LMFDB - Embedded newform 4950.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4950,2,Mod(1,4950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4950, 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("4950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4950.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:	$39.5259490005$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 550)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} -1.00000 q^{11} +3.00000 q^{13} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{19} +1.00000 q^{22} -3.00000 q^{23} -3.00000 q^{26} -5.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -4.00000 q^{34} -12.0000 q^{37} +1.00000 q^{38} -8.00000 q^{41} -5.00000 q^{43} -1.00000 q^{44} +3.00000 q^{46} +8.00000 q^{47} -7.00000 q^{49} +3.00000 q^{52} +10.0000 q^{53} +5.00000 q^{58} -8.00000 q^{59} +10.0000 q^{61} +3.00000 q^{62} +1.00000 q^{64} +14.0000 q^{67} +4.00000 q^{68} +5.00000 q^{71} -4.00000 q^{73} +12.0000 q^{74} -1.00000 q^{76} -8.00000 q^{79} +8.00000 q^{82} +9.00000 q^{83} +5.00000 q^{86} +1.00000 q^{88} -3.00000 q^{89} -3.00000 q^{92} -8.00000 q^{94} +3.00000 q^{97} +7.00000 q^{98} +O(q^{100})$

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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	0	0
$22$	1.00000	0.213201
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	0	0
$26$	−3.00000	−0.588348
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	0	0
$36$	0	0
$37$	−12.0000	−1.97279	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−12.0000	−1.97279	−0.986394	+	0.164399i	$0.947432\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	0	0
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	3.00000	0.442326
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	3.00000	0.416025
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	5.00000	0.656532
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	3.00000	0.381000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	0	0
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	12.0000	1.39497
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	0	0
$82$	8.00000	0.883452
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	0	0
$85$	0	0
$86$	5.00000	0.539164
$87$	0	0
$88$	1.00000	0.106600
$89$	−3.00000	−0.317999	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000	−0.317999	−0.159000	+	0.987279i	$0.550827\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	0	0
$94$	−8.00000	−0.825137
$95$	0	0
$96$	0	0
$97$	3.00000	0.304604	0.152302	−	0.988334i	$-0.451331\pi$
$97$	3.00000	0.304604	0.152302	+	0.988334i	$0.451331\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	0	0
$101$	−17.0000	−1.69156	−0.845782	−	0.533529i	$-0.820865\pi$
$101$	−17.0000	−1.69156	−0.845782	+	0.533529i	$0.820865\pi$
$102$	0	0
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−10.0000	−0.971286
$107$	−17.0000	−1.64345	−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000	−1.64345	−0.821726	+	0.569883i	$0.806989\pi$
$108$	0	0
$109$	−13.0000	−1.24517	−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000	−1.24517	−0.622587	+	0.782551i	$0.713918\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	0	0
$116$	−5.00000	−0.464238
$117$	0	0
$118$	8.00000	0.736460
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−10.0000	−0.905357
$123$	0	0
$124$	−3.00000	−0.269408
$125$	0	0
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	13.0000	1.13582	0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000	1.13582	0.567908	+	0.823092i	$0.307753\pi$
$132$	0	0
$133$	0	0
$134$	−14.0000	−1.20942
$135$	0	0
$136$	−4.00000	−0.342997
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	0	0
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	0	0
$141$	0	0
$142$	−5.00000	−0.419591
$143$	−3.00000	−0.250873
$144$	0	0
$145$	0	0
$146$	4.00000	0.331042
$147$	0	0
$148$	−12.0000	−0.986394
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	0	0
$155$	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	$0.576959\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−8.00000	−0.624695
$165$	0	0
$166$	−9.00000	−0.698535
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	−5.00000	−0.381246
$173$	13.0000	0.988372	0.494186	−	0.869356i	$-0.335466\pi$
$173$	13.0000	0.988372	0.494186	+	0.869356i	$0.335466\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	3.00000	0.224860
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	0	0
$183$	0	0
$184$	3.00000	0.221163
$185$	0	0
$186$	0	0
$187$	−4.00000	−0.292509
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	0	0
$193$	−20.0000	−1.43963	−0.719816	−	0.694165i	$-0.755774\pi$
$193$	−20.0000	−1.43963	−0.719816	+	0.694165i	$0.755774\pi$
$194$	−3.00000	−0.215387
$195$	0	0
$196$	−7.00000	−0.500000
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	0	0
$199$	−13.0000	−0.921546	−0.460773	−	0.887518i	$-0.652428\pi$
$199$	−13.0000	−0.921546	−0.460773	+	0.887518i	$0.652428\pi$
$200$	0	0
$201$	0	0
$202$	17.0000	1.19612
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−1.00000	−0.0696733
$207$	0	0
$208$	3.00000	0.208013
$209$	1.00000	0.0691714
$210$	0	0
$211$	28.0000	1.92760	0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000	1.92760	0.963800	+	0.266627i	$0.0859092\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	17.0000	1.16210
$215$	0	0
$216$	0	0
$217$	0	0
$218$	13.0000	0.880471
$219$	0	0
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	0	0
$225$	0	0
$226$	2.00000	0.133038
$227$	−19.0000	−1.26107	−0.630537	−	0.776159i	$-0.717165\pi$
$227$	−19.0000	−1.26107	−0.630537	+	0.776159i	$0.717165\pi$
$228$	0	0
$229$	−26.0000	−1.71813	−0.859064	−	0.511868i	$-0.828954\pi$
$229$	−26.0000	−1.71813	−0.859064	+	0.511868i	$0.828954\pi$
$230$	0	0
$231$	0	0
$232$	5.00000	0.328266
$233$	−30.0000	−1.96537	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−30.0000	−1.96537	−0.982683	+	0.185296i	$0.940675\pi$
$234$	0	0
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0	0
$238$	0	0
$239$	−22.0000	−1.42306	−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000	−1.42306	−0.711531	+	0.702655i	$0.751998\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	−3.00000	−0.190885
$248$	3.00000	0.190500
$249$	0	0
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	0	0
$253$	3.00000	0.188608
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	−13.0000	−0.803143
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	14.0000	0.855186
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	0	0
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	3.00000	0.181237
$275$	0	0
$276$	0	0
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	−13.0000	−0.779688
$279$	0	0
$280$	0	0
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	5.00000	0.296695
$285$	0	0
$286$	3.00000	0.177394
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−4.00000	−0.234082
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	12.0000	0.697486
$297$	0	0
$298$	6.00000	0.347571
$299$	−9.00000	−0.520483
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−27.0000	−1.53103	−0.765515	−	0.643418i	$-0.777516\pi$
$311$	−27.0000	−1.53103	−0.765515	+	0.643418i	$0.777516\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−32.0000	−1.79730	−0.898650	−	0.438667i	$-0.855451\pi$
$317$	−32.0000	−1.79730	−0.898650	+	0.438667i	$0.855451\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−4.00000	−0.222566
$324$	0	0
$325$	0	0
$326$	−4.00000	−0.221540
$327$	0	0
$328$	8.00000	0.441726
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	9.00000	0.493939
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	10.0000	0.544735	0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000	0.544735	0.272367	+	0.962193i	$0.412193\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	0	0
$341$	3.00000	0.162459
$342$	0	0
$343$	0	0
$344$	5.00000	0.269582
$345$	0	0
$346$	−13.0000	−0.698884
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	21.0000	1.12410	0.562052	−	0.827102i	$-0.310012\pi$
$349$	21.0000	1.12410	0.562052	+	0.827102i	$0.310012\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	17.0000	0.904819	0.452409	−	0.891810i	$-0.350565\pi$
$353$	17.0000	0.904819	0.452409	+	0.891810i	$0.350565\pi$
$354$	0	0
$355$	0	0
$356$	−3.00000	−0.159000
$357$	0	0
$358$	24.0000	1.26844
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	16.0000	0.840941
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.00000	0.0521996	0.0260998	−	0.999659i	$-0.491691\pi$
$367$	1.00000	0.0521996	0.0260998	+	0.999659i	$0.491691\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−8.00000	−0.412568
$377$	−15.0000	−0.772539
$378$	0	0
$379$	6.00000	0.308199	0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000	0.308199	0.154100	+	0.988055i	$0.450752\pi$
$380$	0	0
$381$	0	0
$382$	−9.00000	−0.460480
$383$	−13.0000	−0.664269	−0.332134	−	0.943232i	$-0.607769\pi$
$383$	−13.0000	−0.664269	−0.332134	+	0.943232i	$0.607769\pi$
$384$	0	0
$385$	0	0
$386$	20.0000	1.01797
$387$	0	0
$388$	3.00000	0.152302
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	0	0
$391$	−12.0000	−0.606866
$392$	7.00000	0.353553
$393$	0	0
$394$	−3.00000	−0.151138
$395$	0	0
$396$	0	0
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	13.0000	0.651631
$399$	0	0
$400$	0	0
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	0	0
$403$	−9.00000	−0.448322
$404$	−17.0000	−0.845782
$405$	0	0
$406$	0	0
$407$	12.0000	0.594818
$408$	0	0
$409$	−8.00000	−0.395575	−0.197787	−	0.980245i	$-0.563376\pi$
$409$	−8.00000	−0.395575	−0.197787	+	0.980245i	$0.563376\pi$
$410$	0	0
$411$	0	0
$412$	1.00000	0.0492665
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−3.00000	−0.147087
$417$	0	0
$418$	−1.00000	−0.0489116
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−28.0000	−1.36302
$423$	0	0
$424$	−10.0000	−0.485643
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−17.0000	−0.821726
$429$	0	0
$430$	0	0
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	0	0
$433$	11.0000	0.528626	0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000	0.528626	0.264313	+	0.964437i	$0.414855\pi$
$434$	0	0
$435$	0	0
$436$	−13.0000	−0.622587
$437$	3.00000	0.143509
$438$	0	0
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	0	0
$441$	0	0
$442$	−12.0000	−0.570782
$443$	−16.0000	−0.760183	−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000	−0.760183	−0.380091	+	0.924949i	$0.624107\pi$
$444$	0	0
$445$	0	0
$446$	−24.0000	−1.13643
$447$	0	0
$448$	0	0
$449$	27.0000	1.27421	0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000	1.27421	0.637104	+	0.770778i	$0.280132\pi$
$450$	0	0
$451$	8.00000	0.376705
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	19.0000	0.891714
$455$	0	0
$456$	0	0
$457$	−12.0000	−0.561336	−0.280668	−	0.959805i	$-0.590556\pi$
$457$	−12.0000	−0.561336	−0.280668	+	0.959805i	$0.590556\pi$
$458$	26.0000	1.21490
$459$	0	0
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−29.0000	−1.34774	−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000	−1.34774	−0.673872	+	0.738848i	$0.735370\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	30.0000	1.38972
$467$	−14.0000	−0.647843	−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000	−0.647843	−0.323921	+	0.946084i	$0.605001\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	8.00000	0.368230
$473$	5.00000	0.229900
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	22.0000	1.00626
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	−36.0000	−1.64146
$482$	−18.0000	−0.819878
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	0	0
$487$	−3.00000	−0.135943	−0.0679715	−	0.997687i	$-0.521653\pi$
$487$	−3.00000	−0.135943	−0.0679715	+	0.997687i	$0.521653\pi$
$488$	−10.0000	−0.452679
$489$	0	0
$490$	0	0
$491$	9.00000	0.406164	0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000	0.406164	0.203082	+	0.979162i	$0.434904\pi$
$492$	0	0
$493$	−20.0000	−0.900755
$494$	3.00000	0.134976
$495$	0	0
$496$	−3.00000	−0.134704
$497$	0	0
$498$	0	0
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	0	0
$501$	0	0
$502$	20.0000	0.892644
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	0	0
$506$	−3.00000	−0.133366
$507$	0	0
$508$	−4.00000	−0.177471
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	7.00000	0.308757
$515$	0	0
$516$	0	0
$517$	−8.00000	−0.351840
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−7.00000	−0.306676	−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000	−0.306676	−0.153338	+	0.988174i	$0.549002\pi$
$522$	0	0
$523$	−19.0000	−0.830812	−0.415406	−	0.909636i	$-0.636360\pi$
$523$	−19.0000	−0.830812	−0.415406	+	0.909636i	$0.636360\pi$
$524$	13.0000	0.567908
$525$	0	0
$526$	−12.0000	−0.523225
$527$	−12.0000	−0.522728
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−24.0000	−1.03956
$534$	0	0
$535$	0	0
$536$	−14.0000	−0.604708
$537$	0	0
$538$	−2.00000	−0.0862261
$539$	7.00000	0.301511
$540$	0	0
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	−22.0000	−0.944981
$543$	0	0
$544$	−4.00000	−0.171499
$545$	0	0
$546$	0	0
$547$	−31.0000	−1.32546	−0.662732	−	0.748857i	$-0.730603\pi$
$547$	−31.0000	−1.32546	−0.662732	+	0.748857i	$0.730603\pi$
$548$	−3.00000	−0.128154
$549$	0	0
$550$	0	0
$551$	5.00000	0.213007
$552$	0	0
$553$	0	0
$554$	18.0000	0.764747
$555$	0	0
$556$	13.0000	0.551323
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	0	0
$559$	−15.0000	−0.634432
$560$	0	0
$561$	0	0
$562$	12.0000	0.506189
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	0	0
$565$	0	0
$566$	−12.0000	−0.504398
$567$	0	0
$568$	−5.00000	−0.209795
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	−33.0000	−1.38101	−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000	−1.38101	−0.690504	+	0.723329i	$0.742611\pi$
$572$	−3.00000	−0.125436
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	26.0000	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−10.0000	−0.414158
$584$	4.00000	0.165521
$585$	0	0
$586$	−6.00000	−0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	3.00000	0.123613
$590$	0	0
$591$	0	0
$592$	−12.0000	−0.493197
$593$	−2.00000	−0.0821302	−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000	−0.0821302	−0.0410651	+	0.999156i	$0.513075\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	9.00000	0.368037
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	36.0000	1.46847	0.734235	−	0.678895i	$-0.237541\pi$
$601$	36.0000	1.46847	0.734235	+	0.678895i	$0.237541\pi$
$602$	0	0
$603$	0	0
$604$	8.00000	0.325515
$605$	0	0
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	24.0000	0.970936
$612$	0	0
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	0	0
$617$	19.0000	0.764911	0.382456	−	0.923974i	$-0.375078\pi$
$617$	19.0000	0.764911	0.382456	+	0.923974i	$0.375078\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	27.0000	1.08260
$623$	0	0
$624$	0	0
$625$	0	0
$626$	6.00000	0.239808
$627$	0	0
$628$	−6.00000	−0.239426
$629$	−48.0000	−1.91389
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	32.0000	1.27088
$635$	0	0
$636$	0	0
$637$	−21.0000	−0.832050
$638$	−5.00000	−0.197952
$639$	0	0
$640$	0	0
$641$	3.00000	0.118493	0.0592464	−	0.998243i	$-0.481130\pi$
$641$	3.00000	0.118493	0.0592464	+	0.998243i	$0.481130\pi$
$642$	0	0
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	0	0
$646$	4.00000	0.157378
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	8.00000	0.314027
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	0	0
$655$	0	0
$656$	−8.00000	−0.312348
$657$	0	0
$658$	0	0
$659$	27.0000	1.05177	0.525885	−	0.850555i	$-0.323734\pi$
$659$	27.0000	1.05177	0.525885	+	0.850555i	$0.323734\pi$
$660$	0	0
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	28.0000	1.08825
$663$	0	0
$664$	−9.00000	−0.349268
$665$	0	0
$666$	0	0
$667$	15.0000	0.580802
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−10.0000	−0.386046
$672$	0	0
$673$	20.0000	0.770943	0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000	0.770943	0.385472	+	0.922720i	$0.374039\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	−4.00000	−0.153846
$677$	41.0000	1.57576	0.787879	−	0.615830i	$-0.211179\pi$
$677$	41.0000	1.57576	0.787879	+	0.615830i	$0.211179\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	−3.00000	−0.114876
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−5.00000	−0.190623
$689$	30.0000	1.14291
$690$	0	0
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	13.0000	0.494186
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	−32.0000	−1.21209
$698$	−21.0000	−0.794862
$699$	0	0
$700$	0	0
$701$	29.0000	1.09531	0.547657	−	0.836703i	$-0.315520\pi$
$701$	29.0000	1.09531	0.547657	+	0.836703i	$0.315520\pi$
$702$	0	0
$703$	12.0000	0.452589
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−17.0000	−0.639803
$707$	0	0
$708$	0	0
$709$	44.0000	1.65245	0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000	1.65245	0.826227	+	0.563337i	$0.190483\pi$
$710$	0	0
$711$	0	0
$712$	3.00000	0.112430
$713$	9.00000	0.337053
$714$	0	0
$715$	0	0
$716$	−24.0000	−0.896922
$717$	0	0
$718$	−8.00000	−0.298557
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	0	0
$721$	0	0
$722$	18.0000	0.669891
$723$	0	0
$724$	−16.0000	−0.594635
$725$	0	0
$726$	0	0
$727$	5.00000	0.185440	0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000	0.185440	0.0927199	+	0.995692i	$0.470444\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−20.0000	−0.739727
$732$	0	0
$733$	−45.0000	−1.66211	−0.831056	−	0.556188i	$-0.812263\pi$
$733$	−45.0000	−1.66211	−0.831056	+	0.556188i	$0.812263\pi$
$734$	−1.00000	−0.0369107
$735$	0	0
$736$	3.00000	0.110581
$737$	−14.0000	−0.515697
$738$	0	0
$739$	−32.0000	−1.17714	−0.588570	−	0.808447i	$-0.700309\pi$
$739$	−32.0000	−1.17714	−0.588570	+	0.808447i	$0.700309\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	0	0
$745$	0	0
$746$	−6.00000	−0.219676
$747$	0	0
$748$	−4.00000	−0.146254
$749$	0	0
$750$	0	0
$751$	−25.0000	−0.912263	−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000	−0.912263	−0.456131	+	0.889912i	$0.650765\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	15.0000	0.546268
$755$	0	0
$756$	0	0
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	−6.00000	−0.217930
$759$	0	0
$760$	0	0
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	0	0
$763$	0	0
$764$	9.00000	0.325609
$765$	0	0
$766$	13.0000	0.469709
$767$	−24.0000	−0.866590
$768$	0	0
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	0	0
$771$	0	0
$772$	−20.0000	−0.719816
$773$	−28.0000	−1.00709	−0.503545	−	0.863969i	$-0.667971\pi$
$773$	−28.0000	−1.00709	−0.503545	+	0.863969i	$0.667971\pi$
$774$	0	0
$775$	0	0
$776$	−3.00000	−0.107694
$777$	0	0
$778$	24.0000	0.860442
$779$	8.00000	0.286630
$780$	0	0
$781$	−5.00000	−0.178914
$782$	12.0000	0.429119
$783$	0	0
$784$	−7.00000	−0.250000
$785$	0	0
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	3.00000	0.106871
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	30.0000	1.06533
$794$	38.0000	1.34857
$795$	0	0
$796$	−13.0000	−0.460773
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	32.0000	1.13208
$800$	0	0
$801$	0	0
$802$	−25.0000	−0.882781
$803$	4.00000	0.141157
$804$	0	0
$805$	0	0
$806$	9.00000	0.317011
$807$	0	0
$808$	17.0000	0.598058
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	0	0
$813$	0	0
$814$	−12.0000	−0.420600
$815$	0	0
$816$	0	0
$817$	5.00000	0.174928
$818$	8.00000	0.279713
$819$	0	0
$820$	0	0
$821$	−33.0000	−1.15171	−0.575854	−	0.817553i	$-0.695330\pi$
$821$	−33.0000	−1.15171	−0.575854	+	0.817553i	$0.695330\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−1.00000	−0.0348367
$825$	0	0
$826$	0	0
$827$	−11.0000	−0.382507	−0.191254	−	0.981541i	$-0.561255\pi$
$827$	−11.0000	−0.382507	−0.191254	+	0.981541i	$0.561255\pi$
$828$	0	0
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	0	0
$831$	0	0
$832$	3.00000	0.104006
$833$	−28.0000	−0.970143
$834$	0	0
$835$	0	0
$836$	1.00000	0.0345857
$837$	0	0
$838$	30.0000	1.03633
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−2.00000	−0.0689246
$843$	0	0
$844$	28.0000	0.963800
$845$	0	0
$846$	0	0
$847$	0	0
$848$	10.0000	0.343401
$849$	0	0
$850$	0	0
$851$	36.0000	1.23406
$852$	0	0
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	0	0
$855$	0	0
$856$	17.0000	0.581048
$857$	4.00000	0.136637	0.0683187	−	0.997664i	$-0.478237\pi$
$857$	4.00000	0.136637	0.0683187	+	0.997664i	$0.478237\pi$
$858$	0	0
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	0	0
$861$	0	0
$862$	−8.00000	−0.272481
$863$	−9.00000	−0.306364	−0.153182	−	0.988198i	$-0.548952\pi$
$863$	−9.00000	−0.306364	−0.153182	+	0.988198i	$0.548952\pi$
$864$	0	0
$865$	0	0
$866$	−11.0000	−0.373795
$867$	0	0
$868$	0	0
$869$	8.00000	0.271381
$870$	0	0
$871$	42.0000	1.42312
$872$	13.0000	0.440236
$873$	0	0
$874$	−3.00000	−0.101477
$875$	0	0
$876$	0	0
$877$	17.0000	0.574049	0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000	0.574049	0.287025	+	0.957923i	$0.407334\pi$
$878$	4.00000	0.134993
$879$	0	0
$880$	0	0
$881$	−53.0000	−1.78562	−0.892808	−	0.450438i	$-0.851268\pi$
$881$	−53.0000	−1.78562	−0.892808	+	0.450438i	$0.851268\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	16.0000	0.537531
$887$	46.0000	1.54453	0.772264	−	0.635301i	$-0.219124\pi$
$887$	46.0000	1.54453	0.772264	+	0.635301i	$0.219124\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	24.0000	0.803579
$893$	−8.00000	−0.267710
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−27.0000	−0.901002
$899$	15.0000	0.500278
$900$	0	0
$901$	40.0000	1.33259
$902$	−8.00000	−0.266371
$903$	0	0
$904$	2.00000	0.0665190
$905$	0	0
$906$	0	0
$907$	30.0000	0.996134	0.498067	−	0.867139i	$-0.334043\pi$
$907$	30.0000	0.996134	0.498067	+	0.867139i	$0.334043\pi$
$908$	−19.0000	−0.630537
$909$	0	0
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	0	0
$913$	−9.00000	−0.297857
$914$	12.0000	0.396925
$915$	0	0
$916$	−26.0000	−0.859064
$917$	0	0
$918$	0	0
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	0	0
$921$	0	0
$922$	−18.0000	−0.592798
$923$	15.0000	0.493731
$924$	0	0
$925$	0	0
$926$	29.0000	0.952999
$927$	0	0
$928$	5.00000	0.164133
$929$	25.0000	0.820223	0.410112	−	0.912035i	$-0.365490\pi$
$929$	25.0000	0.820223	0.410112	+	0.912035i	$0.365490\pi$
$930$	0	0
$931$	7.00000	0.229416
$932$	−30.0000	−0.982683
$933$	0	0
$934$	14.0000	0.458094
$935$	0	0
$936$	0	0
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	0	0
$943$	24.0000	0.781548
$944$	−8.00000	−0.260378
$945$	0	0
$946$	−5.00000	−0.162564
$947$	42.0000	1.36482	0.682408	−	0.730971i	$-0.260933\pi$
$947$	42.0000	1.36482	0.682408	+	0.730971i	$0.260933\pi$
$948$	0	0
$949$	−12.0000	−0.389536
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	0	0
$955$	0	0
$956$	−22.0000	−0.711531
$957$	0	0
$958$	6.00000	0.193851
$959$	0	0
$960$	0	0
$961$	−22.0000	−0.709677
$962$	36.0000	1.16069
$963$	0	0
$964$	18.0000	0.579741
$965$	0	0
$966$	0	0
$967$	54.0000	1.73652	0.868261	−	0.496107i	$-0.165238\pi$
$967$	54.0000	1.73652	0.868261	+	0.496107i	$0.165238\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	0	0
$971$	30.0000	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$972$	0	0
$973$	0	0
$974$	3.00000	0.0961262
$975$	0	0
$976$	10.0000	0.320092
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	3.00000	0.0958804
$980$	0	0
$981$	0	0
$982$	−9.00000	−0.287202
$983$	57.0000	1.81802	0.909009	−	0.416777i	$-0.136840\pi$
$983$	57.0000	1.81802	0.909009	+	0.416777i	$0.136840\pi$
$984$	0	0
$985$	0	0
$986$	20.0000	0.636930
$987$	0	0
$988$	−3.00000	−0.0954427
$989$	15.0000	0.476972
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	3.00000	0.0952501
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	10.0000	0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4950.2.a.l.1.1		1
3.2	odd	2		550.2.a.l.1.1	yes	1
5.2	odd	4		4950.2.c.i.199.1		2
5.3	odd	4		4950.2.c.i.199.2		2
5.4	even	2		4950.2.a.bh.1.1		1
12.11	even	2		4400.2.a.g.1.1		1
15.2	even	4		550.2.b.e.199.2		2
15.8	even	4		550.2.b.e.199.1		2
15.14	odd	2		550.2.a.b.1.1	✓	1
33.32	even	2		6050.2.a.p.1.1		1
60.23	odd	4		4400.2.b.d.4049.1		2
60.47	odd	4		4400.2.b.d.4049.2		2
60.59	even	2		4400.2.a.y.1.1		1
165.164	even	2		6050.2.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.a.b.1.1	✓	1	15.14	odd	2
550.2.a.l.1.1	yes	1	3.2	odd	2
550.2.b.e.199.1		2	15.8	even	4
550.2.b.e.199.2		2	15.2	even	4
4400.2.a.g.1.1		1	12.11	even	2
4400.2.a.y.1.1		1	60.59	even	2
4400.2.b.d.4049.1		2	60.23	odd	4
4400.2.b.d.4049.2		2	60.47	odd	4
4950.2.a.l.1.1		1	1.1	even	1	trivial
4950.2.a.bh.1.1		1	5.4	even	2
4950.2.c.i.199.1		2	5.2	odd	4
4950.2.c.i.199.2		2	5.3	odd	4
6050.2.a.p.1.1		1	33.32	even	2
6050.2.a.y.1.1		1	165.164	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:	\( N \)	\(=\)	\( 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4950.a (trivial)

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