LMFDB - Embedded newform 2280.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2280,4,Mod(1,2280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("2280.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2280.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:	$134.524354813$
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	$\chi$	$=$	2280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} +5.00000 q^{5} +22.0000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} +5.00000 q^{5} +22.0000 q^{7} +9.00000 q^{9} -56.0000 q^{11} +42.0000 q^{13} -15.0000 q^{15} -60.0000 q^{17} -19.0000 q^{19} -66.0000 q^{21} +136.000 q^{23} +25.0000 q^{25} -27.0000 q^{27} -150.000 q^{29} +94.0000 q^{31} +168.000 q^{33} +110.000 q^{35} +394.000 q^{37} -126.000 q^{39} -508.000 q^{41} -312.000 q^{43} +45.0000 q^{45} +24.0000 q^{47} +141.000 q^{49} +180.000 q^{51} -562.000 q^{53} -280.000 q^{55} +57.0000 q^{57} -554.000 q^{59} -350.000 q^{61} +198.000 q^{63} +210.000 q^{65} +436.000 q^{67} -408.000 q^{69} +176.000 q^{71} -218.000 q^{73} -75.0000 q^{75} -1232.00 q^{77} -866.000 q^{79} +81.0000 q^{81} +930.000 q^{83} -300.000 q^{85} +450.000 q^{87} -384.000 q^{89} +924.000 q^{91} -282.000 q^{93} -95.0000 q^{95} +1206.00 q^{97} -504.000 q^{99} +O(q^{100})$

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
$2$	0	0
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	22.0000	1.18789	0.593944	−	0.804506i	$-0.297570\pi$
$7$	22.0000	1.18789	0.593944	+	0.804506i	$0.297570\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	−56.0000	−1.53497	−0.767483	−	0.641069i	$-0.778491\pi$
$11$	−56.0000	−1.53497	−0.767483	+	0.641069i	$0.778491\pi$
$12$	0	0
$13$	42.0000	0.896054	0.448027	−	0.894020i	$-0.352127\pi$
$13$	42.0000	0.896054	0.448027	+	0.894020i	$0.352127\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	0	0
$17$	−60.0000	−0.856008	−0.428004	−	0.903777i	$-0.640783\pi$
$17$	−60.0000	−0.856008	−0.428004	+	0.903777i	$0.640783\pi$
$18$	0	0
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−66.0000	−0.685828
$22$	0	0
$23$	136.000	1.23295	0.616477	−	0.787373i	$-0.288559\pi$
$23$	136.000	1.23295	0.616477	+	0.787373i	$0.288559\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−150.000	−0.960493	−0.480247	−	0.877134i	$-0.659453\pi$
$29$	−150.000	−0.960493	−0.480247	+	0.877134i	$0.659453\pi$
$30$	0	0
$31$	94.0000	0.544610	0.272305	−	0.962211i	$-0.412214\pi$
$31$	94.0000	0.544610	0.272305	+	0.962211i	$0.412214\pi$
$32$	0	0
$33$	168.000	0.886214
$34$	0	0
$35$	110.000	0.531240
$36$	0	0
$37$	394.000	1.75063	0.875314	−	0.483556i	$-0.160655\pi$
$37$	394.000	1.75063	0.875314	+	0.483556i	$0.160655\pi$
$38$	0	0
$39$	−126.000	−0.517337
$40$	0	0
$41$	−508.000	−1.93503	−0.967516	−	0.252812i	$-0.918645\pi$
$41$	−508.000	−1.93503	−0.967516	+	0.252812i	$0.918645\pi$
$42$	0	0
$43$	−312.000	−1.10650	−0.553251	−	0.833015i	$-0.686613\pi$
$43$	−312.000	−1.10650	−0.553251	+	0.833015i	$0.686613\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	0	0
$47$	24.0000	0.0744843	0.0372421	−	0.999306i	$-0.488143\pi$
$47$	24.0000	0.0744843	0.0372421	+	0.999306i	$0.488143\pi$
$48$	0	0
$49$	141.000	0.411079
$50$	0	0
$51$	180.000	0.494217
$52$	0	0
$53$	−562.000	−1.45654	−0.728270	−	0.685290i	$-0.759675\pi$
$53$	−562.000	−1.45654	−0.728270	+	0.685290i	$0.759675\pi$
$54$	0	0
$55$	−280.000	−0.686458
$56$	0	0
$57$	57.0000	0.132453
$58$	0	0
$59$	−554.000	−1.22245	−0.611226	−	0.791456i	$-0.709323\pi$
$59$	−554.000	−1.22245	−0.611226	+	0.791456i	$0.709323\pi$
$60$	0	0
$61$	−350.000	−0.734638	−0.367319	−	0.930095i	$-0.619724\pi$
$61$	−350.000	−0.734638	−0.367319	+	0.930095i	$0.619724\pi$
$62$	0	0
$63$	198.000	0.395963
$64$	0	0
$65$	210.000	0.400728
$66$	0	0
$67$	436.000	0.795013	0.397507	−	0.917599i	$-0.369876\pi$
$67$	436.000	0.795013	0.397507	+	0.917599i	$0.369876\pi$
$68$	0	0
$69$	−408.000	−0.711847
$70$	0	0
$71$	176.000	0.294188	0.147094	−	0.989123i	$-0.453008\pi$
$71$	176.000	0.294188	0.147094	+	0.989123i	$0.453008\pi$
$72$	0	0
$73$	−218.000	−0.349520	−0.174760	−	0.984611i	$-0.555915\pi$
$73$	−218.000	−0.349520	−0.174760	+	0.984611i	$0.555915\pi$
$74$	0	0
$75$	−75.0000	−0.115470
$76$	0	0
$77$	−1232.00	−1.82337
$78$	0	0
$79$	−866.000	−1.23332	−0.616662	−	0.787228i	$-0.711516\pi$
$79$	−866.000	−1.23332	−0.616662	+	0.787228i	$0.711516\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	930.000	1.22989	0.614944	−	0.788571i	$-0.289178\pi$
$83$	930.000	1.22989	0.614944	+	0.788571i	$0.289178\pi$
$84$	0	0
$85$	−300.000	−0.382818
$86$	0	0
$87$	450.000	0.554541
$88$	0	0
$89$	−384.000	−0.457347	−0.228674	−	0.973503i	$-0.573439\pi$
$89$	−384.000	−0.457347	−0.228674	+	0.973503i	$0.573439\pi$
$90$	0	0
$91$	924.000	1.06441
$92$	0	0
$93$	−282.000	−0.314431
$94$	0	0
$95$	−95.0000	−0.102598
$96$	0	0
$97$	1206.00	1.26238	0.631189	−	0.775629i	$-0.282567\pi$
$97$	1206.00	1.26238	0.631189	+	0.775629i	$0.282567\pi$
$98$	0	0
$99$	−504.000	−0.511656
$100$	0	0
$101$	162.000	0.159600	0.0798000	−	0.996811i	$-0.474572\pi$
$101$	162.000	0.159600	0.0798000	+	0.996811i	$0.474572\pi$
$102$	0	0
$103$	1608.00	1.53826	0.769131	−	0.639091i	$-0.220689\pi$
$103$	1608.00	1.53826	0.769131	+	0.639091i	$0.220689\pi$
$104$	0	0
$105$	−330.000	−0.306711
$106$	0	0
$107$	360.000	0.325257	0.162629	−	0.986687i	$-0.448003\pi$
$107$	360.000	0.325257	0.162629	+	0.986687i	$0.448003\pi$
$108$	0	0
$109$	−1076.00	−0.945524	−0.472762	−	0.881190i	$-0.656743\pi$
$109$	−1076.00	−0.945524	−0.472762	+	0.881190i	$0.656743\pi$
$110$	0	0
$111$	−1182.00	−1.01073
$112$	0	0
$113$	370.000	0.308024	0.154012	−	0.988069i	$-0.450781\pi$
$113$	370.000	0.308024	0.154012	+	0.988069i	$0.450781\pi$
$114$	0	0
$115$	680.000	0.551394
$116$	0	0
$117$	378.000	0.298685
$118$	0	0
$119$	−1320.00	−1.01684
$120$	0	0
$121$	1805.00	1.35612
$122$	0	0
$123$	1524.00	1.11719
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	528.000	0.368917	0.184458	−	0.982840i	$-0.440947\pi$
$127$	528.000	0.368917	0.184458	+	0.982840i	$0.440947\pi$
$128$	0	0
$129$	936.000	0.638839
$130$	0	0
$131$	−1048.00	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−1048.00	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	0	0
$133$	−418.000	−0.272520
$134$	0	0
$135$	−135.000	−0.0860663
$136$	0	0
$137$	−1232.00	−0.768298	−0.384149	−	0.923271i	$-0.625505\pi$
$137$	−1232.00	−0.768298	−0.384149	+	0.923271i	$0.625505\pi$
$138$	0	0
$139$	844.000	0.515015	0.257508	−	0.966276i	$-0.417099\pi$
$139$	844.000	0.515015	0.257508	+	0.966276i	$0.417099\pi$
$140$	0	0
$141$	−72.0000	−0.0430035
$142$	0	0
$143$	−2352.00	−1.37541
$144$	0	0
$145$	−750.000	−0.429546
$146$	0	0
$147$	−423.000	−0.237336
$148$	0	0
$149$	−462.000	−0.254017	−0.127008	−	0.991902i	$-0.540538\pi$
$149$	−462.000	−0.254017	−0.127008	+	0.991902i	$0.540538\pi$
$150$	0	0
$151$	1530.00	0.824567	0.412284	−	0.911056i	$-0.364731\pi$
$151$	1530.00	0.824567	0.412284	+	0.911056i	$0.364731\pi$
$152$	0	0
$153$	−540.000	−0.285336
$154$	0	0
$155$	470.000	0.243557
$156$	0	0
$157$	1632.00	0.829604	0.414802	−	0.909912i	$-0.363851\pi$
$157$	1632.00	0.829604	0.414802	+	0.909912i	$0.363851\pi$
$158$	0	0
$159$	1686.00	0.840934
$160$	0	0
$161$	2992.00	1.46461
$162$	0	0
$163$	−3948.00	−1.89712	−0.948562	−	0.316591i	$-0.897462\pi$
$163$	−3948.00	−1.89712	−0.948562	+	0.316591i	$0.897462\pi$
$164$	0	0
$165$	840.000	0.396327
$166$	0	0
$167$	−1728.00	−0.800699	−0.400349	−	0.916363i	$-0.631111\pi$
$167$	−1728.00	−0.800699	−0.400349	+	0.916363i	$0.631111\pi$
$168$	0	0
$169$	−433.000	−0.197087
$170$	0	0
$171$	−171.000	−0.0764719
$172$	0	0
$173$	−682.000	−0.299720	−0.149860	−	0.988707i	$-0.547882\pi$
$173$	−682.000	−0.299720	−0.149860	+	0.988707i	$0.547882\pi$
$174$	0	0
$175$	550.000	0.237578
$176$	0	0
$177$	1662.00	0.705783
$178$	0	0
$179$	1050.00	0.438440	0.219220	−	0.975676i	$-0.429649\pi$
$179$	1050.00	0.438440	0.219220	+	0.975676i	$0.429649\pi$
$180$	0	0
$181$	−2788.00	−1.14492	−0.572460	−	0.819933i	$-0.694011\pi$
$181$	−2788.00	−1.14492	−0.572460	+	0.819933i	$0.694011\pi$
$182$	0	0
$183$	1050.00	0.424143
$184$	0	0
$185$	1970.00	0.782904
$186$	0	0
$187$	3360.00	1.31394
$188$	0	0
$189$	−594.000	−0.228609
$190$	0	0
$191$	−2688.00	−1.01831	−0.509154	−	0.860675i	$-0.670042\pi$
$191$	−2688.00	−1.01831	−0.509154	+	0.860675i	$0.670042\pi$
$192$	0	0
$193$	1378.00	0.513941	0.256970	−	0.966419i	$-0.417276\pi$
$193$	1378.00	0.513941	0.256970	+	0.966419i	$0.417276\pi$
$194$	0	0
$195$	−630.000	−0.231360
$196$	0	0
$197$	2322.00	0.839775	0.419887	−	0.907576i	$-0.362070\pi$
$197$	2322.00	0.839775	0.419887	+	0.907576i	$0.362070\pi$
$198$	0	0
$199$	2996.00	1.06724	0.533620	−	0.845724i	$-0.320831\pi$
$199$	2996.00	1.06724	0.533620	+	0.845724i	$0.320831\pi$
$200$	0	0
$201$	−1308.00	−0.459001
$202$	0	0
$203$	−3300.00	−1.14096
$204$	0	0
$205$	−2540.00	−0.865372
$206$	0	0
$207$	1224.00	0.410985
$208$	0	0
$209$	1064.00	0.352146
$210$	0	0
$211$	−4496.00	−1.46691	−0.733454	−	0.679740i	$-0.762093\pi$
$211$	−4496.00	−1.46691	−0.733454	+	0.679740i	$0.762093\pi$
$212$	0	0
$213$	−528.000	−0.169850
$214$	0	0
$215$	−1560.00	−0.494842
$216$	0	0
$217$	2068.00	0.646935
$218$	0	0
$219$	654.000	0.201796
$220$	0	0
$221$	−2520.00	−0.767030
$222$	0	0
$223$	−3868.00	−1.16153	−0.580763	−	0.814072i	$-0.697246\pi$
$223$	−3868.00	−1.16153	−0.580763	+	0.814072i	$0.697246\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	0	0
$227$	−180.000	−0.0526300	−0.0263150	−	0.999654i	$-0.508377\pi$
$227$	−180.000	−0.0526300	−0.0263150	+	0.999654i	$0.508377\pi$
$228$	0	0
$229$	−6690.00	−1.93051	−0.965257	−	0.261303i	$-0.915848\pi$
$229$	−6690.00	−1.93051	−0.965257	+	0.261303i	$0.915848\pi$
$230$	0	0
$231$	3696.00	1.05272
$232$	0	0
$233$	−772.000	−0.217062	−0.108531	−	0.994093i	$-0.534615\pi$
$233$	−772.000	−0.217062	−0.108531	+	0.994093i	$0.534615\pi$
$234$	0	0
$235$	120.000	0.0333104
$236$	0	0
$237$	2598.00	0.712060
$238$	0	0
$239$	1776.00	0.480669	0.240334	−	0.970690i	$-0.422743\pi$
$239$	1776.00	0.480669	0.240334	+	0.970690i	$0.422743\pi$
$240$	0	0
$241$	−4454.00	−1.19049	−0.595243	−	0.803545i	$-0.702944\pi$
$241$	−4454.00	−1.19049	−0.595243	+	0.803545i	$0.702944\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	705.000	0.183840
$246$	0	0
$247$	−798.000	−0.205569
$248$	0	0
$249$	−2790.00	−0.710077
$250$	0	0
$251$	−900.000	−0.226325	−0.113162	−	0.993577i	$-0.536098\pi$
$251$	−900.000	−0.226325	−0.113162	+	0.993577i	$0.536098\pi$
$252$	0	0
$253$	−7616.00	−1.89254
$254$	0	0
$255$	900.000	0.221020
$256$	0	0
$257$	2694.00	0.653880	0.326940	−	0.945045i	$-0.393983\pi$
$257$	2694.00	0.653880	0.326940	+	0.945045i	$0.393983\pi$
$258$	0	0
$259$	8668.00	2.07955
$260$	0	0
$261$	−1350.00	−0.320164
$262$	0	0
$263$	4992.00	1.17042	0.585209	−	0.810883i	$-0.301012\pi$
$263$	4992.00	1.17042	0.585209	+	0.810883i	$0.301012\pi$
$264$	0	0
$265$	−2810.00	−0.651385
$266$	0	0
$267$	1152.00	0.264050
$268$	0	0
$269$	−2094.00	−0.474622	−0.237311	−	0.971434i	$-0.576266\pi$
$269$	−2094.00	−0.474622	−0.237311	+	0.971434i	$0.576266\pi$
$270$	0	0
$271$	−8164.00	−1.82999	−0.914996	−	0.403464i	$-0.867806\pi$
$271$	−8164.00	−1.82999	−0.914996	+	0.403464i	$0.867806\pi$
$272$	0	0
$273$	−2772.00	−0.614539
$274$	0	0
$275$	−1400.00	−0.306993
$276$	0	0
$277$	−2920.00	−0.633378	−0.316689	−	0.948529i	$-0.602571\pi$
$277$	−2920.00	−0.633378	−0.316689	+	0.948529i	$0.602571\pi$
$278$	0	0
$279$	846.000	0.181537
$280$	0	0
$281$	−5652.00	−1.19989	−0.599947	−	0.800040i	$-0.704812\pi$
$281$	−5652.00	−1.19989	−0.599947	+	0.800040i	$0.704812\pi$
$282$	0	0
$283$	1760.00	0.369686	0.184843	−	0.982768i	$-0.440822\pi$
$283$	1760.00	0.369686	0.184843	+	0.982768i	$0.440822\pi$
$284$	0	0
$285$	285.000	0.0592349
$286$	0	0
$287$	−11176.0	−2.29860
$288$	0	0
$289$	−1313.00	−0.267250
$290$	0	0
$291$	−3618.00	−0.728835
$292$	0	0
$293$	−3598.00	−0.717397	−0.358699	−	0.933453i	$-0.616779\pi$
$293$	−3598.00	−0.717397	−0.358699	+	0.933453i	$0.616779\pi$
$294$	0	0
$295$	−2770.00	−0.546697
$296$	0	0
$297$	1512.00	0.295405
$298$	0	0
$299$	5712.00	1.10479
$300$	0	0
$301$	−6864.00	−1.31440
$302$	0	0
$303$	−486.000	−0.0921451
$304$	0	0
$305$	−1750.00	−0.328540
$306$	0	0
$307$	−6244.00	−1.16079	−0.580397	−	0.814333i	$-0.697103\pi$
$307$	−6244.00	−1.16079	−0.580397	+	0.814333i	$0.697103\pi$
$308$	0	0
$309$	−4824.00	−0.888116
$310$	0	0
$311$	8720.00	1.58992	0.794961	−	0.606660i	$-0.207491\pi$
$311$	8720.00	1.58992	0.794961	+	0.606660i	$0.207491\pi$
$312$	0	0
$313$	−2114.00	−0.381758	−0.190879	−	0.981614i	$-0.561134\pi$
$313$	−2114.00	−0.381758	−0.190879	+	0.981614i	$0.561134\pi$
$314$	0	0
$315$	990.000	0.177080
$316$	0	0
$317$	−8006.00	−1.41849	−0.709246	−	0.704961i	$-0.750964\pi$
$317$	−8006.00	−1.41849	−0.709246	+	0.704961i	$0.750964\pi$
$318$	0	0
$319$	8400.00	1.47433
$320$	0	0
$321$	−1080.00	−0.187787
$322$	0	0
$323$	1140.00	0.196382
$324$	0	0
$325$	1050.00	0.179211
$326$	0	0
$327$	3228.00	0.545898
$328$	0	0
$329$	528.000	0.0884790
$330$	0	0
$331$	4628.00	0.768513	0.384257	−	0.923226i	$-0.374458\pi$
$331$	4628.00	0.768513	0.384257	+	0.923226i	$0.374458\pi$
$332$	0	0
$333$	3546.00	0.583542
$334$	0	0
$335$	2180.00	0.355541
$336$	0	0
$337$	−862.000	−0.139336	−0.0696679	−	0.997570i	$-0.522194\pi$
$337$	−862.000	−0.139336	−0.0696679	+	0.997570i	$0.522194\pi$
$338$	0	0
$339$	−1110.00	−0.177838
$340$	0	0
$341$	−5264.00	−0.835958
$342$	0	0
$343$	−4444.00	−0.699573
$344$	0	0
$345$	−2040.00	−0.318348
$346$	0	0
$347$	8374.00	1.29550	0.647752	−	0.761851i	$-0.275709\pi$
$347$	8374.00	1.29550	0.647752	+	0.761851i	$0.275709\pi$
$348$	0	0
$349$	−11410.0	−1.75004	−0.875019	−	0.484088i	$-0.839151\pi$
$349$	−11410.0	−1.75004	−0.875019	+	0.484088i	$0.839151\pi$
$350$	0	0
$351$	−1134.00	−0.172446
$352$	0	0
$353$	4872.00	0.734590	0.367295	−	0.930104i	$-0.380284\pi$
$353$	4872.00	0.734590	0.367295	+	0.930104i	$0.380284\pi$
$354$	0	0
$355$	880.000	0.131565
$356$	0	0
$357$	3960.00	0.587074
$358$	0	0
$359$	−9776.00	−1.43721	−0.718604	−	0.695420i	$-0.755218\pi$
$359$	−9776.00	−1.43721	−0.718604	+	0.695420i	$0.755218\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	0	0
$363$	−5415.00	−0.782958
$364$	0	0
$365$	−1090.00	−0.156310
$366$	0	0
$367$	−12030.0	−1.71107	−0.855533	−	0.517749i	$-0.826770\pi$
$367$	−12030.0	−1.71107	−0.855533	+	0.517749i	$0.826770\pi$
$368$	0	0
$369$	−4572.00	−0.645010
$370$	0	0
$371$	−12364.0	−1.73021
$372$	0	0
$373$	−5298.00	−0.735442	−0.367721	−	0.929936i	$-0.619862\pi$
$373$	−5298.00	−0.735442	−0.367721	+	0.929936i	$0.619862\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	0	0
$377$	−6300.00	−0.860654
$378$	0	0
$379$	9184.00	1.24472	0.622362	−	0.782730i	$-0.286173\pi$
$379$	9184.00	1.24472	0.622362	+	0.782730i	$0.286173\pi$
$380$	0	0
$381$	−1584.00	−0.212994
$382$	0	0
$383$	12896.0	1.72051	0.860254	−	0.509865i	$-0.170305\pi$
$383$	12896.0	1.72051	0.860254	+	0.509865i	$0.170305\pi$
$384$	0	0
$385$	−6160.00	−0.815436
$386$	0	0
$387$	−2808.00	−0.368834
$388$	0	0
$389$	−7494.00	−0.976763	−0.488382	−	0.872630i	$-0.662413\pi$
$389$	−7494.00	−0.976763	−0.488382	+	0.872630i	$0.662413\pi$
$390$	0	0
$391$	−8160.00	−1.05542
$392$	0	0
$393$	3144.00	0.403547
$394$	0	0
$395$	−4330.00	−0.551559
$396$	0	0
$397$	3604.00	0.455616	0.227808	−	0.973706i	$-0.426844\pi$
$397$	3604.00	0.455616	0.227808	+	0.973706i	$0.426844\pi$
$398$	0	0
$399$	1254.00	0.157340
$400$	0	0
$401$	−7864.00	−0.979325	−0.489663	−	0.871912i	$-0.662880\pi$
$401$	−7864.00	−0.979325	−0.489663	+	0.871912i	$0.662880\pi$
$402$	0	0
$403$	3948.00	0.488000
$404$	0	0
$405$	405.000	0.0496904
$406$	0	0
$407$	−22064.0	−2.68715
$408$	0	0
$409$	6970.00	0.842651	0.421326	−	0.906909i	$-0.361565\pi$
$409$	6970.00	0.842651	0.421326	+	0.906909i	$0.361565\pi$
$410$	0	0
$411$	3696.00	0.443577
$412$	0	0
$413$	−12188.0	−1.45214
$414$	0	0
$415$	4650.00	0.550023
$416$	0	0
$417$	−2532.00	−0.297344
$418$	0	0
$419$	6412.00	0.747605	0.373803	−	0.927508i	$-0.378054\pi$
$419$	6412.00	0.747605	0.373803	+	0.927508i	$0.378054\pi$
$420$	0	0
$421$	−3916.00	−0.453335	−0.226668	−	0.973972i	$-0.572783\pi$
$421$	−3916.00	−0.453335	−0.226668	+	0.973972i	$0.572783\pi$
$422$	0	0
$423$	216.000	0.0248281
$424$	0	0
$425$	−1500.00	−0.171202
$426$	0	0
$427$	−7700.00	−0.872668
$428$	0	0
$429$	7056.00	0.794095
$430$	0	0
$431$	−11416.0	−1.27585	−0.637923	−	0.770100i	$-0.720206\pi$
$431$	−11416.0	−1.27585	−0.637923	+	0.770100i	$0.720206\pi$
$432$	0	0
$433$	−7742.00	−0.859254	−0.429627	−	0.903007i	$-0.641355\pi$
$433$	−7742.00	−0.859254	−0.429627	+	0.903007i	$0.641355\pi$
$434$	0	0
$435$	2250.00	0.247998
$436$	0	0
$437$	−2584.00	−0.282859
$438$	0	0
$439$	12054.0	1.31049	0.655246	−	0.755416i	$-0.272565\pi$
$439$	12054.0	1.31049	0.655246	+	0.755416i	$0.272565\pi$
$440$	0	0
$441$	1269.00	0.137026
$442$	0	0
$443$	−10026.0	−1.07528	−0.537641	−	0.843174i	$-0.680684\pi$
$443$	−10026.0	−1.07528	−0.537641	+	0.843174i	$0.680684\pi$
$444$	0	0
$445$	−1920.00	−0.204532
$446$	0	0
$447$	1386.00	0.146657
$448$	0	0
$449$	10140.0	1.06578	0.532891	−	0.846184i	$-0.321106\pi$
$449$	10140.0	1.06578	0.532891	+	0.846184i	$0.321106\pi$
$450$	0	0
$451$	28448.0	2.97021
$452$	0	0
$453$	−4590.00	−0.476064
$454$	0	0
$455$	4620.00	0.476020
$456$	0	0
$457$	−8470.00	−0.866980	−0.433490	−	0.901158i	$-0.642718\pi$
$457$	−8470.00	−0.866980	−0.433490	+	0.901158i	$0.642718\pi$
$458$	0	0
$459$	1620.00	0.164739
$460$	0	0
$461$	9414.00	0.951093	0.475546	−	0.879691i	$-0.342250\pi$
$461$	9414.00	0.951093	0.475546	+	0.879691i	$0.342250\pi$
$462$	0	0
$463$	17950.0	1.80174	0.900872	−	0.434085i	$-0.142928\pi$
$463$	17950.0	1.80174	0.900872	+	0.434085i	$0.142928\pi$
$464$	0	0
$465$	−1410.00	−0.140618
$466$	0	0
$467$	9394.00	0.930840	0.465420	−	0.885090i	$-0.345903\pi$
$467$	9394.00	0.930840	0.465420	+	0.885090i	$0.345903\pi$
$468$	0	0
$469$	9592.00	0.944387
$470$	0	0
$471$	−4896.00	−0.478972
$472$	0	0
$473$	17472.0	1.69844
$474$	0	0
$475$	−475.000	−0.0458831
$476$	0	0
$477$	−5058.00	−0.485513
$478$	0	0
$479$	480.000	0.0457866	0.0228933	−	0.999738i	$-0.492712\pi$
$479$	480.000	0.0457866	0.0228933	+	0.999738i	$0.492712\pi$
$480$	0	0
$481$	16548.0	1.56866
$482$	0	0
$483$	−8976.00	−0.845594
$484$	0	0
$485$	6030.00	0.564553
$486$	0	0
$487$	14144.0	1.31607	0.658035	−	0.752988i	$-0.271388\pi$
$487$	14144.0	1.31607	0.658035	+	0.752988i	$0.271388\pi$
$488$	0	0
$489$	11844.0	1.09531
$490$	0	0
$491$	5400.00	0.496331	0.248166	−	0.968718i	$-0.420172\pi$
$491$	5400.00	0.496331	0.248166	+	0.968718i	$0.420172\pi$
$492$	0	0
$493$	9000.00	0.822190
$494$	0	0
$495$	−2520.00	−0.228819
$496$	0	0
$497$	3872.00	0.349463
$498$	0	0
$499$	5460.00	0.489826	0.244913	−	0.969545i	$-0.421241\pi$
$499$	5460.00	0.489826	0.244913	+	0.969545i	$0.421241\pi$
$500$	0	0
$501$	5184.00	0.462284
$502$	0	0
$503$	−5628.00	−0.498887	−0.249443	−	0.968389i	$-0.580248\pi$
$503$	−5628.00	−0.498887	−0.249443	+	0.968389i	$0.580248\pi$
$504$	0	0
$505$	810.000	0.0713753
$506$	0	0
$507$	1299.00	0.113788
$508$	0	0
$509$	−1190.00	−0.103626	−0.0518132	−	0.998657i	$-0.516500\pi$
$509$	−1190.00	−0.103626	−0.0518132	+	0.998657i	$0.516500\pi$
$510$	0	0
$511$	−4796.00	−0.415191
$512$	0	0
$513$	513.000	0.0441511
$514$	0	0
$515$	8040.00	0.687932
$516$	0	0
$517$	−1344.00	−0.114331
$518$	0	0
$519$	2046.00	0.173043
$520$	0	0
$521$	600.000	0.0504539	0.0252269	−	0.999682i	$-0.491969\pi$
$521$	600.000	0.0504539	0.0252269	+	0.999682i	$0.491969\pi$
$522$	0	0
$523$	−22892.0	−1.91395	−0.956976	−	0.290166i	$-0.906290\pi$
$523$	−22892.0	−1.91395	−0.956976	+	0.290166i	$0.906290\pi$
$524$	0	0
$525$	−1650.00	−0.137166
$526$	0	0
$527$	−5640.00	−0.466190
$528$	0	0
$529$	6329.00	0.520178
$530$	0	0
$531$	−4986.00	−0.407484
$532$	0	0
$533$	−21336.0	−1.73389
$534$	0	0
$535$	1800.00	0.145459
$536$	0	0
$537$	−3150.00	−0.253133
$538$	0	0
$539$	−7896.00	−0.630992
$540$	0	0
$541$	9502.00	0.755125	0.377563	−	0.925984i	$-0.376762\pi$
$541$	9502.00	0.755125	0.377563	+	0.925984i	$0.376762\pi$
$542$	0	0
$543$	8364.00	0.661020
$544$	0	0
$545$	−5380.00	−0.422851
$546$	0	0
$547$	−17596.0	−1.37541	−0.687706	−	0.725989i	$-0.741382\pi$
$547$	−17596.0	−1.37541	−0.687706	+	0.725989i	$0.741382\pi$
$548$	0	0
$549$	−3150.00	−0.244879
$550$	0	0
$551$	2850.00	0.220352
$552$	0	0
$553$	−19052.0	−1.46505
$554$	0	0
$555$	−5910.00	−0.452010
$556$	0	0
$557$	−19874.0	−1.51183	−0.755914	−	0.654671i	$-0.772807\pi$
$557$	−19874.0	−1.51183	−0.755914	+	0.654671i	$0.772807\pi$
$558$	0	0
$559$	−13104.0	−0.991485
$560$	0	0
$561$	−10080.0	−0.758606
$562$	0	0
$563$	672.000	0.0503045	0.0251522	−	0.999684i	$-0.491993\pi$
$563$	672.000	0.0503045	0.0251522	+	0.999684i	$0.491993\pi$
$564$	0	0
$565$	1850.00	0.137752
$566$	0	0
$567$	1782.00	0.131988
$568$	0	0
$569$	−7988.00	−0.588531	−0.294266	−	0.955724i	$-0.595075\pi$
$569$	−7988.00	−0.588531	−0.294266	+	0.955724i	$0.595075\pi$
$570$	0	0
$571$	−20372.0	−1.49307	−0.746534	−	0.665347i	$-0.768283\pi$
$571$	−20372.0	−1.49307	−0.746534	+	0.665347i	$0.768283\pi$
$572$	0	0
$573$	8064.00	0.587920
$574$	0	0
$575$	3400.00	0.246591
$576$	0	0
$577$	11586.0	0.835930	0.417965	−	0.908463i	$-0.362744\pi$
$577$	11586.0	0.835930	0.417965	+	0.908463i	$0.362744\pi$
$578$	0	0
$579$	−4134.00	−0.296724
$580$	0	0
$581$	20460.0	1.46097
$582$	0	0
$583$	31472.0	2.23574
$584$	0	0
$585$	1890.00	0.133576
$586$	0	0
$587$	−26698.0	−1.87725	−0.938624	−	0.344942i	$-0.887898\pi$
$587$	−26698.0	−1.87725	−0.938624	+	0.344942i	$0.887898\pi$
$588$	0	0
$589$	−1786.00	−0.124942
$590$	0	0
$591$	−6966.00	−0.484844
$592$	0	0
$593$	−25392.0	−1.75839	−0.879194	−	0.476463i	$-0.841918\pi$
$593$	−25392.0	−1.75839	−0.879194	+	0.476463i	$0.841918\pi$
$594$	0	0
$595$	−6600.00	−0.454746
$596$	0	0
$597$	−8988.00	−0.616171
$598$	0	0
$599$	−1324.00	−0.0903125	−0.0451562	−	0.998980i	$-0.514379\pi$
$599$	−1324.00	−0.0903125	−0.0451562	+	0.998980i	$0.514379\pi$
$600$	0	0
$601$	8010.00	0.543652	0.271826	−	0.962346i	$-0.412373\pi$
$601$	8010.00	0.543652	0.271826	+	0.962346i	$0.412373\pi$
$602$	0	0
$603$	3924.00	0.265004
$604$	0	0
$605$	9025.00	0.606477
$606$	0	0
$607$	−17664.0	−1.18115	−0.590576	−	0.806982i	$-0.701100\pi$
$607$	−17664.0	−1.18115	−0.590576	+	0.806982i	$0.701100\pi$
$608$	0	0
$609$	9900.00	0.658733
$610$	0	0
$611$	1008.00	0.0667419
$612$	0	0
$613$	7564.00	0.498380	0.249190	−	0.968455i	$-0.419836\pi$
$613$	7564.00	0.498380	0.249190	+	0.968455i	$0.419836\pi$
$614$	0	0
$615$	7620.00	0.499623
$616$	0	0
$617$	3912.00	0.255253	0.127627	−	0.991822i	$-0.459264\pi$
$617$	3912.00	0.255253	0.127627	+	0.991822i	$0.459264\pi$
$618$	0	0
$619$	6476.00	0.420505	0.210252	−	0.977647i	$-0.432571\pi$
$619$	6476.00	0.420505	0.210252	+	0.977647i	$0.432571\pi$
$620$	0	0
$621$	−3672.00	−0.237282
$622$	0	0
$623$	−8448.00	−0.543278
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−3192.00	−0.203311
$628$	0	0
$629$	−23640.0	−1.49855
$630$	0	0
$631$	−4192.00	−0.264470	−0.132235	−	0.991218i	$-0.542215\pi$
$631$	−4192.00	−0.264470	−0.132235	+	0.991218i	$0.542215\pi$
$632$	0	0
$633$	13488.0	0.846919
$634$	0	0
$635$	2640.00	0.164985
$636$	0	0
$637$	5922.00	0.368349
$638$	0	0
$639$	1584.00	0.0980627
$640$	0	0
$641$	−6004.00	−0.369959	−0.184980	−	0.982742i	$-0.559222\pi$
$641$	−6004.00	−0.369959	−0.184980	+	0.982742i	$0.559222\pi$
$642$	0	0
$643$	−8048.00	−0.493596	−0.246798	−	0.969067i	$-0.579378\pi$
$643$	−8048.00	−0.493596	−0.246798	+	0.969067i	$0.579378\pi$
$644$	0	0
$645$	4680.00	0.285697
$646$	0	0
$647$	31260.0	1.89947	0.949735	−	0.313054i	$-0.101352\pi$
$647$	31260.0	1.89947	0.949735	+	0.313054i	$0.101352\pi$
$648$	0	0
$649$	31024.0	1.87642
$650$	0	0
$651$	−6204.00	−0.373508
$652$	0	0
$653$	−4202.00	−0.251818	−0.125909	−	0.992042i	$-0.540185\pi$
$653$	−4202.00	−0.251818	−0.125909	+	0.992042i	$0.540185\pi$
$654$	0	0
$655$	−5240.00	−0.312586
$656$	0	0
$657$	−1962.00	−0.116507
$658$	0	0
$659$	−4934.00	−0.291656	−0.145828	−	0.989310i	$-0.546585\pi$
$659$	−4934.00	−0.291656	−0.145828	+	0.989310i	$0.546585\pi$
$660$	0	0
$661$	−11956.0	−0.703532	−0.351766	−	0.936088i	$-0.614419\pi$
$661$	−11956.0	−0.703532	−0.351766	+	0.936088i	$0.614419\pi$
$662$	0	0
$663$	7560.00	0.442845
$664$	0	0
$665$	−2090.00	−0.121875
$666$	0	0
$667$	−20400.0	−1.18424
$668$	0	0
$669$	11604.0	0.670608
$670$	0	0
$671$	19600.0	1.12764
$672$	0	0
$673$	−178.000	−0.0101952	−0.00509762	−	0.999987i	$-0.501623\pi$
$673$	−178.000	−0.0101952	−0.00509762	+	0.999987i	$0.501623\pi$
$674$	0	0
$675$	−675.000	−0.0384900
$676$	0	0
$677$	−12182.0	−0.691569	−0.345785	−	0.938314i	$-0.612387\pi$
$677$	−12182.0	−0.691569	−0.345785	+	0.938314i	$0.612387\pi$
$678$	0	0
$679$	26532.0	1.49957
$680$	0	0
$681$	540.000	0.0303860
$682$	0	0
$683$	10420.0	0.583763	0.291882	−	0.956454i	$-0.405719\pi$
$683$	10420.0	0.583763	0.291882	+	0.956454i	$0.405719\pi$
$684$	0	0
$685$	−6160.00	−0.343593
$686$	0	0
$687$	20070.0	1.11458
$688$	0	0
$689$	−23604.0	−1.30514
$690$	0	0
$691$	2892.00	0.159214	0.0796070	−	0.996826i	$-0.474633\pi$
$691$	2892.00	0.159214	0.0796070	+	0.996826i	$0.474633\pi$
$692$	0	0
$693$	−11088.0	−0.607790
$694$	0	0
$695$	4220.00	0.230322
$696$	0	0
$697$	30480.0	1.65640
$698$	0	0
$699$	2316.00	0.125321
$700$	0	0
$701$	−18746.0	−1.01002	−0.505012	−	0.863112i	$-0.668512\pi$
$701$	−18746.0	−1.01002	−0.505012	+	0.863112i	$0.668512\pi$
$702$	0	0
$703$	−7486.00	−0.401621
$704$	0	0
$705$	−360.000	−0.0192318
$706$	0	0
$707$	3564.00	0.189587
$708$	0	0
$709$	−29330.0	−1.55361	−0.776806	−	0.629740i	$-0.783162\pi$
$709$	−29330.0	−1.55361	−0.776806	+	0.629740i	$0.783162\pi$
$710$	0	0
$711$	−7794.00	−0.411108
$712$	0	0
$713$	12784.0	0.671479
$714$	0	0
$715$	−11760.0	−0.615104
$716$	0	0
$717$	−5328.00	−0.277514
$718$	0	0
$719$	6376.00	0.330716	0.165358	−	0.986234i	$-0.447122\pi$
$719$	6376.00	0.330716	0.165358	+	0.986234i	$0.447122\pi$
$720$	0	0
$721$	35376.0	1.82728
$722$	0	0
$723$	13362.0	0.687328
$724$	0	0
$725$	−3750.00	−0.192099
$726$	0	0
$727$	−6758.00	−0.344760	−0.172380	−	0.985031i	$-0.555146\pi$
$727$	−6758.00	−0.344760	−0.172380	+	0.985031i	$0.555146\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	18720.0	0.947174
$732$	0	0
$733$	31692.0	1.59696	0.798479	−	0.602022i	$-0.205638\pi$
$733$	31692.0	1.59696	0.798479	+	0.602022i	$0.205638\pi$
$734$	0	0
$735$	−2115.00	−0.106140
$736$	0	0
$737$	−24416.0	−1.22032
$738$	0	0
$739$	34516.0	1.71812	0.859061	−	0.511874i	$-0.171048\pi$
$739$	34516.0	1.71812	0.859061	+	0.511874i	$0.171048\pi$
$740$	0	0
$741$	2394.00	0.118685
$742$	0	0
$743$	8352.00	0.412389	0.206195	−	0.978511i	$-0.433892\pi$
$743$	8352.00	0.412389	0.206195	+	0.978511i	$0.433892\pi$
$744$	0	0
$745$	−2310.00	−0.113600
$746$	0	0
$747$	8370.00	0.409963
$748$	0	0
$749$	7920.00	0.386369
$750$	0	0
$751$	20486.0	0.995399	0.497700	−	0.867349i	$-0.334178\pi$
$751$	20486.0	0.995399	0.497700	+	0.867349i	$0.334178\pi$
$752$	0	0
$753$	2700.00	0.130669
$754$	0	0
$755$	7650.00	0.368758
$756$	0	0
$757$	9068.00	0.435379	0.217690	−	0.976018i	$-0.430148\pi$
$757$	9068.00	0.435379	0.217690	+	0.976018i	$0.430148\pi$
$758$	0	0
$759$	22848.0	1.09266
$760$	0	0
$761$	−15666.0	−0.746244	−0.373122	−	0.927782i	$-0.621713\pi$
$761$	−15666.0	−0.746244	−0.373122	+	0.927782i	$0.621713\pi$
$762$	0	0
$763$	−23672.0	−1.12318
$764$	0	0
$765$	−2700.00	−0.127606
$766$	0	0
$767$	−23268.0	−1.09538
$768$	0	0
$769$	−16594.0	−0.778147	−0.389073	−	0.921207i	$-0.627205\pi$
$769$	−16594.0	−0.778147	−0.389073	+	0.921207i	$0.627205\pi$
$770$	0	0
$771$	−8082.00	−0.377518
$772$	0	0
$773$	14982.0	0.697109	0.348554	−	0.937289i	$-0.386673\pi$
$773$	14982.0	0.697109	0.348554	+	0.937289i	$0.386673\pi$
$774$	0	0
$775$	2350.00	0.108922
$776$	0	0
$777$	−26004.0	−1.20063
$778$	0	0
$779$	9652.00	0.443927
$780$	0	0
$781$	−9856.00	−0.451569
$782$	0	0
$783$	4050.00	0.184847
$784$	0	0
$785$	8160.00	0.371010
$786$	0	0
$787$	5740.00	0.259986	0.129993	−	0.991515i	$-0.458505\pi$
$787$	5740.00	0.259986	0.129993	+	0.991515i	$0.458505\pi$
$788$	0	0
$789$	−14976.0	−0.675741
$790$	0	0
$791$	8140.00	0.365898
$792$	0	0
$793$	−14700.0	−0.658275
$794$	0	0
$795$	8430.00	0.376077
$796$	0	0
$797$	−36350.0	−1.61554	−0.807769	−	0.589500i	$-0.799325\pi$
$797$	−36350.0	−1.61554	−0.807769	+	0.589500i	$0.799325\pi$
$798$	0	0
$799$	−1440.00	−0.0637591
$800$	0	0
$801$	−3456.00	−0.152449
$802$	0	0
$803$	12208.0	0.536502
$804$	0	0
$805$	14960.0	0.654995
$806$	0	0
$807$	6282.00	0.274023
$808$	0	0
$809$	31326.0	1.36139	0.680694	−	0.732568i	$-0.261678\pi$
$809$	31326.0	1.36139	0.680694	+	0.732568i	$0.261678\pi$
$810$	0	0
$811$	23048.0	0.997934	0.498967	−	0.866621i	$-0.333713\pi$
$811$	23048.0	0.997934	0.498967	+	0.866621i	$0.333713\pi$
$812$	0	0
$813$	24492.0	1.05655
$814$	0	0
$815$	−19740.0	−0.848420
$816$	0	0
$817$	5928.00	0.253849
$818$	0	0
$819$	8316.00	0.354804
$820$	0	0
$821$	6434.00	0.273506	0.136753	−	0.990605i	$-0.456333\pi$
$821$	6434.00	0.273506	0.136753	+	0.990605i	$0.456333\pi$
$822$	0	0
$823$	15998.0	0.677588	0.338794	−	0.940861i	$-0.389981\pi$
$823$	15998.0	0.677588	0.338794	+	0.940861i	$0.389981\pi$
$824$	0	0
$825$	4200.00	0.177243
$826$	0	0
$827$	−20328.0	−0.854745	−0.427372	−	0.904076i	$-0.640561\pi$
$827$	−20328.0	−0.854745	−0.427372	+	0.904076i	$0.640561\pi$
$828$	0	0
$829$	14004.0	0.586706	0.293353	−	0.956004i	$-0.405229\pi$
$829$	14004.0	0.586706	0.293353	+	0.956004i	$0.405229\pi$
$830$	0	0
$831$	8760.00	0.365681
$832$	0	0
$833$	−8460.00	−0.351887
$834$	0	0
$835$	−8640.00	−0.358083
$836$	0	0
$837$	−2538.00	−0.104810
$838$	0	0
$839$	−30936.0	−1.27298	−0.636489	−	0.771285i	$-0.719614\pi$
$839$	−30936.0	−1.27298	−0.636489	+	0.771285i	$0.719614\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	0	0
$843$	16956.0	0.692759
$844$	0	0
$845$	−2165.00	−0.0881400
$846$	0	0
$847$	39710.0	1.61092
$848$	0	0
$849$	−5280.00	−0.213438
$850$	0	0
$851$	53584.0	2.15844
$852$	0	0
$853$	−2912.00	−0.116887	−0.0584437	−	0.998291i	$-0.518614\pi$
$853$	−2912.00	−0.116887	−0.0584437	+	0.998291i	$0.518614\pi$
$854$	0	0
$855$	−855.000	−0.0341993
$856$	0	0
$857$	−40898.0	−1.63016	−0.815081	−	0.579347i	$-0.803308\pi$
$857$	−40898.0	−1.63016	−0.815081	+	0.579347i	$0.803308\pi$
$858$	0	0
$859$	20036.0	0.795832	0.397916	−	0.917422i	$-0.369734\pi$
$859$	20036.0	0.795832	0.397916	+	0.917422i	$0.369734\pi$
$860$	0	0
$861$	33528.0	1.32710
$862$	0	0
$863$	−14984.0	−0.591033	−0.295516	−	0.955338i	$-0.595492\pi$
$863$	−14984.0	−0.591033	−0.295516	+	0.955338i	$0.595492\pi$
$864$	0	0
$865$	−3410.00	−0.134039
$866$	0	0
$867$	3939.00	0.154297
$868$	0	0
$869$	48496.0	1.89311
$870$	0	0
$871$	18312.0	0.712375
$872$	0	0
$873$	10854.0	0.420793
$874$	0	0
$875$	2750.00	0.106248
$876$	0	0
$877$	886.000	0.0341141	0.0170571	−	0.999855i	$-0.494570\pi$
$877$	886.000	0.0341141	0.0170571	+	0.999855i	$0.494570\pi$
$878$	0	0
$879$	10794.0	0.414190
$880$	0	0
$881$	−10142.0	−0.387846	−0.193923	−	0.981017i	$-0.562121\pi$
$881$	−10142.0	−0.387846	−0.193923	+	0.981017i	$0.562121\pi$
$882$	0	0
$883$	39280.0	1.49703	0.748515	−	0.663118i	$-0.230767\pi$
$883$	39280.0	1.49703	0.748515	+	0.663118i	$0.230767\pi$
$884$	0	0
$885$	8310.00	0.315636
$886$	0	0
$887$	−4224.00	−0.159896	−0.0799482	−	0.996799i	$-0.525475\pi$
$887$	−4224.00	−0.159896	−0.0799482	+	0.996799i	$0.525475\pi$
$888$	0	0
$889$	11616.0	0.438232
$890$	0	0
$891$	−4536.00	−0.170552
$892$	0	0
$893$	−456.000	−0.0170879
$894$	0	0
$895$	5250.00	0.196076
$896$	0	0
$897$	−17136.0	−0.637853
$898$	0	0
$899$	−14100.0	−0.523094
$900$	0	0
$901$	33720.0	1.24681
$902$	0	0
$903$	20592.0	0.758869
$904$	0	0
$905$	−13940.0	−0.512024
$906$	0	0
$907$	10364.0	0.379417	0.189708	−	0.981840i	$-0.439246\pi$
$907$	10364.0	0.379417	0.189708	+	0.981840i	$0.439246\pi$
$908$	0	0
$909$	1458.00	0.0532000
$910$	0	0
$911$	5780.00	0.210208	0.105104	−	0.994461i	$-0.466482\pi$
$911$	5780.00	0.210208	0.105104	+	0.994461i	$0.466482\pi$
$912$	0	0
$913$	−52080.0	−1.88784
$914$	0	0
$915$	5250.00	0.189683
$916$	0	0
$917$	−23056.0	−0.830290
$918$	0	0
$919$	14248.0	0.511423	0.255712	−	0.966753i	$-0.417690\pi$
$919$	14248.0	0.511423	0.255712	+	0.966753i	$0.417690\pi$
$920$	0	0
$921$	18732.0	0.670185
$922$	0	0
$923$	7392.00	0.263608
$924$	0	0
$925$	9850.00	0.350125
$926$	0	0
$927$	14472.0	0.512754
$928$	0	0
$929$	−18054.0	−0.637602	−0.318801	−	0.947822i	$-0.603280\pi$
$929$	−18054.0	−0.637602	−0.318801	+	0.947822i	$0.603280\pi$
$930$	0	0
$931$	−2679.00	−0.0943079
$932$	0	0
$933$	−26160.0	−0.917942
$934$	0	0
$935$	16800.0	0.587614
$936$	0	0
$937$	11194.0	0.390280	0.195140	−	0.980775i	$-0.437484\pi$
$937$	11194.0	0.390280	0.195140	+	0.980775i	$0.437484\pi$
$938$	0	0
$939$	6342.00	0.220408
$940$	0	0
$941$	−43682.0	−1.51328	−0.756638	−	0.653834i	$-0.773159\pi$
$941$	−43682.0	−1.51328	−0.756638	+	0.653834i	$0.773159\pi$
$942$	0	0
$943$	−69088.0	−2.38581
$944$	0	0
$945$	−2970.00	−0.102237
$946$	0	0
$947$	6794.00	0.233131	0.116566	−	0.993183i	$-0.462811\pi$
$947$	6794.00	0.233131	0.116566	+	0.993183i	$0.462811\pi$
$948$	0	0
$949$	−9156.00	−0.313189
$950$	0	0
$951$	24018.0	0.818966
$952$	0	0
$953$	35982.0	1.22305	0.611527	−	0.791223i	$-0.290555\pi$
$953$	35982.0	1.22305	0.611527	+	0.791223i	$0.290555\pi$
$954$	0	0
$955$	−13440.0	−0.455401
$956$	0	0
$957$	−25200.0	−0.851202
$958$	0	0
$959$	−27104.0	−0.912653
$960$	0	0
$961$	−20955.0	−0.703400
$962$	0	0
$963$	3240.00	0.108419
$964$	0	0
$965$	6890.00	0.229841
$966$	0	0
$967$	1550.00	0.0515456	0.0257728	−	0.999668i	$-0.491795\pi$
$967$	1550.00	0.0515456	0.0257728	+	0.999668i	$0.491795\pi$
$968$	0	0
$969$	−3420.00	−0.113381
$970$	0	0
$971$	21706.0	0.717383	0.358691	−	0.933456i	$-0.383223\pi$
$971$	21706.0	0.717383	0.358691	+	0.933456i	$0.383223\pi$
$972$	0	0
$973$	18568.0	0.611781
$974$	0	0
$975$	−3150.00	−0.103467
$976$	0	0
$977$	42310.0	1.38548	0.692741	−	0.721186i	$-0.256403\pi$
$977$	42310.0	1.38548	0.692741	+	0.721186i	$0.256403\pi$
$978$	0	0
$979$	21504.0	0.702013
$980$	0	0
$981$	−9684.00	−0.315175
$982$	0	0
$983$	7960.00	0.258275	0.129138	−	0.991627i	$-0.458779\pi$
$983$	7960.00	0.258275	0.129138	+	0.991627i	$0.458779\pi$
$984$	0	0
$985$	11610.0	0.375559
$986$	0	0
$987$	−1584.00	−0.0510834
$988$	0	0
$989$	−42432.0	−1.36427
$990$	0	0
$991$	−22166.0	−0.710521	−0.355260	−	0.934767i	$-0.615608\pi$
$991$	−22166.0	−0.710521	−0.355260	+	0.934767i	$0.615608\pi$
$992$	0	0
$993$	−13884.0	−0.443701
$994$	0	0
$995$	14980.0	0.477284
$996$	0	0
$997$	41504.0	1.31840	0.659200	−	0.751968i	$-0.270895\pi$
$997$	41504.0	1.31840	0.659200	+	0.751968i	$0.270895\pi$
$998$	0	0
$999$	−10638.0	−0.336908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2280.4.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2280.4.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:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2280.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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