LMFDB - Embedded newform 1150.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{11} -3.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -8.00000 q^{17} -3.00000 q^{18} -7.00000 q^{19} -3.00000 q^{22} -1.00000 q^{23} -3.00000 q^{26} -1.00000 q^{28} +7.00000 q^{29} +10.0000 q^{31} +1.00000 q^{32} -8.00000 q^{34} -3.00000 q^{36} +4.00000 q^{37} -7.00000 q^{38} +11.0000 q^{41} +5.00000 q^{43} -3.00000 q^{44} -1.00000 q^{46} -10.0000 q^{47} -6.00000 q^{49} -3.00000 q^{52} -6.00000 q^{53} -1.00000 q^{56} +7.00000 q^{58} -8.00000 q^{59} -8.00000 q^{61} +10.0000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -8.00000 q^{68} +10.0000 q^{71} -3.00000 q^{72} -11.0000 q^{73} +4.00000 q^{74} -7.00000 q^{76} +3.00000 q^{77} +3.00000 q^{79} +9.00000 q^{81} +11.0000 q^{82} +1.00000 q^{83} +5.00000 q^{86} -3.00000 q^{88} -6.00000 q^{89} +3.00000 q^{91} -1.00000 q^{92} -10.0000 q^{94} +14.0000 q^{97} -6.00000 q^{98} +9.00000 q^{99} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−8.00000	−1.94029	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−8.00000	−1.94029	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−3.00000	−0.707107
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0	0
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	0	0
$26$	−3.00000	−0.588348
$27$	0	0
$28$	−1.00000	−0.188982
$29$	7.00000	1.29987	0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000	1.29987	0.649934	+	0.759991i	$0.274797\pi$
$30$	0	0
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−8.00000	−1.37199
$35$	0	0
$36$	−3.00000	−0.500000
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−7.00000	−1.13555
$39$	0	0
$40$	0	0
$41$	11.0000	1.71791	0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000	1.71791	0.858956	+	0.512050i	$0.171114\pi$
$42$	0	0
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	−3.00000	−0.416025
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	7.00000	0.919145
$59$	−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
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	10.0000	1.27000
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−8.00000	−0.970143
$69$	0	0
$70$	0	0
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	−3.00000	−0.353553
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	−7.00000	−0.802955
$77$	3.00000	0.341882
$78$	0	0
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	11.0000	1.21475
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	0	0
$85$	0	0
$86$	5.00000	0.539164
$87$	0	0
$88$	−3.00000	−0.319801
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	3.00000	0.314485
$92$	−1.00000	−0.104257
$93$	0	0
$94$	−10.0000	−1.03142
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−6.00000	−0.606092
$99$	9.00000	0.904534
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	0	0
$109$	20.0000	1.91565	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000	1.91565	0.957826	+	0.287348i	$0.0927736\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	7.00000	0.649934
$117$	9.00000	0.832050
$118$	−8.00000	−0.736460
$119$	8.00000	0.733359
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−8.00000	−0.724286
$123$	0	0
$124$	10.0000	0.898027
$125$	0	0
$126$	3.00000	0.267261
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	7.00000	0.606977
$134$	0	0
$135$	0	0
$136$	−8.00000	−0.685994
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	10.0000	0.839181
$143$	9.00000	0.752618
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−11.0000	−0.910366
$147$	0	0
$148$	4.00000	0.328798
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−7.00000	−0.567775
$153$	24.0000	1.94029
$154$	3.00000	0.241747
$155$	0	0
$156$	0	0
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	3.00000	0.238667
$159$	0	0
$160$	0	0
$161$	1.00000	0.0788110
$162$	9.00000	0.707107
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	11.0000	0.858956
$165$	0	0
$166$	1.00000	0.0776151
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	21.0000	1.60591
$172$	5.00000	0.381246
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	0	0
$175$	0	0
$176$	−3.00000	−0.226134
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−4.00000	−0.297318	−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000	−0.297318	−0.148659	+	0.988889i	$0.547496\pi$
$182$	3.00000	0.222375
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	24.0000	1.75505
$188$	−10.0000	−0.729325
$189$	0	0
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	0	0
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−13.0000	−0.926212	−0.463106	−	0.886303i	$-0.653265\pi$
$197$	−13.0000	−0.926212	−0.463106	+	0.886303i	$0.653265\pi$
$198$	9.00000	0.639602
$199$	−9.00000	−0.637993	−0.318997	−	0.947756i	$-0.603346\pi$
$199$	−9.00000	−0.637993	−0.318997	+	0.947756i	$0.603346\pi$
$200$	0	0
$201$	0	0
$202$	10.0000	0.703598
$203$	−7.00000	−0.491304
$204$	0	0
$205$	0	0
$206$	−7.00000	−0.487713
$207$	3.00000	0.208514
$208$	−3.00000	−0.208013
$209$	21.0000	1.45260
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−20.0000	−1.36717
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	20.0000	1.35457
$219$	0	0
$220$	0	0
$221$	24.0000	1.61441
$222$	0	0
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	0	0
$231$	0	0
$232$	7.00000	0.459573
$233$	11.0000	0.720634	0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000	0.720634	0.360317	+	0.932830i	$0.382669\pi$
$234$	9.00000	0.588348
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0	0
$238$	8.00000	0.518563
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	−8.00000	−0.512148
$245$	0	0
$246$	0	0
$247$	21.0000	1.33620
$248$	10.0000	0.635001
$249$	0	0
$250$	0	0
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	3.00000	0.188982
$253$	3.00000	0.188608
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−21.0000	−1.29987
$262$	−18.0000	−1.11204
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	7.00000	0.429198
$267$	0	0
$268$	0	0
$269$	−9.00000	−0.548740	−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000	−0.548740	−0.274370	+	0.961624i	$0.588469\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−8.00000	−0.485071
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	19.0000	1.14160	0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000	1.14160	0.570800	+	0.821089i	$0.306633\pi$
$278$	−4.00000	−0.239904
$279$	−30.0000	−1.79605
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	10.0000	0.593391
$285$	0	0
$286$	9.00000	0.532181
$287$	−11.0000	−0.649309
$288$	−3.00000	−0.176777
$289$	47.0000	2.76471
$290$	0	0
$291$	0	0
$292$	−11.0000	−0.643726
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	0	0
$296$	4.00000	0.232495
$297$	0	0
$298$	6.00000	0.347571
$299$	3.00000	0.173494
$300$	0	0
$301$	−5.00000	−0.288195
$302$	2.00000	0.115087
$303$	0	0
$304$	−7.00000	−0.401478
$305$	0	0
$306$	24.0000	1.37199
$307$	−24.0000	−1.36975	−0.684876	−	0.728659i	$-0.740144\pi$
$307$	−24.0000	−1.36975	−0.684876	+	0.728659i	$0.740144\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	0	0
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	0	0
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	−2.00000	−0.112867
$315$	0	0
$316$	3.00000	0.168763
$317$	3.00000	0.168497	0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000	0.168497	0.0842484	+	0.996445i	$0.473151\pi$
$318$	0	0
$319$	−21.0000	−1.17577
$320$	0	0
$321$	0	0
$322$	1.00000	0.0557278
$323$	56.0000	3.11592
$324$	9.00000	0.500000
$325$	0	0
$326$	−2.00000	−0.110770
$327$	0	0
$328$	11.0000	0.607373
$329$	10.0000	0.551318
$330$	0	0
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	1.00000	0.0548821
$333$	−12.0000	−0.657596
$334$	14.0000	0.766046
$335$	0	0
$336$	0	0
$337$	30.0000	1.63420	0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000	1.63420	0.817102	+	0.576493i	$0.195579\pi$
$338$	−4.00000	−0.217571
$339$	0	0
$340$	0	0
$341$	−30.0000	−1.62459
$342$	21.0000	1.13555
$343$	13.0000	0.701934
$344$	5.00000	0.269582
$345$	0	0
$346$	11.0000	0.591364
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	11.0000	0.588817	0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000	0.588817	0.294408	+	0.955680i	$0.404877\pi$
$350$	0	0
$351$	0	0
$352$	−3.00000	−0.159901
$353$	−27.0000	−1.43706	−0.718532	−	0.695493i	$-0.755186\pi$
$353$	−27.0000	−1.43706	−0.718532	+	0.695493i	$0.755186\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−6.00000	−0.317110
$359$	−17.0000	−0.897226	−0.448613	−	0.893726i	$-0.648082\pi$
$359$	−17.0000	−0.897226	−0.448613	+	0.893726i	$0.648082\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−4.00000	−0.210235
$363$	0	0
$364$	3.00000	0.157243
$365$	0	0
$366$	0	0
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	−1.00000	−0.0521286
$369$	−33.0000	−1.71791
$370$	0	0
$371$	6.00000	0.311504
$372$	0	0
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	−10.0000	−0.515711
$377$	−21.0000	−1.08156
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	0	0
$382$	−15.0000	−0.767467
$383$	−21.0000	−1.07305	−0.536525	−	0.843884i	$-0.680263\pi$
$383$	−21.0000	−1.07305	−0.536525	+	0.843884i	$0.680263\pi$
$384$	0	0
$385$	0	0
$386$	−6.00000	−0.305392
$387$	−15.0000	−0.762493
$388$	14.0000	0.710742
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	−6.00000	−0.303046
$393$	0	0
$394$	−13.0000	−0.654931
$395$	0	0
$396$	9.00000	0.452267
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	−9.00000	−0.451129
$399$	0	0
$400$	0	0
$401$	−8.00000	−0.399501	−0.199750	−	0.979847i	$-0.564013\pi$
$401$	−8.00000	−0.399501	−0.199750	+	0.979847i	$0.564013\pi$
$402$	0	0
$403$	−30.0000	−1.49441
$404$	10.0000	0.497519
$405$	0	0
$406$	−7.00000	−0.347404
$407$	−12.0000	−0.594818
$408$	0	0
$409$	9.00000	0.445021	0.222511	−	0.974930i	$-0.428575\pi$
$409$	9.00000	0.445021	0.222511	+	0.974930i	$0.428575\pi$
$410$	0	0
$411$	0	0
$412$	−7.00000	−0.344865
$413$	8.00000	0.393654
$414$	3.00000	0.147442
$415$	0	0
$416$	−3.00000	−0.147087
$417$	0	0
$418$	21.0000	1.02714
$419$	27.0000	1.31904	0.659518	−	0.751689i	$-0.270760\pi$
$419$	27.0000	1.31904	0.659518	+	0.751689i	$0.270760\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−10.0000	−0.486792
$423$	30.0000	1.45865
$424$	−6.00000	−0.291386
$425$	0	0
$426$	0	0
$427$	8.00000	0.387147
$428$	−20.0000	−0.966736
$429$	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
$433$	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
$436$	20.0000	0.957826
$437$	7.00000	0.334855
$438$	0	0
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	24.0000	1.14156
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	0	0
$445$	0	0
$446$	6.00000	0.284108
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	0	0
$451$	−33.0000	−1.55391
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−4.00000	−0.187729
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	18.0000	0.841085
$459$	0	0
$460$	0	0
$461$	3.00000	0.139724	0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000	0.139724	0.0698620	+	0.997557i	$0.477744\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	7.00000	0.324967
$465$	0	0
$466$	11.0000	0.509565
$467$	−13.0000	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$468$	9.00000	0.416025
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−8.00000	−0.368230
$473$	−15.0000	−0.689701
$474$	0	0
$475$	0	0
$476$	8.00000	0.366679
$477$	18.0000	0.824163
$478$	6.00000	0.274434
$479$	17.0000	0.776750	0.388375	−	0.921501i	$-0.373037\pi$
$479$	17.0000	0.776750	0.388375	+	0.921501i	$0.373037\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	2.00000	0.0910975
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	−8.00000	−0.362143
$489$	0	0
$490$	0	0
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	0	0
$493$	−56.0000	−2.52211
$494$	21.0000	0.944835
$495$	0	0
$496$	10.0000	0.449013
$497$	−10.0000	−0.448561
$498$	0	0
$499$	6.00000	0.268597	0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000	0.268597	0.134298	+	0.990941i	$0.457122\pi$
$500$	0	0
$501$	0	0
$502$	−16.0000	−0.714115
$503$	−27.0000	−1.20387	−0.601935	−	0.798545i	$-0.705603\pi$
$503$	−27.0000	−1.20387	−0.601935	+	0.798545i	$0.705603\pi$
$504$	3.00000	0.133631
$505$	0	0
$506$	3.00000	0.133366
$507$	0	0
$508$	−16.0000	−0.709885
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0	0
$511$	11.0000	0.486611
$512$	1.00000	0.0441942
$513$	0	0
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	0	0
$517$	30.0000	1.31940
$518$	−4.00000	−0.175750
$519$	0	0
$520$	0	0
$521$	−32.0000	−1.40195	−0.700973	−	0.713188i	$-0.747251\pi$
$521$	−32.0000	−1.40195	−0.700973	+	0.713188i	$0.747251\pi$
$522$	−21.0000	−0.919145
$523$	−1.00000	−0.0437269	−0.0218635	−	0.999761i	$-0.506960\pi$
$523$	−1.00000	−0.0437269	−0.0218635	+	0.999761i	$0.506960\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	16.0000	0.697633
$527$	−80.0000	−3.48485
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	24.0000	1.04151
$532$	7.00000	0.303488
$533$	−33.0000	−1.42939
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	−9.00000	−0.388018
$539$	18.0000	0.775315
$540$	0	0
$541$	19.0000	0.816874	0.408437	−	0.912787i	$-0.366074\pi$
$541$	19.0000	0.816874	0.408437	+	0.912787i	$0.366074\pi$
$542$	−2.00000	−0.0859074
$543$	0	0
$544$	−8.00000	−0.342997
$545$	0	0
$546$	0	0
$547$	26.0000	1.11168	0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000	1.11168	0.555840	+	0.831289i	$0.312397\pi$
$548$	−6.00000	−0.256307
$549$	24.0000	1.02430
$550$	0	0
$551$	−49.0000	−2.08747
$552$	0	0
$553$	−3.00000	−0.127573
$554$	19.0000	0.807233
$555$	0	0
$556$	−4.00000	−0.169638
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	−30.0000	−1.27000
$559$	−15.0000	−0.634432
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	0	0
$565$	0	0
$566$	24.0000	1.00880
$567$	−9.00000	−0.377964
$568$	10.0000	0.419591
$569$	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
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	9.00000	0.376309
$573$	0	0
$574$	−11.0000	−0.459131
$575$	0	0
$576$	−3.00000	−0.125000
$577$	25.0000	1.04076	0.520382	−	0.853934i	$-0.325790\pi$
$577$	25.0000	1.04076	0.520382	+	0.853934i	$0.325790\pi$
$578$	47.0000	1.95494
$579$	0	0
$580$	0	0
$581$	−1.00000	−0.0414870
$582$	0	0
$583$	18.0000	0.745484
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−24.0000	−0.991431
$587$	−32.0000	−1.32078	−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000	−1.32078	−0.660391	+	0.750922i	$0.729609\pi$
$588$	0	0
$589$	−70.0000	−2.88430
$590$	0	0
$591$	0	0
$592$	4.00000	0.164399
$593$	−1.00000	−0.0410651	−0.0205325	−	0.999789i	$-0.506536\pi$
$593$	−1.00000	−0.0410651	−0.0205325	+	0.999789i	$0.506536\pi$
$594$	0	0
$595$	0	0
$596$	6.00000	0.245770
$597$	0	0
$598$	3.00000	0.122679
$599$	−14.0000	−0.572024	−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000	−0.572024	−0.286012	+	0.958226i	$0.592330\pi$
$600$	0	0
$601$	34.0000	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$602$	−5.00000	−0.203785
$603$	0	0
$604$	2.00000	0.0813788
$605$	0	0
$606$	0	0
$607$	38.0000	1.54237	0.771186	−	0.636610i	$-0.219664\pi$
$607$	38.0000	1.54237	0.771186	+	0.636610i	$0.219664\pi$
$608$	−7.00000	−0.283887
$609$	0	0
$610$	0	0
$611$	30.0000	1.21367
$612$	24.0000	0.970143
$613$	−4.00000	−0.161558	−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000	−0.161558	−0.0807792	+	0.996732i	$0.525741\pi$
$614$	−24.0000	−0.968561
$615$	0	0
$616$	3.00000	0.120873
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	0	0
$619$	−44.0000	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$620$	0	0
$621$	0	0
$622$	−28.0000	−1.12270
$623$	6.00000	0.240385
$624$	0	0
$625$	0	0
$626$	28.0000	1.11911
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	−32.0000	−1.27592
$630$	0	0
$631$	−15.0000	−0.597141	−0.298570	−	0.954388i	$-0.596510\pi$
$631$	−15.0000	−0.597141	−0.298570	+	0.954388i	$0.596510\pi$
$632$	3.00000	0.119334
$633$	0	0
$634$	3.00000	0.119145
$635$	0	0
$636$	0	0
$637$	18.0000	0.713186
$638$	−21.0000	−0.831398
$639$	−30.0000	−1.18678
$640$	0	0
$641$	24.0000	0.947943	0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000	0.947943	0.473972	+	0.880540i	$0.342820\pi$
$642$	0	0
$643$	−35.0000	−1.38027	−0.690133	−	0.723683i	$-0.742448\pi$
$643$	−35.0000	−1.38027	−0.690133	+	0.723683i	$0.742448\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	56.0000	2.20329
$647$	−10.0000	−0.393141	−0.196570	−	0.980490i	$-0.562980\pi$
$647$	−10.0000	−0.393141	−0.196570	+	0.980490i	$0.562980\pi$
$648$	9.00000	0.353553
$649$	24.0000	0.942082
$650$	0	0
$651$	0	0
$652$	−2.00000	−0.0783260
$653$	−23.0000	−0.900060	−0.450030	−	0.893014i	$-0.648587\pi$
$653$	−23.0000	−0.900060	−0.450030	+	0.893014i	$0.648587\pi$
$654$	0	0
$655$	0	0
$656$	11.0000	0.429478
$657$	33.0000	1.28745
$658$	10.0000	0.389841
$659$	−25.0000	−0.973862	−0.486931	−	0.873441i	$-0.661884\pi$
$659$	−25.0000	−0.973862	−0.486931	+	0.873441i	$0.661884\pi$
$660$	0	0
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	−14.0000	−0.544125
$663$	0	0
$664$	1.00000	0.0388075
$665$	0	0
$666$	−12.0000	−0.464991
$667$	−7.00000	−0.271041
$668$	14.0000	0.541676
$669$	0	0
$670$	0	0
$671$	24.0000	0.926510
$672$	0	0
$673$	−13.0000	−0.501113	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	−13.0000	−0.501113	−0.250557	+	0.968102i	$0.580614\pi$
$674$	30.0000	1.15556
$675$	0	0
$676$	−4.00000	−0.153846
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	0	0
$681$	0	0
$682$	−30.0000	−1.14876
$683$	−2.00000	−0.0765279	−0.0382639	−	0.999268i	$-0.512183\pi$
$683$	−2.00000	−0.0765279	−0.0382639	+	0.999268i	$0.512183\pi$
$684$	21.0000	0.802955
$685$	0	0
$686$	13.0000	0.496342
$687$	0	0
$688$	5.00000	0.190623
$689$	18.0000	0.685745
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	11.0000	0.418157
$693$	−9.00000	−0.341882
$694$	32.0000	1.21470
$695$	0	0
$696$	0	0
$697$	−88.0000	−3.33324
$698$	11.0000	0.416356
$699$	0	0
$700$	0	0
$701$	−20.0000	−0.755390	−0.377695	−	0.925930i	$-0.623283\pi$
$701$	−20.0000	−0.755390	−0.377695	+	0.925930i	$0.623283\pi$
$702$	0	0
$703$	−28.0000	−1.05604
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−27.0000	−1.01616
$707$	−10.0000	−0.376089
$708$	0	0
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	0	0
$711$	−9.00000	−0.337526
$712$	−6.00000	−0.224860
$713$	−10.0000	−0.374503
$714$	0	0
$715$	0	0
$716$	−6.00000	−0.224231
$717$	0	0
$718$	−17.0000	−0.634434
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	7.00000	0.260694
$722$	30.0000	1.11648
$723$	0	0
$724$	−4.00000	−0.148659
$725$	0	0
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	3.00000	0.111187
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−40.0000	−1.47945
$732$	0	0
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	−17.0000	−0.627481
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	−33.0000	−1.21475
$739$	38.0000	1.39785	0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000	1.39785	0.698926	+	0.715194i	$0.253662\pi$
$740$	0	0
$741$	0	0
$742$	6.00000	0.220267
$743$	19.0000	0.697042	0.348521	−	0.937301i	$-0.386684\pi$
$743$	19.0000	0.697042	0.348521	+	0.937301i	$0.386684\pi$
$744$	0	0
$745$	0	0
$746$	−36.0000	−1.31805
$747$	−3.00000	−0.109764
$748$	24.0000	0.877527
$749$	20.0000	0.730784
$750$	0	0
$751$	33.0000	1.20419	0.602094	−	0.798426i	$-0.294333\pi$
$751$	33.0000	1.20419	0.602094	+	0.798426i	$0.294333\pi$
$752$	−10.0000	−0.364662
$753$	0	0
$754$	−21.0000	−0.764775
$755$	0	0
$756$	0	0
$757$	8.00000	0.290765	0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000	0.290765	0.145382	+	0.989376i	$0.453559\pi$
$758$	−28.0000	−1.01701
$759$	0	0
$760$	0	0
$761$	−15.0000	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$762$	0	0
$763$	−20.0000	−0.724049
$764$	−15.0000	−0.542681
$765$	0	0
$766$	−21.0000	−0.758761
$767$	24.0000	0.866590
$768$	0	0
$769$	12.0000	0.432731	0.216366	−	0.976312i	$-0.430580\pi$
$769$	12.0000	0.432731	0.216366	+	0.976312i	$0.430580\pi$
$770$	0	0
$771$	0	0
$772$	−6.00000	−0.215945
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	−15.0000	−0.539164
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−77.0000	−2.75881
$780$	0	0
$781$	−30.0000	−1.07348
$782$	8.00000	0.286079
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	7.00000	0.249523	0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000	0.249523	0.124762	+	0.992187i	$0.460183\pi$
$788$	−13.0000	−0.463106
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	9.00000	0.319801
$793$	24.0000	0.852265
$794$	6.00000	0.212932
$795$	0	0
$796$	−9.00000	−0.318997
$797$	−48.0000	−1.70025	−0.850124	−	0.526583i	$-0.823473\pi$
$797$	−48.0000	−1.70025	−0.850124	+	0.526583i	$0.823473\pi$
$798$	0	0
$799$	80.0000	2.83020
$800$	0	0
$801$	18.0000	0.635999
$802$	−8.00000	−0.282490
$803$	33.0000	1.16454
$804$	0	0
$805$	0	0
$806$	−30.0000	−1.05670
$807$	0	0
$808$	10.0000	0.351799
$809$	25.0000	0.878953	0.439477	−	0.898254i	$-0.355164\pi$
$809$	25.0000	0.878953	0.439477	+	0.898254i	$0.355164\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	−7.00000	−0.245652
$813$	0	0
$814$	−12.0000	−0.420600
$815$	0	0
$816$	0	0
$817$	−35.0000	−1.22449
$818$	9.00000	0.314678
$819$	−9.00000	−0.314485
$820$	0	0
$821$	−35.0000	−1.22151	−0.610754	−	0.791820i	$-0.709134\pi$
$821$	−35.0000	−1.22151	−0.610754	+	0.791820i	$0.709134\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	8.00000	0.278356
$827$	−1.00000	−0.0347734	−0.0173867	−	0.999849i	$-0.505535\pi$
$827$	−1.00000	−0.0347734	−0.0173867	+	0.999849i	$0.505535\pi$
$828$	3.00000	0.104257
$829$	−45.0000	−1.56291	−0.781457	−	0.623959i	$-0.785523\pi$
$829$	−45.0000	−1.56291	−0.781457	+	0.623959i	$0.785523\pi$
$830$	0	0
$831$	0	0
$832$	−3.00000	−0.104006
$833$	48.0000	1.66310
$834$	0	0
$835$	0	0
$836$	21.0000	0.726300
$837$	0	0
$838$	27.0000	0.932700
$839$	−31.0000	−1.07024	−0.535119	−	0.844776i	$-0.679733\pi$
$839$	−31.0000	−1.07024	−0.535119	+	0.844776i	$0.679733\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	−2.00000	−0.0689246
$843$	0	0
$844$	−10.0000	−0.344214
$845$	0	0
$846$	30.0000	1.03142
$847$	2.00000	0.0687208
$848$	−6.00000	−0.206041
$849$	0	0
$850$	0	0
$851$	−4.00000	−0.137118
$852$	0	0
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	−20.0000	−0.683586
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	8.00000	0.272481
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	0	0
$865$	0	0
$866$	16.0000	0.543702
$867$	0	0
$868$	−10.0000	−0.339422
$869$	−9.00000	−0.305304
$870$	0	0
$871$	0	0
$872$	20.0000	0.677285
$873$	−42.0000	−1.42148
$874$	7.00000	0.236779
$875$	0	0
$876$	0	0
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−12.0000	−0.404980
$879$	0	0
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	18.0000	0.606092
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−18.0000	−0.604722
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	−27.0000	−0.904534
$892$	6.00000	0.200895
$893$	70.0000	2.34246
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	14.0000	0.467186
$899$	70.0000	2.33463
$900$	0	0
$901$	48.0000	1.59911
$902$	−33.0000	−1.09878
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0	0
$907$	−5.00000	−0.166022	−0.0830111	−	0.996549i	$-0.526454\pi$
$907$	−5.00000	−0.166022	−0.0830111	+	0.996549i	$0.526454\pi$
$908$	−4.00000	−0.132745
$909$	−30.0000	−0.995037
$910$	0	0
$911$	−25.0000	−0.828287	−0.414143	−	0.910212i	$-0.635919\pi$
$911$	−25.0000	−0.828287	−0.414143	+	0.910212i	$0.635919\pi$
$912$	0	0
$913$	−3.00000	−0.0992855
$914$	10.0000	0.330771
$915$	0	0
$916$	18.0000	0.594737
$917$	18.0000	0.594412
$918$	0	0
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	0	0
$921$	0	0
$922$	3.00000	0.0987997
$923$	−30.0000	−0.987462
$924$	0	0
$925$	0	0
$926$	−20.0000	−0.657241
$927$	21.0000	0.689730
$928$	7.00000	0.229786
$929$	−13.0000	−0.426516	−0.213258	−	0.976996i	$-0.568408\pi$
$929$	−13.0000	−0.426516	−0.213258	+	0.976996i	$0.568408\pi$
$930$	0	0
$931$	42.0000	1.37649
$932$	11.0000	0.360317
$933$	0	0
$934$	−13.0000	−0.425373
$935$	0	0
$936$	9.00000	0.294174
$937$	42.0000	1.37208	0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000	1.37208	0.686040	+	0.727564i	$0.259347\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	−11.0000	−0.358209
$944$	−8.00000	−0.260378
$945$	0	0
$946$	−15.0000	−0.487692
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	33.0000	1.07123
$950$	0	0
$951$	0	0
$952$	8.00000	0.259281
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	18.0000	0.582772
$955$	0	0
$956$	6.00000	0.194054
$957$	0	0
$958$	17.0000	0.549245
$959$	6.00000	0.193750
$960$	0	0
$961$	69.0000	2.22581
$962$	−12.0000	−0.386896
$963$	60.0000	1.93347
$964$	2.00000	0.0644157
$965$	0	0
$966$	0	0
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	0	0
$971$	27.0000	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$972$	0	0
$973$	4.00000	0.128234
$974$	18.0000	0.576757
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−26.0000	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$977$	−26.0000	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$978$	0	0
$979$	18.0000	0.575282
$980$	0	0
$981$	−60.0000	−1.91565
$982$	24.0000	0.765871
$983$	−39.0000	−1.24391	−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000	−1.24391	−0.621953	+	0.783054i	$0.713661\pi$
$984$	0	0
$985$	0	0
$986$	−56.0000	−1.78340
$987$	0	0
$988$	21.0000	0.668099
$989$	−5.00000	−0.158991
$990$	0	0
$991$	14.0000	0.444725	0.222362	−	0.974964i	$-0.428623\pi$
$991$	14.0000	0.444725	0.222362	+	0.974964i	$0.428623\pi$
$992$	10.0000	0.317500
$993$	0	0
$994$	−10.0000	−0.317181
$995$	0	0
$996$	0	0
$997$	−25.0000	−0.791758	−0.395879	−	0.918303i	$-0.629560\pi$
$997$	−25.0000	−0.791758	−0.395879	+	0.918303i	$0.629560\pi$
$998$	6.00000	0.189927
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.g.1.1	yes	1
4.3	odd	2		9200.2.a.v.1.1		1
5.2	odd	4		1150.2.b.c.599.2		2
5.3	odd	4		1150.2.b.c.599.1		2
5.4	even	2		1150.2.a.b.1.1	✓	1
20.19	odd	2		9200.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.a.b.1.1	✓	1	5.4	even	2
1150.2.a.g.1.1	yes	1	1.1	even	1	trivial
1150.2.b.c.599.1		2	5.3	odd	4
1150.2.b.c.599.2		2	5.2	odd	4
9200.2.a.s.1.1		1	20.19	odd	2
9200.2.a.v.1.1		1	4.3	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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