LMFDB - Embedded newform 4017.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
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	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} -2.00000 q^{12} -1.00000 q^{13} +1.00000 q^{15} +4.00000 q^{16} -3.00000 q^{17} -4.00000 q^{19} -2.00000 q^{20} +2.00000 q^{21} -8.00000 q^{23} -4.00000 q^{25} +1.00000 q^{27} -4.00000 q^{28} +5.00000 q^{29} -1.00000 q^{31} +2.00000 q^{35} -2.00000 q^{36} +1.00000 q^{37} -1.00000 q^{39} -6.00000 q^{41} -8.00000 q^{43} +1.00000 q^{45} +3.00000 q^{47} +4.00000 q^{48} -3.00000 q^{49} -3.00000 q^{51} +2.00000 q^{52} -4.00000 q^{57} -2.00000 q^{60} +6.00000 q^{61} +2.00000 q^{63} -8.00000 q^{64} -1.00000 q^{65} -12.0000 q^{67} +6.00000 q^{68} -8.00000 q^{69} -1.00000 q^{71} -7.00000 q^{73} -4.00000 q^{75} +8.00000 q^{76} +13.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -6.00000 q^{83} -4.00000 q^{84} -3.00000 q^{85} +5.00000 q^{87} +2.00000 q^{89} -2.00000 q^{91} +16.0000 q^{92} -1.00000 q^{93} -4.00000 q^{95} +6.00000 q^{97} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−2.00000	−1.00000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−2.00000	−0.577350
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	1.00000	0.258199
$16$	4.00000	1.00000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−2.00000	−0.447214
$21$	2.00000	0.436436
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	2.00000	0.338062
$36$	−2.00000	−0.333333
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	0	0
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	4.00000	0.577350
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−3.00000	−0.420084
$52$	2.00000	0.277350
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.00000	−0.258199
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	−1.00000	−0.124035
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	6.00000	0.727607
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	0	0
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	8.00000	0.917663
$77$	0	0
$78$	0	0
$79$	13.0000	1.46261	0.731307	−	0.682048i	$-0.238911\pi$
$79$	13.0000	1.46261	0.731307	+	0.682048i	$0.238911\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	0	0
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−4.00000	−0.436436
$85$	−3.00000	−0.325396
$86$	0	0
$87$	5.00000	0.536056
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	16.0000	1.66812
$93$	−1.00000	−0.103695
$94$	0	0
$95$	−4.00000	−0.410391
$96$	0	0
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	0	0
$99$	0	0
$100$	8.00000	0.800000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	0	0
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	0	0
$105$	2.00000	0.195180
$106$	0	0
$107$	−5.00000	−0.483368	−0.241684	−	0.970355i	$-0.577700\pi$
$107$	−5.00000	−0.483368	−0.241684	+	0.970355i	$0.577700\pi$
$108$	−2.00000	−0.192450
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	1.00000	0.0949158
$112$	8.00000	0.755929
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	−10.0000	−0.928477
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	−6.00000	−0.541002
$124$	2.00000	0.179605
$125$	−9.00000	−0.804984
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	0	0
$129$	−8.00000	−0.704361
$130$	0	0
$131$	−1.00000	−0.0873704	−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000	−0.0873704	−0.0436852	+	0.999045i	$0.513910\pi$
$132$	0	0
$133$	−8.00000	−0.693688
$134$	0	0
$135$	1.00000	0.0860663
$136$	0	0
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	−11.0000	−0.933008	−0.466504	−	0.884519i	$-0.654487\pi$
$139$	−11.0000	−0.933008	−0.466504	+	0.884519i	$0.654487\pi$
$140$	−4.00000	−0.338062
$141$	3.00000	0.252646
$142$	0	0
$143$	0	0
$144$	4.00000	0.333333
$145$	5.00000	0.415227
$146$	0	0
$147$	−3.00000	−0.247436
$148$	−2.00000	−0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	−3.00000	−0.242536
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	2.00000	0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−16.0000	−1.26098
$162$	0	0
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	0	0
$167$	−20.0000	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−4.00000	−0.305888
$172$	16.0000	1.21999
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	−8.00000	−0.604743
$176$	0	0
$177$	0	0
$178$	0	0
$179$	25.0000	1.86859	0.934294	−	0.356504i	$-0.116031\pi$
$179$	25.0000	1.86859	0.934294	+	0.356504i	$0.116031\pi$
$180$	−2.00000	−0.149071
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	0	0
$185$	1.00000	0.0735215
$186$	0	0
$187$	0	0
$188$	−6.00000	−0.437595
$189$	2.00000	0.145479
$190$	0	0
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	−8.00000	−0.577350
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	6.00000	0.428571
$197$	−27.0000	−1.92367	−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000	−1.92367	−0.961835	+	0.273629i	$0.911776\pi$
$198$	0	0
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	0	0
$201$	−12.0000	−0.846415
$202$	0	0
$203$	10.0000	0.701862
$204$	6.00000	0.420084
$205$	−6.00000	−0.419058
$206$	0	0
$207$	−8.00000	−0.556038
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	0	0
$213$	−1.00000	−0.0685189
$214$	0	0
$215$	−8.00000	−0.545595
$216$	0	0
$217$	−2.00000	−0.135769
$218$	0	0
$219$	−7.00000	−0.473016
$220$	0	0
$221$	3.00000	0.201802
$222$	0	0
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	0	0
$227$	−25.0000	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$227$	−25.0000	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$228$	8.00000	0.529813
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	3.00000	0.195698
$236$	0	0
$237$	13.0000	0.844441
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	4.00000	0.258199
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−12.0000	−0.768221
$245$	−3.00000	−0.191663
$246$	0	0
$247$	4.00000	0.254514
$248$	0	0
$249$	−6.00000	−0.380235
$250$	0	0
$251$	28.0000	1.76734	0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000	1.76734	0.883672	+	0.468106i	$0.155064\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	0	0
$255$	−3.00000	−0.187867
$256$	16.0000	1.00000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	2.00000	0.124035
$261$	5.00000	0.309492
$262$	0	0
$263$	4.00000	0.246651	0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000	0.246651	0.123325	+	0.992366i	$0.460644\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	2.00000	0.122398
$268$	24.0000	1.46603
$269$	−5.00000	−0.304855	−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000	−0.304855	−0.152428	+	0.988315i	$0.548709\pi$
$270$	0	0
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	−12.0000	−0.727607
$273$	−2.00000	−0.121046
$274$	0	0
$275$	0	0
$276$	16.0000	0.963087
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	0	0
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	11.0000	0.656205	0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000	0.656205	0.328102	+	0.944642i	$0.393591\pi$
$282$	0	0
$283$	−24.0000	−1.42665	−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000	−1.42665	−0.713326	+	0.700832i	$0.752812\pi$
$284$	2.00000	0.118678
$285$	−4.00000	−0.236940
$286$	0	0
$287$	−12.0000	−0.708338
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	6.00000	0.351726
$292$	14.0000	0.819288
$293$	−7.00000	−0.408944	−0.204472	−	0.978872i	$-0.565548\pi$
$293$	−7.00000	−0.408944	−0.204472	+	0.978872i	$0.565548\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	8.00000	0.462652
$300$	8.00000	0.461880
$301$	−16.0000	−0.922225
$302$	0	0
$303$	2.00000	0.114897
$304$	−16.0000	−0.917663
$305$	6.00000	0.343559
$306$	0	0
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	1.00000	0.0568880
$310$	0	0
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	0	0
$313$	−7.00000	−0.395663	−0.197832	−	0.980236i	$-0.563390\pi$
$313$	−7.00000	−0.395663	−0.197832	+	0.980236i	$0.563390\pi$
$314$	0	0
$315$	2.00000	0.112687
$316$	−26.0000	−1.46261
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	0	0
$320$	−8.00000	−0.447214
$321$	−5.00000	−0.279073
$322$	0	0
$323$	12.0000	0.667698
$324$	−2.00000	−0.111111
$325$	4.00000	0.221880
$326$	0	0
$327$	11.0000	0.608301
$328$	0	0
$329$	6.00000	0.330791
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	12.0000	0.658586
$333$	1.00000	0.0547997
$334$	0	0
$335$	−12.0000	−0.655630
$336$	8.00000	0.436436
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	0	0
$339$	−12.0000	−0.651751
$340$	6.00000	0.325396
$341$	0	0
$342$	0	0
$343$	−20.0000	−1.07990
$344$	0	0
$345$	−8.00000	−0.430706
$346$	0	0
$347$	9.00000	0.483145	0.241573	−	0.970383i	$-0.422337\pi$
$347$	9.00000	0.483145	0.241573	+	0.970383i	$0.422337\pi$
$348$	−10.0000	−0.536056
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	17.0000	0.904819	0.452409	−	0.891810i	$-0.350565\pi$
$353$	17.0000	0.904819	0.452409	+	0.891810i	$0.350565\pi$
$354$	0	0
$355$	−1.00000	−0.0530745
$356$	−4.00000	−0.212000
$357$	−6.00000	−0.317554
$358$	0	0
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	−11.0000	−0.577350
$364$	4.00000	0.209657
$365$	−7.00000	−0.366397
$366$	0	0
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	−32.0000	−1.66812
$369$	−6.00000	−0.312348
$370$	0	0
$371$	0	0
$372$	2.00000	0.103695
$373$	−23.0000	−1.19089	−0.595447	−	0.803394i	$-0.703025\pi$
$373$	−23.0000	−1.19089	−0.595447	+	0.803394i	$0.703025\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	0	0
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	8.00000	0.410391
$381$	16.0000	0.819705
$382$	0	0
$383$	−11.0000	−0.562074	−0.281037	−	0.959697i	$-0.590678\pi$
$383$	−11.0000	−0.562074	−0.281037	+	0.959697i	$0.590678\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.00000	−0.406663
$388$	−12.0000	−0.609208
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	0	0
$393$	−1.00000	−0.0504433
$394$	0	0
$395$	13.0000	0.654101
$396$	0	0
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	0	0
$399$	−8.00000	−0.400501
$400$	−16.0000	−0.800000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	0	0
$403$	1.00000	0.0498135
$404$	−4.00000	−0.199007
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	8.00000	0.394611
$412$	−2.00000	−0.0985329
$413$	0	0
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−11.0000	−0.538672
$418$	0	0
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	−4.00000	−0.195180
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	0	0
$423$	3.00000	0.145865
$424$	0	0
$425$	12.0000	0.582086
$426$	0	0
$427$	12.0000	0.580721
$428$	10.0000	0.483368
$429$	0	0
$430$	0	0
$431$	4.00000	0.192673	0.0963366	−	0.995349i	$-0.469287\pi$
$431$	4.00000	0.192673	0.0963366	+	0.995349i	$0.469287\pi$
$432$	4.00000	0.192450
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	5.00000	0.239732
$436$	−22.0000	−1.05361
$437$	32.0000	1.53077
$438$	0	0
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	14.0000	0.665160	0.332580	−	0.943075i	$-0.392081\pi$
$443$	14.0000	0.665160	0.332580	+	0.943075i	$0.392081\pi$
$444$	−2.00000	−0.0949158
$445$	2.00000	0.0948091
$446$	0	0
$447$	18.0000	0.851371
$448$	−16.0000	−0.755929
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	0	0
$452$	24.0000	1.12887
$453$	0	0
$454$	0	0
$455$	−2.00000	−0.0937614
$456$	0	0
$457$	9.00000	0.421002	0.210501	−	0.977594i	$-0.432490\pi$
$457$	9.00000	0.421002	0.210501	+	0.977594i	$0.432490\pi$
$458$	0	0
$459$	−3.00000	−0.140028
$460$	16.0000	0.746004
$461$	24.0000	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$462$	0	0
$463$	13.0000	0.604161	0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000	0.604161	0.302081	+	0.953282i	$0.402319\pi$
$464$	20.0000	0.928477
$465$	−1.00000	−0.0463739
$466$	0	0
$467$	15.0000	0.694117	0.347059	−	0.937843i	$-0.387180\pi$
$467$	15.0000	0.694117	0.347059	+	0.937843i	$0.387180\pi$
$468$	2.00000	0.0924500
$469$	−24.0000	−1.10822
$470$	0	0
$471$	−14.0000	−0.645086
$472$	0	0
$473$	0	0
$474$	0	0
$475$	16.0000	0.734130
$476$	12.0000	0.550019
$477$	0	0
$478$	0	0
$479$	−1.00000	−0.0456912	−0.0228456	−	0.999739i	$-0.507273\pi$
$479$	−1.00000	−0.0456912	−0.0228456	+	0.999739i	$0.507273\pi$
$480$	0	0
$481$	−1.00000	−0.0455961
$482$	0	0
$483$	−16.0000	−0.728025
$484$	22.0000	1.00000
$485$	6.00000	0.272446
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	0	0
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−19.0000	−0.857458	−0.428729	−	0.903433i	$-0.641038\pi$
$491$	−19.0000	−0.857458	−0.428729	+	0.903433i	$0.641038\pi$
$492$	12.0000	0.541002
$493$	−15.0000	−0.675566
$494$	0	0
$495$	0	0
$496$	−4.00000	−0.179605
$497$	−2.00000	−0.0897123
$498$	0	0
$499$	7.00000	0.313363	0.156682	−	0.987649i	$-0.449920\pi$
$499$	7.00000	0.313363	0.156682	+	0.987649i	$0.449920\pi$
$500$	18.0000	0.804984
$501$	−20.0000	−0.893534
$502$	0	0
$503$	35.0000	1.56057	0.780286	−	0.625422i	$-0.215073\pi$
$503$	35.0000	1.56057	0.780286	+	0.625422i	$0.215073\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	0	0
$507$	1.00000	0.0444116
$508$	−32.0000	−1.41977
$509$	−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
$511$	−14.0000	−0.619324
$512$	0	0
$513$	−4.00000	−0.176604
$514$	0	0
$515$	1.00000	0.0440653
$516$	16.0000	0.704361
$517$	0	0
$518$	0	0
$519$	6.00000	0.263371
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	1.00000	0.0437269	0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000	0.0437269	0.0218635	+	0.999761i	$0.493040\pi$
$524$	2.00000	0.0873704
$525$	−8.00000	−0.349149
$526$	0	0
$527$	3.00000	0.130682
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	0	0
$532$	16.0000	0.693688
$533$	6.00000	0.259889
$534$	0	0
$535$	−5.00000	−0.216169
$536$	0	0
$537$	25.0000	1.07883
$538$	0	0
$539$	0	0
$540$	−2.00000	−0.0860663
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	0	0
$543$	10.0000	0.429141
$544$	0	0
$545$	11.0000	0.471188
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−16.0000	−0.683486
$549$	6.00000	0.256074
$550$	0	0
$551$	−20.0000	−0.852029
$552$	0	0
$553$	26.0000	1.10563
$554$	0	0
$555$	1.00000	0.0424476
$556$	22.0000	0.933008
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	8.00000	0.338062
$561$	0	0
$562$	0	0
$563$	38.0000	1.60151	0.800755	−	0.598993i	$-0.204432\pi$
$563$	38.0000	1.60151	0.800755	+	0.598993i	$0.204432\pi$
$564$	−6.00000	−0.252646
$565$	−12.0000	−0.504844
$566$	0	0
$567$	2.00000	0.0839921
$568$	0	0
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	0	0
$573$	−20.0000	−0.835512
$574$	0	0
$575$	32.0000	1.33449
$576$	−8.00000	−0.333333
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	0	0
$579$	−2.00000	−0.0831172
$580$	−10.0000	−0.415227
$581$	−12.0000	−0.497844
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−1.00000	−0.0413449
$586$	0	0
$587$	−10.0000	−0.412744	−0.206372	−	0.978474i	$-0.566166\pi$
$587$	−10.0000	−0.412744	−0.206372	+	0.978474i	$0.566166\pi$
$588$	6.00000	0.247436
$589$	4.00000	0.164817
$590$	0	0
$591$	−27.0000	−1.11063
$592$	4.00000	0.164399
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	−6.00000	−0.245976
$596$	−36.0000	−1.47462
$597$	−2.00000	−0.0818546
$598$	0	0
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	−12.0000	−0.488678
$604$	0	0
$605$	−11.0000	−0.447214
$606$	0	0
$607$	−39.0000	−1.58296	−0.791481	−	0.611194i	$-0.790689\pi$
$607$	−39.0000	−1.58296	−0.791481	+	0.611194i	$0.790689\pi$
$608$	0	0
$609$	10.0000	0.405220
$610$	0	0
$611$	−3.00000	−0.121367
$612$	6.00000	0.242536
$613$	4.00000	0.161558	0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000	0.161558	0.0807792	+	0.996732i	$0.474259\pi$
$614$	0	0
$615$	−6.00000	−0.241943
$616$	0	0
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	0	0
$619$	26.0000	1.04503	0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000	1.04503	0.522514	+	0.852631i	$0.324994\pi$
$620$	2.00000	0.0803219
$621$	−8.00000	−0.321029
$622$	0	0
$623$	4.00000	0.160257
$624$	−4.00000	−0.160128
$625$	11.0000	0.440000
$626$	0	0
$627$	0	0
$628$	28.0000	1.11732
$629$	−3.00000	−0.119618
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	0	0
$633$	−16.0000	−0.635943
$634$	0	0
$635$	16.0000	0.634941
$636$	0	0
$637$	3.00000	0.118864
$638$	0	0
$639$	−1.00000	−0.0395594
$640$	0	0
$641$	−39.0000	−1.54041	−0.770204	−	0.637798i	$-0.779845\pi$
$641$	−39.0000	−1.54041	−0.770204	+	0.637798i	$0.779845\pi$
$642$	0	0
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	32.0000	1.26098
$645$	−8.00000	−0.315000
$646$	0	0
$647$	39.0000	1.53325	0.766624	−	0.642096i	$-0.221935\pi$
$647$	39.0000	1.53325	0.766624	+	0.642096i	$0.221935\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	40.0000	1.56652
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	0	0
$655$	−1.00000	−0.0390732
$656$	−24.0000	−0.937043
$657$	−7.00000	−0.273096
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−17.0000	−0.661223	−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000	−0.661223	−0.330612	+	0.943767i	$0.607255\pi$
$662$	0	0
$663$	3.00000	0.116510
$664$	0	0
$665$	−8.00000	−0.310227
$666$	0	0
$667$	−40.0000	−1.54881
$668$	40.0000	1.54765
$669$	6.00000	0.231973
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	0	0
$675$	−4.00000	−0.153960
$676$	−2.00000	−0.0769231
$677$	5.00000	0.192166	0.0960828	−	0.995373i	$-0.469369\pi$
$677$	5.00000	0.192166	0.0960828	+	0.995373i	$0.469369\pi$
$678$	0	0
$679$	12.0000	0.460518
$680$	0	0
$681$	−25.0000	−0.958002
$682$	0	0
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	8.00000	0.305888
$685$	8.00000	0.305664
$686$	0	0
$687$	14.0000	0.534133
$688$	−32.0000	−1.21999
$689$	0	0
$690$	0	0
$691$	25.0000	0.951045	0.475522	−	0.879704i	$-0.342259\pi$
$691$	25.0000	0.951045	0.475522	+	0.879704i	$0.342259\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	0	0
$695$	−11.0000	−0.417254
$696$	0	0
$697$	18.0000	0.681799
$698$	0	0
$699$	0	0
$700$	16.0000	0.604743
$701$	3.00000	0.113308	0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000	0.113308	0.0566542	+	0.998394i	$0.481957\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	0	0
$705$	3.00000	0.112987
$706$	0	0
$707$	4.00000	0.150435
$708$	0	0
$709$	−20.0000	−0.751116	−0.375558	−	0.926799i	$-0.622549\pi$
$709$	−20.0000	−0.751116	−0.375558	+	0.926799i	$0.622549\pi$
$710$	0	0
$711$	13.0000	0.487538
$712$	0	0
$713$	8.00000	0.299602
$714$	0	0
$715$	0	0
$716$	−50.0000	−1.86859
$717$	−6.00000	−0.224074
$718$	0	0
$719$	28.0000	1.04422	0.522112	−	0.852877i	$-0.325144\pi$
$719$	28.0000	1.04422	0.522112	+	0.852877i	$0.325144\pi$
$720$	4.00000	0.149071
$721$	2.00000	0.0744839
$722$	0	0
$723$	−26.0000	−0.966950
$724$	−20.0000	−0.743294
$725$	−20.0000	−0.742781
$726$	0	0
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	24.0000	0.887672
$732$	−12.0000	−0.443533
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	0	0
$735$	−3.00000	−0.110657
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−2.00000	−0.0735215
$741$	4.00000	0.146944
$742$	0	0
$743$	21.0000	0.770415	0.385208	−	0.922830i	$-0.374130\pi$
$743$	21.0000	0.770415	0.385208	+	0.922830i	$0.374130\pi$
$744$	0	0
$745$	18.0000	0.659469
$746$	0	0
$747$	−6.00000	−0.219529
$748$	0	0
$749$	−10.0000	−0.365392
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	12.0000	0.437595
$753$	28.0000	1.02038
$754$	0	0
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−3.00000	−0.109037	−0.0545184	−	0.998513i	$-0.517362\pi$
$757$	−3.00000	−0.109037	−0.0545184	+	0.998513i	$0.517362\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	7.00000	0.253750	0.126875	−	0.991919i	$-0.459505\pi$
$761$	7.00000	0.253750	0.126875	+	0.991919i	$0.459505\pi$
$762$	0	0
$763$	22.0000	0.796453
$764$	40.0000	1.44715
$765$	−3.00000	−0.108465
$766$	0	0
$767$	0	0
$768$	16.0000	0.577350
$769$	−37.0000	−1.33425	−0.667127	−	0.744944i	$-0.732476\pi$
$769$	−37.0000	−1.33425	−0.667127	+	0.744944i	$0.732476\pi$
$770$	0	0
$771$	0	0
$772$	4.00000	0.143963
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	0	0
$775$	4.00000	0.143684
$776$	0	0
$777$	2.00000	0.0717496
$778$	0	0
$779$	24.0000	0.859889
$780$	2.00000	0.0716115
$781$	0	0
$782$	0	0
$783$	5.00000	0.178685
$784$	−12.0000	−0.428571
$785$	−14.0000	−0.499681
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	54.0000	1.92367
$789$	4.00000	0.142404
$790$	0	0
$791$	−24.0000	−0.853342
$792$	0	0
$793$	−6.00000	−0.213066
$794$	0	0
$795$	0	0
$796$	4.00000	0.141776
$797$	−15.0000	−0.531327	−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000	−0.531327	−0.265664	+	0.964066i	$0.585591\pi$
$798$	0	0
$799$	−9.00000	−0.318397
$800$	0	0
$801$	2.00000	0.0706665
$802$	0	0
$803$	0	0
$804$	24.0000	0.846415
$805$	−16.0000	−0.563926
$806$	0	0
$807$	−5.00000	−0.176008
$808$	0	0
$809$	36.0000	1.26569	0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000	1.26569	0.632846	+	0.774277i	$0.281886\pi$
$810$	0	0
$811$	47.0000	1.65039	0.825197	−	0.564846i	$-0.191064\pi$
$811$	47.0000	1.65039	0.825197	+	0.564846i	$0.191064\pi$
$812$	−20.0000	−0.701862
$813$	7.00000	0.245501
$814$	0	0
$815$	−20.0000	−0.700569
$816$	−12.0000	−0.420084
$817$	32.0000	1.11954
$818$	0	0
$819$	−2.00000	−0.0698857
$820$	12.0000	0.419058
$821$	40.0000	1.39601	0.698005	−	0.716093i	$-0.254071\pi$
$821$	40.0000	1.39601	0.698005	+	0.716093i	$0.254071\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	9.00000	0.312961	0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000	0.312961	0.156480	+	0.987681i	$0.449985\pi$
$828$	16.0000	0.556038
$829$	−24.0000	−0.833554	−0.416777	−	0.909009i	$-0.636840\pi$
$829$	−24.0000	−0.833554	−0.416777	+	0.909009i	$0.636840\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	8.00000	0.277350
$833$	9.00000	0.311832
$834$	0	0
$835$	−20.0000	−0.692129
$836$	0	0
$837$	−1.00000	−0.0345651
$838$	0	0
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	11.0000	0.378860
$844$	32.0000	1.10149
$845$	1.00000	0.0344010
$846$	0	0
$847$	−22.0000	−0.755929
$848$	0	0
$849$	−24.0000	−0.823678
$850$	0	0
$851$	−8.00000	−0.274236
$852$	2.00000	0.0685189
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	0	0
$855$	−4.00000	−0.136797
$856$	0	0
$857$	−43.0000	−1.46885	−0.734426	−	0.678689i	$-0.762549\pi$
$857$	−43.0000	−1.46885	−0.734426	+	0.678689i	$0.762549\pi$
$858$	0	0
$859$	−18.0000	−0.614152	−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000	−0.614152	−0.307076	+	0.951685i	$0.599351\pi$
$860$	16.0000	0.545595
$861$	−12.0000	−0.408959
$862$	0	0
$863$	−1.00000	−0.0340404	−0.0170202	−	0.999855i	$-0.505418\pi$
$863$	−1.00000	−0.0340404	−0.0170202	+	0.999855i	$0.505418\pi$
$864$	0	0
$865$	6.00000	0.204006
$866$	0	0
$867$	−8.00000	−0.271694
$868$	4.00000	0.135769
$869$	0	0
$870$	0	0
$871$	12.0000	0.406604
$872$	0	0
$873$	6.00000	0.203069
$874$	0	0
$875$	−18.0000	−0.608511
$876$	14.0000	0.473016
$877$	−43.0000	−1.45201	−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000	−1.45201	−0.726003	+	0.687691i	$0.758624\pi$
$878$	0	0
$879$	−7.00000	−0.236104
$880$	0	0
$881$	−10.0000	−0.336909	−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000	−0.336909	−0.168454	+	0.985709i	$0.553878\pi$
$882$	0	0
$883$	−47.0000	−1.58168	−0.790838	−	0.612026i	$-0.790355\pi$
$883$	−47.0000	−1.58168	−0.790838	+	0.612026i	$0.790355\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	0	0
$887$	35.0000	1.17518	0.587592	−	0.809157i	$-0.300076\pi$
$887$	35.0000	1.17518	0.587592	+	0.809157i	$0.300076\pi$
$888$	0	0
$889$	32.0000	1.07325
$890$	0	0
$891$	0	0
$892$	−12.0000	−0.401790
$893$	−12.0000	−0.401565
$894$	0	0
$895$	25.0000	0.835658
$896$	0	0
$897$	8.00000	0.267112
$898$	0	0
$899$	−5.00000	−0.166759
$900$	8.00000	0.266667
$901$	0	0
$902$	0	0
$903$	−16.0000	−0.532447
$904$	0	0
$905$	10.0000	0.332411
$906$	0	0
$907$	17.0000	0.564476	0.282238	−	0.959344i	$-0.408923\pi$
$907$	17.0000	0.564476	0.282238	+	0.959344i	$0.408923\pi$
$908$	50.0000	1.65931
$909$	2.00000	0.0663358
$910$	0	0
$911$	−58.0000	−1.92163	−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000	−1.92163	−0.960813	+	0.277198i	$0.910594\pi$
$912$	−16.0000	−0.529813
$913$	0	0
$914$	0	0
$915$	6.00000	0.198354
$916$	−28.0000	−0.925146
$917$	−2.00000	−0.0660458
$918$	0	0
$919$	−18.0000	−0.593765	−0.296883	−	0.954914i	$-0.595947\pi$
$919$	−18.0000	−0.593765	−0.296883	+	0.954914i	$0.595947\pi$
$920$	0	0
$921$	−23.0000	−0.757876
$922$	0	0
$923$	1.00000	0.0329154
$924$	0	0
$925$	−4.00000	−0.131519
$926$	0	0
$927$	1.00000	0.0328443
$928$	0	0
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	0	0
$931$	12.0000	0.393284
$932$	0	0
$933$	16.0000	0.523816
$934$	0	0
$935$	0	0
$936$	0	0
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	−7.00000	−0.228436
$940$	−6.00000	−0.195698
$941$	36.0000	1.17357	0.586783	−	0.809744i	$-0.300394\pi$
$941$	36.0000	1.17357	0.586783	+	0.809744i	$0.300394\pi$
$942$	0	0
$943$	48.0000	1.56310
$944$	0	0
$945$	2.00000	0.0650600
$946$	0	0
$947$	40.0000	1.29983	0.649913	−	0.760009i	$-0.274805\pi$
$947$	40.0000	1.29983	0.649913	+	0.760009i	$0.274805\pi$
$948$	−26.0000	−0.844441
$949$	7.00000	0.227230
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	17.0000	0.550684	0.275342	−	0.961346i	$-0.411209\pi$
$953$	17.0000	0.550684	0.275342	+	0.961346i	$0.411209\pi$
$954$	0	0
$955$	−20.0000	−0.647185
$956$	12.0000	0.388108
$957$	0	0
$958$	0	0
$959$	16.0000	0.516667
$960$	−8.00000	−0.258199
$961$	−30.0000	−0.967742
$962$	0	0
$963$	−5.00000	−0.161123
$964$	52.0000	1.67481
$965$	−2.00000	−0.0643823
$966$	0	0
$967$	−11.0000	−0.353736	−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000	−0.353736	−0.176868	+	0.984235i	$0.556597\pi$
$968$	0	0
$969$	12.0000	0.385496
$970$	0	0
$971$	−40.0000	−1.28366	−0.641831	−	0.766846i	$-0.721825\pi$
$971$	−40.0000	−1.28366	−0.641831	+	0.766846i	$0.721825\pi$
$972$	−2.00000	−0.0641500
$973$	−22.0000	−0.705288
$974$	0	0
$975$	4.00000	0.128103
$976$	24.0000	0.768221
$977$	32.0000	1.02377	0.511885	−	0.859054i	$-0.328947\pi$
$977$	32.0000	1.02377	0.511885	+	0.859054i	$0.328947\pi$
$978$	0	0
$979$	0	0
$980$	6.00000	0.191663
$981$	11.0000	0.351203
$982$	0	0
$983$	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
$985$	−27.0000	−0.860292
$986$	0	0
$987$	6.00000	0.190982
$988$	−8.00000	−0.254514
$989$	64.0000	2.03508
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	0	0
$993$	−17.0000	−0.539479
$994$	0	0
$995$	−2.00000	−0.0634043
$996$	12.0000	0.380235
$997$	58.0000	1.83688	0.918439	−	0.395562i	$-0.129450\pi$
$997$	58.0000	1.83688	0.918439	+	0.395562i	$0.129450\pi$
$998$	0	0
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.c.1.1	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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