LMFDB - Embedded newform 588.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,6,Mod(1,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("588.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	588.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:	$94.3056860500$
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	$\chi$	$=$	588.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} -68.0000 q^{5} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} -68.0000 q^{5} +81.0000 q^{9} -388.000 q^{11} +316.000 q^{13} +612.000 q^{15} +1056.00 q^{17} -1052.00 q^{19} +624.000 q^{23} +1499.00 q^{25} -729.000 q^{27} +7250.00 q^{29} -2296.00 q^{31} +3492.00 q^{33} +12426.0 q^{37} -2844.00 q^{39} -5376.00 q^{41} +14164.0 q^{43} -5508.00 q^{45} -4712.00 q^{47} -9504.00 q^{51} +3782.00 q^{53} +26384.0 q^{55} +9468.00 q^{57} -25244.0 q^{59} -20668.0 q^{61} -21488.0 q^{65} +49012.0 q^{67} -5616.00 q^{69} +4760.00 q^{71} +65264.0 q^{73} -13491.0 q^{75} -49736.0 q^{79} +6561.00 q^{81} -7788.00 q^{83} -71808.0 q^{85} -65250.0 q^{87} -36904.0 q^{89} +20664.0 q^{93} +71536.0 q^{95} +98264.0 q^{97} -31428.0 q^{99} +O(q^{100})$

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
$5$	−68.0000	−1.21642	−0.608210	−	0.793776i	$-0.708112\pi$
$5$	−68.0000	−1.21642	−0.608210	+	0.793776i	$0.708112\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	−388.000	−0.966830	−0.483415	−	0.875391i	$-0.660604\pi$
$11$	−388.000	−0.966830	−0.483415	+	0.875391i	$0.660604\pi$
$12$	0	0
$13$	316.000	0.518595	0.259298	−	0.965797i	$-0.416509\pi$
$13$	316.000	0.518595	0.259298	+	0.965797i	$0.416509\pi$
$14$	0	0
$15$	612.000	0.702301
$16$	0	0
$17$	1056.00	0.886220	0.443110	−	0.896467i	$-0.353875\pi$
$17$	1056.00	0.886220	0.443110	+	0.896467i	$0.353875\pi$
$18$	0	0
$19$	−1052.00	−0.668547	−0.334273	−	0.942476i	$-0.608491\pi$
$19$	−1052.00	−0.668547	−0.334273	+	0.942476i	$0.608491\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	624.000	0.245960	0.122980	−	0.992409i	$-0.460755\pi$
$23$	624.000	0.245960	0.122980	+	0.992409i	$0.460755\pi$
$24$	0	0
$25$	1499.00	0.479680
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	7250.00	1.60082	0.800411	−	0.599452i	$-0.204615\pi$
$29$	7250.00	1.60082	0.800411	+	0.599452i	$0.204615\pi$
$30$	0	0
$31$	−2296.00	−0.429109	−0.214555	−	0.976712i	$-0.568830\pi$
$31$	−2296.00	−0.429109	−0.214555	+	0.976712i	$0.568830\pi$
$32$	0	0
$33$	3492.00	0.558199
$34$	0	0
$35$	0	0
$36$	0	0
$37$	12426.0	1.49220	0.746100	−	0.665834i	$-0.231924\pi$
$37$	12426.0	1.49220	0.746100	+	0.665834i	$0.231924\pi$
$38$	0	0
$39$	−2844.00	−0.299411
$40$	0	0
$41$	−5376.00	−0.499459	−0.249729	−	0.968316i	$-0.580342\pi$
$41$	−5376.00	−0.499459	−0.249729	+	0.968316i	$0.580342\pi$
$42$	0	0
$43$	14164.0	1.16819	0.584097	−	0.811684i	$-0.301449\pi$
$43$	14164.0	1.16819	0.584097	+	0.811684i	$0.301449\pi$
$44$	0	0
$45$	−5508.00	−0.405474
$46$	0	0
$47$	−4712.00	−0.311143	−0.155572	−	0.987825i	$-0.549722\pi$
$47$	−4712.00	−0.311143	−0.155572	+	0.987825i	$0.549722\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−9504.00	−0.511659
$52$	0	0
$53$	3782.00	0.184940	0.0924702	−	0.995715i	$-0.470524\pi$
$53$	3782.00	0.184940	0.0924702	+	0.995715i	$0.470524\pi$
$54$	0	0
$55$	26384.0	1.17607
$56$	0	0
$57$	9468.00	0.385986
$58$	0	0
$59$	−25244.0	−0.944122	−0.472061	−	0.881566i	$-0.656490\pi$
$59$	−25244.0	−0.944122	−0.472061	+	0.881566i	$0.656490\pi$
$60$	0	0
$61$	−20668.0	−0.711171	−0.355585	−	0.934644i	$-0.615718\pi$
$61$	−20668.0	−0.711171	−0.355585	+	0.934644i	$0.615718\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−21488.0	−0.630830
$66$	0	0
$67$	49012.0	1.33388	0.666938	−	0.745113i	$-0.267605\pi$
$67$	49012.0	1.33388	0.666938	+	0.745113i	$0.267605\pi$
$68$	0	0
$69$	−5616.00	−0.142005
$70$	0	0
$71$	4760.00	0.112063	0.0560313	−	0.998429i	$-0.482155\pi$
$71$	4760.00	0.112063	0.0560313	+	0.998429i	$0.482155\pi$
$72$	0	0
$73$	65264.0	1.43340	0.716699	−	0.697383i	$-0.245652\pi$
$73$	65264.0	1.43340	0.716699	+	0.697383i	$0.245652\pi$
$74$	0	0
$75$	−13491.0	−0.276943
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−49736.0	−0.896609	−0.448305	−	0.893881i	$-0.647972\pi$
$79$	−49736.0	−0.896609	−0.448305	+	0.893881i	$0.647972\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−7788.00	−0.124088	−0.0620441	−	0.998073i	$-0.519762\pi$
$83$	−7788.00	−0.124088	−0.0620441	+	0.998073i	$0.519762\pi$
$84$	0	0
$85$	−71808.0	−1.07802
$86$	0	0
$87$	−65250.0	−0.924235
$88$	0	0
$89$	−36904.0	−0.493854	−0.246927	−	0.969034i	$-0.579421\pi$
$89$	−36904.0	−0.493854	−0.246927	+	0.969034i	$0.579421\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	20664.0	0.247746
$94$	0	0
$95$	71536.0	0.813234
$96$	0	0
$97$	98264.0	1.06039	0.530194	−	0.847876i	$-0.322119\pi$
$97$	98264.0	1.06039	0.530194	+	0.847876i	$0.322119\pi$
$98$	0	0
$99$	−31428.0	−0.322277
$100$	0	0
$101$	−197060.	−1.92218	−0.961092	−	0.276228i	$-0.910916\pi$
$101$	−197060.	−1.92218	−0.961092	+	0.276228i	$0.910916\pi$
$102$	0	0
$103$	−183464.	−1.70395	−0.851977	−	0.523579i	$-0.824596\pi$
$103$	−183464.	−1.70395	−0.851977	+	0.523579i	$0.824596\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−55004.0	−0.464446	−0.232223	−	0.972663i	$-0.574600\pi$
$107$	−55004.0	−0.464446	−0.232223	+	0.972663i	$0.574600\pi$
$108$	0	0
$109$	−118430.	−0.954763	−0.477381	−	0.878696i	$-0.658414\pi$
$109$	−118430.	−0.954763	−0.477381	+	0.878696i	$0.658414\pi$
$110$	0	0
$111$	−111834.	−0.861522
$112$	0	0
$113$	−151694.	−1.11756	−0.558782	−	0.829315i	$-0.688731\pi$
$113$	−151694.	−1.11756	−0.558782	+	0.829315i	$0.688731\pi$
$114$	0	0
$115$	−42432.0	−0.299191
$116$	0	0
$117$	25596.0	0.172865
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−10507.0	−0.0652402
$122$	0	0
$123$	48384.0	0.288363
$124$	0	0
$125$	110568.	0.632928
$126$	0	0
$127$	239216.	1.31608	0.658038	−	0.752985i	$-0.271387\pi$
$127$	239216.	1.31608	0.658038	+	0.752985i	$0.271387\pi$
$128$	0	0
$129$	−127476.	−0.674457
$130$	0	0
$131$	−164652.	−0.838279	−0.419140	−	0.907922i	$-0.637668\pi$
$131$	−164652.	−0.838279	−0.419140	+	0.907922i	$0.637668\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	49572.0	0.234100
$136$	0	0
$137$	−179050.	−0.815029	−0.407514	−	0.913199i	$-0.633604\pi$
$137$	−179050.	−0.815029	−0.407514	+	0.913199i	$0.633604\pi$
$138$	0	0
$139$	392172.	1.72163	0.860815	−	0.508919i	$-0.169955\pi$
$139$	392172.	1.72163	0.860815	+	0.508919i	$0.169955\pi$
$140$	0	0
$141$	42408.0	0.179639
$142$	0	0
$143$	−122608.	−0.501394
$144$	0	0
$145$	−493000.	−1.94727
$146$	0	0
$147$	0	0
$148$	0	0
$149$	429062.	1.58327	0.791634	−	0.610996i	$-0.209231\pi$
$149$	429062.	1.58327	0.791634	+	0.610996i	$0.209231\pi$
$150$	0	0
$151$	−263048.	−0.938842	−0.469421	−	0.882974i	$-0.655537\pi$
$151$	−263048.	−0.938842	−0.469421	+	0.882974i	$0.655537\pi$
$152$	0	0
$153$	85536.0	0.295407
$154$	0	0
$155$	156128.	0.521977
$156$	0	0
$157$	−145796.	−0.472059	−0.236030	−	0.971746i	$-0.575846\pi$
$157$	−145796.	−0.472059	−0.236030	+	0.971746i	$0.575846\pi$
$158$	0	0
$159$	−34038.0	−0.106775
$160$	0	0
$161$	0	0
$162$	0	0
$163$	248604.	0.732891	0.366445	−	0.930440i	$-0.380575\pi$
$163$	248604.	0.732891	0.366445	+	0.930440i	$0.380575\pi$
$164$	0	0
$165$	−237456.	−0.679005
$166$	0	0
$167$	−75064.0	−0.208277	−0.104138	−	0.994563i	$-0.533208\pi$
$167$	−75064.0	−0.208277	−0.104138	+	0.994563i	$0.533208\pi$
$168$	0	0
$169$	−271437.	−0.731059
$170$	0	0
$171$	−85212.0	−0.222849
$172$	0	0
$173$	−608572.	−1.54595	−0.772977	−	0.634434i	$-0.781233\pi$
$173$	−608572.	−1.54595	−0.772977	+	0.634434i	$0.781233\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	227196.	0.545089
$178$	0	0
$179$	5676.00	0.0132407	0.00662033	−	0.999978i	$-0.497893\pi$
$179$	5676.00	0.0132407	0.00662033	+	0.999978i	$0.497893\pi$
$180$	0	0
$181$	111980.	0.254065	0.127032	−	0.991899i	$-0.459455\pi$
$181$	111980.	0.254065	0.127032	+	0.991899i	$0.459455\pi$
$182$	0	0
$183$	186012.	0.410595
$184$	0	0
$185$	−844968.	−1.81514
$186$	0	0
$187$	−409728.	−0.856824
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−871824.	−1.72920	−0.864600	−	0.502460i	$-0.832428\pi$
$191$	−871824.	−1.72920	−0.864600	+	0.502460i	$0.832428\pi$
$192$	0	0
$193$	384770.	0.743546	0.371773	−	0.928324i	$-0.378750\pi$
$193$	384770.	0.743546	0.371773	+	0.928324i	$0.378750\pi$
$194$	0	0
$195$	193392.	0.364210
$196$	0	0
$197$	−365226.	−0.670496	−0.335248	−	0.942130i	$-0.608820\pi$
$197$	−365226.	−0.670496	−0.335248	+	0.942130i	$0.608820\pi$
$198$	0	0
$199$	−819928.	−1.46772	−0.733860	−	0.679301i	$-0.762283\pi$
$199$	−819928.	−1.46772	−0.733860	+	0.679301i	$0.762283\pi$
$200$	0	0
$201$	−441108.	−0.770114
$202$	0	0
$203$	0	0
$204$	0	0
$205$	365568.	0.607552
$206$	0	0
$207$	50544.0	0.0819868
$208$	0	0
$209$	408176.	0.646371
$210$	0	0
$211$	348596.	0.539034	0.269517	−	0.962996i	$-0.413136\pi$
$211$	348596.	0.539034	0.269517	+	0.962996i	$0.413136\pi$
$212$	0	0
$213$	−42840.0	−0.0646994
$214$	0	0
$215$	−963152.	−1.42102
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−587376.	−0.827572
$220$	0	0
$221$	333696.	0.459590
$222$	0	0
$223$	−421168.	−0.567144	−0.283572	−	0.958951i	$-0.591519\pi$
$223$	−421168.	−0.567144	−0.283572	+	0.958951i	$0.591519\pi$
$224$	0	0
$225$	121419.	0.159893
$226$	0	0
$227$	133364.	0.171781	0.0858903	−	0.996305i	$-0.472627\pi$
$227$	133364.	0.171781	0.0858903	+	0.996305i	$0.472627\pi$
$228$	0	0
$229$	442300.	0.557350	0.278675	−	0.960385i	$-0.410105\pi$
$229$	442300.	0.557350	0.278675	+	0.960385i	$0.410105\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−798826.	−0.963967	−0.481984	−	0.876180i	$-0.660084\pi$
$233$	−798826.	−0.963967	−0.481984	+	0.876180i	$0.660084\pi$
$234$	0	0
$235$	320416.	0.378481
$236$	0	0
$237$	447624.	0.517657
$238$	0	0
$239$	−1.22695e6	−1.38942	−0.694709	−	0.719291i	$-0.744467\pi$
$239$	−1.22695e6	−1.38942	−0.694709	+	0.719291i	$0.744467\pi$
$240$	0	0
$241$	−960232.	−1.06496	−0.532480	−	0.846442i	$-0.678740\pi$
$241$	−960232.	−1.06496	−0.532480	+	0.846442i	$0.678740\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−332432.	−0.346705
$248$	0	0
$249$	70092.0	0.0716424
$250$	0	0
$251$	1.46177e6	1.46452	0.732260	−	0.681025i	$-0.238466\pi$
$251$	1.46177e6	1.46452	0.732260	+	0.681025i	$0.238466\pi$
$252$	0	0
$253$	−242112.	−0.237802
$254$	0	0
$255$	646272.	0.622393
$256$	0	0
$257$	−124360.	−0.117449	−0.0587243	−	0.998274i	$-0.518703\pi$
$257$	−124360.	−0.117449	−0.0587243	+	0.998274i	$0.518703\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	587250.	0.533607
$262$	0	0
$263$	1.19718e6	1.06726	0.533628	−	0.845719i	$-0.320828\pi$
$263$	1.19718e6	1.06726	0.533628	+	0.845719i	$0.320828\pi$
$264$	0	0
$265$	−257176.	−0.224965
$266$	0	0
$267$	332136.	0.285127
$268$	0	0
$269$	797092.	0.671626	0.335813	−	0.941929i	$-0.390989\pi$
$269$	797092.	0.671626	0.335813	+	0.941929i	$0.390989\pi$
$270$	0	0
$271$	−1.96102e6	−1.62203	−0.811016	−	0.585023i	$-0.801085\pi$
$271$	−1.96102e6	−1.62203	−0.811016	+	0.585023i	$0.801085\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−581612.	−0.463769
$276$	0	0
$277$	421510.	0.330072	0.165036	−	0.986288i	$-0.447226\pi$
$277$	421510.	0.330072	0.165036	+	0.986288i	$0.447226\pi$
$278$	0	0
$279$	−185976.	−0.143036
$280$	0	0
$281$	223206.	0.168632	0.0843160	−	0.996439i	$-0.473129\pi$
$281$	223206.	0.168632	0.0843160	+	0.996439i	$0.473129\pi$
$282$	0	0
$283$	−2.13804e6	−1.58690	−0.793452	−	0.608633i	$-0.791718\pi$
$283$	−2.13804e6	−1.58690	−0.793452	+	0.608633i	$0.791718\pi$
$284$	0	0
$285$	−643824.	−0.469521
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−304721.	−0.214614
$290$	0	0
$291$	−884376.	−0.612216
$292$	0	0
$293$	418572.	0.284840	0.142420	−	0.989806i	$-0.454512\pi$
$293$	418572.	0.284840	0.142420	+	0.989806i	$0.454512\pi$
$294$	0	0
$295$	1.71659e6	1.14845
$296$	0	0
$297$	282852.	0.186066
$298$	0	0
$299$	197184.	0.127554
$300$	0	0
$301$	0	0
$302$	0	0
$303$	1.77354e6	1.10977
$304$	0	0
$305$	1.40542e6	0.865083
$306$	0	0
$307$	−1.65972e6	−1.00506	−0.502528	−	0.864561i	$-0.667596\pi$
$307$	−1.65972e6	−1.00506	−0.502528	+	0.864561i	$0.667596\pi$
$308$	0	0
$309$	1.65118e6	0.983778
$310$	0	0
$311$	95936.0	0.0562446	0.0281223	−	0.999604i	$-0.491047\pi$
$311$	95936.0	0.0562446	0.0281223	+	0.999604i	$0.491047\pi$
$312$	0	0
$313$	3.03434e6	1.75067	0.875334	−	0.483518i	$-0.160641\pi$
$313$	3.03434e6	1.75067	0.875334	+	0.483518i	$0.160641\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	27918.0	0.0156040	0.00780200	−	0.999970i	$-0.497517\pi$
$317$	27918.0	0.0156040	0.00780200	+	0.999970i	$0.497517\pi$
$318$	0	0
$319$	−2.81300e6	−1.54772
$320$	0	0
$321$	495036.	0.268148
$322$	0	0
$323$	−1.11091e6	−0.592480
$324$	0	0
$325$	473684.	0.248760
$326$	0	0
$327$	1.06587e6	0.551233
$328$	0	0
$329$	0	0
$330$	0	0
$331$	1.39236e6	0.698522	0.349261	−	0.937025i	$-0.386433\pi$
$331$	1.39236e6	0.698522	0.349261	+	0.937025i	$0.386433\pi$
$332$	0	0
$333$	1.00651e6	0.497400
$334$	0	0
$335$	−3.33282e6	−1.62255
$336$	0	0
$337$	3.41473e6	1.63788	0.818940	−	0.573879i	$-0.194562\pi$
$337$	3.41473e6	1.63788	0.818940	+	0.573879i	$0.194562\pi$
$338$	0	0
$339$	1.36525e6	0.645226
$340$	0	0
$341$	890848.	0.414875
$342$	0	0
$343$	0	0
$344$	0	0
$345$	381888.	0.172738
$346$	0	0
$347$	−3.43055e6	−1.52947	−0.764733	−	0.644347i	$-0.777129\pi$
$347$	−3.43055e6	−1.52947	−0.764733	+	0.644347i	$0.777129\pi$
$348$	0	0
$349$	388620.	0.170790	0.0853948	−	0.996347i	$-0.472785\pi$
$349$	388620.	0.170790	0.0853948	+	0.996347i	$0.472785\pi$
$350$	0	0
$351$	−230364.	−0.0998037
$352$	0	0
$353$	293016.	0.125157	0.0625784	−	0.998040i	$-0.480068\pi$
$353$	293016.	0.125157	0.0625784	+	0.998040i	$0.480068\pi$
$354$	0	0
$355$	−323680.	−0.136315
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−976928.	−0.400061	−0.200031	−	0.979790i	$-0.564104\pi$
$359$	−976928.	−0.400061	−0.200031	+	0.979790i	$0.564104\pi$
$360$	0	0
$361$	−1.36940e6	−0.553045
$362$	0	0
$363$	94563.0	0.0376664
$364$	0	0
$365$	−4.43795e6	−1.74361
$366$	0	0
$367$	4.16514e6	1.61422	0.807112	−	0.590398i	$-0.201029\pi$
$367$	4.16514e6	1.61422	0.807112	+	0.590398i	$0.201029\pi$
$368$	0	0
$369$	−435456.	−0.166486
$370$	0	0
$371$	0	0
$372$	0	0
$373$	3.10989e6	1.15737	0.578687	−	0.815550i	$-0.303565\pi$
$373$	3.10989e6	1.15737	0.578687	+	0.815550i	$0.303565\pi$
$374$	0	0
$375$	−995112.	−0.365421
$376$	0	0
$377$	2.29100e6	0.830179
$378$	0	0
$379$	−1.23592e6	−0.441968	−0.220984	−	0.975277i	$-0.570927\pi$
$379$	−1.23592e6	−0.441968	−0.220984	+	0.975277i	$0.570927\pi$
$380$	0	0
$381$	−2.15294e6	−0.759837
$382$	0	0
$383$	2.71116e6	0.944405	0.472202	−	0.881490i	$-0.343459\pi$
$383$	2.71116e6	0.944405	0.472202	+	0.881490i	$0.343459\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1.14728e6	0.389398
$388$	0	0
$389$	5.14276e6	1.72315	0.861574	−	0.507633i	$-0.169479\pi$
$389$	5.14276e6	1.72315	0.861574	+	0.507633i	$0.169479\pi$
$390$	0	0
$391$	658944.	0.217975
$392$	0	0
$393$	1.48187e6	0.483981
$394$	0	0
$395$	3.38205e6	1.09065
$396$	0	0
$397$	5.72825e6	1.82409	0.912044	−	0.410092i	$-0.134503\pi$
$397$	5.72825e6	1.82409	0.912044	+	0.410092i	$0.134503\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−5.06229e6	−1.57212	−0.786061	−	0.618149i	$-0.787883\pi$
$401$	−5.06229e6	−1.57212	−0.786061	+	0.618149i	$0.787883\pi$
$402$	0	0
$403$	−725536.	−0.222534
$404$	0	0
$405$	−446148.	−0.135158
$406$	0	0
$407$	−4.82129e6	−1.44270
$408$	0	0
$409$	5.60335e6	1.65630	0.828151	−	0.560505i	$-0.189393\pi$
$409$	5.60335e6	1.65630	0.828151	+	0.560505i	$0.189393\pi$
$410$	0	0
$411$	1.61145e6	0.470557
$412$	0	0
$413$	0	0
$414$	0	0
$415$	529584.	0.150944
$416$	0	0
$417$	−3.52955e6	−0.993983
$418$	0	0
$419$	−5.55808e6	−1.54664	−0.773321	−	0.634014i	$-0.781406\pi$
$419$	−5.55808e6	−1.54664	−0.773321	+	0.634014i	$0.781406\pi$
$420$	0	0
$421$	−689226.	−0.189521	−0.0947603	−	0.995500i	$-0.530208\pi$
$421$	−689226.	−0.189521	−0.0947603	+	0.995500i	$0.530208\pi$
$422$	0	0
$423$	−381672.	−0.103714
$424$	0	0
$425$	1.58294e6	0.425102
$426$	0	0
$427$	0	0
$428$	0	0
$429$	1.10347e6	0.289480
$430$	0	0
$431$	2.37897e6	0.616873	0.308436	−	0.951245i	$-0.400194\pi$
$431$	2.37897e6	0.616873	0.308436	+	0.951245i	$0.400194\pi$
$432$	0	0
$433$	790312.	0.202572	0.101286	−	0.994857i	$-0.467704\pi$
$433$	790312.	0.202572	0.101286	+	0.994857i	$0.467704\pi$
$434$	0	0
$435$	4.43700e6	1.12426
$436$	0	0
$437$	−656448.	−0.164436
$438$	0	0
$439$	−899904.	−0.222861	−0.111431	−	0.993772i	$-0.535543\pi$
$439$	−899904.	−0.222861	−0.111431	+	0.993772i	$0.535543\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−5.17691e6	−1.25332	−0.626659	−	0.779294i	$-0.715578\pi$
$443$	−5.17691e6	−1.25332	−0.626659	+	0.779294i	$0.715578\pi$
$444$	0	0
$445$	2.50947e6	0.600734
$446$	0	0
$447$	−3.86156e6	−0.914100
$448$	0	0
$449$	−6.34717e6	−1.48581	−0.742906	−	0.669395i	$-0.766553\pi$
$449$	−6.34717e6	−1.48581	−0.742906	+	0.669395i	$0.766553\pi$
$450$	0	0
$451$	2.08589e6	0.482892
$452$	0	0
$453$	2.36743e6	0.542041
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−219382.	−0.0491372	−0.0245686	−	0.999698i	$-0.507821\pi$
$457$	−219382.	−0.0491372	−0.0245686	+	0.999698i	$0.507821\pi$
$458$	0	0
$459$	−769824.	−0.170553
$460$	0	0
$461$	−1.60859e6	−0.352527	−0.176264	−	0.984343i	$-0.556401\pi$
$461$	−1.60859e6	−0.352527	−0.176264	+	0.984343i	$0.556401\pi$
$462$	0	0
$463$	−3.95250e6	−0.856880	−0.428440	−	0.903570i	$-0.640937\pi$
$463$	−3.95250e6	−0.856880	−0.428440	+	0.903570i	$0.640937\pi$
$464$	0	0
$465$	−1.40515e6	−0.301364
$466$	0	0
$467$	8.13170e6	1.72540	0.862699	−	0.505718i	$-0.168772\pi$
$467$	8.13170e6	1.72540	0.862699	+	0.505718i	$0.168772\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	1.31216e6	0.272544
$472$	0	0
$473$	−5.49563e6	−1.12944
$474$	0	0
$475$	−1.57695e6	−0.320688
$476$	0	0
$477$	306342.	0.0616468
$478$	0	0
$479$	5.43060e6	1.08146	0.540728	−	0.841197i	$-0.318149\pi$
$479$	5.43060e6	1.08146	0.540728	+	0.841197i	$0.318149\pi$
$480$	0	0
$481$	3.92662e6	0.773848
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−6.68195e6	−1.28988
$486$	0	0
$487$	2.26982e6	0.433679	0.216839	−	0.976207i	$-0.430425\pi$
$487$	2.26982e6	0.433679	0.216839	+	0.976207i	$0.430425\pi$
$488$	0	0
$489$	−2.23744e6	−0.423135
$490$	0	0
$491$	−6.00020e6	−1.12321	−0.561607	−	0.827404i	$-0.689817\pi$
$491$	−6.00020e6	−1.12321	−0.561607	+	0.827404i	$0.689817\pi$
$492$	0	0
$493$	7.65600e6	1.41868
$494$	0	0
$495$	2.13710e6	0.392024
$496$	0	0
$497$	0	0
$498$	0	0
$499$	4.90784e6	0.882347	0.441173	−	0.897422i	$-0.354562\pi$
$499$	4.90784e6	0.882347	0.441173	+	0.897422i	$0.354562\pi$
$500$	0	0
$501$	675576.	0.120249
$502$	0	0
$503$	−3.70974e6	−0.653768	−0.326884	−	0.945064i	$-0.605999\pi$
$503$	−3.70974e6	−0.653768	−0.326884	+	0.945064i	$0.605999\pi$
$504$	0	0
$505$	1.34001e7	2.33819
$506$	0	0
$507$	2.44293e6	0.422077
$508$	0	0
$509$	6.77594e6	1.15924	0.579622	−	0.814885i	$-0.303200\pi$
$509$	6.77594e6	1.15924	0.579622	+	0.814885i	$0.303200\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	766908.	0.128662
$514$	0	0
$515$	1.24756e7	2.07273
$516$	0	0
$517$	1.82826e6	0.300823
$518$	0	0
$519$	5.47715e6	0.892557
$520$	0	0
$521$	−6.92925e6	−1.11839	−0.559193	−	0.829037i	$-0.688889\pi$
$521$	−6.92925e6	−1.11839	−0.559193	+	0.829037i	$0.688889\pi$
$522$	0	0
$523$	−8.08732e6	−1.29286	−0.646429	−	0.762974i	$-0.723738\pi$
$523$	−8.08732e6	−1.29286	−0.646429	+	0.762974i	$0.723738\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−2.42458e6	−0.380285
$528$	0	0
$529$	−6.04697e6	−0.939504
$530$	0	0
$531$	−2.04476e6	−0.314707
$532$	0	0
$533$	−1.69882e6	−0.259017
$534$	0	0
$535$	3.74027e6	0.564961
$536$	0	0
$537$	−51084.0	−0.00764450
$538$	0	0
$539$	0	0
$540$	0	0
$541$	9.11361e6	1.33874	0.669372	−	0.742927i	$-0.266563\pi$
$541$	9.11361e6	1.33874	0.669372	+	0.742927i	$0.266563\pi$
$542$	0	0
$543$	−1.00782e6	−0.146684
$544$	0	0
$545$	8.05324e6	1.16139
$546$	0	0
$547$	1.27702e7	1.82486	0.912432	−	0.409228i	$-0.134202\pi$
$547$	1.27702e7	1.82486	0.912432	+	0.409228i	$0.134202\pi$
$548$	0	0
$549$	−1.67411e6	−0.237057
$550$	0	0
$551$	−7.62700e6	−1.07022
$552$	0	0
$553$	0	0
$554$	0	0
$555$	7.60471e6	1.04797
$556$	0	0
$557$	4.10633e6	0.560811	0.280405	−	0.959882i	$-0.409531\pi$
$557$	4.10633e6	0.560811	0.280405	+	0.959882i	$0.409531\pi$
$558$	0	0
$559$	4.47582e6	0.605820
$560$	0	0
$561$	3.68755e6	0.494688
$562$	0	0
$563$	5.71036e6	0.759264	0.379632	−	0.925138i	$-0.376051\pi$
$563$	5.71036e6	0.759264	0.379632	+	0.925138i	$0.376051\pi$
$564$	0	0
$565$	1.03152e7	1.35943
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−6.47279e6	−0.838129	−0.419065	−	0.907956i	$-0.637642\pi$
$569$	−6.47279e6	−0.838129	−0.419065	+	0.907956i	$0.637642\pi$
$570$	0	0
$571$	−2.82942e6	−0.363168	−0.181584	−	0.983375i	$-0.558122\pi$
$571$	−2.82942e6	−0.363168	−0.181584	+	0.983375i	$0.558122\pi$
$572$	0	0
$573$	7.84642e6	0.998354
$574$	0	0
$575$	935376.	0.117982
$576$	0	0
$577$	−1.01253e6	−0.126610	−0.0633049	−	0.997994i	$-0.520164\pi$
$577$	−1.01253e6	−0.126610	−0.0633049	+	0.997994i	$0.520164\pi$
$578$	0	0
$579$	−3.46293e6	−0.429287
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−1.46742e6	−0.178806
$584$	0	0
$585$	−1.74053e6	−0.210277
$586$	0	0
$587$	−1.36384e7	−1.63368	−0.816842	−	0.576861i	$-0.804277\pi$
$587$	−1.36384e7	−1.63368	−0.816842	+	0.576861i	$0.804277\pi$
$588$	0	0
$589$	2.41539e6	0.286879
$590$	0	0
$591$	3.28703e6	0.387111
$592$	0	0
$593$	9.26710e6	1.08220	0.541099	−	0.840959i	$-0.318008\pi$
$593$	9.26710e6	1.08220	0.541099	+	0.840959i	$0.318008\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	7.37935e6	0.847388
$598$	0	0
$599$	8.55012e6	0.973655	0.486828	−	0.873498i	$-0.338154\pi$
$599$	8.55012e6	0.973655	0.486828	+	0.873498i	$0.338154\pi$
$600$	0	0
$601$	−2.10675e6	−0.237918	−0.118959	−	0.992899i	$-0.537956\pi$
$601$	−2.10675e6	−0.237918	−0.118959	+	0.992899i	$0.537956\pi$
$602$	0	0
$603$	3.96997e6	0.444625
$604$	0	0
$605$	714476.	0.0793596
$606$	0	0
$607$	−2.71018e6	−0.298556	−0.149278	−	0.988795i	$-0.547695\pi$
$607$	−2.71018e6	−0.298556	−0.149278	+	0.988795i	$0.547695\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−1.48899e6	−0.161358
$612$	0	0
$613$	−1.00044e7	−1.07532	−0.537661	−	0.843161i	$-0.680692\pi$
$613$	−1.00044e7	−1.07532	−0.537661	+	0.843161i	$0.680692\pi$
$614$	0	0
$615$	−3.29011e6	−0.350770
$616$	0	0
$617$	−1.67826e7	−1.77479	−0.887394	−	0.461012i	$-0.847486\pi$
$617$	−1.67826e7	−1.77479	−0.887394	+	0.461012i	$0.847486\pi$
$618$	0	0
$619$	−9.93800e6	−1.04249	−0.521245	−	0.853407i	$-0.674532\pi$
$619$	−9.93800e6	−1.04249	−0.521245	+	0.853407i	$0.674532\pi$
$620$	0	0
$621$	−454896.	−0.0473351
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.22030e7	−1.24959
$626$	0	0
$627$	−3.67358e6	−0.373182
$628$	0	0
$629$	1.31219e7	1.32242
$630$	0	0
$631$	1.58563e6	0.158536	0.0792682	−	0.996853i	$-0.474742\pi$
$631$	1.58563e6	0.158536	0.0792682	+	0.996853i	$0.474742\pi$
$632$	0	0
$633$	−3.13736e6	−0.311211
$634$	0	0
$635$	−1.62667e7	−1.60090
$636$	0	0
$637$	0	0
$638$	0	0
$639$	385560.	0.0373542
$640$	0	0
$641$	−7.27623e6	−0.699457	−0.349729	−	0.936851i	$-0.613726\pi$
$641$	−7.27623e6	−0.699457	−0.349729	+	0.936851i	$0.613726\pi$
$642$	0	0
$643$	−1.98124e7	−1.88977	−0.944887	−	0.327395i	$-0.893829\pi$
$643$	−1.98124e7	−1.88977	−0.944887	+	0.327395i	$0.893829\pi$
$644$	0	0
$645$	8.66837e6	0.820423
$646$	0	0
$647$	−7.96553e6	−0.748090	−0.374045	−	0.927411i	$-0.622029\pi$
$647$	−7.96553e6	−0.748090	−0.374045	+	0.927411i	$0.622029\pi$
$648$	0	0
$649$	9.79467e6	0.912805
$650$	0	0
$651$	0	0
$652$	0	0
$653$	1.51767e6	0.139281	0.0696407	−	0.997572i	$-0.477815\pi$
$653$	1.51767e6	0.139281	0.0696407	+	0.997572i	$0.477815\pi$
$654$	0	0
$655$	1.11963e7	1.01970
$656$	0	0
$657$	5.28638e6	0.477799
$658$	0	0
$659$	−1.00208e7	−0.898850	−0.449425	−	0.893318i	$-0.648371\pi$
$659$	−1.00208e7	−0.898850	−0.449425	+	0.893318i	$0.648371\pi$
$660$	0	0
$661$	−1.52180e7	−1.35473	−0.677367	−	0.735645i	$-0.736879\pi$
$661$	−1.52180e7	−1.35473	−0.677367	+	0.735645i	$0.736879\pi$
$662$	0	0
$663$	−3.00326e6	−0.265344
$664$	0	0
$665$	0	0
$666$	0	0
$667$	4.52400e6	0.393739
$668$	0	0
$669$	3.79051e6	0.327441
$670$	0	0
$671$	8.01918e6	0.687581
$672$	0	0
$673$	−6.83024e6	−0.581297	−0.290649	−	0.956830i	$-0.593871\pi$
$673$	−6.83024e6	−0.581297	−0.290649	+	0.956830i	$0.593871\pi$
$674$	0	0
$675$	−1.09277e6	−0.0923145
$676$	0	0
$677$	−2.03576e7	−1.70708	−0.853541	−	0.521025i	$-0.825550\pi$
$677$	−2.03576e7	−1.70708	−0.853541	+	0.521025i	$0.825550\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−1.20028e6	−0.0991775
$682$	0	0
$683$	5.71637e6	0.468888	0.234444	−	0.972130i	$-0.424673\pi$
$683$	5.71637e6	0.468888	0.234444	+	0.972130i	$0.424673\pi$
$684$	0	0
$685$	1.21754e7	0.991418
$686$	0	0
$687$	−3.98070e6	−0.321786
$688$	0	0
$689$	1.19511e6	0.0959093
$690$	0	0
$691$	−1.83950e7	−1.46557	−0.732783	−	0.680463i	$-0.761779\pi$
$691$	−1.83950e7	−1.46557	−0.732783	+	0.680463i	$0.761779\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−2.66677e7	−2.09423
$696$	0	0
$697$	−5.67706e6	−0.442630
$698$	0	0
$699$	7.18943e6	0.556547
$700$	0	0
$701$	−2.34726e7	−1.80412	−0.902061	−	0.431608i	$-0.857946\pi$
$701$	−2.34726e7	−1.80412	−0.902061	+	0.431608i	$0.857946\pi$
$702$	0	0
$703$	−1.30722e7	−0.997605
$704$	0	0
$705$	−2.88374e6	−0.218516
$706$	0	0
$707$	0	0
$708$	0	0
$709$	1.69921e7	1.26950	0.634748	−	0.772719i	$-0.281104\pi$
$709$	1.69921e7	1.26950	0.634748	+	0.772719i	$0.281104\pi$
$710$	0	0
$711$	−4.02862e6	−0.298870
$712$	0	0
$713$	−1.43270e6	−0.105544
$714$	0	0
$715$	8.33734e6	0.609906
$716$	0	0
$717$	1.10426e7	0.802181
$718$	0	0
$719$	−8.41663e6	−0.607178	−0.303589	−	0.952803i	$-0.598185\pi$
$719$	−8.41663e6	−0.607178	−0.303589	+	0.952803i	$0.598185\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	8.64209e6	0.614855
$724$	0	0
$725$	1.08677e7	0.767882
$726$	0	0
$727$	−5.81598e6	−0.408119	−0.204059	−	0.978959i	$-0.565414\pi$
$727$	−5.81598e6	−0.408119	−0.204059	+	0.978959i	$0.565414\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	1.49572e7	1.03528
$732$	0	0
$733$	−1.56330e7	−1.07468	−0.537342	−	0.843364i	$-0.680572\pi$
$733$	−1.56330e7	−1.07468	−0.537342	+	0.843364i	$0.680572\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−1.90167e7	−1.28963
$738$	0	0
$739$	−4.66970e6	−0.314541	−0.157271	−	0.987556i	$-0.550270\pi$
$739$	−4.66970e6	−0.314541	−0.157271	+	0.987556i	$0.550270\pi$
$740$	0	0
$741$	2.99189e6	0.200170
$742$	0	0
$743$	−1.57172e7	−1.04449	−0.522243	−	0.852797i	$-0.674904\pi$
$743$	−1.57172e7	−1.04449	−0.522243	+	0.852797i	$0.674904\pi$
$744$	0	0
$745$	−2.91762e7	−1.92592
$746$	0	0
$747$	−630828.	−0.0413628
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.70359e7	1.10221	0.551105	−	0.834436i	$-0.314206\pi$
$751$	1.70359e7	1.10221	0.551105	+	0.834436i	$0.314206\pi$
$752$	0	0
$753$	−1.31559e7	−0.845541
$754$	0	0
$755$	1.78873e7	1.14203
$756$	0	0
$757$	−1.41750e7	−0.899050	−0.449525	−	0.893268i	$-0.648407\pi$
$757$	−1.41750e7	−0.899050	−0.449525	+	0.893268i	$0.648407\pi$
$758$	0	0
$759$	2.17901e6	0.137295
$760$	0	0
$761$	8.51493e6	0.532990	0.266495	−	0.963836i	$-0.414134\pi$
$761$	8.51493e6	0.532990	0.266495	+	0.963836i	$0.414134\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−5.81645e6	−0.359339
$766$	0	0
$767$	−7.97710e6	−0.489617
$768$	0	0
$769$	2.11392e7	1.28906	0.644529	−	0.764580i	$-0.277053\pi$
$769$	2.11392e7	1.28906	0.644529	+	0.764580i	$0.277053\pi$
$770$	0	0
$771$	1.11924e6	0.0678090
$772$	0	0
$773$	−2.75355e7	−1.65747	−0.828733	−	0.559644i	$-0.810938\pi$
$773$	−2.75355e7	−1.65747	−0.828733	+	0.559644i	$0.810938\pi$
$774$	0	0
$775$	−3.44170e6	−0.205835
$776$	0	0
$777$	0	0
$778$	0	0
$779$	5.65555e6	0.333911
$780$	0	0
$781$	−1.84688e6	−0.108346
$782$	0	0
$783$	−5.28525e6	−0.308078
$784$	0	0
$785$	9.91413e6	0.574223
$786$	0	0
$787$	−165196.	−0.00950742	−0.00475371	−	0.999989i	$-0.501513\pi$
$787$	−165196.	−0.00950742	−0.00475371	+	0.999989i	$0.501513\pi$
$788$	0	0
$789$	−1.07746e7	−0.616181
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−6.53109e6	−0.368810
$794$	0	0
$795$	2.31458e6	0.129884
$796$	0	0
$797$	2.05169e7	1.14411	0.572053	−	0.820217i	$-0.306147\pi$
$797$	2.05169e7	1.14411	0.572053	+	0.820217i	$0.306147\pi$
$798$	0	0
$799$	−4.97587e6	−0.275742
$800$	0	0
$801$	−2.98922e6	−0.164618
$802$	0	0
$803$	−2.53224e7	−1.38585
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−7.17383e6	−0.387764
$808$	0	0
$809$	−1.67666e7	−0.900689	−0.450345	−	0.892855i	$-0.648699\pi$
$809$	−1.67666e7	−0.900689	−0.450345	+	0.892855i	$0.648699\pi$
$810$	0	0
$811$	−2.49085e7	−1.32983	−0.664914	−	0.746920i	$-0.731532\pi$
$811$	−2.49085e7	−1.32983	−0.664914	+	0.746920i	$0.731532\pi$
$812$	0	0
$813$	1.76492e7	0.936481
$814$	0	0
$815$	−1.69051e7	−0.891503
$816$	0	0
$817$	−1.49005e7	−0.780992
$818$	0	0
$819$	0	0
$820$	0	0
$821$	1.90271e7	0.985180	0.492590	−	0.870261i	$-0.336050\pi$
$821$	1.90271e7	0.985180	0.492590	+	0.870261i	$0.336050\pi$
$822$	0	0
$823$	−8.67886e6	−0.446646	−0.223323	−	0.974745i	$-0.571690\pi$
$823$	−8.67886e6	−0.446646	−0.223323	+	0.974745i	$0.571690\pi$
$824$	0	0
$825$	5.23451e6	0.267757
$826$	0	0
$827$	1.49462e7	0.759917	0.379959	−	0.925003i	$-0.375938\pi$
$827$	1.49462e7	0.759917	0.379959	+	0.925003i	$0.375938\pi$
$828$	0	0
$829$	−1.09614e7	−0.553959	−0.276980	−	0.960876i	$-0.589333\pi$
$829$	−1.09614e7	−0.553959	−0.276980	+	0.960876i	$0.589333\pi$
$830$	0	0
$831$	−3.79359e6	−0.190567
$832$	0	0
$833$	0	0
$834$	0	0
$835$	5.10435e6	0.253352
$836$	0	0
$837$	1.67378e6	0.0825821
$838$	0	0
$839$	−3.94433e7	−1.93450	−0.967249	−	0.253829i	$-0.918310\pi$
$839$	−3.94433e7	−1.93450	−0.967249	+	0.253829i	$0.918310\pi$
$840$	0	0
$841$	3.20514e7	1.56263
$842$	0	0
$843$	−2.00885e6	−0.0973597
$844$	0	0
$845$	1.84577e7	0.889275
$846$	0	0
$847$	0	0
$848$	0	0
$849$	1.92424e7	0.916199
$850$	0	0
$851$	7.75382e6	0.367022
$852$	0	0
$853$	2.50962e7	1.18096	0.590480	−	0.807052i	$-0.298938\pi$
$853$	2.50962e7	1.18096	0.590480	+	0.807052i	$0.298938\pi$
$854$	0	0
$855$	5.79442e6	0.271078
$856$	0	0
$857$	−1.18078e7	−0.549183	−0.274592	−	0.961561i	$-0.588543\pi$
$857$	−1.18078e7	−0.549183	−0.274592	+	0.961561i	$0.588543\pi$
$858$	0	0
$859$	−1.36552e7	−0.631414	−0.315707	−	0.948857i	$-0.602242\pi$
$859$	−1.36552e7	−0.631414	−0.315707	+	0.948857i	$0.602242\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	9.55181e6	0.436575	0.218287	−	0.975885i	$-0.429953\pi$
$863$	9.55181e6	0.436575	0.218287	+	0.975885i	$0.429953\pi$
$864$	0	0
$865$	4.13829e7	1.88053
$866$	0	0
$867$	2.74249e6	0.123907
$868$	0	0
$869$	1.92976e7	0.866868
$870$	0	0
$871$	1.54878e7	0.691742
$872$	0	0
$873$	7.95938e6	0.353463
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−3.04774e6	−0.133807	−0.0669036	−	0.997759i	$-0.521312\pi$
$877$	−3.04774e6	−0.133807	−0.0669036	+	0.997759i	$0.521312\pi$
$878$	0	0
$879$	−3.76715e6	−0.164453
$880$	0	0
$881$	2.83230e7	1.22942	0.614709	−	0.788754i	$-0.289273\pi$
$881$	2.83230e7	1.22942	0.614709	+	0.788754i	$0.289273\pi$
$882$	0	0
$883$	5.31394e6	0.229359	0.114679	−	0.993403i	$-0.463416\pi$
$883$	5.31394e6	0.229359	0.114679	+	0.993403i	$0.463416\pi$
$884$	0	0
$885$	−1.54493e7	−0.663058
$886$	0	0
$887$	−3.17727e7	−1.35595	−0.677977	−	0.735083i	$-0.737143\pi$
$887$	−3.17727e7	−1.35595	−0.677977	+	0.735083i	$0.737143\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−2.54567e6	−0.107426
$892$	0	0
$893$	4.95702e6	0.208014
$894$	0	0
$895$	−385968.	−0.0161062
$896$	0	0
$897$	−1.77466e6	−0.0736433
$898$	0	0
$899$	−1.66460e7	−0.686927
$900$	0	0
$901$	3.99379e6	0.163898
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−7.61464e6	−0.309049
$906$	0	0
$907$	−4.84483e7	−1.95551	−0.977755	−	0.209748i	$-0.932736\pi$
$907$	−4.84483e7	−1.95551	−0.977755	+	0.209748i	$0.932736\pi$
$908$	0	0
$909$	−1.59619e7	−0.640728
$910$	0	0
$911$	−1.96512e7	−0.784499	−0.392249	−	0.919859i	$-0.628303\pi$
$911$	−1.96512e7	−0.784499	−0.392249	+	0.919859i	$0.628303\pi$
$912$	0	0
$913$	3.02174e6	0.119972
$914$	0	0
$915$	−1.26488e7	−0.499456
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−1.08466e6	−0.0423646	−0.0211823	−	0.999776i	$-0.506743\pi$
$919$	−1.08466e6	−0.0423646	−0.0211823	+	0.999776i	$0.506743\pi$
$920$	0	0
$921$	1.49375e7	0.580269
$922$	0	0
$923$	1.50416e6	0.0581152
$924$	0	0
$925$	1.86266e7	0.715779
$926$	0	0
$927$	−1.48606e7	−0.567985
$928$	0	0
$929$	−2.21130e7	−0.840636	−0.420318	−	0.907377i	$-0.638081\pi$
$929$	−2.21130e7	−0.840636	−0.420318	+	0.907377i	$0.638081\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−863424.	−0.0324728
$934$	0	0
$935$	2.78615e7	1.04226
$936$	0	0
$937$	1.55016e7	0.576803	0.288402	−	0.957510i	$-0.406876\pi$
$937$	1.55016e7	0.576803	0.288402	+	0.957510i	$0.406876\pi$
$938$	0	0
$939$	−2.73091e7	−1.01075
$940$	0	0
$941$	1.85343e7	0.682344	0.341172	−	0.940001i	$-0.389176\pi$
$941$	1.85343e7	0.682344	0.341172	+	0.940001i	$0.389176\pi$
$942$	0	0
$943$	−3.35462e6	−0.122847
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−4.06016e6	−0.147119	−0.0735593	−	0.997291i	$-0.523436\pi$
$947$	−4.06016e6	−0.147119	−0.0735593	+	0.997291i	$0.523436\pi$
$948$	0	0
$949$	2.06234e7	0.743353
$950$	0	0
$951$	−251262.	−0.00900898
$952$	0	0
$953$	−4.72676e6	−0.168590	−0.0842949	−	0.996441i	$-0.526864\pi$
$953$	−4.72676e6	−0.168590	−0.0842949	+	0.996441i	$0.526864\pi$
$954$	0	0
$955$	5.92840e7	2.10344
$956$	0	0
$957$	2.53170e7	0.893578
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−2.33575e7	−0.815865
$962$	0	0
$963$	−4.45532e6	−0.154815
$964$	0	0
$965$	−2.61644e7	−0.904465
$966$	0	0
$967$	−1.50253e7	−0.516721	−0.258360	−	0.966049i	$-0.583182\pi$
$967$	−1.50253e7	−0.516721	−0.258360	+	0.966049i	$0.583182\pi$
$968$	0	0
$969$	9.99821e6	0.342068
$970$	0	0
$971$	3.47511e7	1.18283	0.591413	−	0.806369i	$-0.298570\pi$
$971$	3.47511e7	1.18283	0.591413	+	0.806369i	$0.298570\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−4.26316e6	−0.143622
$976$	0	0
$977$	1.15367e7	0.386675	0.193337	−	0.981132i	$-0.438069\pi$
$977$	1.15367e7	0.386675	0.193337	+	0.981132i	$0.438069\pi$
$978$	0	0
$979$	1.43188e7	0.477473
$980$	0	0
$981$	−9.59283e6	−0.318254
$982$	0	0
$983$	2.66786e7	0.880601	0.440300	−	0.897851i	$-0.354872\pi$
$983$	2.66786e7	0.880601	0.440300	+	0.897851i	$0.354872\pi$
$984$	0	0
$985$	2.48354e7	0.815605
$986$	0	0
$987$	0	0
$988$	0	0
$989$	8.83834e6	0.287329
$990$	0	0
$991$	−1.59159e7	−0.514811	−0.257406	−	0.966303i	$-0.582868\pi$
$991$	−1.59159e7	−0.514811	−0.257406	+	0.966303i	$0.582868\pi$
$992$	0	0
$993$	−1.25312e7	−0.403292
$994$	0	0
$995$	5.57551e7	1.78536
$996$	0	0
$997$	5.18775e6	0.165288	0.0826439	−	0.996579i	$-0.473664\pi$
$997$	5.18775e6	0.165288	0.0826439	+	0.996579i	$0.473664\pi$
$998$	0	0
$999$	−9.05855e6	−0.287174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.6.a.a.1.1	✓	1
7.2	even	3		588.6.i.g.361.1		2
7.3	odd	6		588.6.i.a.373.1		2
7.4	even	3		588.6.i.g.373.1		2
7.5	odd	6		588.6.i.a.361.1		2
7.6	odd	2		588.6.a.f.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.6.a.a.1.1	✓	1	1.1	even	1	trivial
588.6.a.f.1.1	yes	1	7.6	odd	2
588.6.i.a.361.1		2	7.5	odd	6
588.6.i.a.373.1		2	7.3	odd	6
588.6.i.g.361.1		2	7.2	even	3
588.6.i.g.373.1		2	7.4	even	3

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	588.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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