LMFDB - Embedded newform 2394.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, 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("2394.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.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:	$19.1161862439$
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	$\chi$	$=$	2394.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} -6.00000 q^{11} +2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{19} +6.00000 q^{22} +6.00000 q^{23} -5.00000 q^{25} -2.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} +8.00000 q^{31} -1.00000 q^{32} -10.0000 q^{37} -1.00000 q^{38} +6.00000 q^{41} -4.00000 q^{43} -6.00000 q^{44} -6.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} +5.00000 q^{50} +2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{56} +6.00000 q^{58} -12.0000 q^{59} +2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +2.00000 q^{73} +10.0000 q^{74} +1.00000 q^{76} -6.00000 q^{77} -4.00000 q^{79} -6.00000 q^{82} -6.00000 q^{83} +4.00000 q^{86} +6.00000 q^{88} +6.00000 q^{89} +2.00000 q^{91} +6.00000 q^{92} +6.00000 q^{94} +14.0000 q^{97} -1.00000 q^{98} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−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
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	0	0
$22$	6.00000	1.27920
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	−2.00000	−0.392232
$27$	0	0
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−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
$39$	0	0
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	5.00000	0.707107
$51$	0	0
$52$	2.00000	0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	−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	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	1.00000	0.114708
$77$	−6.00000	−0.683763
$78$	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
$81$	0	0
$82$	−6.00000	−0.662589
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	0	0
$86$	4.00000	0.431331
$87$	0	0
$88$	6.00000	0.639602
$89$	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
$91$	2.00000	0.209657
$92$	6.00000	0.625543
$93$	0	0
$94$	6.00000	0.618853
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−5.00000	−0.500000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.00000	−0.196116
$105$	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
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	−6.00000	−0.557086
$117$	0	0
$118$	12.0000	1.10469
$119$	0	0
$120$	0	0
$121$	25.0000	2.27273
$122$	−2.00000	−0.181071
$123$	0	0
$124$	8.00000	0.718421
$125$	0	0
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	4.00000	0.345547
$135$	0	0
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−12.0000	−1.00349
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	−10.0000	−0.821995
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	6.00000	0.483494
$155$	0	0
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	0	0
$161$	6.00000	0.472866
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	6.00000	0.465690
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	−4.00000	−0.304997
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−5.00000	−0.377964
$176$	−6.00000	−0.452267
$177$	0	0
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	−6.00000	−0.442326
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−6.00000	−0.437595
$189$	0	0
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	0	0
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	1.00000	0.0714286
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	5.00000	0.353553
$201$	0	0
$202$	12.0000	0.844317
$203$	−6.00000	−0.421117
$204$	0	0
$205$	0	0
$206$	4.00000	0.278693
$207$	0	0
$208$	2.00000	0.138675
$209$	−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
$218$	−2.00000	−0.135457
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−28.0000	−1.87502	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000	−1.87502	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	6.00000	0.399114
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	0	0
$235$	0	0
$236$	−12.0000	−0.781133
$237$	0	0
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−25.0000	−1.60706
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	2.00000	0.127257
$248$	−8.00000	−0.508001
$249$	0	0
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	−36.0000	−2.26330
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	0	0
$261$	0	0
$262$	18.0000	1.11204
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	0	0
$274$	−12.0000	−0.724947
$275$	30.0000	1.80907
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	12.0000	0.709575
$287$	6.00000	0.354169
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	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	$0.556077\pi$
$294$	0	0
$295$	0	0
$296$	10.0000	0.581238
$297$	0	0
$298$	0	0
$299$	12.0000	0.693978
$300$	0	0
$301$	−4.00000	−0.230556
$302$	4.00000	0.230174
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	0	0
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	−6.00000	−0.341882
$309$	0	0
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	−4.00000	−0.225018
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	36.0000	2.01561
$320$	0	0
$321$	0	0
$322$	−6.00000	−0.334367
$323$	0	0
$324$	0	0
$325$	−10.0000	−0.554700
$326$	4.00000	0.221540
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−6.00000	−0.330791
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	0	0
$341$	−48.0000	−2.59935
$342$	0	0
$343$	1.00000	0.0539949
$344$	4.00000	0.215666
$345$	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
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	5.00000	0.267261
$351$	0	0
$352$	6.00000	0.319801
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	0	0
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−2.00000	−0.105118
$363$	0	0
$364$	2.00000	0.104828
$365$	0	0
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	−6.00000	−0.311504
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	0	0
$376$	6.00000	0.309426
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	0	0
$382$	6.00000	0.306987
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	0	0
$385$	0	0
$386$	22.0000	1.11977
$387$	0	0
$388$	14.0000	0.710742
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−5.00000	−0.250000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	16.0000	0.797017
$404$	−12.0000	−0.597022
$405$	0	0
$406$	6.00000	0.297775
$407$	60.0000	2.97409
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	0	0
$412$	−4.00000	−0.197066
$413$	−12.0000	−0.590481
$414$	0	0
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	6.00000	0.293470
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	2.00000	0.0967868
$428$	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
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	2.00000	0.0957826
$437$	6.00000	0.287019
$438$	0	0
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	0	0
$445$	0	0
$446$	28.0000	1.32584
$447$	0	0
$448$	1.00000	0.0472456
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	−36.0000	−1.69517
$452$	−6.00000	−0.282216
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−26.0000	−1.21490
$459$	0	0
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	0	0
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−24.0000	−1.11178
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	12.0000	0.552345
$473$	24.0000	1.10352
$474$	0	0
$475$	−5.00000	−0.229416
$476$	0	0
$477$	0	0
$478$	6.00000	0.274434
$479$	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
$481$	−20.0000	−0.911922
$482$	10.0000	0.455488
$483$	0	0
$484$	25.0000	1.13636
$485$	0	0
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	0	0
$491$	42.0000	1.89543	0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000	1.89543	0.947717	+	0.319113i	$0.103385\pi$
$492$	0	0
$493$	0	0
$494$	−2.00000	−0.0899843
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	0	0
$501$	0	0
$502$	−18.0000	−0.803379
$503$	30.0000	1.33763	0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000	1.33763	0.668817	+	0.743427i	$0.266801\pi$
$504$	0	0
$505$	0	0
$506$	36.0000	1.60040
$507$	0	0
$508$	−16.0000	−0.709885
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−18.0000	−0.793946
$515$	0	0
$516$	0	0
$517$	36.0000	1.58328
$518$	10.0000	0.439375
$519$	0	0
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	6.00000	0.261612
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	1.00000	0.0433555
$533$	12.0000	0.519778
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	30.0000	1.29339
$539$	−6.00000	−0.258438
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	−30.0000	−1.27920
$551$	−6.00000	−0.255609
$552$	0	0
$553$	−4.00000	−0.170097
$554$	−26.0000	−1.10463
$555$	0	0
$556$	−4.00000	−0.169638
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	0	0
$566$	4.00000	0.168133
$567$	0	0
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−12.0000	−0.501745
$573$	0	0
$574$	−6.00000	−0.250435
$575$	−30.0000	−1.25109
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	17.0000	0.707107
$579$	0	0
$580$	0	0
$581$	−6.00000	−0.248922
$582$	0	0
$583$	36.0000	1.49097
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	6.00000	0.247858
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	0	0
$591$	0	0
$592$	−10.0000	−0.410997
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−12.0000	−0.490716
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	4.00000	0.163028
$603$	0	0
$604$	−4.00000	−0.162758
$605$	0	0
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	−12.0000	−0.485468
$612$	0	0
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	6.00000	0.241747
$617$	36.0000	1.44931	0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000	1.44931	0.724653	+	0.689114i	$0.242000\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	−18.0000	−0.721734
$623$	6.00000	0.240385
$624$	0	0
$625$	25.0000	1.00000
$626$	10.0000	0.399680
$627$	0	0
$628$	−22.0000	−0.877896
$629$	0	0
$630$	0	0
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	4.00000	0.159111
$633$	0	0
$634$	−6.00000	−0.238290
$635$	0	0
$636$	0	0
$637$	2.00000	0.0792429
$638$	−36.0000	−1.42525
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	0	0
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	72.0000	2.82625
$650$	10.0000	0.392232
$651$	0	0
$652$	−4.00000	−0.156652
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	6.00000	0.233904
$659$	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
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−8.00000	−0.310929
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	−36.0000	−1.39393
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	−14.0000	−0.539260
$675$	0	0
$676$	−9.00000	−0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	14.0000	0.537271
$680$	0	0
$681$	0	0
$682$	48.0000	1.83801
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	6.00000	0.227757
$695$	0	0
$696$	0	0
$697$	0	0
$698$	34.0000	1.28692
$699$	0	0
$700$	−5.00000	−0.188982
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	0	0
$703$	−10.0000	−0.377157
$704$	−6.00000	−0.226134
$705$	0	0
$706$	0	0
$707$	−12.0000	−0.451306
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	0	0
$712$	−6.00000	−0.224860
$713$	48.0000	1.79761
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−18.0000	−0.671754
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	−1.00000	−0.0372161
$723$	0	0
$724$	2.00000	0.0743294
$725$	30.0000	1.11417
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	−2.00000	−0.0741249
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	−6.00000	−0.221163
$737$	24.0000	0.884051
$738$	0	0
$739$	−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
$741$	0	0
$742$	6.00000	0.220267
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	0	0
$746$	−14.0000	−0.512576
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	12.0000	0.437014
$755$	0	0
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	0	0
$763$	2.00000	0.0724049
$764$	−6.00000	−0.217072
$765$	0	0
$766$	36.0000	1.30073
$767$	−24.0000	−0.866590
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	0	0
$771$	0	0
$772$	−22.0000	−0.791797
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−40.0000	−1.43684
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−12.0000	−0.430221
$779$	6.00000	0.214972
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−12.0000	−0.427482
$789$	0	0
$790$	0	0
$791$	−6.00000	−0.213335
$792$	0	0
$793$	4.00000	0.142044
$794$	−14.0000	−0.496841
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−6.00000	−0.212531	−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000	−0.212531	−0.106265	+	0.994338i	$0.533889\pi$
$798$	0	0
$799$	0	0
$800$	5.00000	0.176777
$801$	0	0
$802$	−18.0000	−0.635602
$803$	−12.0000	−0.423471
$804$	0	0
$805$	0	0
$806$	−16.0000	−0.563576
$807$	0	0
$808$	12.0000	0.422159
$809$	−24.0000	−0.843795	−0.421898	−	0.906644i	$-0.638636\pi$
$809$	−24.0000	−0.843795	−0.421898	+	0.906644i	$0.638636\pi$
$810$	0	0
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	−60.0000	−2.10300
$815$	0	0
$816$	0	0
$817$	−4.00000	−0.139942
$818$	10.0000	0.349642
$819$	0	0
$820$	0	0
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	0	0
$823$	56.0000	1.95204	0.976019	−	0.217687i	$-0.0698512\pi$
$823$	56.0000	1.95204	0.976019	+	0.217687i	$0.0698512\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	12.0000	0.417533
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	0	0
$836$	−6.00000	−0.207514
$837$	0	0
$838$	−30.0000	−1.03633
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	0	0
$844$	−4.00000	−0.137686
$845$	0	0
$846$	0	0
$847$	25.0000	0.859010
$848$	−6.00000	−0.206041
$849$	0	0
$850$	0	0
$851$	−60.0000	−2.05677
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	0	0
$857$	−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
$859$	−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
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	−26.0000	−0.883516
$867$	0	0
$868$	8.00000	0.271538
$869$	24.0000	0.814144
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−2.00000	−0.0677285
$873$	0	0
$874$	−6.00000	−0.202953
$875$	0	0
$876$	0	0
$877$	−10.0000	−0.337676	−0.168838	−	0.985644i	$-0.554001\pi$
$877$	−10.0000	−0.337676	−0.168838	+	0.985644i	$0.554001\pi$
$878$	28.0000	0.944954
$879$	0	0
$880$	0	0
$881$	−48.0000	−1.61716	−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000	−1.61716	−0.808581	+	0.588386i	$0.799764\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	0	0
$885$	0	0
$886$	−18.0000	−0.604722
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	0	0
$891$	0	0
$892$	−28.0000	−0.937509
$893$	−6.00000	−0.200782
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−48.0000	−1.60089
$900$	0	0
$901$	0	0
$902$	36.0000	1.19867
$903$	0	0
$904$	6.00000	0.199557
$905$	0	0
$906$	0	0
$907$	−52.0000	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	36.0000	1.19143
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	26.0000	0.859064
$917$	−18.0000	−0.594412
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	0	0
$922$	−12.0000	−0.395199
$923$	0	0
$924$	0	0
$925$	50.0000	1.64399
$926$	40.0000	1.31448
$927$	0	0
$928$	6.00000	0.196960
$929$	−12.0000	−0.393707	−0.196854	−	0.980433i	$-0.563072\pi$
$929$	−12.0000	−0.393707	−0.196854	+	0.980433i	$0.563072\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	24.0000	0.786146
$933$	0	0
$934$	6.00000	0.196326
$935$	0	0
$936$	0	0
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	36.0000	1.17232
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−24.0000	−0.780307
$947$	42.0000	1.36482	0.682408	−	0.730971i	$-0.260933\pi$
$947$	42.0000	1.36482	0.682408	+	0.730971i	$0.260933\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	5.00000	0.162221
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	0	0
$956$	−6.00000	−0.194054
$957$	0	0
$958$	−30.0000	−0.969256
$959$	12.0000	0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	20.0000	0.644826
$963$	0	0
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−25.0000	−0.803530
$969$	0	0
$970$	0	0
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	16.0000	0.512673
$975$	0	0
$976$	2.00000	0.0640184
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	0	0
$979$	−36.0000	−1.15056
$980$	0	0
$981$	0	0
$982$	−42.0000	−1.34027
$983$	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
$986$	0	0
$987$	0	0
$988$	2.00000	0.0636285
$989$	−24.0000	−0.763156
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	28.0000	0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.a.c.1.1	✓	1
3.2	odd	2		2394.2.a.l.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.a.c.1.1	✓	1	1.1	even	1	trivial
2394.2.a.l.1.1	yes	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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