LMFDB - Embedded newform 1848.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1848,2,Mod(1,1848)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1848, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1848.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1848.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:	$14.7563542935$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1848.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} +1.00000 q^{13} -1.00000 q^{15} -6.00000 q^{17} -7.00000 q^{19} -1.00000 q^{21} -4.00000 q^{23} -4.00000 q^{25} +1.00000 q^{27} +3.00000 q^{29} -2.00000 q^{31} +1.00000 q^{33} +1.00000 q^{35} -7.00000 q^{37} +1.00000 q^{39} +8.00000 q^{41} -1.00000 q^{45} +13.0000 q^{47} +1.00000 q^{49} -6.00000 q^{51} -12.0000 q^{53} -1.00000 q^{55} -7.00000 q^{57} +1.00000 q^{59} +14.0000 q^{61} -1.00000 q^{63} -1.00000 q^{65} -15.0000 q^{67} -4.00000 q^{69} -8.00000 q^{71} -1.00000 q^{73} -4.00000 q^{75} -1.00000 q^{77} -4.00000 q^{79} +1.00000 q^{81} -14.0000 q^{83} +6.00000 q^{85} +3.00000 q^{87} -6.00000 q^{89} -1.00000 q^{91} -2.00000 q^{93} +7.00000 q^{95} -8.00000 q^{97} +1.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0	0
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	1.00000	0.192450
$28$	0	0
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	0	0
$33$	1.00000	0.174078
$34$	0	0
$35$	1.00000	0.169031
$36$	0	0
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	13.0000	1.89624	0.948122	−	0.317905i	$-0.102979\pi$
$47$	13.0000	1.89624	0.948122	+	0.317905i	$0.102979\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	−6.00000	−0.840168
$52$	0	0
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−7.00000	−0.927173
$58$	0	0
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	0	0
$65$	−1.00000	−0.124035
$66$	0	0
$67$	−15.0000	−1.83254	−0.916271	−	0.400559i	$-0.868816\pi$
$67$	−15.0000	−1.83254	−0.916271	+	0.400559i	$0.868816\pi$
$68$	0	0
$69$	−4.00000	−0.481543
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	0	0
$77$	−1.00000	−0.113961
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−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
$85$	6.00000	0.650791
$86$	0	0
$87$	3.00000	0.321634
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	0	0
$93$	−2.00000	−0.207390
$94$	0	0
$95$	7.00000	0.718185
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	0	0
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	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
$105$	1.00000	0.0975900
$106$	0	0
$107$	7.00000	0.676716	0.338358	−	0.941018i	$-0.390129\pi$
$107$	7.00000	0.676716	0.338358	+	0.941018i	$0.390129\pi$
$108$	0	0
$109$	−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
$111$	−7.00000	−0.664411
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	0	0
$117$	1.00000	0.0924500
$118$	0	0
$119$	6.00000	0.550019
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	8.00000	0.721336
$124$	0	0
$125$	9.00000	0.804984
$126$	0	0
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	7.00000	0.606977
$134$	0	0
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	13.0000	1.09480
$142$	0	0
$143$	1.00000	0.0836242
$144$	0	0
$145$	−3.00000	−0.249136
$146$	0	0
$147$	1.00000	0.0824786
$148$	0	0
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	2.00000	0.160644
$156$	0	0
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	0	0
$159$	−12.0000	−0.951662
$160$	0	0
$161$	4.00000	0.315244
$162$	0	0
$163$	17.0000	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$164$	0	0
$165$	−1.00000	−0.0778499
$166$	0	0
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−7.00000	−0.535303
$172$	0	0
$173$	20.0000	1.52057	0.760286	−	0.649589i	$-0.225059\pi$
$173$	20.0000	1.52057	0.760286	+	0.649589i	$0.225059\pi$
$174$	0	0
$175$	4.00000	0.302372
$176$	0	0
$177$	1.00000	0.0751646
$178$	0	0
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	24.0000	1.78391	0.891953	−	0.452128i	$-0.149335\pi$
$181$	24.0000	1.78391	0.891953	+	0.452128i	$0.149335\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	0	0
$185$	7.00000	0.514650
$186$	0	0
$187$	−6.00000	−0.438763
$188$	0	0
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−10.0000	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$192$	0	0
$193$	−24.0000	−1.72756	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−24.0000	−1.72756	−0.863779	+	0.503871i	$0.831909\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−15.0000	−1.05802
$202$	0	0
$203$	−3.00000	−0.210559
$204$	0	0
$205$	−8.00000	−0.558744
$206$	0	0
$207$	−4.00000	−0.278019
$208$	0	0
$209$	−7.00000	−0.484200
$210$	0	0
$211$	−6.00000	−0.413057	−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000	−0.413057	−0.206529	+	0.978441i	$0.566217\pi$
$212$	0	0
$213$	−8.00000	−0.548151
$214$	0	0
$215$	0	0
$216$	0	0
$217$	2.00000	0.135769
$218$	0	0
$219$	−1.00000	−0.0675737
$220$	0	0
$221$	−6.00000	−0.403604
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	0	0
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	0	0
$229$	24.0000	1.58596	0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000	1.58596	0.792982	+	0.609245i	$0.208527\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	−13.0000	−0.848026
$236$	0	0
$237$	−4.00000	−0.259828
$238$	0	0
$239$	21.0000	1.35838	0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000	1.35838	0.679189	+	0.733964i	$0.262332\pi$
$240$	0	0
$241$	29.0000	1.86805	0.934027	−	0.357202i	$-0.116269\pi$
$241$	29.0000	1.86805	0.934027	+	0.357202i	$0.116269\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	−7.00000	−0.445399
$248$	0	0
$249$	−14.0000	−0.887214
$250$	0	0
$251$	23.0000	1.45175	0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000	1.45175	0.725874	+	0.687828i	$0.241436\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	0	0
$255$	6.00000	0.375735
$256$	0	0
$257$	−1.00000	−0.0623783	−0.0311891	−	0.999514i	$-0.509929\pi$
$257$	−1.00000	−0.0623783	−0.0311891	+	0.999514i	$0.509929\pi$
$258$	0	0
$259$	7.00000	0.434959
$260$	0	0
$261$	3.00000	0.185695
$262$	0	0
$263$	−5.00000	−0.308313	−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000	−0.308313	−0.154157	+	0.988046i	$0.549266\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	−6.00000	−0.367194
$268$	0	0
$269$	22.0000	1.34136	0.670682	−	0.741745i	$-0.266002\pi$
$269$	22.0000	1.34136	0.670682	+	0.741745i	$0.266002\pi$
$270$	0	0
$271$	−11.0000	−0.668202	−0.334101	−	0.942537i	$-0.608433\pi$
$271$	−11.0000	−0.668202	−0.334101	+	0.942537i	$0.608433\pi$
$272$	0	0
$273$	−1.00000	−0.0605228
$274$	0	0
$275$	−4.00000	−0.241209
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	0	0
$279$	−2.00000	−0.119737
$280$	0	0
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	0	0
$283$	−15.0000	−0.891657	−0.445829	−	0.895118i	$-0.647091\pi$
$283$	−15.0000	−0.891657	−0.445829	+	0.895118i	$0.647091\pi$
$284$	0	0
$285$	7.00000	0.414644
$286$	0	0
$287$	−8.00000	−0.472225
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−8.00000	−0.468968
$292$	0	0
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	0	0
$295$	−1.00000	−0.0582223
$296$	0	0
$297$	1.00000	0.0580259
$298$	0	0
$299$	−4.00000	−0.231326
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−2.00000	−0.114897
$304$	0	0
$305$	−14.0000	−0.801638
$306$	0	0
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	−18.0000	−1.02398
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	0	0
$315$	1.00000	0.0563436
$316$	0	0
$317$	4.00000	0.224662	0.112331	−	0.993671i	$-0.464168\pi$
$317$	4.00000	0.224662	0.112331	+	0.993671i	$0.464168\pi$
$318$	0	0
$319$	3.00000	0.167968
$320$	0	0
$321$	7.00000	0.390702
$322$	0	0
$323$	42.0000	2.33694
$324$	0	0
$325$	−4.00000	−0.221880
$326$	0	0
$327$	−10.0000	−0.553001
$328$	0	0
$329$	−13.0000	−0.716713
$330$	0	0
$331$	−32.0000	−1.75888	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000	−1.75888	−0.879440	+	0.476011i	$0.842082\pi$
$332$	0	0
$333$	−7.00000	−0.383598
$334$	0	0
$335$	15.0000	0.819538
$336$	0	0
$337$	12.0000	0.653682	0.326841	−	0.945079i	$-0.394016\pi$
$337$	12.0000	0.653682	0.326841	+	0.945079i	$0.394016\pi$
$338$	0	0
$339$	−2.00000	−0.108625
$340$	0	0
$341$	−2.00000	−0.108306
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	4.00000	0.215353
$346$	0	0
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	0	0
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0	0
$353$	5.00000	0.266123	0.133062	−	0.991108i	$-0.457519\pi$
$353$	5.00000	0.266123	0.133062	+	0.991108i	$0.457519\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	0	0
$357$	6.00000	0.317554
$358$	0	0
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	1.00000	0.0524864
$364$	0	0
$365$	1.00000	0.0523424
$366$	0	0
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	0	0
$369$	8.00000	0.416463
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	0	0
$375$	9.00000	0.464758
$376$	0	0
$377$	3.00000	0.154508
$378$	0	0
$379$	23.0000	1.18143	0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000	1.18143	0.590715	+	0.806880i	$0.298846\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	0	0
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	1.00000	0.0509647
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−28.0000	−1.41966	−0.709828	−	0.704375i	$-0.751227\pi$
$389$	−28.0000	−1.41966	−0.709828	+	0.704375i	$0.751227\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	0	0
$393$	0	0
$394$	0	0
$395$	4.00000	0.201262
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	0	0
$399$	7.00000	0.350438
$400$	0	0
$401$	−20.0000	−0.998752	−0.499376	−	0.866385i	$-0.666437\pi$
$401$	−20.0000	−0.998752	−0.499376	+	0.866385i	$0.666437\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−7.00000	−0.346977
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	0	0
$413$	−1.00000	−0.0492068
$414$	0	0
$415$	14.0000	0.687233
$416$	0	0
$417$	−16.0000	−0.783523
$418$	0	0
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	0	0
$421$	−33.0000	−1.60832	−0.804161	−	0.594412i	$-0.797385\pi$
$421$	−33.0000	−1.60832	−0.804161	+	0.594412i	$0.797385\pi$
$422$	0	0
$423$	13.0000	0.632082
$424$	0	0
$425$	24.0000	1.16417
$426$	0	0
$427$	−14.0000	−0.677507
$428$	0	0
$429$	1.00000	0.0482805
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	0	0
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	−3.00000	−0.143839
$436$	0	0
$437$	28.0000	1.33942
$438$	0	0
$439$	−27.0000	−1.28864	−0.644320	−	0.764756i	$-0.722859\pi$
$439$	−27.0000	−1.28864	−0.644320	+	0.764756i	$0.722859\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	6.00000	0.284427
$446$	0	0
$447$	15.0000	0.709476
$448$	0	0
$449$	−20.0000	−0.943858	−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000	−0.943858	−0.471929	+	0.881636i	$0.656442\pi$
$450$	0	0
$451$	8.00000	0.376705
$452$	0	0
$453$	−2.00000	−0.0939682
$454$	0	0
$455$	1.00000	0.0468807
$456$	0	0
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	0	0
$459$	−6.00000	−0.280056
$460$	0	0
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	0	0
$463$	−7.00000	−0.325318	−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000	−0.325318	−0.162659	+	0.986682i	$0.552007\pi$
$464$	0	0
$465$	2.00000	0.0927478
$466$	0	0
$467$	29.0000	1.34196	0.670980	−	0.741475i	$-0.265874\pi$
$467$	29.0000	1.34196	0.670980	+	0.741475i	$0.265874\pi$
$468$	0	0
$469$	15.0000	0.692636
$470$	0	0
$471$	8.00000	0.368621
$472$	0	0
$473$	0	0
$474$	0	0
$475$	28.0000	1.28473
$476$	0	0
$477$	−12.0000	−0.549442
$478$	0	0
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	−7.00000	−0.319173
$482$	0	0
$483$	4.00000	0.182006
$484$	0	0
$485$	8.00000	0.363261
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	0	0
$489$	17.0000	0.768767
$490$	0	0
$491$	39.0000	1.76005	0.880023	−	0.474932i	$-0.157527\pi$
$491$	39.0000	1.76005	0.880023	+	0.474932i	$0.157527\pi$
$492$	0	0
$493$	−18.0000	−0.810679
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	0	0
$497$	8.00000	0.358849
$498$	0	0
$499$	31.0000	1.38775	0.693875	−	0.720095i	$-0.255902\pi$
$499$	31.0000	1.38775	0.693875	+	0.720095i	$0.255902\pi$
$500$	0	0
$501$	16.0000	0.714827
$502$	0	0
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	0	0
$507$	−12.0000	−0.532939
$508$	0	0
$509$	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
$511$	1.00000	0.0442374
$512$	0	0
$513$	−7.00000	−0.309058
$514$	0	0
$515$	18.0000	0.793175
$516$	0	0
$517$	13.0000	0.571739
$518$	0	0
$519$	20.0000	0.877903
$520$	0	0
$521$	−33.0000	−1.44576	−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000	−1.44576	−0.722878	+	0.690976i	$0.757181\pi$
$522$	0	0
$523$	−9.00000	−0.393543	−0.196771	−	0.980449i	$-0.563046\pi$
$523$	−9.00000	−0.393543	−0.196771	+	0.980449i	$0.563046\pi$
$524$	0	0
$525$	4.00000	0.174574
$526$	0	0
$527$	12.0000	0.522728
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	1.00000	0.0433963
$532$	0	0
$533$	8.00000	0.346518
$534$	0	0
$535$	−7.00000	−0.302636
$536$	0	0
$537$	−24.0000	−1.03568
$538$	0	0
$539$	1.00000	0.0430730
$540$	0	0
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	0	0
$543$	24.0000	1.02994
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	0	0
$549$	14.0000	0.597505
$550$	0	0
$551$	−21.0000	−0.894630
$552$	0	0
$553$	4.00000	0.170097
$554$	0	0
$555$	7.00000	0.297133
$556$	0	0
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−6.00000	−0.253320
$562$	0	0
$563$	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
$565$	2.00000	0.0841406
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	0	0
$573$	−10.0000	−0.417756
$574$	0	0
$575$	16.0000	0.667246
$576$	0	0
$577$	30.0000	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$578$	0	0
$579$	−24.0000	−0.997406
$580$	0	0
$581$	14.0000	0.580818
$582$	0	0
$583$	−12.0000	−0.496989
$584$	0	0
$585$	−1.00000	−0.0413449
$586$	0	0
$587$	−21.0000	−0.866763	−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000	−0.866763	−0.433381	+	0.901211i	$0.642680\pi$
$588$	0	0
$589$	14.0000	0.576860
$590$	0	0
$591$	22.0000	0.904959
$592$	0	0
$593$	24.0000	0.985562	0.492781	−	0.870153i	$-0.335980\pi$
$593$	24.0000	0.985562	0.492781	+	0.870153i	$0.335980\pi$
$594$	0	0
$595$	−6.00000	−0.245976
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	−13.0000	−0.530281	−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000	−0.530281	−0.265141	+	0.964210i	$0.585418\pi$
$602$	0	0
$603$	−15.0000	−0.610847
$604$	0	0
$605$	−1.00000	−0.0406558
$606$	0	0
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	0	0
$609$	−3.00000	−0.121566
$610$	0	0
$611$	13.0000	0.525924
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	0	0
$615$	−8.00000	−0.322591
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	42.0000	1.68812	0.844061	−	0.536247i	$-0.180158\pi$
$619$	42.0000	1.68812	0.844061	+	0.536247i	$0.180158\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	0	0
$623$	6.00000	0.240385
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	−7.00000	−0.279553
$628$	0	0
$629$	42.0000	1.67465
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	0	0
$633$	−6.00000	−0.238479
$634$	0	0
$635$	−2.00000	−0.0793676
$636$	0	0
$637$	1.00000	0.0396214
$638$	0	0
$639$	−8.00000	−0.316475
$640$	0	0
$641$	−34.0000	−1.34292	−0.671460	−	0.741041i	$-0.734332\pi$
$641$	−34.0000	−1.34292	−0.671460	+	0.741041i	$0.734332\pi$
$642$	0	0
$643$	−32.0000	−1.26196	−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000	−1.26196	−0.630978	+	0.775800i	$0.717346\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	31.0000	1.21874	0.609368	−	0.792888i	$-0.291423\pi$
$647$	31.0000	1.21874	0.609368	+	0.792888i	$0.291423\pi$
$648$	0	0
$649$	1.00000	0.0392534
$650$	0	0
$651$	2.00000	0.0783862
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−1.00000	−0.0390137
$658$	0	0
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	0	0
$663$	−6.00000	−0.233021
$664$	0	0
$665$	−7.00000	−0.271448
$666$	0	0
$667$	−12.0000	−0.464642
$668$	0	0
$669$	−14.0000	−0.541271
$670$	0	0
$671$	14.0000	0.540464
$672$	0	0
$673$	−4.00000	−0.154189	−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000	−0.154189	−0.0770943	+	0.997024i	$0.524564\pi$
$674$	0	0
$675$	−4.00000	−0.153960
$676$	0	0
$677$	−26.0000	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$678$	0	0
$679$	8.00000	0.307012
$680$	0	0
$681$	−18.0000	−0.689761
$682$	0	0
$683$	−34.0000	−1.30097	−0.650487	−	0.759517i	$-0.725435\pi$
$683$	−34.0000	−1.30097	−0.650487	+	0.759517i	$0.725435\pi$
$684$	0	0
$685$	−10.0000	−0.382080
$686$	0	0
$687$	24.0000	0.915657
$688$	0	0
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−18.0000	−0.684752	−0.342376	−	0.939563i	$-0.611232\pi$
$691$	−18.0000	−0.684752	−0.342376	+	0.939563i	$0.611232\pi$
$692$	0	0
$693$	−1.00000	−0.0379869
$694$	0	0
$695$	16.0000	0.606915
$696$	0	0
$697$	−48.0000	−1.81813
$698$	0	0
$699$	6.00000	0.226941
$700$	0	0
$701$	14.0000	0.528773	0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000	0.528773	0.264386	+	0.964417i	$0.414831\pi$
$702$	0	0
$703$	49.0000	1.84807
$704$	0	0
$705$	−13.0000	−0.489608
$706$	0	0
$707$	2.00000	0.0752177
$708$	0	0
$709$	3.00000	0.112667	0.0563337	−	0.998412i	$-0.482059\pi$
$709$	3.00000	0.112667	0.0563337	+	0.998412i	$0.482059\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	0	0
$713$	8.00000	0.299602
$714$	0	0
$715$	−1.00000	−0.0373979
$716$	0	0
$717$	21.0000	0.784259
$718$	0	0
$719$	−13.0000	−0.484818	−0.242409	−	0.970174i	$-0.577938\pi$
$719$	−13.0000	−0.484818	−0.242409	+	0.970174i	$0.577938\pi$
$720$	0	0
$721$	18.0000	0.670355
$722$	0	0
$723$	29.0000	1.07852
$724$	0	0
$725$	−12.0000	−0.445669
$726$	0	0
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	0	0
$735$	−1.00000	−0.0368856
$736$	0	0
$737$	−15.0000	−0.552532
$738$	0	0
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	0	0
$741$	−7.00000	−0.257151
$742$	0	0
$743$	43.0000	1.57752	0.788759	−	0.614703i	$-0.210724\pi$
$743$	43.0000	1.57752	0.788759	+	0.614703i	$0.210724\pi$
$744$	0	0
$745$	−15.0000	−0.549557
$746$	0	0
$747$	−14.0000	−0.512233
$748$	0	0
$749$	−7.00000	−0.255774
$750$	0	0
$751$	33.0000	1.20419	0.602094	−	0.798426i	$-0.294333\pi$
$751$	33.0000	1.20419	0.602094	+	0.798426i	$0.294333\pi$
$752$	0	0
$753$	23.0000	0.838167
$754$	0	0
$755$	2.00000	0.0727875
$756$	0	0
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	0	0
$759$	−4.00000	−0.145191
$760$	0	0
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	0	0
$765$	6.00000	0.216930
$766$	0	0
$767$	1.00000	0.0361079
$768$	0	0
$769$	37.0000	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$769$	37.0000	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$770$	0	0
$771$	−1.00000	−0.0360141
$772$	0	0
$773$	−5.00000	−0.179838	−0.0899188	−	0.995949i	$-0.528661\pi$
$773$	−5.00000	−0.179838	−0.0899188	+	0.995949i	$0.528661\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	0	0
$777$	7.00000	0.251124
$778$	0	0
$779$	−56.0000	−2.00641
$780$	0	0
$781$	−8.00000	−0.286263
$782$	0	0
$783$	3.00000	0.107211
$784$	0	0
$785$	−8.00000	−0.285532
$786$	0	0
$787$	23.0000	0.819861	0.409931	−	0.912117i	$-0.365553\pi$
$787$	23.0000	0.819861	0.409931	+	0.912117i	$0.365553\pi$
$788$	0	0
$789$	−5.00000	−0.178005
$790$	0	0
$791$	2.00000	0.0711118
$792$	0	0
$793$	14.0000	0.497155
$794$	0	0
$795$	12.0000	0.425596
$796$	0	0
$797$	−27.0000	−0.956389	−0.478195	−	0.878254i	$-0.658709\pi$
$797$	−27.0000	−0.956389	−0.478195	+	0.878254i	$0.658709\pi$
$798$	0	0
$799$	−78.0000	−2.75944
$800$	0	0
$801$	−6.00000	−0.212000
$802$	0	0
$803$	−1.00000	−0.0352892
$804$	0	0
$805$	−4.00000	−0.140981
$806$	0	0
$807$	22.0000	0.774437
$808$	0	0
$809$	11.0000	0.386739	0.193370	−	0.981126i	$-0.438058\pi$
$809$	11.0000	0.386739	0.193370	+	0.981126i	$0.438058\pi$
$810$	0	0
$811$	−1.00000	−0.0351147	−0.0175574	−	0.999846i	$-0.505589\pi$
$811$	−1.00000	−0.0351147	−0.0175574	+	0.999846i	$0.505589\pi$
$812$	0	0
$813$	−11.0000	−0.385787
$814$	0	0
$815$	−17.0000	−0.595484
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	−15.0000	−0.523504	−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000	−0.523504	−0.261752	+	0.965135i	$0.584300\pi$
$822$	0	0
$823$	−31.0000	−1.08059	−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000	−1.08059	−0.540296	+	0.841475i	$0.681688\pi$
$824$	0	0
$825$	−4.00000	−0.139262
$826$	0	0
$827$	7.00000	0.243414	0.121707	−	0.992566i	$-0.461163\pi$
$827$	7.00000	0.243414	0.121707	+	0.992566i	$0.461163\pi$
$828$	0	0
$829$	32.0000	1.11141	0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000	1.11141	0.555703	+	0.831381i	$0.312449\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	0	0
$833$	−6.00000	−0.207888
$834$	0	0
$835$	−16.0000	−0.553703
$836$	0	0
$837$	−2.00000	−0.0691301
$838$	0	0
$839$	−27.0000	−0.932144	−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	15.0000	0.516627
$844$	0	0
$845$	12.0000	0.412813
$846$	0	0
$847$	−1.00000	−0.0343604
$848$	0	0
$849$	−15.0000	−0.514799
$850$	0	0
$851$	28.0000	0.959828
$852$	0	0
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	0	0
$855$	7.00000	0.239395
$856$	0	0
$857$	−46.0000	−1.57133	−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000	−1.57133	−0.785665	+	0.618652i	$0.787679\pi$
$858$	0	0
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	0	0
$861$	−8.00000	−0.272639
$862$	0	0
$863$	−56.0000	−1.90626	−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000	−1.90626	−0.953131	+	0.302558i	$0.902160\pi$
$864$	0	0
$865$	−20.0000	−0.680020
$866$	0	0
$867$	19.0000	0.645274
$868$	0	0
$869$	−4.00000	−0.135691
$870$	0	0
$871$	−15.0000	−0.508256
$872$	0	0
$873$	−8.00000	−0.270759
$874$	0	0
$875$	−9.00000	−0.304256
$876$	0	0
$877$	16.0000	0.540282	0.270141	−	0.962821i	$-0.412930\pi$
$877$	16.0000	0.540282	0.270141	+	0.962821i	$0.412930\pi$
$878$	0	0
$879$	−16.0000	−0.539667
$880$	0	0
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	0	0
$883$	55.0000	1.85090	0.925449	−	0.378873i	$-0.123688\pi$
$883$	55.0000	1.85090	0.925449	+	0.378873i	$0.123688\pi$
$884$	0	0
$885$	−1.00000	−0.0336146
$886$	0	0
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	0	0
$889$	−2.00000	−0.0670778
$890$	0	0
$891$	1.00000	0.0335013
$892$	0	0
$893$	−91.0000	−3.04520
$894$	0	0
$895$	24.0000	0.802232
$896$	0	0
$897$	−4.00000	−0.133556
$898$	0	0
$899$	−6.00000	−0.200111
$900$	0	0
$901$	72.0000	2.39867
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−24.0000	−0.797787
$906$	0	0
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	0	0
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	0	0
$913$	−14.0000	−0.463332
$914$	0	0
$915$	−14.0000	−0.462826
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	0	0
$923$	−8.00000	−0.263323
$924$	0	0
$925$	28.0000	0.920634
$926$	0	0
$927$	−18.0000	−0.591198
$928$	0	0
$929$	45.0000	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$930$	0	0
$931$	−7.00000	−0.229416
$932$	0	0
$933$	24.0000	0.785725
$934$	0	0
$935$	6.00000	0.196221
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	−18.0000	−0.587408
$940$	0	0
$941$	−16.0000	−0.521585	−0.260793	−	0.965395i	$-0.583984\pi$
$941$	−16.0000	−0.521585	−0.260793	+	0.965395i	$0.583984\pi$
$942$	0	0
$943$	−32.0000	−1.04206
$944$	0	0
$945$	1.00000	0.0325300
$946$	0	0
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	−1.00000	−0.0324614
$950$	0	0
$951$	4.00000	0.129709
$952$	0	0
$953$	−53.0000	−1.71684	−0.858419	−	0.512949i	$-0.828553\pi$
$953$	−53.0000	−1.71684	−0.858419	+	0.512949i	$0.828553\pi$
$954$	0	0
$955$	10.0000	0.323592
$956$	0	0
$957$	3.00000	0.0969762
$958$	0	0
$959$	−10.0000	−0.322917
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	7.00000	0.225572
$964$	0	0
$965$	24.0000	0.772587
$966$	0	0
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	0	0
$969$	42.0000	1.34923
$970$	0	0
$971$	−29.0000	−0.930654	−0.465327	−	0.885139i	$-0.654063\pi$
$971$	−29.0000	−0.930654	−0.465327	+	0.885139i	$0.654063\pi$
$972$	0	0
$973$	16.0000	0.512936
$974$	0	0
$975$	−4.00000	−0.128103
$976$	0	0
$977$	−40.0000	−1.27971	−0.639857	−	0.768494i	$-0.721006\pi$
$977$	−40.0000	−1.27971	−0.639857	+	0.768494i	$0.721006\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	0	0
$981$	−10.0000	−0.319275
$982$	0	0
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	−22.0000	−0.700978
$986$	0	0
$987$	−13.0000	−0.413795
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−15.0000	−0.476491	−0.238245	−	0.971205i	$-0.576572\pi$
$991$	−15.0000	−0.476491	−0.238245	+	0.971205i	$0.576572\pi$
$992$	0	0
$993$	−32.0000	−1.01549
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	0	0
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1848.2.a.h.1.1	✓	1
3.2	odd	2		5544.2.a.m.1.1		1
4.3	odd	2		3696.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1848.2.a.h.1.1	✓	1	1.1	even	1	trivial
3696.2.a.g.1.1		1	4.3	odd	2
5544.2.a.m.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:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.a (trivial)

Introduction

L-functions

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