LMFDB - Embedded newform 2850.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, 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("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} +6.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} -4.00000 q^{21} -8.00000 q^{23} -1.00000 q^{24} -6.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +2.00000 q^{29} -8.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -1.00000 q^{38} +6.00000 q^{39} +6.00000 q^{41} +4.00000 q^{42} +8.00000 q^{43} +8.00000 q^{46} +1.00000 q^{48} +9.00000 q^{49} -2.00000 q^{51} +6.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +4.00000 q^{56} +1.00000 q^{57} -2.00000 q^{58} -12.0000 q^{59} -2.00000 q^{61} +8.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +12.0000 q^{67} -2.00000 q^{68} -8.00000 q^{69} -8.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +10.0000 q^{74} +1.00000 q^{76} -6.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} -4.00000 q^{84} -8.00000 q^{86} +2.00000 q^{87} +6.00000 q^{89} -24.0000 q^{91} -8.00000 q^{92} -8.00000 q^{93} -1.00000 q^{96} +10.0000 q^{97} -9.00000 q^{98} +O(q^{100})\)

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−4.00000	−0.872872
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−6.00000	−1.17670
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−1.00000	−0.162221
$39$	6.00000	0.960769
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.00000	0.617213
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	0	0
$46$	8.00000	1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	0	0
$51$	−2.00000	−0.280056
$52$	6.00000	0.832050
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.00000	0.534522
$57$	1.00000	0.132453
$58$	−2.00000	−0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	8.00000	1.01600
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	−2.00000	−0.242536
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	1.00000	0.114708
$77$	0	0
$78$	−6.00000	−0.679366
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	−8.00000	−0.862662
$87$	2.00000	0.214423
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	−24.0000	−2.51588
$92$	−8.00000	−0.834058
$93$	−8.00000	−0.829561
$94$	0	0
$95$	0	0
$96$	−1.00000	−0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	−9.00000	−0.909137
$99$	0	0
$100$	0	0
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	2.00000	0.198030
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−2.00000	−0.194257
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	1.00000	0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	−4.00000	−0.377964
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	2.00000	0.185695
$117$	6.00000	0.554700
$118$	12.0000	1.10469
$119$	8.00000	0.733359
$120$	0	0
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	6.00000	0.541002
$124$	−8.00000	−0.718421
$125$	0	0
$126$	4.00000	0.356348
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−12.0000	−1.03664
$135$	0	0
$136$	2.00000	0.171499
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	8.00000	0.681005
$139$	−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
$142$	8.00000	0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	9.00000	0.742307
$148$	−10.0000	−0.821995
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−1.00000	−0.0811107
$153$	−2.00000	−0.161690
$154$	0	0
$155$	0	0
$156$	6.00000	0.480384
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	16.0000	1.27289
$159$	2.00000	0.158610
$160$	0	0
$161$	32.0000	2.52195
$162$	−1.00000	−0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	4.00000	0.308607
$169$	23.0000	1.76923
$170$	0	0
$171$	1.00000	0.0764719
$172$	8.00000	0.609994
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−2.00000	−0.151620
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	−6.00000	−0.449719
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	24.0000	1.77900
$183$	−2.00000	−0.147844
$184$	8.00000	0.589768
$185$	0	0
$186$	8.00000	0.586588
$187$	0	0
$188$	0	0
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	1.00000	0.0721688
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	9.00000	0.642857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	12.0000	0.846415
$202$	18.0000	1.26648
$203$	−8.00000	−0.561490
$204$	−2.00000	−0.140028
$205$	0	0
$206$	8.00000	0.557386
$207$	−8.00000	−0.556038
$208$	6.00000	0.416025
$209$	0	0
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	2.00000	0.137361
$213$	−8.00000	−0.548151
$214$	20.0000	1.36717
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	32.0000	2.17230
$218$	−6.00000	−0.406371
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−12.0000	−0.807207
$222$	10.0000	0.671156
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	18.0000	1.19734
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	1.00000	0.0662266
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	0	0
$232$	−2.00000	−0.131306
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−12.0000	−0.781133
$237$	−16.0000	−1.03931
$238$	−8.00000	−0.518563
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	11.0000	0.707107
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−6.00000	−0.382546
$247$	6.00000	0.381771
$248$	8.00000	0.508001
$249$	4.00000	0.253490
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−8.00000	−0.498058
$259$	40.0000	2.48548
$260$	0	0
$261$	2.00000	0.123797
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	6.00000	0.367194
$268$	12.0000	0.733017
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−2.00000	−0.121268
$273$	−24.0000	−1.45255
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−8.00000	−0.481543
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	12.0000	0.719712
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	0	0
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	0	0
$287$	−24.0000	−1.41668
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	10.0000	0.586210
$292$	−2.00000	−0.117041
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−9.00000	−0.524891
$295$	0	0
$296$	10.0000	0.581238
$297$	0	0
$298$	2.00000	0.115857
$299$	−48.0000	−2.77591
$300$	0	0
$301$	−32.0000	−1.84445
$302$	0	0
$303$	−18.0000	−1.03407
$304$	1.00000	0.0573539
$305$	0	0
$306$	2.00000	0.114332
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−6.00000	−0.339683
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−16.0000	−0.900070
$317$	26.0000	1.46031	0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000	1.46031	0.730153	+	0.683284i	$0.239449\pi$
$318$	−2.00000	−0.112154
$319$	0	0
$320$	0	0
$321$	−20.0000	−1.11629
$322$	−32.0000	−1.78329
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	0	0
$326$	8.00000	0.443079
$327$	6.00000	0.331801
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	4.00000	0.219529
$333$	−10.0000	−0.547997
$334$	8.00000	0.437741
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−23.0000	−1.25104
$339$	−18.0000	−0.977626
$340$	0	0
$341$	0	0
$342$	−1.00000	−0.0540738
$343$	−8.00000	−0.431959
$344$	−8.00000	−0.431331
$345$	0	0
$346$	14.0000	0.752645
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	2.00000	0.107211
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	6.00000	0.320256
$352$	0	0
$353$	−2.00000	−0.106449	−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000	−0.106449	−0.0532246	+	0.998583i	$0.516950\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	6.00000	0.317999
$357$	8.00000	0.423405
$358$	20.0000	1.05703
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	18.0000	0.946059
$363$	−11.0000	−0.577350
$364$	−24.0000	−1.25794
$365$	0	0
$366$	2.00000	0.104542
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−8.00000	−0.417029
$369$	6.00000	0.312348
$370$	0	0
$371$	−8.00000	−0.415339
$372$	−8.00000	−0.414781
$373$	−34.0000	−1.76045	−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000	−1.76045	−0.880227	+	0.474554i	$0.842610\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	12.0000	0.618031
$378$	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
$381$	8.00000	0.409852
$382$	12.0000	0.613973
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−2.00000	−0.101797
$387$	8.00000	0.406663
$388$	10.0000	0.507673
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	−9.00000	−0.454569
$393$	0	0
$394$	6.00000	0.302276
$395$	0	0
$396$	0	0
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	−16.0000	−0.802008
$399$	−4.00000	−0.200250
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	−12.0000	−0.598506
$403$	−48.0000	−2.39105
$404$	−18.0000	−0.895533
$405$	0	0
$406$	8.00000	0.397033
$407$	0	0
$408$	2.00000	0.0990148
$409$	18.0000	0.890043	0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000	0.890043	0.445021	+	0.895520i	$0.353196\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	−8.00000	−0.394132
$413$	48.0000	2.36193
$414$	8.00000	0.393179
$415$	0	0
$416$	−6.00000	−0.294174
$417$	−12.0000	−0.587643
$418$	0	0
$419$	−40.0000	−1.95413	−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000	−1.95413	−0.977064	+	0.212946i	$0.931694\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	0	0
$426$	8.00000	0.387601
$427$	8.00000	0.387147
$428$	−20.0000	−0.966736
$429$	0	0
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	1.00000	0.0481125
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	−32.0000	−1.53605
$435$	0	0
$436$	6.00000	0.287348
$437$	−8.00000	−0.382692
$438$	2.00000	0.0955637
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	12.0000	0.570782
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	−10.0000	−0.474579
$445$	0	0
$446$	−16.0000	−0.757622
$447$	−2.00000	−0.0945968
$448$	−4.00000	−0.188982
$449$	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
$451$	0	0
$452$	−18.0000	−0.846649
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−6.00000	−0.280362
$459$	−2.00000	−0.0933520
$460$	0	0
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−6.00000	−0.277945
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	6.00000	0.277350
$469$	−48.0000	−2.21643
$470$	0	0
$471$	10.0000	0.460776
$472$	12.0000	0.552345
$473$	0	0
$474$	16.0000	0.734904
$475$	0	0
$476$	8.00000	0.366679
$477$	2.00000	0.0915737
$478$	20.0000	0.914779
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	0	0
$481$	−60.0000	−2.73576
$482$	14.0000	0.637683
$483$	32.0000	1.45605
$484$	−11.0000	−0.500000
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	2.00000	0.0905357
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−40.0000	−1.80517	−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000	−1.80517	−0.902587	+	0.430507i	$0.858335\pi$
$492$	6.00000	0.270501
$493$	−4.00000	−0.180151
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−8.00000	−0.359211
$497$	32.0000	1.43540
$498$	−4.00000	−0.179244
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	−8.00000	−0.357414
$502$	0	0
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	4.00000	0.178174
$505$	0	0
$506$	0	0
$507$	23.0000	1.02147
$508$	8.00000	0.354943
$509$	−22.0000	−0.975133	−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000	−0.975133	−0.487566	+	0.873086i	$0.662115\pi$
$510$	0	0
$511$	8.00000	0.353899
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	18.0000	0.793946
$515$	0	0
$516$	8.00000	0.352180
$517$	0	0
$518$	−40.0000	−1.75750
$519$	−14.0000	−0.614532
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	−2.00000	−0.0875376
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	16.0000	0.696971
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	−12.0000	−0.520756
$532$	−4.00000	−0.173422
$533$	36.0000	1.55933
$534$	−6.00000	−0.259645
$535$	0	0
$536$	−12.0000	−0.518321
$537$	−20.0000	−0.863064
$538$	−18.0000	−0.776035
$539$	0	0
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−8.00000	−0.343629
$543$	−18.0000	−0.772454
$544$	2.00000	0.0857493
$545$	0	0
$546$	24.0000	1.02711
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	6.00000	0.256307
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	2.00000	0.0852029
$552$	8.00000	0.340503
$553$	64.0000	2.72156
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	−12.0000	−0.508913
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	8.00000	0.338667
$559$	48.0000	2.03018
$560$	0	0
$561$	0	0
$562$	2.00000	0.0843649
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	0	0
$566$	−16.0000	−0.672530
$567$	−4.00000	−0.167984
$568$	8.00000	0.335673
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	0	0
$573$	−12.0000	−0.501307
$574$	24.0000	1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	13.0000	0.540729
$579$	2.00000	0.0831172
$580$	0	0
$581$	−16.0000	−0.663792
$582$	−10.0000	−0.414513
$583$	0	0
$584$	2.00000	0.0827606
$585$	0	0
$586$	6.00000	0.247858
$587$	20.0000	0.825488	0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000	0.825488	0.412744	+	0.910847i	$0.364570\pi$
$588$	9.00000	0.371154
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−6.00000	−0.246807
$592$	−10.0000	−0.410997
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	16.0000	0.654836
$598$	48.0000	1.96287
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−14.0000	−0.571072	−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000	−0.571072	−0.285536	+	0.958368i	$0.592172\pi$
$602$	32.0000	1.30422
$603$	12.0000	0.488678
$604$	0	0
$605$	0	0
$606$	18.0000	0.731200
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	−1.00000	−0.0405554
$609$	−8.00000	−0.324176
$610$	0	0
$611$	0	0
$612$	−2.00000	−0.0808452
$613$	−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
$616$	0	0
$617$	−26.0000	−1.04672	−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000	−1.04672	−0.523360	+	0.852111i	$0.675322\pi$
$618$	8.00000	0.321807
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	−8.00000	−0.321029
$622$	−12.0000	−0.481156
$623$	−24.0000	−0.961540
$624$	6.00000	0.240192
$625$	0	0
$626$	−6.00000	−0.239808
$627$	0	0
$628$	10.0000	0.399043
$629$	20.0000	0.797452
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	16.0000	0.636446
$633$	20.0000	0.794929
$634$	−26.0000	−1.03259
$635$	0	0
$636$	2.00000	0.0793052
$637$	54.0000	2.13956
$638$	0	0
$639$	−8.00000	−0.316475
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	20.0000	0.789337
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	32.0000	1.26098
$645$	0	0
$646$	2.00000	0.0786889
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	0	0
$651$	32.0000	1.25418
$652$	−8.00000	−0.313304
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	6.00000	0.234261
$657$	−2.00000	−0.0780274
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	−34.0000	−1.32245	−0.661223	−	0.750189i	$-0.729962\pi$
$661$	−34.0000	−1.32245	−0.661223	+	0.750189i	$0.729962\pi$
$662$	−20.0000	−0.777322
$663$	−12.0000	−0.466041
$664$	−4.00000	−0.155230
$665$	0	0
$666$	10.0000	0.387492
$667$	−16.0000	−0.619522
$668$	−8.00000	−0.309529
$669$	16.0000	0.618596
$670$	0	0
$671$	0	0
$672$	4.00000	0.154303
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	23.0000	0.884615
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	18.0000	0.691286
$679$	−40.0000	−1.53506
$680$	0	0
$681$	−20.0000	−0.766402
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	8.00000	0.305441
$687$	6.00000	0.228914
$688$	8.00000	0.304997
$689$	12.0000	0.457164
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	20.0000	0.759190
$695$	0	0
$696$	−2.00000	−0.0758098
$697$	−12.0000	−0.454532
$698$	−14.0000	−0.529908
$699$	6.00000	0.226941
$700$	0	0
$701$	38.0000	1.43524	0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000	1.43524	0.717620	+	0.696435i	$0.245231\pi$
$702$	−6.00000	−0.226455
$703$	−10.0000	−0.377157
$704$	0	0
$705$	0	0
$706$	2.00000	0.0752710
$707$	72.0000	2.70784
$708$	−12.0000	−0.450988
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	0	0
$711$	−16.0000	−0.600047
$712$	−6.00000	−0.224860
$713$	64.0000	2.39682
$714$	−8.00000	−0.299392
$715$	0	0
$716$	−20.0000	−0.747435
$717$	−20.0000	−0.746914
$718$	−12.0000	−0.447836
$719$	28.0000	1.04422	0.522112	−	0.852877i	$-0.325144\pi$
$719$	28.0000	1.04422	0.522112	+	0.852877i	$0.325144\pi$
$720$	0	0
$721$	32.0000	1.19174
$722$	−1.00000	−0.0372161
$723$	−14.0000	−0.520666
$724$	−18.0000	−0.668965
$725$	0	0
$726$	11.0000	0.408248
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	24.0000	0.889499
$729$	1.00000	0.0370370
$730$	0	0
$731$	−16.0000	−0.591781
$732$	−2.00000	−0.0739221
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	8.00000	0.294884
$737$	0	0
$738$	−6.00000	−0.220863
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	8.00000	0.293689
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	8.00000	0.293294
$745$	0	0
$746$	34.0000	1.24483
$747$	4.00000	0.146352
$748$	0	0
$749$	80.0000	2.92314
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	0	0
$753$	0	0
$754$	−12.0000	−0.437014
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	0	0
$761$	34.0000	1.23250	0.616250	−	0.787551i	$-0.288651\pi$
$761$	34.0000	1.23250	0.616250	+	0.787551i	$0.288651\pi$
$762$	−8.00000	−0.289809
$763$	−24.0000	−0.868858
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−72.0000	−2.59977
$768$	1.00000	0.0360844
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	2.00000	0.0719816
$773$	−46.0000	−1.65451	−0.827253	−	0.561830i	$-0.810097\pi$
$773$	−46.0000	−1.65451	−0.827253	+	0.561830i	$0.810097\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−10.0000	−0.358979
$777$	40.0000	1.43499
$778$	−6.00000	−0.215110
$779$	6.00000	0.214972
$780$	0	0
$781$	0	0
$782$	−16.0000	−0.572159
$783$	2.00000	0.0714742
$784$	9.00000	0.321429
$785$	0	0
$786$	0	0
$787$	20.0000	0.712923	0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000	0.712923	0.356462	+	0.934310i	$0.383983\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	0	0
$791$	72.0000	2.56003
$792$	0	0
$793$	−12.0000	−0.426132
$794$	38.0000	1.34857
$795$	0	0
$796$	16.0000	0.567105
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	4.00000	0.141598
$799$	0	0
$800$	0	0
$801$	6.00000	0.212000
$802$	−6.00000	−0.211867
$803$	0	0
$804$	12.0000	0.423207
$805$	0	0
$806$	48.0000	1.69073
$807$	18.0000	0.633630
$808$	18.0000	0.633238
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	−8.00000	−0.280745
$813$	8.00000	0.280572
$814$	0	0
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	8.00000	0.279885
$818$	−18.0000	−0.629355
$819$	−24.0000	−0.838628
$820$	0	0
$821$	−2.00000	−0.0698005	−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000	−0.0698005	−0.0349002	+	0.999391i	$0.511111\pi$
$822$	−6.00000	−0.209274
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−48.0000	−1.67013
$827$	52.0000	1.80822	0.904109	−	0.427303i	$-0.140536\pi$
$827$	52.0000	1.80822	0.904109	+	0.427303i	$0.140536\pi$
$828$	−8.00000	−0.278019
$829$	22.0000	0.764092	0.382046	−	0.924143i	$-0.375220\pi$
$829$	22.0000	0.764092	0.382046	+	0.924143i	$0.375220\pi$
$830$	0	0
$831$	2.00000	0.0693792
$832$	6.00000	0.208013
$833$	−18.0000	−0.623663
$834$	12.0000	0.415526
$835$	0	0
$836$	0	0
$837$	−8.00000	−0.276520
$838$	40.0000	1.38178
$839$	−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
$841$	−25.0000	−0.862069
$842$	−22.0000	−0.758170
$843$	−2.00000	−0.0688837
$844$	20.0000	0.688428
$845$	0	0
$846$	0	0
$847$	44.0000	1.51186
$848$	2.00000	0.0686803
$849$	16.0000	0.549119
$850$	0	0
$851$	80.0000	2.74236
$852$	−8.00000	−0.274075
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	20.0000	0.683586
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	0	0
$861$	−24.0000	−0.817918
$862$	−24.0000	−0.817443
$863$	−8.00000	−0.272323	−0.136162	−	0.990687i	$-0.543477\pi$
$863$	−8.00000	−0.272323	−0.136162	+	0.990687i	$0.543477\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−34.0000	−1.15537
$867$	−13.0000	−0.441503
$868$	32.0000	1.08615
$869$	0	0
$870$	0	0
$871$	72.0000	2.43963
$872$	−6.00000	−0.203186
$873$	10.0000	0.338449
$874$	8.00000	0.270604
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	−8.00000	−0.269987
$879$	−6.00000	−0.202375
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	−9.00000	−0.303046
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	−4.00000	−0.134383
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	10.0000	0.335578
$889$	−32.0000	−1.07325
$890$	0	0
$891$	0	0
$892$	16.0000	0.535720
$893$	0	0
$894$	2.00000	0.0668900
$895$	0	0
$896$	4.00000	0.133631
$897$	−48.0000	−1.60267
$898$	−30.0000	−1.00111
$899$	−16.0000	−0.533630
$900$	0	0
$901$	−4.00000	−0.133259
$902$	0	0
$903$	−32.0000	−1.06489
$904$	18.0000	0.598671
$905$	0	0
$906$	0	0
$907$	60.0000	1.99227	0.996134	−	0.0878507i	$-0.0279999\pi$
$907$	60.0000	1.99227	0.996134	+	0.0878507i	$0.0279999\pi$
$908$	−20.0000	−0.663723
$909$	−18.0000	−0.597022
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	10.0000	0.330771
$915$	0	0
$916$	6.00000	0.198246
$917$	0	0
$918$	2.00000	0.0660098
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	−6.00000	−0.197599
$923$	−48.0000	−1.57994
$924$	0	0
$925$	0	0
$926$	4.00000	0.131448
$927$	−8.00000	−0.262754
$928$	−2.00000	−0.0656532
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	0	0
$931$	9.00000	0.294963
$932$	6.00000	0.196537
$933$	12.0000	0.392862
$934$	−28.0000	−0.916188
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	48.0000	1.56726
$939$	6.00000	0.195803
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	−10.0000	−0.325818
$943$	−48.0000	−1.56310
$944$	−12.0000	−0.390567
$945$	0	0
$946$	0	0
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	−16.0000	−0.519656
$949$	−12.0000	−0.389536
$950$	0	0
$951$	26.0000	0.843108
$952$	−8.00000	−0.259281
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−2.00000	−0.0647524
$955$	0	0
$956$	−20.0000	−0.646846
$957$	0	0
$958$	−36.0000	−1.16311
$959$	−24.0000	−0.775000
$960$	0	0
$961$	33.0000	1.06452
$962$	60.0000	1.93448
$963$	−20.0000	−0.644491
$964$	−14.0000	−0.450910
$965$	0	0
$966$	−32.0000	−1.02958
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	11.0000	0.353553
$969$	−2.00000	−0.0642493
$970$	0	0
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	1.00000	0.0320750
$973$	48.0000	1.53881
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	54.0000	1.72761	0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000	1.72761	0.863807	+	0.503824i	$0.168074\pi$
$978$	8.00000	0.255812
$979$	0	0
$980$	0	0
$981$	6.00000	0.191565
$982$	40.0000	1.27645
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−6.00000	−0.191273
$985$	0	0
$986$	4.00000	0.127386
$987$	0	0
$988$	6.00000	0.190885
$989$	−64.0000	−2.03508
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	8.00000	0.254000
$993$	20.0000	0.634681
$994$	−32.0000	−1.01498
$995$	0	0
$996$	4.00000	0.126745
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	20.0000	0.633089
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.h.1.1		1
3.2	odd	2		8550.2.a.s.1.1		1
5.2	odd	4		2850.2.d.c.799.1		2
5.3	odd	4		2850.2.d.c.799.2		2
5.4	even	2		570.2.a.i.1.1	✓	1
15.14	odd	2		1710.2.a.e.1.1		1
20.19	odd	2		4560.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.i.1.1	✓	1	5.4	even	2
1710.2.a.e.1.1		1	15.14	odd	2
2850.2.a.h.1.1		1	1.1	even	1	trivial
2850.2.d.c.799.1		2	5.2	odd	4
2850.2.d.c.799.2		2	5.3	odd	4
4560.2.a.x.1.1		1	20.19	odd	2
8550.2.a.s.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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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