LMFDB - Embedded newform 1568.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,4,Mod(1,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1568.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1568.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:	$92.5149948890$
Analytic rank:	$0$
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	$\chi$	$=$	1568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -14.0000 q^{5} -23.0000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} -14.0000 q^{5} -23.0000 q^{9} -20.0000 q^{11} +6.00000 q^{13} +28.0000 q^{15} -20.0000 q^{17} -102.000 q^{19} -124.000 q^{23} +71.0000 q^{25} +100.000 q^{27} -78.0000 q^{29} -236.000 q^{31} +40.0000 q^{33} +66.0000 q^{37} -12.0000 q^{39} -268.000 q^{41} +132.000 q^{43} +322.000 q^{45} -516.000 q^{47} +40.0000 q^{51} -354.000 q^{53} +280.000 q^{55} +204.000 q^{57} -438.000 q^{59} -486.000 q^{61} -84.0000 q^{65} +804.000 q^{67} +248.000 q^{69} +248.000 q^{71} -768.000 q^{73} -142.000 q^{75} +192.000 q^{79} +421.000 q^{81} -294.000 q^{83} +280.000 q^{85} +156.000 q^{87} -80.0000 q^{89} +472.000 q^{93} +1428.00 q^{95} -1404.00 q^{97} +460.000 q^{99} +O(q^{100})$

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
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	0	0
$5$	−14.0000	−1.25220	−0.626099	−	0.779744i	$-0.715349\pi$
$5$	−14.0000	−1.25220	−0.626099	+	0.779744i	$0.715349\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−23.0000	−0.851852
$10$	0	0
$11$	−20.0000	−0.548202	−0.274101	−	0.961701i	$-0.588380\pi$
$11$	−20.0000	−0.548202	−0.274101	+	0.961701i	$0.588380\pi$
$12$	0	0
$13$	6.00000	0.128008	0.0640039	−	0.997950i	$-0.479613\pi$
$13$	6.00000	0.128008	0.0640039	+	0.997950i	$0.479613\pi$
$14$	0	0
$15$	28.0000	0.481971
$16$	0	0
$17$	−20.0000	−0.285336	−0.142668	−	0.989771i	$-0.545568\pi$
$17$	−20.0000	−0.285336	−0.142668	+	0.989771i	$0.545568\pi$
$18$	0	0
$19$	−102.000	−1.23160	−0.615800	−	0.787902i	$-0.711167\pi$
$19$	−102.000	−1.23160	−0.615800	+	0.787902i	$0.711167\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−124.000	−1.12416	−0.562082	−	0.827081i	$-0.690000\pi$
$23$	−124.000	−1.12416	−0.562082	+	0.827081i	$0.690000\pi$
$24$	0	0
$25$	71.0000	0.568000
$26$	0	0
$27$	100.000	0.712778
$28$	0	0
$29$	−78.0000	−0.499456	−0.249728	−	0.968316i	$-0.580341\pi$
$29$	−78.0000	−0.499456	−0.249728	+	0.968316i	$0.580341\pi$
$30$	0	0
$31$	−236.000	−1.36732	−0.683659	−	0.729802i	$-0.739612\pi$
$31$	−236.000	−1.36732	−0.683659	+	0.729802i	$0.739612\pi$
$32$	0	0
$33$	40.0000	0.211003
$34$	0	0
$35$	0	0
$36$	0	0
$37$	66.0000	0.293252	0.146626	−	0.989192i	$-0.453159\pi$
$37$	66.0000	0.293252	0.146626	+	0.989192i	$0.453159\pi$
$38$	0	0
$39$	−12.0000	−0.0492702
$40$	0	0
$41$	−268.000	−1.02084	−0.510422	−	0.859924i	$-0.670511\pi$
$41$	−268.000	−1.02084	−0.510422	+	0.859924i	$0.670511\pi$
$42$	0	0
$43$	132.000	0.468135	0.234068	−	0.972220i	$-0.424796\pi$
$43$	132.000	0.468135	0.234068	+	0.972220i	$0.424796\pi$
$44$	0	0
$45$	322.000	1.06669
$46$	0	0
$47$	−516.000	−1.60141	−0.800706	−	0.599058i	$-0.795542\pi$
$47$	−516.000	−1.60141	−0.800706	+	0.599058i	$0.795542\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	40.0000	0.109826
$52$	0	0
$53$	−354.000	−0.917465	−0.458732	−	0.888574i	$-0.651696\pi$
$53$	−354.000	−0.917465	−0.458732	+	0.888574i	$0.651696\pi$
$54$	0	0
$55$	280.000	0.686458
$56$	0	0
$57$	204.000	0.474043
$58$	0	0
$59$	−438.000	−0.966487	−0.483244	−	0.875486i	$-0.660541\pi$
$59$	−438.000	−0.966487	−0.483244	+	0.875486i	$0.660541\pi$
$60$	0	0
$61$	−486.000	−1.02010	−0.510049	−	0.860146i	$-0.670373\pi$
$61$	−486.000	−1.02010	−0.510049	+	0.860146i	$0.670373\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−84.0000	−0.160291
$66$	0	0
$67$	804.000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	804.000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	0	0
$69$	248.000	0.432691
$70$	0	0
$71$	248.000	0.414538	0.207269	−	0.978284i	$-0.433542\pi$
$71$	248.000	0.414538	0.207269	+	0.978284i	$0.433542\pi$
$72$	0	0
$73$	−768.000	−1.23134	−0.615669	−	0.788005i	$-0.711114\pi$
$73$	−768.000	−1.23134	−0.615669	+	0.788005i	$0.711114\pi$
$74$	0	0
$75$	−142.000	−0.218623
$76$	0	0
$77$	0	0
$78$	0	0
$79$	192.000	0.273439	0.136720	−	0.990610i	$-0.456344\pi$
$79$	192.000	0.273439	0.136720	+	0.990610i	$0.456344\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	0	0
$83$	−294.000	−0.388804	−0.194402	−	0.980922i	$-0.562277\pi$
$83$	−294.000	−0.388804	−0.194402	+	0.980922i	$0.562277\pi$
$84$	0	0
$85$	280.000	0.357297
$86$	0	0
$87$	156.000	0.192241
$88$	0	0
$89$	−80.0000	−0.0952807	−0.0476404	−	0.998865i	$-0.515170\pi$
$89$	−80.0000	−0.0952807	−0.0476404	+	0.998865i	$0.515170\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	472.000	0.526281
$94$	0	0
$95$	1428.00	1.54221
$96$	0	0
$97$	−1404.00	−1.46964	−0.734818	−	0.678265i	$-0.762732\pi$
$97$	−1404.00	−1.46964	−0.734818	+	0.678265i	$0.762732\pi$
$98$	0	0
$99$	460.000	0.466987
$100$	0	0
$101$	1522.00	1.49945	0.749726	−	0.661748i	$-0.230185\pi$
$101$	1522.00	1.49945	0.749726	+	0.661748i	$0.230185\pi$
$102$	0	0
$103$	524.000	0.501274	0.250637	−	0.968081i	$-0.419360\pi$
$103$	524.000	0.501274	0.250637	+	0.968081i	$0.419360\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−748.000	−0.675812	−0.337906	−	0.941180i	$-0.609719\pi$
$107$	−748.000	−0.675812	−0.337906	+	0.941180i	$0.609719\pi$
$108$	0	0
$109$	506.000	0.444642	0.222321	−	0.974973i	$-0.428637\pi$
$109$	506.000	0.444642	0.222321	+	0.974973i	$0.428637\pi$
$110$	0	0
$111$	−132.000	−0.112873
$112$	0	0
$113$	−1146.00	−0.954041	−0.477020	−	0.878892i	$-0.658283\pi$
$113$	−1146.00	−0.954041	−0.477020	+	0.878892i	$0.658283\pi$
$114$	0	0
$115$	1736.00	1.40768
$116$	0	0
$117$	−138.000	−0.109044
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−931.000	−0.699474
$122$	0	0
$123$	536.000	0.392923
$124$	0	0
$125$	756.000	0.540950
$126$	0	0
$127$	2196.00	1.53436	0.767179	−	0.641433i	$-0.221660\pi$
$127$	2196.00	1.53436	0.767179	+	0.641433i	$0.221660\pi$
$128$	0	0
$129$	−264.000	−0.180185
$130$	0	0
$131$	2682.00	1.78876	0.894379	−	0.447309i	$-0.147618\pi$
$131$	2682.00	1.78876	0.894379	+	0.447309i	$0.147618\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1400.00	−0.892539
$136$	0	0
$137$	−1098.00	−0.684733	−0.342367	−	0.939566i	$-0.611229\pi$
$137$	−1098.00	−0.684733	−0.342367	+	0.939566i	$0.611229\pi$
$138$	0	0
$139$	−610.000	−0.372227	−0.186113	−	0.982528i	$-0.559589\pi$
$139$	−610.000	−0.372227	−0.186113	+	0.982528i	$0.559589\pi$
$140$	0	0
$141$	1032.00	0.616384
$142$	0	0
$143$	−120.000	−0.0701742
$144$	0	0
$145$	1092.00	0.625418
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−474.000	−0.260615	−0.130307	−	0.991474i	$-0.541596\pi$
$149$	−474.000	−0.260615	−0.130307	+	0.991474i	$0.541596\pi$
$150$	0	0
$151$	2316.00	1.24817	0.624084	−	0.781357i	$-0.285472\pi$
$151$	2316.00	1.24817	0.624084	+	0.781357i	$0.285472\pi$
$152$	0	0
$153$	460.000	0.243064
$154$	0	0
$155$	3304.00	1.71215
$156$	0	0
$157$	−1074.00	−0.545952	−0.272976	−	0.962021i	$-0.588008\pi$
$157$	−1074.00	−0.545952	−0.272976	+	0.962021i	$0.588008\pi$
$158$	0	0
$159$	708.000	0.353132
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−2844.00	−1.36662	−0.683311	−	0.730128i	$-0.739461\pi$
$163$	−2844.00	−1.36662	−0.683311	+	0.730128i	$0.739461\pi$
$164$	0	0
$165$	−560.000	−0.264218
$166$	0	0
$167$	−1500.00	−0.695051	−0.347525	−	0.937671i	$-0.612978\pi$
$167$	−1500.00	−0.695051	−0.347525	+	0.937671i	$0.612978\pi$
$168$	0	0
$169$	−2161.00	−0.983614
$170$	0	0
$171$	2346.00	1.04914
$172$	0	0
$173$	−1226.00	−0.538792	−0.269396	−	0.963029i	$-0.586824\pi$
$173$	−1226.00	−0.538792	−0.269396	+	0.963029i	$0.586824\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	876.000	0.372001
$178$	0	0
$179$	3764.00	1.57170	0.785851	−	0.618416i	$-0.212225\pi$
$179$	3764.00	1.57170	0.785851	+	0.618416i	$0.212225\pi$
$180$	0	0
$181$	−138.000	−0.0566710	−0.0283355	−	0.999598i	$-0.509021\pi$
$181$	−138.000	−0.0566710	−0.0283355	+	0.999598i	$0.509021\pi$
$182$	0	0
$183$	972.000	0.392636
$184$	0	0
$185$	−924.000	−0.367210
$186$	0	0
$187$	400.000	0.156422
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−2168.00	−0.821314	−0.410657	−	0.911790i	$-0.634701\pi$
$191$	−2168.00	−0.821314	−0.410657	+	0.911790i	$0.634701\pi$
$192$	0	0
$193$	1806.00	0.673569	0.336784	−	0.941582i	$-0.390661\pi$
$193$	1806.00	0.673569	0.336784	+	0.941582i	$0.390661\pi$
$194$	0	0
$195$	168.000	0.0616961
$196$	0	0
$197$	3966.00	1.43434	0.717172	−	0.696896i	$-0.245436\pi$
$197$	3966.00	1.43434	0.717172	+	0.696896i	$0.245436\pi$
$198$	0	0
$199$	36.0000	0.0128240	0.00641199	−	0.999979i	$-0.497959\pi$
$199$	36.0000	0.0128240	0.00641199	+	0.999979i	$0.497959\pi$
$200$	0	0
$201$	−1608.00	−0.564276
$202$	0	0
$203$	0	0
$204$	0	0
$205$	3752.00	1.27830
$206$	0	0
$207$	2852.00	0.957622
$208$	0	0
$209$	2040.00	0.675166
$210$	0	0
$211$	3684.00	1.20198	0.600988	−	0.799258i	$-0.294774\pi$
$211$	3684.00	1.20198	0.600988	+	0.799258i	$0.294774\pi$
$212$	0	0
$213$	−496.000	−0.159556
$214$	0	0
$215$	−1848.00	−0.586198
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1536.00	0.473942
$220$	0	0
$221$	−120.000	−0.0365252
$222$	0	0
$223$	2808.00	0.843218	0.421609	−	0.906778i	$-0.361466\pi$
$223$	2808.00	0.843218	0.421609	+	0.906778i	$0.361466\pi$
$224$	0	0
$225$	−1633.00	−0.483852
$226$	0	0
$227$	−5358.00	−1.56662	−0.783310	−	0.621631i	$-0.786470\pi$
$227$	−5358.00	−1.56662	−0.783310	+	0.621631i	$0.786470\pi$
$228$	0	0
$229$	6102.00	1.76084	0.880418	−	0.474198i	$-0.157262\pi$
$229$	6102.00	1.76084	0.880418	+	0.474198i	$0.157262\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−5130.00	−1.44239	−0.721196	−	0.692731i	$-0.756407\pi$
$233$	−5130.00	−1.44239	−0.721196	+	0.692731i	$0.756407\pi$
$234$	0	0
$235$	7224.00	2.00528
$236$	0	0
$237$	−384.000	−0.105247
$238$	0	0
$239$	4796.00	1.29802	0.649011	−	0.760779i	$-0.275183\pi$
$239$	4796.00	1.29802	0.649011	+	0.760779i	$0.275183\pi$
$240$	0	0
$241$	5700.00	1.52352	0.761762	−	0.647857i	$-0.224335\pi$
$241$	5700.00	1.52352	0.761762	+	0.647857i	$0.224335\pi$
$242$	0	0
$243$	−3542.00	−0.935059
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−612.000	−0.157654
$248$	0	0
$249$	588.000	0.149651
$250$	0	0
$251$	−1674.00	−0.420964	−0.210482	−	0.977598i	$-0.567503\pi$
$251$	−1674.00	−0.420964	−0.210482	+	0.977598i	$0.567503\pi$
$252$	0	0
$253$	2480.00	0.616270
$254$	0	0
$255$	−560.000	−0.137524
$256$	0	0
$257$	3536.00	0.858248	0.429124	−	0.903246i	$-0.358822\pi$
$257$	3536.00	0.858248	0.429124	+	0.903246i	$0.358822\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	1794.00	0.425463
$262$	0	0
$263$	7816.00	1.83253	0.916265	−	0.400573i	$-0.131189\pi$
$263$	7816.00	1.83253	0.916265	+	0.400573i	$0.131189\pi$
$264$	0	0
$265$	4956.00	1.14885
$266$	0	0
$267$	160.000	0.0366736
$268$	0	0
$269$	−6658.00	−1.50909	−0.754545	−	0.656248i	$-0.772143\pi$
$269$	−6658.00	−1.50909	−0.754545	+	0.656248i	$0.772143\pi$
$270$	0	0
$271$	−5168.00	−1.15843	−0.579213	−	0.815176i	$-0.696640\pi$
$271$	−5168.00	−1.15843	−0.579213	+	0.815176i	$0.696640\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−1420.00	−0.311379
$276$	0	0
$277$	−5994.00	−1.30016	−0.650080	−	0.759865i	$-0.725265\pi$
$277$	−5994.00	−1.30016	−0.650080	+	0.759865i	$0.725265\pi$
$278$	0	0
$279$	5428.00	1.16475
$280$	0	0
$281$	−4074.00	−0.864891	−0.432446	−	0.901660i	$-0.642349\pi$
$281$	−4074.00	−0.864891	−0.432446	+	0.901660i	$0.642349\pi$
$282$	0	0
$283$	−222.000	−0.0466308	−0.0233154	−	0.999728i	$-0.507422\pi$
$283$	−222.000	−0.0466308	−0.0233154	+	0.999728i	$0.507422\pi$
$284$	0	0
$285$	−2856.00	−0.593596
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−4513.00	−0.918583
$290$	0	0
$291$	2808.00	0.565663
$292$	0	0
$293$	−5558.00	−1.10820	−0.554099	−	0.832451i	$-0.686937\pi$
$293$	−5558.00	−1.10820	−0.554099	+	0.832451i	$0.686937\pi$
$294$	0	0
$295$	6132.00	1.21023
$296$	0	0
$297$	−2000.00	−0.390747
$298$	0	0
$299$	−744.000	−0.143902
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−3044.00	−0.577139
$304$	0	0
$305$	6804.00	1.27736
$306$	0	0
$307$	5274.00	0.980466	0.490233	−	0.871591i	$-0.336912\pi$
$307$	5274.00	0.980466	0.490233	+	0.871591i	$0.336912\pi$
$308$	0	0
$309$	−1048.00	−0.192941
$310$	0	0
$311$	−8832.00	−1.61034	−0.805172	−	0.593042i	$-0.797927\pi$
$311$	−8832.00	−1.61034	−0.805172	+	0.593042i	$0.797927\pi$
$312$	0	0
$313$	−9372.00	−1.69245	−0.846225	−	0.532826i	$-0.821130\pi$
$313$	−9372.00	−1.69245	−0.846225	+	0.532826i	$0.821130\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	6294.00	1.11516	0.557581	−	0.830123i	$-0.311730\pi$
$317$	6294.00	1.11516	0.557581	+	0.830123i	$0.311730\pi$
$318$	0	0
$319$	1560.00	0.273803
$320$	0	0
$321$	1496.00	0.260120
$322$	0	0
$323$	2040.00	0.351420
$324$	0	0
$325$	426.000	0.0727084
$326$	0	0
$327$	−1012.00	−0.171143
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−5244.00	−0.870805	−0.435402	−	0.900236i	$-0.643394\pi$
$331$	−5244.00	−0.870805	−0.435402	+	0.900236i	$0.643394\pi$
$332$	0	0
$333$	−1518.00	−0.249807
$334$	0	0
$335$	−11256.0	−1.83576
$336$	0	0
$337$	−5974.00	−0.965651	−0.482826	−	0.875716i	$-0.660390\pi$
$337$	−5974.00	−0.965651	−0.482826	+	0.875716i	$0.660390\pi$
$338$	0	0
$339$	2292.00	0.367210
$340$	0	0
$341$	4720.00	0.749567
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−3472.00	−0.541815
$346$	0	0
$347$	1556.00	0.240722	0.120361	−	0.992730i	$-0.461595\pi$
$347$	1556.00	0.240722	0.120361	+	0.992730i	$0.461595\pi$
$348$	0	0
$349$	4158.00	0.637744	0.318872	−	0.947798i	$-0.396696\pi$
$349$	4158.00	0.637744	0.318872	+	0.947798i	$0.396696\pi$
$350$	0	0
$351$	600.000	0.0912411
$352$	0	0
$353$	6872.00	1.03615	0.518073	−	0.855336i	$-0.326649\pi$
$353$	6872.00	1.03615	0.518073	+	0.855336i	$0.326649\pi$
$354$	0	0
$355$	−3472.00	−0.519083
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−3004.00	−0.441630	−0.220815	−	0.975316i	$-0.570872\pi$
$359$	−3004.00	−0.441630	−0.220815	+	0.975316i	$0.570872\pi$
$360$	0	0
$361$	3545.00	0.516839
$362$	0	0
$363$	1862.00	0.269228
$364$	0	0
$365$	10752.0	1.54188
$366$	0	0
$367$	7944.00	1.12990	0.564950	−	0.825125i	$-0.308895\pi$
$367$	7944.00	1.12990	0.564950	+	0.825125i	$0.308895\pi$
$368$	0	0
$369$	6164.00	0.869607
$370$	0	0
$371$	0	0
$372$	0	0
$373$	6662.00	0.924786	0.462393	−	0.886675i	$-0.346991\pi$
$373$	6662.00	0.924786	0.462393	+	0.886675i	$0.346991\pi$
$374$	0	0
$375$	−1512.00	−0.208212
$376$	0	0
$377$	−468.000	−0.0639343
$378$	0	0
$379$	10308.0	1.39706	0.698531	−	0.715580i	$-0.253837\pi$
$379$	10308.0	1.39706	0.698531	+	0.715580i	$0.253837\pi$
$380$	0	0
$381$	−4392.00	−0.590575
$382$	0	0
$383$	11196.0	1.49370	0.746852	−	0.664990i	$-0.231564\pi$
$383$	11196.0	1.49370	0.746852	+	0.664990i	$0.231564\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−3036.00	−0.398782
$388$	0	0
$389$	−6654.00	−0.867278	−0.433639	−	0.901087i	$-0.642771\pi$
$389$	−6654.00	−0.867278	−0.433639	+	0.901087i	$0.642771\pi$
$390$	0	0
$391$	2480.00	0.320765
$392$	0	0
$393$	−5364.00	−0.688494
$394$	0	0
$395$	−2688.00	−0.342400
$396$	0	0
$397$	−3642.00	−0.460420	−0.230210	−	0.973141i	$-0.573941\pi$
$397$	−3642.00	−0.460420	−0.230210	+	0.973141i	$0.573941\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−8430.00	−1.04981	−0.524905	−	0.851161i	$-0.675899\pi$
$401$	−8430.00	−1.04981	−0.524905	+	0.851161i	$0.675899\pi$
$402$	0	0
$403$	−1416.00	−0.175027
$404$	0	0
$405$	−5894.00	−0.723149
$406$	0	0
$407$	−1320.00	−0.160762
$408$	0	0
$409$	−300.000	−0.0362691	−0.0181345	−	0.999836i	$-0.505773\pi$
$409$	−300.000	−0.0362691	−0.0181345	+	0.999836i	$0.505773\pi$
$410$	0	0
$411$	2196.00	0.263554
$412$	0	0
$413$	0	0
$414$	0	0
$415$	4116.00	0.486859
$416$	0	0
$417$	1220.00	0.143270
$418$	0	0
$419$	−6306.00	−0.735246	−0.367623	−	0.929975i	$-0.619828\pi$
$419$	−6306.00	−0.735246	−0.367623	+	0.929975i	$0.619828\pi$
$420$	0	0
$421$	15606.0	1.80663	0.903313	−	0.428981i	$-0.141127\pi$
$421$	15606.0	1.80663	0.903313	+	0.428981i	$0.141127\pi$
$422$	0	0
$423$	11868.0	1.36417
$424$	0	0
$425$	−1420.00	−0.162071
$426$	0	0
$427$	0	0
$428$	0	0
$429$	240.000	0.0270100
$430$	0	0
$431$	2164.00	0.241847	0.120924	−	0.992662i	$-0.461414\pi$
$431$	2164.00	0.241847	0.120924	+	0.992662i	$0.461414\pi$
$432$	0	0
$433$	−13884.0	−1.54093	−0.770465	−	0.637483i	$-0.779976\pi$
$433$	−13884.0	−1.54093	−0.770465	+	0.637483i	$0.779976\pi$
$434$	0	0
$435$	−2184.00	−0.240724
$436$	0	0
$437$	12648.0	1.38452
$438$	0	0
$439$	10752.0	1.16894	0.584470	−	0.811415i	$-0.301302\pi$
$439$	10752.0	1.16894	0.584470	+	0.811415i	$0.301302\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−3092.00	−0.331615	−0.165807	−	0.986158i	$-0.553023\pi$
$443$	−3092.00	−0.331615	−0.165807	+	0.986158i	$0.553023\pi$
$444$	0	0
$445$	1120.00	0.119310
$446$	0	0
$447$	948.000	0.100311
$448$	0	0
$449$	−10014.0	−1.05254	−0.526269	−	0.850318i	$-0.676410\pi$
$449$	−10014.0	−1.05254	−0.526269	+	0.850318i	$0.676410\pi$
$450$	0	0
$451$	5360.00	0.559629
$452$	0	0
$453$	−4632.00	−0.480420
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−2378.00	−0.243410	−0.121705	−	0.992566i	$-0.538836\pi$
$457$	−2378.00	−0.243410	−0.121705	+	0.992566i	$0.538836\pi$
$458$	0	0
$459$	−2000.00	−0.203381
$460$	0	0
$461$	422.000	0.0426345	0.0213172	−	0.999773i	$-0.493214\pi$
$461$	422.000	0.0426345	0.0213172	+	0.999773i	$0.493214\pi$
$462$	0	0
$463$	−10392.0	−1.04310	−0.521552	−	0.853219i	$-0.674647\pi$
$463$	−10392.0	−1.04310	−0.521552	+	0.853219i	$0.674647\pi$
$464$	0	0
$465$	−6608.00	−0.659008
$466$	0	0
$467$	14082.0	1.39537	0.697684	−	0.716405i	$-0.254214\pi$
$467$	14082.0	1.39537	0.697684	+	0.716405i	$0.254214\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	2148.00	0.210137
$472$	0	0
$473$	−2640.00	−0.256633
$474$	0	0
$475$	−7242.00	−0.699549
$476$	0	0
$477$	8142.00	0.781544
$478$	0	0
$479$	−1740.00	−0.165976	−0.0829881	−	0.996551i	$-0.526446\pi$
$479$	−1740.00	−0.165976	−0.0829881	+	0.996551i	$0.526446\pi$
$480$	0	0
$481$	396.000	0.0375386
$482$	0	0
$483$	0	0
$484$	0	0
$485$	19656.0	1.84027
$486$	0	0
$487$	−3276.00	−0.304825	−0.152412	−	0.988317i	$-0.548704\pi$
$487$	−3276.00	−0.304825	−0.152412	+	0.988317i	$0.548704\pi$
$488$	0	0
$489$	5688.00	0.526013
$490$	0	0
$491$	−14420.0	−1.32539	−0.662694	−	0.748890i	$-0.730587\pi$
$491$	−14420.0	−1.32539	−0.662694	+	0.748890i	$0.730587\pi$
$492$	0	0
$493$	1560.00	0.142513
$494$	0	0
$495$	−6440.00	−0.584761
$496$	0	0
$497$	0	0
$498$	0	0
$499$	21228.0	1.90440	0.952200	−	0.305475i	$-0.0988151\pi$
$499$	21228.0	1.90440	0.952200	+	0.305475i	$0.0988151\pi$
$500$	0	0
$501$	3000.00	0.267525
$502$	0	0
$503$	−3528.00	−0.312735	−0.156368	−	0.987699i	$-0.549978\pi$
$503$	−3528.00	−0.312735	−0.156368	+	0.987699i	$0.549978\pi$
$504$	0	0
$505$	−21308.0	−1.87761
$506$	0	0
$507$	4322.00	0.378593
$508$	0	0
$509$	−13498.0	−1.17542	−0.587710	−	0.809072i	$-0.699970\pi$
$509$	−13498.0	−1.17542	−0.587710	+	0.809072i	$0.699970\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−10200.0	−0.877858
$514$	0	0
$515$	−7336.00	−0.627695
$516$	0	0
$517$	10320.0	0.877898
$518$	0	0
$519$	2452.00	0.207381
$520$	0	0
$521$	−15316.0	−1.28792	−0.643960	−	0.765059i	$-0.722710\pi$
$521$	−15316.0	−1.28792	−0.643960	+	0.765059i	$0.722710\pi$
$522$	0	0
$523$	−7670.00	−0.641273	−0.320636	−	0.947202i	$-0.603897\pi$
$523$	−7670.00	−0.641273	−0.320636	+	0.947202i	$0.603897\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	4720.00	0.390145
$528$	0	0
$529$	3209.00	0.263746
$530$	0	0
$531$	10074.0	0.823304
$532$	0	0
$533$	−1608.00	−0.130676
$534$	0	0
$535$	10472.0	0.846251
$536$	0	0
$537$	−7528.00	−0.604948
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−5298.00	−0.421033	−0.210516	−	0.977590i	$-0.567515\pi$
$541$	−5298.00	−0.421033	−0.210516	+	0.977590i	$0.567515\pi$
$542$	0	0
$543$	276.000	0.0218127
$544$	0	0
$545$	−7084.00	−0.556780
$546$	0	0
$547$	−3612.00	−0.282336	−0.141168	−	0.989986i	$-0.545086\pi$
$547$	−3612.00	−0.282336	−0.141168	+	0.989986i	$0.545086\pi$
$548$	0	0
$549$	11178.0	0.868972
$550$	0	0
$551$	7956.00	0.615131
$552$	0	0
$553$	0	0
$554$	0	0
$555$	1848.00	0.141339
$556$	0	0
$557$	−3018.00	−0.229581	−0.114791	−	0.993390i	$-0.536620\pi$
$557$	−3018.00	−0.229581	−0.114791	+	0.993390i	$0.536620\pi$
$558$	0	0
$559$	792.000	0.0599249
$560$	0	0
$561$	−800.000	−0.0602068
$562$	0	0
$563$	−16986.0	−1.27154	−0.635768	−	0.771880i	$-0.719316\pi$
$563$	−16986.0	−1.27154	−0.635768	+	0.771880i	$0.719316\pi$
$564$	0	0
$565$	16044.0	1.19465
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−1782.00	−0.131292	−0.0656462	−	0.997843i	$-0.520911\pi$
$569$	−1782.00	−0.131292	−0.0656462	+	0.997843i	$0.520911\pi$
$570$	0	0
$571$	−14028.0	−1.02811	−0.514057	−	0.857756i	$-0.671858\pi$
$571$	−14028.0	−1.02811	−0.514057	+	0.857756i	$0.671858\pi$
$572$	0	0
$573$	4336.00	0.316124
$574$	0	0
$575$	−8804.00	−0.638526
$576$	0	0
$577$	2952.00	0.212987	0.106493	−	0.994313i	$-0.466038\pi$
$577$	2952.00	0.212987	0.106493	+	0.994313i	$0.466038\pi$
$578$	0	0
$579$	−3612.00	−0.259257
$580$	0	0
$581$	0	0
$582$	0	0
$583$	7080.00	0.502957
$584$	0	0
$585$	1932.00	0.136544
$586$	0	0
$587$	−3882.00	−0.272960	−0.136480	−	0.990643i	$-0.543579\pi$
$587$	−3882.00	−0.272960	−0.136480	+	0.990643i	$0.543579\pi$
$588$	0	0
$589$	24072.0	1.68399
$590$	0	0
$591$	−7932.00	−0.552079
$592$	0	0
$593$	18088.0	1.25259	0.626294	−	0.779587i	$-0.284571\pi$
$593$	18088.0	1.25259	0.626294	+	0.779587i	$0.284571\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−72.0000	−0.00493595
$598$	0	0
$599$	−28192.0	−1.92303	−0.961514	−	0.274756i	$-0.911403\pi$
$599$	−28192.0	−1.92303	−0.961514	+	0.274756i	$0.911403\pi$
$600$	0	0
$601$	−25728.0	−1.74620	−0.873101	−	0.487540i	$-0.837894\pi$
$601$	−25728.0	−1.74620	−0.873101	+	0.487540i	$0.837894\pi$
$602$	0	0
$603$	−18492.0	−1.24884
$604$	0	0
$605$	13034.0	0.875880
$606$	0	0
$607$	−14208.0	−0.950058	−0.475029	−	0.879970i	$-0.657562\pi$
$607$	−14208.0	−0.950058	−0.475029	+	0.879970i	$0.657562\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−3096.00	−0.204993
$612$	0	0
$613$	−11734.0	−0.773135	−0.386568	−	0.922261i	$-0.626339\pi$
$613$	−11734.0	−0.773135	−0.386568	+	0.922261i	$0.626339\pi$
$614$	0	0
$615$	−7504.00	−0.492017
$616$	0	0
$617$	−18222.0	−1.18896	−0.594481	−	0.804109i	$-0.702643\pi$
$617$	−18222.0	−1.18896	−0.594481	+	0.804109i	$0.702643\pi$
$618$	0	0
$619$	−4934.00	−0.320378	−0.160189	−	0.987086i	$-0.551210\pi$
$619$	−4934.00	−0.320378	−0.160189	+	0.987086i	$0.551210\pi$
$620$	0	0
$621$	−12400.0	−0.801280
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−19459.0	−1.24538
$626$	0	0
$627$	−4080.00	−0.259872
$628$	0	0
$629$	−1320.00	−0.0836754
$630$	0	0
$631$	−9648.00	−0.608686	−0.304343	−	0.952563i	$-0.598437\pi$
$631$	−9648.00	−0.608686	−0.304343	+	0.952563i	$0.598437\pi$
$632$	0	0
$633$	−7368.00	−0.462641
$634$	0	0
$635$	−30744.0	−1.92132
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−5704.00	−0.353125
$640$	0	0
$641$	16242.0	1.00081	0.500406	−	0.865791i	$-0.333184\pi$
$641$	16242.0	1.00081	0.500406	+	0.865791i	$0.333184\pi$
$642$	0	0
$643$	20166.0	1.23681	0.618405	−	0.785859i	$-0.287779\pi$
$643$	20166.0	1.23681	0.618405	+	0.785859i	$0.287779\pi$
$644$	0	0
$645$	3696.00	0.225628
$646$	0	0
$647$	−23772.0	−1.44447	−0.722236	−	0.691646i	$-0.756886\pi$
$647$	−23772.0	−1.44447	−0.722236	+	0.691646i	$0.756886\pi$
$648$	0	0
$649$	8760.00	0.529831
$650$	0	0
$651$	0	0
$652$	0	0
$653$	12930.0	0.774870	0.387435	−	0.921897i	$-0.373361\pi$
$653$	12930.0	0.774870	0.387435	+	0.921897i	$0.373361\pi$
$654$	0	0
$655$	−37548.0	−2.23988
$656$	0	0
$657$	17664.0	1.04892
$658$	0	0
$659$	−11404.0	−0.674107	−0.337054	−	0.941485i	$-0.609430\pi$
$659$	−11404.0	−0.674107	−0.337054	+	0.941485i	$0.609430\pi$
$660$	0	0
$661$	−9678.00	−0.569486	−0.284743	−	0.958604i	$-0.591908\pi$
$661$	−9678.00	−0.569486	−0.284743	+	0.958604i	$0.591908\pi$
$662$	0	0
$663$	240.000	0.0140586
$664$	0	0
$665$	0	0
$666$	0	0
$667$	9672.00	0.561471
$668$	0	0
$669$	−5616.00	−0.324555
$670$	0	0
$671$	9720.00	0.559220
$672$	0	0
$673$	10542.0	0.603810	0.301905	−	0.953338i	$-0.402377\pi$
$673$	10542.0	0.603810	0.301905	+	0.953338i	$0.402377\pi$
$674$	0	0
$675$	7100.00	0.404858
$676$	0	0
$677$	−3418.00	−0.194039	−0.0970195	−	0.995282i	$-0.530931\pi$
$677$	−3418.00	−0.194039	−0.0970195	+	0.995282i	$0.530931\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	10716.0	0.602993
$682$	0	0
$683$	−17036.0	−0.954414	−0.477207	−	0.878791i	$-0.658351\pi$
$683$	−17036.0	−0.954414	−0.477207	+	0.878791i	$0.658351\pi$
$684$	0	0
$685$	15372.0	0.857422
$686$	0	0
$687$	−12204.0	−0.677746
$688$	0	0
$689$	−2124.00	−0.117443
$690$	0	0
$691$	3386.00	0.186410	0.0932051	−	0.995647i	$-0.470289\pi$
$691$	3386.00	0.186410	0.0932051	+	0.995647i	$0.470289\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	8540.00	0.466102
$696$	0	0
$697$	5360.00	0.291283
$698$	0	0
$699$	10260.0	0.555177
$700$	0	0
$701$	9954.00	0.536316	0.268158	−	0.963375i	$-0.413585\pi$
$701$	9954.00	0.536316	0.268158	+	0.963375i	$0.413585\pi$
$702$	0	0
$703$	−6732.00	−0.361170
$704$	0	0
$705$	−14448.0	−0.771834
$706$	0	0
$707$	0	0
$708$	0	0
$709$	29266.0	1.55022	0.775111	−	0.631825i	$-0.217694\pi$
$709$	29266.0	1.55022	0.775111	+	0.631825i	$0.217694\pi$
$710$	0	0
$711$	−4416.00	−0.232930
$712$	0	0
$713$	29264.0	1.53709
$714$	0	0
$715$	1680.00	0.0878719
$716$	0	0
$717$	−9592.00	−0.499609
$718$	0	0
$719$	−12540.0	−0.650435	−0.325218	−	0.945639i	$-0.605438\pi$
$719$	−12540.0	−0.650435	−0.325218	+	0.945639i	$0.605438\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−11400.0	−0.586405
$724$	0	0
$725$	−5538.00	−0.283691
$726$	0	0
$727$	14956.0	0.762981	0.381491	−	0.924373i	$-0.375411\pi$
$727$	14956.0	0.762981	0.381491	+	0.924373i	$0.375411\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	0	0
$731$	−2640.00	−0.133576
$732$	0	0
$733$	24690.0	1.24413	0.622064	−	0.782966i	$-0.286294\pi$
$733$	24690.0	1.24413	0.622064	+	0.782966i	$0.286294\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−16080.0	−0.803683
$738$	0	0
$739$	−33564.0	−1.67073	−0.835367	−	0.549693i	$-0.814745\pi$
$739$	−33564.0	−1.67073	−0.835367	+	0.549693i	$0.814745\pi$
$740$	0	0
$741$	1224.00	0.0606812
$742$	0	0
$743$	−28460.0	−1.40524	−0.702622	−	0.711563i	$-0.747987\pi$
$743$	−28460.0	−1.40524	−0.702622	+	0.711563i	$0.747987\pi$
$744$	0	0
$745$	6636.00	0.326341
$746$	0	0
$747$	6762.00	0.331203
$748$	0	0
$749$	0	0
$750$	0	0
$751$	10884.0	0.528845	0.264423	−	0.964407i	$-0.414819\pi$
$751$	10884.0	0.528845	0.264423	+	0.964407i	$0.414819\pi$
$752$	0	0
$753$	3348.00	0.162029
$754$	0	0
$755$	−32424.0	−1.56295
$756$	0	0
$757$	−27542.0	−1.32237	−0.661183	−	0.750225i	$-0.729945\pi$
$757$	−27542.0	−1.32237	−0.661183	+	0.750225i	$0.729945\pi$
$758$	0	0
$759$	−4960.00	−0.237202
$760$	0	0
$761$	4076.00	0.194159	0.0970794	−	0.995277i	$-0.469050\pi$
$761$	4076.00	0.194159	0.0970794	+	0.995277i	$0.469050\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−6440.00	−0.304364
$766$	0	0
$767$	−2628.00	−0.123718
$768$	0	0
$769$	−17796.0	−0.834513	−0.417256	−	0.908789i	$-0.637008\pi$
$769$	−17796.0	−0.834513	−0.417256	+	0.908789i	$0.637008\pi$
$770$	0	0
$771$	−7072.00	−0.330340
$772$	0	0
$773$	−13510.0	−0.628617	−0.314308	−	0.949321i	$-0.601773\pi$
$773$	−13510.0	−0.628617	−0.314308	+	0.949321i	$0.601773\pi$
$774$	0	0
$775$	−16756.0	−0.776637
$776$	0	0
$777$	0	0
$778$	0	0
$779$	27336.0	1.25727
$780$	0	0
$781$	−4960.00	−0.227251
$782$	0	0
$783$	−7800.00	−0.356002
$784$	0	0
$785$	15036.0	0.683641
$786$	0	0
$787$	−5870.00	−0.265874	−0.132937	−	0.991124i	$-0.542441\pi$
$787$	−5870.00	−0.265874	−0.132937	+	0.991124i	$0.542441\pi$
$788$	0	0
$789$	−15632.0	−0.705341
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−2916.00	−0.130580
$794$	0	0
$795$	−9912.00	−0.442192
$796$	0	0
$797$	−21538.0	−0.957234	−0.478617	−	0.878024i	$-0.658862\pi$
$797$	−21538.0	−0.957234	−0.478617	+	0.878024i	$0.658862\pi$
$798$	0	0
$799$	10320.0	0.456940
$800$	0	0
$801$	1840.00	0.0811650
$802$	0	0
$803$	15360.0	0.675022
$804$	0	0
$805$	0	0
$806$	0	0
$807$	13316.0	0.580849
$808$	0	0
$809$	−12474.0	−0.542104	−0.271052	−	0.962565i	$-0.587372\pi$
$809$	−12474.0	−0.542104	−0.271052	+	0.962565i	$0.587372\pi$
$810$	0	0
$811$	−12278.0	−0.531614	−0.265807	−	0.964026i	$-0.585638\pi$
$811$	−12278.0	−0.531614	−0.265807	+	0.964026i	$0.585638\pi$
$812$	0	0
$813$	10336.0	0.445879
$814$	0	0
$815$	39816.0	1.71128
$816$	0	0
$817$	−13464.0	−0.576555
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−11034.0	−0.469049	−0.234525	−	0.972110i	$-0.575353\pi$
$821$	−11034.0	−0.469049	−0.234525	+	0.972110i	$0.575353\pi$
$822$	0	0
$823$	−3096.00	−0.131130	−0.0655649	−	0.997848i	$-0.520885\pi$
$823$	−3096.00	−0.131130	−0.0655649	+	0.997848i	$0.520885\pi$
$824$	0	0
$825$	2840.00	0.119850
$826$	0	0
$827$	−33884.0	−1.42474	−0.712371	−	0.701803i	$-0.752379\pi$
$827$	−33884.0	−1.42474	−0.712371	+	0.701803i	$0.752379\pi$
$828$	0	0
$829$	−10038.0	−0.420548	−0.210274	−	0.977643i	$-0.567436\pi$
$829$	−10038.0	−0.420548	−0.210274	+	0.977643i	$0.567436\pi$
$830$	0	0
$831$	11988.0	0.500432
$832$	0	0
$833$	0	0
$834$	0	0
$835$	21000.0	0.870341
$836$	0	0
$837$	−23600.0	−0.974594
$838$	0	0
$839$	25308.0	1.04139	0.520697	−	0.853742i	$-0.325672\pi$
$839$	25308.0	1.04139	0.520697	+	0.853742i	$0.325672\pi$
$840$	0	0
$841$	−18305.0	−0.750543
$842$	0	0
$843$	8148.00	0.332897
$844$	0	0
$845$	30254.0	1.23168
$846$	0	0
$847$	0	0
$848$	0	0
$849$	444.000	0.0179482
$850$	0	0
$851$	−8184.00	−0.329664
$852$	0	0
$853$	11382.0	0.456873	0.228436	−	0.973559i	$-0.426639\pi$
$853$	11382.0	0.456873	0.228436	+	0.973559i	$0.426639\pi$
$854$	0	0
$855$	−32844.0	−1.31373
$856$	0	0
$857$	38468.0	1.53330	0.766652	−	0.642063i	$-0.221921\pi$
$857$	38468.0	1.53330	0.766652	+	0.642063i	$0.221921\pi$
$858$	0	0
$859$	40590.0	1.61224	0.806119	−	0.591753i	$-0.201564\pi$
$859$	40590.0	1.61224	0.806119	+	0.591753i	$0.201564\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	680.000	0.0268221	0.0134110	−	0.999910i	$-0.495731\pi$
$863$	680.000	0.0268221	0.0134110	+	0.999910i	$0.495731\pi$
$864$	0	0
$865$	17164.0	0.674675
$866$	0	0
$867$	9026.00	0.353563
$868$	0	0
$869$	−3840.00	−0.149900
$870$	0	0
$871$	4824.00	0.187664
$872$	0	0
$873$	32292.0	1.25191
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−21526.0	−0.828827	−0.414414	−	0.910089i	$-0.636013\pi$
$877$	−21526.0	−0.828827	−0.414414	+	0.910089i	$0.636013\pi$
$878$	0	0
$879$	11116.0	0.426545
$880$	0	0
$881$	39632.0	1.51559	0.757796	−	0.652492i	$-0.226276\pi$
$881$	39632.0	1.51559	0.757796	+	0.652492i	$0.226276\pi$
$882$	0	0
$883$	−7572.00	−0.288582	−0.144291	−	0.989535i	$-0.546090\pi$
$883$	−7572.00	−0.288582	−0.144291	+	0.989535i	$0.546090\pi$
$884$	0	0
$885$	−12264.0	−0.465819
$886$	0	0
$887$	15276.0	0.578261	0.289131	−	0.957290i	$-0.406634\pi$
$887$	15276.0	0.578261	0.289131	+	0.957290i	$0.406634\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−8420.00	−0.316589
$892$	0	0
$893$	52632.0	1.97230
$894$	0	0
$895$	−52696.0	−1.96808
$896$	0	0
$897$	1488.00	0.0553878
$898$	0	0
$899$	18408.0	0.682916
$900$	0	0
$901$	7080.00	0.261786
$902$	0	0
$903$	0	0
$904$	0	0
$905$	1932.00	0.0709634
$906$	0	0
$907$	−13044.0	−0.477529	−0.238765	−	0.971077i	$-0.576742\pi$
$907$	−13044.0	−0.477529	−0.238765	+	0.971077i	$0.576742\pi$
$908$	0	0
$909$	−35006.0	−1.27731
$910$	0	0
$911$	−13684.0	−0.497663	−0.248832	−	0.968547i	$-0.580047\pi$
$911$	−13684.0	−0.497663	−0.248832	+	0.968547i	$0.580047\pi$
$912$	0	0
$913$	5880.00	0.213143
$914$	0	0
$915$	−13608.0	−0.491657
$916$	0	0
$917$	0	0
$918$	0	0
$919$	25704.0	0.922630	0.461315	−	0.887236i	$-0.347378\pi$
$919$	25704.0	0.922630	0.461315	+	0.887236i	$0.347378\pi$
$920$	0	0
$921$	−10548.0	−0.377382
$922$	0	0
$923$	1488.00	0.0530640
$924$	0	0
$925$	4686.00	0.166567
$926$	0	0
$927$	−12052.0	−0.427011
$928$	0	0
$929$	−22564.0	−0.796879	−0.398440	−	0.917195i	$-0.630448\pi$
$929$	−22564.0	−0.796879	−0.398440	+	0.917195i	$0.630448\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	17664.0	0.619821
$934$	0	0
$935$	−5600.00	−0.195871
$936$	0	0
$937$	14208.0	0.495363	0.247681	−	0.968842i	$-0.420331\pi$
$937$	14208.0	0.495363	0.247681	+	0.968842i	$0.420331\pi$
$938$	0	0
$939$	18744.0	0.651424
$940$	0	0
$941$	2626.00	0.0909725	0.0454863	−	0.998965i	$-0.485516\pi$
$941$	2626.00	0.0909725	0.0454863	+	0.998965i	$0.485516\pi$
$942$	0	0
$943$	33232.0	1.14760
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−18860.0	−0.647168	−0.323584	−	0.946200i	$-0.604888\pi$
$947$	−18860.0	−0.647168	−0.323584	+	0.946200i	$0.604888\pi$
$948$	0	0
$949$	−4608.00	−0.157621
$950$	0	0
$951$	−12588.0	−0.429226
$952$	0	0
$953$	42.0000	0.00142761	0.000713806	−	1.00000i	$-0.499773\pi$
$953$	42.0000	0.00142761	0.000713806		1.00000i	$0.499773\pi$
$954$	0	0
$955$	30352.0	1.02845
$956$	0	0
$957$	−3120.00	−0.105387
$958$	0	0
$959$	0	0
$960$	0	0
$961$	25905.0	0.869558
$962$	0	0
$963$	17204.0	0.575692
$964$	0	0
$965$	−25284.0	−0.843441
$966$	0	0
$967$	42804.0	1.42346	0.711729	−	0.702454i	$-0.247912\pi$
$967$	42804.0	1.42346	0.711729	+	0.702454i	$0.247912\pi$
$968$	0	0
$969$	−4080.00	−0.135262
$970$	0	0
$971$	25770.0	0.851698	0.425849	−	0.904794i	$-0.359975\pi$
$971$	25770.0	0.851698	0.425849	+	0.904794i	$0.359975\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−852.000	−0.0279855
$976$	0	0
$977$	2766.00	0.0905754	0.0452877	−	0.998974i	$-0.485580\pi$
$977$	2766.00	0.0905754	0.0452877	+	0.998974i	$0.485580\pi$
$978$	0	0
$979$	1600.00	0.0522331
$980$	0	0
$981$	−11638.0	−0.378769
$982$	0	0
$983$	2988.00	0.0969506	0.0484753	−	0.998824i	$-0.484564\pi$
$983$	2988.00	0.0969506	0.0484753	+	0.998824i	$0.484564\pi$
$984$	0	0
$985$	−55524.0	−1.79608
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−16368.0	−0.526261
$990$	0	0
$991$	−32400.0	−1.03857	−0.519284	−	0.854602i	$-0.673801\pi$
$991$	−32400.0	−1.03857	−0.519284	+	0.854602i	$0.673801\pi$
$992$	0	0
$993$	10488.0	0.335173
$994$	0	0
$995$	−504.000	−0.0160582
$996$	0	0
$997$	−24294.0	−0.771714	−0.385857	−	0.922559i	$-0.626094\pi$
$997$	−24294.0	−0.771714	−0.385857	+	0.922559i	$0.626094\pi$
$998$	0	0
$999$	6600.00	0.209024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.4.a.d.1.1	✓	1
4.3	odd	2		1568.4.a.j.1.1	yes	1
7.6	odd	2		1568.4.a.l.1.1	yes	1
28.27	even	2		1568.4.a.f.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1568.4.a.d.1.1	✓	1	1.1	even	1	trivial
1568.4.a.f.1.1	yes	1	28.27	even	2
1568.4.a.j.1.1	yes	1	4.3	odd	2
1568.4.a.l.1.1	yes	1	7.6	odd	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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1568.a (trivial)

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