LMFDB - Embedded newform 8550.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8550.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$68.2720937282$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1710)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{7} -1.00000 q^{8} -6.00000 q^{11} -4.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{19} +6.00000 q^{22} +4.00000 q^{23} +4.00000 q^{28} -10.0000 q^{29} -2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} +4.00000 q^{37} +1.00000 q^{38} +10.0000 q^{41} +12.0000 q^{43} -6.00000 q^{44} -4.00000 q^{46} +9.00000 q^{49} +6.00000 q^{53} -4.00000 q^{56} +10.0000 q^{58} +4.00000 q^{59} -10.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +8.00000 q^{67} -4.00000 q^{68} -6.00000 q^{73} -4.00000 q^{74} -1.00000 q^{76} -24.0000 q^{77} -10.0000 q^{79} -10.0000 q^{82} -14.0000 q^{83} -12.0000 q^{86} +6.00000 q^{88} +10.0000 q^{89} +4.00000 q^{92} +6.00000 q^{97} -9.00000 q^{98} +O(q^{100})$

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
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	0	0
$22$	6.00000	1.27920
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	4.00000	0.755929
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	−4.00000	−0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	−4.00000	−0.534522
$57$	0	0
$58$	10.0000	1.31306
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−24.0000	−2.73505
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	0	0
$82$	−10.0000	−1.10432
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	0	0
$85$	0	0
$86$	−12.0000	−1.29399
$87$	0	0
$88$	6.00000	0.639602
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	0	0
$92$	4.00000	0.417029
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−9.00000	−0.909137
$99$	0	0
$100$	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
$103$	−18.0000	−1.77359	−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000	−1.77359	−0.886796	+	0.462160i	$0.847074\pi$
$104$	0	0
$105$	0	0
$106$	−6.00000	−0.582772
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−8.00000	−0.766261	−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000	−0.766261	−0.383131	+	0.923694i	$0.625154\pi$
$110$	0	0
$111$	0	0
$112$	4.00000	0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	0	0
$116$	−10.0000	−0.928477
$117$	0	0
$118$	−4.00000	−0.368230
$119$	−16.0000	−1.46672
$120$	0	0
$121$	25.0000	2.27273
$122$	10.0000	0.905357
$123$	0	0
$124$	−2.00000	−0.179605
$125$	0	0
$126$	0	0
$127$	−18.0000	−1.59724	−0.798621	−	0.601834i	$-0.794437\pi$
$127$	−18.0000	−1.59724	−0.798621	+	0.601834i	$0.794437\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−8.00000	−0.691095
$135$	0	0
$136$	4.00000	0.342997
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	6.00000	0.496564
$147$	0	0
$148$	4.00000	0.328798
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	24.0000	1.93398
$155$	0	0
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	0	0
$161$	16.0000	1.26098
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	14.0000	1.08661
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	12.0000	0.914991
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	0	0
$175$	0	0
$176$	−6.00000	−0.452267
$177$	0	0
$178$	−10.0000	−0.749532
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	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
$184$	−4.00000	−0.294884
$185$	0	0
$186$	0	0
$187$	24.0000	1.75505
$188$	0	0
$189$	0	0
$190$	0	0
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	9.00000	0.642857
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	0	0
$201$	0	0
$202$	−10.0000	−0.703598
$203$	−40.0000	−2.80745
$204$	0	0
$205$	0	0
$206$	18.0000	1.25412
$207$	0	0
$208$	0	0
$209$	6.00000	0.415029
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−8.00000	−0.543075
$218$	8.00000	0.541828
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	−2.00000	−0.133038
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	0	0
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	0	0
$231$	0	0
$232$	10.0000	0.656532
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	0	0
$235$	0	0
$236$	4.00000	0.260378
$237$	0	0
$238$	16.0000	1.03713
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−25.0000	−1.60706
$243$	0	0
$244$	−10.0000	−0.640184
$245$	0	0
$246$	0	0
$247$	0	0
$248$	2.00000	0.127000
$249$	0	0
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	0	0
$253$	−24.0000	−1.50887
$254$	18.0000	1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	16.0000	0.994192
$260$	0	0
$261$	0	0
$262$	10.0000	0.617802
$263$	−20.0000	−1.23325	−0.616626	−	0.787256i	$-0.711501\pi$
$263$	−20.0000	−1.23325	−0.616626	+	0.787256i	$0.711501\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	0	0
$268$	8.00000	0.488678
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	12.0000	0.724947
$275$	0	0
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	12.0000	0.719712
$279$	0	0
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	40.0000	2.36113
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−6.00000	−0.351123
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	0	0
$295$	0	0
$296$	−4.00000	−0.232495
$297$	0	0
$298$	10.0000	0.579284
$299$	0	0
$300$	0	0
$301$	48.0000	2.76667
$302$	18.0000	1.03578
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	−24.0000	−1.36753
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	−10.0000	−0.562544
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	0	0
$319$	60.0000	3.35936
$320$	0	0
$321$	0	0
$322$	−16.0000	−0.891645
$323$	4.00000	0.222566
$324$	0	0
$325$	0	0
$326$	12.0000	0.664619
$327$	0	0
$328$	−10.0000	−0.552158
$329$	0	0
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	−14.0000	−0.768350
$333$	0	0
$334$	−8.00000	−0.437741
$335$	0	0
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	13.0000	0.707107
$339$	0	0
$340$	0	0
$341$	12.0000	0.649836
$342$	0	0
$343$	8.00000	0.431959
$344$	−12.0000	−0.646997
$345$	0	0
$346$	18.0000	0.967686
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	0	0
$352$	6.00000	0.319801
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	0	0
$355$	0	0
$356$	10.0000	0.529999
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	16.0000	0.840941
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	0	0
$371$	24.0000	1.24602
$372$	0	0
$373$	−12.0000	−0.621336	−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000	−0.621336	−0.310668	+	0.950518i	$0.600553\pi$
$374$	−24.0000	−1.24101
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	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
$381$	0	0
$382$	−16.0000	−0.818631
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−2.00000	−0.101797
$387$	0	0
$388$	6.00000	0.304604
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	−9.00000	−0.454569
$393$	0	0
$394$	10.0000	0.503793
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−20.0000	−1.00251
$399$	0	0
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	0	0
$404$	10.0000	0.497519
$405$	0	0
$406$	40.0000	1.98517
$407$	−24.0000	−1.18964
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	0	0
$412$	−18.0000	−0.886796
$413$	16.0000	0.787309
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	−6.00000	−0.293470
$419$	26.0000	1.27018	0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000	1.27018	0.635092	+	0.772437i	$0.280962\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−6.00000	−0.291386
$425$	0	0
$426$	0	0
$427$	−40.0000	−1.93574
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−8.00000	−0.383131
$437$	−4.00000	−0.191346
$438$	0	0
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	0	0
$445$	0	0
$446$	14.0000	0.662919
$447$	0	0
$448$	4.00000	0.188982
$449$	−26.0000	−1.22702	−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000	−1.22702	−0.613508	+	0.789689i	$0.710242\pi$
$450$	0	0
$451$	−60.0000	−2.82529
$452$	2.00000	0.0940721
$453$	0	0
$454$	−8.00000	−0.375459
$455$	0	0
$456$	0	0
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	18.0000	0.841085
$459$	0	0
$460$	0	0
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	4.00000	0.185296
$467$	10.0000	0.462745	0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000	0.462745	0.231372	+	0.972865i	$0.425678\pi$
$468$	0	0
$469$	32.0000	1.47762
$470$	0	0
$471$	0	0
$472$	−4.00000	−0.184115
$473$	−72.0000	−3.31056
$474$	0	0
$475$	0	0
$476$	−16.0000	−0.733359
$477$	0	0
$478$	12.0000	0.548867
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	0	0
$482$	22.0000	1.00207
$483$	0	0
$484$	25.0000	1.13636
$485$	0	0
$486$	0	0
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	0	0
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	0	0
$493$	40.0000	1.80151
$494$	0	0
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0	0
$499$	−36.0000	−1.61158	−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000	−1.61158	−0.805791	+	0.592200i	$0.798259\pi$
$500$	0	0
$501$	0	0
$502$	−2.00000	−0.0892644
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	0	0
$505$	0	0
$506$	24.0000	1.06693
$507$	0	0
$508$	−18.0000	−0.798621
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	−24.0000	−1.06170
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−16.0000	−0.703000
$519$	0	0
$520$	0	0
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−10.0000	−0.436852
$525$	0	0
$526$	20.0000	0.872041
$527$	8.00000	0.348485
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	−4.00000	−0.173422
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−8.00000	−0.345547
$537$	0	0
$538$	14.0000	0.603583
$539$	−54.0000	−2.32594
$540$	0	0
$541$	−22.0000	−0.945854	−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000	−0.945854	−0.472927	+	0.881102i	$0.656803\pi$
$542$	4.00000	0.171815
$543$	0	0
$544$	4.00000	0.171499
$545$	0	0
$546$	0	0
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−12.0000	−0.512615
$549$	0	0
$550$	0	0
$551$	10.0000	0.426014
$552$	0	0
$553$	−40.0000	−1.70097
$554$	10.0000	0.424859
$555$	0	0
$556$	−12.0000	−0.508913
$557$	−22.0000	−0.932170	−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000	−0.932170	−0.466085	+	0.884740i	$0.654336\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	0	0
$566$	28.0000	1.17693
$567$	0	0
$568$	0	0
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	0	0
$573$	0	0
$574$	−40.0000	−1.66957
$575$	0	0
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	−56.0000	−2.32327
$582$	0	0
$583$	−36.0000	−1.49097
$584$	6.00000	0.248282
$585$	0	0
$586$	26.0000	1.07405
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	0	0
$589$	2.00000	0.0824086
$590$	0	0
$591$	0	0
$592$	4.00000	0.164399
$593$	44.0000	1.80686	0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000	1.80686	0.903432	+	0.428732i	$0.141040\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	−48.0000	−1.95633
$603$	0	0
$604$	−18.0000	−0.732410
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	24.0000	0.966988
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	40.0000	1.60257
$624$	0	0
$625$	0	0
$626$	−14.0000	−0.559553
$627$	0	0
$628$	18.0000	0.718278
$629$	−16.0000	−0.637962
$630$	0	0
$631$	−36.0000	−1.43314	−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000	−1.43314	−0.716569	+	0.697517i	$0.754288\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	−30.0000	−1.19145
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−60.0000	−2.37542
$639$	0	0
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	16.0000	0.630488
$645$	0	0
$646$	−4.00000	−0.157378
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	0	0
$649$	−24.0000	−0.942082
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	0	0
$656$	10.0000	0.390434
$657$	0	0
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	−28.0000	−1.08825
$663$	0	0
$664$	14.0000	0.543305
$665$	0	0
$666$	0	0
$667$	−40.0000	−1.54881
$668$	8.00000	0.309529
$669$	0	0
$670$	0	0
$671$	60.0000	2.31627
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	0	0
$679$	24.0000	0.921035
$680$	0	0
$681$	0	0
$682$	−12.0000	−0.459504
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	0	0
$685$	0	0
$686$	−8.00000	−0.305441
$687$	0	0
$688$	12.0000	0.457496
$689$	0	0
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	6.00000	0.227757
$695$	0	0
$696$	0	0
$697$	−40.0000	−1.51511
$698$	−10.0000	−0.378506
$699$	0	0
$700$	0	0
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	−6.00000	−0.226134
$705$	0	0
$706$	24.0000	0.903252
$707$	40.0000	1.50435
$708$	0	0
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	0	0
$712$	−10.0000	−0.374766
$713$	−8.00000	−0.299602
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	0	0
$721$	−72.0000	−2.68142
$722$	−1.00000	−0.0372161
$723$	0	0
$724$	−16.0000	−0.594635
$725$	0	0
$726$	0	0
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−48.0000	−1.77534
$732$	0	0
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−48.0000	−1.76810
$738$	0	0
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	0	0
$741$	0	0
$742$	−24.0000	−0.881068
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	0	0
$745$	0	0
$746$	12.0000	0.439351
$747$	0	0
$748$	24.0000	0.877527
$749$	0	0
$750$	0	0
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	26.0000	0.944986	0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000	0.944986	0.472493	+	0.881334i	$0.343354\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	0	0
$761$	24.0000	0.869999	0.435000	−	0.900431i	$-0.356748\pi$
$761$	24.0000	0.869999	0.435000	+	0.900431i	$0.356748\pi$
$762$	0	0
$763$	−32.0000	−1.15848
$764$	16.0000	0.578860
$765$	0	0
$766$	−24.0000	−0.867155
$767$	0	0
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	0	0
$772$	2.00000	0.0719816
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	0	0
$775$	0	0
$776$	−6.00000	−0.215387
$777$	0	0
$778$	18.0000	0.645331
$779$	−10.0000	−0.358287
$780$	0	0
$781$	0	0
$782$	16.0000	0.572159
$783$	0	0
$784$	9.00000	0.321429
$785$	0	0
$786$	0	0
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	8.00000	0.284447
$792$	0	0
$793$	0	0
$794$	22.0000	0.780751
$795$	0	0
$796$	20.0000	0.708881
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	6.00000	0.211867
$803$	36.0000	1.27041
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−10.0000	−0.351799
$809$	36.0000	1.26569	0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000	1.26569	0.632846	+	0.774277i	$0.281886\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−40.0000	−1.40372
$813$	0	0
$814$	24.0000	0.841200
$815$	0	0
$816$	0	0
$817$	−12.0000	−0.419827
$818$	−2.00000	−0.0699284
$819$	0	0
$820$	0	0
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	18.0000	0.627060
$825$	0	0
$826$	−16.0000	−0.556711
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−36.0000	−1.24733
$834$	0	0
$835$	0	0
$836$	6.00000	0.207514
$837$	0	0
$838$	−26.0000	−0.898155
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−28.0000	−0.964944
$843$	0	0
$844$	−4.00000	−0.137686
$845$	0	0
$846$	0	0
$847$	100.000	3.43604
$848$	6.00000	0.206041
$849$	0	0
$850$	0	0
$851$	16.0000	0.548473
$852$	0	0
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	40.0000	1.36877
$855$	0	0
$856$	0	0
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	0	0
$861$	0	0
$862$	24.0000	0.817443
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	0	0
$865$	0	0
$866$	6.00000	0.203888
$867$	0	0
$868$	−8.00000	−0.271538
$869$	60.0000	2.03536
$870$	0	0
$871$	0	0
$872$	8.00000	0.270914
$873$	0	0
$874$	4.00000	0.135302
$875$	0	0
$876$	0	0
$877$	−4.00000	−0.135070	−0.0675352	−	0.997717i	$-0.521513\pi$
$877$	−4.00000	−0.135070	−0.0675352	+	0.997717i	$0.521513\pi$
$878$	−10.0000	−0.337484
$879$	0	0
$880$	0	0
$881$	−20.0000	−0.673817	−0.336909	−	0.941537i	$-0.609381\pi$
$881$	−20.0000	−0.673817	−0.336909	+	0.941537i	$0.609381\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	0	0
$886$	6.00000	0.201574
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	0	0
$889$	−72.0000	−2.41480
$890$	0	0
$891$	0	0
$892$	−14.0000	−0.468755
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−4.00000	−0.133631
$897$	0	0
$898$	26.0000	0.867631
$899$	20.0000	0.667037
$900$	0	0
$901$	−24.0000	−0.799556
$902$	60.0000	1.99778
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	0	0
$906$	0	0
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	8.00000	0.265489
$909$	0	0
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	0	0
$913$	84.0000	2.77999
$914$	−38.0000	−1.25693
$915$	0	0
$916$	−18.0000	−0.594737
$917$	−40.0000	−1.32092
$918$	0	0
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	0	0
$921$	0	0
$922$	2.00000	0.0658665
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	0	0
$928$	10.0000	0.328266
$929$	−36.0000	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$930$	0	0
$931$	−9.00000	−0.294963
$932$	−4.00000	−0.131024
$933$	0	0
$934$	−10.0000	−0.327210
$935$	0	0
$936$	0	0
$937$	−14.0000	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$938$	−32.0000	−1.04484
$939$	0	0
$940$	0	0
$941$	−50.0000	−1.62995	−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000	−1.62995	−0.814977	+	0.579494i	$0.803250\pi$
$942$	0	0
$943$	40.0000	1.30258
$944$	4.00000	0.130189
$945$	0	0
$946$	72.0000	2.34092
$947$	38.0000	1.23483	0.617417	−	0.786636i	$-0.288179\pi$
$947$	38.0000	1.23483	0.617417	+	0.786636i	$0.288179\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	16.0000	0.518563
$953$	−34.0000	−1.10137	−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000	−1.10137	−0.550684	+	0.834714i	$0.685633\pi$
$954$	0	0
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	24.0000	0.775405
$959$	−48.0000	−1.55000
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	0	0
$964$	−22.0000	−0.708572
$965$	0	0
$966$	0	0
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	−25.0000	−0.803530
$969$	0	0
$970$	0	0
$971$	−60.0000	−1.92549	−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000	−1.92549	−0.962746	+	0.270408i	$0.912841\pi$
$972$	0	0
$973$	−48.0000	−1.53881
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−10.0000	−0.320092
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	−60.0000	−1.91761
$980$	0	0
$981$	0	0
$982$	26.0000	0.829693
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	0	0
$986$	−40.0000	−1.27386
$987$	0	0
$988$	0	0
$989$	48.0000	1.52631
$990$	0	0
$991$	−34.0000	−1.08005	−0.540023	−	0.841650i	$-0.681584\pi$
$991$	−34.0000	−1.08005	−0.540023	+	0.841650i	$0.681584\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	36.0000	1.13956
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8550.2.a.q.1.1		1
3.2	odd	2		8550.2.a.bl.1.1		1
5.4	even	2		1710.2.a.p.1.1	yes	1
15.14	odd	2		1710.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.a.a.1.1	✓	1	15.14	odd	2
1710.2.a.p.1.1	yes	1	5.4	even	2
8550.2.a.q.1.1		1	1.1	even	1	trivial
8550.2.a.bl.1.1		1	3.2	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:	\( N \)	\(=\)	\( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8550.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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