LMFDB - Embedded newform 2205.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2205,4,Mod(1,2205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2205, 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("2205.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2205 = 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2205.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:	$130.099211563$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} +1.00000 q^{4} -5.00000 q^{5} +21.0000 q^{8} +15.0000 q^{10} +24.0000 q^{11} -74.0000 q^{13} -71.0000 q^{16} +54.0000 q^{17} +124.000 q^{19} -5.00000 q^{20} -72.0000 q^{22} +120.000 q^{23} +25.0000 q^{25} +222.000 q^{26} +78.0000 q^{29} -200.000 q^{31} +45.0000 q^{32} -162.000 q^{34} -70.0000 q^{37} -372.000 q^{38} -105.000 q^{40} +330.000 q^{41} +92.0000 q^{43} +24.0000 q^{44} -360.000 q^{46} -24.0000 q^{47} -75.0000 q^{50} -74.0000 q^{52} -450.000 q^{53} -120.000 q^{55} -234.000 q^{58} +24.0000 q^{59} +322.000 q^{61} +600.000 q^{62} +433.000 q^{64} +370.000 q^{65} -196.000 q^{67} +54.0000 q^{68} +288.000 q^{71} +430.000 q^{73} +210.000 q^{74} +124.000 q^{76} -520.000 q^{79} +355.000 q^{80} -990.000 q^{82} +156.000 q^{83} -270.000 q^{85} -276.000 q^{86} +504.000 q^{88} +1026.00 q^{89} +120.000 q^{92} +72.0000 q^{94} -620.000 q^{95} +286.000 q^{97} +O(q^{100})$

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 $

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	0	0
$3$	0	0
$4$	1.00000	0.125000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	0	0
$7$	0	0
$8$	21.0000	0.928078
$9$	0	0
$10$	15.0000	0.474342
$11$	24.0000	0.657843	0.328921	−	0.944357i	$-0.393315\pi$
$11$	24.0000	0.657843	0.328921	+	0.944357i	$0.393315\pi$
$12$	0	0
$13$	−74.0000	−1.57876	−0.789381	−	0.613904i	$-0.789598\pi$
$13$	−74.0000	−1.57876	−0.789381	+	0.613904i	$0.789598\pi$
$14$	0	0
$15$	0	0
$16$	−71.0000	−1.10938
$17$	54.0000	0.770407	0.385204	−	0.922832i	$-0.374131\pi$
$17$	54.0000	0.770407	0.385204	+	0.922832i	$0.374131\pi$
$18$	0	0
$19$	124.000	1.49724	0.748620	−	0.663000i	$-0.230717\pi$
$19$	124.000	1.49724	0.748620	+	0.663000i	$0.230717\pi$
$20$	−5.00000	−0.0559017
$21$	0	0
$22$	−72.0000	−0.697748
$23$	120.000	1.08790	0.543951	−	0.839117i	$-0.316928\pi$
$23$	120.000	1.08790	0.543951	+	0.839117i	$0.316928\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	222.000	1.67453
$27$	0	0
$28$	0	0
$29$	78.0000	0.499456	0.249728	−	0.968316i	$-0.419659\pi$
$29$	78.0000	0.499456	0.249728	+	0.968316i	$0.419659\pi$
$30$	0	0
$31$	−200.000	−1.15874	−0.579372	−	0.815063i	$-0.696702\pi$
$31$	−200.000	−1.15874	−0.579372	+	0.815063i	$0.696702\pi$
$32$	45.0000	0.248592
$33$	0	0
$34$	−162.000	−0.817140
$35$	0	0
$36$	0	0
$37$	−70.0000	−0.311025	−0.155513	−	0.987834i	$-0.549703\pi$
$37$	−70.0000	−0.311025	−0.155513	+	0.987834i	$0.549703\pi$
$38$	−372.000	−1.58806
$39$	0	0
$40$	−105.000	−0.415049
$41$	330.000	1.25701	0.628504	−	0.777806i	$-0.283668\pi$
$41$	330.000	1.25701	0.628504	+	0.777806i	$0.283668\pi$
$42$	0	0
$43$	92.0000	0.326276	0.163138	−	0.986603i	$-0.447838\pi$
$43$	92.0000	0.326276	0.163138	+	0.986603i	$0.447838\pi$
$44$	24.0000	0.0822304
$45$	0	0
$46$	−360.000	−1.15389
$47$	−24.0000	−0.0744843	−0.0372421	−	0.999306i	$-0.511857\pi$
$47$	−24.0000	−0.0744843	−0.0372421	+	0.999306i	$0.511857\pi$
$48$	0	0
$49$	0	0
$50$	−75.0000	−0.212132
$51$	0	0
$52$	−74.0000	−0.197345
$53$	−450.000	−1.16627	−0.583134	−	0.812376i	$-0.698174\pi$
$53$	−450.000	−1.16627	−0.583134	+	0.812376i	$0.698174\pi$
$54$	0	0
$55$	−120.000	−0.294196
$56$	0	0
$57$	0	0
$58$	−234.000	−0.529754
$59$	24.0000	0.0529582	0.0264791	−	0.999649i	$-0.491570\pi$
$59$	24.0000	0.0529582	0.0264791	+	0.999649i	$0.491570\pi$
$60$	0	0
$61$	322.000	0.675867	0.337933	−	0.941170i	$-0.390272\pi$
$61$	322.000	0.675867	0.337933	+	0.941170i	$0.390272\pi$
$62$	600.000	1.22903
$63$	0	0
$64$	433.000	0.845703
$65$	370.000	0.706044
$66$	0	0
$67$	−196.000	−0.357391	−0.178696	−	0.983904i	$-0.557188\pi$
$67$	−196.000	−0.357391	−0.178696	+	0.983904i	$0.557188\pi$
$68$	54.0000	0.0963009
$69$	0	0
$70$	0	0
$71$	288.000	0.481399	0.240699	−	0.970600i	$-0.422623\pi$
$71$	288.000	0.481399	0.240699	+	0.970600i	$0.422623\pi$
$72$	0	0
$73$	430.000	0.689420	0.344710	−	0.938709i	$-0.387977\pi$
$73$	430.000	0.689420	0.344710	+	0.938709i	$0.387977\pi$
$74$	210.000	0.329892
$75$	0	0
$76$	124.000	0.187155
$77$	0	0
$78$	0	0
$79$	−520.000	−0.740564	−0.370282	−	0.928919i	$-0.620739\pi$
$79$	−520.000	−0.740564	−0.370282	+	0.928919i	$0.620739\pi$
$80$	355.000	0.496128
$81$	0	0
$82$	−990.000	−1.33326
$83$	156.000	0.206304	0.103152	−	0.994666i	$-0.467107\pi$
$83$	156.000	0.206304	0.103152	+	0.994666i	$0.467107\pi$
$84$	0	0
$85$	−270.000	−0.344537
$86$	−276.000	−0.346068
$87$	0	0
$88$	504.000	0.610529
$89$	1026.00	1.22198	0.610988	−	0.791640i	$-0.290773\pi$
$89$	1026.00	1.22198	0.610988	+	0.791640i	$0.290773\pi$
$90$	0	0
$91$	0	0
$92$	120.000	0.135988
$93$	0	0
$94$	72.0000	0.0790025
$95$	−620.000	−0.669586
$96$	0	0
$97$	286.000	0.299370	0.149685	−	0.988734i	$-0.452174\pi$
$97$	286.000	0.299370	0.149685	+	0.988734i	$0.452174\pi$
$98$	0	0
$99$	0	0
$100$	25.0000	0.0250000
$101$	−1734.00	−1.70831	−0.854156	−	0.520017i	$-0.825925\pi$
$101$	−1734.00	−1.70831	−0.854156	+	0.520017i	$0.825925\pi$
$102$	0	0
$103$	−452.000	−0.432397	−0.216198	−	0.976349i	$-0.569366\pi$
$103$	−452.000	−0.432397	−0.216198	+	0.976349i	$0.569366\pi$
$104$	−1554.00	−1.46521
$105$	0	0
$106$	1350.00	1.23702
$107$	1404.00	1.26850	0.634251	−	0.773127i	$-0.281308\pi$
$107$	1404.00	1.26850	0.634251	+	0.773127i	$0.281308\pi$
$108$	0	0
$109$	−1474.00	−1.29526	−0.647631	−	0.761954i	$-0.724240\pi$
$109$	−1474.00	−1.29526	−0.647631	+	0.761954i	$0.724240\pi$
$110$	360.000	0.312042
$111$	0	0
$112$	0	0
$113$	−1086.00	−0.904091	−0.452046	−	0.891995i	$-0.649306\pi$
$113$	−1086.00	−0.904091	−0.452046	+	0.891995i	$0.649306\pi$
$114$	0	0
$115$	−600.000	−0.486524
$116$	78.0000	0.0624321
$117$	0	0
$118$	−72.0000	−0.0561707
$119$	0	0
$120$	0	0
$121$	−755.000	−0.567243
$122$	−966.000	−0.716865
$123$	0	0
$124$	−200.000	−0.144843
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1244.00	0.869190	0.434595	−	0.900626i	$-0.356891\pi$
$127$	1244.00	0.869190	0.434595	+	0.900626i	$0.356891\pi$
$128$	−1659.00	−1.14560
$129$	0	0
$130$	−1110.00	−0.748873
$131$	2328.00	1.55266	0.776329	−	0.630327i	$-0.217079\pi$
$131$	2328.00	1.55266	0.776329	+	0.630327i	$0.217079\pi$
$132$	0	0
$133$	0	0
$134$	588.000	0.379071
$135$	0	0
$136$	1134.00	0.714998
$137$	−2118.00	−1.32082	−0.660412	−	0.750903i	$-0.729618\pi$
$137$	−2118.00	−1.32082	−0.660412	+	0.750903i	$0.729618\pi$
$138$	0	0
$139$	−2324.00	−1.41812	−0.709062	−	0.705147i	$-0.750881\pi$
$139$	−2324.00	−1.41812	−0.709062	+	0.705147i	$0.750881\pi$
$140$	0	0
$141$	0	0
$142$	−864.000	−0.510600
$143$	−1776.00	−1.03858
$144$	0	0
$145$	−390.000	−0.223364
$146$	−1290.00	−0.731241
$147$	0	0
$148$	−70.0000	−0.0388781
$149$	−258.000	−0.141854	−0.0709268	−	0.997482i	$-0.522596\pi$
$149$	−258.000	−0.141854	−0.0709268	+	0.997482i	$0.522596\pi$
$150$	0	0
$151$	−808.000	−0.435458	−0.217729	−	0.976009i	$-0.569865\pi$
$151$	−808.000	−0.435458	−0.217729	+	0.976009i	$0.569865\pi$
$152$	2604.00	1.38955
$153$	0	0
$154$	0	0
$155$	1000.00	0.518206
$156$	0	0
$157$	−2378.00	−1.20882	−0.604411	−	0.796673i	$-0.706592\pi$
$157$	−2378.00	−1.20882	−0.604411	+	0.796673i	$0.706592\pi$
$158$	1560.00	0.785487
$159$	0	0
$160$	−225.000	−0.111174
$161$	0	0
$162$	0	0
$163$	−52.0000	−0.0249874	−0.0124937	−	0.999922i	$-0.503977\pi$
$163$	−52.0000	−0.0249874	−0.0124937	+	0.999922i	$0.503977\pi$
$164$	330.000	0.157126
$165$	0	0
$166$	−468.000	−0.218818
$167$	−3720.00	−1.72373	−0.861863	−	0.507141i	$-0.830702\pi$
$167$	−3720.00	−1.72373	−0.861863	+	0.507141i	$0.830702\pi$
$168$	0	0
$169$	3279.00	1.49249
$170$	810.000	0.365436
$171$	0	0
$172$	92.0000	0.0407845
$173$	426.000	0.187215	0.0936075	−	0.995609i	$-0.470160\pi$
$173$	426.000	0.187215	0.0936075	+	0.995609i	$0.470160\pi$
$174$	0	0
$175$	0	0
$176$	−1704.00	−0.729795
$177$	0	0
$178$	−3078.00	−1.29610
$179$	1440.00	0.601289	0.300644	−	0.953736i	$-0.402798\pi$
$179$	1440.00	0.601289	0.300644	+	0.953736i	$0.402798\pi$
$180$	0	0
$181$	3130.00	1.28537	0.642683	−	0.766133i	$-0.277821\pi$
$181$	3130.00	1.28537	0.642683	+	0.766133i	$0.277821\pi$
$182$	0	0
$183$	0	0
$184$	2520.00	1.00966
$185$	350.000	0.139095
$186$	0	0
$187$	1296.00	0.506807
$188$	−24.0000	−0.00931053
$189$	0	0
$190$	1860.00	0.710203
$191$	−3576.00	−1.35471	−0.677357	−	0.735655i	$-0.736875\pi$
$191$	−3576.00	−1.35471	−0.677357	+	0.735655i	$0.736875\pi$
$192$	0	0
$193$	2666.00	0.994315	0.497158	−	0.867660i	$-0.334377\pi$
$193$	2666.00	0.994315	0.497158	+	0.867660i	$0.334377\pi$
$194$	−858.000	−0.317530
$195$	0	0
$196$	0	0
$197$	2718.00	0.982992	0.491496	−	0.870880i	$-0.336450\pi$
$197$	2718.00	0.982992	0.491496	+	0.870880i	$0.336450\pi$
$198$	0	0
$199$	3832.00	1.36504	0.682521	−	0.730866i	$-0.260884\pi$
$199$	3832.00	1.36504	0.682521	+	0.730866i	$0.260884\pi$
$200$	525.000	0.185616
$201$	0	0
$202$	5202.00	1.81194
$203$	0	0
$204$	0	0
$205$	−1650.00	−0.562151
$206$	1356.00	0.458626
$207$	0	0
$208$	5254.00	1.75144
$209$	2976.00	0.984948
$210$	0	0
$211$	1100.00	0.358896	0.179448	−	0.983767i	$-0.442569\pi$
$211$	1100.00	0.358896	0.179448	+	0.983767i	$0.442569\pi$
$212$	−450.000	−0.145784
$213$	0	0
$214$	−4212.00	−1.34545
$215$	−460.000	−0.145915
$216$	0	0
$217$	0	0
$218$	4422.00	1.37383
$219$	0	0
$220$	−120.000	−0.0367745
$221$	−3996.00	−1.21629
$222$	0	0
$223$	−1964.00	−0.589772	−0.294886	−	0.955532i	$-0.595282\pi$
$223$	−1964.00	−0.589772	−0.294886	+	0.955532i	$0.595282\pi$
$224$	0	0
$225$	0	0
$226$	3258.00	0.958933
$227$	660.000	0.192977	0.0964884	−	0.995334i	$-0.469239\pi$
$227$	660.000	0.192977	0.0964884	+	0.995334i	$0.469239\pi$
$228$	0	0
$229$	1906.00	0.550009	0.275004	−	0.961443i	$-0.411321\pi$
$229$	1906.00	0.550009	0.275004	+	0.961443i	$0.411321\pi$
$230$	1800.00	0.516037
$231$	0	0
$232$	1638.00	0.463534
$233$	1458.00	0.409943	0.204972	−	0.978768i	$-0.434290\pi$
$233$	1458.00	0.409943	0.204972	+	0.978768i	$0.434290\pi$
$234$	0	0
$235$	120.000	0.0333104
$236$	24.0000	0.00661978
$237$	0	0
$238$	0	0
$239$	−1176.00	−0.318281	−0.159140	−	0.987256i	$-0.550872\pi$
$239$	−1176.00	−0.318281	−0.159140	+	0.987256i	$0.550872\pi$
$240$	0	0
$241$	−866.000	−0.231469	−0.115734	−	0.993280i	$-0.536922\pi$
$241$	−866.000	−0.231469	−0.115734	+	0.993280i	$0.536922\pi$
$242$	2265.00	0.601652
$243$	0	0
$244$	322.000	0.0844834
$245$	0	0
$246$	0	0
$247$	−9176.00	−2.36379
$248$	−4200.00	−1.07540
$249$	0	0
$250$	375.000	0.0948683
$251$	432.000	0.108636	0.0543179	−	0.998524i	$-0.482702\pi$
$251$	432.000	0.108636	0.0543179	+	0.998524i	$0.482702\pi$
$252$	0	0
$253$	2880.00	0.715668
$254$	−3732.00	−0.921915
$255$	0	0
$256$	1513.00	0.369385
$257$	2526.00	0.613103	0.306552	−	0.951854i	$-0.400825\pi$
$257$	2526.00	0.613103	0.306552	+	0.951854i	$0.400825\pi$
$258$	0	0
$259$	0	0
$260$	370.000	0.0882555
$261$	0	0
$262$	−6984.00	−1.64684
$263$	−5448.00	−1.27733	−0.638666	−	0.769484i	$-0.720513\pi$
$263$	−5448.00	−1.27733	−0.638666	+	0.769484i	$0.720513\pi$
$264$	0	0
$265$	2250.00	0.521571
$266$	0	0
$267$	0	0
$268$	−196.000	−0.0446739
$269$	−2574.00	−0.583418	−0.291709	−	0.956507i	$-0.594224\pi$
$269$	−2574.00	−0.583418	−0.291709	+	0.956507i	$0.594224\pi$
$270$	0	0
$271$	3184.00	0.713706	0.356853	−	0.934161i	$-0.383850\pi$
$271$	3184.00	0.713706	0.356853	+	0.934161i	$0.383850\pi$
$272$	−3834.00	−0.854671
$273$	0	0
$274$	6354.00	1.40095
$275$	600.000	0.131569
$276$	0	0
$277$	3962.00	0.859399	0.429699	−	0.902972i	$-0.358620\pi$
$277$	3962.00	0.859399	0.429699	+	0.902972i	$0.358620\pi$
$278$	6972.00	1.50415
$279$	0	0
$280$	0	0
$281$	8286.00	1.75908	0.879540	−	0.475825i	$-0.157851\pi$
$281$	8286.00	1.75908	0.879540	+	0.475825i	$0.157851\pi$
$282$	0	0
$283$	2716.00	0.570493	0.285246	−	0.958454i	$-0.407925\pi$
$283$	2716.00	0.570493	0.285246	+	0.958454i	$0.407925\pi$
$284$	288.000	0.0601748
$285$	0	0
$286$	5328.00	1.10158
$287$	0	0
$288$	0	0
$289$	−1997.00	−0.406473
$290$	1170.00	0.236913
$291$	0	0
$292$	430.000	0.0861776
$293$	6018.00	1.19992	0.599958	−	0.800032i	$-0.295184\pi$
$293$	6018.00	1.19992	0.599958	+	0.800032i	$0.295184\pi$
$294$	0	0
$295$	−120.000	−0.0236836
$296$	−1470.00	−0.288655
$297$	0	0
$298$	774.000	0.150458
$299$	−8880.00	−1.71754
$300$	0	0
$301$	0	0
$302$	2424.00	0.461873
$303$	0	0
$304$	−8804.00	−1.66100
$305$	−1610.00	−0.302257
$306$	0	0
$307$	−9236.00	−1.71702	−0.858512	−	0.512793i	$-0.828611\pi$
$307$	−9236.00	−1.71702	−0.858512	+	0.512793i	$0.828611\pi$
$308$	0	0
$309$	0	0
$310$	−3000.00	−0.549640
$311$	1536.00	0.280060	0.140030	−	0.990147i	$-0.455280\pi$
$311$	1536.00	0.280060	0.140030	+	0.990147i	$0.455280\pi$
$312$	0	0
$313$	7342.00	1.32586	0.662930	−	0.748681i	$-0.269313\pi$
$313$	7342.00	1.32586	0.662930	+	0.748681i	$0.269313\pi$
$314$	7134.00	1.28215
$315$	0	0
$316$	−520.000	−0.0925705
$317$	3894.00	0.689933	0.344967	−	0.938615i	$-0.387890\pi$
$317$	3894.00	0.689933	0.344967	+	0.938615i	$0.387890\pi$
$318$	0	0
$319$	1872.00	0.328564
$320$	−2165.00	−0.378210
$321$	0	0
$322$	0	0
$323$	6696.00	1.15348
$324$	0	0
$325$	−1850.00	−0.315752
$326$	156.000	0.0265032
$327$	0	0
$328$	6930.00	1.16660
$329$	0	0
$330$	0	0
$331$	3692.00	0.613084	0.306542	−	0.951857i	$-0.400828\pi$
$331$	3692.00	0.613084	0.306542	+	0.951857i	$0.400828\pi$
$332$	156.000	0.0257880
$333$	0	0
$334$	11160.0	1.82829
$335$	980.000	0.159830
$336$	0	0
$337$	−8998.00	−1.45446	−0.727229	−	0.686395i	$-0.759192\pi$
$337$	−8998.00	−1.45446	−0.727229	+	0.686395i	$0.759192\pi$
$338$	−9837.00	−1.58302
$339$	0	0
$340$	−270.000	−0.0430671
$341$	−4800.00	−0.762271
$342$	0	0
$343$	0	0
$344$	1932.00	0.302809
$345$	0	0
$346$	−1278.00	−0.198571
$347$	−5244.00	−0.811276	−0.405638	−	0.914034i	$-0.632951\pi$
$347$	−5244.00	−0.811276	−0.405638	+	0.914034i	$0.632951\pi$
$348$	0	0
$349$	−6302.00	−0.966585	−0.483293	−	0.875459i	$-0.660559\pi$
$349$	−6302.00	−0.966585	−0.483293	+	0.875459i	$0.660559\pi$
$350$	0	0
$351$	0	0
$352$	1080.00	0.163535
$353$	3414.00	0.514756	0.257378	−	0.966311i	$-0.417141\pi$
$353$	3414.00	0.514756	0.257378	+	0.966311i	$0.417141\pi$
$354$	0	0
$355$	−1440.00	−0.215288
$356$	1026.00	0.152747
$357$	0	0
$358$	−4320.00	−0.637763
$359$	−4824.00	−0.709195	−0.354597	−	0.935019i	$-0.615382\pi$
$359$	−4824.00	−0.709195	−0.354597	+	0.935019i	$0.615382\pi$
$360$	0	0
$361$	8517.00	1.24173
$362$	−9390.00	−1.36334
$363$	0	0
$364$	0	0
$365$	−2150.00	−0.308318
$366$	0	0
$367$	3508.00	0.498954	0.249477	−	0.968381i	$-0.419741\pi$
$367$	3508.00	0.498954	0.249477	+	0.968381i	$0.419741\pi$
$368$	−8520.00	−1.20689
$369$	0	0
$370$	−1050.00	−0.147532
$371$	0	0
$372$	0	0
$373$	10802.0	1.49948	0.749740	−	0.661732i	$-0.230178\pi$
$373$	10802.0	1.49948	0.749740	+	0.661732i	$0.230178\pi$
$374$	−3888.00	−0.537550
$375$	0	0
$376$	−504.000	−0.0691272
$377$	−5772.00	−0.788523
$378$	0	0
$379$	1460.00	0.197876	0.0989382	−	0.995094i	$-0.468455\pi$
$379$	1460.00	0.197876	0.0989382	+	0.995094i	$0.468455\pi$
$380$	−620.000	−0.0836982
$381$	0	0
$382$	10728.0	1.43689
$383$	−4872.00	−0.649994	−0.324997	−	0.945715i	$-0.605363\pi$
$383$	−4872.00	−0.649994	−0.324997	+	0.945715i	$0.605363\pi$
$384$	0	0
$385$	0	0
$386$	−7998.00	−1.05463
$387$	0	0
$388$	286.000	0.0374213
$389$	14046.0	1.83075	0.915373	−	0.402606i	$-0.131896\pi$
$389$	14046.0	1.83075	0.915373	+	0.402606i	$0.131896\pi$
$390$	0	0
$391$	6480.00	0.838127
$392$	0	0
$393$	0	0
$394$	−8154.00	−1.04262
$395$	2600.00	0.331190
$396$	0	0
$397$	2734.00	0.345631	0.172816	−	0.984954i	$-0.444714\pi$
$397$	2734.00	0.345631	0.172816	+	0.984954i	$0.444714\pi$
$398$	−11496.0	−1.44785
$399$	0	0
$400$	−1775.00	−0.221875
$401$	15942.0	1.98530	0.992650	−	0.121019i	$-0.0386161\pi$
$401$	15942.0	1.98530	0.992650	+	0.121019i	$0.0386161\pi$
$402$	0	0
$403$	14800.0	1.82938
$404$	−1734.00	−0.213539
$405$	0	0
$406$	0	0
$407$	−1680.00	−0.204606
$408$	0	0
$409$	−8714.00	−1.05350	−0.526748	−	0.850022i	$-0.676589\pi$
$409$	−8714.00	−1.05350	−0.526748	+	0.850022i	$0.676589\pi$
$410$	4950.00	0.596251
$411$	0	0
$412$	−452.000	−0.0540496
$413$	0	0
$414$	0	0
$415$	−780.000	−0.0922619
$416$	−3330.00	−0.392468
$417$	0	0
$418$	−8928.00	−1.04470
$419$	11976.0	1.39634	0.698169	−	0.715933i	$-0.253998\pi$
$419$	11976.0	1.39634	0.698169	+	0.715933i	$0.253998\pi$
$420$	0	0
$421$	11054.0	1.27967	0.639833	−	0.768514i	$-0.279004\pi$
$421$	11054.0	1.27967	0.639833	+	0.768514i	$0.279004\pi$
$422$	−3300.00	−0.380667
$423$	0	0
$424$	−9450.00	−1.08239
$425$	1350.00	0.154081
$426$	0	0
$427$	0	0
$428$	1404.00	0.158563
$429$	0	0
$430$	1380.00	0.154766
$431$	−720.000	−0.0804668	−0.0402334	−	0.999190i	$-0.512810\pi$
$431$	−720.000	−0.0804668	−0.0402334	+	0.999190i	$0.512810\pi$
$432$	0	0
$433$	15622.0	1.73382	0.866912	−	0.498462i	$-0.166102\pi$
$433$	15622.0	1.73382	0.866912	+	0.498462i	$0.166102\pi$
$434$	0	0
$435$	0	0
$436$	−1474.00	−0.161908
$437$	14880.0	1.62885
$438$	0	0
$439$	9880.00	1.07414	0.537069	−	0.843538i	$-0.319531\pi$
$439$	9880.00	1.07414	0.537069	+	0.843538i	$0.319531\pi$
$440$	−2520.00	−0.273037
$441$	0	0
$442$	11988.0	1.29007
$443$	16116.0	1.72843	0.864215	−	0.503123i	$-0.167816\pi$
$443$	16116.0	1.72843	0.864215	+	0.503123i	$0.167816\pi$
$444$	0	0
$445$	−5130.00	−0.546484
$446$	5892.00	0.625548
$447$	0	0
$448$	0	0
$449$	−9018.00	−0.947852	−0.473926	−	0.880565i	$-0.657164\pi$
$449$	−9018.00	−0.947852	−0.473926	+	0.880565i	$0.657164\pi$
$450$	0	0
$451$	7920.00	0.826914
$452$	−1086.00	−0.113011
$453$	0	0
$454$	−1980.00	−0.204683
$455$	0	0
$456$	0	0
$457$	−3670.00	−0.375657	−0.187829	−	0.982202i	$-0.560145\pi$
$457$	−3670.00	−0.375657	−0.187829	+	0.982202i	$0.560145\pi$
$458$	−5718.00	−0.583372
$459$	0	0
$460$	−600.000	−0.0608155
$461$	17562.0	1.77428	0.887141	−	0.461499i	$-0.152688\pi$
$461$	17562.0	1.77428	0.887141	+	0.461499i	$0.152688\pi$
$462$	0	0
$463$	1172.00	0.117640	0.0588202	−	0.998269i	$-0.481266\pi$
$463$	1172.00	0.117640	0.0588202	+	0.998269i	$0.481266\pi$
$464$	−5538.00	−0.554084
$465$	0	0
$466$	−4374.00	−0.434810
$467$	6876.00	0.681335	0.340667	−	0.940184i	$-0.389347\pi$
$467$	6876.00	0.681335	0.340667	+	0.940184i	$0.389347\pi$
$468$	0	0
$469$	0	0
$470$	−360.000	−0.0353310
$471$	0	0
$472$	504.000	0.0491493
$473$	2208.00	0.214638
$474$	0	0
$475$	3100.00	0.299448
$476$	0	0
$477$	0	0
$478$	3528.00	0.337588
$479$	2280.00	0.217486	0.108743	−	0.994070i	$-0.465317\pi$
$479$	2280.00	0.217486	0.108743	+	0.994070i	$0.465317\pi$
$480$	0	0
$481$	5180.00	0.491035
$482$	2598.00	0.245510
$483$	0	0
$484$	−755.000	−0.0709053
$485$	−1430.00	−0.133882
$486$	0	0
$487$	−3076.00	−0.286215	−0.143108	−	0.989707i	$-0.545710\pi$
$487$	−3076.00	−0.286215	−0.143108	+	0.989707i	$0.545710\pi$
$488$	6762.00	0.627257
$489$	0	0
$490$	0	0
$491$	18912.0	1.73826	0.869131	−	0.494582i	$-0.164679\pi$
$491$	18912.0	1.73826	0.869131	+	0.494582i	$0.164679\pi$
$492$	0	0
$493$	4212.00	0.384785
$494$	27528.0	2.50717
$495$	0	0
$496$	14200.0	1.28548
$497$	0	0
$498$	0	0
$499$	9956.00	0.893170	0.446585	−	0.894741i	$-0.352640\pi$
$499$	9956.00	0.893170	0.446585	+	0.894741i	$0.352640\pi$
$500$	−125.000	−0.0111803
$501$	0	0
$502$	−1296.00	−0.115226
$503$	−10656.0	−0.944588	−0.472294	−	0.881441i	$-0.656574\pi$
$503$	−10656.0	−0.944588	−0.472294	+	0.881441i	$0.656574\pi$
$504$	0	0
$505$	8670.00	0.763980
$506$	−8640.00	−0.759081
$507$	0	0
$508$	1244.00	0.108649
$509$	−2766.00	−0.240866	−0.120433	−	0.992721i	$-0.538428\pi$
$509$	−2766.00	−0.240866	−0.120433	+	0.992721i	$0.538428\pi$
$510$	0	0
$511$	0	0
$512$	8733.00	0.753804
$513$	0	0
$514$	−7578.00	−0.650294
$515$	2260.00	0.193374
$516$	0	0
$517$	−576.000	−0.0489989
$518$	0	0
$519$	0	0
$520$	7770.00	0.655264
$521$	10530.0	0.885466	0.442733	−	0.896654i	$-0.354009\pi$
$521$	10530.0	0.885466	0.442733	+	0.896654i	$0.354009\pi$
$522$	0	0
$523$	−12692.0	−1.06115	−0.530576	−	0.847637i	$-0.678024\pi$
$523$	−12692.0	−1.06115	−0.530576	+	0.847637i	$0.678024\pi$
$524$	2328.00	0.194082
$525$	0	0
$526$	16344.0	1.35481
$527$	−10800.0	−0.892705
$528$	0	0
$529$	2233.00	0.183529
$530$	−6750.00	−0.553210
$531$	0	0
$532$	0	0
$533$	−24420.0	−1.98452
$534$	0	0
$535$	−7020.00	−0.567292
$536$	−4116.00	−0.331687
$537$	0	0
$538$	7722.00	0.618809
$539$	0	0
$540$	0	0
$541$	18110.0	1.43920	0.719602	−	0.694386i	$-0.244324\pi$
$541$	18110.0	1.43920	0.719602	+	0.694386i	$0.244324\pi$
$542$	−9552.00	−0.756999
$543$	0	0
$544$	2430.00	0.191517
$545$	7370.00	0.579259
$546$	0	0
$547$	3620.00	0.282962	0.141481	−	0.989941i	$-0.454814\pi$
$547$	3620.00	0.282962	0.141481	+	0.989941i	$0.454814\pi$
$548$	−2118.00	−0.165103
$549$	0	0
$550$	−1800.00	−0.139550
$551$	9672.00	0.747806
$552$	0	0
$553$	0	0
$554$	−11886.0	−0.911530
$555$	0	0
$556$	−2324.00	−0.177265
$557$	14166.0	1.07762	0.538809	−	0.842428i	$-0.318875\pi$
$557$	14166.0	1.07762	0.538809	+	0.842428i	$0.318875\pi$
$558$	0	0
$559$	−6808.00	−0.515112
$560$	0	0
$561$	0	0
$562$	−24858.0	−1.86579
$563$	−13404.0	−1.00339	−0.501697	−	0.865043i	$-0.667291\pi$
$563$	−13404.0	−1.00339	−0.501697	+	0.865043i	$0.667291\pi$
$564$	0	0
$565$	5430.00	0.404322
$566$	−8148.00	−0.605099
$567$	0	0
$568$	6048.00	0.446775
$569$	18654.0	1.37437	0.687185	−	0.726483i	$-0.258846\pi$
$569$	18654.0	1.37437	0.687185	+	0.726483i	$0.258846\pi$
$570$	0	0
$571$	−7684.00	−0.563162	−0.281581	−	0.959537i	$-0.590859\pi$
$571$	−7684.00	−0.563162	−0.281581	+	0.959537i	$0.590859\pi$
$572$	−1776.00	−0.129822
$573$	0	0
$574$	0	0
$575$	3000.00	0.217580
$576$	0	0
$577$	1726.00	0.124531	0.0622654	−	0.998060i	$-0.480167\pi$
$577$	1726.00	0.124531	0.0622654	+	0.998060i	$0.480167\pi$
$578$	5991.00	0.431129
$579$	0	0
$580$	−390.000	−0.0279205
$581$	0	0
$582$	0	0
$583$	−10800.0	−0.767222
$584$	9030.00	0.639836
$585$	0	0
$586$	−18054.0	−1.27270
$587$	10596.0	0.745049	0.372524	−	0.928022i	$-0.378492\pi$
$587$	10596.0	0.745049	0.372524	+	0.928022i	$0.378492\pi$
$588$	0	0
$589$	−24800.0	−1.73492
$590$	360.000	0.0251203
$591$	0	0
$592$	4970.00	0.345043
$593$	2862.00	0.198193	0.0990963	−	0.995078i	$-0.468405\pi$
$593$	2862.00	0.198193	0.0990963	+	0.995078i	$0.468405\pi$
$594$	0	0
$595$	0	0
$596$	−258.000	−0.0177317
$597$	0	0
$598$	26640.0	1.82172
$599$	23592.0	1.60925	0.804627	−	0.593781i	$-0.202365\pi$
$599$	23592.0	1.60925	0.804627	+	0.593781i	$0.202365\pi$
$600$	0	0
$601$	9574.00	0.649803	0.324902	−	0.945748i	$-0.394669\pi$
$601$	9574.00	0.649803	0.324902	+	0.945748i	$0.394669\pi$
$602$	0	0
$603$	0	0
$604$	−808.000	−0.0544322
$605$	3775.00	0.253679
$606$	0	0
$607$	−17444.0	−1.16644	−0.583221	−	0.812314i	$-0.698208\pi$
$607$	−17444.0	−1.16644	−0.583221	+	0.812314i	$0.698208\pi$
$608$	5580.00	0.372202
$609$	0	0
$610$	4830.00	0.320592
$611$	1776.00	0.117593
$612$	0	0
$613$	−2374.00	−0.156419	−0.0782096	−	0.996937i	$-0.524920\pi$
$613$	−2374.00	−0.156419	−0.0782096	+	0.996937i	$0.524920\pi$
$614$	27708.0	1.82118
$615$	0	0
$616$	0	0
$617$	12162.0	0.793555	0.396778	−	0.917915i	$-0.370128\pi$
$617$	12162.0	0.793555	0.396778	+	0.917915i	$0.370128\pi$
$618$	0	0
$619$	−8804.00	−0.571668	−0.285834	−	0.958279i	$-0.592271\pi$
$619$	−8804.00	−0.571668	−0.285834	+	0.958279i	$0.592271\pi$
$620$	1000.00	0.0647758
$621$	0	0
$622$	−4608.00	−0.297048
$623$	0	0
$624$	0	0
$625$	625.000	0.0400000
$626$	−22026.0	−1.40629
$627$	0	0
$628$	−2378.00	−0.151103
$629$	−3780.00	−0.239616
$630$	0	0
$631$	−12688.0	−0.800478	−0.400239	−	0.916411i	$-0.631073\pi$
$631$	−12688.0	−0.800478	−0.400239	+	0.916411i	$0.631073\pi$
$632$	−10920.0	−0.687301
$633$	0	0
$634$	−11682.0	−0.731785
$635$	−6220.00	−0.388714
$636$	0	0
$637$	0	0
$638$	−5616.00	−0.348495
$639$	0	0
$640$	8295.00	0.512326
$641$	9150.00	0.563812	0.281906	−	0.959442i	$-0.409033\pi$
$641$	9150.00	0.563812	0.281906	+	0.959442i	$0.409033\pi$
$642$	0	0
$643$	−25292.0	−1.55120	−0.775598	−	0.631227i	$-0.782552\pi$
$643$	−25292.0	−1.55120	−0.775598	+	0.631227i	$0.782552\pi$
$644$	0	0
$645$	0	0
$646$	−20088.0	−1.22345
$647$	−2736.00	−0.166249	−0.0831246	−	0.996539i	$-0.526490\pi$
$647$	−2736.00	−0.166249	−0.0831246	+	0.996539i	$0.526490\pi$
$648$	0	0
$649$	576.000	0.0348382
$650$	5550.00	0.334906
$651$	0	0
$652$	−52.0000	−0.00312343
$653$	−22218.0	−1.33148	−0.665741	−	0.746183i	$-0.731884\pi$
$653$	−22218.0	−1.33148	−0.665741	+	0.746183i	$0.731884\pi$
$654$	0	0
$655$	−11640.0	−0.694370
$656$	−23430.0	−1.39449
$657$	0	0
$658$	0	0
$659$	−14520.0	−0.858299	−0.429149	−	0.903234i	$-0.641187\pi$
$659$	−14520.0	−0.858299	−0.429149	+	0.903234i	$0.641187\pi$
$660$	0	0
$661$	10618.0	0.624799	0.312400	−	0.949951i	$-0.398867\pi$
$661$	10618.0	0.624799	0.312400	+	0.949951i	$0.398867\pi$
$662$	−11076.0	−0.650273
$663$	0	0
$664$	3276.00	0.191466
$665$	0	0
$666$	0	0
$667$	9360.00	0.543359
$668$	−3720.00	−0.215466
$669$	0	0
$670$	−2940.00	−0.169526
$671$	7728.00	0.444614
$672$	0	0
$673$	1370.00	0.0784690	0.0392345	−	0.999230i	$-0.487508\pi$
$673$	1370.00	0.0784690	0.0392345	+	0.999230i	$0.487508\pi$
$674$	26994.0	1.54269
$675$	0	0
$676$	3279.00	0.186561
$677$	−13758.0	−0.781038	−0.390519	−	0.920595i	$-0.627704\pi$
$677$	−13758.0	−0.781038	−0.390519	+	0.920595i	$0.627704\pi$
$678$	0	0
$679$	0	0
$680$	−5670.00	−0.319757
$681$	0	0
$682$	14400.0	0.808511
$683$	−11988.0	−0.671608	−0.335804	−	0.941932i	$-0.609008\pi$
$683$	−11988.0	−0.671608	−0.335804	+	0.941932i	$0.609008\pi$
$684$	0	0
$685$	10590.0	0.590691
$686$	0	0
$687$	0	0
$688$	−6532.00	−0.361962
$689$	33300.0	1.84126
$690$	0	0
$691$	−32996.0	−1.81654	−0.908268	−	0.418388i	$-0.862595\pi$
$691$	−32996.0	−1.81654	−0.908268	+	0.418388i	$0.862595\pi$
$692$	426.000	0.0234019
$693$	0	0
$694$	15732.0	0.860488
$695$	11620.0	0.634204
$696$	0	0
$697$	17820.0	0.968408
$698$	18906.0	1.02522
$699$	0	0
$700$	0	0
$701$	25902.0	1.39558	0.697792	−	0.716300i	$-0.254166\pi$
$701$	25902.0	1.39558	0.697792	+	0.716300i	$0.254166\pi$
$702$	0	0
$703$	−8680.00	−0.465679
$704$	10392.0	0.556340
$705$	0	0
$706$	−10242.0	−0.545981
$707$	0	0
$708$	0	0
$709$	−27394.0	−1.45106	−0.725531	−	0.688189i	$-0.758406\pi$
$709$	−27394.0	−1.45106	−0.725531	+	0.688189i	$0.758406\pi$
$710$	4320.00	0.228347
$711$	0	0
$712$	21546.0	1.13409
$713$	−24000.0	−1.26060
$714$	0	0
$715$	8880.00	0.464466
$716$	1440.00	0.0751611
$717$	0	0
$718$	14472.0	0.752215
$719$	34848.0	1.80753	0.903763	−	0.428033i	$-0.140793\pi$
$719$	34848.0	1.80753	0.903763	+	0.428033i	$0.140793\pi$
$720$	0	0
$721$	0	0
$722$	−25551.0	−1.31705
$723$	0	0
$724$	3130.00	0.160671
$725$	1950.00	0.0998913
$726$	0	0
$727$	−28028.0	−1.42985	−0.714925	−	0.699201i	$-0.753539\pi$
$727$	−28028.0	−1.42985	−0.714925	+	0.699201i	$0.753539\pi$
$728$	0	0
$729$	0	0
$730$	6450.00	0.327021
$731$	4968.00	0.251365
$732$	0	0
$733$	−18002.0	−0.907120	−0.453560	−	0.891226i	$-0.649846\pi$
$733$	−18002.0	−0.907120	−0.453560	+	0.891226i	$0.649846\pi$
$734$	−10524.0	−0.529221
$735$	0	0
$736$	5400.00	0.270444
$737$	−4704.00	−0.235107
$738$	0	0
$739$	15284.0	0.760800	0.380400	−	0.924822i	$-0.375786\pi$
$739$	15284.0	0.760800	0.380400	+	0.924822i	$0.375786\pi$
$740$	350.000	0.0173868
$741$	0	0
$742$	0	0
$743$	18768.0	0.926691	0.463345	−	0.886178i	$-0.346649\pi$
$743$	18768.0	0.926691	0.463345	+	0.886178i	$0.346649\pi$
$744$	0	0
$745$	1290.00	0.0634388
$746$	−32406.0	−1.59044
$747$	0	0
$748$	1296.00	0.0633509
$749$	0	0
$750$	0	0
$751$	8696.00	0.422532	0.211266	−	0.977429i	$-0.432241\pi$
$751$	8696.00	0.422532	0.211266	+	0.977429i	$0.432241\pi$
$752$	1704.00	0.0826310
$753$	0	0
$754$	17316.0	0.836355
$755$	4040.00	0.194743
$756$	0	0
$757$	−38662.0	−1.85627	−0.928134	−	0.372247i	$-0.878587\pi$
$757$	−38662.0	−1.85627	−0.928134	+	0.372247i	$0.878587\pi$
$758$	−4380.00	−0.209880
$759$	0	0
$760$	−13020.0	−0.621428
$761$	23874.0	1.13723	0.568615	−	0.822604i	$-0.307479\pi$
$761$	23874.0	1.13723	0.568615	+	0.822604i	$0.307479\pi$
$762$	0	0
$763$	0	0
$764$	−3576.00	−0.169339
$765$	0	0
$766$	14616.0	0.689422
$767$	−1776.00	−0.0836084
$768$	0	0
$769$	−23618.0	−1.10753	−0.553763	−	0.832675i	$-0.686808\pi$
$769$	−23618.0	−1.10753	−0.553763	+	0.832675i	$0.686808\pi$
$770$	0	0
$771$	0	0
$772$	2666.00	0.124289
$773$	11538.0	0.536860	0.268430	−	0.963299i	$-0.413495\pi$
$773$	11538.0	0.536860	0.268430	+	0.963299i	$0.413495\pi$
$774$	0	0
$775$	−5000.00	−0.231749
$776$	6006.00	0.277839
$777$	0	0
$778$	−42138.0	−1.94180
$779$	40920.0	1.88204
$780$	0	0
$781$	6912.00	0.316685
$782$	−19440.0	−0.888968
$783$	0	0
$784$	0	0
$785$	11890.0	0.540602
$786$	0	0
$787$	14884.0	0.674152	0.337076	−	0.941478i	$-0.390562\pi$
$787$	14884.0	0.674152	0.337076	+	0.941478i	$0.390562\pi$
$788$	2718.00	0.122874
$789$	0	0
$790$	−7800.00	−0.351280
$791$	0	0
$792$	0	0
$793$	−23828.0	−1.06703
$794$	−8202.00	−0.366597
$795$	0	0
$796$	3832.00	0.170630
$797$	−11334.0	−0.503728	−0.251864	−	0.967763i	$-0.581043\pi$
$797$	−11334.0	−0.503728	−0.251864	+	0.967763i	$0.581043\pi$
$798$	0	0
$799$	−1296.00	−0.0573832
$800$	1125.00	0.0497184
$801$	0	0
$802$	−47826.0	−2.10573
$803$	10320.0	0.453530
$804$	0	0
$805$	0	0
$806$	−44400.0	−1.94035
$807$	0	0
$808$	−36414.0	−1.58545
$809$	−44730.0	−1.94391	−0.971955	−	0.235167i	$-0.924436\pi$
$809$	−44730.0	−1.94391	−0.971955	+	0.235167i	$0.924436\pi$
$810$	0	0
$811$	42748.0	1.85091	0.925453	−	0.378862i	$-0.123684\pi$
$811$	42748.0	1.85091	0.925453	+	0.378862i	$0.123684\pi$
$812$	0	0
$813$	0	0
$814$	5040.00	0.217017
$815$	260.000	0.0111747
$816$	0	0
$817$	11408.0	0.488513
$818$	26142.0	1.11740
$819$	0	0
$820$	−1650.00	−0.0702689
$821$	31686.0	1.34695	0.673477	−	0.739208i	$-0.264800\pi$
$821$	31686.0	1.34695	0.673477	+	0.739208i	$0.264800\pi$
$822$	0	0
$823$	11036.0	0.467425	0.233713	−	0.972306i	$-0.424913\pi$
$823$	11036.0	0.467425	0.233713	+	0.972306i	$0.424913\pi$
$824$	−9492.00	−0.401298
$825$	0	0
$826$	0	0
$827$	−25884.0	−1.08836	−0.544181	−	0.838968i	$-0.683159\pi$
$827$	−25884.0	−1.08836	−0.544181	+	0.838968i	$0.683159\pi$
$828$	0	0
$829$	−15950.0	−0.668234	−0.334117	−	0.942532i	$-0.608438\pi$
$829$	−15950.0	−0.668234	−0.334117	+	0.942532i	$0.608438\pi$
$830$	2340.00	0.0978585
$831$	0	0
$832$	−32042.0	−1.33516
$833$	0	0
$834$	0	0
$835$	18600.0	0.770874
$836$	2976.00	0.123119
$837$	0	0
$838$	−35928.0	−1.48104
$839$	13800.0	0.567853	0.283927	−	0.958846i	$-0.408363\pi$
$839$	13800.0	0.567853	0.283927	+	0.958846i	$0.408363\pi$
$840$	0	0
$841$	−18305.0	−0.750543
$842$	−33162.0	−1.35729
$843$	0	0
$844$	1100.00	0.0448620
$845$	−16395.0	−0.667462
$846$	0	0
$847$	0	0
$848$	31950.0	1.29383
$849$	0	0
$850$	−4050.00	−0.163428
$851$	−8400.00	−0.338365
$852$	0	0
$853$	27862.0	1.11838	0.559189	−	0.829040i	$-0.311113\pi$
$853$	27862.0	1.11838	0.559189	+	0.829040i	$0.311113\pi$
$854$	0	0
$855$	0	0
$856$	29484.0	1.17727
$857$	−7314.00	−0.291530	−0.145765	−	0.989319i	$-0.546564\pi$
$857$	−7314.00	−0.291530	−0.145765	+	0.989319i	$0.546564\pi$
$858$	0	0
$859$	28780.0	1.14314	0.571572	−	0.820552i	$-0.306334\pi$
$859$	28780.0	1.14314	0.571572	+	0.820552i	$0.306334\pi$
$860$	−460.000	−0.0182394
$861$	0	0
$862$	2160.00	0.0853479
$863$	32688.0	1.28935	0.644677	−	0.764455i	$-0.276992\pi$
$863$	32688.0	1.28935	0.644677	+	0.764455i	$0.276992\pi$
$864$	0	0
$865$	−2130.00	−0.0837251
$866$	−46866.0	−1.83900
$867$	0	0
$868$	0	0
$869$	−12480.0	−0.487175
$870$	0	0
$871$	14504.0	0.564236
$872$	−30954.0	−1.20210
$873$	0	0
$874$	−44640.0	−1.72766
$875$	0	0
$876$	0	0
$877$	36650.0	1.41115	0.705577	−	0.708633i	$-0.250688\pi$
$877$	36650.0	1.41115	0.705577	+	0.708633i	$0.250688\pi$
$878$	−29640.0	−1.13930
$879$	0	0
$880$	8520.00	0.326374
$881$	−2646.00	−0.101187	−0.0505936	−	0.998719i	$-0.516111\pi$
$881$	−2646.00	−0.101187	−0.0505936	+	0.998719i	$0.516111\pi$
$882$	0	0
$883$	10892.0	0.415113	0.207557	−	0.978223i	$-0.433449\pi$
$883$	10892.0	0.415113	0.207557	+	0.978223i	$0.433449\pi$
$884$	−3996.00	−0.152036
$885$	0	0
$886$	−48348.0	−1.83328
$887$	−43464.0	−1.64530	−0.822648	−	0.568550i	$-0.807504\pi$
$887$	−43464.0	−1.64530	−0.822648	+	0.568550i	$0.807504\pi$
$888$	0	0
$889$	0	0
$890$	15390.0	0.579634
$891$	0	0
$892$	−1964.00	−0.0737215
$893$	−2976.00	−0.111521
$894$	0	0
$895$	−7200.00	−0.268904
$896$	0	0
$897$	0	0
$898$	27054.0	1.00535
$899$	−15600.0	−0.578742
$900$	0	0
$901$	−24300.0	−0.898502
$902$	−23760.0	−0.877075
$903$	0	0
$904$	−22806.0	−0.839067
$905$	−15650.0	−0.574833
$906$	0	0
$907$	−14884.0	−0.544890	−0.272445	−	0.962171i	$-0.587832\pi$
$907$	−14884.0	−0.544890	−0.272445	+	0.962171i	$0.587832\pi$
$908$	660.000	0.0241221
$909$	0	0
$910$	0	0
$911$	1248.00	0.0453876	0.0226938	−	0.999742i	$-0.492776\pi$
$911$	1248.00	0.0453876	0.0226938	+	0.999742i	$0.492776\pi$
$912$	0	0
$913$	3744.00	0.135716
$914$	11010.0	0.398445
$915$	0	0
$916$	1906.00	0.0687511
$917$	0	0
$918$	0	0
$919$	−6640.00	−0.238339	−0.119169	−	0.992874i	$-0.538023\pi$
$919$	−6640.00	−0.238339	−0.119169	+	0.992874i	$0.538023\pi$
$920$	−12600.0	−0.451532
$921$	0	0
$922$	−52686.0	−1.88191
$923$	−21312.0	−0.760014
$924$	0	0
$925$	−1750.00	−0.0622050
$926$	−3516.00	−0.124776
$927$	0	0
$928$	3510.00	0.124161
$929$	29946.0	1.05758	0.528792	−	0.848751i	$-0.322645\pi$
$929$	29946.0	1.05758	0.528792	+	0.848751i	$0.322645\pi$
$930$	0	0
$931$	0	0
$932$	1458.00	0.0512429
$933$	0	0
$934$	−20628.0	−0.722665
$935$	−6480.00	−0.226651
$936$	0	0
$937$	−45002.0	−1.56900	−0.784499	−	0.620130i	$-0.787080\pi$
$937$	−45002.0	−1.56900	−0.784499	+	0.620130i	$0.787080\pi$
$938$	0	0
$939$	0	0
$940$	120.000	0.00416380
$941$	6090.00	0.210976	0.105488	−	0.994421i	$-0.466360\pi$
$941$	6090.00	0.210976	0.105488	+	0.994421i	$0.466360\pi$
$942$	0	0
$943$	39600.0	1.36750
$944$	−1704.00	−0.0587505
$945$	0	0
$946$	−6624.00	−0.227658
$947$	−56388.0	−1.93491	−0.967457	−	0.253035i	$-0.918571\pi$
$947$	−56388.0	−1.93491	−0.967457	+	0.253035i	$0.918571\pi$
$948$	0	0
$949$	−31820.0	−1.08843
$950$	−9300.00	−0.317612
$951$	0	0
$952$	0	0
$953$	−10854.0	−0.368936	−0.184468	−	0.982839i	$-0.559056\pi$
$953$	−10854.0	−0.368936	−0.184468	+	0.982839i	$0.559056\pi$
$954$	0	0
$955$	17880.0	0.605846
$956$	−1176.00	−0.0397851
$957$	0	0
$958$	−6840.00	−0.230679
$959$	0	0
$960$	0	0
$961$	10209.0	0.342687
$962$	−15540.0	−0.520821
$963$	0	0
$964$	−866.000	−0.0289336
$965$	−13330.0	−0.444671
$966$	0	0
$967$	−42316.0	−1.40723	−0.703615	−	0.710582i	$-0.748432\pi$
$967$	−42316.0	−1.40723	−0.703615	+	0.710582i	$0.748432\pi$
$968$	−15855.0	−0.526445
$969$	0	0
$970$	4290.00	0.142004
$971$	24480.0	0.809063	0.404532	−	0.914524i	$-0.367435\pi$
$971$	24480.0	0.809063	0.404532	+	0.914524i	$0.367435\pi$
$972$	0	0
$973$	0	0
$974$	9228.00	0.303577
$975$	0	0
$976$	−22862.0	−0.749790
$977$	6906.00	0.226144	0.113072	−	0.993587i	$-0.463931\pi$
$977$	6906.00	0.226144	0.113072	+	0.993587i	$0.463931\pi$
$978$	0	0
$979$	24624.0	0.803868
$980$	0	0
$981$	0	0
$982$	−56736.0	−1.84371
$983$	6960.00	0.225829	0.112914	−	0.993605i	$-0.463981\pi$
$983$	6960.00	0.225829	0.112914	+	0.993605i	$0.463981\pi$
$984$	0	0
$985$	−13590.0	−0.439608
$986$	−12636.0	−0.408126
$987$	0	0
$988$	−9176.00	−0.295473
$989$	11040.0	0.354956
$990$	0	0
$991$	47792.0	1.53195	0.765975	−	0.642870i	$-0.222256\pi$
$991$	47792.0	1.53195	0.765975	+	0.642870i	$0.222256\pi$
$992$	−9000.00	−0.288055
$993$	0	0
$994$	0	0
$995$	−19160.0	−0.610465
$996$	0	0
$997$	−9938.00	−0.315687	−0.157843	−	0.987464i	$-0.550454\pi$
$997$	−9938.00	−0.315687	−0.157843	+	0.987464i	$0.550454\pi$
$998$	−29868.0	−0.947350
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.4.a.c.1.1		1
3.2	odd	2		735.4.a.i.1.1		1
7.6	odd	2		45.4.a.b.1.1		1
21.20	even	2		15.4.a.b.1.1	✓	1
28.27	even	2		720.4.a.r.1.1		1
35.13	even	4		225.4.b.d.199.2		2
35.27	even	4		225.4.b.d.199.1		2
35.34	odd	2		225.4.a.g.1.1		1
63.13	odd	6		405.4.e.k.136.1		2
63.20	even	6		405.4.e.d.271.1		2
63.34	odd	6		405.4.e.k.271.1		2
63.41	even	6		405.4.e.d.136.1		2
84.83	odd	2		240.4.a.f.1.1		1
105.62	odd	4		75.4.b.a.49.2		2
105.83	odd	4		75.4.b.a.49.1		2
105.104	even	2		75.4.a.a.1.1		1
168.83	odd	2		960.4.a.l.1.1		1
168.125	even	2		960.4.a.bi.1.1		1
231.230	odd	2		1815.4.a.a.1.1		1
420.83	even	4		1200.4.f.m.49.2		2
420.167	even	4		1200.4.f.m.49.1		2
420.419	odd	2		1200.4.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.a.b.1.1	✓	1	21.20	even	2
45.4.a.b.1.1		1	7.6	odd	2
75.4.a.a.1.1		1	105.104	even	2
75.4.b.a.49.1		2	105.83	odd	4
75.4.b.a.49.2		2	105.62	odd	4
225.4.a.g.1.1		1	35.34	odd	2
225.4.b.d.199.1		2	35.27	even	4
225.4.b.d.199.2		2	35.13	even	4
240.4.a.f.1.1		1	84.83	odd	2
405.4.e.d.136.1		2	63.41	even	6
405.4.e.d.271.1		2	63.20	even	6
405.4.e.k.136.1		2	63.13	odd	6
405.4.e.k.271.1		2	63.34	odd	6
720.4.a.r.1.1		1	28.27	even	2
735.4.a.i.1.1		1	3.2	odd	2
960.4.a.l.1.1		1	168.83	odd	2
960.4.a.bi.1.1		1	168.125	even	2
1200.4.a.o.1.1		1	420.419	odd	2
1200.4.f.m.49.1		2	420.167	even	4
1200.4.f.m.49.2		2	420.83	even	4
1815.4.a.a.1.1		1	231.230	odd	2
2205.4.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:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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