LMFDB - Embedded newform 8550.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8550,2,Mod(1,8550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8550, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8550.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:	$68.2720937282$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +5.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +5.00000 q^{7} +1.00000 q^{8} +4.00000 q^{11} +1.00000 q^{13} +5.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{19} +4.00000 q^{22} +7.00000 q^{23} +1.00000 q^{26} +5.00000 q^{28} +3.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +2.00000 q^{37} +1.00000 q^{38} +6.00000 q^{41} -6.00000 q^{43} +4.00000 q^{44} +7.00000 q^{46} +18.0000 q^{49} +1.00000 q^{52} -13.0000 q^{53} +5.00000 q^{56} +3.00000 q^{58} +9.00000 q^{59} -12.0000 q^{61} -2.00000 q^{62} +1.00000 q^{64} +3.00000 q^{67} -3.00000 q^{68} -11.0000 q^{73} +2.00000 q^{74} +1.00000 q^{76} +20.0000 q^{77} -2.00000 q^{79} +6.00000 q^{82} -10.0000 q^{83} -6.00000 q^{86} +4.00000 q^{88} -2.00000 q^{89} +5.00000 q^{91} +7.00000 q^{92} +2.00000 q^{97} +18.0000 q^{98} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	5.00000	1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	0	0
$22$	4.00000	0.852803
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	5.00000	0.944911
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	7.00000	1.03209
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	−13.0000	−1.78569	−0.892844	−	0.450367i	$-0.851293\pi$
$53$	−13.0000	−1.78569	−0.892844	+	0.450367i	$0.851293\pi$
$54$	0	0
$55$	0	0
$56$	5.00000	0.668153
$57$	0	0
$58$	3.00000	0.393919
$59$	9.00000	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$60$	0	0
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	1.00000	0.114708
$77$	20.0000	2.27921
$78$	0	0
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	0	0
$81$	0	0
$82$	6.00000	0.662589
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	0	0
$85$	0	0
$86$	−6.00000	−0.646997
$87$	0	0
$88$	4.00000	0.426401
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	7.00000	0.729800
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	18.0000	1.81827
$99$	0	0
$100$	0	0
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−13.0000	−1.26267
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	0	0
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	0	0
$112$	5.00000	0.472456
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	3.00000	0.278543
$117$	0	0
$118$	9.00000	0.828517
$119$	−15.0000	−1.37505
$120$	0	0
$121$	5.00000	0.454545
$122$	−12.0000	−1.08643
$123$	0	0
$124$	−2.00000	−0.179605
$125$	0	0
$126$	0	0
$127$	6.00000	0.532414	0.266207	−	0.963916i	$-0.414230\pi$
$127$	6.00000	0.532414	0.266207	+	0.963916i	$0.414230\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−16.0000	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$132$	0	0
$133$	5.00000	0.433555
$134$	3.00000	0.259161
$135$	0	0
$136$	−3.00000	−0.257248
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	0	0
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	4.00000	0.334497
$144$	0	0
$145$	0	0
$146$	−11.0000	−0.910366
$147$	0	0
$148$	2.00000	0.164399
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	20.0000	1.61165
$155$	0	0
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	−2.00000	−0.159111
$159$	0	0
$160$	0	0
$161$	35.0000	2.75839
$162$	0	0
$163$	−22.0000	−1.72317	−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000	−1.72317	−0.861586	+	0.507611i	$0.830529\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−10.0000	−0.776151
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−6.00000	−0.457496
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−2.00000	−0.149906
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	7.00000	0.516047
$185$	0	0
$186$	0	0
$187$	−12.0000	−0.877527
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	18.0000	1.28571
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	0	0
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	0	0
$201$	0	0
$202$	8.00000	0.562878
$203$	15.0000	1.05279
$204$	0	0
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	1.00000	0.0693375
$209$	4.00000	0.276686
$210$	0	0
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	−13.0000	−0.892844
$213$	0	0
$214$	−13.0000	−0.888662
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	19.0000	1.28684
$219$	0	0
$220$	0	0
$221$	−3.00000	−0.201802
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	0	0
$227$	5.00000	0.331862	0.165931	−	0.986137i	$-0.446937\pi$
$227$	5.00000	0.331862	0.165931	+	0.986137i	$0.446937\pi$
$228$	0	0
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	0	0
$235$	0	0
$236$	9.00000	0.585850
$237$	0	0
$238$	−15.0000	−0.972306
$239$	11.0000	0.711531	0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000	0.711531	0.355765	+	0.934575i	$0.384220\pi$
$240$	0	0
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−12.0000	−0.768221
$245$	0	0
$246$	0	0
$247$	1.00000	0.0636285
$248$	−2.00000	−0.127000
$249$	0	0
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	28.0000	1.76034
$254$	6.00000	0.376473
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	−16.0000	−0.988483
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	0	0
$266$	5.00000	0.306570
$267$	0	0
$268$	3.00000	0.183254
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	0	0
$271$	−27.0000	−1.64013	−0.820067	−	0.572268i	$-0.806064\pi$
$271$	−27.0000	−1.64013	−0.820067	+	0.572268i	$0.806064\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	9.00000	0.543710
$275$	0	0
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	16.0000	0.959616
$279$	0	0
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	0	0
$285$	0	0
$286$	4.00000	0.236525
$287$	30.0000	1.77084
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	−11.0000	−0.643726
$293$	−27.0000	−1.57736	−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000	−1.57736	−0.788678	+	0.614806i	$0.789234\pi$
$294$	0	0
$295$	0	0
$296$	2.00000	0.116248
$297$	0	0
$298$	4.00000	0.231714
$299$	7.00000	0.404820
$300$	0	0
$301$	−30.0000	−1.72917
$302$	−10.0000	−0.575435
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	0	0
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	20.0000	1.13961
$309$	0	0
$310$	0	0
$311$	−25.0000	−1.41762	−0.708810	−	0.705399i	$-0.750768\pi$
$311$	−25.0000	−1.41762	−0.708810	+	0.705399i	$0.750768\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	−2.00000	−0.112509
$317$	9.00000	0.505490	0.252745	−	0.967533i	$-0.418667\pi$
$317$	9.00000	0.505490	0.252745	+	0.967533i	$0.418667\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	0	0
$321$	0	0
$322$	35.0000	1.95047
$323$	−3.00000	−0.166924
$324$	0	0
$325$	0	0
$326$	−22.0000	−1.21847
$327$	0	0
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	−7.00000	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$332$	−10.0000	−0.548821
$333$	0	0
$334$	−2.00000	−0.109435
$335$	0	0
$336$	0	0
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	−8.00000	−0.433224
$342$	0	0
$343$	55.0000	2.96972
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−14.0000	−0.752645
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	0	0
$352$	4.00000	0.213201
$353$	7.00000	0.372572	0.186286	−	0.982496i	$-0.440355\pi$
$353$	7.00000	0.372572	0.186286	+	0.982496i	$0.440355\pi$
$354$	0	0
$355$	0	0
$356$	−2.00000	−0.106000
$357$	0	0
$358$	8.00000	0.422813
$359$	5.00000	0.263890	0.131945	−	0.991257i	$-0.457878\pi$
$359$	5.00000	0.263890	0.131945	+	0.991257i	$0.457878\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	26.0000	1.36653
$363$	0	0
$364$	5.00000	0.262071
$365$	0	0
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	7.00000	0.364900
$369$	0	0
$370$	0	0
$371$	−65.0000	−3.37463
$372$	0	0
$373$	23.0000	1.19089	0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000	1.19089	0.595447	+	0.803394i	$0.296975\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	0	0
$377$	3.00000	0.154508
$378$	0	0
$379$	−33.0000	−1.69510	−0.847548	−	0.530719i	$-0.821922\pi$
$379$	−33.0000	−1.69510	−0.847548	+	0.530719i	$0.821922\pi$
$380$	0	0
$381$	0	0
$382$	−9.00000	−0.460480
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	0	0
$386$	−10.0000	−0.508987
$387$	0	0
$388$	2.00000	0.101535
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	0	0
$391$	−21.0000	−1.06202
$392$	18.0000	0.909137
$393$	0	0
$394$	−22.0000	−1.10834
$395$	0	0
$396$	0	0
$397$	16.0000	0.803017	0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000	0.803017	0.401508	+	0.915855i	$0.368486\pi$
$398$	−15.0000	−0.751882
$399$	0	0
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	8.00000	0.398015
$405$	0	0
$406$	15.0000	0.744438
$407$	8.00000	0.396545
$408$	0	0
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	0	0
$411$	0	0
$412$	−4.00000	−0.197066
$413$	45.0000	2.21431
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	4.00000	0.195646
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−5.00000	−0.243396
$423$	0	0
$424$	−13.0000	−0.631336
$425$	0	0
$426$	0	0
$427$	−60.0000	−2.90360
$428$	−13.0000	−0.628379
$429$	0	0
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	0	0
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	−10.0000	−0.480015
$435$	0	0
$436$	19.0000	0.909935
$437$	7.00000	0.334855
$438$	0	0
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	0	0
$442$	−3.00000	−0.142695
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	0	0
$446$	2.00000	0.0947027
$447$	0	0
$448$	5.00000	0.236228
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	0	0
$453$	0	0
$454$	5.00000	0.234662
$455$	0	0
$456$	0	0
$457$	29.0000	1.35656	0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000	1.35656	0.678281	+	0.734802i	$0.262725\pi$
$458$	−6.00000	−0.280362
$459$	0	0
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	10.0000	0.463241
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	15.0000	0.692636
$470$	0	0
$471$	0	0
$472$	9.00000	0.414259
$473$	−24.0000	−1.10352
$474$	0	0
$475$	0	0
$476$	−15.0000	−0.687524
$477$	0	0
$478$	11.0000	0.503128
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	−12.0000	−0.546585
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	0	0
$487$	38.0000	1.72194	0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000	1.72194	0.860972	+	0.508652i	$0.169856\pi$
$488$	−12.0000	−0.543214
$489$	0	0
$490$	0	0
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	0	0
$493$	−9.00000	−0.405340
$494$	1.00000	0.0449921
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0	0
$499$	42.0000	1.88018	0.940089	−	0.340929i	$-0.110742\pi$
$499$	42.0000	1.88018	0.940089	+	0.340929i	$0.110742\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	0	0
$506$	28.0000	1.24475
$507$	0	0
$508$	6.00000	0.266207
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	0	0
$511$	−55.0000	−2.43306
$512$	1.00000	0.0441942
$513$	0	0
$514$	22.0000	0.970378
$515$	0	0
$516$	0	0
$517$	0	0
$518$	10.0000	0.439375
$519$	0	0
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	9.00000	0.393543	0.196771	−	0.980449i	$-0.436954\pi$
$523$	9.00000	0.393543	0.196771	+	0.980449i	$0.436954\pi$
$524$	−16.0000	−0.698963
$525$	0	0
$526$	8.00000	0.348817
$527$	6.00000	0.261364
$528$	0	0
$529$	26.0000	1.13043
$530$	0	0
$531$	0	0
$532$	5.00000	0.216777
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	3.00000	0.129580
$537$	0	0
$538$	−2.00000	−0.0862261
$539$	72.0000	3.10126
$540$	0	0
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−27.0000	−1.15975
$543$	0	0
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	9.00000	0.384461
$549$	0	0
$550$	0	0
$551$	3.00000	0.127804
$552$	0	0
$553$	−10.0000	−0.425243
$554$	8.00000	0.339887
$555$	0	0
$556$	16.0000	0.678551
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	−6.00000	−0.253773
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	0	0
$566$	2.00000	0.0840663
$567$	0	0
$568$	0	0
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	6.00000	0.251092	0.125546	−	0.992088i	$-0.459932\pi$
$571$	6.00000	0.251092	0.125546	+	0.992088i	$0.459932\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	30.0000	1.25218
$575$	0	0
$576$	0	0
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	−50.0000	−2.07435
$582$	0	0
$583$	−52.0000	−2.15362
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−27.0000	−1.11536
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	0	0
$592$	2.00000	0.0821995
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	0	0
$596$	4.00000	0.163846
$597$	0	0
$598$	7.00000	0.286251
$599$	26.0000	1.06233	0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000	1.06233	0.531166	+	0.847268i	$0.321754\pi$
$600$	0	0
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	−30.0000	−1.22271
$603$	0	0
$604$	−10.0000	−0.406894
$605$	0	0
$606$	0	0
$607$	26.0000	1.05531	0.527654	−	0.849460i	$-0.323072\pi$
$607$	26.0000	1.05531	0.527654	+	0.849460i	$0.323072\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	20.0000	0.805823
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	0	0
$619$	−24.0000	−0.964641	−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000	−0.964641	−0.482321	+	0.875995i	$0.660206\pi$
$620$	0	0
$621$	0	0
$622$	−25.0000	−1.00241
$623$	−10.0000	−0.400642
$624$	0	0
$625$	0	0
$626$	1.00000	0.0399680
$627$	0	0
$628$	−6.00000	−0.239426
$629$	−6.00000	−0.239236
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−2.00000	−0.0795557
$633$	0	0
$634$	9.00000	0.357436
$635$	0	0
$636$	0	0
$637$	18.0000	0.713186
$638$	12.0000	0.475085
$639$	0	0
$640$	0	0
$641$	−8.00000	−0.315981	−0.157991	−	0.987441i	$-0.550502\pi$
$641$	−8.00000	−0.315981	−0.157991	+	0.987441i	$0.550502\pi$
$642$	0	0
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	35.0000	1.37919
$645$	0	0
$646$	−3.00000	−0.118033
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	0	0
$649$	36.0000	1.41312
$650$	0	0
$651$	0	0
$652$	−22.0000	−0.861586
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	0	0
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	0	0
$661$	15.0000	0.583432	0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000	0.583432	0.291716	+	0.956505i	$0.405774\pi$
$662$	−7.00000	−0.272063
$663$	0	0
$664$	−10.0000	−0.388075
$665$	0	0
$666$	0	0
$667$	21.0000	0.813123
$668$	−2.00000	−0.0773823
$669$	0	0
$670$	0	0
$671$	−48.0000	−1.85302
$672$	0	0
$673$	44.0000	1.69608	0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000	1.69608	0.848038	+	0.529936i	$0.177784\pi$
$674$	−6.00000	−0.231111
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−39.0000	−1.49889	−0.749446	−	0.662066i	$-0.769680\pi$
$677$	−39.0000	−1.49889	−0.749446	+	0.662066i	$0.769680\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	0	0
$681$	0	0
$682$	−8.00000	−0.306336
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	0	0
$686$	55.0000	2.09991
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−13.0000	−0.495261
$690$	0	0
$691$	−42.0000	−1.59776	−0.798878	−	0.601494i	$-0.794573\pi$
$691$	−42.0000	−1.59776	−0.798878	+	0.601494i	$0.794573\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−6.00000	−0.227757
$695$	0	0
$696$	0	0
$697$	−18.0000	−0.681799
$698$	14.0000	0.529908
$699$	0	0
$700$	0	0
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	0	0
$703$	2.00000	0.0754314
$704$	4.00000	0.150756
$705$	0	0
$706$	7.00000	0.263448
$707$	40.0000	1.50435
$708$	0	0
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	0	0
$711$	0	0
$712$	−2.00000	−0.0749532
$713$	−14.0000	−0.524304
$714$	0	0
$715$	0	0
$716$	8.00000	0.298974
$717$	0	0
$718$	5.00000	0.186598
$719$	27.0000	1.00693	0.503465	−	0.864016i	$-0.332058\pi$
$719$	27.0000	1.00693	0.503465	+	0.864016i	$0.332058\pi$
$720$	0	0
$721$	−20.0000	−0.744839
$722$	1.00000	0.0372161
$723$	0	0
$724$	26.0000	0.966282
$725$	0	0
$726$	0	0
$727$	−23.0000	−0.853023	−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000	−0.853023	−0.426511	+	0.904482i	$0.640258\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	0	0
$731$	18.0000	0.665754
$732$	0	0
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	7.00000	0.258023
$737$	12.0000	0.442026
$738$	0	0
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	0	0
$741$	0	0
$742$	−65.0000	−2.38623
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	0	0
$746$	23.0000	0.842090
$747$	0	0
$748$	−12.0000	−0.438763
$749$	−65.0000	−2.37505
$750$	0	0
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	0	0
$753$	0	0
$754$	3.00000	0.109254
$755$	0	0
$756$	0	0
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	−33.0000	−1.19861
$759$	0	0
$760$	0	0
$761$	−11.0000	−0.398750	−0.199375	−	0.979923i	$-0.563891\pi$
$761$	−11.0000	−0.398750	−0.199375	+	0.979923i	$0.563891\pi$
$762$	0	0
$763$	95.0000	3.43923
$764$	−9.00000	−0.325609
$765$	0	0
$766$	−4.00000	−0.144526
$767$	9.00000	0.324971
$768$	0	0
$769$	−47.0000	−1.69486	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	−47.0000	−1.69486	−0.847432	+	0.530904i	$0.821852\pi$
$770$	0	0
$771$	0	0
$772$	−10.0000	−0.359908
$773$	−51.0000	−1.83434	−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000	−1.83434	−0.917171	+	0.398493i	$0.869533\pi$
$774$	0	0
$775$	0	0
$776$	2.00000	0.0717958
$777$	0	0
$778$	4.00000	0.143407
$779$	6.00000	0.214972
$780$	0	0
$781$	0	0
$782$	−21.0000	−0.750958
$783$	0	0
$784$	18.0000	0.642857
$785$	0	0
$786$	0	0
$787$	39.0000	1.39020	0.695100	−	0.718913i	$-0.255360\pi$
$787$	39.0000	1.39020	0.695100	+	0.718913i	$0.255360\pi$
$788$	−22.0000	−0.783718
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−12.0000	−0.426132
$794$	16.0000	0.567819
$795$	0	0
$796$	−15.0000	−0.531661
$797$	31.0000	1.09808	0.549038	−	0.835797i	$-0.314994\pi$
$797$	31.0000	1.09808	0.549038	+	0.835797i	$0.314994\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	6.00000	0.211867
$803$	−44.0000	−1.55273
$804$	0	0
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	0	0
$808$	8.00000	0.281439
$809$	−25.0000	−0.878953	−0.439477	−	0.898254i	$-0.644836\pi$
$809$	−25.0000	−0.878953	−0.439477	+	0.898254i	$0.644836\pi$
$810$	0	0
$811$	37.0000	1.29925	0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000	1.29925	0.649623	+	0.760257i	$0.274927\pi$
$812$	15.0000	0.526397
$813$	0	0
$814$	8.00000	0.280400
$815$	0	0
$816$	0	0
$817$	−6.00000	−0.209913
$818$	22.0000	0.769212
$819$	0	0
$820$	0	0
$821$	52.0000	1.81481	0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000	1.81481	0.907406	+	0.420255i	$0.138059\pi$
$822$	0	0
$823$	43.0000	1.49889	0.749443	−	0.662069i	$-0.230321\pi$
$823$	43.0000	1.49889	0.749443	+	0.662069i	$0.230321\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	45.0000	1.56575
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	0	0
$829$	35.0000	1.21560	0.607800	−	0.794090i	$-0.292052\pi$
$829$	35.0000	1.21560	0.607800	+	0.794090i	$0.292052\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	0.0346688
$833$	−54.0000	−1.87099
$834$	0	0
$835$	0	0
$836$	4.00000	0.138343
$837$	0	0
$838$	−14.0000	−0.483622
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	1.00000	0.0344623
$843$	0	0
$844$	−5.00000	−0.172107
$845$	0	0
$846$	0	0
$847$	25.0000	0.859010
$848$	−13.0000	−0.446422
$849$	0	0
$850$	0	0
$851$	14.0000	0.479914
$852$	0	0
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	−60.0000	−2.05316
$855$	0	0
$856$	−13.0000	−0.444331
$857$	−40.0000	−1.36637	−0.683187	−	0.730243i	$-0.739407\pi$
$857$	−40.0000	−1.36637	−0.683187	+	0.730243i	$0.739407\pi$
$858$	0	0
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	0	0
$861$	0	0
$862$	36.0000	1.22616
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	0	0
$865$	0	0
$866$	16.0000	0.543702
$867$	0	0
$868$	−10.0000	−0.339422
$869$	−8.00000	−0.271381
$870$	0	0
$871$	3.00000	0.101651
$872$	19.0000	0.643421
$873$	0	0
$874$	7.00000	0.236779
$875$	0	0
$876$	0	0
$877$	−33.0000	−1.11433	−0.557165	−	0.830402i	$-0.688111\pi$
$877$	−33.0000	−1.11433	−0.557165	+	0.830402i	$0.688111\pi$
$878$	26.0000	0.877457
$879$	0	0
$880$	0	0
$881$	−10.0000	−0.336909	−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000	−0.336909	−0.168454	+	0.985709i	$0.553878\pi$
$882$	0	0
$883$	−30.0000	−1.00958	−0.504790	−	0.863242i	$-0.668430\pi$
$883$	−30.0000	−1.00958	−0.504790	+	0.863242i	$0.668430\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	36.0000	1.20944
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	0	0
$889$	30.0000	1.00617
$890$	0	0
$891$	0	0
$892$	2.00000	0.0669650
$893$	0	0
$894$	0	0
$895$	0	0
$896$	5.00000	0.167038
$897$	0	0
$898$	22.0000	0.734150
$899$	−6.00000	−0.200111
$900$	0	0
$901$	39.0000	1.29928
$902$	24.0000	0.799113
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	1.00000	0.0332045	0.0166022	−	0.999862i	$-0.494715\pi$
$907$	1.00000	0.0332045	0.0166022	+	0.999862i	$0.494715\pi$
$908$	5.00000	0.165931
$909$	0	0
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	−40.0000	−1.32381
$914$	29.0000	0.959235
$915$	0	0
$916$	−6.00000	−0.198246
$917$	−80.0000	−2.64183
$918$	0	0
$919$	−5.00000	−0.164935	−0.0824674	−	0.996594i	$-0.526280\pi$
$919$	−5.00000	−0.164935	−0.0824674	+	0.996594i	$0.526280\pi$
$920$	0	0
$921$	0	0
$922$	−18.0000	−0.592798
$923$	0	0
$924$	0	0
$925$	0	0
$926$	8.00000	0.262896
$927$	0	0
$928$	3.00000	0.0984798
$929$	3.00000	0.0984268	0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000	0.0984268	0.0492134	+	0.998788i	$0.484329\pi$
$930$	0	0
$931$	18.0000	0.589926
$932$	10.0000	0.327561
$933$	0	0
$934$	−8.00000	−0.261768
$935$	0	0
$936$	0	0
$937$	−47.0000	−1.53542	−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000	−1.53542	−0.767712	+	0.640796i	$0.778605\pi$
$938$	15.0000	0.489767
$939$	0	0
$940$	0	0
$941$	51.0000	1.66255	0.831276	−	0.555860i	$-0.187611\pi$
$941$	51.0000	1.66255	0.831276	+	0.555860i	$0.187611\pi$
$942$	0	0
$943$	42.0000	1.36771
$944$	9.00000	0.292925
$945$	0	0
$946$	−24.0000	−0.780307
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	−11.0000	−0.357075
$950$	0	0
$951$	0	0
$952$	−15.0000	−0.486153
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	0	0
$956$	11.0000	0.355765
$957$	0	0
$958$	0	0
$959$	45.0000	1.45313
$960$	0	0
$961$	−27.0000	−0.870968
$962$	2.00000	0.0644826
$963$	0	0
$964$	−12.0000	−0.386494
$965$	0	0
$966$	0	0
$967$	44.0000	1.41494	0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000	1.41494	0.707472	+	0.706741i	$0.249835\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	0	0
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	0	0
$973$	80.0000	2.56468
$974$	38.0000	1.21760
$975$	0	0
$976$	−12.0000	−0.384111
$977$	−62.0000	−1.98356	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000	−1.98356	−0.991778	+	0.127971i	$0.959153\pi$
$978$	0	0
$979$	−8.00000	−0.255681
$980$	0	0
$981$	0	0
$982$	−18.0000	−0.574403
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	0	0
$986$	−9.00000	−0.286618
$987$	0	0
$988$	1.00000	0.0318142
$989$	−42.0000	−1.33552
$990$	0	0
$991$	30.0000	0.952981	0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000	0.952981	0.476491	+	0.879180i	$0.341909\pi$
$992$	−2.00000	−0.0635001
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	42.0000	1.32949
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8550.2.a.bm.1.1		1
3.2	odd	2		950.2.a.c.1.1		1
5.4	even	2		1710.2.a.g.1.1		1
12.11	even	2		7600.2.a.a.1.1		1
15.2	even	4		950.2.b.a.799.1		2
15.8	even	4		950.2.b.a.799.2		2
15.14	odd	2		190.2.a.b.1.1	✓	1
60.59	even	2		1520.2.a.j.1.1		1
105.104	even	2		9310.2.a.u.1.1		1
120.29	odd	2		6080.2.a.x.1.1		1
120.59	even	2		6080.2.a.b.1.1		1
285.284	even	2		3610.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.b.1.1	✓	1	15.14	odd	2
950.2.a.c.1.1		1	3.2	odd	2
950.2.b.a.799.1		2	15.2	even	4
950.2.b.a.799.2		2	15.8	even	4
1520.2.a.j.1.1		1	60.59	even	2
1710.2.a.g.1.1		1	5.4	even	2
3610.2.a.e.1.1		1	285.284	even	2
6080.2.a.b.1.1		1	120.59	even	2
6080.2.a.x.1.1		1	120.29	odd	2
7600.2.a.a.1.1		1	12.11	even	2
8550.2.a.bm.1.1		1	1.1	even	1	trivial
9310.2.a.u.1.1		1	105.104	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:	\( N \)	\(=\)	\( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8550.a (trivial)

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