{7} +81.0000 q^{9} +596.000 q^{11} -122.000 q^{13} -225.000 q^{15} -1078.00 q^{17} -796.000 q^{19} -1440.00 q^{21} +1088.00 q^{23} +625.000 q^{25} -729.000 q^{27} +46.0000 q^{29} +4952.00 q^{31} -5364.00 q^{33} +4000.00 q^{35} -6114.00 q^{37} +1098.00 q^{39} -6.00000 q^{41} +24116.0 q^{43} +2025.00 q^{45} -13480.0 q^{47} +8793.00 q^{49} +9702.00 q^{51} +20598.0 q^{53} +14900.0 q^{55} +7164.00 q^{57} +46756.0 q^{59} -9602.00 q^{61} +12960.0 q^{63} -3050.00 q^{65} +17404.0 q^{67} -9792.00 q^{69} -26568.0 q^{71} +75450.0 q^{73} -5625.00 q^{75} +95360.0 q^{77} -50472.0 q^{79} +6561.00 q^{81} -33236.0 q^{83} -26950.0 q^{85} -414.000 q^{87} +133194. q^{89} -19520.0 q^{91} -44568.0 q^{93} -19900.0 q^{95} -42878.0 q^{97} +48276.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	160.000	1.23417	0.617085	−	0.786897i	$-0.288314\pi$
$7$	160.000	1.23417	0.617085	+	0.786897i	$0.288314\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	596.000	1.48513	0.742565	−	0.669774i	$-0.233609\pi$
$11$	596.000	1.48513	0.742565	+	0.669774i	$0.233609\pi$
$12$	0	0
$13$	−122.000	−0.200217	−0.100109	−	0.994977i	$-0.531919\pi$
$13$	−122.000	−0.200217	−0.100109	+	0.994977i	$0.531919\pi$
$14$	0	0
$15$	−225.000	−0.258199
$16$	0	0
$17$	−1078.00	−0.904683	−0.452342	−	0.891845i	$-0.649411\pi$
$17$	−1078.00	−0.904683	−0.452342	+	0.891845i	$0.649411\pi$
$18$	0	0
$19$	−796.000	−0.505859	−0.252929	−	0.967485i	$-0.581394\pi$
$19$	−796.000	−0.505859	−0.252929	+	0.967485i	$0.581394\pi$
$20$	0	0
$21$	−1440.00	−0.712548
$22$	0	0
$23$	1088.00	0.428854	0.214427	−	0.976740i	$-0.431212\pi$
$23$	1088.00	0.428854	0.214427	+	0.976740i	$0.431212\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	46.0000	0.0101569	0.00507847	−	0.999987i	$-0.498383\pi$
$29$	46.0000	0.0101569	0.00507847	+	0.999987i	$0.498383\pi$
$30$	0	0
$31$	4952.00	0.925500	0.462750	−	0.886489i	$-0.346863\pi$
$31$	4952.00	0.925500	0.462750	+	0.886489i	$0.346863\pi$
$32$	0	0
$33$	−5364.00	−0.857440
$34$	0	0
$35$	4000.00	0.551937
$36$	0	0
$37$	−6114.00	−0.734211	−0.367106	−	0.930179i	$-0.619651\pi$
$37$	−6114.00	−0.734211	−0.367106	+	0.930179i	$0.619651\pi$
$38$	0	0
$39$	1098.00	0.115595
$40$	0	0
$41$	−6.00000	−0.000557432 0	−0.000278716	−	1.00000i	$-0.500089\pi$
$41$	−6.00000	−0.000557432 0	−0.000278716		1.00000i	$0.500089\pi$
$42$	0	0
$43$	24116.0	1.98900	0.994499	−	0.104751i	$-0.0334044\pi$
$43$	24116.0	1.98900	0.994499	+	0.104751i	$0.0334044\pi$
$44$	0	0
$45$	2025.00	0.149071
$46$	0	0
$47$	−13480.0	−0.890113	−0.445057	−	0.895502i	$-0.646816\pi$
$47$	−13480.0	−0.890113	−0.445057	+	0.895502i	$0.646816\pi$
$48$	0	0
$49$	8793.00	0.523175
$50$	0	0
$51$	9702.00	0.522319
$52$	0	0
$53$	20598.0	1.00725	0.503623	−	0.863924i	$-0.332000\pi$
$53$	20598.0	1.00725	0.503623	+	0.863924i	$0.332000\pi$
$54$	0	0
$55$	14900.0	0.664170
$56$	0	0
$57$	7164.00	0.292058
$58$	0	0
$59$	46756.0	1.74867	0.874334	−	0.485325i	$-0.161299\pi$
$59$	46756.0	1.74867	0.874334	+	0.485325i	$0.161299\pi$
$60$	0	0
$61$	−9602.00	−0.330398	−0.165199	−	0.986260i	$-0.552827\pi$
$61$	−9602.00	−0.330398	−0.165199	+	0.986260i	$0.552827\pi$
$62$	0	0
$63$	12960.0	0.411390
$64$	0	0
$65$	−3050.00	−0.0895399
$66$	0	0
$67$	17404.0	0.473655	0.236827	−	0.971552i	$-0.423892\pi$
$67$	17404.0	0.473655	0.236827	+	0.971552i	$0.423892\pi$
$68$	0	0
$69$	−9792.00	−0.247599
$70$	0	0
$71$	−26568.0	−0.625479	−0.312740	−	0.949839i	$-0.601247\pi$
$71$	−26568.0	−0.625479	−0.312740	+	0.949839i	$0.601247\pi$
$72$	0	0
$73$	75450.0	1.65711	0.828556	−	0.559906i	$-0.189163\pi$
$73$	75450.0	1.65711	0.828556	+	0.559906i	$0.189163\pi$
$74$	0	0
$75$	−5625.00	−0.115470
$76$	0	0
$77$	95360.0	1.83290
$78$	0	0
$79$	−50472.0	−0.909877	−0.454939	−	0.890523i	$-0.650339\pi$
$79$	−50472.0	−0.909877	−0.454939	+	0.890523i	$0.650339\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−33236.0	−0.529558	−0.264779	−	0.964309i	$-0.585299\pi$
$83$	−33236.0	−0.529558	−0.264779	+	0.964309i	$0.585299\pi$
$84$	0	0
$85$	−26950.0	−0.404587
$86$	0	0
$87$	−414.000	−0.00586411
$88$	0	0
$89$	133194.	1.78242	0.891209	−	0.453593i	$-0.149858\pi$
$89$	133194.	1.78242	0.891209	+	0.453593i	$0.149858\pi$
$90$	0	0
$91$	−19520.0	−0.247102
$92$	0	0
$93$	−44568.0	−0.534338
$94$	0	0
$95$	−19900.0	−0.226227
$96$	0	0
$97$	−42878.0	−0.462706	−0.231353	−	0.972870i	$-0.574315\pi$
$97$	−42878.0	−0.462706	−0.231353	+	0.972870i	$0.574315\pi$
$98$	0	0
$99$	48276.0	0.495043
$100$	0	0
$101$	165462.	1.61397	0.806984	−	0.590574i	$-0.201098\pi$
$101$	165462.	1.61397	0.806984	+	0.590574i	$0.201098\pi$
$102$	0	0
$103$	211904.	1.96810	0.984048	−	0.177905i	$-0.0569321\pi$
$103$	211904.	1.96810	0.984048	+	0.177905i	$0.0569321\pi$
$104$	0	0
$105$	−36000.0	−0.318661
$106$	0	0
$107$	−185148.	−1.56336	−0.781681	−	0.623678i	$-0.785637\pi$
$107$	−185148.	−1.56336	−0.781681	+	0.623678i	$0.785637\pi$
$108$	0	0
$109$	87998.0	0.709425	0.354713	−	0.934975i	$-0.384579\pi$
$109$	87998.0	0.709425	0.354713	+	0.934975i	$0.384579\pi$
$110$	0	0
$111$	55026.0	0.423897
$112$	0	0
$113$	−260982.	−1.92271	−0.961356	−	0.275307i	$-0.911221\pi$
$113$	−260982.	−1.92271	−0.961356	+	0.275307i	$0.911221\pi$
$114$	0	0
$115$	27200.0	0.191789
$116$	0	0
$117$	−9882.00	−0.0667391
$118$	0	0
$119$	−172480.	−1.11653
$120$	0	0
$121$	194165.	1.20561
$122$	0	0
$123$	54.0000	0.000321833 0
$124$	0	0
$125$	15625.0	0.0894427
$126$	0	0
$127$	16968.0	0.0933515	0.0466758	−	0.998910i	$-0.485137\pi$
$127$	16968.0	0.0933515	0.0466758	+	0.998910i	$0.485137\pi$
$128$	0	0
$129$	−217044.	−1.14835
$130$	0	0
$131$	−112116.	−0.570807	−0.285404	−	0.958407i	$-0.592128\pi$
$131$	−112116.	−0.570807	−0.285404	+	0.958407i	$0.592128\pi$
$132$	0	0
$133$	−127360.	−0.624315
$134$	0	0
$135$	−18225.0	−0.0860663
$136$	0	0
$137$	−235886.	−1.07374	−0.536872	−	0.843664i	$-0.680394\pi$
$137$	−235886.	−1.07374	−0.536872	+	0.843664i	$0.680394\pi$
$138$	0	0
$139$	333852.	1.46561	0.732803	−	0.680441i	$-0.238212\pi$
$139$	333852.	1.46561	0.732803	+	0.680441i	$0.238212\pi$
$140$	0	0
$141$	121320.	0.513907
$142$	0	0
$143$	−72712.0	−0.297349
$144$	0	0
$145$	1150.00	0.00454232
$146$	0	0
$147$	−79137.0	−0.302055
$148$	0	0
$149$	88454.0	0.326401	0.163201	−	0.986593i	$-0.447818\pi$
$149$	88454.0	0.326401	0.163201	+	0.986593i	$0.447818\pi$
$150$	0	0
$151$	123616.	0.441197	0.220598	−	0.975365i	$-0.429199\pi$
$151$	123616.	0.441197	0.220598	+	0.975365i	$0.429199\pi$
$152$	0	0
$153$	−87318.0	−0.301561
$154$	0	0
$155$	123800.	0.413896
$156$	0	0
$157$	−62042.0	−0.200880	−0.100440	−	0.994943i	$-0.532025\pi$
$157$	−62042.0	−0.200880	−0.100440	+	0.994943i	$0.532025\pi$
$158$	0	0
$159$	−185382.	−0.581534
$160$	0	0
$161$	174080.	0.529278
$162$	0	0
$163$	403868.	1.19061	0.595306	−	0.803499i	$-0.297031\pi$
$163$	403868.	1.19061	0.595306	+	0.803499i	$0.297031\pi$
$164$	0	0
$165$	−134100.	−0.383459
$166$	0	0
$167$	−98544.0	−0.273425	−0.136713	−	0.990611i	$-0.543654\pi$
$167$	−98544.0	−0.273425	−0.136713	+	0.990611i	$0.543654\pi$
$168$	0	0
$169$	−356409.	−0.959913
$170$	0	0
$171$	−64476.0	−0.168620
$172$	0	0
$173$	−332674.	−0.845091	−0.422546	−	0.906342i	$-0.638863\pi$
$173$	−332674.	−0.845091	−0.422546	+	0.906342i	$0.638863\pi$
$174$	0	0
$175$	100000.	0.246834
$176$	0	0
$177$	−420804.	−1.00959
$178$	0	0
$179$	396988.	0.926072	0.463036	−	0.886339i	$-0.346760\pi$
$179$	396988.	0.926072	0.463036	+	0.886339i	$0.346760\pi$
$180$	0	0
$181$	544166.	1.23462	0.617312	−	0.786718i	$-0.288221\pi$
$181$	544166.	1.23462	0.617312	+	0.786718i	$0.288221\pi$
$182$	0	0
$183$	86418.0	0.190755
$184$	0	0
$185$	−152850.	−0.328349
$186$	0	0
$187$	−642488.	−1.34357
$188$	0	0
$189$	−116640.	−0.237516
$190$	0	0
$191$	−871520.	−1.72860	−0.864299	−	0.502979i	$-0.832237\pi$
$191$	−871520.	−1.72860	−0.864299	+	0.502979i	$0.832237\pi$
$192$	0	0
$193$	−889838.	−1.71956	−0.859781	−	0.510663i	$-0.829400\pi$
$193$	−889838.	−1.71956	−0.859781	+	0.510663i	$0.829400\pi$
$194$	0	0
$195$	27450.0	0.0516959
$196$	0	0
$197$	−212378.	−0.389892	−0.194946	−	0.980814i	$-0.562453\pi$
$197$	−212378.	−0.389892	−0.194946	+	0.980814i	$0.562453\pi$
$198$	0	0
$199$	−627056.	−1.12247	−0.561234	−	0.827657i	$-0.689673\pi$
$199$	−627056.	−1.12247	−0.561234	+	0.827657i	$0.689673\pi$
$200$	0	0
$201$	−156636.	−0.273465
$202$	0	0
$203$	7360.00	0.0125354
$204$	0	0
$205$	−150.000	−0.000249291 0
$206$	0	0
$207$	88128.0	0.142951
$208$	0	0
$209$	−474416.	−0.751266
$210$	0	0
$211$	−130220.	−0.201359	−0.100680	−	0.994919i	$-0.532102\pi$
$211$	−130220.	−0.201359	−0.100680	+	0.994919i	$0.532102\pi$
$212$	0	0
$213$	239112.	0.361121
$214$	0	0
$215$	602900.	0.889507
$216$	0	0
$217$	792320.	1.14222
$218$	0	0
$219$	−679050.	−0.956735
$220$	0	0
$221$	131516.	0.181133
$222$	0	0
$223$	865528.	1.16552	0.582759	−	0.812645i	$-0.301973\pi$
$223$	865528.	1.16552	0.582759	+	0.812645i	$0.301973\pi$
$224$	0	0
$225$	50625.0	0.0666667
$226$	0	0
$227$	−1.18045e6	−1.52049	−0.760245	−	0.649636i	$-0.774921\pi$
$227$	−1.18045e6	−1.52049	−0.760245	+	0.649636i	$0.774921\pi$
$228$	0	0
$229$	1.32890e6	1.67457	0.837287	−	0.546764i	$-0.184140\pi$
$229$	1.32890e6	1.67457	0.837287	+	0.546764i	$0.184140\pi$
$230$	0	0
$231$	−858240.	−1.05823
$232$	0	0
$233$	−454830.	−0.548857	−0.274429	−	0.961607i	$-0.588489\pi$
$233$	−454830.	−0.548857	−0.274429	+	0.961607i	$0.588489\pi$
$234$	0	0
$235$	−337000.	−0.398071
$236$	0	0
$237$	454248.	0.525318
$238$	0	0
$239$	−401184.	−0.454306	−0.227153	−	0.973859i	$-0.572942\pi$
$239$	−401184.	−0.454306	−0.227153	+	0.973859i	$0.572942\pi$
$240$	0	0
$241$	657458.	0.729164	0.364582	−	0.931171i	$-0.381212\pi$
$241$	657458.	0.729164	0.364582	+	0.931171i	$0.381212\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	219825.	0.233971
$246$	0	0
$247$	97112.0	0.101282
$248$	0	0
$249$	299124.	0.305740
$250$	0	0
$251$	599700.	0.600827	0.300414	−	0.953809i	$-0.402875\pi$
$251$	599700.	0.600827	0.300414	+	0.953809i	$0.402875\pi$
$252$	0	0
$253$	648448.	0.636904
$254$	0	0
$255$	242550.	0.233588
$256$	0	0
$257$	−1.00292e6	−0.947180	−0.473590	−	0.880745i	$-0.657042\pi$
$257$	−1.00292e6	−0.947180	−0.473590	+	0.880745i	$0.657042\pi$
$258$	0	0
$259$	−978240.	−0.906141
$260$	0	0
$261$	3726.00	0.00338565
$262$	0	0
$263$	825888.	0.736261	0.368130	−	0.929774i	$-0.379998\pi$
$263$	825888.	0.736261	0.368130	+	0.929774i	$0.379998\pi$
$264$	0	0
$265$	514950.	0.450454
$266$	0	0
$267$	−1.19875e6	−1.02908
$268$	0	0
$269$	−851170.	−0.717192	−0.358596	−	0.933493i	$-0.616744\pi$
$269$	−851170.	−0.717192	−0.358596	+	0.933493i	$0.616744\pi$
$270$	0	0
$271$	2.14327e6	1.77278	0.886388	−	0.462942i	$-0.153206\pi$
$271$	2.14327e6	1.77278	0.886388	+	0.462942i	$0.153206\pi$
$272$	0	0
$273$	175680.	0.142664
$274$	0	0
$275$	372500.	0.297026
$276$	0	0
$277$	1.04185e6	0.815845	0.407922	−	0.913017i	$-0.366253\pi$
$277$	1.04185e6	0.815845	0.407922	+	0.913017i	$0.366253\pi$
$278$	0	0
$279$	401112.	0.308500
$280$	0	0
$281$	−405014.	−0.305988	−0.152994	−	0.988227i	$-0.548892\pi$
$281$	−405014.	−0.305988	−0.152994	+	0.988227i	$0.548892\pi$
$282$	0	0
$283$	139588.	0.103605	0.0518027	−	0.998657i	$-0.483503\pi$
$283$	139588.	0.103605	0.0518027	+	0.998657i	$0.483503\pi$
$284$	0	0
$285$	179100.	0.130612
$286$	0	0
$287$	−960.000	−0.000687965 0
$288$	0	0
$289$	−257773.	−0.181549
$290$	0	0
$291$	385902.	0.267143
$292$	0	0
$293$	617542.	0.420240	0.210120	−	0.977676i	$-0.432615\pi$
$293$	617542.	0.420240	0.210120	+	0.977676i	$0.432615\pi$
$294$	0	0
$295$	1.16890e6	0.782028
$296$	0	0
$297$	−434484.	−0.285813
$298$	0	0
$299$	−132736.	−0.0858639
$300$	0	0
$301$	3.85856e6	2.45476
$302$	0	0
$303$	−1.48916e6	−0.931825
$304$	0	0
$305$	−240050.	−0.147758
$306$	0	0
$307$	1.25299e6	0.758754	0.379377	−	0.925242i	$-0.376138\pi$
$307$	1.25299e6	0.758754	0.379377	+	0.925242i	$0.376138\pi$
$308$	0	0
$309$	−1.90714e6	−1.13628
$310$	0	0
$311$	2.08482e6	1.22227	0.611137	−	0.791525i	$-0.290713\pi$
$311$	2.08482e6	1.22227	0.611137	+	0.791525i	$0.290713\pi$
$312$	0	0
$313$	−1.48121e6	−0.854584	−0.427292	−	0.904114i	$-0.640532\pi$
$313$	−1.48121e6	−0.854584	−0.427292	+	0.904114i	$0.640532\pi$
$314$	0	0
$315$	324000.	0.183979
$316$	0	0
$317$	−269154.	−0.150436	−0.0752182	−	0.997167i	$-0.523965\pi$
$317$	−269154.	−0.150436	−0.0752182	+	0.997167i	$0.523965\pi$
$318$	0	0
$319$	27416.0	0.0150844
$320$	0	0
$321$	1.66633e6	0.902608
$322$	0	0
$323$	858088.	0.457642
$324$	0	0
$325$	−76250.0	−0.0400434
$326$	0	0
$327$	−791982.	−0.409587
$328$	0	0
$329$	−2.15680e6	−1.09855
$330$	0	0
$331$	3.74070e6	1.87665	0.938324	−	0.345757i	$-0.112378\pi$
$331$	3.74070e6	1.87665	0.938324	+	0.345757i	$0.112378\pi$
$332$	0	0
$333$	−495234.	−0.244737
$334$	0	0
$335$	435100.	0.211825
$336$	0	0
$337$	−2.67990e6	−1.28542	−0.642709	−	0.766111i	$-0.722189\pi$
$337$	−2.67990e6	−1.28542	−0.642709	+	0.766111i	$0.722189\pi$
$338$	0	0
$339$	2.34884e6	1.11008
$340$	0	0
$341$	2.95139e6	1.37449
$342$	0	0
$343$	−1.28224e6	−0.588483
$344$	0	0
$345$	−244800.	−0.110730
$346$	0	0
$347$	1.60805e6	0.716929	0.358465	−	0.933543i	$-0.383300\pi$
$347$	1.60805e6	0.716929	0.358465	+	0.933543i	$0.383300\pi$
$348$	0	0
$349$	3.35667e6	1.47518	0.737590	−	0.675249i	$-0.235964\pi$
$349$	3.35667e6	1.47518	0.737590	+	0.675249i	$0.235964\pi$
$350$	0	0
$351$	88938.0	0.0385318
$352$	0	0
$353$	−1.11468e6	−0.476116	−0.238058	−	0.971251i	$-0.576511\pi$
$353$	−1.11468e6	−0.476116	−0.238058	+	0.971251i	$0.576511\pi$
$354$	0	0
$355$	−664200.	−0.279723
$356$	0	0
$357$	1.55232e6	0.644630
$358$	0	0
$359$	689784.	0.282473	0.141237	−	0.989976i	$-0.454892\pi$
$359$	689784.	0.282473	0.141237	+	0.989976i	$0.454892\pi$
$360$	0	0
$361$	−1.84248e6	−0.744107
$362$	0	0
$363$	−1.74748e6	−0.696060
$364$	0	0
$365$	1.88625e6	0.741083
$366$	0	0
$367$	333928.	0.129416	0.0647080	−	0.997904i	$-0.479388\pi$
$367$	333928.	0.129416	0.0647080	+	0.997904i	$0.479388\pi$
$368$	0	0
$369$	−486.000	−0.000185811 0
$370$	0	0
$371$	3.29568e6	1.24311
$372$	0	0
$373$	161470.	0.0600924	0.0300462	−	0.999549i	$-0.490435\pi$
$373$	161470.	0.0600924	0.0300462	+	0.999549i	$0.490435\pi$
$374$	0	0
$375$	−140625.	−0.0516398
$376$	0	0
$377$	−5612.00	−0.00203359
$378$	0	0
$379$	−3.52762e6	−1.26149	−0.630745	−	0.775990i	$-0.717251\pi$
$379$	−3.52762e6	−1.26149	−0.630745	+	0.775990i	$0.717251\pi$
$380$	0	0
$381$	−152712.	−0.0538965
$382$	0	0
$383$	−2.07324e6	−0.722192	−0.361096	−	0.932529i	$-0.617597\pi$
$383$	−2.07324e6	−0.722192	−0.361096	+	0.932529i	$0.617597\pi$
$384$	0	0
$385$	2.38400e6	0.819699
$386$	0	0
$387$	1.95340e6	0.662999
$388$	0	0
$389$	−4.01572e6	−1.34552	−0.672759	−	0.739862i	$-0.734891\pi$
$389$	−4.01572e6	−1.34552	−0.672759	+	0.739862i	$0.734891\pi$
$390$	0	0
$391$	−1.17286e6	−0.387977
$392$	0	0
$393$	1.00904e6	0.329556
$394$	0	0
$395$	−1.26180e6	−0.406909
$396$	0	0
$397$	−4.69923e6	−1.49641	−0.748204	−	0.663469i	$-0.769084\pi$
$397$	−4.69923e6	−1.49641	−0.748204	+	0.663469i	$0.769084\pi$
$398$	0	0
$399$	1.14624e6	0.360449
$400$	0	0
$401$	−1.14939e6	−0.356949	−0.178475	−	0.983945i	$-0.557116\pi$
$401$	−1.14939e6	−0.356949	−0.178475	+	0.983945i	$0.557116\pi$
$402$	0	0
$403$	−604144.	−0.185301
$404$	0	0
$405$	164025.	0.0496904
$406$	0	0
$407$	−3.64394e6	−1.09040
$408$	0	0
$409$	359674.	0.106317	0.0531583	−	0.998586i	$-0.483071\pi$
$409$	359674.	0.106317	0.0531583	+	0.998586i	$0.483071\pi$
$410$	0	0
$411$	2.12297e6	0.619926
$412$	0	0
$413$	7.48096e6	2.15815
$414$	0	0
$415$	−830900.	−0.236826
$416$	0	0
$417$	−3.00467e6	−0.846168
$418$	0	0
$419$	−2.41189e6	−0.671155	−0.335577	−	0.942013i	$-0.608931\pi$
$419$	−2.41189e6	−0.671155	−0.335577	+	0.942013i	$0.608931\pi$
$420$	0	0
$421$	−6.83769e6	−1.88020	−0.940100	−	0.340898i	$-0.889269\pi$
$421$	−6.83769e6	−1.88020	−0.940100	+	0.340898i	$0.889269\pi$
$422$	0	0
$423$	−1.09188e6	−0.296704
$424$	0	0
$425$	−673750.	−0.180937
$426$	0	0
$427$	−1.53632e6	−0.407767
$428$	0	0
$429$	654408.	0.171674
$430$	0	0
$431$	−2.62587e6	−0.680895	−0.340448	−	0.940263i	$-0.610579\pi$
$431$	−2.62587e6	−0.680895	−0.340448	+	0.940263i	$0.610579\pi$
$432$	0	0
$433$	−4.10169e6	−1.05134	−0.525670	−	0.850688i	$-0.676185\pi$
$433$	−4.10169e6	−1.05134	−0.525670	+	0.850688i	$0.676185\pi$
$434$	0	0
$435$	−10350.0	−0.00262251
$436$	0	0
$437$	−866048.	−0.216939
$438$	0	0
$439$	−1.93216e6	−0.478500	−0.239250	−	0.970958i	$-0.576902\pi$
$439$	−1.93216e6	−0.478500	−0.239250	+	0.970958i	$0.576902\pi$
$440$	0	0
$441$	712233.	0.174392
$442$	0	0
$443$	−6.03366e6	−1.46074	−0.730368	−	0.683054i	$-0.760651\pi$
$443$	−6.03366e6	−1.46074	−0.730368	+	0.683054i	$0.760651\pi$
$444$	0	0
$445$	3.32985e6	0.797122
$446$	0	0
$447$	−796086.	−0.188448
$448$	0	0
$449$	1.54327e6	0.361264	0.180632	−	0.983551i	$-0.442186\pi$
$449$	1.54327e6	0.361264	0.180632	+	0.983551i	$0.442186\pi$
$450$	0	0
$451$	−3576.00	−0.000827859 0
$452$	0	0
$453$	−1.11254e6	−0.254725
$454$	0	0
$455$	−488000.	−0.110507
$456$	0	0
$457$	−3.21042e6	−0.719071	−0.359535	−	0.933131i	$-0.617065\pi$
$457$	−3.21042e6	−0.719071	−0.359535	+	0.933131i	$0.617065\pi$
$458$	0	0
$459$	785862.	0.174106
$460$	0	0
$461$	8.87513e6	1.94501	0.972507	−	0.232875i	$-0.0748132\pi$
$461$	8.87513e6	1.94501	0.972507	+	0.232875i	$0.0748132\pi$
$462$	0	0
$463$	5.34415e6	1.15858	0.579290	−	0.815121i	$-0.303330\pi$
$463$	5.34415e6	1.15858	0.579290	+	0.815121i	$0.303330\pi$
$464$	0	0
$465$	−1.11420e6	−0.238963
$466$	0	0
$467$	−1.96960e6	−0.417914	−0.208957	−	0.977925i	$-0.567007\pi$
$467$	−1.96960e6	−0.417914	−0.208957	+	0.977925i	$0.567007\pi$
$468$	0	0
$469$	2.78464e6	0.584571
$470$	0	0
$471$	558378.	0.115978
$472$	0	0
$473$	1.43731e7	2.95392
$474$	0	0
$475$	−497500.	−0.101172
$476$	0	0
$477$	1.66844e6	0.335749
$478$	0	0
$479$	−934624.	−0.186122	−0.0930611	−	0.995660i	$-0.529665\pi$
$479$	−934624.	−0.186122	−0.0930611	+	0.995660i	$0.529665\pi$
$480$	0	0
$481$	745908.	0.147002
$482$	0	0
$483$	−1.56672e6	−0.305579
$484$	0	0
$485$	−1.07195e6	−0.206928
$486$	0	0
$487$	−9.28629e6	−1.77427	−0.887135	−	0.461510i	$-0.847308\pi$
$487$	−9.28629e6	−1.77427	−0.887135	+	0.461510i	$0.847308\pi$
$488$	0	0
$489$	−3.63481e6	−0.687400
$490$	0	0
$491$	1.17061e6	0.219134	0.109567	−	0.993979i	$-0.465054\pi$
$491$	1.17061e6	0.219134	0.109567	+	0.993979i	$0.465054\pi$
$492$	0	0
$493$	−49588.0	−0.00918881
$494$	0	0
$495$	1.20690e6	0.221390
$496$	0	0
$497$	−4.25088e6	−0.771948
$498$	0	0
$499$	−4.99185e6	−0.897450	−0.448725	−	0.893670i	$-0.648122\pi$
$499$	−4.99185e6	−0.897450	−0.448725	+	0.893670i	$0.648122\pi$
$500$	0	0
$501$	886896.	0.157862
$502$	0	0
$503$	−562704.	−0.0991654	−0.0495827	−	0.998770i	$-0.515789\pi$
$503$	−562704.	−0.0991654	−0.0495827	+	0.998770i	$0.515789\pi$
$504$	0	0
$505$	4.13655e6	0.721788
$506$	0	0
$507$	3.20768e6	0.554206
$508$	0	0
$509$	−8.23771e6	−1.40933	−0.704664	−	0.709541i	$-0.748902\pi$
$509$	−8.23771e6	−1.40933	−0.704664	+	0.709541i	$0.748902\pi$
$510$	0	0
$511$	1.20720e7	2.04516
$512$	0	0
$513$	580284.	0.0973525
$514$	0	0
$515$	5.29760e6	0.880159
$516$	0	0
$517$	−8.03408e6	−1.32193
$518$	0	0
$519$	2.99407e6	0.487914
$520$	0	0
$521$	−8.23045e6	−1.32840	−0.664201	−	0.747554i	$-0.731228\pi$
$521$	−8.23045e6	−1.32840	−0.664201	+	0.747554i	$0.731228\pi$
$522$	0	0
$523$	−8.31228e6	−1.32882	−0.664410	−	0.747368i	$-0.731317\pi$
$523$	−8.31228e6	−1.32882	−0.664410	+	0.747368i	$0.731317\pi$
$524$	0	0
$525$	−900000.	−0.142510
$526$	0	0
$527$	−5.33826e6	−0.837284
$528$	0	0
$529$	−5.25260e6	−0.816084
$530$	0	0
$531$	3.78724e6	0.582889
$532$	0	0
$533$	732.000	0.000111607 0
$534$	0	0
$535$	−4.62870e6	−0.699157
$536$	0	0
$537$	−3.57289e6	−0.534668
$538$	0	0
$539$	5.24063e6	0.776983
$540$	0	0
$541$	−6.52738e6	−0.958839	−0.479419	−	0.877586i	$-0.659153\pi$
$541$	−6.52738e6	−0.958839	−0.479419	+	0.877586i	$0.659153\pi$
$542$	0	0
$543$	−4.89749e6	−0.712811
$544$	0	0
$545$	2.19995e6	0.317265
$546$	0	0
$547$	−3.52432e6	−0.503625	−0.251813	−	0.967776i	$-0.581027\pi$
$547$	−3.52432e6	−0.503625	−0.251813	+	0.967776i	$0.581027\pi$
$548$	0	0
$549$	−777762.	−0.110133
$550$	0	0
$551$	−36616.0	−0.00513797
$552$	0	0
$553$	−8.07552e6	−1.12294
$554$	0	0
$555$	1.37565e6	0.189573
$556$	0	0
$557$	−1.03183e7	−1.40919	−0.704596	−	0.709608i	$-0.748872\pi$
$557$	−1.03183e7	−1.40919	−0.704596	+	0.709608i	$0.748872\pi$
$558$	0	0
$559$	−2.94215e6	−0.398231
$560$	0	0
$561$	5.78239e6	0.775712
$562$	0	0
$563$	−6.25479e6	−0.831652	−0.415826	−	0.909444i	$-0.636507\pi$
$563$	−6.25479e6	−0.831652	−0.415826	+	0.909444i	$0.636507\pi$
$564$	0	0
$565$	−6.52455e6	−0.859863
$566$	0	0
$567$	1.04976e6	0.137130
$568$	0	0
$569$	1.05796e7	1.36990	0.684950	−	0.728590i	$-0.259824\pi$
$569$	1.05796e7	1.36990	0.684950	+	0.728590i	$0.259824\pi$
$570$	0	0
$571$	6.36340e6	0.816769	0.408384	−	0.912810i	$-0.366092\pi$
$571$	6.36340e6	0.816769	0.408384	+	0.912810i	$0.366092\pi$
$572$	0	0
$573$	7.84368e6	0.998006
$574$	0	0
$575$	680000.	0.0857708
$576$	0	0
$577$	9.66528e6	1.20858	0.604289	−	0.796765i	$-0.293457\pi$
$577$	9.66528e6	1.20858	0.604289	+	0.796765i	$0.293457\pi$
$578$	0	0
$579$	8.00854e6	0.992789
$580$	0	0
$581$	−5.31776e6	−0.653564
$582$	0	0
$583$	1.22764e7	1.49589
$584$	0	0
$585$	−247050.	−0.0298466
$586$	0	0
$587$	1.53440e6	0.183800	0.0918998	−	0.995768i	$-0.470706\pi$
$587$	1.53440e6	0.183800	0.0918998	+	0.995768i	$0.470706\pi$
$588$	0	0
$589$	−3.94179e6	−0.468172
$590$	0	0
$591$	1.91140e6	0.225104
$592$	0	0
$593$	−1.80293e6	−0.210544	−0.105272	−	0.994443i	$-0.533571\pi$
$593$	−1.80293e6	−0.210544	−0.105272	+	0.994443i	$0.533571\pi$
$594$	0	0
$595$	−4.31200e6	−0.499328
$596$	0	0
$597$	5.64350e6	0.648057
$598$	0	0
$599$	2.92942e6	0.333591	0.166795	−	0.985992i	$-0.446658\pi$
$599$	2.92942e6	0.333591	0.166795	+	0.985992i	$0.446658\pi$
$600$	0	0
$601$	−4.36084e6	−0.492475	−0.246237	−	0.969210i	$-0.579194\pi$
$601$	−4.36084e6	−0.492475	−0.246237	+	0.969210i	$0.579194\pi$
$602$	0	0
$603$	1.40972e6	0.157885
$604$	0	0
$605$	4.85412e6	0.539166
$606$	0	0
$607$	1.30465e7	1.43722	0.718610	−	0.695414i	$-0.244779\pi$
$607$	1.30465e7	1.43722	0.718610	+	0.695414i	$0.244779\pi$
$608$	0	0
$609$	−66240.0	−0.00723731
$610$	0	0
$611$	1.64456e6	0.178216
$612$	0	0
$613$	−1.19790e7	−1.28757	−0.643785	−	0.765206i	$-0.722637\pi$
$613$	−1.19790e7	−1.28757	−0.643785	+	0.765206i	$0.722637\pi$
$614$	0	0
$615$	1350.00	0.000143928 0
$616$	0	0
$617$	8.22088e6	0.869372	0.434686	−	0.900582i	$-0.356859\pi$
$617$	8.22088e6	0.869372	0.434686	+	0.900582i	$0.356859\pi$
$618$	0	0
$619$	−1.23205e7	−1.29242	−0.646208	−	0.763161i	$-0.723646\pi$
$619$	−1.23205e7	−1.29242	−0.646208	+	0.763161i	$0.723646\pi$
$620$	0	0
$621$	−793152.	−0.0825330
$622$	0	0
$623$	2.13110e7	2.19981
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	4.26974e6	0.433744
$628$	0	0
$629$	6.59089e6	0.664229
$630$	0	0
$631$	−5.71970e6	−0.571873	−0.285936	−	0.958249i	$-0.592305\pi$
$631$	−5.71970e6	−0.571873	−0.285936	+	0.958249i	$0.592305\pi$
$632$	0	0
$633$	1.17198e6	0.116255
$634$	0	0
$635$	424200.	0.0417481
$636$	0	0
$637$	−1.07275e6	−0.104749
$638$	0	0
$639$	−2.15201e6	−0.208493
$640$	0	0
$641$	3.85087e6	0.370180	0.185090	−	0.982722i	$-0.440742\pi$
$641$	3.85087e6	0.370180	0.185090	+	0.982722i	$0.440742\pi$
$642$	0	0
$643$	−1.17750e7	−1.12314	−0.561570	−	0.827429i	$-0.689802\pi$
$643$	−1.17750e7	−1.12314	−0.561570	+	0.827429i	$0.689802\pi$
$644$	0	0
$645$	−5.42610e6	−0.513557
$646$	0	0
$647$	−5.56997e6	−0.523109	−0.261554	−	0.965189i	$-0.584235\pi$
$647$	−5.56997e6	−0.523109	−0.261554	+	0.965189i	$0.584235\pi$
$648$	0	0
$649$	2.78666e7	2.59700
$650$	0	0
$651$	−7.13088e6	−0.659463
$652$	0	0
$653$	−618754.	−0.0567852	−0.0283926	−	0.999597i	$-0.509039\pi$
$653$	−618754.	−0.0567852	−0.0283926	+	0.999597i	$0.509039\pi$
$654$	0	0
$655$	−2.80290e6	−0.255273
$656$	0	0
$657$	6.11145e6	0.552371
$658$	0	0
$659$	1.77183e7	1.58931	0.794657	−	0.607059i	$-0.207651\pi$
$659$	1.77183e7	1.58931	0.794657	+	0.607059i	$0.207651\pi$
$660$	0	0
$661$	1.27106e7	1.13152	0.565758	−	0.824571i	$-0.308584\pi$
$661$	1.27106e7	1.13152	0.565758	+	0.824571i	$0.308584\pi$
$662$	0	0
$663$	−1.18364e6	−0.104577
$664$	0	0
$665$	−3.18400e6	−0.279202
$666$	0	0
$667$	50048.0	0.00435584
$668$	0	0
$669$	−7.78975e6	−0.672912
$670$	0	0
$671$	−5.72279e6	−0.490684
$672$	0	0
$673$	−1.28327e7	−1.09214	−0.546072	−	0.837738i	$-0.683878\pi$
$673$	−1.28327e7	−1.09214	−0.546072	+	0.837738i	$0.683878\pi$
$674$	0	0
$675$	−455625.	−0.0384900
$676$	0	0
$677$	1.11553e7	0.935428	0.467714	−	0.883880i	$-0.345078\pi$
$677$	1.11553e7	0.935428	0.467714	+	0.883880i	$0.345078\pi$
$678$	0	0
$679$	−6.86048e6	−0.571058
$680$	0	0
$681$	1.06241e7	0.877856
$682$	0	0
$683$	1.26034e7	1.03380	0.516899	−	0.856046i	$-0.327086\pi$
$683$	1.26034e7	1.03380	0.516899	+	0.856046i	$0.327086\pi$
$684$	0	0
$685$	−5.89715e6	−0.480193
$686$	0	0
$687$	−1.19601e7	−0.966816
$688$	0	0
$689$	−2.51296e6	−0.201668
$690$	0	0
$691$	−919436.	−0.0732532	−0.0366266	−	0.999329i	$-0.511661\pi$
$691$	−919436.	−0.0732532	−0.0366266	+	0.999329i	$0.511661\pi$
$692$	0	0
$693$	7.72416e6	0.610968
$694$	0	0
$695$	8.34630e6	0.655439
$696$	0	0
$697$	6468.00	0.000504299 0
$698$	0	0
$699$	4.09347e6	0.316883
$700$	0	0
$701$	−2.67915e6	−0.205922	−0.102961	−	0.994685i	$-0.532832\pi$
$701$	−2.67915e6	−0.205922	−0.102961	+	0.994685i	$0.532832\pi$
$702$	0	0
$703$	4.86674e6	0.371407
$704$	0	0
$705$	3.03300e6	0.229826
$706$	0	0
$707$	2.64739e7	1.99191
$708$	0	0
$709$	5.20199e6	0.388646	0.194323	−	0.980938i	$-0.437749\pi$
$709$	5.20199e6	0.388646	0.194323	+	0.980938i	$0.437749\pi$
$710$	0	0
$711$	−4.08823e6	−0.303292
$712$	0	0
$713$	5.38778e6	0.396904
$714$	0	0
$715$	−1.81780e6	−0.132978
$716$	0	0
$717$	3.61066e6	0.262294
$718$	0	0
$719$	1.49040e7	1.07518	0.537590	−	0.843206i	$-0.319335\pi$
$719$	1.49040e7	1.07518	0.537590	+	0.843206i	$0.319335\pi$
$720$	0	0
$721$	3.39046e7	2.42896
$722$	0	0
$723$	−5.91712e6	−0.420983
$724$	0	0
$725$	28750.0	0.00203139
$726$	0	0
$727$	1.71095e7	1.20061	0.600303	−	0.799773i	$-0.295047\pi$
$727$	1.71095e7	1.20061	0.600303	+	0.799773i	$0.295047\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−2.59970e7	−1.79941
$732$	0	0
$733$	561414.	0.0385943	0.0192972	−	0.999814i	$-0.493857\pi$
$733$	561414.	0.0385943	0.0192972	+	0.999814i	$0.493857\pi$
$734$	0	0
$735$	−1.97842e6	−0.135083
$736$	0	0
$737$	1.03728e7	0.703439
$738$	0	0
$739$	−1.58800e7	−1.06964	−0.534822	−	0.844965i	$-0.679621\pi$
$739$	−1.58800e7	−1.06964	−0.534822	+	0.844965i	$0.679621\pi$
$740$	0	0
$741$	−874008.	−0.0584750
$742$	0	0
$743$	−2.41464e7	−1.60465	−0.802323	−	0.596889i	$-0.796403\pi$
$743$	−2.41464e7	−1.60465	−0.802323	+	0.596889i	$0.796403\pi$
$744$	0	0
$745$	2.21135e6	0.145971
$746$	0	0
$747$	−2.69212e6	−0.176519
$748$	0	0
$749$	−2.96237e7	−1.92945
$750$	0	0
$751$	2.38798e6	0.154501	0.0772503	−	0.997012i	$-0.475386\pi$
$751$	2.38798e6	0.154501	0.0772503	+	0.997012i	$0.475386\pi$
$752$	0	0
$753$	−5.39730e6	−0.346888
$754$	0	0
$755$	3.09040e6	0.197309
$756$	0	0
$757$	2.80058e7	1.77626	0.888132	−	0.459588i	$-0.152003\pi$
$757$	2.80058e7	1.77626	0.888132	+	0.459588i	$0.152003\pi$
$758$	0	0
$759$	−5.83603e6	−0.367717
$760$	0	0
$761$	−2.34985e7	−1.47088	−0.735442	−	0.677587i	$-0.763026\pi$
$761$	−2.34985e7	−1.47088	−0.735442	+	0.677587i	$0.763026\pi$
$762$	0	0
$763$	1.40797e7	0.875551
$764$	0	0
$765$	−2.18295e6	−0.134862
$766$	0	0
$767$	−5.70423e6	−0.350113
$768$	0	0
$769$	1.68795e7	1.02931	0.514653	−	0.857399i	$-0.327921\pi$
$769$	1.68795e7	1.02931	0.514653	+	0.857399i	$0.327921\pi$
$770$	0	0
$771$	9.02626e6	0.546855
$772$	0	0
$773$	5.67514e6	0.341608	0.170804	−	0.985305i	$-0.445364\pi$
$773$	5.67514e6	0.341608	0.170804	+	0.985305i	$0.445364\pi$
$774$	0	0
$775$	3.09500e6	0.185100
$776$	0	0
$777$	8.80416e6	0.523161
$778$	0	0
$779$	4776.00	0.000281982 0
$780$	0	0
$781$	−1.58345e7	−0.928918
$782$	0	0
$783$	−33534.0	−0.00195470
$784$	0	0
$785$	−1.55105e6	−0.0898363
$786$	0	0
$787$	−1.34233e7	−0.772541	−0.386270	−	0.922386i	$-0.626237\pi$
$787$	−1.34233e7	−0.772541	−0.386270	+	0.922386i	$0.626237\pi$
$788$	0	0
$789$	−7.43299e6	−0.425080
$790$	0	0
$791$	−4.17571e7	−2.37295
$792$	0	0
$793$	1.17144e6	0.0661513
$794$	0	0
$795$	−4.63455e6	−0.260070
$796$	0	0
$797$	−2.55629e7	−1.42549	−0.712745	−	0.701423i	$-0.752548\pi$
$797$	−2.55629e7	−1.42549	−0.712745	+	0.701423i	$0.752548\pi$
$798$	0	0
$799$	1.45314e7	0.805270
$800$	0	0
$801$	1.07887e7	0.594139
$802$	0	0
$803$	4.49682e7	2.46103
$804$	0	0
$805$	4.35200e6	0.236701
$806$	0	0
$807$	7.66053e6	0.414071
$808$	0	0
$809$	6.67891e6	0.358785	0.179392	−	0.983778i	$-0.442587\pi$
$809$	6.67891e6	0.358785	0.179392	+	0.983778i	$0.442587\pi$
$810$	0	0
$811$	−2.62811e7	−1.40311	−0.701555	−	0.712615i	$-0.747511\pi$
$811$	−2.62811e7	−1.40311	−0.701555	+	0.712615i	$0.747511\pi$
$812$	0	0
$813$	−1.92894e7	−1.02351
$814$	0	0
$815$	1.00967e7	0.532458
$816$	0	0
$817$	−1.91963e7	−1.00615
$818$	0	0
$819$	−1.58112e6	−0.0823673
$820$	0	0
$821$	1.04343e7	0.540264	0.270132	−	0.962823i	$-0.412933\pi$
$821$	1.04343e7	0.540264	0.270132	+	0.962823i	$0.412933\pi$
$822$	0	0
$823$	1.27360e7	0.655442	0.327721	−	0.944775i	$-0.393719\pi$
$823$	1.27360e7	0.655442	0.327721	+	0.944775i	$0.393719\pi$
$824$	0	0
$825$	−3.35250e6	−0.171488
$826$	0	0
$827$	−3.11753e7	−1.58506	−0.792532	−	0.609830i	$-0.791238\pi$
$827$	−3.11753e7	−1.58506	−0.792532	+	0.609830i	$0.791238\pi$
$828$	0	0
$829$	−6.41765e6	−0.324332	−0.162166	−	0.986763i	$-0.551848\pi$
$829$	−6.41765e6	−0.324332	−0.162166	+	0.986763i	$0.551848\pi$
$830$	0	0
$831$	−9.37669e6	−0.471028
$832$	0	0
$833$	−9.47885e6	−0.473307
$834$	0	0
$835$	−2.46360e6	−0.122280
$836$	0	0
$837$	−3.61001e6	−0.178113
$838$	0	0
$839$	−1.84587e7	−0.905307	−0.452654	−	0.891686i	$-0.649523\pi$
$839$	−1.84587e7	−0.905307	−0.452654	+	0.891686i	$0.649523\pi$
$840$	0	0
$841$	−2.05090e7	−0.999897
$842$	0	0
$843$	3.64513e6	0.176662
$844$	0	0
$845$	−8.91022e6	−0.429286
$846$	0	0
$847$	3.10664e7	1.48793
$848$	0	0
$849$	−1.25629e6	−0.0598166
$850$	0	0
$851$	−6.65203e6	−0.314869
$852$	0	0
$853$	−3.41356e7	−1.60633	−0.803165	−	0.595757i	$-0.796852\pi$
$853$	−3.41356e7	−1.60633	−0.803165	+	0.595757i	$0.796852\pi$
$854$	0	0
$855$	−1.61190e6	−0.0754089
$856$	0	0
$857$	1.38239e7	0.642953	0.321476	−	0.946918i	$-0.395821\pi$
$857$	1.38239e7	0.642953	0.321476	+	0.946918i	$0.395821\pi$
$858$	0	0
$859$	−1.79847e7	−0.831611	−0.415806	−	0.909453i	$-0.636500\pi$
$859$	−1.79847e7	−0.831611	−0.415806	+	0.909453i	$0.636500\pi$
$860$	0	0
$861$	8640.00	0.000397197 0
$862$	0	0
$863$	2.28373e7	1.04380	0.521900	−	0.853007i	$-0.325223\pi$
$863$	2.28373e7	1.04380	0.521900	+	0.853007i	$0.325223\pi$
$864$	0	0
$865$	−8.31685e6	−0.377936
$866$	0	0
$867$	2.31996e6	0.104817
$868$	0	0
$869$	−3.00813e7	−1.35129
$870$	0	0
$871$	−2.12329e6	−0.0948339
$872$	0	0
$873$	−3.47312e6	−0.154235
$874$	0	0
$875$	2.50000e6	0.110387
$876$	0	0
$877$	3.44741e7	1.51354	0.756770	−	0.653681i	$-0.226776\pi$
$877$	3.44741e7	1.51354	0.756770	+	0.653681i	$0.226776\pi$
$878$	0	0
$879$	−5.55788e6	−0.242626
$880$	0	0
$881$	−2.90535e7	−1.26113	−0.630563	−	0.776138i	$-0.717176\pi$
$881$	−2.90535e7	−1.26113	−0.630563	+	0.776138i	$0.717176\pi$
$882$	0	0
$883$	2.38516e7	1.02947	0.514737	−	0.857348i	$-0.327890\pi$
$883$	2.38516e7	1.02947	0.514737	+	0.857348i	$0.327890\pi$
$884$	0	0
$885$	−1.05201e7	−0.451504
$886$	0	0
$887$	1.25252e7	0.534532	0.267266	−	0.963623i	$-0.413880\pi$
$887$	1.25252e7	0.534532	0.267266	+	0.963623i	$0.413880\pi$
$888$	0	0
$889$	2.71488e6	0.115212
$890$	0	0
$891$	3.91036e6	0.165014
$892$	0	0
$893$	1.07301e7	0.450271
$894$	0	0
$895$	9.92470e6	0.414152
$896$	0	0
$897$	1.19462e6	0.0495736
$898$	0	0
$899$	227792.	0.00940025
$900$	0	0
$901$	−2.22046e7	−0.911238
$902$	0	0
$903$	−3.47270e7	−1.41726
$904$	0	0
$905$	1.36042e7	0.552141
$906$	0	0
$907$	1.09828e6	0.0443295	0.0221648	−	0.999754i	$-0.492944\pi$
$907$	1.09828e6	0.0443295	0.0221648	+	0.999754i	$0.492944\pi$
$908$	0	0
$909$	1.34024e7	0.537989
$910$	0	0
$911$	−1.76825e7	−0.705907	−0.352954	−	0.935641i	$-0.614823\pi$
$911$	−1.76825e7	−0.705907	−0.352954	+	0.935641i	$0.614823\pi$
$912$	0	0
$913$	−1.98087e7	−0.786463
$914$	0	0
$915$	2.16045e6	0.0853083
$916$	0	0
$917$	−1.79386e7	−0.704473
$918$	0	0
$919$	1.59365e7	0.622451	0.311226	−	0.950336i	$-0.399261\pi$
$919$	1.59365e7	0.622451	0.311226	+	0.950336i	$0.399261\pi$
$920$	0	0
$921$	−1.12769e7	−0.438067
$922$	0	0
$923$	3.24130e6	0.125232
$924$	0	0
$925$	−3.82125e6	−0.146842
$926$	0	0
$927$	1.71642e7	0.656032
$928$	0	0
$929$	4.33302e7	1.64722	0.823610	−	0.567157i	$-0.191957\pi$
$929$	4.33302e7	1.64722	0.823610	+	0.567157i	$0.191957\pi$
$930$	0	0
$931$	−6.99923e6	−0.264652
$932$	0	0
$933$	−1.87634e7	−0.705680
$934$	0	0
$935$	−1.60622e7	−0.600864
$936$	0	0
$937$	2.10463e7	0.783117	0.391558	−	0.920153i	$-0.371936\pi$
$937$	2.10463e7	0.783117	0.391558	+	0.920153i	$0.371936\pi$
$938$	0	0
$939$	1.33309e7	0.493394
$940$	0	0
$941$	−4.55282e7	−1.67612	−0.838062	−	0.545574i	$-0.816312\pi$
$941$	−4.55282e7	−1.67612	−0.838062	+	0.545574i	$0.816312\pi$
$942$	0	0
$943$	−6528.00	−0.000239057 0
$944$	0	0
$945$	−2.91600e6	−0.106220
$946$	0	0
$947$	1.35818e7	0.492132	0.246066	−	0.969253i	$-0.420862\pi$
$947$	1.35818e7	0.492132	0.246066	+	0.969253i	$0.420862\pi$
$948$	0	0
$949$	−9.20490e6	−0.331783
$950$	0	0
$951$	2.42239e6	0.0868544
$952$	0	0
$953$	−570174.	−0.0203365	−0.0101682	−	0.999948i	$-0.503237\pi$
$953$	−570174.	−0.0203365	−0.0101682	+	0.999948i	$0.503237\pi$
$954$	0	0
$955$	−2.17880e7	−0.773052
$956$	0	0
$957$	−246744.	−0.00870897
$958$	0	0
$959$	−3.77418e7	−1.32518
$960$	0	0
$961$	−4.10685e6	−0.143450
$962$	0	0
$963$	−1.49970e7	−0.521121
$964$	0	0
$965$	−2.22460e7	−0.769011
$966$	0	0
$967$	−1.12955e7	−0.388454	−0.194227	−	0.980957i	$-0.562220\pi$
$967$	−1.12955e7	−0.388454	−0.194227	+	0.980957i	$0.562220\pi$
$968$	0	0
$969$	−7.72279e6	−0.264220
$970$	0	0
$971$	−9.09456e6	−0.309552	−0.154776	−	0.987950i	$-0.549466\pi$
$971$	−9.09456e6	−0.309552	−0.154776	+	0.987950i	$0.549466\pi$
$972$	0	0
$973$	5.34163e7	1.80881
$974$	0	0
$975$	686250.	0.0231191
$976$	0	0
$977$	5.07827e7	1.70208	0.851039	−	0.525102i	$-0.175973\pi$
$977$	5.07827e7	1.70208	0.851039	+	0.525102i	$0.175973\pi$
$978$	0	0
$979$	7.93836e7	2.64712
$980$	0	0
$981$	7.12784e6	0.236475
$982$	0	0
$983$	−3.11060e7	−1.02674	−0.513370	−	0.858167i	$-0.671603\pi$
$983$	−3.11060e7	−1.02674	−0.513370	+	0.858167i	$0.671603\pi$
$984$	0	0
$985$	−5.30945e6	−0.174365
$986$	0	0
$987$	1.94112e7	0.634249
$988$	0	0
$989$	2.62382e7	0.852989
$990$	0	0
$991$	1.44148e6	0.0466256	0.0233128	−	0.999728i	$-0.492579\pi$
$991$	1.44148e6	0.0466256	0.0233128	+	0.999728i	$0.492579\pi$
$992$	0	0
$993$	−3.36663e7	−1.08348
$994$	0	0
$995$	−1.56764e7	−0.501983
$996$	0	0
$997$	1.65026e7	0.525792	0.262896	−	0.964824i	$-0.415322\pi$
$997$	1.65026e7	0.525792	0.262896	+	0.964824i	$0.415322\pi$
$998$	0	0
$999$	4.45711e6	0.141299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.6.a.g.1.1		1
3.2	odd	2		720.6.a.i.1.1		1
4.3	odd	2		120.6.a.f.1.1	✓	1
8.3	odd	2		960.6.a.a.1.1		1
8.5	even	2		960.6.a.t.1.1		1
12.11	even	2		360.6.a.a.1.1		1
20.3	even	4		600.6.f.a.49.2		2
20.7	even	4		600.6.f.a.49.1		2
20.19	odd	2		600.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.6.a.f.1.1	✓	1	4.3	odd	2
240.6.a.g.1.1		1	1.1	even	1	trivial
360.6.a.a.1.1		1	12.11	even	2
600.6.a.c.1.1		1	20.19	odd	2
600.6.f.a.49.1		2	20.7	even	4
600.6.f.a.49.2		2	20.3	even	4
720.6.a.i.1.1		1	3.2	odd	2
960.6.a.a.1.1		1	8.3	odd	2
960.6.a.t.1.1		1	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	240.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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