LMFDB - Embedded newform 1150.2.a.i.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} -1.00000 q^{19} +2.00000 q^{21} +3.00000 q^{22} -1.00000 q^{23} +2.00000 q^{24} +1.00000 q^{26} -4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} +1.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} +2.00000 q^{39} +3.00000 q^{41} +2.00000 q^{42} +1.00000 q^{43} +3.00000 q^{44} -1.00000 q^{46} +2.00000 q^{48} -6.00000 q^{49} +1.00000 q^{52} +12.0000 q^{53} -4.00000 q^{54} +1.00000 q^{56} -2.00000 q^{57} -3.00000 q^{58} -6.00000 q^{59} +2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.00000 q^{66} -8.00000 q^{67} -2.00000 q^{69} -6.00000 q^{71} +1.00000 q^{72} +7.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} +3.00000 q^{77} +2.00000 q^{78} -1.00000 q^{79} -11.0000 q^{81} +3.00000 q^{82} +9.00000 q^{83} +2.00000 q^{84} +1.00000 q^{86} -6.00000 q^{87} +3.00000 q^{88} -18.0000 q^{89} +1.00000 q^{91} -1.00000 q^{92} +4.00000 q^{93} +2.00000 q^{96} +4.00000 q^{97} -6.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	2.00000	0.577350
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.00000	0.235702
$19$	−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
$21$	2.00000	0.436436
$22$	3.00000	0.639602
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.00000	0.408248
$25$	0	0
$26$	1.00000	0.196116
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	6.00000	1.04447
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.00000	−0.162221
$39$	2.00000	0.320256
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	2.00000	0.308607
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−1.00000	−0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	2.00000	0.288675
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	−2.00000	−0.264906
$58$	−3.00000	−0.393919
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	2.00000	0.254000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.00000	0.117851
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	3.00000	0.341882
$78$	2.00000	0.226455
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	3.00000	0.331295
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	1.00000	0.107833
$87$	−6.00000	−0.643268
$88$	3.00000	0.319801
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−1.00000	−0.104257
$93$	4.00000	0.414781
$94$	0	0
$95$	0	0
$96$	2.00000	0.204124
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	−6.00000	−0.606092
$99$	3.00000	0.301511
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−5.00000	−0.492665	−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000	−0.492665	−0.246332	+	0.969185i	$0.579225\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	12.0000	1.16554
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−4.00000	−0.384900
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	1.00000	0.0944911
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	−3.00000	−0.278543
$117$	1.00000	0.0924500
$118$	−6.00000	−0.552345
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	2.00000	0.181071
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	0	0
$126$	1.00000	0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	6.00000	0.522233
$133$	−1.00000	−0.0867110
$134$	−8.00000	−0.691095
$135$	0	0
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−2.00000	−0.170251
$139$	−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
$142$	−6.00000	−0.503509
$143$	3.00000	0.250873
$144$	1.00000	0.0833333
$145$	0	0
$146$	7.00000	0.579324
$147$	−12.0000	−0.989743
$148$	−2.00000	−0.164399
$149$	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
$151$	−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
$154$	3.00000	0.241747
$155$	0	0
$156$	2.00000	0.160128
$157$	16.0000	1.27694	0.638470	−	0.769647i	$-0.279568\pi$
$157$	16.0000	1.27694	0.638470	+	0.769647i	$0.279568\pi$
$158$	−1.00000	−0.0795557
$159$	24.0000	1.90332
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−11.0000	−0.864242
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	9.00000	0.698535
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	2.00000	0.154303
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	1.00000	0.0762493
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	3.00000	0.226134
$177$	−12.0000	−0.901975
$178$	−18.0000	−1.34916
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	8.00000	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$182$	1.00000	0.0741249
$183$	4.00000	0.295689
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	4.00000	0.293294
$187$	0	0
$188$	0	0
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	2.00000	0.144338
$193$	−26.0000	−1.87152	−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000	−1.87152	−0.935760	+	0.352636i	$0.885285\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	−6.00000	−0.428571
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	3.00000	0.213201
$199$	23.0000	1.63043	0.815213	−	0.579161i	$-0.196620\pi$
$199$	23.0000	1.63043	0.815213	+	0.579161i	$0.196620\pi$
$200$	0	0
$201$	−16.0000	−1.12855
$202$	−6.00000	−0.422159
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	−5.00000	−0.348367
$207$	−1.00000	−0.0695048
$208$	1.00000	0.0693375
$209$	−3.00000	−0.207514
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	12.0000	0.824163
$213$	−12.0000	−0.822226
$214$	0	0
$215$	0	0
$216$	−4.00000	−0.272166
$217$	2.00000	0.135769
$218$	−10.0000	−0.677285
$219$	14.0000	0.946032
$220$	0	0
$221$	0	0
$222$	−4.00000	−0.268462
$223$	−20.0000	−1.33930	−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000	−1.33930	−0.669650	+	0.742677i	$0.733556\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	0	0
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−2.00000	−0.132453
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	−3.00000	−0.196960
$233$	9.00000	0.589610	0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000	0.589610	0.294805	+	0.955557i	$0.404745\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	−6.00000	−0.390567
$237$	−2.00000	−0.129914
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	−2.00000	−0.128565
$243$	−10.0000	−0.641500
$244$	2.00000	0.128037
$245$	0	0
$246$	6.00000	0.382546
$247$	−1.00000	−0.0636285
$248$	2.00000	0.127000
$249$	18.0000	1.14070
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	1.00000	0.0629941
$253$	−3.00000	−0.188608
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	2.00000	0.124515
$259$	−2.00000	−0.124274
$260$	0	0
$261$	−3.00000	−0.185695
$262$	−18.0000	−1.11204
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	6.00000	0.369274
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	−36.0000	−2.20316
$268$	−8.00000	−0.488678
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	0	0
$273$	2.00000	0.121046
$274$	18.0000	1.08742
$275$	0	0
$276$	−2.00000	−0.120386
$277$	−17.0000	−1.02143	−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000	−1.02143	−0.510716	+	0.859750i	$0.670619\pi$
$278$	−4.00000	−0.239904
$279$	2.00000	0.119737
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	3.00000	0.177394
$287$	3.00000	0.177084
$288$	1.00000	0.0589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	8.00000	0.468968
$292$	7.00000	0.409644
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	−12.0000	−0.699854
$295$	0	0
$296$	−2.00000	−0.116248
$297$	−12.0000	−0.696311
$298$	6.00000	0.347571
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	1.00000	0.0576390
$302$	−10.0000	−0.575435
$303$	−12.0000	−0.689382
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	3.00000	0.170941
$309$	−10.0000	−0.568880
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	2.00000	0.113228
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	16.0000	0.902932
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	3.00000	0.168497	0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000	0.168497	0.0842484	+	0.996445i	$0.473151\pi$
$318$	24.0000	1.34585
$319$	−9.00000	−0.503903
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−20.0000	−1.10770
$327$	−20.0000	−1.10600
$328$	3.00000	0.165647
$329$	0	0
$330$	0	0
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	9.00000	0.493939
$333$	−2.00000	−0.109599
$334$	18.0000	0.984916
$335$	0	0
$336$	2.00000	0.109109
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	6.00000	0.324918
$342$	−1.00000	−0.0540738
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	0	0
$346$	−9.00000	−0.483843
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	−6.00000	−0.321634
$349$	−19.0000	−1.01705	−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000	−1.01705	−0.508523	+	0.861048i	$0.669808\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	3.00000	0.159901
$353$	27.0000	1.43706	0.718532	−	0.695493i	$-0.244814\pi$
$353$	27.0000	1.43706	0.718532	+	0.695493i	$0.244814\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−18.0000	−0.953998
$357$	0	0
$358$	12.0000	0.634220
$359$	15.0000	0.791670	0.395835	−	0.918322i	$-0.370455\pi$
$359$	15.0000	0.791670	0.395835	+	0.918322i	$0.370455\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	8.00000	0.420471
$363$	−4.00000	−0.209946
$364$	1.00000	0.0524142
$365$	0	0
$366$	4.00000	0.209083
$367$	13.0000	0.678594	0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000	0.678594	0.339297	+	0.940679i	$0.389811\pi$
$368$	−1.00000	−0.0521286
$369$	3.00000	0.156174
$370$	0	0
$371$	12.0000	0.623009
$372$	4.00000	0.207390
$373$	−8.00000	−0.414224	−0.207112	−	0.978317i	$-0.566407\pi$
$373$	−8.00000	−0.414224	−0.207112	+	0.978317i	$0.566407\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.00000	−0.154508
$378$	−4.00000	−0.205738
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	−3.00000	−0.153493
$383$	21.0000	1.07305	0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000	1.07305	0.536525	+	0.843884i	$0.319737\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−26.0000	−1.32337
$387$	1.00000	0.0508329
$388$	4.00000	0.203069
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	0	0
$391$	0	0
$392$	−6.00000	−0.303046
$393$	−36.0000	−1.81596
$394$	3.00000	0.151138
$395$	0	0
$396$	3.00000	0.150756
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	23.0000	1.15289
$399$	−2.00000	−0.100125
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	−16.0000	−0.798007
$403$	2.00000	0.0996271
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−3.00000	−0.148888
$407$	−6.00000	−0.297409
$408$	0	0
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	0	0
$411$	36.0000	1.77575
$412$	−5.00000	−0.246332
$413$	−6.00000	−0.295241
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	1.00000	0.0490290
$417$	−8.00000	−0.391762
$418$	−3.00000	−0.146735
$419$	−27.0000	−1.31904	−0.659518	−	0.751689i	$-0.729240\pi$
$419$	−27.0000	−1.31904	−0.659518	+	0.751689i	$0.729240\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	14.0000	0.681509
$423$	0	0
$424$	12.0000	0.582772
$425$	0	0
$426$	−12.0000	−0.581402
$427$	2.00000	0.0967868
$428$	0	0
$429$	6.00000	0.289683
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	−4.00000	−0.192450
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	−10.0000	−0.478913
$437$	1.00000	0.0478365
$438$	14.0000	0.668946
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	0	0
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	−20.0000	−0.947027
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	0	0
$453$	−20.0000	−0.939682
$454$	−12.0000	−0.563188
$455$	0	0
$456$	−2.00000	−0.0936586
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	0	0
$461$	21.0000	0.978068	0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000	0.978068	0.489034	+	0.872265i	$0.337349\pi$
$462$	6.00000	0.279145
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	9.00000	0.416917
$467$	27.0000	1.24941	0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000	1.24941	0.624705	+	0.780860i	$0.285219\pi$
$468$	1.00000	0.0462250
$469$	−8.00000	−0.369406
$470$	0	0
$471$	32.0000	1.47448
$472$	−6.00000	−0.276172
$473$	3.00000	0.137940
$474$	−2.00000	−0.0918630
$475$	0	0
$476$	0	0
$477$	12.0000	0.549442
$478$	24.0000	1.09773
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	8.00000	0.364390
$483$	−2.00000	−0.0910032
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	−10.0000	−0.453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	2.00000	0.0905357
$489$	−40.0000	−1.80886
$490$	0	0
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	6.00000	0.270501
$493$	0	0
$494$	−1.00000	−0.0449921
$495$	0	0
$496$	2.00000	0.0898027
$497$	−6.00000	−0.269137
$498$	18.0000	0.806599
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	0	0
$501$	36.0000	1.60836
$502$	−12.0000	−0.535586
$503$	39.0000	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−3.00000	−0.133366
$507$	−24.0000	−1.06588
$508$	−2.00000	−0.0887357
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	7.00000	0.309662
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	18.0000	0.793946
$515$	0	0
$516$	2.00000	0.0880451
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	−18.0000	−0.790112
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	−3.00000	−0.131306
$523$	−17.0000	−0.743358	−0.371679	−	0.928361i	$-0.621218\pi$
$523$	−17.0000	−0.743358	−0.371679	+	0.928361i	$0.621218\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	6.00000	0.261116
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.00000	−0.260378
$532$	−1.00000	−0.0433555
$533$	3.00000	0.129944
$534$	−36.0000	−1.55787
$535$	0	0
$536$	−8.00000	−0.345547
$537$	24.0000	1.03568
$538$	9.00000	0.388018
$539$	−18.0000	−0.775315
$540$	0	0
$541$	−19.0000	−0.816874	−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000	−0.816874	−0.408437	+	0.912787i	$0.633926\pi$
$542$	20.0000	0.859074
$543$	16.0000	0.686626
$544$	0	0
$545$	0	0
$546$	2.00000	0.0855921
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	18.0000	0.768922
$549$	2.00000	0.0853579
$550$	0	0
$551$	3.00000	0.127804
$552$	−2.00000	−0.0851257
$553$	−1.00000	−0.0425243
$554$	−17.0000	−0.722261
$555$	0	0
$556$	−4.00000	−0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	2.00000	0.0846668
$559$	1.00000	0.0422955
$560$	0	0
$561$	0	0
$562$	0	0
$563$	9.00000	0.379305	0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000	0.379305	0.189652	+	0.981851i	$0.439264\pi$
$564$	0	0
$565$	0	0
$566$	28.0000	1.17693
$567$	−11.0000	−0.461957
$568$	−6.00000	−0.251754
$569$	−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
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	3.00000	0.125436
$573$	−6.00000	−0.250654
$574$	3.00000	0.125218
$575$	0	0
$576$	1.00000	0.0416667
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	−17.0000	−0.707107
$579$	−52.0000	−2.16105
$580$	0	0
$581$	9.00000	0.373383
$582$	8.00000	0.331611
$583$	36.0000	1.49097
$584$	7.00000	0.289662
$585$	0	0
$586$	−24.0000	−0.991431
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	−12.0000	−0.494872
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	6.00000	0.246807
$592$	−2.00000	−0.0821995
$593$	−15.0000	−0.615976	−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000	−0.615976	−0.307988	+	0.951390i	$0.599656\pi$
$594$	−12.0000	−0.492366
$595$	0	0
$596$	6.00000	0.245770
$597$	46.0000	1.88265
$598$	−1.00000	−0.0408930
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	1.00000	0.0407570
$603$	−8.00000	−0.325785
$604$	−10.0000	−0.406894
$605$	0	0
$606$	−12.0000	−0.487467
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	−1.00000	−0.0405554
$609$	−6.00000	−0.243132
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	3.00000	0.120873
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	−10.0000	−0.402259
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	−18.0000	−0.721734
$623$	−18.0000	−0.721155
$624$	2.00000	0.0800641
$625$	0	0
$626$	10.0000	0.399680
$627$	−6.00000	−0.239617
$628$	16.0000	0.638470
$629$	0	0
$630$	0	0
$631$	5.00000	0.199047	0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000	0.199047	0.0995234	+	0.995035i	$0.468268\pi$
$632$	−1.00000	−0.0397779
$633$	28.0000	1.11290
$634$	3.00000	0.119145
$635$	0	0
$636$	24.0000	0.951662
$637$	−6.00000	−0.237729
$638$	−9.00000	−0.356313
$639$	−6.00000	−0.237356
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	13.0000	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	0	0
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	−11.0000	−0.432121
$649$	−18.0000	−0.706562
$650$	0	0
$651$	4.00000	0.156772
$652$	−20.0000	−0.783260
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	−20.0000	−0.782062
$655$	0	0
$656$	3.00000	0.117130
$657$	7.00000	0.273096
$658$	0	0
$659$	45.0000	1.75295	0.876476	−	0.481446i	$-0.159888\pi$
$659$	45.0000	1.75295	0.876476	+	0.481446i	$0.159888\pi$
$660$	0	0
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	−10.0000	−0.388661
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	3.00000	0.116160
$668$	18.0000	0.696441
$669$	−40.0000	−1.54649
$670$	0	0
$671$	6.00000	0.231627
$672$	2.00000	0.0771517
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−12.0000	−0.461538
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	0	0
$679$	4.00000	0.153506
$680$	0	0
$681$	−24.0000	−0.919682
$682$	6.00000	0.229752
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	−13.0000	−0.496342
$687$	−20.0000	−0.763048
$688$	1.00000	0.0381246
$689$	12.0000	0.457164
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	−9.00000	−0.342129
$693$	3.00000	0.113961
$694$	−12.0000	−0.455514
$695$	0	0
$696$	−6.00000	−0.227429
$697$	0	0
$698$	−19.0000	−0.719161
$699$	18.0000	0.680823
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	−4.00000	−0.150970
$703$	2.00000	0.0754314
$704$	3.00000	0.113067
$705$	0	0
$706$	27.0000	1.01616
$707$	−6.00000	−0.225653
$708$	−12.0000	−0.450988
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	−18.0000	−0.674579
$713$	−2.00000	−0.0749006
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	48.0000	1.79259
$718$	15.0000	0.559795
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	−5.00000	−0.186210
$722$	−18.0000	−0.669891
$723$	16.0000	0.595046
$724$	8.00000	0.297318
$725$	0	0
$726$	−4.00000	−0.148454
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	1.00000	0.0370625
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	4.00000	0.147844
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	13.0000	0.479839
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−24.0000	−0.884051
$738$	3.00000	0.110432
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	12.0000	0.440534
$743$	9.00000	0.330178	0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000	0.330178	0.165089	+	0.986279i	$0.447209\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	−8.00000	−0.292901
$747$	9.00000	0.329293
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	0	0
$753$	−24.0000	−0.874609
$754$	−3.00000	−0.109254
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	20.0000	0.726433
$759$	−6.00000	−0.217786
$760$	0	0
$761$	−15.0000	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$762$	−4.00000	−0.144905
$763$	−10.0000	−0.362024
$764$	−3.00000	−0.108536
$765$	0	0
$766$	21.0000	0.758761
$767$	−6.00000	−0.216647
$768$	2.00000	0.0721688
$769$	−46.0000	−1.65880	−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000	−1.65880	−0.829401	+	0.558653i	$0.811318\pi$
$770$	0	0
$771$	36.0000	1.29651
$772$	−26.0000	−0.935760
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	4.00000	0.143592
$777$	−4.00000	−0.143499
$778$	24.0000	0.860442
$779$	−3.00000	−0.107486
$780$	0	0
$781$	−18.0000	−0.644091
$782$	0	0
$783$	12.0000	0.428845
$784$	−6.00000	−0.214286
$785$	0	0
$786$	−36.0000	−1.28408
$787$	7.00000	0.249523	0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000	0.249523	0.124762	+	0.992187i	$0.460183\pi$
$788$	3.00000	0.106871
$789$	48.0000	1.70885
$790$	0	0
$791$	0	0
$792$	3.00000	0.106600
$793$	2.00000	0.0710221
$794$	22.0000	0.780751
$795$	0	0
$796$	23.0000	0.815213
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	−2.00000	−0.0707992
$799$	0	0
$800$	0	0
$801$	−18.0000	−0.635999
$802$	−30.0000	−1.05934
$803$	21.0000	0.741074
$804$	−16.0000	−0.564276
$805$	0	0
$806$	2.00000	0.0704470
$807$	18.0000	0.633630
$808$	−6.00000	−0.211079
$809$	−15.0000	−0.527372	−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000	−0.527372	−0.263686	+	0.964609i	$0.584938\pi$
$810$	0	0
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−3.00000	−0.105279
$813$	40.0000	1.40286
$814$	−6.00000	−0.210300
$815$	0	0
$816$	0	0
$817$	−1.00000	−0.0349856
$818$	−19.0000	−0.664319
$819$	1.00000	0.0349428
$820$	0	0
$821$	−9.00000	−0.314102	−0.157051	−	0.987590i	$-0.550199\pi$
$821$	−9.00000	−0.314102	−0.157051	+	0.987590i	$0.550199\pi$
$822$	36.0000	1.25564
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	−5.00000	−0.174183
$825$	0	0
$826$	−6.00000	−0.208767
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	−1.00000	−0.0347524
$829$	29.0000	1.00721	0.503606	−	0.863934i	$-0.332006\pi$
$829$	29.0000	1.00721	0.503606	+	0.863934i	$0.332006\pi$
$830$	0	0
$831$	−34.0000	−1.17945
$832$	1.00000	0.0346688
$833$	0	0
$834$	−8.00000	−0.277017
$835$	0	0
$836$	−3.00000	−0.103757
$837$	−8.00000	−0.276520
$838$	−27.0000	−0.932700
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	26.0000	0.896019
$843$	0	0
$844$	14.0000	0.481900
$845$	0	0
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	12.0000	0.412082
$849$	56.0000	1.92192
$850$	0	0
$851$	2.00000	0.0685591
$852$	−12.0000	−0.411113
$853$	−47.0000	−1.60925	−0.804625	−	0.593784i	$-0.797633\pi$
$853$	−47.0000	−1.60925	−0.804625	+	0.593784i	$0.797633\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	0	0
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	6.00000	0.204837
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	−24.0000	−0.817443
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	−14.0000	−0.475739
$867$	−34.0000	−1.15470
$868$	2.00000	0.0678844
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−10.0000	−0.338643
$873$	4.00000	0.135379
$874$	1.00000	0.0338255
$875$	0	0
$876$	14.0000	0.473016
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−16.0000	−0.539974
$879$	−48.0000	−1.61900
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	−6.00000	−0.202031
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	0	0
$885$	0	0
$886$	−6.00000	−0.201574
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	−4.00000	−0.134231
$889$	−2.00000	−0.0670778
$890$	0	0
$891$	−33.0000	−1.10554
$892$	−20.0000	−0.669650
$893$	0	0
$894$	12.0000	0.401340
$895$	0	0
$896$	1.00000	0.0334077
$897$	−2.00000	−0.0667781
$898$	30.0000	1.00111
$899$	−6.00000	−0.200111
$900$	0	0
$901$	0	0
$902$	9.00000	0.299667
$903$	2.00000	0.0665558
$904$	0	0
$905$	0	0
$906$	−20.0000	−0.664455
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	−12.0000	−0.398234
$909$	−6.00000	−0.199007
$910$	0	0
$911$	15.0000	0.496972	0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000	0.496972	0.248486	+	0.968635i	$0.420067\pi$
$912$	−2.00000	−0.0662266
$913$	27.0000	0.893570
$914$	−8.00000	−0.264616
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−18.0000	−0.594412
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	8.00000	0.263609
$922$	21.0000	0.691598
$923$	−6.00000	−0.197492
$924$	6.00000	0.197386
$925$	0	0
$926$	4.00000	0.131448
$927$	−5.00000	−0.164222
$928$	−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
$931$	6.00000	0.196642
$932$	9.00000	0.294805
$933$	−36.0000	−1.17859
$934$	27.0000	0.883467
$935$	0	0
$936$	1.00000	0.0326860
$937$	4.00000	0.130674	0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000	0.130674	0.0653372	+	0.997863i	$0.479188\pi$
$938$	−8.00000	−0.261209
$939$	20.0000	0.652675
$940$	0	0
$941$	24.0000	0.782378	0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000	0.782378	0.391189	+	0.920310i	$0.372064\pi$
$942$	32.0000	1.04262
$943$	−3.00000	−0.0976934
$944$	−6.00000	−0.195283
$945$	0	0
$946$	3.00000	0.0975384
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	−2.00000	−0.0649570
$949$	7.00000	0.227230
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	24.0000	0.776215
$957$	−18.0000	−0.581857
$958$	21.0000	0.678479
$959$	18.0000	0.581250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	8.00000	0.257663
$965$	0	0
$966$	−2.00000	−0.0643489
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	0	0
$971$	−15.0000	−0.481373	−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000	−0.481373	−0.240686	+	0.970603i	$0.577373\pi$
$972$	−10.0000	−0.320750
$973$	−4.00000	−0.128234
$974$	40.0000	1.28168
$975$	0	0
$976$	2.00000	0.0640184
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	−40.0000	−1.27906
$979$	−54.0000	−1.72585
$980$	0	0
$981$	−10.0000	−0.319275
$982$	30.0000	0.957338
$983$	3.00000	0.0956851	0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000	0.0956851	0.0478426	+	0.998855i	$0.484765\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−1.00000	−0.0318142
$989$	−1.00000	−0.0317982
$990$	0	0
$991$	−28.0000	−0.889449	−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000	−0.889449	−0.444725	+	0.895667i	$0.646698\pi$
$992$	2.00000	0.0635001
$993$	−20.0000	−0.634681
$994$	−6.00000	−0.190308
$995$	0	0
$996$	18.0000	0.570352
$997$	−17.0000	−0.538395	−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000	−0.538395	−0.269198	+	0.963085i	$0.586759\pi$
$998$	8.00000	0.253236
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.i.1.1	yes	1
4.3	odd	2		9200.2.a.f.1.1		1
5.2	odd	4		1150.2.b.e.599.2		2
5.3	odd	4		1150.2.b.e.599.1		2
5.4	even	2		1150.2.a.a.1.1	✓	1
20.19	odd	2		9200.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.a.a.1.1	✓	1	5.4	even	2
1150.2.a.i.1.1	yes	1	1.1	even	1	trivial
1150.2.b.e.599.1		2	5.3	odd	4
1150.2.b.e.599.2		2	5.2	odd	4
9200.2.a.f.1.1		1	4.3	odd	2
9200.2.a.bf.1.1		1	20.19	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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