LMFDB - Embedded newform 585.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,4,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	585.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:	$34.5161173534$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-5.00000 q^{2} +17.0000 q^{4} +5.00000 q^{5} -12.0000 q^{7} -45.0000 q^{8} +O(q^{10})$

\(q-5.00000 q^{2} +17.0000 q^{4} +5.00000 q^{5} -12.0000 q^{7} -45.0000 q^{8} -25.0000 q^{10} -14.0000 q^{11} -13.0000 q^{13} +60.0000 q^{14} +89.0000 q^{16} -98.0000 q^{17} -26.0000 q^{19} +85.0000 q^{20} +70.0000 q^{22} +114.000 q^{23} +25.0000 q^{25} +65.0000 q^{26} -204.000 q^{28} -58.0000 q^{29} +306.000 q^{31} -85.0000 q^{32} +490.000 q^{34} -60.0000 q^{35} +86.0000 q^{37} +130.000 q^{38} -225.000 q^{40} +374.000 q^{41} -314.000 q^{43} -238.000 q^{44} -570.000 q^{46} -620.000 q^{47} -199.000 q^{49} -125.000 q^{50} -221.000 q^{52} -362.000 q^{53} -70.0000 q^{55} +540.000 q^{56} +290.000 q^{58} -266.000 q^{59} +634.000 q^{61} -1530.00 q^{62} -287.000 q^{64} -65.0000 q^{65} +612.000 q^{67} -1666.00 q^{68} +300.000 q^{70} +686.000 q^{71} +202.000 q^{73} -430.000 q^{74} -442.000 q^{76} +168.000 q^{77} -516.000 q^{79} +445.000 q^{80} -1870.00 q^{82} -48.0000 q^{83} -490.000 q^{85} +1570.00 q^{86} +630.000 q^{88} +1230.00 q^{89} +156.000 q^{91} +1938.00 q^{92} +3100.00 q^{94} -130.000 q^{95} +350.000 q^{97} +995.000 q^{98} +O(q^{100})\)

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 $

$2$	−5.00000	−1.76777	−0.883883	−	0.467707i	$-0.845080\pi$
$2$	−5.00000	−1.76777	−0.883883	+	0.467707i	$0.845080\pi$
$3$	0	0
$3$	0	0
$4$	17.0000	2.12500
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−12.0000	−0.647939	−0.323970	−	0.946068i	$-0.605018\pi$
$7$	−12.0000	−0.647939	−0.323970	+	0.946068i	$0.605018\pi$
$8$	−45.0000	−1.98874
$9$	0	0
$10$	−25.0000	−0.790569
$11$	−14.0000	−0.383742	−0.191871	−	0.981420i	$-0.561455\pi$
$11$	−14.0000	−0.383742	−0.191871	+	0.981420i	$0.561455\pi$
$12$	0	0
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	60.0000	1.14541
$15$	0	0
$16$	89.0000	1.39062
$17$	−98.0000	−1.39815	−0.699073	−	0.715050i	$-0.746404\pi$
$17$	−98.0000	−1.39815	−0.699073	+	0.715050i	$0.746404\pi$
$18$	0	0
$19$	−26.0000	−0.313937	−0.156969	−	0.987604i	$-0.550172\pi$
$19$	−26.0000	−0.313937	−0.156969	+	0.987604i	$0.550172\pi$
$20$	85.0000	0.950329
$21$	0	0
$22$	70.0000	0.678366
$23$	114.000	1.03351	0.516753	−	0.856134i	$-0.327141\pi$
$23$	114.000	1.03351	0.516753	+	0.856134i	$0.327141\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	65.0000	0.490290
$27$	0	0
$28$	−204.000	−1.37687
$29$	−58.0000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−58.0000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	306.000	1.77288	0.886439	−	0.462845i	$-0.153171\pi$
$31$	306.000	1.77288	0.886439	+	0.462845i	$0.153171\pi$
$32$	−85.0000	−0.469563
$33$	0	0
$34$	490.000	2.47160
$35$	−60.0000	−0.289767
$36$	0	0
$37$	86.0000	0.382117	0.191058	−	0.981579i	$-0.438808\pi$
$37$	86.0000	0.382117	0.191058	+	0.981579i	$0.438808\pi$
$38$	130.000	0.554968
$39$	0	0
$40$	−225.000	−0.889391
$41$	374.000	1.42461	0.712305	−	0.701870i	$-0.247651\pi$
$41$	374.000	1.42461	0.712305	+	0.701870i	$0.247651\pi$
$42$	0	0
$43$	−314.000	−1.11359	−0.556797	−	0.830649i	$-0.687970\pi$
$43$	−314.000	−1.11359	−0.556797	+	0.830649i	$0.687970\pi$
$44$	−238.000	−0.815451
$45$	0	0
$46$	−570.000	−1.82700
$47$	−620.000	−1.92418	−0.962088	−	0.272738i	$-0.912071\pi$
$47$	−620.000	−1.92418	−0.962088	+	0.272738i	$0.912071\pi$
$48$	0	0
$49$	−199.000	−0.580175
$50$	−125.000	−0.353553
$51$	0	0
$52$	−221.000	−0.589369
$53$	−362.000	−0.938199	−0.469099	−	0.883145i	$-0.655421\pi$
$53$	−362.000	−0.938199	−0.469099	+	0.883145i	$0.655421\pi$
$54$	0	0
$55$	−70.0000	−0.171615
$56$	540.000	1.28858
$57$	0	0
$58$	290.000	0.656532
$59$	−266.000	−0.586953	−0.293477	−	0.955966i	$-0.594812\pi$
$59$	−266.000	−0.586953	−0.293477	+	0.955966i	$0.594812\pi$
$60$	0	0
$61$	634.000	1.33074	0.665372	−	0.746512i	$-0.268273\pi$
$61$	634.000	1.33074	0.665372	+	0.746512i	$0.268273\pi$
$62$	−1530.00	−3.13404
$63$	0	0
$64$	−287.000	−0.560547
$65$	−65.0000	−0.124035
$66$	0	0
$67$	612.000	1.11594	0.557968	−	0.829863i	$-0.311581\pi$
$67$	612.000	1.11594	0.557968	+	0.829863i	$0.311581\pi$
$68$	−1666.00	−2.97106
$69$	0	0
$70$	300.000	0.512241
$71$	686.000	1.14667	0.573333	−	0.819323i	$-0.305650\pi$
$71$	686.000	1.14667	0.573333	+	0.819323i	$0.305650\pi$
$72$	0	0
$73$	202.000	0.323867	0.161934	−	0.986802i	$-0.448227\pi$
$73$	202.000	0.323867	0.161934	+	0.986802i	$0.448227\pi$
$74$	−430.000	−0.675493
$75$	0	0
$76$	−442.000	−0.667117
$77$	168.000	0.248641
$78$	0	0
$79$	−516.000	−0.734868	−0.367434	−	0.930050i	$-0.619764\pi$
$79$	−516.000	−0.734868	−0.367434	+	0.930050i	$0.619764\pi$
$80$	445.000	0.621906
$81$	0	0
$82$	−1870.00	−2.51838
$83$	−48.0000	−0.0634781	−0.0317391	−	0.999496i	$-0.510105\pi$
$83$	−48.0000	−0.0634781	−0.0317391	+	0.999496i	$0.510105\pi$
$84$	0	0
$85$	−490.000	−0.625270
$86$	1570.00	1.96858
$87$	0	0
$88$	630.000	0.763162
$89$	1230.00	1.46494	0.732470	−	0.680799i	$-0.238367\pi$
$89$	1230.00	1.46494	0.732470	+	0.680799i	$0.238367\pi$
$90$	0	0
$91$	156.000	0.179706
$92$	1938.00	2.19620
$93$	0	0
$94$	3100.00	3.40150
$95$	−130.000	−0.140397
$96$	0	0
$97$	350.000	0.366362	0.183181	−	0.983079i	$-0.441361\pi$
$97$	350.000	0.366362	0.183181	+	0.983079i	$0.441361\pi$
$98$	995.000	1.02561
$99$	0	0
$100$	425.000	0.425000
$101$	1530.00	1.50733	0.753667	−	0.657257i	$-0.228283\pi$
$101$	1530.00	1.50733	0.753667	+	0.657257i	$0.228283\pi$
$102$	0	0
$103$	−58.0000	−0.0554846	−0.0277423	−	0.999615i	$-0.508832\pi$
$103$	−58.0000	−0.0554846	−0.0277423	+	0.999615i	$0.508832\pi$
$104$	585.000	0.551577
$105$	0	0
$106$	1810.00	1.65852
$107$	186.000	0.168050	0.0840248	−	0.996464i	$-0.473223\pi$
$107$	186.000	0.168050	0.0840248	+	0.996464i	$0.473223\pi$
$108$	0	0
$109$	−1342.00	−1.17927	−0.589634	−	0.807670i	$-0.700728\pi$
$109$	−1342.00	−1.17927	−0.589634	+	0.807670i	$0.700728\pi$
$110$	350.000	0.303374
$111$	0	0
$112$	−1068.00	−0.901040
$113$	1966.00	1.63669	0.818344	−	0.574729i	$-0.194892\pi$
$113$	1966.00	1.63669	0.818344	+	0.574729i	$0.194892\pi$
$114$	0	0
$115$	570.000	0.462198
$116$	−986.000	−0.789205
$117$	0	0
$118$	1330.00	1.03760
$119$	1176.00	0.905914
$120$	0	0
$121$	−1135.00	−0.852742
$122$	−3170.00	−2.35245
$123$	0	0
$124$	5202.00	3.76737
$125$	125.000	0.0894427
$126$	0	0
$127$	1738.00	1.21435	0.607175	−	0.794568i	$-0.292303\pi$
$127$	1738.00	1.21435	0.607175	+	0.794568i	$0.292303\pi$
$128$	2115.00	1.46048
$129$	0	0
$130$	325.000	0.219265
$131$	−780.000	−0.520221	−0.260110	−	0.965579i	$-0.583759\pi$
$131$	−780.000	−0.520221	−0.260110	+	0.965579i	$0.583759\pi$
$132$	0	0
$133$	312.000	0.203412
$134$	−3060.00	−1.97271
$135$	0	0
$136$	4410.00	2.78055
$137$	1074.00	0.669767	0.334883	−	0.942260i	$-0.391303\pi$
$137$	1074.00	0.669767	0.334883	+	0.942260i	$0.391303\pi$
$138$	0	0
$139$	416.000	0.253846	0.126923	−	0.991913i	$-0.459490\pi$
$139$	416.000	0.253846	0.126923	+	0.991913i	$0.459490\pi$
$140$	−1020.00	−0.615755
$141$	0	0
$142$	−3430.00	−2.02704
$143$	182.000	0.106431
$144$	0	0
$145$	−290.000	−0.166091
$146$	−1010.00	−0.572522
$147$	0	0
$148$	1462.00	0.811998
$149$	2054.00	1.12933	0.564665	−	0.825320i	$-0.309005\pi$
$149$	2054.00	1.12933	0.564665	+	0.825320i	$0.309005\pi$
$150$	0	0
$151$	2302.00	1.24062	0.620312	−	0.784355i	$-0.287006\pi$
$151$	2302.00	1.24062	0.620312	+	0.784355i	$0.287006\pi$
$152$	1170.00	0.624339
$153$	0	0
$154$	−840.000	−0.439540
$155$	1530.00	0.792855
$156$	0	0
$157$	−2350.00	−1.19459	−0.597294	−	0.802022i	$-0.703758\pi$
$157$	−2350.00	−1.19459	−0.597294	+	0.802022i	$0.703758\pi$
$158$	2580.00	1.29907
$159$	0	0
$160$	−425.000	−0.209995
$161$	−1368.00	−0.669649
$162$	0	0
$163$	2924.00	1.40506	0.702532	−	0.711652i	$-0.252053\pi$
$163$	2924.00	1.40506	0.702532	+	0.711652i	$0.252053\pi$
$164$	6358.00	3.02730
$165$	0	0
$166$	240.000	0.112215
$167$	−3036.00	−1.40678	−0.703391	−	0.710803i	$-0.748332\pi$
$167$	−3036.00	−1.40678	−0.703391	+	0.710803i	$0.748332\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	2450.00	1.10533
$171$	0	0
$172$	−5338.00	−2.36639
$173$	−2226.00	−0.978264	−0.489132	−	0.872210i	$-0.662686\pi$
$173$	−2226.00	−0.978264	−0.489132	+	0.872210i	$0.662686\pi$
$174$	0	0
$175$	−300.000	−0.129588
$176$	−1246.00	−0.533641
$177$	0	0
$178$	−6150.00	−2.58967
$179$	3244.00	1.35457	0.677285	−	0.735721i	$-0.263157\pi$
$179$	3244.00	1.35457	0.677285	+	0.735721i	$0.263157\pi$
$180$	0	0
$181$	−1678.00	−0.689087	−0.344544	−	0.938770i	$-0.611966\pi$
$181$	−1678.00	−0.689087	−0.344544	+	0.938770i	$0.611966\pi$
$182$	−780.000	−0.317678
$183$	0	0
$184$	−5130.00	−2.05537
$185$	430.000	0.170888
$186$	0	0
$187$	1372.00	0.536527
$188$	−10540.0	−4.08888
$189$	0	0
$190$	650.000	0.248189
$191$	3968.00	1.50322	0.751608	−	0.659610i	$-0.229278\pi$
$191$	3968.00	1.50322	0.751608	+	0.659610i	$0.229278\pi$
$192$	0	0
$193$	3998.00	1.49110	0.745550	−	0.666450i	$-0.232187\pi$
$193$	3998.00	1.49110	0.745550	+	0.666450i	$0.232187\pi$
$194$	−1750.00	−0.647643
$195$	0	0
$196$	−3383.00	−1.23287
$197$	−4194.00	−1.51680	−0.758401	−	0.651788i	$-0.774019\pi$
$197$	−4194.00	−1.51680	−0.758401	+	0.651788i	$0.774019\pi$
$198$	0	0
$199$	4240.00	1.51038	0.755190	−	0.655506i	$-0.227545\pi$
$199$	4240.00	1.51038	0.755190	+	0.655506i	$0.227545\pi$
$200$	−1125.00	−0.397748
$201$	0	0
$202$	−7650.00	−2.66461
$203$	696.000	0.240639
$204$	0	0
$205$	1870.00	0.637105
$206$	290.000	0.0980838
$207$	0	0
$208$	−1157.00	−0.385690
$209$	364.000	0.120471
$210$	0	0
$211$	596.000	0.194457	0.0972283	−	0.995262i	$-0.469002\pi$
$211$	596.000	0.194457	0.0972283	+	0.995262i	$0.469002\pi$
$212$	−6154.00	−1.99367
$213$	0	0
$214$	−930.000	−0.297072
$215$	−1570.00	−0.498014
$216$	0	0
$217$	−3672.00	−1.14872
$218$	6710.00	2.08467
$219$	0	0
$220$	−1190.00	−0.364681
$221$	1274.00	0.387776
$222$	0	0
$223$	4268.00	1.28164	0.640822	−	0.767690i	$-0.278594\pi$
$223$	4268.00	1.28164	0.640822	+	0.767690i	$0.278594\pi$
$224$	1020.00	0.304248
$225$	0	0
$226$	−9830.00	−2.89328
$227$	5924.00	1.73211	0.866057	−	0.499946i	$-0.166647\pi$
$227$	5924.00	1.73211	0.866057	+	0.499946i	$0.166647\pi$
$228$	0	0
$229$	−750.000	−0.216425	−0.108213	−	0.994128i	$-0.534513\pi$
$229$	−750.000	−0.216425	−0.108213	+	0.994128i	$0.534513\pi$
$230$	−2850.00	−0.817058
$231$	0	0
$232$	2610.00	0.738599
$233$	−474.000	−0.133274	−0.0666369	−	0.997777i	$-0.521227\pi$
$233$	−474.000	−0.133274	−0.0666369	+	0.997777i	$0.521227\pi$
$234$	0	0
$235$	−3100.00	−0.860518
$236$	−4522.00	−1.24728
$237$	0	0
$238$	−5880.00	−1.60144
$239$	−1598.00	−0.432494	−0.216247	−	0.976339i	$-0.569382\pi$
$239$	−1598.00	−0.432494	−0.216247	+	0.976339i	$0.569382\pi$
$240$	0	0
$241$	2410.00	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	2410.00	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	5675.00	1.50745
$243$	0	0
$244$	10778.0	2.82783
$245$	−995.000	−0.259462
$246$	0	0
$247$	338.000	0.0870705
$248$	−13770.0	−3.52579
$249$	0	0
$250$	−625.000	−0.158114
$251$	312.000	0.0784592	0.0392296	−	0.999230i	$-0.487510\pi$
$251$	312.000	0.0784592	0.0392296	+	0.999230i	$0.487510\pi$
$252$	0	0
$253$	−1596.00	−0.396599
$254$	−8690.00	−2.14669
$255$	0	0
$256$	−8279.00	−2.02124
$257$	5886.00	1.42863	0.714316	−	0.699823i	$-0.246738\pi$
$257$	5886.00	1.42863	0.714316	+	0.699823i	$0.246738\pi$
$258$	0	0
$259$	−1032.00	−0.247588
$260$	−1105.00	−0.263574
$261$	0	0
$262$	3900.00	0.919629
$263$	−1258.00	−0.294949	−0.147475	−	0.989066i	$-0.547114\pi$
$263$	−1258.00	−0.294949	−0.147475	+	0.989066i	$0.547114\pi$
$264$	0	0
$265$	−1810.00	−0.419575
$266$	−1560.00	−0.359585
$267$	0	0
$268$	10404.0	2.37136
$269$	−2414.00	−0.547153	−0.273577	−	0.961850i	$-0.588207\pi$
$269$	−2414.00	−0.547153	−0.273577	+	0.961850i	$0.588207\pi$
$270$	0	0
$271$	598.000	0.134044	0.0670220	−	0.997751i	$-0.478650\pi$
$271$	598.000	0.134044	0.0670220	+	0.997751i	$0.478650\pi$
$272$	−8722.00	−1.94430
$273$	0	0
$274$	−5370.00	−1.18399
$275$	−350.000	−0.0767483
$276$	0	0
$277$	−4710.00	−1.02165	−0.510824	−	0.859685i	$-0.670660\pi$
$277$	−4710.00	−1.02165	−0.510824	+	0.859685i	$0.670660\pi$
$278$	−2080.00	−0.448741
$279$	0	0
$280$	2700.00	0.576271
$281$	−4266.00	−0.905652	−0.452826	−	0.891599i	$-0.649584\pi$
$281$	−4266.00	−0.905652	−0.452826	+	0.891599i	$0.649584\pi$
$282$	0	0
$283$	−978.000	−0.205428	−0.102714	−	0.994711i	$-0.532753\pi$
$283$	−978.000	−0.205428	−0.102714	+	0.994711i	$0.532753\pi$
$284$	11662.0	2.43666
$285$	0	0
$286$	−910.000	−0.188145
$287$	−4488.00	−0.923060
$288$	0	0
$289$	4691.00	0.954814
$290$	1450.00	0.293610
$291$	0	0
$292$	3434.00	0.688218
$293$	882.000	0.175860	0.0879300	−	0.996127i	$-0.471975\pi$
$293$	882.000	0.175860	0.0879300	+	0.996127i	$0.471975\pi$
$294$	0	0
$295$	−1330.00	−0.262494
$296$	−3870.00	−0.759930
$297$	0	0
$298$	−10270.0	−1.99639
$299$	−1482.00	−0.286643
$300$	0	0
$301$	3768.00	0.721541
$302$	−11510.0	−2.19313
$303$	0	0
$304$	−2314.00	−0.436569
$305$	3170.00	0.595127
$306$	0	0
$307$	1816.00	0.337605	0.168802	−	0.985650i	$-0.446010\pi$
$307$	1816.00	0.337605	0.168802	+	0.985650i	$0.446010\pi$
$308$	2856.00	0.528363
$309$	0	0
$310$	−7650.00	−1.40158
$311$	−2292.00	−0.417902	−0.208951	−	0.977926i	$-0.567005\pi$
$311$	−2292.00	−0.417902	−0.208951	+	0.977926i	$0.567005\pi$
$312$	0	0
$313$	8474.00	1.53028	0.765142	−	0.643862i	$-0.222669\pi$
$313$	8474.00	1.53028	0.765142	+	0.643862i	$0.222669\pi$
$314$	11750.0	2.11175
$315$	0	0
$316$	−8772.00	−1.56159
$317$	4586.00	0.812541	0.406270	−	0.913753i	$-0.366829\pi$
$317$	4586.00	0.812541	0.406270	+	0.913753i	$0.366829\pi$
$318$	0	0
$319$	812.000	0.142518
$320$	−1435.00	−0.250684
$321$	0	0
$322$	6840.00	1.18378
$323$	2548.00	0.438930
$324$	0	0
$325$	−325.000	−0.0554700
$326$	−14620.0	−2.48382
$327$	0	0
$328$	−16830.0	−2.83317
$329$	7440.00	1.24675
$330$	0	0
$331$	−2046.00	−0.339753	−0.169877	−	0.985465i	$-0.554337\pi$
$331$	−2046.00	−0.339753	−0.169877	+	0.985465i	$0.554337\pi$
$332$	−816.000	−0.134891
$333$	0	0
$334$	15180.0	2.48686
$335$	3060.00	0.499062
$336$	0	0
$337$	−1286.00	−0.207872	−0.103936	−	0.994584i	$-0.533144\pi$
$337$	−1286.00	−0.207872	−0.103936	+	0.994584i	$0.533144\pi$
$338$	−845.000	−0.135982
$339$	0	0
$340$	−8330.00	−1.32870
$341$	−4284.00	−0.680327
$342$	0	0
$343$	6504.00	1.02386
$344$	14130.0	2.21465
$345$	0	0
$346$	11130.0	1.72934
$347$	634.000	0.0980833	0.0490416	−	0.998797i	$-0.484383\pi$
$347$	634.000	0.0980833	0.0490416	+	0.998797i	$0.484383\pi$
$348$	0	0
$349$	2266.00	0.347554	0.173777	−	0.984785i	$-0.444403\pi$
$349$	2266.00	0.347554	0.173777	+	0.984785i	$0.444403\pi$
$350$	1500.00	0.229081
$351$	0	0
$352$	1190.00	0.180191
$353$	−210.000	−0.0316634	−0.0158317	−	0.999875i	$-0.505040\pi$
$353$	−210.000	−0.0316634	−0.0158317	+	0.999875i	$0.505040\pi$
$354$	0	0
$355$	3430.00	0.512804
$356$	20910.0	3.11300
$357$	0	0
$358$	−16220.0	−2.39456
$359$	−162.000	−0.0238162	−0.0119081	−	0.999929i	$-0.503791\pi$
$359$	−162.000	−0.0238162	−0.0119081	+	0.999929i	$0.503791\pi$
$360$	0	0
$361$	−6183.00	−0.901443
$362$	8390.00	1.21815
$363$	0	0
$364$	2652.00	0.381875
$365$	1010.00	0.144838
$366$	0	0
$367$	678.000	0.0964341	0.0482170	−	0.998837i	$-0.484646\pi$
$367$	678.000	0.0964341	0.0482170	+	0.998837i	$0.484646\pi$
$368$	10146.0	1.43722
$369$	0	0
$370$	−2150.00	−0.302090
$371$	4344.00	0.607896
$372$	0	0
$373$	−6902.00	−0.958102	−0.479051	−	0.877787i	$-0.659019\pi$
$373$	−6902.00	−0.958102	−0.479051	+	0.877787i	$0.659019\pi$
$374$	−6860.00	−0.948455
$375$	0	0
$376$	27900.0	3.82668
$377$	754.000	0.103005
$378$	0	0
$379$	8998.00	1.21952	0.609758	−	0.792588i	$-0.291267\pi$
$379$	8998.00	1.21952	0.609758	+	0.792588i	$0.291267\pi$
$380$	−2210.00	−0.298344
$381$	0	0
$382$	−19840.0	−2.65734
$383$	−132.000	−0.0176107	−0.00880533	−	0.999961i	$-0.502803\pi$
$383$	−132.000	−0.0176107	−0.00880533	+	0.999961i	$0.502803\pi$
$384$	0	0
$385$	840.000	0.111196
$386$	−19990.0	−2.63592
$387$	0	0
$388$	5950.00	0.778519
$389$	−11694.0	−1.52419	−0.762094	−	0.647466i	$-0.775829\pi$
$389$	−11694.0	−1.52419	−0.762094	+	0.647466i	$0.775829\pi$
$390$	0	0
$391$	−11172.0	−1.44499
$392$	8955.00	1.15382
$393$	0	0
$394$	20970.0	2.68135
$395$	−2580.00	−0.328643
$396$	0	0
$397$	13678.0	1.72917	0.864583	−	0.502490i	$-0.167582\pi$
$397$	13678.0	1.72917	0.864583	+	0.502490i	$0.167582\pi$
$398$	−21200.0	−2.67000
$399$	0	0
$400$	2225.00	0.278125
$401$	−8490.00	−1.05728	−0.528641	−	0.848845i	$-0.677298\pi$
$401$	−8490.00	−1.05728	−0.528641	+	0.848845i	$0.677298\pi$
$402$	0	0
$403$	−3978.00	−0.491708
$404$	26010.0	3.20308
$405$	0	0
$406$	−3480.00	−0.425393
$407$	−1204.00	−0.146634
$408$	0	0
$409$	−9982.00	−1.20679	−0.603396	−	0.797442i	$-0.706186\pi$
$409$	−9982.00	−1.20679	−0.603396	+	0.797442i	$0.706186\pi$
$410$	−9350.00	−1.12625
$411$	0	0
$412$	−986.000	−0.117905
$413$	3192.00	0.380310
$414$	0	0
$415$	−240.000	−0.0283883
$416$	1105.00	0.130233
$417$	0	0
$418$	−1820.00	−0.212964
$419$	9848.00	1.14823	0.574113	−	0.818776i	$-0.305347\pi$
$419$	9848.00	1.14823	0.574113	+	0.818776i	$0.305347\pi$
$420$	0	0
$421$	7666.00	0.887454	0.443727	−	0.896162i	$-0.353656\pi$
$421$	7666.00	0.887454	0.443727	+	0.896162i	$0.353656\pi$
$422$	−2980.00	−0.343754
$423$	0	0
$424$	16290.0	1.86583
$425$	−2450.00	−0.279629
$426$	0	0
$427$	−7608.00	−0.862241
$428$	3162.00	0.357105
$429$	0	0
$430$	7850.00	0.880374
$431$	8742.00	0.977001	0.488500	−	0.872564i	$-0.337544\pi$
$431$	8742.00	0.977001	0.488500	+	0.872564i	$0.337544\pi$
$432$	0	0
$433$	−5654.00	−0.627515	−0.313757	−	0.949503i	$-0.601588\pi$
$433$	−5654.00	−0.627515	−0.313757	+	0.949503i	$0.601588\pi$
$434$	18360.0	2.03066
$435$	0	0
$436$	−22814.0	−2.50595
$437$	−2964.00	−0.324456
$438$	0	0
$439$	6976.00	0.758420	0.379210	−	0.925311i	$-0.376196\pi$
$439$	6976.00	0.758420	0.379210	+	0.925311i	$0.376196\pi$
$440$	3150.00	0.341296
$441$	0	0
$442$	−6370.00	−0.685498
$443$	−66.0000	−0.00707845	−0.00353923	−	0.999994i	$-0.501127\pi$
$443$	−66.0000	−0.00707845	−0.00353923	+	0.999994i	$0.501127\pi$
$444$	0	0
$445$	6150.00	0.655141
$446$	−21340.0	−2.26565
$447$	0	0
$448$	3444.00	0.363200
$449$	−2426.00	−0.254989	−0.127494	−	0.991839i	$-0.540694\pi$
$449$	−2426.00	−0.254989	−0.127494	+	0.991839i	$0.540694\pi$
$450$	0	0
$451$	−5236.00	−0.546682
$452$	33422.0	3.47796
$453$	0	0
$454$	−29620.0	−3.06197
$455$	780.000	0.0803670
$456$	0	0
$457$	−2186.00	−0.223757	−0.111878	−	0.993722i	$-0.535687\pi$
$457$	−2186.00	−0.223757	−0.111878	+	0.993722i	$0.535687\pi$
$458$	3750.00	0.382590
$459$	0	0
$460$	9690.00	0.982171
$461$	−2370.00	−0.239440	−0.119720	−	0.992808i	$-0.538200\pi$
$461$	−2370.00	−0.239440	−0.119720	+	0.992808i	$0.538200\pi$
$462$	0	0
$463$	11832.0	1.18765	0.593823	−	0.804596i	$-0.297618\pi$
$463$	11832.0	1.18765	0.593823	+	0.804596i	$0.297618\pi$
$464$	−5162.00	−0.516465
$465$	0	0
$466$	2370.00	0.235597
$467$	10070.0	0.997824	0.498912	−	0.866653i	$-0.333733\pi$
$467$	10070.0	0.997824	0.498912	+	0.866653i	$0.333733\pi$
$468$	0	0
$469$	−7344.00	−0.723058
$470$	15500.0	1.52120
$471$	0	0
$472$	11970.0	1.16730
$473$	4396.00	0.427333
$474$	0	0
$475$	−650.000	−0.0627875
$476$	19992.0	1.92507
$477$	0	0
$478$	7990.00	0.764548
$479$	−15402.0	−1.46918	−0.734588	−	0.678513i	$-0.762625\pi$
$479$	−15402.0	−1.46918	−0.734588	+	0.678513i	$0.762625\pi$
$480$	0	0
$481$	−1118.00	−0.105980
$482$	−12050.0	−1.13872
$483$	0	0
$484$	−19295.0	−1.81208
$485$	1750.00	0.163842
$486$	0	0
$487$	−760.000	−0.0707164	−0.0353582	−	0.999375i	$-0.511257\pi$
$487$	−760.000	−0.0707164	−0.0353582	+	0.999375i	$0.511257\pi$
$488$	−28530.0	−2.64650
$489$	0	0
$490$	4975.00	0.458669
$491$	13448.0	1.23605	0.618024	−	0.786159i	$-0.287933\pi$
$491$	13448.0	1.23605	0.618024	+	0.786159i	$0.287933\pi$
$492$	0	0
$493$	5684.00	0.519259
$494$	−1690.00	−0.153920
$495$	0	0
$496$	27234.0	2.46541
$497$	−8232.00	−0.742969
$498$	0	0
$499$	−170.000	−0.0152510	−0.00762550	−	0.999971i	$-0.502427\pi$
$499$	−170.000	−0.0152510	−0.00762550	+	0.999971i	$0.502427\pi$
$500$	2125.00	0.190066
$501$	0	0
$502$	−1560.00	−0.138698
$503$	−298.000	−0.0264158	−0.0132079	−	0.999913i	$-0.504204\pi$
$503$	−298.000	−0.0264158	−0.0132079	+	0.999913i	$0.504204\pi$
$504$	0	0
$505$	7650.00	0.674100
$506$	7980.00	0.701095
$507$	0	0
$508$	29546.0	2.58050
$509$	14446.0	1.25797	0.628986	−	0.777417i	$-0.283470\pi$
$509$	14446.0	1.25797	0.628986	+	0.777417i	$0.283470\pi$
$510$	0	0
$511$	−2424.00	−0.209846
$512$	24475.0	2.11260
$513$	0	0
$514$	−29430.0	−2.52549
$515$	−290.000	−0.0248135
$516$	0	0
$517$	8680.00	0.738387
$518$	5160.00	0.437678
$519$	0	0
$520$	2925.00	0.246673
$521$	−8278.00	−0.696096	−0.348048	−	0.937477i	$-0.613155\pi$
$521$	−8278.00	−0.696096	−0.348048	+	0.937477i	$0.613155\pi$
$522$	0	0
$523$	−12950.0	−1.08272	−0.541361	−	0.840790i	$-0.682091\pi$
$523$	−12950.0	−1.08272	−0.541361	+	0.840790i	$0.682091\pi$
$524$	−13260.0	−1.10547
$525$	0	0
$526$	6290.00	0.521401
$527$	−29988.0	−2.47874
$528$	0	0
$529$	829.000	0.0681351
$530$	9050.00	0.741711
$531$	0	0
$532$	5304.00	0.432251
$533$	−4862.00	−0.395116
$534$	0	0
$535$	930.000	0.0751540
$536$	−27540.0	−2.21930
$537$	0	0
$538$	12070.0	0.967239
$539$	2786.00	0.222637
$540$	0	0
$541$	−11838.0	−0.940768	−0.470384	−	0.882462i	$-0.655885\pi$
$541$	−11838.0	−0.940768	−0.470384	+	0.882462i	$0.655885\pi$
$542$	−2990.00	−0.236958
$543$	0	0
$544$	8330.00	0.656518
$545$	−6710.00	−0.527385
$546$	0	0
$547$	11590.0	0.905946	0.452973	−	0.891524i	$-0.350363\pi$
$547$	11590.0	0.905946	0.452973	+	0.891524i	$0.350363\pi$
$548$	18258.0	1.42325
$549$	0	0
$550$	1750.00	0.135673
$551$	1508.00	0.116593
$552$	0	0
$553$	6192.00	0.476149
$554$	23550.0	1.80604
$555$	0	0
$556$	7072.00	0.539424
$557$	13170.0	1.00185	0.500925	−	0.865491i	$-0.332993\pi$
$557$	13170.0	1.00185	0.500925	+	0.865491i	$0.332993\pi$
$558$	0	0
$559$	4082.00	0.308855
$560$	−5340.00	−0.402957
$561$	0	0
$562$	21330.0	1.60098
$563$	16074.0	1.20327	0.601633	−	0.798773i	$-0.294517\pi$
$563$	16074.0	1.20327	0.601633	+	0.798773i	$0.294517\pi$
$564$	0	0
$565$	9830.00	0.731949
$566$	4890.00	0.363148
$567$	0	0
$568$	−30870.0	−2.28042
$569$	−17622.0	−1.29834	−0.649168	−	0.760645i	$-0.724883\pi$
$569$	−17622.0	−1.29834	−0.649168	+	0.760645i	$0.724883\pi$
$570$	0	0
$571$	12872.0	0.943391	0.471696	−	0.881761i	$-0.343642\pi$
$571$	12872.0	0.943391	0.471696	+	0.881761i	$0.343642\pi$
$572$	3094.00	0.226165
$573$	0	0
$574$	22440.0	1.63176
$575$	2850.00	0.206701
$576$	0	0
$577$	−1918.00	−0.138384	−0.0691918	−	0.997603i	$-0.522042\pi$
$577$	−1918.00	−0.138384	−0.0691918	+	0.997603i	$0.522042\pi$
$578$	−23455.0	−1.68789
$579$	0	0
$580$	−4930.00	−0.352943
$581$	576.000	0.0411300
$582$	0	0
$583$	5068.00	0.360026
$584$	−9090.00	−0.644087
$585$	0	0
$586$	−4410.00	−0.310880
$587$	−20844.0	−1.46563	−0.732814	−	0.680429i	$-0.761794\pi$
$587$	−20844.0	−1.46563	−0.732814	+	0.680429i	$0.761794\pi$
$588$	0	0
$589$	−7956.00	−0.556573
$590$	6650.00	0.464027
$591$	0	0
$592$	7654.00	0.531381
$593$	16754.0	1.16021	0.580105	−	0.814542i	$-0.303012\pi$
$593$	16754.0	1.16021	0.580105	+	0.814542i	$0.303012\pi$
$594$	0	0
$595$	5880.00	0.405137
$596$	34918.0	2.39983
$597$	0	0
$598$	7410.00	0.506718
$599$	−17140.0	−1.16915	−0.584575	−	0.811339i	$-0.698739\pi$
$599$	−17140.0	−1.16915	−0.584575	+	0.811339i	$0.698739\pi$
$600$	0	0
$601$	−12550.0	−0.851789	−0.425894	−	0.904773i	$-0.640041\pi$
$601$	−12550.0	−0.851789	−0.425894	+	0.904773i	$0.640041\pi$
$602$	−18840.0	−1.27552
$603$	0	0
$604$	39134.0	2.63632
$605$	−5675.00	−0.381358
$606$	0	0
$607$	−3434.00	−0.229624	−0.114812	−	0.993387i	$-0.536627\pi$
$607$	−3434.00	−0.229624	−0.114812	+	0.993387i	$0.536627\pi$
$608$	2210.00	0.147413
$609$	0	0
$610$	−15850.0	−1.05205
$611$	8060.00	0.533671
$612$	0	0
$613$	−6110.00	−0.402578	−0.201289	−	0.979532i	$-0.564513\pi$
$613$	−6110.00	−0.402578	−0.201289	+	0.979532i	$0.564513\pi$
$614$	−9080.00	−0.596806
$615$	0	0
$616$	−7560.00	−0.494482
$617$	−9702.00	−0.633043	−0.316522	−	0.948585i	$-0.602515\pi$
$617$	−9702.00	−0.633043	−0.316522	+	0.948585i	$0.602515\pi$
$618$	0	0
$619$	−18574.0	−1.20606	−0.603031	−	0.797718i	$-0.706040\pi$
$619$	−18574.0	−1.20606	−0.603031	+	0.797718i	$0.706040\pi$
$620$	26010.0	1.68482
$621$	0	0
$622$	11460.0	0.738753
$623$	−14760.0	−0.949192
$624$	0	0
$625$	625.000	0.0400000
$626$	−42370.0	−2.70518
$627$	0	0
$628$	−39950.0	−2.53850
$629$	−8428.00	−0.534255
$630$	0	0
$631$	−3530.00	−0.222705	−0.111353	−	0.993781i	$-0.535518\pi$
$631$	−3530.00	−0.222705	−0.111353	+	0.993781i	$0.535518\pi$
$632$	23220.0	1.46146
$633$	0	0
$634$	−22930.0	−1.43638
$635$	8690.00	0.543074
$636$	0	0
$637$	2587.00	0.160912
$638$	−4060.00	−0.251939
$639$	0	0
$640$	10575.0	0.653146
$641$	−21330.0	−1.31433	−0.657164	−	0.753748i	$-0.728244\pi$
$641$	−21330.0	−1.31433	−0.657164	+	0.753748i	$0.728244\pi$
$642$	0	0
$643$	−18768.0	−1.15107	−0.575535	−	0.817777i	$-0.695206\pi$
$643$	−18768.0	−1.15107	−0.575535	+	0.817777i	$0.695206\pi$
$644$	−23256.0	−1.42300
$645$	0	0
$646$	−12740.0	−0.775927
$647$	−5618.00	−0.341370	−0.170685	−	0.985326i	$-0.554598\pi$
$647$	−5618.00	−0.341370	−0.170685	+	0.985326i	$0.554598\pi$
$648$	0	0
$649$	3724.00	0.225239
$650$	1625.00	0.0980581
$651$	0	0
$652$	49708.0	2.98576
$653$	−15730.0	−0.942668	−0.471334	−	0.881955i	$-0.656227\pi$
$653$	−15730.0	−0.942668	−0.471334	+	0.881955i	$0.656227\pi$
$654$	0	0
$655$	−3900.00	−0.232650
$656$	33286.0	1.98110
$657$	0	0
$658$	−37200.0	−2.20396
$659$	2080.00	0.122952	0.0614759	−	0.998109i	$-0.480419\pi$
$659$	2080.00	0.122952	0.0614759	+	0.998109i	$0.480419\pi$
$660$	0	0
$661$	25066.0	1.47497	0.737484	−	0.675364i	$-0.236014\pi$
$661$	25066.0	1.47497	0.737484	+	0.675364i	$0.236014\pi$
$662$	10230.0	0.600605
$663$	0	0
$664$	2160.00	0.126241
$665$	1560.00	0.0909687
$666$	0	0
$667$	−6612.00	−0.383835
$668$	−51612.0	−2.98941
$669$	0	0
$670$	−15300.0	−0.882225
$671$	−8876.00	−0.510662
$672$	0	0
$673$	12642.0	0.724091	0.362046	−	0.932160i	$-0.382078\pi$
$673$	12642.0	0.724091	0.362046	+	0.932160i	$0.382078\pi$
$674$	6430.00	0.367469
$675$	0	0
$676$	2873.00	0.163462
$677$	−11490.0	−0.652284	−0.326142	−	0.945321i	$-0.605749\pi$
$677$	−11490.0	−0.652284	−0.326142	+	0.945321i	$0.605749\pi$
$678$	0	0
$679$	−4200.00	−0.237380
$680$	22050.0	1.24350
$681$	0	0
$682$	21420.0	1.20266
$683$	−13716.0	−0.768416	−0.384208	−	0.923247i	$-0.625525\pi$
$683$	−13716.0	−0.768416	−0.384208	+	0.923247i	$0.625525\pi$
$684$	0	0
$685$	5370.00	0.299529
$686$	−32520.0	−1.80994
$687$	0	0
$688$	−27946.0	−1.54859
$689$	4706.00	0.260209
$690$	0	0
$691$	−15350.0	−0.845067	−0.422534	−	0.906347i	$-0.638859\pi$
$691$	−15350.0	−0.845067	−0.422534	+	0.906347i	$0.638859\pi$
$692$	−37842.0	−2.07881
$693$	0	0
$694$	−3170.00	−0.173388
$695$	2080.00	0.113524
$696$	0	0
$697$	−36652.0	−1.99181
$698$	−11330.0	−0.614394
$699$	0	0
$700$	−5100.00	−0.275374
$701$	30098.0	1.62166	0.810832	−	0.585280i	$-0.199015\pi$
$701$	30098.0	1.62166	0.810832	+	0.585280i	$0.199015\pi$
$702$	0	0
$703$	−2236.00	−0.119961
$704$	4018.00	0.215105
$705$	0	0
$706$	1050.00	0.0559735
$707$	−18360.0	−0.976660
$708$	0	0
$709$	−32270.0	−1.70934	−0.854672	−	0.519168i	$-0.826242\pi$
$709$	−32270.0	−1.70934	−0.854672	+	0.519168i	$0.826242\pi$
$710$	−17150.0	−0.906518
$711$	0	0
$712$	−55350.0	−2.91338
$713$	34884.0	1.83228
$714$	0	0
$715$	910.000	0.0475973
$716$	55148.0	2.87846
$717$	0	0
$718$	810.000	0.0421016
$719$	1632.00	0.0846500	0.0423250	−	0.999104i	$-0.486524\pi$
$719$	1632.00	0.0846500	0.0423250	+	0.999104i	$0.486524\pi$
$720$	0	0
$721$	696.000	0.0359506
$722$	30915.0	1.59354
$723$	0	0
$724$	−28526.0	−1.46431
$725$	−1450.00	−0.0742781
$726$	0	0
$727$	29354.0	1.49750	0.748748	−	0.662855i	$-0.230655\pi$
$727$	29354.0	1.49750	0.748748	+	0.662855i	$0.230655\pi$
$728$	−7020.00	−0.357388
$729$	0	0
$730$	−5050.00	−0.256040
$731$	30772.0	1.55697
$732$	0	0
$733$	18650.0	0.939773	0.469886	−	0.882727i	$-0.344295\pi$
$733$	18650.0	0.939773	0.469886	+	0.882727i	$0.344295\pi$
$734$	−3390.00	−0.170473
$735$	0	0
$736$	−9690.00	−0.485296
$737$	−8568.00	−0.428231
$738$	0	0
$739$	−28550.0	−1.42115	−0.710574	−	0.703622i	$-0.751565\pi$
$739$	−28550.0	−1.42115	−0.710574	+	0.703622i	$0.751565\pi$
$740$	7310.00	0.363136
$741$	0	0
$742$	−21720.0	−1.07462
$743$	27556.0	1.36061	0.680304	−	0.732930i	$-0.261848\pi$
$743$	27556.0	1.36061	0.680304	+	0.732930i	$0.261848\pi$
$744$	0	0
$745$	10270.0	0.505052
$746$	34510.0	1.69370
$747$	0	0
$748$	23324.0	1.14012
$749$	−2232.00	−0.108886
$750$	0	0
$751$	−23732.0	−1.15312	−0.576560	−	0.817055i	$-0.695605\pi$
$751$	−23732.0	−1.15312	−0.576560	+	0.817055i	$0.695605\pi$
$752$	−55180.0	−2.67581
$753$	0	0
$754$	−3770.00	−0.182089
$755$	11510.0	0.554824
$756$	0	0
$757$	−30806.0	−1.47908	−0.739540	−	0.673113i	$-0.764957\pi$
$757$	−30806.0	−1.47908	−0.739540	+	0.673113i	$0.764957\pi$
$758$	−44990.0	−2.15582
$759$	0	0
$760$	5850.00	0.279213
$761$	−24642.0	−1.17381	−0.586907	−	0.809655i	$-0.699654\pi$
$761$	−24642.0	−1.17381	−0.586907	+	0.809655i	$0.699654\pi$
$762$	0	0
$763$	16104.0	0.764094
$764$	67456.0	3.19434
$765$	0	0
$766$	660.000	0.0311316
$767$	3458.00	0.162792
$768$	0	0
$769$	−14566.0	−0.683047	−0.341524	−	0.939873i	$-0.610943\pi$
$769$	−14566.0	−0.683047	−0.341524	+	0.939873i	$0.610943\pi$
$770$	−4200.00	−0.196568
$771$	0	0
$772$	67966.0	3.16859
$773$	1386.00	0.0644902	0.0322451	−	0.999480i	$-0.489734\pi$
$773$	1386.00	0.0644902	0.0322451	+	0.999480i	$0.489734\pi$
$774$	0	0
$775$	7650.00	0.354576
$776$	−15750.0	−0.728598
$777$	0	0
$778$	58470.0	2.69441
$779$	−9724.00	−0.447238
$780$	0	0
$781$	−9604.00	−0.440023
$782$	55860.0	2.55441
$783$	0	0
$784$	−17711.0	−0.806806
$785$	−11750.0	−0.534236
$786$	0	0
$787$	−26984.0	−1.22221	−0.611103	−	0.791551i	$-0.709274\pi$
$787$	−26984.0	−1.22221	−0.611103	+	0.791551i	$0.709274\pi$
$788$	−71298.0	−3.22321
$789$	0	0
$790$	12900.0	0.580964
$791$	−23592.0	−1.06047
$792$	0	0
$793$	−8242.00	−0.369082
$794$	−68390.0	−3.05676
$795$	0	0
$796$	72080.0	3.20956
$797$	29438.0	1.30834	0.654170	−	0.756347i	$-0.273018\pi$
$797$	29438.0	1.30834	0.654170	+	0.756347i	$0.273018\pi$
$798$	0	0
$799$	60760.0	2.69028
$800$	−2125.00	−0.0939126
$801$	0	0
$802$	42450.0	1.86903
$803$	−2828.00	−0.124281
$804$	0	0
$805$	−6840.00	−0.299476
$806$	19890.0	0.869225
$807$	0	0
$808$	−68850.0	−2.99769
$809$	−40462.0	−1.75843	−0.879214	−	0.476427i	$-0.841932\pi$
$809$	−40462.0	−1.75843	−0.879214	+	0.476427i	$0.841932\pi$
$810$	0	0
$811$	−1830.00	−0.0792355	−0.0396178	−	0.999215i	$-0.512614\pi$
$811$	−1830.00	−0.0792355	−0.0396178	+	0.999215i	$0.512614\pi$
$812$	11832.0	0.511357
$813$	0	0
$814$	6020.00	0.259215
$815$	14620.0	0.628364
$816$	0	0
$817$	8164.00	0.349599
$818$	49910.0	2.13333
$819$	0	0
$820$	31790.0	1.35385
$821$	42726.0	1.81626	0.908129	−	0.418691i	$-0.137511\pi$
$821$	42726.0	1.81626	0.908129	+	0.418691i	$0.137511\pi$
$822$	0	0
$823$	11798.0	0.499699	0.249850	−	0.968285i	$-0.419619\pi$
$823$	11798.0	0.499699	0.249850	+	0.968285i	$0.419619\pi$
$824$	2610.00	0.110344
$825$	0	0
$826$	−15960.0	−0.672300
$827$	22528.0	0.947249	0.473625	−	0.880727i	$-0.342945\pi$
$827$	22528.0	0.947249	0.473625	+	0.880727i	$0.342945\pi$
$828$	0	0
$829$	−8934.00	−0.374295	−0.187148	−	0.982332i	$-0.559924\pi$
$829$	−8934.00	−0.374295	−0.187148	+	0.982332i	$0.559924\pi$
$830$	1200.00	0.0501839
$831$	0	0
$832$	3731.00	0.155468
$833$	19502.0	0.811170
$834$	0	0
$835$	−15180.0	−0.629132
$836$	6188.00	0.256001
$837$	0	0
$838$	−49240.0	−2.02979
$839$	13454.0	0.553616	0.276808	−	0.960925i	$-0.410723\pi$
$839$	13454.0	0.553616	0.276808	+	0.960925i	$0.410723\pi$
$840$	0	0
$841$	−21025.0	−0.862069
$842$	−38330.0	−1.56881
$843$	0	0
$844$	10132.0	0.413220
$845$	845.000	0.0344010
$846$	0	0
$847$	13620.0	0.552525
$848$	−32218.0	−1.30468
$849$	0	0
$850$	12250.0	0.494319
$851$	9804.00	0.394920
$852$	0	0
$853$	−21282.0	−0.854258	−0.427129	−	0.904191i	$-0.640475\pi$
$853$	−21282.0	−0.854258	−0.427129	+	0.904191i	$0.640475\pi$
$854$	38040.0	1.52424
$855$	0	0
$856$	−8370.00	−0.334206
$857$	−12674.0	−0.505176	−0.252588	−	0.967574i	$-0.581282\pi$
$857$	−12674.0	−0.505176	−0.252588	+	0.967574i	$0.581282\pi$
$858$	0	0
$859$	19000.0	0.754682	0.377341	−	0.926074i	$-0.376839\pi$
$859$	19000.0	0.754682	0.377341	+	0.926074i	$0.376839\pi$
$860$	−26690.0	−1.05828
$861$	0	0
$862$	−43710.0	−1.72711
$863$	6908.00	0.272481	0.136240	−	0.990676i	$-0.456498\pi$
$863$	6908.00	0.272481	0.136240	+	0.990676i	$0.456498\pi$
$864$	0	0
$865$	−11130.0	−0.437493
$866$	28270.0	1.10930
$867$	0	0
$868$	−62424.0	−2.44102
$869$	7224.00	0.281999
$870$	0	0
$871$	−7956.00	−0.309505
$872$	60390.0	2.34526
$873$	0	0
$874$	14820.0	0.573563
$875$	−1500.00	−0.0579534
$876$	0	0
$877$	−13014.0	−0.501085	−0.250543	−	0.968106i	$-0.580609\pi$
$877$	−13014.0	−0.501085	−0.250543	+	0.968106i	$0.580609\pi$
$878$	−34880.0	−1.34071
$879$	0	0
$880$	−6230.00	−0.238651
$881$	−17318.0	−0.662268	−0.331134	−	0.943584i	$-0.607431\pi$
$881$	−17318.0	−0.662268	−0.331134	+	0.943584i	$0.607431\pi$
$882$	0	0
$883$	42038.0	1.60214	0.801071	−	0.598569i	$-0.204264\pi$
$883$	42038.0	1.60214	0.801071	+	0.598569i	$0.204264\pi$
$884$	21658.0	0.824024
$885$	0	0
$886$	330.000	0.0125131
$887$	24882.0	0.941889	0.470945	−	0.882163i	$-0.343913\pi$
$887$	24882.0	0.941889	0.470945	+	0.882163i	$0.343913\pi$
$888$	0	0
$889$	−20856.0	−0.786825
$890$	−30750.0	−1.15814
$891$	0	0
$892$	72556.0	2.72349
$893$	16120.0	0.604071
$894$	0	0
$895$	16220.0	0.605782
$896$	−25380.0	−0.946302
$897$	0	0
$898$	12130.0	0.450761
$899$	−17748.0	−0.658430
$900$	0	0
$901$	35476.0	1.31174
$902$	26180.0	0.966406
$903$	0	0
$904$	−88470.0	−3.25494
$905$	−8390.00	−0.308169
$906$	0	0
$907$	24018.0	0.879277	0.439639	−	0.898175i	$-0.355106\pi$
$907$	24018.0	0.879277	0.439639	+	0.898175i	$0.355106\pi$
$908$	100708.	3.68074
$909$	0	0
$910$	−3900.00	−0.142070
$911$	−9584.00	−0.348553	−0.174277	−	0.984697i	$-0.555759\pi$
$911$	−9584.00	−0.348553	−0.174277	+	0.984697i	$0.555759\pi$
$912$	0	0
$913$	672.000	0.0243592
$914$	10930.0	0.395550
$915$	0	0
$916$	−12750.0	−0.459904
$917$	9360.00	0.337071
$918$	0	0
$919$	49252.0	1.76787	0.883936	−	0.467609i	$-0.154884\pi$
$919$	49252.0	1.76787	0.883936	+	0.467609i	$0.154884\pi$
$920$	−25650.0	−0.919191
$921$	0	0
$922$	11850.0	0.423274
$923$	−8918.00	−0.318028
$924$	0	0
$925$	2150.00	0.0764233
$926$	−59160.0	−2.09948
$927$	0	0
$928$	4930.00	0.174391
$929$	48614.0	1.71687	0.858436	−	0.512921i	$-0.171437\pi$
$929$	48614.0	1.71687	0.858436	+	0.512921i	$0.171437\pi$
$930$	0	0
$931$	5174.00	0.182139
$932$	−8058.00	−0.283207
$933$	0	0
$934$	−50350.0	−1.76392
$935$	6860.00	0.239942
$936$	0	0
$937$	−37326.0	−1.30137	−0.650687	−	0.759346i	$-0.725519\pi$
$937$	−37326.0	−1.30137	−0.650687	+	0.759346i	$0.725519\pi$
$938$	36720.0	1.27820
$939$	0	0
$940$	−52700.0	−1.82860
$941$	−10474.0	−0.362851	−0.181425	−	0.983405i	$-0.558071\pi$
$941$	−10474.0	−0.362851	−0.181425	+	0.983405i	$0.558071\pi$
$942$	0	0
$943$	42636.0	1.47234
$944$	−23674.0	−0.816232
$945$	0	0
$946$	−21980.0	−0.755424
$947$	15096.0	0.518009	0.259004	−	0.965876i	$-0.416606\pi$
$947$	15096.0	0.518009	0.259004	+	0.965876i	$0.416606\pi$
$948$	0	0
$949$	−2626.00	−0.0898246
$950$	3250.00	0.110994
$951$	0	0
$952$	−52920.0	−1.80163
$953$	3262.00	0.110878	0.0554389	−	0.998462i	$-0.482344\pi$
$953$	3262.00	0.110878	0.0554389	+	0.998462i	$0.482344\pi$
$954$	0	0
$955$	19840.0	0.672259
$956$	−27166.0	−0.919049
$957$	0	0
$958$	77010.0	2.59716
$959$	−12888.0	−0.433968
$960$	0	0
$961$	63845.0	2.14310
$962$	5590.00	0.187348
$963$	0	0
$964$	40970.0	1.36883
$965$	19990.0	0.666840
$966$	0	0
$967$	48872.0	1.62525	0.812625	−	0.582786i	$-0.198038\pi$
$967$	48872.0	1.62525	0.812625	+	0.582786i	$0.198038\pi$
$968$	51075.0	1.69588
$969$	0	0
$970$	−8750.00	−0.289635
$971$	−43932.0	−1.45195	−0.725976	−	0.687720i	$-0.758612\pi$
$971$	−43932.0	−1.45195	−0.725976	+	0.687720i	$0.758612\pi$
$972$	0	0
$973$	−4992.00	−0.164477
$974$	3800.00	0.125010
$975$	0	0
$976$	56426.0	1.85057
$977$	3406.00	0.111533	0.0557664	−	0.998444i	$-0.482240\pi$
$977$	3406.00	0.111533	0.0557664	+	0.998444i	$0.482240\pi$
$978$	0	0
$979$	−17220.0	−0.562159
$980$	−16915.0	−0.551357
$981$	0	0
$982$	−67240.0	−2.18505
$983$	−35496.0	−1.15173	−0.575863	−	0.817546i	$-0.695334\pi$
$983$	−35496.0	−1.15173	−0.575863	+	0.817546i	$0.695334\pi$
$984$	0	0
$985$	−20970.0	−0.678335
$986$	−28420.0	−0.917928
$987$	0	0
$988$	5746.00	0.185025
$989$	−35796.0	−1.15091
$990$	0	0
$991$	−20464.0	−0.655964	−0.327982	−	0.944684i	$-0.606369\pi$
$991$	−20464.0	−0.655964	−0.327982	+	0.944684i	$0.606369\pi$
$992$	−26010.0	−0.832478
$993$	0	0
$994$	41160.0	1.31340
$995$	21200.0	0.675462
$996$	0	0
$997$	−30318.0	−0.963070	−0.481535	−	0.876427i	$-0.659921\pi$
$997$	−30318.0	−0.963070	−0.481535	+	0.876427i	$0.659921\pi$
$998$	850.000	0.0269602
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.4.a.a.1.1		1
3.2	odd	2		65.4.a.a.1.1	✓	1
12.11	even	2		1040.4.a.a.1.1		1
15.2	even	4		325.4.b.a.274.2		2
15.8	even	4		325.4.b.a.274.1		2
15.14	odd	2		325.4.a.a.1.1		1
39.38	odd	2		845.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.a.a.1.1	✓	1	3.2	odd	2
325.4.a.a.1.1		1	15.14	odd	2
325.4.b.a.274.1		2	15.8	even	4
325.4.b.a.274.2		2	15.2	even	4
585.4.a.a.1.1		1	1.1	even	1	trivial
845.4.a.a.1.1		1	39.38	odd	2
1040.4.a.a.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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