LMFDB - Embedded newform 4014.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4014,2,Mod(1,4014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4014 = 2 \cdot 3^{2} \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4014.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:	$32.0519513713$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{8} +3.00000 q^{10} -2.00000 q^{11} -2.00000 q^{13} +1.00000 q^{16} +4.00000 q^{17} +2.00000 q^{19} +3.00000 q^{20} -2.00000 q^{22} -2.00000 q^{23} +4.00000 q^{25} -2.00000 q^{26} +8.00000 q^{31} +1.00000 q^{32} +4.00000 q^{34} +3.00000 q^{37} +2.00000 q^{38} +3.00000 q^{40} -2.00000 q^{41} +6.00000 q^{43} -2.00000 q^{44} -2.00000 q^{46} +9.00000 q^{47} -7.00000 q^{49} +4.00000 q^{50} -2.00000 q^{52} -6.00000 q^{53} -6.00000 q^{55} +14.0000 q^{59} +10.0000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} -3.00000 q^{67} +4.00000 q^{68} +10.0000 q^{71} +13.0000 q^{73} +3.00000 q^{74} +2.00000 q^{76} -15.0000 q^{79} +3.00000 q^{80} -2.00000 q^{82} -7.00000 q^{83} +12.0000 q^{85} +6.00000 q^{86} -2.00000 q^{88} +4.00000 q^{89} -2.00000 q^{92} +9.00000 q^{94} +6.00000 q^{95} +2.00000 q^{97} -7.00000 q^{98} +O(q^{100})$

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
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	3.00000	0.948683
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	−2.00000	−0.392232
$27$	0	0
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	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
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	3.00000	0.474342
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−2.00000	−0.294884
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	4.00000	0.565685
$51$	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
$55$	−6.00000	−0.809040
$56$	0	0
$57$	0	0
$58$	0	0
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	0	0
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	2.00000	0.229416
$77$	0	0
$78$	0	0
$79$	−15.0000	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	−2.00000	−0.220863
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	6.00000	0.646997
$87$	0	0
$88$	−2.00000	−0.213201
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	0	0
$92$	−2.00000	−0.208514
$93$	0	0
$94$	9.00000	0.928279
$95$	6.00000	0.615587
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−7.00000	−0.707107
$99$	0	0
$100$	4.00000	0.400000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	19.0000	1.87213	0.936063	−	0.351833i	$-0.114441\pi$
$103$	19.0000	1.87213	0.936063	+	0.351833i	$0.114441\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−6.00000	−0.582772
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	−19.0000	−1.81987	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−19.0000	−1.81987	−0.909935	+	0.414751i	$0.863869\pi$
$110$	−6.00000	−0.572078
$111$	0	0
$112$	0	0
$113$	−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
$115$	−6.00000	−0.559503
$116$	0	0
$117$	0	0
$118$	14.0000	1.28880
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	0	0
$124$	8.00000	0.718421
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−6.00000	−0.526235
$131$	17.0000	1.48530	0.742648	−	0.669681i	$-0.233569\pi$
$131$	17.0000	1.48530	0.742648	+	0.669681i	$0.233569\pi$
$132$	0	0
$133$	0	0
$134$	−3.00000	−0.259161
$135$	0	0
$136$	4.00000	0.342997
$137$	−17.0000	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$137$	−17.0000	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$138$	0	0
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	0	0
$142$	10.0000	0.839181
$143$	4.00000	0.334497
$144$	0	0
$145$	0	0
$146$	13.0000	1.07589
$147$	0	0
$148$	3.00000	0.246598
$149$	−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
$151$	3.00000	0.244137	0.122068	−	0.992522i	$-0.461047\pi$
$151$	3.00000	0.244137	0.122068	+	0.992522i	$0.461047\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	0	0
$155$	24.0000	1.92773
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	−15.0000	−1.19334
$159$	0	0
$160$	3.00000	0.237171
$161$	0	0
$162$	0	0
$163$	−5.00000	−0.391630	−0.195815	−	0.980641i	$-0.562735\pi$
$163$	−5.00000	−0.391630	−0.195815	+	0.980641i	$0.562735\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−7.00000	−0.543305
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	12.0000	0.920358
$171$	0	0
$172$	6.00000	0.457496
$173$	23.0000	1.74866	0.874329	−	0.485334i	$-0.161302\pi$
$173$	23.0000	1.74866	0.874329	+	0.485334i	$0.161302\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	4.00000	0.299813
$179$	17.0000	1.27064	0.635320	−	0.772249i	$-0.280868\pi$
$179$	17.0000	1.27064	0.635320	+	0.772249i	$0.280868\pi$
$180$	0	0
$181$	−3.00000	−0.222988	−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000	−0.222988	−0.111494	+	0.993765i	$0.535564\pi$
$182$	0	0
$183$	0	0
$184$	−2.00000	−0.147442
$185$	9.00000	0.661693
$186$	0	0
$187$	−8.00000	−0.585018
$188$	9.00000	0.656392
$189$	0	0
$190$	6.00000	0.435286
$191$	−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	$0.790854\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−7.00000	−0.500000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	−10.0000	−0.703598
$203$	0	0
$204$	0	0
$205$	−6.00000	−0.419058
$206$	19.0000	1.32379
$207$	0	0
$208$	−2.00000	−0.138675
$209$	−4.00000	−0.276686
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	6.00000	0.410152
$215$	18.0000	1.22759
$216$	0	0
$217$	0	0
$218$	−19.0000	−1.28684
$219$	0	0
$220$	−6.00000	−0.404520
$221$	−8.00000	−0.538138
$222$	0	0
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	0	0
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−17.0000	−1.12833	−0.564165	−	0.825662i	$-0.690802\pi$
$227$	−17.0000	−1.12833	−0.564165	+	0.825662i	$0.690802\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	0	0
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	0	0
$235$	27.0000	1.76129
$236$	14.0000	0.911322
$237$	0	0
$238$	0	0
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	10.0000	0.640184
$245$	−21.0000	−1.34164
$246$	0	0
$247$	−4.00000	−0.254514
$248$	8.00000	0.508001
$249$	0	0
$250$	−3.00000	−0.189737
$251$	19.0000	1.19927	0.599635	−	0.800274i	$-0.295313\pi$
$251$	19.0000	1.19927	0.599635	+	0.800274i	$0.295313\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	−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	$0.689739\pi$
$258$	0	0
$259$	0	0
$260$	−6.00000	−0.372104
$261$	0	0
$262$	17.0000	1.05026
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	−18.0000	−1.10573
$266$	0	0
$267$	0	0
$268$	−3.00000	−0.183254
$269$	5.00000	0.304855	0.152428	−	0.988315i	$-0.451291\pi$
$269$	5.00000	0.304855	0.152428	+	0.988315i	$0.451291\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−17.0000	−1.02701
$275$	−8.00000	−0.482418
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−14.0000	−0.839664
$279$	0	0
$280$	0	0
$281$	20.0000	1.19310	0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000	1.19310	0.596550	+	0.802576i	$0.296538\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	10.0000	0.593391
$285$	0	0
$286$	4.00000	0.236525
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	13.0000	0.760767
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	42.0000	2.44533
$296$	3.00000	0.174371
$297$	0	0
$298$	−2.00000	−0.115857
$299$	4.00000	0.231326
$300$	0	0
$301$	0	0
$302$	3.00000	0.172631
$303$	0	0
$304$	2.00000	0.114708
$305$	30.0000	1.71780
$306$	0	0
$307$	7.00000	0.399511	0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000	0.399511	0.199756	+	0.979846i	$0.435985\pi$
$308$	0	0
$309$	0	0
$310$	24.0000	1.36311
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−15.0000	−0.843816
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	0	0
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	8.00000	0.445132
$324$	0	0
$325$	−8.00000	−0.443760
$326$	−5.00000	−0.276924
$327$	0	0
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−7.00000	−0.384175
$333$	0	0
$334$	−16.0000	−0.875481
$335$	−9.00000	−0.491723
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	12.0000	0.650791
$341$	−16.0000	−0.866449
$342$	0	0
$343$	0	0
$344$	6.00000	0.323498
$345$	0	0
$346$	23.0000	1.23649
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	0	0
$349$	33.0000	1.76645	0.883225	−	0.468950i	$-0.155368\pi$
$349$	33.0000	1.76645	0.883225	+	0.468950i	$0.155368\pi$
$350$	0	0
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	0	0
$355$	30.0000	1.59223
$356$	4.00000	0.212000
$357$	0	0
$358$	17.0000	0.898478
$359$	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
$361$	−15.0000	−0.789474
$362$	−3.00000	−0.157676
$363$	0	0
$364$	0	0
$365$	39.0000	2.04135
$366$	0	0
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−2.00000	−0.104257
$369$	0	0
$370$	9.00000	0.467888
$371$	0	0
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	9.00000	0.464140
$377$	0	0
$378$	0	0
$379$	−14.0000	−0.719132	−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000	−0.719132	−0.359566	+	0.933120i	$0.617075\pi$
$380$	6.00000	0.307794
$381$	0	0
$382$	−6.00000	−0.306987
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	0	0
$385$	0	0
$386$	−22.0000	−1.11977
$387$	0	0
$388$	2.00000	0.101535
$389$	−20.0000	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	−7.00000	−0.353553
$393$	0	0
$394$	0	0
$395$	−45.0000	−2.26420
$396$	0	0
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	4.00000	0.200000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	0	0
$403$	−16.0000	−0.797017
$404$	−10.0000	−0.497519
$405$	0	0
$406$	0	0
$407$	−6.00000	−0.297409
$408$	0	0
$409$	−18.0000	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$410$	−6.00000	−0.296319
$411$	0	0
$412$	19.0000	0.936063
$413$	0	0
$414$	0	0
$415$	−21.0000	−1.03085
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	−4.00000	−0.195646
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	0	0
$423$	0	0
$424$	−6.00000	−0.291386
$425$	16.0000	0.776114
$426$	0	0
$427$	0	0
$428$	6.00000	0.290021
$429$	0	0
$430$	18.0000	0.868037
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	0	0
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	0	0
$435$	0	0
$436$	−19.0000	−0.909935
$437$	−4.00000	−0.191346
$438$	0	0
$439$	−3.00000	−0.143182	−0.0715911	−	0.997434i	$-0.522808\pi$
$439$	−3.00000	−0.143182	−0.0715911	+	0.997434i	$0.522808\pi$
$440$	−6.00000	−0.286039
$441$	0	0
$442$	−8.00000	−0.380521
$443$	3.00000	0.142534	0.0712672	−	0.997457i	$-0.477296\pi$
$443$	3.00000	0.142534	0.0712672	+	0.997457i	$0.477296\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	−1.00000	−0.0473514
$447$	0	0
$448$	0	0
$449$	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
$451$	4.00000	0.188353
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−17.0000	−0.797850
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	−16.0000	−0.747631
$459$	0	0
$460$	−6.00000	−0.279751
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	0	0
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	0	0
$465$	0	0
$466$	10.0000	0.463241
$467$	24.0000	1.11059	0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000	1.11059	0.555294	+	0.831654i	$0.312606\pi$
$468$	0	0
$469$	0	0
$470$	27.0000	1.24542
$471$	0	0
$472$	14.0000	0.644402
$473$	−12.0000	−0.551761
$474$	0	0
$475$	8.00000	0.367065
$476$	0	0
$477$	0	0
$478$	15.0000	0.686084
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−17.0000	−0.774329
$483$	0	0
$484$	−7.00000	−0.318182
$485$	6.00000	0.272446
$486$	0	0
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	−21.0000	−0.948683
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	0	0
$493$	0	0
$494$	−4.00000	−0.179969
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	19.0000	0.848012
$503$	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
$505$	−30.0000	−1.33498
$506$	4.00000	0.177822
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−36.0000	−1.59567	−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000	−1.59567	−0.797836	+	0.602875i	$0.794022\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−18.0000	−0.793946
$515$	57.0000	2.51172
$516$	0	0
$517$	−18.0000	−0.791639
$518$	0	0
$519$	0	0
$520$	−6.00000	−0.263117
$521$	−21.0000	−0.920027	−0.460013	−	0.887912i	$-0.652155\pi$
$521$	−21.0000	−0.920027	−0.460013	+	0.887912i	$0.652155\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	17.0000	0.742648
$525$	0	0
$526$	−12.0000	−0.523225
$527$	32.0000	1.39394
$528$	0	0
$529$	−19.0000	−0.826087
$530$	−18.0000	−0.781870
$531$	0	0
$532$	0	0
$533$	4.00000	0.173259
$534$	0	0
$535$	18.0000	0.778208
$536$	−3.00000	−0.129580
$537$	0	0
$538$	5.00000	0.215565
$539$	14.0000	0.603023
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	4.00000	0.171499
$545$	−57.0000	−2.44161
$546$	0	0
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	−17.0000	−0.726204
$549$	0	0
$550$	−8.00000	−0.341121
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−8.00000	−0.339887
$555$	0	0
$556$	−14.0000	−0.593732
$557$	−13.0000	−0.550828	−0.275414	−	0.961326i	$-0.588815\pi$
$557$	−13.0000	−0.550828	−0.275414	+	0.961326i	$0.588815\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	0	0
$561$	0	0
$562$	20.0000	0.843649
$563$	−26.0000	−1.09577	−0.547885	−	0.836554i	$-0.684567\pi$
$563$	−26.0000	−1.09577	−0.547885	+	0.836554i	$0.684567\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	6.00000	0.252199
$567$	0	0
$568$	10.0000	0.419591
$569$	11.0000	0.461144	0.230572	−	0.973055i	$-0.425940\pi$
$569$	11.0000	0.461144	0.230572	+	0.973055i	$0.425940\pi$
$570$	0	0
$571$	35.0000	1.46470	0.732352	−	0.680926i	$-0.238422\pi$
$571$	35.0000	1.46470	0.732352	+	0.680926i	$0.238422\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	0	0
$575$	−8.00000	−0.333623
$576$	0	0
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	12.0000	0.496989
$584$	13.0000	0.537944
$585$	0	0
$586$	18.0000	0.743573
$587$	34.0000	1.40333	0.701665	−	0.712507i	$-0.252440\pi$
$587$	34.0000	1.40333	0.701665	+	0.712507i	$0.252440\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	42.0000	1.72911
$591$	0	0
$592$	3.00000	0.123299
$593$	31.0000	1.27302	0.636509	−	0.771270i	$-0.280378\pi$
$593$	31.0000	1.27302	0.636509	+	0.771270i	$0.280378\pi$
$594$	0	0
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	4.00000	0.163572
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	0	0
$601$	−40.0000	−1.63163	−0.815817	−	0.578310i	$-0.803712\pi$
$601$	−40.0000	−1.63163	−0.815817	+	0.578310i	$0.803712\pi$
$602$	0	0
$603$	0	0
$604$	3.00000	0.122068
$605$	−21.0000	−0.853771
$606$	0	0
$607$	−3.00000	−0.121766	−0.0608831	−	0.998145i	$-0.519392\pi$
$607$	−3.00000	−0.121766	−0.0608831	+	0.998145i	$0.519392\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	30.0000	1.21466
$611$	−18.0000	−0.728202
$612$	0	0
$613$	−38.0000	−1.53481	−0.767403	−	0.641165i	$-0.778451\pi$
$613$	−38.0000	−1.53481	−0.767403	+	0.641165i	$0.778451\pi$
$614$	7.00000	0.282497
$615$	0	0
$616$	0	0
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	0	0
$619$	21.0000	0.844061	0.422031	−	0.906582i	$-0.361317\pi$
$619$	21.0000	0.844061	0.422031	+	0.906582i	$0.361317\pi$
$620$	24.0000	0.963863
$621$	0	0
$622$	12.0000	0.481156
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	16.0000	0.639489
$627$	0	0
$628$	−10.0000	−0.399043
$629$	12.0000	0.478471
$630$	0	0
$631$	1.00000	0.0398094	0.0199047	−	0.999802i	$-0.493664\pi$
$631$	1.00000	0.0398094	0.0199047	+	0.999802i	$0.493664\pi$
$632$	−15.0000	−0.596668
$633$	0	0
$634$	18.0000	0.714871
$635$	−24.0000	−0.952411
$636$	0	0
$637$	14.0000	0.554700
$638$	0	0
$639$	0	0
$640$	3.00000	0.118585
$641$	25.0000	0.987441	0.493720	−	0.869621i	$-0.335637\pi$
$641$	25.0000	0.987441	0.493720	+	0.869621i	$0.335637\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	0	0
$646$	8.00000	0.314756
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	0	0
$649$	−28.0000	−1.09910
$650$	−8.00000	−0.313786
$651$	0	0
$652$	−5.00000	−0.195815
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	0	0
$655$	51.0000	1.99273
$656$	−2.00000	−0.0780869
$657$	0	0
$658$	0	0
$659$	−9.00000	−0.350590	−0.175295	−	0.984516i	$-0.556088\pi$
$659$	−9.00000	−0.350590	−0.175295	+	0.984516i	$0.556088\pi$
$660$	0	0
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	−28.0000	−1.08825
$663$	0	0
$664$	−7.00000	−0.271653
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−16.0000	−0.619059
$669$	0	0
$670$	−9.00000	−0.347700
$671$	−20.0000	−0.772091
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	0	0
$679$	0	0
$680$	12.0000	0.460179
$681$	0	0
$682$	−16.0000	−0.612672
$683$	−1.00000	−0.0382639	−0.0191320	−	0.999817i	$-0.506090\pi$
$683$	−1.00000	−0.0382639	−0.0191320	+	0.999817i	$0.506090\pi$
$684$	0	0
$685$	−51.0000	−1.94861
$686$	0	0
$687$	0	0
$688$	6.00000	0.228748
$689$	12.0000	0.457164
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	23.0000	0.874329
$693$	0	0
$694$	−20.0000	−0.759190
$695$	−42.0000	−1.59315
$696$	0	0
$697$	−8.00000	−0.303022
$698$	33.0000	1.24907
$699$	0	0
$700$	0	0
$701$	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
$703$	6.00000	0.226294
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−14.0000	−0.526897
$707$	0	0
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	30.0000	1.12588
$711$	0	0
$712$	4.00000	0.149906
$713$	−16.0000	−0.599205
$714$	0	0
$715$	12.0000	0.448775
$716$	17.0000	0.635320
$717$	0	0
$718$	12.0000	0.447836
$719$	−31.0000	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$719$	−31.0000	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$720$	0	0
$721$	0	0
$722$	−15.0000	−0.558242
$723$	0	0
$724$	−3.00000	−0.111494
$725$	0	0
$726$	0	0
$727$	2.00000	0.0741759	0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000	0.0741759	0.0370879	+	0.999312i	$0.488192\pi$
$728$	0	0
$729$	0	0
$730$	39.0000	1.44345
$731$	24.0000	0.887672
$732$	0	0
$733$	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
$736$	−2.00000	−0.0737210
$737$	6.00000	0.221013
$738$	0	0
$739$	29.0000	1.06678	0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000	1.06678	0.533391	+	0.845869i	$0.320917\pi$
$740$	9.00000	0.330847
$741$	0	0
$742$	0	0
$743$	−27.0000	−0.990534	−0.495267	−	0.868741i	$-0.664930\pi$
$743$	−27.0000	−0.990534	−0.495267	+	0.868741i	$0.664930\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	−14.0000	−0.512576
$747$	0	0
$748$	−8.00000	−0.292509
$749$	0	0
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	0	0
$755$	9.00000	0.327544
$756$	0	0
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	−14.0000	−0.508503
$759$	0	0
$760$	6.00000	0.217643
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	0	0
$763$	0	0
$764$	−6.00000	−0.217072
$765$	0	0
$766$	4.00000	0.144526
$767$	−28.0000	−1.01102
$768$	0	0
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	0	0
$772$	−22.0000	−0.791797
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	0	0
$775$	32.0000	1.14947
$776$	2.00000	0.0717958
$777$	0	0
$778$	−20.0000	−0.717035
$779$	−4.00000	−0.143315
$780$	0	0
$781$	−20.0000	−0.715656
$782$	−8.00000	−0.286079
$783$	0	0
$784$	−7.00000	−0.250000
$785$	−30.0000	−1.07075
$786$	0	0
$787$	−15.0000	−0.534692	−0.267346	−	0.963601i	$-0.586147\pi$
$787$	−15.0000	−0.534692	−0.267346	+	0.963601i	$0.586147\pi$
$788$	0	0
$789$	0	0
$790$	−45.0000	−1.60103
$791$	0	0
$792$	0	0
$793$	−20.0000	−0.710221
$794$	8.00000	0.283909
$795$	0	0
$796$	4.00000	0.141776
$797$	−10.0000	−0.354218	−0.177109	−	0.984191i	$-0.556675\pi$
$797$	−10.0000	−0.354218	−0.177109	+	0.984191i	$0.556675\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	4.00000	0.141421
$801$	0	0
$802$	22.0000	0.776847
$803$	−26.0000	−0.917520
$804$	0	0
$805$	0	0
$806$	−16.0000	−0.563576
$807$	0	0
$808$	−10.0000	−0.351799
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	0	0
$814$	−6.00000	−0.210300
$815$	−15.0000	−0.525427
$816$	0	0
$817$	12.0000	0.419827
$818$	−18.0000	−0.629355
$819$	0	0
$820$	−6.00000	−0.209529
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−17.0000	−0.592583	−0.296291	−	0.955098i	$-0.595750\pi$
$823$	−17.0000	−0.592583	−0.296291	+	0.955098i	$0.595750\pi$
$824$	19.0000	0.661896
$825$	0	0
$826$	0	0
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	−21.0000	−0.728921
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	−28.0000	−0.970143
$834$	0	0
$835$	−48.0000	−1.66111
$836$	−4.00000	−0.138343
$837$	0	0
$838$	12.0000	0.414533
$839$	−40.0000	−1.38095	−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000	−1.38095	−0.690477	+	0.723355i	$0.742599\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	28.0000	0.964944
$843$	0	0
$844$	0	0
$845$	−27.0000	−0.928828
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	0	0
$850$	16.0000	0.548795
$851$	−6.00000	−0.205677
$852$	0	0
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	0	0
$856$	6.00000	0.205076
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	0	0
$859$	−3.00000	−0.102359	−0.0511793	−	0.998689i	$-0.516298\pi$
$859$	−3.00000	−0.102359	−0.0511793	+	0.998689i	$0.516298\pi$
$860$	18.0000	0.613795
$861$	0	0
$862$	24.0000	0.817443
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	0	0
$865$	69.0000	2.34607
$866$	−1.00000	−0.0339814
$867$	0	0
$868$	0	0
$869$	30.0000	1.01768
$870$	0	0
$871$	6.00000	0.203302
$872$	−19.0000	−0.643421
$873$	0	0
$874$	−4.00000	−0.135302
$875$	0	0
$876$	0	0
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	−3.00000	−0.101245
$879$	0	0
$880$	−6.00000	−0.202260
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	0	0
$883$	−15.0000	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$883$	−15.0000	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	3.00000	0.100787
$887$	−27.0000	−0.906571	−0.453286	−	0.891365i	$-0.649748\pi$
$887$	−27.0000	−0.906571	−0.453286	+	0.891365i	$0.649748\pi$
$888$	0	0
$889$	0	0
$890$	12.0000	0.402241
$891$	0	0
$892$	−1.00000	−0.0334825
$893$	18.0000	0.602347
$894$	0	0
$895$	51.0000	1.70474
$896$	0	0
$897$	0	0
$898$	30.0000	1.00111
$899$	0	0
$900$	0	0
$901$	−24.0000	−0.799556
$902$	4.00000	0.133185
$903$	0	0
$904$	−6.00000	−0.199557
$905$	−9.00000	−0.299170
$906$	0	0
$907$	−22.0000	−0.730498	−0.365249	−	0.930910i	$-0.619016\pi$
$907$	−22.0000	−0.730498	−0.365249	+	0.930910i	$0.619016\pi$
$908$	−17.0000	−0.564165
$909$	0	0
$910$	0	0
$911$	−17.0000	−0.563235	−0.281618	−	0.959527i	$-0.590871\pi$
$911$	−17.0000	−0.563235	−0.281618	+	0.959527i	$0.590871\pi$
$912$	0	0
$913$	14.0000	0.463332
$914$	0	0
$915$	0	0
$916$	−16.0000	−0.528655
$917$	0	0
$918$	0	0
$919$	−24.0000	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$920$	−6.00000	−0.197814
$921$	0	0
$922$	−28.0000	−0.922131
$923$	−20.0000	−0.658308
$924$	0	0
$925$	12.0000	0.394558
$926$	−26.0000	−0.854413
$927$	0	0
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	−14.0000	−0.458831
$932$	10.0000	0.327561
$933$	0	0
$934$	24.0000	0.785304
$935$	−24.0000	−0.784884
$936$	0	0
$937$	24.0000	0.784046	0.392023	−	0.919955i	$-0.371775\pi$
$937$	24.0000	0.784046	0.392023	+	0.919955i	$0.371775\pi$
$938$	0	0
$939$	0	0
$940$	27.0000	0.880643
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	0	0
$943$	4.00000	0.130258
$944$	14.0000	0.455661
$945$	0	0
$946$	−12.0000	−0.390154
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	−26.0000	−0.843996
$950$	8.00000	0.259554
$951$	0	0
$952$	0	0
$953$	15.0000	0.485898	0.242949	−	0.970039i	$-0.421885\pi$
$953$	15.0000	0.485898	0.242949	+	0.970039i	$0.421885\pi$
$954$	0	0
$955$	−18.0000	−0.582466
$956$	15.0000	0.485135
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	0	0
$961$	33.0000	1.06452
$962$	−6.00000	−0.193448
$963$	0	0
$964$	−17.0000	−0.547533
$965$	−66.0000	−2.12462
$966$	0	0
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	6.00000	0.192648
$971$	16.0000	0.513464	0.256732	−	0.966483i	$-0.417354\pi$
$971$	16.0000	0.513464	0.256732	+	0.966483i	$0.417354\pi$
$972$	0	0
$973$	0	0
$974$	−34.0000	−1.08943
$975$	0	0
$976$	10.0000	0.320092
$977$	31.0000	0.991778	0.495889	−	0.868386i	$-0.334842\pi$
$977$	31.0000	0.991778	0.495889	+	0.868386i	$0.334842\pi$
$978$	0	0
$979$	−8.00000	−0.255681
$980$	−21.0000	−0.670820
$981$	0	0
$982$	−42.0000	−1.34027
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−4.00000	−0.127257
$989$	−12.0000	−0.381578
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	8.00000	0.254000
$993$	0	0
$994$	0	0
$995$	12.0000	0.380426
$996$	0	0
$997$	7.00000	0.221692	0.110846	−	0.993838i	$-0.464644\pi$
$997$	7.00000	0.221692	0.110846	+	0.993838i	$0.464644\pi$
$998$	16.0000	0.506471
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4014.2.a.g.1.1	yes	1
3.2	odd	2		4014.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4014.2.a.a.1.1	✓	1	3.2	odd	2
4014.2.a.g.1.1	yes	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4014.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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