LMFDB - Embedded newform 2205.4.a.a.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
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)

$f(q)$

$=$

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

$q-5.00000 q^{2} +17.0000 q^{4} -5.00000 q^{5} -45.0000 q^{8} +25.0000 q^{10} -50.0000 q^{11} +20.0000 q^{13} +89.0000 q^{16} -10.0000 q^{17} +44.0000 q^{19} -85.0000 q^{20} +250.000 q^{22} -120.000 q^{23} +25.0000 q^{25} -100.000 q^{26} +50.0000 q^{29} -108.000 q^{31} -85.0000 q^{32} +50.0000 q^{34} -40.0000 q^{37} -220.000 q^{38} +225.000 q^{40} +400.000 q^{41} +280.000 q^{43} -850.000 q^{44} +600.000 q^{46} -280.000 q^{47} -125.000 q^{50} +340.000 q^{52} +610.000 q^{53} +250.000 q^{55} -250.000 q^{58} +50.0000 q^{59} +518.000 q^{61} +540.000 q^{62} -287.000 q^{64} -100.000 q^{65} -180.000 q^{67} -170.000 q^{68} -700.000 q^{71} +410.000 q^{73} +200.000 q^{74} +748.000 q^{76} -516.000 q^{79} -445.000 q^{80} -2000.00 q^{82} +660.000 q^{83} +50.0000 q^{85} -1400.00 q^{86} +2250.00 q^{88} -1500.00 q^{89} -2040.00 q^{92} +1400.00 q^{94} -220.000 q^{95} +1630.00 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−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
$7$	0	0
$7$	0	0
$8$	−45.0000	−1.98874
$9$	0	0
$10$	25.0000	0.790569
$11$	−50.0000	−1.37051	−0.685253	−	0.728305i	$-0.740308\pi$
$11$	−50.0000	−1.37051	−0.685253	+	0.728305i	$0.740308\pi$
$12$	0	0
$13$	20.0000	0.426692	0.213346	−	0.976977i	$-0.431564\pi$
$13$	20.0000	0.426692	0.213346	+	0.976977i	$0.431564\pi$
$14$	0	0
$15$	0	0
$16$	89.0000	1.39062
$17$	−10.0000	−0.142668	−0.0713340	−	0.997452i	$-0.522726\pi$
$17$	−10.0000	−0.142668	−0.0713340	+	0.997452i	$0.522726\pi$
$18$	0	0
$19$	44.0000	0.531279	0.265639	−	0.964072i	$-0.414417\pi$
$19$	44.0000	0.531279	0.265639	+	0.964072i	$0.414417\pi$
$20$	−85.0000	−0.950329
$21$	0	0
$22$	250.000	2.42274
$23$	−120.000	−1.08790	−0.543951	−	0.839117i	$-0.683072\pi$
$23$	−120.000	−1.08790	−0.543951	+	0.839117i	$0.683072\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−100.000	−0.754293
$27$	0	0
$28$	0	0
$29$	50.0000	0.320164	0.160082	−	0.987104i	$-0.448824\pi$
$29$	50.0000	0.320164	0.160082	+	0.987104i	$0.448824\pi$
$30$	0	0
$31$	−108.000	−0.625722	−0.312861	−	0.949799i	$-0.601287\pi$
$31$	−108.000	−0.625722	−0.312861	+	0.949799i	$0.601287\pi$
$32$	−85.0000	−0.469563
$33$	0	0
$34$	50.0000	0.252204
$35$	0	0
$36$	0	0
$37$	−40.0000	−0.177729	−0.0888643	−	0.996044i	$-0.528324\pi$
$37$	−40.0000	−0.177729	−0.0888643	+	0.996044i	$0.528324\pi$
$38$	−220.000	−0.939177
$39$	0	0
$40$	225.000	0.889391
$41$	400.000	1.52365	0.761823	−	0.647785i	$-0.224304\pi$
$41$	400.000	1.52365	0.761823	+	0.647785i	$0.224304\pi$
$42$	0	0
$43$	280.000	0.993014	0.496507	−	0.868033i	$-0.334616\pi$
$43$	280.000	0.993014	0.496507	+	0.868033i	$0.334616\pi$
$44$	−850.000	−2.91233
$45$	0	0
$46$	600.000	1.92316
$47$	−280.000	−0.868983	−0.434491	−	0.900676i	$-0.643072\pi$
$47$	−280.000	−0.868983	−0.434491	+	0.900676i	$0.643072\pi$
$48$	0	0
$49$	0	0
$50$	−125.000	−0.353553
$51$	0	0
$52$	340.000	0.906721
$53$	610.000	1.58094	0.790471	−	0.612499i	$-0.209836\pi$
$53$	610.000	1.58094	0.790471	+	0.612499i	$0.209836\pi$
$54$	0	0
$55$	250.000	0.612909
$56$	0	0
$57$	0	0
$58$	−250.000	−0.565976
$59$	50.0000	0.110330	0.0551648	−	0.998477i	$-0.482432\pi$
$59$	50.0000	0.110330	0.0551648	+	0.998477i	$0.482432\pi$
$60$	0	0
$61$	518.000	1.08726	0.543632	−	0.839324i	$-0.317049\pi$
$61$	518.000	1.08726	0.543632	+	0.839324i	$0.317049\pi$
$62$	540.000	1.10613
$63$	0	0
$64$	−287.000	−0.560547
$65$	−100.000	−0.190823
$66$	0	0
$67$	−180.000	−0.328216	−0.164108	−	0.986442i	$-0.552475\pi$
$67$	−180.000	−0.328216	−0.164108	+	0.986442i	$0.552475\pi$
$68$	−170.000	−0.303170
$69$	0	0
$70$	0	0
$71$	−700.000	−1.17007	−0.585033	−	0.811009i	$-0.698919\pi$
$71$	−700.000	−1.17007	−0.585033	+	0.811009i	$0.698919\pi$
$72$	0	0
$73$	410.000	0.657354	0.328677	−	0.944442i	$-0.393397\pi$
$73$	410.000	0.657354	0.328677	+	0.944442i	$0.393397\pi$
$74$	200.000	0.314183
$75$	0	0
$76$	748.000	1.12897
$77$	0	0
$78$	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
$82$	−2000.00	−2.69345
$83$	660.000	0.872824	0.436412	−	0.899747i	$-0.356249\pi$
$83$	660.000	0.872824	0.436412	+	0.899747i	$0.356249\pi$
$84$	0	0
$85$	50.0000	0.0638031
$86$	−1400.00	−1.75542
$87$	0	0
$88$	2250.00	2.72558
$89$	−1500.00	−1.78651	−0.893257	−	0.449547i	$-0.851585\pi$
$89$	−1500.00	−1.78651	−0.893257	+	0.449547i	$0.851585\pi$
$90$	0	0
$91$	0	0
$92$	−2040.00	−2.31179
$93$	0	0
$94$	1400.00	1.53616
$95$	−220.000	−0.237595
$96$	0	0
$97$	1630.00	1.70620	0.853100	−	0.521747i	$-0.174720\pi$
$97$	1630.00	1.70620	0.853100	+	0.521747i	$0.174720\pi$
$98$	0	0
$99$	0	0
$100$	425.000	0.425000
$101$	−450.000	−0.443333	−0.221667	−	0.975122i	$-0.571150\pi$
$101$	−450.000	−0.443333	−0.221667	+	0.975122i	$0.571150\pi$
$102$	0	0
$103$	−770.000	−0.736605	−0.368303	−	0.929706i	$-0.620061\pi$
$103$	−770.000	−0.736605	−0.368303	+	0.929706i	$0.620061\pi$
$104$	−900.000	−0.848579
$105$	0	0
$106$	−3050.00	−2.79474
$107$	−660.000	−0.596305	−0.298152	−	0.954518i	$-0.596370\pi$
$107$	−660.000	−0.596305	−0.298152	+	0.954518i	$0.596370\pi$
$108$	0	0
$109$	1754.00	1.54131	0.770655	−	0.637253i	$-0.219929\pi$
$109$	1754.00	1.54131	0.770655	+	0.637253i	$0.219929\pi$
$110$	−1250.00	−1.08348
$111$	0	0
$112$	0	0
$113$	310.000	0.258074	0.129037	−	0.991640i	$-0.458811\pi$
$113$	310.000	0.258074	0.129037	+	0.991640i	$0.458811\pi$
$114$	0	0
$115$	600.000	0.486524
$116$	850.000	0.680349
$117$	0	0
$118$	−250.000	−0.195037
$119$	0	0
$120$	0	0
$121$	1169.00	0.878287
$122$	−2590.00	−1.92203
$123$	0	0
$124$	−1836.00	−1.32966
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1070.00	−0.747615	−0.373808	−	0.927506i	$-0.621948\pi$
$127$	−1070.00	−0.747615	−0.373808	+	0.927506i	$0.621948\pi$
$128$	2115.00	1.46048
$129$	0	0
$130$	500.000	0.337330
$131$	1950.00	1.30055	0.650276	−	0.759698i	$-0.274653\pi$
$131$	1950.00	1.30055	0.650276	+	0.759698i	$0.274653\pi$
$132$	0	0
$133$	0	0
$134$	900.000	0.580210
$135$	0	0
$136$	450.000	0.283729
$137$	−1050.00	−0.654800	−0.327400	−	0.944886i	$-0.606172\pi$
$137$	−1050.00	−0.654800	−0.327400	+	0.944886i	$0.606172\pi$
$138$	0	0
$139$	−1676.00	−1.02271	−0.511354	−	0.859370i	$-0.670856\pi$
$139$	−1676.00	−1.02271	−0.511354	+	0.859370i	$0.670856\pi$
$140$	0	0
$141$	0	0
$142$	3500.00	2.06840
$143$	−1000.00	−0.584785
$144$	0	0
$145$	−250.000	−0.143182
$146$	−2050.00	−1.16205
$147$	0	0
$148$	−680.000	−0.377673
$149$	−2050.00	−1.12713	−0.563566	−	0.826071i	$-0.690571\pi$
$149$	−2050.00	−1.12713	−0.563566	+	0.826071i	$0.690571\pi$
$150$	0	0
$151$	448.000	0.241442	0.120721	−	0.992686i	$-0.461479\pi$
$151$	448.000	0.241442	0.120721	+	0.992686i	$0.461479\pi$
$152$	−1980.00	−1.05657
$153$	0	0
$154$	0	0
$155$	540.000	0.279831
$156$	0	0
$157$	100.000	0.0508336	0.0254168	−	0.999677i	$-0.491909\pi$
$157$	100.000	0.0508336	0.0254168	+	0.999677i	$0.491909\pi$
$158$	2580.00	1.29907
$159$	0	0
$160$	425.000	0.209995
$161$	0	0
$162$	0	0
$163$	−1900.00	−0.913003	−0.456501	−	0.889723i	$-0.650898\pi$
$163$	−1900.00	−0.913003	−0.456501	+	0.889723i	$0.650898\pi$
$164$	6800.00	3.23775
$165$	0	0
$166$	−3300.00	−1.54295
$167$	1920.00	0.889665	0.444833	−	0.895614i	$-0.353263\pi$
$167$	1920.00	0.889665	0.444833	+	0.895614i	$0.353263\pi$
$168$	0	0
$169$	−1797.00	−0.817934
$170$	−250.000	−0.112789
$171$	0	0
$172$	4760.00	2.11015
$173$	2550.00	1.12065	0.560326	−	0.828272i	$-0.310676\pi$
$173$	2550.00	1.12065	0.560326	+	0.828272i	$0.310676\pi$
$174$	0	0
$175$	0	0
$176$	−4450.00	−1.90586
$177$	0	0
$178$	7500.00	3.15814
$179$	−3650.00	−1.52410	−0.762050	−	0.647518i	$-0.775807\pi$
$179$	−3650.00	−1.52410	−0.762050	+	0.647518i	$0.775807\pi$
$180$	0	0
$181$	4342.00	1.78308	0.891542	−	0.452937i	$-0.149624\pi$
$181$	4342.00	1.78308	0.891542	+	0.452937i	$0.149624\pi$
$182$	0	0
$183$	0	0
$184$	5400.00	2.16355
$185$	200.000	0.0794827
$186$	0	0
$187$	500.000	0.195527
$188$	−4760.00	−1.84659
$189$	0	0
$190$	1100.00	0.420013
$191$	3500.00	1.32592	0.662961	−	0.748654i	$-0.269299\pi$
$191$	3500.00	1.32592	0.662961	+	0.748654i	$0.269299\pi$
$192$	0	0
$193$	3350.00	1.24942	0.624711	−	0.780856i	$-0.285217\pi$
$193$	3350.00	1.24942	0.624711	+	0.780856i	$0.285217\pi$
$194$	−8150.00	−3.01616
$195$	0	0
$196$	0	0
$197$	−90.0000	−0.0325494	−0.0162747	−	0.999868i	$-0.505181\pi$
$197$	−90.0000	−0.0325494	−0.0162747	+	0.999868i	$0.505181\pi$
$198$	0	0
$199$	−3664.00	−1.30520	−0.652598	−	0.757704i	$-0.726321\pi$
$199$	−3664.00	−1.30520	−0.652598	+	0.757704i	$0.726321\pi$
$200$	−1125.00	−0.397748
$201$	0	0
$202$	2250.00	0.783710
$203$	0	0
$204$	0	0
$205$	−2000.00	−0.681395
$206$	3850.00	1.30215
$207$	0	0
$208$	1780.00	0.593369
$209$	−2200.00	−0.728120
$210$	0	0
$211$	−268.000	−0.0874402	−0.0437201	−	0.999044i	$-0.513921\pi$
$211$	−268.000	−0.0874402	−0.0437201	+	0.999044i	$0.513921\pi$
$212$	10370.0	3.35950
$213$	0	0
$214$	3300.00	1.05413
$215$	−1400.00	−0.444089
$216$	0	0
$217$	0	0
$218$	−8770.00	−2.72468
$219$	0	0
$220$	4250.00	1.30243
$221$	−200.000	−0.0608754
$222$	0	0
$223$	3670.00	1.10207	0.551034	−	0.834482i	$-0.314233\pi$
$223$	3670.00	1.10207	0.551034	+	0.834482i	$0.314233\pi$
$224$	0	0
$225$	0	0
$226$	−1550.00	−0.456214
$227$	3760.00	1.09938	0.549692	−	0.835368i	$-0.314745\pi$
$227$	3760.00	1.09938	0.549692	+	0.835368i	$0.314745\pi$
$228$	0	0
$229$	1434.00	0.413805	0.206903	−	0.978362i	$-0.433662\pi$
$229$	1434.00	0.413805	0.206903	+	0.978362i	$0.433662\pi$
$230$	−3000.00	−0.860061
$231$	0	0
$232$	−2250.00	−0.636723
$233$	3450.00	0.970030	0.485015	−	0.874506i	$-0.338814\pi$
$233$	3450.00	0.970030	0.485015	+	0.874506i	$0.338814\pi$
$234$	0	0
$235$	1400.00	0.388621
$236$	850.000	0.234450
$237$	0	0
$238$	0	0
$239$	4900.00	1.32617	0.663085	−	0.748544i	$-0.269247\pi$
$239$	4900.00	1.32617	0.663085	+	0.748544i	$0.269247\pi$
$240$	0	0
$241$	−4822.00	−1.28885	−0.644424	−	0.764668i	$-0.722903\pi$
$241$	−4822.00	−1.28885	−0.644424	+	0.764668i	$0.722903\pi$
$242$	−5845.00	−1.55261
$243$	0	0
$244$	8806.00	2.31044
$245$	0	0
$246$	0	0
$247$	880.000	0.226693
$248$	4860.00	1.24440
$249$	0	0
$250$	625.000	0.158114
$251$	−4650.00	−1.16934	−0.584672	−	0.811270i	$-0.698777\pi$
$251$	−4650.00	−1.16934	−0.584672	+	0.811270i	$0.698777\pi$
$252$	0	0
$253$	6000.00	1.49098
$254$	5350.00	1.32161
$255$	0	0
$256$	−8279.00	−2.02124
$257$	5130.00	1.24514	0.622569	−	0.782565i	$-0.286089\pi$
$257$	5130.00	1.24514	0.622569	+	0.782565i	$0.286089\pi$
$258$	0	0
$259$	0	0
$260$	−1700.00	−0.405498
$261$	0	0
$262$	−9750.00	−2.29907
$263$	1280.00	0.300107	0.150054	−	0.988678i	$-0.452055\pi$
$263$	1280.00	0.300107	0.150054	+	0.988678i	$0.452055\pi$
$264$	0	0
$265$	−3050.00	−0.707019
$266$	0	0
$267$	0	0
$268$	−3060.00	−0.697460
$269$	3350.00	0.759305	0.379653	−	0.925129i	$-0.376044\pi$
$269$	3350.00	0.759305	0.379653	+	0.925129i	$0.376044\pi$
$270$	0	0
$271$	−5512.00	−1.23554	−0.617768	−	0.786361i	$-0.711963\pi$
$271$	−5512.00	−1.23554	−0.617768	+	0.786361i	$0.711963\pi$
$272$	−890.000	−0.198398
$273$	0	0
$274$	5250.00	1.15753
$275$	−1250.00	−0.274101
$276$	0	0
$277$	4920.00	1.06720	0.533600	−	0.845737i	$-0.320839\pi$
$277$	4920.00	1.06720	0.533600	+	0.845737i	$0.320839\pi$
$278$	8380.00	1.80791
$279$	0	0
$280$	0	0
$281$	−4500.00	−0.955329	−0.477665	−	0.878542i	$-0.658517\pi$
$281$	−4500.00	−0.955329	−0.477665	+	0.878542i	$0.658517\pi$
$282$	0	0
$283$	6900.00	1.44934	0.724669	−	0.689098i	$-0.241993\pi$
$283$	6900.00	1.44934	0.724669	+	0.689098i	$0.241993\pi$
$284$	−11900.0	−2.48639
$285$	0	0
$286$	5000.00	1.03376
$287$	0	0
$288$	0	0
$289$	−4813.00	−0.979646
$290$	1250.00	0.253112
$291$	0	0
$292$	6970.00	1.39688
$293$	1530.00	0.305063	0.152532	−	0.988299i	$-0.451257\pi$
$293$	1530.00	0.305063	0.152532	+	0.988299i	$0.451257\pi$
$294$	0	0
$295$	−250.000	−0.0493409
$296$	1800.00	0.353456
$297$	0	0
$298$	10250.0	1.99251
$299$	−2400.00	−0.464199
$300$	0	0
$301$	0	0
$302$	−2240.00	−0.426813
$303$	0	0
$304$	3916.00	0.738809
$305$	−2590.00	−0.486239
$306$	0	0
$307$	−3040.00	−0.565153	−0.282576	−	0.959245i	$-0.591189\pi$
$307$	−3040.00	−0.565153	−0.282576	+	0.959245i	$0.591189\pi$
$308$	0	0
$309$	0	0
$310$	−2700.00	−0.494676
$311$	−5700.00	−1.03928	−0.519642	−	0.854384i	$-0.673935\pi$
$311$	−5700.00	−1.03928	−0.519642	+	0.854384i	$0.673935\pi$
$312$	0	0
$313$	−3110.00	−0.561622	−0.280811	−	0.959763i	$-0.590603\pi$
$313$	−3110.00	−0.561622	−0.280811	+	0.959763i	$0.590603\pi$
$314$	−500.000	−0.0898619
$315$	0	0
$316$	−8772.00	−1.56159
$317$	950.000	0.168320	0.0841598	−	0.996452i	$-0.473179\pi$
$317$	950.000	0.168320	0.0841598	+	0.996452i	$0.473179\pi$
$318$	0	0
$319$	−2500.00	−0.438787
$320$	1435.00	0.250684
$321$	0	0
$322$	0	0
$323$	−440.000	−0.0757965
$324$	0	0
$325$	500.000	0.0853385
$326$	9500.00	1.61398
$327$	0	0
$328$	−18000.0	−3.03013
$329$	0	0
$330$	0	0
$331$	2292.00	0.380603	0.190302	−	0.981726i	$-0.439053\pi$
$331$	2292.00	0.380603	0.190302	+	0.981726i	$0.439053\pi$
$332$	11220.0	1.85475
$333$	0	0
$334$	−9600.00	−1.57272
$335$	900.000	0.146783
$336$	0	0
$337$	−7730.00	−1.24950	−0.624748	−	0.780827i	$-0.714798\pi$
$337$	−7730.00	−1.24950	−0.624748	+	0.780827i	$0.714798\pi$
$338$	8985.00	1.44592
$339$	0	0
$340$	850.000	0.135582
$341$	5400.00	0.857555
$342$	0	0
$343$	0	0
$344$	−12600.0	−1.97484
$345$	0	0
$346$	−12750.0	−1.98105
$347$	1120.00	0.173270	0.0866351	−	0.996240i	$-0.472389\pi$
$347$	1120.00	0.173270	0.0866351	+	0.996240i	$0.472389\pi$
$348$	0	0
$349$	−1186.00	−0.181906	−0.0909529	−	0.995855i	$-0.528991\pi$
$349$	−1186.00	−0.181906	−0.0909529	+	0.995855i	$0.528991\pi$
$350$	0	0
$351$	0	0
$352$	4250.00	0.643539
$353$	3630.00	0.547324	0.273662	−	0.961826i	$-0.411765\pi$
$353$	3630.00	0.547324	0.273662	+	0.961826i	$0.411765\pi$
$354$	0	0
$355$	3500.00	0.523270
$356$	−25500.0	−3.79634
$357$	0	0
$358$	18250.0	2.69425
$359$	1800.00	0.264625	0.132312	−	0.991208i	$-0.457760\pi$
$359$	1800.00	0.264625	0.132312	+	0.991208i	$0.457760\pi$
$360$	0	0
$361$	−4923.00	−0.717743
$362$	−21710.0	−3.15208
$363$	0	0
$364$	0	0
$365$	−2050.00	−0.293978
$366$	0	0
$367$	−8490.00	−1.20756	−0.603780	−	0.797151i	$-0.706339\pi$
$367$	−8490.00	−1.20756	−0.603780	+	0.797151i	$0.706339\pi$
$368$	−10680.0	−1.51286
$369$	0	0
$370$	−1000.00	−0.140507
$371$	0	0
$372$	0	0
$373$	100.000	0.0138815	0.00694076	−	0.999976i	$-0.497791\pi$
$373$	100.000	0.0138815	0.00694076	+	0.999976i	$0.497791\pi$
$374$	−2500.00	−0.345647
$375$	0	0
$376$	12600.0	1.72818
$377$	1000.00	0.136612
$378$	0	0
$379$	−8084.00	−1.09564	−0.547820	−	0.836597i	$-0.684542\pi$
$379$	−8084.00	−1.09564	−0.547820	+	0.836597i	$0.684542\pi$
$380$	−3740.00	−0.504889
$381$	0	0
$382$	−17500.0	−2.34392
$383$	−9480.00	−1.26477	−0.632383	−	0.774656i	$-0.717923\pi$
$383$	−9480.00	−1.26477	−0.632383	+	0.774656i	$0.717923\pi$
$384$	0	0
$385$	0	0
$386$	−16750.0	−2.20869
$387$	0	0
$388$	27710.0	3.62568
$389$	10950.0	1.42722	0.713608	−	0.700545i	$-0.247060\pi$
$389$	10950.0	1.42722	0.713608	+	0.700545i	$0.247060\pi$
$390$	0	0
$391$	1200.00	0.155209
$392$	0	0
$393$	0	0
$394$	450.000	0.0575398
$395$	2580.00	0.328643
$396$	0	0
$397$	−13840.0	−1.74965	−0.874823	−	0.484442i	$-0.839023\pi$
$397$	−13840.0	−1.74965	−0.874823	+	0.484442i	$0.839023\pi$
$398$	18320.0	2.30728
$399$	0	0
$400$	2225.00	0.278125
$401$	−9300.00	−1.15815	−0.579077	−	0.815273i	$-0.696587\pi$
$401$	−9300.00	−1.15815	−0.579077	+	0.815273i	$0.696587\pi$
$402$	0	0
$403$	−2160.00	−0.266991
$404$	−7650.00	−0.942083
$405$	0	0
$406$	0	0
$407$	2000.00	0.243578
$408$	0	0
$409$	2854.00	0.345040	0.172520	−	0.985006i	$-0.444809\pi$
$409$	2854.00	0.345040	0.172520	+	0.985006i	$0.444809\pi$
$410$	10000.0	1.20455
$411$	0	0
$412$	−13090.0	−1.56529
$413$	0	0
$414$	0	0
$415$	−3300.00	−0.390339
$416$	−1700.00	−0.200359
$417$	0	0
$418$	11000.0	1.28715
$419$	1150.00	0.134084	0.0670420	−	0.997750i	$-0.478644\pi$
$419$	1150.00	0.134084	0.0670420	+	0.997750i	$0.478644\pi$
$420$	0	0
$421$	−11162.0	−1.29217	−0.646084	−	0.763266i	$-0.723594\pi$
$421$	−11162.0	−1.29217	−0.646084	+	0.763266i	$0.723594\pi$
$422$	1340.00	0.154574
$423$	0	0
$424$	−27450.0	−3.14408
$425$	−250.000	−0.0285336
$426$	0	0
$427$	0	0
$428$	−11220.0	−1.26715
$429$	0	0
$430$	7000.00	0.785046
$431$	1200.00	0.134111	0.0670556	−	0.997749i	$-0.478639\pi$
$431$	1200.00	0.134111	0.0670556	+	0.997749i	$0.478639\pi$
$432$	0	0
$433$	−1510.00	−0.167589	−0.0837944	−	0.996483i	$-0.526704\pi$
$433$	−1510.00	−0.167589	−0.0837944	+	0.996483i	$0.526704\pi$
$434$	0	0
$435$	0	0
$436$	29818.0	3.27528
$437$	−5280.00	−0.577979
$438$	0	0
$439$	−424.000	−0.0460966	−0.0230483	−	0.999734i	$-0.507337\pi$
$439$	−424.000	−0.0460966	−0.0230483	+	0.999734i	$0.507337\pi$
$440$	−11250.0	−1.21892
$441$	0	0
$442$	1000.00	0.107613
$443$	−12360.0	−1.32560	−0.662801	−	0.748796i	$-0.730632\pi$
$443$	−12360.0	−1.32560	−0.662801	+	0.748796i	$0.730632\pi$
$444$	0	0
$445$	7500.00	0.798953
$446$	−18350.0	−1.94820
$447$	0	0
$448$	0	0
$449$	1300.00	0.136639	0.0683194	−	0.997664i	$-0.478236\pi$
$449$	1300.00	0.136639	0.0683194	+	0.997664i	$0.478236\pi$
$450$	0	0
$451$	−20000.0	−2.08817
$452$	5270.00	0.548407
$453$	0	0
$454$	−18800.0	−1.94345
$455$	0	0
$456$	0	0
$457$	−7190.00	−0.735961	−0.367980	−	0.929834i	$-0.619951\pi$
$457$	−7190.00	−0.735961	−0.367980	+	0.929834i	$0.619951\pi$
$458$	−7170.00	−0.731511
$459$	0	0
$460$	10200.0	1.03386
$461$	−150.000	−0.0151544	−0.00757722	−	0.999971i	$-0.502412\pi$
$461$	−150.000	−0.0151544	−0.00757722	+	0.999971i	$0.502412\pi$
$462$	0	0
$463$	2670.00	0.268003	0.134002	−	0.990981i	$-0.457217\pi$
$463$	2670.00	0.268003	0.134002	+	0.990981i	$0.457217\pi$
$464$	4450.00	0.445229
$465$	0	0
$466$	−17250.0	−1.71479
$467$	1180.00	0.116925	0.0584624	−	0.998290i	$-0.481380\pi$
$467$	1180.00	0.116925	0.0584624	+	0.998290i	$0.481380\pi$
$468$	0	0
$469$	0	0
$470$	−7000.00	−0.686991
$471$	0	0
$472$	−2250.00	−0.219417
$473$	−14000.0	−1.36093
$474$	0	0
$475$	1100.00	0.106256
$476$	0	0
$477$	0	0
$478$	−24500.0	−2.34436
$479$	−14100.0	−1.34498	−0.672490	−	0.740106i	$-0.734775\pi$
$479$	−14100.0	−1.34498	−0.672490	+	0.740106i	$0.734775\pi$
$480$	0	0
$481$	−800.000	−0.0758355
$482$	24110.0	2.27838
$483$	0	0
$484$	19873.0	1.86636
$485$	−8150.00	−0.763036
$486$	0	0
$487$	−9850.00	−0.916522	−0.458261	−	0.888818i	$-0.651527\pi$
$487$	−9850.00	−0.916522	−0.458261	+	0.888818i	$0.651527\pi$
$488$	−23310.0	−2.16228
$489$	0	0
$490$	0	0
$491$	2450.00	0.225187	0.112594	−	0.993641i	$-0.464084\pi$
$491$	2450.00	0.225187	0.112594	+	0.993641i	$0.464084\pi$
$492$	0	0
$493$	−500.000	−0.0456772
$494$	−4400.00	−0.400740
$495$	0	0
$496$	−9612.00	−0.870144
$497$	0	0
$498$	0	0
$499$	−17036.0	−1.52833	−0.764164	−	0.645021i	$-0.776848\pi$
$499$	−17036.0	−1.52833	−0.764164	+	0.645021i	$0.776848\pi$
$500$	−2125.00	−0.190066
$501$	0	0
$502$	23250.0	2.06713
$503$	−20600.0	−1.82606	−0.913030	−	0.407891i	$-0.866264\pi$
$503$	−20600.0	−1.82606	−0.913030	+	0.407891i	$0.866264\pi$
$504$	0	0
$505$	2250.00	0.198265
$506$	−30000.0	−2.63570
$507$	0	0
$508$	−18190.0	−1.58868
$509$	5750.00	0.500716	0.250358	−	0.968153i	$-0.419452\pi$
$509$	5750.00	0.500716	0.250358	+	0.968153i	$0.419452\pi$
$510$	0	0
$511$	0	0
$512$	24475.0	2.11260
$513$	0	0
$514$	−25650.0	−2.20111
$515$	3850.00	0.329420
$516$	0	0
$517$	14000.0	1.19095
$518$	0	0
$519$	0	0
$520$	4500.00	0.379496
$521$	−15500.0	−1.30339	−0.651696	−	0.758480i	$-0.725942\pi$
$521$	−15500.0	−1.30339	−0.651696	+	0.758480i	$0.725942\pi$
$522$	0	0
$523$	13940.0	1.16549	0.582747	−	0.812653i	$-0.301978\pi$
$523$	13940.0	1.16549	0.582747	+	0.812653i	$0.301978\pi$
$524$	33150.0	2.76367
$525$	0	0
$526$	−6400.00	−0.530520
$527$	1080.00	0.0892705
$528$	0	0
$529$	2233.00	0.183529
$530$	15250.0	1.24984
$531$	0	0
$532$	0	0
$533$	8000.00	0.650128
$534$	0	0
$535$	3300.00	0.266676
$536$	8100.00	0.652736
$537$	0	0
$538$	−16750.0	−1.34227
$539$	0	0
$540$	0	0
$541$	−20478.0	−1.62739	−0.813695	−	0.581292i	$-0.802547\pi$
$541$	−20478.0	−1.62739	−0.813695	+	0.581292i	$0.802547\pi$
$542$	27560.0	2.18414
$543$	0	0
$544$	850.000	0.0669916
$545$	−8770.00	−0.689295
$546$	0	0
$547$	12040.0	0.941121	0.470561	−	0.882368i	$-0.344052\pi$
$547$	12040.0	0.941121	0.470561	+	0.882368i	$0.344052\pi$
$548$	−17850.0	−1.39145
$549$	0	0
$550$	6250.00	0.484547
$551$	2200.00	0.170096
$552$	0	0
$553$	0	0
$554$	−24600.0	−1.88656
$555$	0	0
$556$	−28492.0	−2.17326
$557$	−23550.0	−1.79146	−0.895732	−	0.444594i	$-0.853348\pi$
$557$	−23550.0	−1.79146	−0.895732	+	0.444594i	$0.853348\pi$
$558$	0	0
$559$	5600.00	0.423712
$560$	0	0
$561$	0	0
$562$	22500.0	1.68880
$563$	−6120.00	−0.458130	−0.229065	−	0.973411i	$-0.573567\pi$
$563$	−6120.00	−0.458130	−0.229065	+	0.973411i	$0.573567\pi$
$564$	0	0
$565$	−1550.00	−0.115414
$566$	−34500.0	−2.56209
$567$	0	0
$568$	31500.0	2.32696
$569$	11700.0	0.862020	0.431010	−	0.902347i	$-0.358157\pi$
$569$	11700.0	0.862020	0.431010	+	0.902347i	$0.358157\pi$
$570$	0	0
$571$	−8188.00	−0.600100	−0.300050	−	0.953923i	$-0.597003\pi$
$571$	−8188.00	−0.600100	−0.300050	+	0.953923i	$0.597003\pi$
$572$	−17000.0	−1.24267
$573$	0	0
$574$	0	0
$575$	−3000.00	−0.217580
$576$	0	0
$577$	−11690.0	−0.843433	−0.421717	−	0.906728i	$-0.638572\pi$
$577$	−11690.0	−0.843433	−0.421717	+	0.906728i	$0.638572\pi$
$578$	24065.0	1.73179
$579$	0	0
$580$	−4250.00	−0.304261
$581$	0	0
$582$	0	0
$583$	−30500.0	−2.16669
$584$	−18450.0	−1.30731
$585$	0	0
$586$	−7650.00	−0.539281
$587$	21060.0	1.48082	0.740408	−	0.672157i	$-0.234632\pi$
$587$	21060.0	1.48082	0.740408	+	0.672157i	$0.234632\pi$
$588$	0	0
$589$	−4752.00	−0.332433
$590$	1250.00	0.0872232
$591$	0	0
$592$	−3560.00	−0.247154
$593$	−22910.0	−1.58651	−0.793255	−	0.608889i	$-0.791615\pi$
$593$	−22910.0	−1.58651	−0.793255	+	0.608889i	$0.791615\pi$
$594$	0	0
$595$	0	0
$596$	−34850.0	−2.39515
$597$	0	0
$598$	12000.0	0.820596
$599$	1400.00	0.0954966	0.0477483	−	0.998859i	$-0.484795\pi$
$599$	1400.00	0.0954966	0.0477483	+	0.998859i	$0.484795\pi$
$600$	0	0
$601$	11002.0	0.746724	0.373362	−	0.927686i	$-0.378205\pi$
$601$	11002.0	0.746724	0.373362	+	0.927686i	$0.378205\pi$
$602$	0	0
$603$	0	0
$604$	7616.00	0.513064
$605$	−5845.00	−0.392782
$606$	0	0
$607$	−4630.00	−0.309598	−0.154799	−	0.987946i	$-0.549473\pi$
$607$	−4630.00	−0.309598	−0.154799	+	0.987946i	$0.549473\pi$
$608$	−3740.00	−0.249469
$609$	0	0
$610$	12950.0	0.859558
$611$	−5600.00	−0.370788
$612$	0	0
$613$	24040.0	1.58396	0.791979	−	0.610548i	$-0.209051\pi$
$613$	24040.0	1.58396	0.791979	+	0.610548i	$0.209051\pi$
$614$	15200.0	0.999059
$615$	0	0
$616$	0	0
$617$	1890.00	0.123320	0.0616601	−	0.998097i	$-0.480361\pi$
$617$	1890.00	0.123320	0.0616601	+	0.998097i	$0.480361\pi$
$618$	0	0
$619$	−19244.0	−1.24957	−0.624783	−	0.780798i	$-0.714813\pi$
$619$	−19244.0	−1.24957	−0.624783	+	0.780798i	$0.714813\pi$
$620$	9180.00	0.594641
$621$	0	0
$622$	28500.0	1.83721
$623$	0	0
$624$	0	0
$625$	625.000	0.0400000
$626$	15550.0	0.992816
$627$	0	0
$628$	1700.00	0.108021
$629$	400.000	0.0253562
$630$	0	0
$631$	15892.0	1.00262	0.501308	−	0.865269i	$-0.332852\pi$
$631$	15892.0	1.00262	0.501308	+	0.865269i	$0.332852\pi$
$632$	23220.0	1.46146
$633$	0	0
$634$	−4750.00	−0.297550
$635$	5350.00	0.334344
$636$	0	0
$637$	0	0
$638$	12500.0	0.775674
$639$	0	0
$640$	−10575.0	−0.653146
$641$	12600.0	0.776396	0.388198	−	0.921576i	$-0.373098\pi$
$641$	12600.0	0.776396	0.388198	+	0.921576i	$0.373098\pi$
$642$	0	0
$643$	−7260.00	−0.445267	−0.222633	−	0.974902i	$-0.571465\pi$
$643$	−7260.00	−0.445267	−0.222633	+	0.974902i	$0.571465\pi$
$644$	0	0
$645$	0	0
$646$	2200.00	0.133990
$647$	7400.00	0.449651	0.224825	−	0.974399i	$-0.427819\pi$
$647$	7400.00	0.449651	0.224825	+	0.974399i	$0.427819\pi$
$648$	0	0
$649$	−2500.00	−0.151207
$650$	−2500.00	−0.150859
$651$	0	0
$652$	−32300.0	−1.94013
$653$	4790.00	0.287055	0.143528	−	0.989646i	$-0.454155\pi$
$653$	4790.00	0.287055	0.143528	+	0.989646i	$0.454155\pi$
$654$	0	0
$655$	−9750.00	−0.581624
$656$	35600.0	2.11882
$657$	0	0
$658$	0	0
$659$	1450.00	0.0857117	0.0428558	−	0.999081i	$-0.486354\pi$
$659$	1450.00	0.0857117	0.0428558	+	0.999081i	$0.486354\pi$
$660$	0	0
$661$	−11818.0	−0.695411	−0.347706	−	0.937604i	$-0.613039\pi$
$661$	−11818.0	−0.695411	−0.347706	+	0.937604i	$0.613039\pi$
$662$	−11460.0	−0.672818
$663$	0	0
$664$	−29700.0	−1.73582
$665$	0	0
$666$	0	0
$667$	−6000.00	−0.348307
$668$	32640.0	1.89054
$669$	0	0
$670$	−4500.00	−0.259478
$671$	−25900.0	−1.49010
$672$	0	0
$673$	5550.00	0.317885	0.158943	−	0.987288i	$-0.449192\pi$
$673$	5550.00	0.317885	0.158943	+	0.987288i	$0.449192\pi$
$674$	38650.0	2.20882
$675$	0	0
$676$	−30549.0	−1.73811
$677$	12930.0	0.734033	0.367016	−	0.930214i	$-0.380379\pi$
$677$	12930.0	0.734033	0.367016	+	0.930214i	$0.380379\pi$
$678$	0	0
$679$	0	0
$680$	−2250.00	−0.126888
$681$	0	0
$682$	−27000.0	−1.51596
$683$	−32580.0	−1.82524	−0.912620	−	0.408809i	$-0.865944\pi$
$683$	−32580.0	−1.82524	−0.912620	+	0.408809i	$0.865944\pi$
$684$	0	0
$685$	5250.00	0.292835
$686$	0	0
$687$	0	0
$688$	24920.0	1.38091
$689$	12200.0	0.674576
$690$	0	0
$691$	−10228.0	−0.563085	−0.281542	−	0.959549i	$-0.590846\pi$
$691$	−10228.0	−0.563085	−0.281542	+	0.959549i	$0.590846\pi$
$692$	43350.0	2.38139
$693$	0	0
$694$	−5600.00	−0.306301
$695$	8380.00	0.457369
$696$	0	0
$697$	−4000.00	−0.217376
$698$	5930.00	0.321567
$699$	0	0
$700$	0	0
$701$	−8350.00	−0.449893	−0.224947	−	0.974371i	$-0.572221\pi$
$701$	−8350.00	−0.449893	−0.224947	+	0.974371i	$0.572221\pi$
$702$	0	0
$703$	−1760.00	−0.0944234
$704$	14350.0	0.768233
$705$	0	0
$706$	−18150.0	−0.967541
$707$	0	0
$708$	0	0
$709$	−14954.0	−0.792115	−0.396057	−	0.918226i	$-0.629622\pi$
$709$	−14954.0	−0.792115	−0.396057	+	0.918226i	$0.629622\pi$
$710$	−17500.0	−0.925019
$711$	0	0
$712$	67500.0	3.55291
$713$	12960.0	0.680723
$714$	0	0
$715$	5000.00	0.261524
$716$	−62050.0	−3.23871
$717$	0	0
$718$	−9000.00	−0.467795
$719$	29400.0	1.52494	0.762472	−	0.647021i	$-0.223985\pi$
$719$	29400.0	1.52494	0.762472	+	0.647021i	$0.223985\pi$
$720$	0	0
$721$	0	0
$722$	24615.0	1.26880
$723$	0	0
$724$	73814.0	3.78905
$725$	1250.00	0.0640329
$726$	0	0
$727$	16330.0	0.833076	0.416538	−	0.909118i	$-0.363243\pi$
$727$	16330.0	0.833076	0.416538	+	0.909118i	$0.363243\pi$
$728$	0	0
$729$	0	0
$730$	10250.0	0.519684
$731$	−2800.00	−0.141671
$732$	0	0
$733$	−30800.0	−1.55201	−0.776005	−	0.630726i	$-0.782757\pi$
$733$	−30800.0	−1.55201	−0.776005	+	0.630726i	$0.782757\pi$
$734$	42450.0	2.13468
$735$	0	0
$736$	10200.0	0.510838
$737$	9000.00	0.449823
$738$	0	0
$739$	−9524.00	−0.474081	−0.237041	−	0.971500i	$-0.576177\pi$
$739$	−9524.00	−0.474081	−0.237041	+	0.971500i	$0.576177\pi$
$740$	3400.00	0.168901
$741$	0	0
$742$	0	0
$743$	28600.0	1.41216	0.706078	−	0.708134i	$-0.250463\pi$
$743$	28600.0	1.41216	0.706078	+	0.708134i	$0.250463\pi$
$744$	0	0
$745$	10250.0	0.504068
$746$	−500.000	−0.0245393
$747$	0	0
$748$	8500.00	0.415496
$749$	0	0
$750$	0	0
$751$	−8252.00	−0.400958	−0.200479	−	0.979698i	$-0.564250\pi$
$751$	−8252.00	−0.400958	−0.200479	+	0.979698i	$0.564250\pi$
$752$	−24920.0	−1.20843
$753$	0	0
$754$	−5000.00	−0.241498
$755$	−2240.00	−0.107976
$756$	0	0
$757$	−24920.0	−1.19648	−0.598238	−	0.801318i	$-0.704132\pi$
$757$	−24920.0	−1.19648	−0.598238	+	0.801318i	$0.704132\pi$
$758$	40420.0	1.93683
$759$	0	0
$760$	9900.00	0.472514
$761$	27900.0	1.32901	0.664503	−	0.747285i	$-0.268643\pi$
$761$	27900.0	1.32901	0.664503	+	0.747285i	$0.268643\pi$
$762$	0	0
$763$	0	0
$764$	59500.0	2.81758
$765$	0	0
$766$	47400.0	2.23581
$767$	1000.00	0.0470768
$768$	0	0
$769$	11506.0	0.539554	0.269777	−	0.962923i	$-0.413050\pi$
$769$	11506.0	0.539554	0.269777	+	0.962923i	$0.413050\pi$
$770$	0	0
$771$	0	0
$772$	56950.0	2.65502
$773$	−12510.0	−0.582087	−0.291044	−	0.956710i	$-0.594002\pi$
$773$	−12510.0	−0.582087	−0.291044	+	0.956710i	$0.594002\pi$
$774$	0	0
$775$	−2700.00	−0.125144
$776$	−73350.0	−3.39318
$777$	0	0
$778$	−54750.0	−2.52299
$779$	17600.0	0.809481
$780$	0	0
$781$	35000.0	1.60358
$782$	−6000.00	−0.274373
$783$	0	0
$784$	0	0
$785$	−500.000	−0.0227335
$786$	0	0
$787$	1100.00	0.0498231	0.0249115	−	0.999690i	$-0.492070\pi$
$787$	1100.00	0.0498231	0.0249115	+	0.999690i	$0.492070\pi$
$788$	−1530.00	−0.0691675
$789$	0	0
$790$	−12900.0	−0.580964
$791$	0	0
$792$	0	0
$793$	10360.0	0.463927
$794$	69200.0	3.09297
$795$	0	0
$796$	−62288.0	−2.77354
$797$	−4490.00	−0.199553	−0.0997766	−	0.995010i	$-0.531813\pi$
$797$	−4490.00	−0.199553	−0.0997766	+	0.995010i	$0.531813\pi$
$798$	0	0
$799$	2800.00	0.123976
$800$	−2125.00	−0.0939126
$801$	0	0
$802$	46500.0	2.04735
$803$	−20500.0	−0.900908
$804$	0	0
$805$	0	0
$806$	10800.0	0.471977
$807$	0	0
$808$	20250.0	0.881674
$809$	−28600.0	−1.24292	−0.621460	−	0.783446i	$-0.713460\pi$
$809$	−28600.0	−1.24292	−0.621460	+	0.783446i	$0.713460\pi$
$810$	0	0
$811$	−10068.0	−0.435925	−0.217963	−	0.975957i	$-0.569941\pi$
$811$	−10068.0	−0.435925	−0.217963	+	0.975957i	$0.569941\pi$
$812$	0	0
$813$	0	0
$814$	−10000.0	−0.430589
$815$	9500.00	0.408307
$816$	0	0
$817$	12320.0	0.527567
$818$	−14270.0	−0.609950
$819$	0	0
$820$	−34000.0	−1.44797
$821$	14250.0	0.605759	0.302880	−	0.953029i	$-0.402052\pi$
$821$	14250.0	0.605759	0.302880	+	0.953029i	$0.402052\pi$
$822$	0	0
$823$	6830.00	0.289282	0.144641	−	0.989484i	$-0.453797\pi$
$823$	6830.00	0.289282	0.144641	+	0.989484i	$0.453797\pi$
$824$	34650.0	1.46491
$825$	0	0
$826$	0	0
$827$	8920.00	0.375065	0.187533	−	0.982258i	$-0.439951\pi$
$827$	8920.00	0.375065	0.187533	+	0.982258i	$0.439951\pi$
$828$	0	0
$829$	3534.00	0.148059	0.0740295	−	0.997256i	$-0.476414\pi$
$829$	3534.00	0.148059	0.0740295	+	0.997256i	$0.476414\pi$
$830$	16500.0	0.690028
$831$	0	0
$832$	−5740.00	−0.239181
$833$	0	0
$834$	0	0
$835$	−9600.00	−0.397870
$836$	−37400.0	−1.54726
$837$	0	0
$838$	−5750.00	−0.237029
$839$	−8000.00	−0.329190	−0.164595	−	0.986361i	$-0.552632\pi$
$839$	−8000.00	−0.329190	−0.164595	+	0.986361i	$0.552632\pi$
$840$	0	0
$841$	−21889.0	−0.897495
$842$	55810.0	2.28425
$843$	0	0
$844$	−4556.00	−0.185810
$845$	8985.00	0.365791
$846$	0	0
$847$	0	0
$848$	54290.0	2.19850
$849$	0	0
$850$	1250.00	0.0504408
$851$	4800.00	0.193351
$852$	0	0
$853$	−5160.00	−0.207122	−0.103561	−	0.994623i	$-0.533024\pi$
$853$	−5160.00	−0.207122	−0.103561	+	0.994623i	$0.533024\pi$
$854$	0	0
$855$	0	0
$856$	29700.0	1.18589
$857$	7670.00	0.305720	0.152860	−	0.988248i	$-0.451152\pi$
$857$	7670.00	0.305720	0.152860	+	0.988248i	$0.451152\pi$
$858$	0	0
$859$	−25804.0	−1.02494	−0.512469	−	0.858706i	$-0.671269\pi$
$859$	−25804.0	−1.02494	−0.512469	+	0.858706i	$0.671269\pi$
$860$	−23800.0	−0.943690
$861$	0	0
$862$	−6000.00	−0.237078
$863$	−400.000	−0.0157777	−0.00788885	−	0.999969i	$-0.502511\pi$
$863$	−400.000	−0.0157777	−0.00788885	+	0.999969i	$0.502511\pi$
$864$	0	0
$865$	−12750.0	−0.501171
$866$	7550.00	0.296258
$867$	0	0
$868$	0	0
$869$	25800.0	1.00714
$870$	0	0
$871$	−3600.00	−0.140047
$872$	−78930.0	−3.06526
$873$	0	0
$874$	26400.0	1.02173
$875$	0	0
$876$	0	0
$877$	−35100.0	−1.35147	−0.675737	−	0.737143i	$-0.736175\pi$
$877$	−35100.0	−1.35147	−0.675737	+	0.737143i	$0.736175\pi$
$878$	2120.00	0.0814881
$879$	0	0
$880$	22250.0	0.852327
$881$	−18700.0	−0.715118	−0.357559	−	0.933891i	$-0.616391\pi$
$881$	−18700.0	−0.715118	−0.357559	+	0.933891i	$0.616391\pi$
$882$	0	0
$883$	−2980.00	−0.113573	−0.0567865	−	0.998386i	$-0.518085\pi$
$883$	−2980.00	−0.113573	−0.0567865	+	0.998386i	$0.518085\pi$
$884$	−3400.00	−0.129360
$885$	0	0
$886$	61800.0	2.34335
$887$	−35880.0	−1.35821	−0.679105	−	0.734041i	$-0.737632\pi$
$887$	−35880.0	−1.35821	−0.679105	+	0.734041i	$0.737632\pi$
$888$	0	0
$889$	0	0
$890$	−37500.0	−1.41236
$891$	0	0
$892$	62390.0	2.34190
$893$	−12320.0	−0.461672
$894$	0	0
$895$	18250.0	0.681598
$896$	0	0
$897$	0	0
$898$	−6500.00	−0.241545
$899$	−5400.00	−0.200334
$900$	0	0
$901$	−6100.00	−0.225550
$902$	100000.	3.69139
$903$	0	0
$904$	−13950.0	−0.513241
$905$	−21710.0	−0.797420
$906$	0	0
$907$	45240.0	1.65620	0.828098	−	0.560584i	$-0.189423\pi$
$907$	45240.0	1.65620	0.828098	+	0.560584i	$0.189423\pi$
$908$	63920.0	2.33619
$909$	0	0
$910$	0	0
$911$	−33200.0	−1.20743	−0.603713	−	0.797202i	$-0.706313\pi$
$911$	−33200.0	−1.20743	−0.603713	+	0.797202i	$0.706313\pi$
$912$	0	0
$913$	−33000.0	−1.19621
$914$	35950.0	1.30101
$915$	0	0
$916$	24378.0	0.879336
$917$	0	0
$918$	0	0
$919$	35356.0	1.26908	0.634541	−	0.772889i	$-0.281189\pi$
$919$	35356.0	1.26908	0.634541	+	0.772889i	$0.281189\pi$
$920$	−27000.0	−0.967569
$921$	0	0
$922$	750.000	0.0267895
$923$	−14000.0	−0.499259
$924$	0	0
$925$	−1000.00	−0.0355457
$926$	−13350.0	−0.473767
$927$	0	0
$928$	−4250.00	−0.150337
$929$	−25700.0	−0.907631	−0.453816	−	0.891096i	$-0.649938\pi$
$929$	−25700.0	−0.907631	−0.453816	+	0.891096i	$0.649938\pi$
$930$	0	0
$931$	0	0
$932$	58650.0	2.06131
$933$	0	0
$934$	−5900.00	−0.206696
$935$	−2500.00	−0.0874425
$936$	0	0
$937$	−52890.0	−1.84401	−0.922007	−	0.387173i	$-0.873451\pi$
$937$	−52890.0	−1.84401	−0.922007	+	0.387173i	$0.873451\pi$
$938$	0	0
$939$	0	0
$940$	23800.0	0.825820
$941$	38050.0	1.31817	0.659083	−	0.752070i	$-0.270945\pi$
$941$	38050.0	1.31817	0.659083	+	0.752070i	$0.270945\pi$
$942$	0	0
$943$	−48000.0	−1.65758
$944$	4450.00	0.153427
$945$	0	0
$946$	70000.0	2.40581
$947$	29640.0	1.01708	0.508538	−	0.861040i	$-0.330186\pi$
$947$	29640.0	1.01708	0.508538	+	0.861040i	$0.330186\pi$
$948$	0	0
$949$	8200.00	0.280488
$950$	−5500.00	−0.187835
$951$	0	0
$952$	0	0
$953$	−15170.0	−0.515640	−0.257820	−	0.966193i	$-0.583004\pi$
$953$	−15170.0	−0.515640	−0.257820	+	0.966193i	$0.583004\pi$
$954$	0	0
$955$	−17500.0	−0.592970
$956$	83300.0	2.81811
$957$	0	0
$958$	70500.0	2.37761
$959$	0	0
$960$	0	0
$961$	−18127.0	−0.608472
$962$	4000.00	0.134059
$963$	0	0
$964$	−81974.0	−2.73880
$965$	−16750.0	−0.558758
$966$	0	0
$967$	−5470.00	−0.181906	−0.0909531	−	0.995855i	$-0.528991\pi$
$967$	−5470.00	−0.181906	−0.0909531	+	0.995855i	$0.528991\pi$
$968$	−52605.0	−1.74668
$969$	0	0
$970$	40750.0	1.34887
$971$	15150.0	0.500707	0.250354	−	0.968154i	$-0.419453\pi$
$971$	15150.0	0.500707	0.250354	+	0.968154i	$0.419453\pi$
$972$	0	0
$973$	0	0
$974$	49250.0	1.62020
$975$	0	0
$976$	46102.0	1.51198
$977$	−31190.0	−1.02135	−0.510674	−	0.859775i	$-0.670604\pi$
$977$	−31190.0	−1.02135	−0.510674	+	0.859775i	$0.670604\pi$
$978$	0	0
$979$	75000.0	2.44843
$980$	0	0
$981$	0	0
$982$	−12250.0	−0.398079
$983$	−7560.00	−0.245297	−0.122648	−	0.992450i	$-0.539139\pi$
$983$	−7560.00	−0.245297	−0.122648	+	0.992450i	$0.539139\pi$
$984$	0	0
$985$	450.000	0.0145565
$986$	2500.00	0.0807467
$987$	0	0
$988$	14960.0	0.481722
$989$	−33600.0	−1.08030
$990$	0	0
$991$	32672.0	1.04729	0.523643	−	0.851938i	$-0.324573\pi$
$991$	32672.0	1.04729	0.523643	+	0.851938i	$0.324573\pi$
$992$	9180.00	0.293816
$993$	0	0
$994$	0	0
$995$	18320.0	0.583702
$996$	0	0
$997$	4740.00	0.150569	0.0752845	−	0.997162i	$-0.476014\pi$
$997$	4740.00	0.150569	0.0752845	+	0.997162i	$0.476014\pi$
$998$	85180.0	2.70173
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.4.a.a.1.1		1
3.2	odd	2		2205.4.a.t.1.1		1
7.6	odd	2		45.4.a.a.1.1	✓	1
21.20	even	2		45.4.a.e.1.1	yes	1
28.27	even	2		720.4.a.bc.1.1		1
35.13	even	4		225.4.b.a.199.2		2
35.27	even	4		225.4.b.a.199.1		2
35.34	odd	2		225.4.a.h.1.1		1
63.13	odd	6		405.4.e.n.136.1		2
63.20	even	6		405.4.e.b.271.1		2
63.34	odd	6		405.4.e.n.271.1		2
63.41	even	6		405.4.e.b.136.1		2
84.83	odd	2		720.4.a.o.1.1		1
105.62	odd	4		225.4.b.b.199.2		2
105.83	odd	4		225.4.b.b.199.1		2
105.104	even	2		225.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.a.a.1.1	✓	1	7.6	odd	2
45.4.a.e.1.1	yes	1	21.20	even	2
225.4.a.a.1.1		1	105.104	even	2
225.4.a.h.1.1		1	35.34	odd	2
225.4.b.a.199.1		2	35.27	even	4
225.4.b.a.199.2		2	35.13	even	4
225.4.b.b.199.1		2	105.83	odd	4
225.4.b.b.199.2		2	105.62	odd	4
405.4.e.b.136.1		2	63.41	even	6
405.4.e.b.271.1		2	63.20	even	6
405.4.e.n.136.1		2	63.13	odd	6
405.4.e.n.271.1		2	63.34	odd	6
720.4.a.o.1.1		1	84.83	odd	2
720.4.a.bc.1.1		1	28.27	even	2
2205.4.a.a.1.1		1	1.1	even	1	trivial
2205.4.a.t.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.a (trivial)

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