LMFDB - Embedded newform 1710.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,4,Mod(1,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1710.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1710.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:	$100.893266110$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -8.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -8.00000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +20.0000 q^{11} -82.0000 q^{13} +16.0000 q^{14} +16.0000 q^{16} +18.0000 q^{17} +19.0000 q^{19} +20.0000 q^{20} -40.0000 q^{22} +88.0000 q^{23} +25.0000 q^{25} +164.000 q^{26} -32.0000 q^{28} +186.000 q^{29} -248.000 q^{31} -32.0000 q^{32} -36.0000 q^{34} -40.0000 q^{35} +262.000 q^{37} -38.0000 q^{38} -40.0000 q^{40} -246.000 q^{41} +288.000 q^{43} +80.0000 q^{44} -176.000 q^{46} +168.000 q^{47} -279.000 q^{49} -50.0000 q^{50} -328.000 q^{52} +302.000 q^{53} +100.000 q^{55} +64.0000 q^{56} -372.000 q^{58} -72.0000 q^{59} -546.000 q^{61} +496.000 q^{62} +64.0000 q^{64} -410.000 q^{65} -804.000 q^{67} +72.0000 q^{68} +80.0000 q^{70} -240.000 q^{71} +602.000 q^{73} -524.000 q^{74} +76.0000 q^{76} -160.000 q^{77} -800.000 q^{79} +80.0000 q^{80} +492.000 q^{82} +116.000 q^{83} +90.0000 q^{85} -576.000 q^{86} -160.000 q^{88} -766.000 q^{89} +656.000 q^{91} +352.000 q^{92} -336.000 q^{94} +95.0000 q^{95} +790.000 q^{97} +558.000 q^{98} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−8.00000	−0.431959	−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−8.00000	−0.431959	−0.215980	+	0.976398i	$0.569295\pi$
$8$	−8.00000	−0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	20.0000	0.548202	0.274101	−	0.961701i	$-0.411620\pi$
$11$	20.0000	0.548202	0.274101	+	0.961701i	$0.411620\pi$
$12$	0	0
$13$	−82.0000	−1.74944	−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000	−1.74944	−0.874720	+	0.484629i	$0.838954\pi$
$14$	16.0000	0.305441
$15$	0	0
$16$	16.0000	0.250000
$17$	18.0000	0.256802	0.128401	−	0.991722i	$-0.459015\pi$
$17$	18.0000	0.256802	0.128401	+	0.991722i	$0.459015\pi$
$18$	0	0
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	20.0000	0.223607
$21$	0	0
$22$	−40.0000	−0.387638
$23$	88.0000	0.797794	0.398897	−	0.916996i	$-0.369393\pi$
$23$	88.0000	0.797794	0.398897	+	0.916996i	$0.369393\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	164.000	1.23704
$27$	0	0
$28$	−32.0000	−0.215980
$29$	186.000	1.19101	0.595506	−	0.803351i	$-0.296952\pi$
$29$	186.000	1.19101	0.595506	+	0.803351i	$0.296952\pi$
$30$	0	0
$31$	−248.000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−248.000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−36.0000	−0.181587
$35$	−40.0000	−0.193178
$36$	0	0
$37$	262.000	1.16412	0.582061	−	0.813145i	$-0.302246\pi$
$37$	262.000	1.16412	0.582061	+	0.813145i	$0.302246\pi$
$38$	−38.0000	−0.162221
$39$	0	0
$40$	−40.0000	−0.158114
$41$	−246.000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−246.000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	288.000	1.02139	0.510693	−	0.859763i	$-0.329389\pi$
$43$	288.000	1.02139	0.510693	+	0.859763i	$0.329389\pi$
$44$	80.0000	0.274101
$45$	0	0
$46$	−176.000	−0.564126
$47$	168.000	0.521390	0.260695	−	0.965421i	$-0.416048\pi$
$47$	168.000	0.521390	0.260695	+	0.965421i	$0.416048\pi$
$48$	0	0
$49$	−279.000	−0.813411
$50$	−50.0000	−0.141421
$51$	0	0
$52$	−328.000	−0.874720
$53$	302.000	0.782696	0.391348	−	0.920243i	$-0.372009\pi$
$53$	302.000	0.782696	0.391348	+	0.920243i	$0.372009\pi$
$54$	0	0
$55$	100.000	0.245164
$56$	64.0000	0.152721
$57$	0	0
$58$	−372.000	−0.842172
$59$	−72.0000	−0.158875	−0.0794373	−	0.996840i	$-0.525312\pi$
$59$	−72.0000	−0.158875	−0.0794373	+	0.996840i	$0.525312\pi$
$60$	0	0
$61$	−546.000	−1.14604	−0.573018	−	0.819543i	$-0.694227\pi$
$61$	−546.000	−1.14604	−0.573018	+	0.819543i	$0.694227\pi$
$62$	496.000	1.01600
$63$	0	0
$64$	64.0000	0.125000
$65$	−410.000	−0.782373
$66$	0	0
$67$	−804.000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−804.000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	72.0000	0.128401
$69$	0	0
$70$	80.0000	0.136598
$71$	−240.000	−0.401166	−0.200583	−	0.979677i	$-0.564284\pi$
$71$	−240.000	−0.401166	−0.200583	+	0.979677i	$0.564284\pi$
$72$	0	0
$73$	602.000	0.965189	0.482594	−	0.875844i	$-0.339695\pi$
$73$	602.000	0.965189	0.482594	+	0.875844i	$0.339695\pi$
$74$	−524.000	−0.823159
$75$	0	0
$76$	76.0000	0.114708
$77$	−160.000	−0.236801
$78$	0	0
$79$	−800.000	−1.13933	−0.569665	−	0.821877i	$-0.692927\pi$
$79$	−800.000	−1.13933	−0.569665	+	0.821877i	$0.692927\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	492.000	0.662589
$83$	116.000	0.153405	0.0767027	−	0.997054i	$-0.475561\pi$
$83$	116.000	0.153405	0.0767027	+	0.997054i	$0.475561\pi$
$84$	0	0
$85$	90.0000	0.114846
$86$	−576.000	−0.722229
$87$	0	0
$88$	−160.000	−0.193819
$89$	−766.000	−0.912313	−0.456156	−	0.889900i	$-0.650774\pi$
$89$	−766.000	−0.912313	−0.456156	+	0.889900i	$0.650774\pi$
$90$	0	0
$91$	656.000	0.755687
$92$	352.000	0.398897
$93$	0	0
$94$	−336.000	−0.368678
$95$	95.0000	0.102598
$96$	0	0
$97$	790.000	0.826931	0.413466	−	0.910520i	$-0.364318\pi$
$97$	790.000	0.826931	0.413466	+	0.910520i	$0.364318\pi$
$98$	558.000	0.575168
$99$	0	0
$100$	100.000	0.100000
$101$	−290.000	−0.285704	−0.142852	−	0.989744i	$-0.545627\pi$
$101$	−290.000	−0.285704	−0.142852	+	0.989744i	$0.545627\pi$
$102$	0	0
$103$	1540.00	1.47321	0.736605	−	0.676323i	$-0.236428\pi$
$103$	1540.00	1.47321	0.736605	+	0.676323i	$0.236428\pi$
$104$	656.000	0.618520
$105$	0	0
$106$	−604.000	−0.553450
$107$	−1564.00	−1.41306	−0.706531	−	0.707682i	$-0.749741\pi$
$107$	−1564.00	−1.41306	−0.706531	+	0.707682i	$0.749741\pi$
$108$	0	0
$109$	−554.000	−0.486822	−0.243411	−	0.969923i	$-0.578266\pi$
$109$	−554.000	−0.486822	−0.243411	+	0.969923i	$0.578266\pi$
$110$	−200.000	−0.173357
$111$	0	0
$112$	−128.000	−0.107990
$113$	834.000	0.694302	0.347151	−	0.937809i	$-0.387149\pi$
$113$	834.000	0.694302	0.347151	+	0.937809i	$0.387149\pi$
$114$	0	0
$115$	440.000	0.356784
$116$	744.000	0.595506
$117$	0	0
$118$	144.000	0.112341
$119$	−144.000	−0.110928
$120$	0	0
$121$	−931.000	−0.699474
$122$	1092.00	0.810369
$123$	0	0
$124$	−992.000	−0.718421
$125$	125.000	0.0894427
$126$	0	0
$127$	−876.000	−0.612066	−0.306033	−	0.952021i	$-0.599002\pi$
$127$	−876.000	−0.612066	−0.306033	+	0.952021i	$0.599002\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	820.000	0.553221
$131$	508.000	0.338810	0.169405	−	0.985546i	$-0.445815\pi$
$131$	508.000	0.338810	0.169405	+	0.985546i	$0.445815\pi$
$132$	0	0
$133$	−152.000	−0.0990983
$134$	1608.00	1.03664
$135$	0	0
$136$	−144.000	−0.0907934
$137$	1506.00	0.939170	0.469585	−	0.882887i	$-0.344404\pi$
$137$	1506.00	0.939170	0.469585	+	0.882887i	$0.344404\pi$
$138$	0	0
$139$	−620.000	−0.378329	−0.189164	−	0.981945i	$-0.560578\pi$
$139$	−620.000	−0.378329	−0.189164	+	0.981945i	$0.560578\pi$
$140$	−160.000	−0.0965891
$141$	0	0
$142$	480.000	0.283667
$143$	−1640.00	−0.959047
$144$	0	0
$145$	930.000	0.532637
$146$	−1204.00	−0.682491
$147$	0	0
$148$	1048.00	0.582061
$149$	−1738.00	−0.955587	−0.477794	−	0.878472i	$-0.658563\pi$
$149$	−1738.00	−0.955587	−0.477794	+	0.878472i	$0.658563\pi$
$150$	0	0
$151$	−1720.00	−0.926964	−0.463482	−	0.886106i	$-0.653400\pi$
$151$	−1720.00	−0.926964	−0.463482	+	0.886106i	$0.653400\pi$
$152$	−152.000	−0.0811107
$153$	0	0
$154$	320.000	0.167444
$155$	−1240.00	−0.642575
$156$	0	0
$157$	−1446.00	−0.735053	−0.367527	−	0.930013i	$-0.619795\pi$
$157$	−1446.00	−0.735053	−0.367527	+	0.930013i	$0.619795\pi$
$158$	1600.00	0.805628
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−704.000	−0.344615
$162$	0	0
$163$	−392.000	−0.188367	−0.0941835	−	0.995555i	$-0.530024\pi$
$163$	−392.000	−0.188367	−0.0941835	+	0.995555i	$0.530024\pi$
$164$	−984.000	−0.468521
$165$	0	0
$166$	−232.000	−0.108474
$167$	544.000	0.252072	0.126036	−	0.992026i	$-0.459775\pi$
$167$	544.000	0.252072	0.126036	+	0.992026i	$0.459775\pi$
$168$	0	0
$169$	4527.00	2.06054
$170$	−180.000	−0.0812081
$171$	0	0
$172$	1152.00	0.510693
$173$	−1154.00	−0.507150	−0.253575	−	0.967316i	$-0.581607\pi$
$173$	−1154.00	−0.507150	−0.253575	+	0.967316i	$0.581607\pi$
$174$	0	0
$175$	−200.000	−0.0863919
$176$	320.000	0.137051
$177$	0	0
$178$	1532.00	0.645103
$179$	−2528.00	−1.05560	−0.527798	−	0.849370i	$-0.676982\pi$
$179$	−2528.00	−1.05560	−0.527798	+	0.849370i	$0.676982\pi$
$180$	0	0
$181$	1454.00	0.597099	0.298550	−	0.954394i	$-0.403497\pi$
$181$	1454.00	0.597099	0.298550	+	0.954394i	$0.403497\pi$
$182$	−1312.00	−0.534351
$183$	0	0
$184$	−704.000	−0.282063
$185$	1310.00	0.520611
$186$	0	0
$187$	360.000	0.140780
$188$	672.000	0.260695
$189$	0	0
$190$	−190.000	−0.0725476
$191$	4332.00	1.64111	0.820556	−	0.571566i	$-0.193664\pi$
$191$	4332.00	1.64111	0.820556	+	0.571566i	$0.193664\pi$
$192$	0	0
$193$	−2330.00	−0.869000	−0.434500	−	0.900672i	$-0.643075\pi$
$193$	−2330.00	−0.869000	−0.434500	+	0.900672i	$0.643075\pi$
$194$	−1580.00	−0.584729
$195$	0	0
$196$	−1116.00	−0.406706
$197$	−1714.00	−0.619886	−0.309943	−	0.950755i	$-0.600310\pi$
$197$	−1714.00	−0.619886	−0.309943	+	0.950755i	$0.600310\pi$
$198$	0	0
$199$	1320.00	0.470213	0.235106	−	0.971970i	$-0.424456\pi$
$199$	1320.00	0.470213	0.235106	+	0.971970i	$0.424456\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	580.000	0.202023
$203$	−1488.00	−0.514469
$204$	0	0
$205$	−1230.00	−0.419058
$206$	−3080.00	−1.04172
$207$	0	0
$208$	−1312.00	−0.437360
$209$	380.000	0.125766
$210$	0	0
$211$	196.000	0.0639488	0.0319744	−	0.999489i	$-0.489820\pi$
$211$	196.000	0.0639488	0.0319744	+	0.999489i	$0.489820\pi$
$212$	1208.00	0.391348
$213$	0	0
$214$	3128.00	0.999185
$215$	1440.00	0.456778
$216$	0	0
$217$	1984.00	0.620658
$218$	1108.00	0.344235
$219$	0	0
$220$	400.000	0.122582
$221$	−1476.00	−0.449260
$222$	0	0
$223$	−1076.00	−0.323113	−0.161557	−	0.986863i	$-0.551651\pi$
$223$	−1076.00	−0.323113	−0.161557	+	0.986863i	$0.551651\pi$
$224$	256.000	0.0763604
$225$	0	0
$226$	−1668.00	−0.490946
$227$	−1684.00	−0.492383	−0.246192	−	0.969221i	$-0.579179\pi$
$227$	−1684.00	−0.492383	−0.246192	+	0.969221i	$0.579179\pi$
$228$	0	0
$229$	3150.00	0.908986	0.454493	−	0.890750i	$-0.349820\pi$
$229$	3150.00	0.908986	0.454493	+	0.890750i	$0.349820\pi$
$230$	−880.000	−0.252285
$231$	0	0
$232$	−1488.00	−0.421086
$233$	−1622.00	−0.456055	−0.228027	−	0.973655i	$-0.573228\pi$
$233$	−1622.00	−0.456055	−0.228027	+	0.973655i	$0.573228\pi$
$234$	0	0
$235$	840.000	0.233173
$236$	−288.000	−0.0794373
$237$	0	0
$238$	288.000	0.0784381
$239$	−5708.00	−1.54485	−0.772426	−	0.635104i	$-0.780957\pi$
$239$	−5708.00	−1.54485	−0.772426	+	0.635104i	$0.780957\pi$
$240$	0	0
$241$	1314.00	0.351212	0.175606	−	0.984460i	$-0.443811\pi$
$241$	1314.00	0.351212	0.175606	+	0.984460i	$0.443811\pi$
$242$	1862.00	0.494603
$243$	0	0
$244$	−2184.00	−0.573018
$245$	−1395.00	−0.363768
$246$	0	0
$247$	−1558.00	−0.401349
$248$	1984.00	0.508001
$249$	0	0
$250$	−250.000	−0.0632456
$251$	−3732.00	−0.938493	−0.469247	−	0.883067i	$-0.655474\pi$
$251$	−3732.00	−0.938493	−0.469247	+	0.883067i	$0.655474\pi$
$252$	0	0
$253$	1760.00	0.437353
$254$	1752.00	0.432796
$255$	0	0
$256$	256.000	0.0625000
$257$	994.000	0.241261	0.120630	−	0.992697i	$-0.461508\pi$
$257$	994.000	0.241261	0.120630	+	0.992697i	$0.461508\pi$
$258$	0	0
$259$	−2096.00	−0.502854
$260$	−1640.00	−0.391186
$261$	0	0
$262$	−1016.00	−0.239575
$263$	−6256.00	−1.46677	−0.733387	−	0.679812i	$-0.762062\pi$
$263$	−6256.00	−1.46677	−0.733387	+	0.679812i	$0.762062\pi$
$264$	0	0
$265$	1510.00	0.350032
$266$	304.000	0.0700731
$267$	0	0
$268$	−3216.00	−0.733017
$269$	−3766.00	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−3766.00	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−6240.00	−1.39872	−0.699360	−	0.714770i	$-0.746531\pi$
$271$	−6240.00	−1.39872	−0.699360	+	0.714770i	$0.746531\pi$
$272$	288.000	0.0642006
$273$	0	0
$274$	−3012.00	−0.664093
$275$	500.000	0.109640
$276$	0	0
$277$	6010.00	1.30363	0.651816	−	0.758377i	$-0.274008\pi$
$277$	6010.00	1.30363	0.651816	+	0.758377i	$0.274008\pi$
$278$	1240.00	0.267519
$279$	0	0
$280$	320.000	0.0682988
$281$	1098.00	0.233100	0.116550	−	0.993185i	$-0.462816\pi$
$281$	1098.00	0.233100	0.116550	+	0.993185i	$0.462816\pi$
$282$	0	0
$283$	688.000	0.144514	0.0722568	−	0.997386i	$-0.476980\pi$
$283$	688.000	0.144514	0.0722568	+	0.997386i	$0.476980\pi$
$284$	−960.000	−0.200583
$285$	0	0
$286$	3280.00	0.678148
$287$	1968.00	0.404764
$288$	0	0
$289$	−4589.00	−0.934053
$290$	−1860.00	−0.376631
$291$	0	0
$292$	2408.00	0.482594
$293$	−8442.00	−1.68323	−0.841616	−	0.540077i	$-0.818395\pi$
$293$	−8442.00	−1.68323	−0.841616	+	0.540077i	$0.818395\pi$
$294$	0	0
$295$	−360.000	−0.0710509
$296$	−2096.00	−0.411579
$297$	0	0
$298$	3476.00	0.675702
$299$	−7216.00	−1.39569
$300$	0	0
$301$	−2304.00	−0.441197
$302$	3440.00	0.655463
$303$	0	0
$304$	304.000	0.0573539
$305$	−2730.00	−0.512522
$306$	0	0
$307$	1588.00	0.295218	0.147609	−	0.989046i	$-0.452842\pi$
$307$	1588.00	0.295218	0.147609	+	0.989046i	$0.452842\pi$
$308$	−640.000	−0.118401
$309$	0	0
$310$	2480.00	0.454369
$311$	8260.00	1.50605	0.753025	−	0.657992i	$-0.228594\pi$
$311$	8260.00	1.50605	0.753025	+	0.657992i	$0.228594\pi$
$312$	0	0
$313$	−9790.00	−1.76793	−0.883967	−	0.467549i	$-0.845137\pi$
$313$	−9790.00	−1.76793	−0.883967	+	0.467549i	$0.845137\pi$
$314$	2892.00	0.519761
$315$	0	0
$316$	−3200.00	−0.569665
$317$	3654.00	0.647410	0.323705	−	0.946158i	$-0.395071\pi$
$317$	3654.00	0.647410	0.323705	+	0.946158i	$0.395071\pi$
$318$	0	0
$319$	3720.00	0.652915
$320$	320.000	0.0559017
$321$	0	0
$322$	1408.00	0.243679
$323$	342.000	0.0589145
$324$	0	0
$325$	−2050.00	−0.349888
$326$	784.000	0.133196
$327$	0	0
$328$	1968.00	0.331295
$329$	−1344.00	−0.225219
$330$	0	0
$331$	−4132.00	−0.686149	−0.343074	−	0.939308i	$-0.611468\pi$
$331$	−4132.00	−0.686149	−0.343074	+	0.939308i	$0.611468\pi$
$332$	464.000	0.0767027
$333$	0	0
$334$	−1088.00	−0.178242
$335$	−4020.00	−0.655630
$336$	0	0
$337$	−7506.00	−1.21329	−0.606644	−	0.794974i	$-0.707485\pi$
$337$	−7506.00	−1.21329	−0.606644	+	0.794974i	$0.707485\pi$
$338$	−9054.00	−1.45702
$339$	0	0
$340$	360.000	0.0574228
$341$	−4960.00	−0.787681
$342$	0	0
$343$	4976.00	0.783320
$344$	−2304.00	−0.361114
$345$	0	0
$346$	2308.00	0.358609
$347$	8292.00	1.28282	0.641409	−	0.767199i	$-0.278350\pi$
$347$	8292.00	1.28282	0.641409	+	0.767199i	$0.278350\pi$
$348$	0	0
$349$	−11362.0	−1.74268	−0.871338	−	0.490683i	$-0.836747\pi$
$349$	−11362.0	−1.74268	−0.871338	+	0.490683i	$0.836747\pi$
$350$	400.000	0.0610883
$351$	0	0
$352$	−640.000	−0.0969094
$353$	−11102.0	−1.67394	−0.836969	−	0.547251i	$-0.815674\pi$
$353$	−11102.0	−1.67394	−0.836969	+	0.547251i	$0.815674\pi$
$354$	0	0
$355$	−1200.00	−0.179407
$356$	−3064.00	−0.456156
$357$	0	0
$358$	5056.00	0.746419
$359$	−2036.00	−0.299320	−0.149660	−	0.988738i	$-0.547818\pi$
$359$	−2036.00	−0.299320	−0.149660	+	0.988738i	$0.547818\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	−2908.00	−0.422213
$363$	0	0
$364$	2624.00	0.377843
$365$	3010.00	0.431645
$366$	0	0
$367$	1592.00	0.226435	0.113218	−	0.993570i	$-0.463884\pi$
$367$	1592.00	0.226435	0.113218	+	0.993570i	$0.463884\pi$
$368$	1408.00	0.199449
$369$	0	0
$370$	−2620.00	−0.368128
$371$	−2416.00	−0.338093
$372$	0	0
$373$	−7082.00	−0.983089	−0.491544	−	0.870853i	$-0.663567\pi$
$373$	−7082.00	−0.983089	−0.491544	+	0.870853i	$0.663567\pi$
$374$	−720.000	−0.0995463
$375$	0	0
$376$	−1344.00	−0.184339
$377$	−15252.0	−2.08360
$378$	0	0
$379$	−12588.0	−1.70607	−0.853037	−	0.521850i	$-0.825242\pi$
$379$	−12588.0	−1.70607	−0.853037	+	0.521850i	$0.825242\pi$
$380$	380.000	0.0512989
$381$	0	0
$382$	−8664.00	−1.16044
$383$	−10552.0	−1.40779	−0.703893	−	0.710306i	$-0.748557\pi$
$383$	−10552.0	−1.40779	−0.703893	+	0.710306i	$0.748557\pi$
$384$	0	0
$385$	−800.000	−0.105901
$386$	4660.00	0.614476
$387$	0	0
$388$	3160.00	0.413466
$389$	2174.00	0.283358	0.141679	−	0.989913i	$-0.454750\pi$
$389$	2174.00	0.283358	0.141679	+	0.989913i	$0.454750\pi$
$390$	0	0
$391$	1584.00	0.204876
$392$	2232.00	0.287584
$393$	0	0
$394$	3428.00	0.438325
$395$	−4000.00	−0.509524
$396$	0	0
$397$	−12718.0	−1.60780	−0.803902	−	0.594762i	$-0.797246\pi$
$397$	−12718.0	−1.60780	−0.803902	+	0.594762i	$0.797246\pi$
$398$	−2640.00	−0.332491
$399$	0	0
$400$	400.000	0.0500000
$401$	3330.00	0.414694	0.207347	−	0.978267i	$-0.433517\pi$
$401$	3330.00	0.414694	0.207347	+	0.978267i	$0.433517\pi$
$402$	0	0
$403$	20336.0	2.51367
$404$	−1160.00	−0.142852
$405$	0	0
$406$	2976.00	0.363784
$407$	5240.00	0.638175
$408$	0	0
$409$	−4334.00	−0.523967	−0.261984	−	0.965072i	$-0.584377\pi$
$409$	−4334.00	−0.523967	−0.261984	+	0.965072i	$0.584377\pi$
$410$	2460.00	0.296319
$411$	0	0
$412$	6160.00	0.736605
$413$	576.000	0.0686274
$414$	0	0
$415$	580.000	0.0686050
$416$	2624.00	0.309260
$417$	0	0
$418$	−760.000	−0.0889302
$419$	−13420.0	−1.56470	−0.782351	−	0.622838i	$-0.785980\pi$
$419$	−13420.0	−1.56470	−0.782351	+	0.622838i	$0.785980\pi$
$420$	0	0
$421$	−16418.0	−1.90063	−0.950314	−	0.311293i	$-0.899238\pi$
$421$	−16418.0	−1.90063	−0.950314	+	0.311293i	$0.899238\pi$
$422$	−392.000	−0.0452186
$423$	0	0
$424$	−2416.00	−0.276725
$425$	450.000	0.0513605
$426$	0	0
$427$	4368.00	0.495041
$428$	−6256.00	−0.706531
$429$	0	0
$430$	−2880.00	−0.322991
$431$	14232.0	1.59056	0.795280	−	0.606242i	$-0.207324\pi$
$431$	14232.0	1.59056	0.795280	+	0.606242i	$0.207324\pi$
$432$	0	0
$433$	−17530.0	−1.94558	−0.972792	−	0.231679i	$-0.925578\pi$
$433$	−17530.0	−1.94558	−0.972792	+	0.231679i	$0.925578\pi$
$434$	−3968.00	−0.438871
$435$	0	0
$436$	−2216.00	−0.243411
$437$	1672.00	0.183027
$438$	0	0
$439$	6464.00	0.702756	0.351378	−	0.936234i	$-0.385713\pi$
$439$	6464.00	0.702756	0.351378	+	0.936234i	$0.385713\pi$
$440$	−800.000	−0.0866784
$441$	0	0
$442$	2952.00	0.317675
$443$	−3732.00	−0.400254	−0.200127	−	0.979770i	$-0.564136\pi$
$443$	−3732.00	−0.400254	−0.200127	+	0.979770i	$0.564136\pi$
$444$	0	0
$445$	−3830.00	−0.407999
$446$	2152.00	0.228476
$447$	0	0
$448$	−512.000	−0.0539949
$449$	2330.00	0.244899	0.122449	−	0.992475i	$-0.460925\pi$
$449$	2330.00	0.244899	0.122449	+	0.992475i	$0.460925\pi$
$450$	0	0
$451$	−4920.00	−0.513689
$452$	3336.00	0.347151
$453$	0	0
$454$	3368.00	0.348168
$455$	3280.00	0.337953
$456$	0	0
$457$	7594.00	0.777314	0.388657	−	0.921383i	$-0.372939\pi$
$457$	7594.00	0.777314	0.388657	+	0.921383i	$0.372939\pi$
$458$	−6300.00	−0.642750
$459$	0	0
$460$	1760.00	0.178392
$461$	9678.00	0.977764	0.488882	−	0.872350i	$-0.337405\pi$
$461$	9678.00	0.977764	0.488882	+	0.872350i	$0.337405\pi$
$462$	0	0
$463$	17728.0	1.77946	0.889730	−	0.456487i	$-0.150893\pi$
$463$	17728.0	1.77946	0.889730	+	0.456487i	$0.150893\pi$
$464$	2976.00	0.297753
$465$	0	0
$466$	3244.00	0.322479
$467$	2572.00	0.254856	0.127428	−	0.991848i	$-0.459328\pi$
$467$	2572.00	0.254856	0.127428	+	0.991848i	$0.459328\pi$
$468$	0	0
$469$	6432.00	0.633267
$470$	−1680.00	−0.164878
$471$	0	0
$472$	576.000	0.0561707
$473$	5760.00	0.559926
$474$	0	0
$475$	475.000	0.0458831
$476$	−576.000	−0.0554641
$477$	0	0
$478$	11416.0	1.09238
$479$	11244.0	1.07255	0.536275	−	0.844043i	$-0.319831\pi$
$479$	11244.0	1.07255	0.536275	+	0.844043i	$0.319831\pi$
$480$	0	0
$481$	−21484.0	−2.03656
$482$	−2628.00	−0.248345
$483$	0	0
$484$	−3724.00	−0.349737
$485$	3950.00	0.369815
$486$	0	0
$487$	2236.00	0.208055	0.104028	−	0.994574i	$-0.466827\pi$
$487$	2236.00	0.208055	0.104028	+	0.994574i	$0.466827\pi$
$488$	4368.00	0.405185
$489$	0	0
$490$	2790.00	0.257223
$491$	15924.0	1.46363	0.731813	−	0.681506i	$-0.238675\pi$
$491$	15924.0	1.46363	0.731813	+	0.681506i	$0.238675\pi$
$492$	0	0
$493$	3348.00	0.305855
$494$	3116.00	0.283796
$495$	0	0
$496$	−3968.00	−0.359211
$497$	1920.00	0.173287
$498$	0	0
$499$	7284.00	0.653460	0.326730	−	0.945118i	$-0.394053\pi$
$499$	7284.00	0.653460	0.326730	+	0.945118i	$0.394053\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	7464.00	0.663615
$503$	−16488.0	−1.46156	−0.730779	−	0.682614i	$-0.760843\pi$
$503$	−16488.0	−1.46156	−0.730779	+	0.682614i	$0.760843\pi$
$504$	0	0
$505$	−1450.00	−0.127771
$506$	−3520.00	−0.309255
$507$	0	0
$508$	−3504.00	−0.306033
$509$	11954.0	1.04097	0.520483	−	0.853872i	$-0.325752\pi$
$509$	11954.0	1.04097	0.520483	+	0.853872i	$0.325752\pi$
$510$	0	0
$511$	−4816.00	−0.416922
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−1988.00	−0.170597
$515$	7700.00	0.658840
$516$	0	0
$517$	3360.00	0.285827
$518$	4192.00	0.355571
$519$	0	0
$520$	3280.00	0.276611
$521$	−15750.0	−1.32441	−0.662207	−	0.749321i	$-0.730380\pi$
$521$	−15750.0	−1.32441	−0.662207	+	0.749321i	$0.730380\pi$
$522$	0	0
$523$	7884.00	0.659165	0.329582	−	0.944127i	$-0.393092\pi$
$523$	7884.00	0.659165	0.329582	+	0.944127i	$0.393092\pi$
$524$	2032.00	0.169405
$525$	0	0
$526$	12512.0	1.03717
$527$	−4464.00	−0.368985
$528$	0	0
$529$	−4423.00	−0.363524
$530$	−3020.00	−0.247510
$531$	0	0
$532$	−608.000	−0.0495491
$533$	20172.0	1.63930
$534$	0	0
$535$	−7820.00	−0.631940
$536$	6432.00	0.518321
$537$	0	0
$538$	7532.00	0.603583
$539$	−5580.00	−0.445914
$540$	0	0
$541$	−14402.0	−1.14453	−0.572265	−	0.820069i	$-0.693935\pi$
$541$	−14402.0	−1.14453	−0.572265	+	0.820069i	$0.693935\pi$
$542$	12480.0	0.989044
$543$	0	0
$544$	−576.000	−0.0453967
$545$	−2770.00	−0.217713
$546$	0	0
$547$	−9676.00	−0.756336	−0.378168	−	0.925737i	$-0.623446\pi$
$547$	−9676.00	−0.756336	−0.378168	+	0.925737i	$0.623446\pi$
$548$	6024.00	0.469585
$549$	0	0
$550$	−1000.00	−0.0775275
$551$	3534.00	0.273237
$552$	0	0
$553$	6400.00	0.492144
$554$	−12020.0	−0.921807
$555$	0	0
$556$	−2480.00	−0.189164
$557$	20406.0	1.55230	0.776149	−	0.630550i	$-0.217170\pi$
$557$	20406.0	1.55230	0.776149	+	0.630550i	$0.217170\pi$
$558$	0	0
$559$	−23616.0	−1.78685
$560$	−640.000	−0.0482945
$561$	0	0
$562$	−2196.00	−0.164827
$563$	18428.0	1.37948	0.689740	−	0.724057i	$-0.257725\pi$
$563$	18428.0	1.37948	0.689740	+	0.724057i	$0.257725\pi$
$564$	0	0
$565$	4170.00	0.310501
$566$	−1376.00	−0.102187
$567$	0	0
$568$	1920.00	0.141833
$569$	24162.0	1.78018	0.890091	−	0.455783i	$-0.150641\pi$
$569$	24162.0	1.78018	0.890091	+	0.455783i	$0.150641\pi$
$570$	0	0
$571$	−9828.00	−0.720296	−0.360148	−	0.932895i	$-0.617274\pi$
$571$	−9828.00	−0.720296	−0.360148	+	0.932895i	$0.617274\pi$
$572$	−6560.00	−0.479523
$573$	0	0
$574$	−3936.00	−0.286212
$575$	2200.00	0.159559
$576$	0	0
$577$	−25966.0	−1.87345	−0.936723	−	0.350071i	$-0.886158\pi$
$577$	−25966.0	−1.87345	−0.936723	+	0.350071i	$0.886158\pi$
$578$	9178.00	0.660475
$579$	0	0
$580$	3720.00	0.266318
$581$	−928.000	−0.0662649
$582$	0	0
$583$	6040.00	0.429076
$584$	−4816.00	−0.341246
$585$	0	0
$586$	16884.0	1.19022
$587$	−7020.00	−0.493605	−0.246803	−	0.969066i	$-0.579380\pi$
$587$	−7020.00	−0.493605	−0.246803	+	0.969066i	$0.579380\pi$
$588$	0	0
$589$	−4712.00	−0.329634
$590$	720.000	0.0502406
$591$	0	0
$592$	4192.00	0.291031
$593$	4698.00	0.325335	0.162668	−	0.986681i	$-0.447990\pi$
$593$	4698.00	0.325335	0.162668	+	0.986681i	$0.447990\pi$
$594$	0	0
$595$	−720.000	−0.0496086
$596$	−6952.00	−0.477794
$597$	0	0
$598$	14432.0	0.986904
$599$	1408.00	0.0960423	0.0480211	−	0.998846i	$-0.484709\pi$
$599$	1408.00	0.0960423	0.0480211	+	0.998846i	$0.484709\pi$
$600$	0	0
$601$	−18942.0	−1.28562	−0.642812	−	0.766024i	$-0.722232\pi$
$601$	−18942.0	−1.28562	−0.642812	+	0.766024i	$0.722232\pi$
$602$	4608.00	0.311974
$603$	0	0
$604$	−6880.00	−0.463482
$605$	−4655.00	−0.312814
$606$	0	0
$607$	−4268.00	−0.285392	−0.142696	−	0.989767i	$-0.545577\pi$
$607$	−4268.00	−0.285392	−0.142696	+	0.989767i	$0.545577\pi$
$608$	−608.000	−0.0405554
$609$	0	0
$610$	5460.00	0.362408
$611$	−13776.0	−0.912140
$612$	0	0
$613$	106.000	0.00698418	0.00349209	−	0.999994i	$-0.498888\pi$
$613$	106.000	0.00698418	0.00349209	+	0.999994i	$0.498888\pi$
$614$	−3176.00	−0.208751
$615$	0	0
$616$	1280.00	0.0837219
$617$	4250.00	0.277307	0.138654	−	0.990341i	$-0.455723\pi$
$617$	4250.00	0.277307	0.138654	+	0.990341i	$0.455723\pi$
$618$	0	0
$619$	−11436.0	−0.742571	−0.371286	−	0.928519i	$-0.621083\pi$
$619$	−11436.0	−0.742571	−0.371286	+	0.928519i	$0.621083\pi$
$620$	−4960.00	−0.321288
$621$	0	0
$622$	−16520.0	−1.06494
$623$	6128.00	0.394082
$624$	0	0
$625$	625.000	0.0400000
$626$	19580.0	1.25012
$627$	0	0
$628$	−5784.00	−0.367527
$629$	4716.00	0.298949
$630$	0	0
$631$	−1528.00	−0.0964005	−0.0482003	−	0.998838i	$-0.515349\pi$
$631$	−1528.00	−0.0964005	−0.0482003	+	0.998838i	$0.515349\pi$
$632$	6400.00	0.402814
$633$	0	0
$634$	−7308.00	−0.457788
$635$	−4380.00	−0.273724
$636$	0	0
$637$	22878.0	1.42301
$638$	−7440.00	−0.461681
$639$	0	0
$640$	−640.000	−0.0395285
$641$	11186.0	0.689267	0.344634	−	0.938737i	$-0.388003\pi$
$641$	11186.0	0.689267	0.344634	+	0.938737i	$0.388003\pi$
$642$	0	0
$643$	18968.0	1.16334	0.581668	−	0.813426i	$-0.302400\pi$
$643$	18968.0	1.16334	0.581668	+	0.813426i	$0.302400\pi$
$644$	−2816.00	−0.172307
$645$	0	0
$646$	−684.000	−0.0416589
$647$	21192.0	1.28770	0.643851	−	0.765151i	$-0.277336\pi$
$647$	21192.0	1.28770	0.643851	+	0.765151i	$0.277336\pi$
$648$	0	0
$649$	−1440.00	−0.0870954
$650$	4100.00	0.247408
$651$	0	0
$652$	−1568.00	−0.0941835
$653$	−18538.0	−1.11095	−0.555473	−	0.831534i	$-0.687463\pi$
$653$	−18538.0	−1.11095	−0.555473	+	0.831534i	$0.687463\pi$
$654$	0	0
$655$	2540.00	0.151521
$656$	−3936.00	−0.234261
$657$	0	0
$658$	2688.00	0.159254
$659$	−12192.0	−0.720687	−0.360344	−	0.932820i	$-0.617341\pi$
$659$	−12192.0	−0.720687	−0.360344	+	0.932820i	$0.617341\pi$
$660$	0	0
$661$	16926.0	0.995984	0.497992	−	0.867182i	$-0.334071\pi$
$661$	16926.0	0.995984	0.497992	+	0.867182i	$0.334071\pi$
$662$	8264.00	0.485180
$663$	0	0
$664$	−928.000	−0.0542370
$665$	−760.000	−0.0443181
$666$	0	0
$667$	16368.0	0.950182
$668$	2176.00	0.126036
$669$	0	0
$670$	8040.00	0.463600
$671$	−10920.0	−0.628259
$672$	0	0
$673$	14830.0	0.849412	0.424706	−	0.905331i	$-0.360377\pi$
$673$	14830.0	0.849412	0.424706	+	0.905331i	$0.360377\pi$
$674$	15012.0	0.857924
$675$	0	0
$676$	18108.0	1.03027
$677$	21246.0	1.20613	0.603065	−	0.797692i	$-0.293946\pi$
$677$	21246.0	1.20613	0.603065	+	0.797692i	$0.293946\pi$
$678$	0	0
$679$	−6320.00	−0.357201
$680$	−720.000	−0.0406040
$681$	0	0
$682$	9920.00	0.556974
$683$	−2924.00	−0.163812	−0.0819061	−	0.996640i	$-0.526101\pi$
$683$	−2924.00	−0.163812	−0.0819061	+	0.996640i	$0.526101\pi$
$684$	0	0
$685$	7530.00	0.420010
$686$	−9952.00	−0.553891
$687$	0	0
$688$	4608.00	0.255346
$689$	−24764.0	−1.36928
$690$	0	0
$691$	33732.0	1.85706	0.928528	−	0.371262i	$-0.121075\pi$
$691$	33732.0	1.85706	0.928528	+	0.371262i	$0.121075\pi$
$692$	−4616.00	−0.253575
$693$	0	0
$694$	−16584.0	−0.907089
$695$	−3100.00	−0.169194
$696$	0	0
$697$	−4428.00	−0.240635
$698$	22724.0	1.23226
$699$	0	0
$700$	−800.000	−0.0431959
$701$	19398.0	1.04515	0.522577	−	0.852592i	$-0.324971\pi$
$701$	19398.0	1.04515	0.522577	+	0.852592i	$0.324971\pi$
$702$	0	0
$703$	4978.00	0.267068
$704$	1280.00	0.0685253
$705$	0	0
$706$	22204.0	1.18365
$707$	2320.00	0.123412
$708$	0	0
$709$	−21250.0	−1.12561	−0.562807	−	0.826588i	$-0.690279\pi$
$709$	−21250.0	−1.12561	−0.562807	+	0.826588i	$0.690279\pi$
$710$	2400.00	0.126860
$711$	0	0
$712$	6128.00	0.322551
$713$	−21824.0	−1.14630
$714$	0	0
$715$	−8200.00	−0.428899
$716$	−10112.0	−0.527798
$717$	0	0
$718$	4072.00	0.211651
$719$	−24708.0	−1.28158	−0.640788	−	0.767718i	$-0.721392\pi$
$719$	−24708.0	−1.28158	−0.640788	+	0.767718i	$0.721392\pi$
$720$	0	0
$721$	−12320.0	−0.636367
$722$	−722.000	−0.0372161
$723$	0	0
$724$	5816.00	0.298550
$725$	4650.00	0.238202
$726$	0	0
$727$	9176.00	0.468114	0.234057	−	0.972223i	$-0.424800\pi$
$727$	9176.00	0.468114	0.234057	+	0.972223i	$0.424800\pi$
$728$	−5248.00	−0.267176
$729$	0	0
$730$	−6020.00	−0.305219
$731$	5184.00	0.262294
$732$	0	0
$733$	−18870.0	−0.950859	−0.475429	−	0.879754i	$-0.657707\pi$
$733$	−18870.0	−0.950859	−0.475429	+	0.879754i	$0.657707\pi$
$734$	−3184.00	−0.160114
$735$	0	0
$736$	−2816.00	−0.141031
$737$	−16080.0	−0.803683
$738$	0	0
$739$	−15076.0	−0.750446	−0.375223	−	0.926935i	$-0.622434\pi$
$739$	−15076.0	−0.750446	−0.375223	+	0.926935i	$0.622434\pi$
$740$	5240.00	0.260306
$741$	0	0
$742$	4832.00	0.239068
$743$	4656.00	0.229895	0.114948	−	0.993372i	$-0.463330\pi$
$743$	4656.00	0.229895	0.114948	+	0.993372i	$0.463330\pi$
$744$	0	0
$745$	−8690.00	−0.427352
$746$	14164.0	0.695149
$747$	0	0
$748$	1440.00	0.0703899
$749$	12512.0	0.610385
$750$	0	0
$751$	20920.0	1.01649	0.508243	−	0.861213i	$-0.330295\pi$
$751$	20920.0	1.01649	0.508243	+	0.861213i	$0.330295\pi$
$752$	2688.00	0.130347
$753$	0	0
$754$	30504.0	1.47333
$755$	−8600.00	−0.414551
$756$	0	0
$757$	34578.0	1.66018	0.830092	−	0.557627i	$-0.188288\pi$
$757$	34578.0	1.66018	0.830092	+	0.557627i	$0.188288\pi$
$758$	25176.0	1.20638
$759$	0	0
$760$	−760.000	−0.0362738
$761$	28214.0	1.34396	0.671982	−	0.740567i	$-0.265443\pi$
$761$	28214.0	1.34396	0.671982	+	0.740567i	$0.265443\pi$
$762$	0	0
$763$	4432.00	0.210287
$764$	17328.0	0.820556
$765$	0	0
$766$	21104.0	0.995455
$767$	5904.00	0.277941
$768$	0	0
$769$	−36734.0	−1.72258	−0.861289	−	0.508116i	$-0.830342\pi$
$769$	−36734.0	−1.72258	−0.861289	+	0.508116i	$0.830342\pi$
$770$	1600.00	0.0748831
$771$	0	0
$772$	−9320.00	−0.434500
$773$	−21762.0	−1.01258	−0.506290	−	0.862363i	$-0.668984\pi$
$773$	−21762.0	−1.01258	−0.506290	+	0.862363i	$0.668984\pi$
$774$	0	0
$775$	−6200.00	−0.287368
$776$	−6320.00	−0.292364
$777$	0	0
$778$	−4348.00	−0.200364
$779$	−4674.00	−0.214972
$780$	0	0
$781$	−4800.00	−0.219920
$782$	−3168.00	−0.144869
$783$	0	0
$784$	−4464.00	−0.203353
$785$	−7230.00	−0.328726
$786$	0	0
$787$	28260.0	1.28000	0.640000	−	0.768375i	$-0.278934\pi$
$787$	28260.0	1.28000	0.640000	+	0.768375i	$0.278934\pi$
$788$	−6856.00	−0.309943
$789$	0	0
$790$	8000.00	0.360288
$791$	−6672.00	−0.299910
$792$	0	0
$793$	44772.0	2.00492
$794$	25436.0	1.13689
$795$	0	0
$796$	5280.00	0.235106
$797$	29854.0	1.32683	0.663415	−	0.748252i	$-0.269107\pi$
$797$	29854.0	1.32683	0.663415	+	0.748252i	$0.269107\pi$
$798$	0	0
$799$	3024.00	0.133894
$800$	−800.000	−0.0353553
$801$	0	0
$802$	−6660.00	−0.293233
$803$	12040.0	0.529119
$804$	0	0
$805$	−3520.00	−0.154116
$806$	−40672.0	−1.77743
$807$	0	0
$808$	2320.00	0.101012
$809$	−21482.0	−0.933581	−0.466790	−	0.884368i	$-0.654590\pi$
$809$	−21482.0	−0.933581	−0.466790	+	0.884368i	$0.654590\pi$
$810$	0	0
$811$	−14756.0	−0.638907	−0.319453	−	0.947602i	$-0.603499\pi$
$811$	−14756.0	−0.638907	−0.319453	+	0.947602i	$0.603499\pi$
$812$	−5952.00	−0.257234
$813$	0	0
$814$	−10480.0	−0.451258
$815$	−1960.00	−0.0842403
$816$	0	0
$817$	5472.00	0.234322
$818$	8668.00	0.370501
$819$	0	0
$820$	−4920.00	−0.209529
$821$	13214.0	0.561720	0.280860	−	0.959749i	$-0.409380\pi$
$821$	13214.0	0.561720	0.280860	+	0.959749i	$0.409380\pi$
$822$	0	0
$823$	19256.0	0.815580	0.407790	−	0.913076i	$-0.366300\pi$
$823$	19256.0	0.815580	0.407790	+	0.913076i	$0.366300\pi$
$824$	−12320.0	−0.520859
$825$	0	0
$826$	−1152.00	−0.0485269
$827$	−25356.0	−1.06616	−0.533080	−	0.846065i	$-0.678966\pi$
$827$	−25356.0	−1.06616	−0.533080	+	0.846065i	$0.678966\pi$
$828$	0	0
$829$	37286.0	1.56212	0.781059	−	0.624457i	$-0.214680\pi$
$829$	37286.0	1.56212	0.781059	+	0.624457i	$0.214680\pi$
$830$	−1160.00	−0.0485111
$831$	0	0
$832$	−5248.00	−0.218680
$833$	−5022.00	−0.208886
$834$	0	0
$835$	2720.00	0.112730
$836$	1520.00	0.0628831
$837$	0	0
$838$	26840.0	1.10641
$839$	35816.0	1.47379	0.736893	−	0.676010i	$-0.236292\pi$
$839$	35816.0	1.47379	0.736893	+	0.676010i	$0.236292\pi$
$840$	0	0
$841$	10207.0	0.418508
$842$	32836.0	1.34395
$843$	0	0
$844$	784.000	0.0319744
$845$	22635.0	0.921500
$846$	0	0
$847$	7448.00	0.302144
$848$	4832.00	0.195674
$849$	0	0
$850$	−900.000	−0.0363173
$851$	23056.0	0.928730
$852$	0	0
$853$	−4206.00	−0.168828	−0.0844142	−	0.996431i	$-0.526902\pi$
$853$	−4206.00	−0.168828	−0.0844142	+	0.996431i	$0.526902\pi$
$854$	−8736.00	−0.350047
$855$	0	0
$856$	12512.0	0.499593
$857$	−29446.0	−1.17369	−0.586847	−	0.809698i	$-0.699631\pi$
$857$	−29446.0	−1.17369	−0.586847	+	0.809698i	$0.699631\pi$
$858$	0	0
$859$	−5572.00	−0.221320	−0.110660	−	0.993858i	$-0.535297\pi$
$859$	−5572.00	−0.221320	−0.110660	+	0.993858i	$0.535297\pi$
$860$	5760.00	0.228389
$861$	0	0
$862$	−28464.0	−1.12470
$863$	−11056.0	−0.436096	−0.218048	−	0.975938i	$-0.569969\pi$
$863$	−11056.0	−0.436096	−0.218048	+	0.975938i	$0.569969\pi$
$864$	0	0
$865$	−5770.00	−0.226804
$866$	35060.0	1.37574
$867$	0	0
$868$	7936.00	0.310329
$869$	−16000.0	−0.624583
$870$	0	0
$871$	65928.0	2.56474
$872$	4432.00	0.172117
$873$	0	0
$874$	−3344.00	−0.129419
$875$	−1000.00	−0.0386356
$876$	0	0
$877$	−2322.00	−0.0894052	−0.0447026	−	0.999000i	$-0.514234\pi$
$877$	−2322.00	−0.0894052	−0.0447026	+	0.999000i	$0.514234\pi$
$878$	−12928.0	−0.496924
$879$	0	0
$880$	1600.00	0.0612909
$881$	12910.0	0.493699	0.246850	−	0.969054i	$-0.420605\pi$
$881$	12910.0	0.493699	0.246850	+	0.969054i	$0.420605\pi$
$882$	0	0
$883$	−4440.00	−0.169216	−0.0846081	−	0.996414i	$-0.526964\pi$
$883$	−4440.00	−0.169216	−0.0846081	+	0.996414i	$0.526964\pi$
$884$	−5904.00	−0.224630
$885$	0	0
$886$	7464.00	0.283023
$887$	6056.00	0.229245	0.114623	−	0.993409i	$-0.463434\pi$
$887$	6056.00	0.229245	0.114623	+	0.993409i	$0.463434\pi$
$888$	0	0
$889$	7008.00	0.264388
$890$	7660.00	0.288499
$891$	0	0
$892$	−4304.00	−0.161557
$893$	3192.00	0.119615
$894$	0	0
$895$	−12640.0	−0.472077
$896$	1024.00	0.0381802
$897$	0	0
$898$	−4660.00	−0.173170
$899$	−46128.0	−1.71130
$900$	0	0
$901$	5436.00	0.200998
$902$	9840.00	0.363233
$903$	0	0
$904$	−6672.00	−0.245473
$905$	7270.00	0.267031
$906$	0	0
$907$	25076.0	0.918010	0.459005	−	0.888434i	$-0.348206\pi$
$907$	25076.0	0.918010	0.459005	+	0.888434i	$0.348206\pi$
$908$	−6736.00	−0.246192
$909$	0	0
$910$	−6560.00	−0.238969
$911$	20208.0	0.734930	0.367465	−	0.930037i	$-0.380226\pi$
$911$	20208.0	0.734930	0.367465	+	0.930037i	$0.380226\pi$
$912$	0	0
$913$	2320.00	0.0840973
$914$	−15188.0	−0.549644
$915$	0	0
$916$	12600.0	0.454493
$917$	−4064.00	−0.146352
$918$	0	0
$919$	30136.0	1.08171	0.540857	−	0.841115i	$-0.318100\pi$
$919$	30136.0	1.08171	0.540857	+	0.841115i	$0.318100\pi$
$920$	−3520.00	−0.126142
$921$	0	0
$922$	−19356.0	−0.691384
$923$	19680.0	0.701815
$924$	0	0
$925$	6550.00	0.232825
$926$	−35456.0	−1.25827
$927$	0	0
$928$	−5952.00	−0.210543
$929$	−15594.0	−0.550724	−0.275362	−	0.961341i	$-0.588798\pi$
$929$	−15594.0	−0.550724	−0.275362	+	0.961341i	$0.588798\pi$
$930$	0	0
$931$	−5301.00	−0.186609
$932$	−6488.00	−0.228027
$933$	0	0
$934$	−5144.00	−0.180211
$935$	1800.00	0.0629586
$936$	0	0
$937$	25634.0	0.893731	0.446866	−	0.894601i	$-0.352540\pi$
$937$	25634.0	0.893731	0.446866	+	0.894601i	$0.352540\pi$
$938$	−12864.0	−0.447787
$939$	0	0
$940$	3360.00	0.116586
$941$	−37758.0	−1.30805	−0.654025	−	0.756473i	$-0.726921\pi$
$941$	−37758.0	−1.30805	−0.654025	+	0.756473i	$0.726921\pi$
$942$	0	0
$943$	−21648.0	−0.747567
$944$	−1152.00	−0.0397187
$945$	0	0
$946$	−11520.0	−0.395928
$947$	−40356.0	−1.38479	−0.692394	−	0.721520i	$-0.743444\pi$
$947$	−40356.0	−1.38479	−0.692394	+	0.721520i	$0.743444\pi$
$948$	0	0
$949$	−49364.0	−1.68854
$950$	−950.000	−0.0324443
$951$	0	0
$952$	1152.00	0.0392190
$953$	27978.0	0.950993	0.475496	−	0.879718i	$-0.342268\pi$
$953$	27978.0	0.950993	0.475496	+	0.879718i	$0.342268\pi$
$954$	0	0
$955$	21660.0	0.733928
$956$	−22832.0	−0.772426
$957$	0	0
$958$	−22488.0	−0.758407
$959$	−12048.0	−0.405683
$960$	0	0
$961$	31713.0	1.06452
$962$	42968.0	1.44007
$963$	0	0
$964$	5256.00	0.175606
$965$	−11650.0	−0.388629
$966$	0	0
$967$	−19616.0	−0.652335	−0.326168	−	0.945312i	$-0.605757\pi$
$967$	−19616.0	−0.652335	−0.326168	+	0.945312i	$0.605757\pi$
$968$	7448.00	0.247301
$969$	0	0
$970$	−7900.00	−0.261499
$971$	−8648.00	−0.285816	−0.142908	−	0.989736i	$-0.545645\pi$
$971$	−8648.00	−0.285816	−0.142908	+	0.989736i	$0.545645\pi$
$972$	0	0
$973$	4960.00	0.163423
$974$	−4472.00	−0.147117
$975$	0	0
$976$	−8736.00	−0.286509
$977$	5746.00	0.188158	0.0940792	−	0.995565i	$-0.470009\pi$
$977$	5746.00	0.188158	0.0940792	+	0.995565i	$0.470009\pi$
$978$	0	0
$979$	−15320.0	−0.500132
$980$	−5580.00	−0.181884
$981$	0	0
$982$	−31848.0	−1.03494
$983$	5304.00	0.172097	0.0860485	−	0.996291i	$-0.472576\pi$
$983$	5304.00	0.172097	0.0860485	+	0.996291i	$0.472576\pi$
$984$	0	0
$985$	−8570.00	−0.277221
$986$	−6696.00	−0.216272
$987$	0	0
$988$	−6232.00	−0.200674
$989$	25344.0	0.814856
$990$	0	0
$991$	7416.00	0.237716	0.118858	−	0.992911i	$-0.462077\pi$
$991$	7416.00	0.237716	0.118858	+	0.992911i	$0.462077\pi$
$992$	7936.00	0.254000
$993$	0	0
$994$	−3840.00	−0.122533
$995$	6600.00	0.210285
$996$	0	0
$997$	−13358.0	−0.424325	−0.212163	−	0.977234i	$-0.568051\pi$
$997$	−13358.0	−0.424325	−0.212163	+	0.977234i	$0.568051\pi$
$998$	−14568.0	−0.462066
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.4.a.f.1.1		1
3.2	odd	2		570.4.a.f.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.a.f.1.1	✓	1	3.2	odd	2
1710.4.a.f.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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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