LMFDB - Embedded newform 1225.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1225,4,Mod(1,1225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1225, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1225.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1225.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:	$72.2773397570$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -6.00000 q^{6} +21.0000 q^{8} -23.0000 q^{9} +O(q^{10})$

\(q-3.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -6.00000 q^{6} +21.0000 q^{8} -23.0000 q^{9} -45.0000 q^{11} +2.00000 q^{12} -59.0000 q^{13} -71.0000 q^{16} +54.0000 q^{17} +69.0000 q^{18} -121.000 q^{19} +135.000 q^{22} -69.0000 q^{23} +42.0000 q^{24} +177.000 q^{26} -100.000 q^{27} -162.000 q^{29} -88.0000 q^{31} +45.0000 q^{32} -90.0000 q^{33} -162.000 q^{34} -23.0000 q^{36} +259.000 q^{37} +363.000 q^{38} -118.000 q^{39} +195.000 q^{41} +286.000 q^{43} -45.0000 q^{44} +207.000 q^{46} -45.0000 q^{47} -142.000 q^{48} +108.000 q^{51} -59.0000 q^{52} -597.000 q^{53} +300.000 q^{54} -242.000 q^{57} +486.000 q^{58} -360.000 q^{59} +392.000 q^{61} +264.000 q^{62} +433.000 q^{64} +270.000 q^{66} +280.000 q^{67} +54.0000 q^{68} -138.000 q^{69} +48.0000 q^{71} -483.000 q^{72} -668.000 q^{73} -777.000 q^{74} -121.000 q^{76} +354.000 q^{78} +782.000 q^{79} +421.000 q^{81} -585.000 q^{82} -768.000 q^{83} -858.000 q^{86} -324.000 q^{87} -945.000 q^{88} -1194.00 q^{89} -69.0000 q^{92} -176.000 q^{93} +135.000 q^{94} +90.0000 q^{96} -902.000 q^{97} +1035.00 q^{99} +O(q^{100})\)

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 $

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	2.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	2.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	21.0000	0.928078
$9$	−23.0000	−0.851852
$10$	0	0
$11$	−45.0000	−1.23346	−0.616728	−	0.787177i	$-0.711542\pi$
$11$	−45.0000	−1.23346	−0.616728	+	0.787177i	$0.711542\pi$
$12$	2.00000	0.0481125
$13$	−59.0000	−1.25874	−0.629371	−	0.777105i	$-0.716688\pi$
$13$	−59.0000	−1.25874	−0.629371	+	0.777105i	$0.716688\pi$
$14$	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	$0.374131\pi$
$18$	69.0000	0.903525
$19$	−121.000	−1.46102	−0.730508	−	0.682904i	$-0.760717\pi$
$19$	−121.000	−1.46102	−0.730508	+	0.682904i	$0.760717\pi$
$20$	0	0
$21$	0	0
$22$	135.000	1.30828
$23$	−69.0000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−69.0000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	42.0000	0.357217
$25$	0	0
$26$	177.000	1.33510
$27$	−100.000	−0.712778
$28$	0	0
$29$	−162.000	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$30$	0	0
$31$	−88.0000	−0.509847	−0.254924	−	0.966961i	$-0.582050\pi$
$31$	−88.0000	−0.509847	−0.254924	+	0.966961i	$0.582050\pi$
$32$	45.0000	0.248592
$33$	−90.0000	−0.474757
$34$	−162.000	−0.817140
$35$	0	0
$36$	−23.0000	−0.106481
$37$	259.000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	259.000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	363.000	1.54964
$39$	−118.000	−0.484490
$40$	0	0
$41$	195.000	0.742778	0.371389	−	0.928477i	$-0.378882\pi$
$41$	195.000	0.742778	0.371389	+	0.928477i	$0.378882\pi$
$42$	0	0
$43$	286.000	1.01429	0.507146	−	0.861860i	$-0.330700\pi$
$43$	286.000	1.01429	0.507146	+	0.861860i	$0.330700\pi$
$44$	−45.0000	−0.154182
$45$	0	0
$46$	207.000	0.663489
$47$	−45.0000	−0.139658	−0.0698290	−	0.997559i	$-0.522245\pi$
$47$	−45.0000	−0.139658	−0.0698290	+	0.997559i	$0.522245\pi$
$48$	−142.000	−0.426999
$49$	0	0
$50$	0	0
$51$	108.000	0.296530
$52$	−59.0000	−0.157343
$53$	−597.000	−1.54725	−0.773625	−	0.633644i	$-0.781559\pi$
$53$	−597.000	−1.54725	−0.773625	+	0.633644i	$0.781559\pi$
$54$	300.000	0.756015
$55$	0	0
$56$	0	0
$57$	−242.000	−0.562345
$58$	486.000	1.10026
$59$	−360.000	−0.794373	−0.397187	−	0.917738i	$-0.630013\pi$
$59$	−360.000	−0.794373	−0.397187	+	0.917738i	$0.630013\pi$
$60$	0	0
$61$	392.000	0.822794	0.411397	−	0.911456i	$-0.365041\pi$
$61$	392.000	0.822794	0.411397	+	0.911456i	$0.365041\pi$
$62$	264.000	0.540775
$63$	0	0
$64$	433.000	0.845703
$65$	0	0
$66$	270.000	0.503556
$67$	280.000	0.510559	0.255279	−	0.966867i	$-0.417833\pi$
$67$	280.000	0.510559	0.255279	+	0.966867i	$0.417833\pi$
$68$	54.0000	0.0963009
$69$	−138.000	−0.240772
$70$	0	0
$71$	48.0000	0.0802331	0.0401166	−	0.999195i	$-0.487227\pi$
$71$	48.0000	0.0802331	0.0401166	+	0.999195i	$0.487227\pi$
$72$	−483.000	−0.790585
$73$	−668.000	−1.07101	−0.535503	−	0.844533i	$-0.679878\pi$
$73$	−668.000	−1.07101	−0.535503	+	0.844533i	$0.679878\pi$
$74$	−777.000	−1.22060
$75$	0	0
$76$	−121.000	−0.182627
$77$	0	0
$78$	354.000	0.513880
$79$	782.000	1.11369	0.556847	−	0.830615i	$-0.312011\pi$
$79$	782.000	1.11369	0.556847	+	0.830615i	$0.312011\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	−585.000	−0.787835
$83$	−768.000	−1.01565	−0.507825	−	0.861460i	$-0.669550\pi$
$83$	−768.000	−1.01565	−0.507825	+	0.861460i	$0.669550\pi$
$84$	0	0
$85$	0	0
$86$	−858.000	−1.07582
$87$	−324.000	−0.399269
$88$	−945.000	−1.14474
$89$	−1194.00	−1.42206	−0.711032	−	0.703159i	$-0.751772\pi$
$89$	−1194.00	−1.42206	−0.711032	+	0.703159i	$0.751772\pi$
$90$	0	0
$91$	0	0
$92$	−69.0000	−0.0781929
$93$	−176.000	−0.196240
$94$	135.000	0.148130
$95$	0	0
$96$	90.0000	0.0956832
$97$	−902.000	−0.944167	−0.472084	−	0.881554i	$-0.656498\pi$
$97$	−902.000	−0.944167	−0.472084	+	0.881554i	$0.656498\pi$
$98$	0	0
$99$	1035.00	1.05072
$100$	0	0
$101$	684.000	0.673867	0.336933	−	0.941528i	$-0.390610\pi$
$101$	684.000	0.673867	0.336933	+	0.941528i	$0.390610\pi$
$102$	−324.000	−0.314517
$103$	1516.00	1.45025	0.725126	−	0.688616i	$-0.241782\pi$
$103$	1516.00	1.45025	0.725126	+	0.688616i	$0.241782\pi$
$104$	−1239.00	−1.16821
$105$	0	0
$106$	1791.00	1.64111
$107$	732.000	0.661356	0.330678	−	0.943744i	$-0.392723\pi$
$107$	732.000	0.661356	0.330678	+	0.943744i	$0.392723\pi$
$108$	−100.000	−0.0890973
$109$	−1600.00	−1.40598	−0.702992	−	0.711198i	$-0.748153\pi$
$109$	−1600.00	−1.40598	−0.702992	+	0.711198i	$0.748153\pi$
$110$	0	0
$111$	518.000	0.442940
$112$	0	0
$113$	1392.00	1.15883	0.579417	−	0.815031i	$-0.303280\pi$
$113$	1392.00	1.15883	0.579417	+	0.815031i	$0.303280\pi$
$114$	726.000	0.596457
$115$	0	0
$116$	−162.000	−0.129667
$117$	1357.00	1.07226
$118$	1080.00	0.842560
$119$	0	0
$120$	0	0
$121$	694.000	0.521412
$122$	−1176.00	−0.872705
$123$	390.000	0.285895
$124$	−88.0000	−0.0637309
$125$	0	0
$126$	0	0
$127$	−803.000	−0.561061	−0.280530	−	0.959845i	$-0.590510\pi$
$127$	−803.000	−0.561061	−0.280530	+	0.959845i	$0.590510\pi$
$128$	−1659.00	−1.14560
$129$	572.000	0.390401
$130$	0	0
$131$	2019.00	1.34657	0.673286	−	0.739382i	$-0.264882\pi$
$131$	2019.00	1.34657	0.673286	+	0.739382i	$0.264882\pi$
$132$	−90.0000	−0.0593447
$133$	0	0
$134$	−840.000	−0.541529
$135$	0	0
$136$	1134.00	0.714998
$137$	−60.0000	−0.0374171	−0.0187086	−	0.999825i	$-0.505955\pi$
$137$	−60.0000	−0.0374171	−0.0187086	+	0.999825i	$0.505955\pi$
$138$	414.000	0.255377
$139$	−1708.00	−1.04224	−0.521118	−	0.853485i	$-0.674485\pi$
$139$	−1708.00	−1.04224	−0.521118	+	0.853485i	$0.674485\pi$
$140$	0	0
$141$	−90.0000	−0.0537544
$142$	−144.000	−0.0851001
$143$	2655.00	1.55260
$144$	1633.00	0.945023
$145$	0	0
$146$	2004.00	1.13597
$147$	0	0
$148$	259.000	0.143849
$149$	−1086.00	−0.597105	−0.298552	−	0.954393i	$-0.596504\pi$
$149$	−1086.00	−0.597105	−0.298552	+	0.954393i	$0.596504\pi$
$150$	0	0
$151$	−2866.00	−1.54458	−0.772291	−	0.635269i	$-0.780889\pi$
$151$	−2866.00	−1.54458	−0.772291	+	0.635269i	$0.780889\pi$
$152$	−2541.00	−1.35594
$153$	−1242.00	−0.656273
$154$	0	0
$155$	0	0
$156$	−118.000	−0.0605613
$157$	229.000	0.116409	0.0582044	−	0.998305i	$-0.481462\pi$
$157$	229.000	0.116409	0.0582044	+	0.998305i	$0.481462\pi$
$158$	−2346.00	−1.18125
$159$	−1194.00	−0.595537
$160$	0	0
$161$	0	0
$162$	−1263.00	−0.612535
$163$	1228.00	0.590088	0.295044	−	0.955484i	$-0.404666\pi$
$163$	1228.00	0.590088	0.295044	+	0.955484i	$0.404666\pi$
$164$	195.000	0.0928472
$165$	0	0
$166$	2304.00	1.07726
$167$	1929.00	0.893835	0.446918	−	0.894575i	$-0.352522\pi$
$167$	1929.00	0.893835	0.446918	+	0.894575i	$0.352522\pi$
$168$	0	0
$169$	1284.00	0.584433
$170$	0	0
$171$	2783.00	1.24457
$172$	286.000	0.126787
$173$	699.000	0.307191	0.153595	−	0.988134i	$-0.450915\pi$
$173$	699.000	0.307191	0.153595	+	0.988134i	$0.450915\pi$
$174$	972.000	0.423489
$175$	0	0
$176$	3195.00	1.36836
$177$	−720.000	−0.305754
$178$	3582.00	1.50833
$179$	3117.00	1.30154	0.650770	−	0.759275i	$-0.274446\pi$
$179$	3117.00	1.30154	0.650770	+	0.759275i	$0.274446\pi$
$180$	0	0
$181$	−1798.00	−0.738366	−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00	−0.738366	−0.369183	+	0.929357i	$0.620362\pi$
$182$	0	0
$183$	784.000	0.316694
$184$	−1449.00	−0.580553
$185$	0	0
$186$	528.000	0.208144
$187$	−2430.00	−0.950263
$188$	−45.0000	−0.0174572
$189$	0	0
$190$	0	0
$191$	−2388.00	−0.904658	−0.452329	−	0.891851i	$-0.649407\pi$
$191$	−2388.00	−0.904658	−0.452329	+	0.891851i	$0.649407\pi$
$192$	866.000	0.325511
$193$	−272.000	−0.101446	−0.0507228	−	0.998713i	$-0.516152\pi$
$193$	−272.000	−0.101446	−0.0507228	+	0.998713i	$0.516152\pi$
$194$	2706.00	1.00144
$195$	0	0
$196$	0	0
$197$	2109.00	0.762741	0.381371	−	0.924422i	$-0.375452\pi$
$197$	2109.00	0.762741	0.381371	+	0.924422i	$0.375452\pi$
$198$	−3105.00	−1.11446
$199$	1424.00	0.507260	0.253630	−	0.967301i	$-0.418375\pi$
$199$	1424.00	0.507260	0.253630	+	0.967301i	$0.418375\pi$
$200$	0	0
$201$	560.000	0.196514
$202$	−2052.00	−0.714744
$203$	0	0
$204$	108.000	0.0370662
$205$	0	0
$206$	−4548.00	−1.53822
$207$	1587.00	0.532870
$208$	4189.00	1.39642
$209$	5445.00	1.80210
$210$	0	0
$211$	−3625.00	−1.18273	−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00	−1.18273	−0.591363	+	0.806405i	$0.701410\pi$
$212$	−597.000	−0.193406
$213$	96.0000	0.0308817
$214$	−2196.00	−0.701474
$215$	0	0
$216$	−2100.00	−0.661513
$217$	0	0
$218$	4800.00	1.49127
$219$	−1336.00	−0.412231
$220$	0	0
$221$	−3186.00	−0.969745
$222$	−1554.00	−0.469809
$223$	4960.00	1.48944	0.744722	−	0.667374i	$-0.232582\pi$
$223$	4960.00	1.48944	0.744722	+	0.667374i	$0.232582\pi$
$224$	0	0
$225$	0	0
$226$	−4176.00	−1.22913
$227$	1500.00	0.438584	0.219292	−	0.975659i	$-0.429625\pi$
$227$	1500.00	0.438584	0.219292	+	0.975659i	$0.429625\pi$
$228$	−242.000	−0.0702932
$229$	6092.00	1.75795	0.878975	−	0.476867i	$-0.158228\pi$
$229$	6092.00	1.75795	0.878975	+	0.476867i	$0.158228\pi$
$230$	0	0
$231$	0	0
$232$	−3402.00	−0.962725
$233$	−138.000	−0.0388012	−0.0194006	−	0.999812i	$-0.506176\pi$
$233$	−138.000	−0.0388012	−0.0194006	+	0.999812i	$0.506176\pi$
$234$	−4071.00	−1.13731
$235$	0	0
$236$	−360.000	−0.0992966
$237$	1564.00	0.428661
$238$	0	0
$239$	−5502.00	−1.48910	−0.744550	−	0.667567i	$-0.767336\pi$
$239$	−5502.00	−1.48910	−0.744550	+	0.667567i	$0.767336\pi$
$240$	0	0
$241$	3551.00	0.949129	0.474564	−	0.880221i	$-0.342606\pi$
$241$	3551.00	0.949129	0.474564	+	0.880221i	$0.342606\pi$
$242$	−2082.00	−0.553041
$243$	3542.00	0.935059
$244$	392.000	0.102849
$245$	0	0
$246$	−1170.00	−0.303238
$247$	7139.00	1.83904
$248$	−1848.00	−0.473178
$249$	−1536.00	−0.390924
$250$	0	0
$251$	7065.00	1.77665	0.888324	−	0.459216i	$-0.151870\pi$
$251$	7065.00	1.77665	0.888324	+	0.459216i	$0.151870\pi$
$252$	0	0
$253$	3105.00	0.771580
$254$	2409.00	0.595095
$255$	0	0
$256$	1513.00	0.369385
$257$	4080.00	0.990286	0.495143	−	0.868812i	$-0.335116\pi$
$257$	4080.00	0.990286	0.495143	+	0.868812i	$0.335116\pi$
$258$	−1716.00	−0.414083
$259$	0	0
$260$	0	0
$261$	3726.00	0.883654
$262$	−6057.00	−1.42825
$263$	3288.00	0.770900	0.385450	−	0.922729i	$-0.374046\pi$
$263$	3288.00	0.770900	0.385450	+	0.922729i	$0.374046\pi$
$264$	−1890.00	−0.440612
$265$	0	0
$266$	0	0
$267$	−2388.00	−0.547353
$268$	280.000	0.0638199
$269$	−3264.00	−0.739813	−0.369906	−	0.929069i	$-0.620610\pi$
$269$	−3264.00	−0.739813	−0.369906	+	0.929069i	$0.620610\pi$
$270$	0	0
$271$	−2752.00	−0.616871	−0.308436	−	0.951245i	$-0.599805\pi$
$271$	−2752.00	−0.616871	−0.308436	+	0.951245i	$0.599805\pi$
$272$	−3834.00	−0.854671
$273$	0	0
$274$	180.000	0.0396869
$275$	0	0
$276$	−138.000	−0.0300965
$277$	4690.00	1.01731	0.508655	−	0.860971i	$-0.330143\pi$
$277$	4690.00	1.01731	0.508655	+	0.860971i	$0.330143\pi$
$278$	5124.00	1.10546
$279$	2024.00	0.434314
$280$	0	0
$281$	7821.00	1.66036	0.830181	−	0.557494i	$-0.188237\pi$
$281$	7821.00	1.66036	0.830181	+	0.557494i	$0.188237\pi$
$282$	270.000	0.0570151
$283$	658.000	0.138212	0.0691061	−	0.997609i	$-0.477985\pi$
$283$	658.000	0.138212	0.0691061	+	0.997609i	$0.477985\pi$
$284$	48.0000	0.0100291
$285$	0	0
$286$	−7965.00	−1.64678
$287$	0	0
$288$	−1035.00	−0.211764
$289$	−1997.00	−0.406473
$290$	0	0
$291$	−1804.00	−0.363410
$292$	−668.000	−0.133876
$293$	5997.00	1.19573	0.597864	−	0.801597i	$-0.296016\pi$
$293$	5997.00	1.19573	0.597864	+	0.801597i	$0.296016\pi$
$294$	0	0
$295$	0	0
$296$	5439.00	1.06803
$297$	4500.00	0.879180
$298$	3258.00	0.633325
$299$	4071.00	0.787398
$300$	0	0
$301$	0	0
$302$	8598.00	1.63828
$303$	1368.00	0.259371
$304$	8591.00	1.62081
$305$	0	0
$306$	3726.00	0.696082
$307$	6226.00	1.15745	0.578724	−	0.815523i	$-0.303551\pi$
$307$	6226.00	1.15745	0.578724	+	0.815523i	$0.303551\pi$
$308$	0	0
$309$	3032.00	0.558202
$310$	0	0
$311$	4680.00	0.853307	0.426653	−	0.904415i	$-0.359692\pi$
$311$	4680.00	0.853307	0.426653	+	0.904415i	$0.359692\pi$
$312$	−2478.00	−0.449645
$313$	−1028.00	−0.185642	−0.0928211	−	0.995683i	$-0.529588\pi$
$313$	−1028.00	−0.185642	−0.0928211	+	0.995683i	$0.529588\pi$
$314$	−687.000	−0.123470
$315$	0	0
$316$	782.000	0.139212
$317$	−8622.00	−1.52763	−0.763817	−	0.645433i	$-0.776677\pi$
$317$	−8622.00	−1.52763	−0.763817	+	0.645433i	$0.776677\pi$
$318$	3582.00	0.631662
$319$	7290.00	1.27950
$320$	0	0
$321$	1464.00	0.254556
$322$	0	0
$323$	−6534.00	−1.12558
$324$	421.000	0.0721879
$325$	0	0
$326$	−3684.00	−0.625883
$327$	−3200.00	−0.541163
$328$	4095.00	0.689355
$329$	0	0
$330$	0	0
$331$	−1999.00	−0.331949	−0.165974	−	0.986130i	$-0.553077\pi$
$331$	−1999.00	−0.331949	−0.165974	+	0.986130i	$0.553077\pi$
$332$	−768.000	−0.126956
$333$	−5957.00	−0.980305
$334$	−5787.00	−0.948056
$335$	0	0
$336$	0	0
$337$	−5114.00	−0.826639	−0.413319	−	0.910586i	$-0.635631\pi$
$337$	−5114.00	−0.826639	−0.413319	+	0.910586i	$0.635631\pi$
$338$	−3852.00	−0.619885
$339$	2784.00	0.446036
$340$	0	0
$341$	3960.00	0.628874
$342$	−8349.00	−1.32006
$343$	0	0
$344$	6006.00	0.941342
$345$	0	0
$346$	−2097.00	−0.325825
$347$	−4320.00	−0.668328	−0.334164	−	0.942515i	$-0.608454\pi$
$347$	−4320.00	−0.668328	−0.334164	+	0.942515i	$0.608454\pi$
$348$	−324.000	−0.0499087
$349$	7922.00	1.21506	0.607529	−	0.794298i	$-0.292161\pi$
$349$	7922.00	1.21506	0.607529	+	0.794298i	$0.292161\pi$
$350$	0	0
$351$	5900.00	0.897204
$352$	−2025.00	−0.306627
$353$	−828.000	−0.124844	−0.0624221	−	0.998050i	$-0.519882\pi$
$353$	−828.000	−0.124844	−0.0624221	+	0.998050i	$0.519882\pi$
$354$	2160.00	0.324301
$355$	0	0
$356$	−1194.00	−0.177758
$357$	0	0
$358$	−9351.00	−1.38049
$359$	−1350.00	−0.198469	−0.0992344	−	0.995064i	$-0.531639\pi$
$359$	−1350.00	−0.198469	−0.0992344	+	0.995064i	$0.531639\pi$
$360$	0	0
$361$	7782.00	1.13457
$362$	5394.00	0.783156
$363$	1388.00	0.200692
$364$	0	0
$365$	0	0
$366$	−2352.00	−0.335904
$367$	−2801.00	−0.398395	−0.199198	−	0.979959i	$-0.563834\pi$
$367$	−2801.00	−0.398395	−0.199198	+	0.979959i	$0.563834\pi$
$368$	4899.00	0.693962
$369$	−4485.00	−0.632737
$370$	0	0
$371$	0	0
$372$	−176.000	−0.0245300
$373$	−6602.00	−0.916457	−0.458229	−	0.888834i	$-0.651516\pi$
$373$	−6602.00	−0.916457	−0.458229	+	0.888834i	$0.651516\pi$
$374$	7290.00	1.00791
$375$	0	0
$376$	−945.000	−0.129613
$377$	9558.00	1.30573
$378$	0	0
$379$	−8305.00	−1.12559	−0.562796	−	0.826596i	$-0.690274\pi$
$379$	−8305.00	−1.12559	−0.562796	+	0.826596i	$0.690274\pi$
$380$	0	0
$381$	−1606.00	−0.215952
$382$	7164.00	0.959534
$383$	−945.000	−0.126076	−0.0630382	−	0.998011i	$-0.520079\pi$
$383$	−945.000	−0.126076	−0.0630382	+	0.998011i	$0.520079\pi$
$384$	−3318.00	−0.440940
$385$	0	0
$386$	816.000	0.107599
$387$	−6578.00	−0.864027
$388$	−902.000	−0.118021
$389$	12036.0	1.56876	0.784382	−	0.620278i	$-0.212980\pi$
$389$	12036.0	1.56876	0.784382	+	0.620278i	$0.212980\pi$
$390$	0	0
$391$	−3726.00	−0.481923
$392$	0	0
$393$	4038.00	0.518296
$394$	−6327.00	−0.809009
$395$	0	0
$396$	1035.00	0.131340
$397$	2698.00	0.341080	0.170540	−	0.985351i	$-0.445449\pi$
$397$	2698.00	0.341080	0.170540	+	0.985351i	$0.445449\pi$
$398$	−4272.00	−0.538030
$399$	0	0
$400$	0	0
$401$	7053.00	0.878329	0.439165	−	0.898407i	$-0.355274\pi$
$401$	7053.00	0.878329	0.439165	+	0.898407i	$0.355274\pi$
$402$	−1680.00	−0.208435
$403$	5192.00	0.641767
$404$	684.000	0.0842333
$405$	0	0
$406$	0	0
$407$	−11655.0	−1.41945
$408$	2268.00	0.275203
$409$	−10870.0	−1.31415	−0.657074	−	0.753826i	$-0.728206\pi$
$409$	−10870.0	−1.31415	−0.657074	+	0.753826i	$0.728206\pi$
$410$	0	0
$411$	−120.000	−0.0144019
$412$	1516.00	0.181281
$413$	0	0
$414$	−4761.00	−0.565194
$415$	0	0
$416$	−2655.00	−0.312914
$417$	−3416.00	−0.401156
$418$	−16335.0	−1.91141
$419$	−9729.00	−1.13435	−0.567175	−	0.823597i	$-0.691964\pi$
$419$	−9729.00	−1.13435	−0.567175	+	0.823597i	$0.691964\pi$
$420$	0	0
$421$	−12550.0	−1.45285	−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0	−1.45285	−0.726425	+	0.687246i	$0.758819\pi$
$422$	10875.0	1.25447
$423$	1035.00	0.118968
$424$	−12537.0	−1.43597
$425$	0	0
$426$	−288.000	−0.0327550
$427$	0	0
$428$	732.000	0.0826695
$429$	5310.00	0.597597
$430$	0	0
$431$	2988.00	0.333937	0.166969	−	0.985962i	$-0.446602\pi$
$431$	2988.00	0.333937	0.166969	+	0.985962i	$0.446602\pi$
$432$	7100.00	0.790738
$433$	−16616.0	−1.84414	−0.922072	−	0.387019i	$-0.873505\pi$
$433$	−16616.0	−1.84414	−0.922072	+	0.387019i	$0.873505\pi$
$434$	0	0
$435$	0	0
$436$	−1600.00	−0.175748
$437$	8349.00	0.913929
$438$	4008.00	0.437237
$439$	7346.00	0.798646	0.399323	−	0.916810i	$-0.369245\pi$
$439$	7346.00	0.798646	0.399323	+	0.916810i	$0.369245\pi$
$440$	0	0
$441$	0	0
$442$	9558.00	1.02857
$443$	−12.0000	−0.00128699	−0.000643496	−	1.00000i	$-0.500205\pi$
$443$	−12.0000	−0.00128699	−0.000643496		1.00000i	$0.500205\pi$
$444$	518.000	0.0553675
$445$	0	0
$446$	−14880.0	−1.57979
$447$	−2172.00	−0.229826
$448$	0	0
$449$	9669.00	1.01628	0.508138	−	0.861275i	$-0.330334\pi$
$449$	9669.00	1.01628	0.508138	+	0.861275i	$0.330334\pi$
$450$	0	0
$451$	−8775.00	−0.916183
$452$	1392.00	0.144854
$453$	−5732.00	−0.594510
$454$	−4500.00	−0.465188
$455$	0	0
$456$	−5082.00	−0.521900
$457$	9634.00	0.986126	0.493063	−	0.869994i	$-0.335877\pi$
$457$	9634.00	0.986126	0.493063	+	0.869994i	$0.335877\pi$
$458$	−18276.0	−1.86459
$459$	−5400.00	−0.549129
$460$	0	0
$461$	−342.000	−0.0345521	−0.0172761	−	0.999851i	$-0.505499\pi$
$461$	−342.000	−0.0345521	−0.0172761	+	0.999851i	$0.505499\pi$
$462$	0	0
$463$	−2411.00	−0.242006	−0.121003	−	0.992652i	$-0.538611\pi$
$463$	−2411.00	−0.242006	−0.121003	+	0.992652i	$0.538611\pi$
$464$	11502.0	1.15079
$465$	0	0
$466$	414.000	0.0411549
$467$	1206.00	0.119501	0.0597506	−	0.998213i	$-0.480969\pi$
$467$	1206.00	0.119501	0.0597506	+	0.998213i	$0.480969\pi$
$468$	1357.00	0.134033
$469$	0	0
$470$	0	0
$471$	458.000	0.0448058
$472$	−7560.00	−0.737240
$473$	−12870.0	−1.25109
$474$	−4692.00	−0.454664
$475$	0	0
$476$	0	0
$477$	13731.0	1.31803
$478$	16506.0	1.57943
$479$	−432.000	−0.0412079	−0.0206039	−	0.999788i	$-0.506559\pi$
$479$	−432.000	−0.0412079	−0.0206039	+	0.999788i	$0.506559\pi$
$480$	0	0
$481$	−15281.0	−1.44855
$482$	−10653.0	−1.00670
$483$	0	0
$484$	694.000	0.0651766
$485$	0	0
$486$	−10626.0	−0.991780
$487$	11896.0	1.10690	0.553449	−	0.832883i	$-0.313311\pi$
$487$	11896.0	1.10690	0.553449	+	0.832883i	$0.313311\pi$
$488$	8232.00	0.763617
$489$	2456.00	0.227125
$490$	0	0
$491$	−12276.0	−1.12833	−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0	−1.12833	−0.564163	+	0.825663i	$0.690801\pi$
$492$	390.000	0.0357369
$493$	−8748.00	−0.799169
$494$	−21417.0	−1.95060
$495$	0	0
$496$	6248.00	0.565612
$497$	0	0
$498$	4608.00	0.414637
$499$	−10876.0	−0.975705	−0.487852	−	0.872926i	$-0.662220\pi$
$499$	−10876.0	−0.975705	−0.487852	+	0.872926i	$0.662220\pi$
$500$	0	0
$501$	3858.00	0.344037
$502$	−21195.0	−1.88442
$503$	−12000.0	−1.06372	−0.531862	−	0.846831i	$-0.678508\pi$
$503$	−12000.0	−1.06372	−0.531862	+	0.846831i	$0.678508\pi$
$504$	0	0
$505$	0	0
$506$	−9315.00	−0.818384
$507$	2568.00	0.224948
$508$	−803.000	−0.0701326
$509$	−11682.0	−1.01728	−0.508640	−	0.860979i	$-0.669852\pi$
$509$	−11682.0	−1.01728	−0.508640	+	0.860979i	$0.669852\pi$
$510$	0	0
$511$	0	0
$512$	8733.00	0.753804
$513$	12100.0	1.04138
$514$	−12240.0	−1.05036
$515$	0	0
$516$	572.000	0.0488002
$517$	2025.00	0.172262
$518$	0	0
$519$	1398.00	0.118238
$520$	0	0
$521$	9609.00	0.808019	0.404010	−	0.914755i	$-0.367616\pi$
$521$	9609.00	0.808019	0.404010	+	0.914755i	$0.367616\pi$
$522$	−11178.0	−0.937256
$523$	−21188.0	−1.77148	−0.885742	−	0.464177i	$-0.846350\pi$
$523$	−21188.0	−1.77148	−0.885742	+	0.464177i	$0.846350\pi$
$524$	2019.00	0.168321
$525$	0	0
$526$	−9864.00	−0.817663
$527$	−4752.00	−0.392790
$528$	6390.00	0.526684
$529$	−7406.00	−0.608696
$530$	0	0
$531$	8280.00	0.676688
$532$	0	0
$533$	−11505.0	−0.934966
$534$	7164.00	0.580555
$535$	0	0
$536$	5880.00	0.473838
$537$	6234.00	0.500963
$538$	9792.00	0.784690
$539$	0	0
$540$	0	0
$541$	8072.00	0.641483	0.320742	−	0.947167i	$-0.396068\pi$
$541$	8072.00	0.641483	0.320742	+	0.947167i	$0.396068\pi$
$542$	8256.00	0.654291
$543$	−3596.00	−0.284197
$544$	2430.00	0.191517
$545$	0	0
$546$	0	0
$547$	−344.000	−0.0268892	−0.0134446	−	0.999910i	$-0.504280\pi$
$547$	−344.000	−0.0268892	−0.0134446	+	0.999910i	$0.504280\pi$
$548$	−60.0000	−0.00467714
$549$	−9016.00	−0.700899
$550$	0	0
$551$	19602.0	1.51556
$552$	−2898.00	−0.223455
$553$	0	0
$554$	−14070.0	−1.07902
$555$	0	0
$556$	−1708.00	−0.130279
$557$	−18363.0	−1.39689	−0.698443	−	0.715666i	$-0.746123\pi$
$557$	−18363.0	−1.39689	−0.698443	+	0.715666i	$0.746123\pi$
$558$	−6072.00	−0.460660
$559$	−16874.0	−1.27673
$560$	0	0
$561$	−4860.00	−0.365756
$562$	−23463.0	−1.76108
$563$	6294.00	0.471155	0.235578	−	0.971856i	$-0.424302\pi$
$563$	6294.00	0.471155	0.235578	+	0.971856i	$0.424302\pi$
$564$	−90.0000	−0.00671930
$565$	0	0
$566$	−1974.00	−0.146596
$567$	0	0
$568$	1008.00	0.0744626
$569$	11733.0	0.864452	0.432226	−	0.901765i	$-0.357728\pi$
$569$	11733.0	0.864452	0.432226	+	0.901765i	$0.357728\pi$
$570$	0	0
$571$	1052.00	0.0771013	0.0385506	−	0.999257i	$-0.487726\pi$
$571$	1052.00	0.0771013	0.0385506	+	0.999257i	$0.487726\pi$
$572$	2655.00	0.194075
$573$	−4776.00	−0.348203
$574$	0	0
$575$	0	0
$576$	−9959.00	−0.720414
$577$	13156.0	0.949205	0.474603	−	0.880200i	$-0.342592\pi$
$577$	13156.0	0.949205	0.474603	+	0.880200i	$0.342592\pi$
$578$	5991.00	0.431129
$579$	−544.000	−0.0390464
$580$	0	0
$581$	0	0
$582$	5412.00	0.385455
$583$	26865.0	1.90846
$584$	−14028.0	−0.993977
$585$	0	0
$586$	−17991.0	−1.26826
$587$	13368.0	0.939960	0.469980	−	0.882677i	$-0.344261\pi$
$587$	13368.0	0.939960	0.469980	+	0.882677i	$0.344261\pi$
$588$	0	0
$589$	10648.0	0.744895
$590$	0	0
$591$	4218.00	0.293579
$592$	−18389.0	−1.27666
$593$	−26664.0	−1.84647	−0.923237	−	0.384231i	$-0.874467\pi$
$593$	−26664.0	−1.84647	−0.923237	+	0.384231i	$0.874467\pi$
$594$	−13500.0	−0.932511
$595$	0	0
$596$	−1086.00	−0.0746381
$597$	2848.00	0.195244
$598$	−12213.0	−0.835162
$599$	7614.00	0.519365	0.259682	−	0.965694i	$-0.416382\pi$
$599$	7614.00	0.519365	0.259682	+	0.965694i	$0.416382\pi$
$600$	0	0
$601$	6410.00	0.435057	0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00	0.435057	0.217529	+	0.976054i	$0.430200\pi$
$602$	0	0
$603$	−6440.00	−0.434921
$604$	−2866.00	−0.193073
$605$	0	0
$606$	−4104.00	−0.275105
$607$	21469.0	1.43558	0.717792	−	0.696257i	$-0.245153\pi$
$607$	21469.0	1.43558	0.717792	+	0.696257i	$0.245153\pi$
$608$	−5445.00	−0.363197
$609$	0	0
$610$	0	0
$611$	2655.00	0.175793
$612$	−1242.00	−0.0820341
$613$	−3737.00	−0.246225	−0.123113	−	0.992393i	$-0.539288\pi$
$613$	−3737.00	−0.246225	−0.123113	+	0.992393i	$0.539288\pi$
$614$	−18678.0	−1.22766
$615$	0	0
$616$	0	0
$617$	−18078.0	−1.17957	−0.589784	−	0.807561i	$-0.700787\pi$
$617$	−18078.0	−1.17957	−0.589784	+	0.807561i	$0.700787\pi$
$618$	−9096.00	−0.592063
$619$	12287.0	0.797829	0.398915	−	0.916988i	$-0.369387\pi$
$619$	12287.0	0.797829	0.398915	+	0.916988i	$0.369387\pi$
$620$	0	0
$621$	6900.00	0.445874
$622$	−14040.0	−0.905069
$623$	0	0
$624$	8378.00	0.537481
$625$	0	0
$626$	3084.00	0.196903
$627$	10890.0	0.693628
$628$	229.000	0.0145511
$629$	13986.0	0.886579
$630$	0	0
$631$	−9580.00	−0.604396	−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00	−0.604396	−0.302198	+	0.953245i	$0.597720\pi$
$632$	16422.0	1.03360
$633$	−7250.00	−0.455232
$634$	25866.0	1.62030
$635$	0	0
$636$	−1194.00	−0.0744421
$637$	0	0
$638$	−21870.0	−1.35712
$639$	−1104.00	−0.0683467
$640$	0	0
$641$	10779.0	0.664189	0.332094	−	0.943246i	$-0.392245\pi$
$641$	10779.0	0.664189	0.332094	+	0.943246i	$0.392245\pi$
$642$	−4392.00	−0.269998
$643$	−8882.00	−0.544746	−0.272373	−	0.962192i	$-0.587809\pi$
$643$	−8882.00	−0.544746	−0.272373	+	0.962192i	$0.587809\pi$
$644$	0	0
$645$	0	0
$646$	19602.0	1.19386
$647$	11019.0	0.669554	0.334777	−	0.942297i	$-0.391339\pi$
$647$	11019.0	0.669554	0.334777	+	0.942297i	$0.391339\pi$
$648$	8841.00	0.535968
$649$	16200.0	0.979824
$650$	0	0
$651$	0	0
$652$	1228.00	0.0737610
$653$	−22323.0	−1.33777	−0.668887	−	0.743364i	$-0.733229\pi$
$653$	−22323.0	−1.33777	−0.668887	+	0.743364i	$0.733229\pi$
$654$	9600.00	0.573990
$655$	0	0
$656$	−13845.0	−0.824019
$657$	15364.0	0.912339
$658$	0	0
$659$	−11856.0	−0.700826	−0.350413	−	0.936595i	$-0.613959\pi$
$659$	−11856.0	−0.700826	−0.350413	+	0.936595i	$0.613959\pi$
$660$	0	0
$661$	−33244.0	−1.95619	−0.978095	−	0.208158i	$-0.933253\pi$
$661$	−33244.0	−1.95619	−0.978095	+	0.208158i	$0.933253\pi$
$662$	5997.00	0.352085
$663$	−6372.00	−0.373255
$664$	−16128.0	−0.942602
$665$	0	0
$666$	17871.0	1.03977
$667$	11178.0	0.648896
$668$	1929.00	0.111729
$669$	9920.00	0.573288
$670$	0	0
$671$	−17640.0	−1.01488
$672$	0	0
$673$	12322.0	0.705763	0.352881	−	0.935668i	$-0.385202\pi$
$673$	12322.0	0.705763	0.352881	+	0.935668i	$0.385202\pi$
$674$	15342.0	0.876783
$675$	0	0
$676$	1284.00	0.0730542
$677$	12597.0	0.715129	0.357564	−	0.933889i	$-0.383607\pi$
$677$	12597.0	0.715129	0.357564	+	0.933889i	$0.383607\pi$
$678$	−8352.00	−0.473092
$679$	0	0
$680$	0	0
$681$	3000.00	0.168811
$682$	−11880.0	−0.667022
$683$	8340.00	0.467235	0.233617	−	0.972329i	$-0.424944\pi$
$683$	8340.00	0.467235	0.233617	+	0.972329i	$0.424944\pi$
$684$	2783.00	0.155571
$685$	0	0
$686$	0	0
$687$	12184.0	0.676636
$688$	−20306.0	−1.12523
$689$	35223.0	1.94759
$690$	0	0
$691$	−20200.0	−1.11208	−0.556038	−	0.831157i	$-0.687679\pi$
$691$	−20200.0	−1.11208	−0.556038	+	0.831157i	$0.687679\pi$
$692$	699.000	0.0383988
$693$	0	0
$694$	12960.0	0.708869
$695$	0	0
$696$	−6804.00	−0.370553
$697$	10530.0	0.572241
$698$	−23766.0	−1.28876
$699$	−276.000	−0.0149346
$700$	0	0
$701$	474.000	0.0255388	0.0127694	−	0.999918i	$-0.495935\pi$
$701$	474.000	0.0255388	0.0127694	+	0.999918i	$0.495935\pi$
$702$	−17700.0	−0.951629
$703$	−31339.0	−1.68133
$704$	−19485.0	−1.04314
$705$	0	0
$706$	2484.00	0.132417
$707$	0	0
$708$	−720.000	−0.0382193
$709$	−25126.0	−1.33093	−0.665463	−	0.746431i	$-0.731766\pi$
$709$	−25126.0	−1.33093	−0.665463	+	0.746431i	$0.731766\pi$
$710$	0	0
$711$	−17986.0	−0.948703
$712$	−25074.0	−1.31979
$713$	6072.00	0.318932
$714$	0	0
$715$	0	0
$716$	3117.00	0.162692
$717$	−11004.0	−0.573155
$718$	4050.00	0.210508
$719$	−7296.00	−0.378435	−0.189218	−	0.981935i	$-0.560595\pi$
$719$	−7296.00	−0.378435	−0.189218	+	0.981935i	$0.560595\pi$
$720$	0	0
$721$	0	0
$722$	−23346.0	−1.20339
$723$	7102.00	0.365320
$724$	−1798.00	−0.0922958
$725$	0	0
$726$	−4164.00	−0.212866
$727$	15421.0	0.786703	0.393352	−	0.919388i	$-0.371316\pi$
$727$	15421.0	0.786703	0.393352	+	0.919388i	$0.371316\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	0	0
$731$	15444.0	0.781419
$732$	784.000	0.0395867
$733$	29167.0	1.46972	0.734862	−	0.678217i	$-0.237247\pi$
$733$	29167.0	1.46972	0.734862	+	0.678217i	$0.237247\pi$
$734$	8403.00	0.422562
$735$	0	0
$736$	−3105.00	−0.155505
$737$	−12600.0	−0.629752
$738$	13455.0	0.671118
$739$	−13381.0	−0.666073	−0.333037	−	0.942914i	$-0.608073\pi$
$739$	−13381.0	−0.666073	−0.333037	+	0.942914i	$0.608073\pi$
$740$	0	0
$741$	14278.0	0.707848
$742$	0	0
$743$	−5487.00	−0.270927	−0.135463	−	0.990782i	$-0.543252\pi$
$743$	−5487.00	−0.270927	−0.135463	+	0.990782i	$0.543252\pi$
$744$	−3696.00	−0.182126
$745$	0	0
$746$	19806.0	0.972050
$747$	17664.0	0.865183
$748$	−2430.00	−0.118783
$749$	0	0
$750$	0	0
$751$	6638.00	0.322535	0.161268	−	0.986911i	$-0.448442\pi$
$751$	6638.00	0.322535	0.161268	+	0.986911i	$0.448442\pi$
$752$	3195.00	0.154933
$753$	14130.0	0.683832
$754$	−28674.0	−1.38494
$755$	0	0
$756$	0	0
$757$	−14846.0	−0.712797	−0.356398	−	0.934334i	$-0.615995\pi$
$757$	−14846.0	−0.712797	−0.356398	+	0.934334i	$0.615995\pi$
$758$	24915.0	1.19387
$759$	6210.00	0.296981
$760$	0	0
$761$	−3651.00	−0.173914	−0.0869571	−	0.996212i	$-0.527714\pi$
$761$	−3651.00	−0.173914	−0.0869571	+	0.996212i	$0.527714\pi$
$762$	4818.00	0.229052
$763$	0	0
$764$	−2388.00	−0.113082
$765$	0	0
$766$	2835.00	0.133724
$767$	21240.0	0.999911
$768$	3026.00	0.142176
$769$	29855.0	1.40000	0.699999	−	0.714144i	$-0.253184\pi$
$769$	29855.0	1.40000	0.699999	+	0.714144i	$0.253184\pi$
$770$	0	0
$771$	8160.00	0.381161
$772$	−272.000	−0.0126807
$773$	6519.00	0.303327	0.151664	−	0.988432i	$-0.451537\pi$
$773$	6519.00	0.303327	0.151664	+	0.988432i	$0.451537\pi$
$774$	19734.0	0.916439
$775$	0	0
$776$	−18942.0	−0.876261
$777$	0	0
$778$	−36108.0	−1.66393
$779$	−23595.0	−1.08521
$780$	0	0
$781$	−2160.00	−0.0989640
$782$	11178.0	0.511157
$783$	16200.0	0.739388
$784$	0	0
$785$	0	0
$786$	−12114.0	−0.549735
$787$	−35114.0	−1.59044	−0.795222	−	0.606319i	$-0.792646\pi$
$787$	−35114.0	−1.59044	−0.795222	+	0.606319i	$0.792646\pi$
$788$	2109.00	0.0953427
$789$	6576.00	0.296720
$790$	0	0
$791$	0	0
$792$	21735.0	0.975151
$793$	−23128.0	−1.03569
$794$	−8094.00	−0.361770
$795$	0	0
$796$	1424.00	0.0634075
$797$	−20910.0	−0.929323	−0.464661	−	0.885488i	$-0.653824\pi$
$797$	−20910.0	−0.929323	−0.464661	+	0.885488i	$0.653824\pi$
$798$	0	0
$799$	−2430.00	−0.107594
$800$	0	0
$801$	27462.0	1.21139
$802$	−21159.0	−0.931609
$803$	30060.0	1.32104
$804$	560.000	0.0245643
$805$	0	0
$806$	−15576.0	−0.680696
$807$	−6528.00	−0.284754
$808$	14364.0	0.625401
$809$	4431.00	0.192566	0.0962829	−	0.995354i	$-0.469305\pi$
$809$	4431.00	0.192566	0.0962829	+	0.995354i	$0.469305\pi$
$810$	0	0
$811$	−9577.00	−0.414666	−0.207333	−	0.978270i	$-0.566478\pi$
$811$	−9577.00	−0.414666	−0.207333	+	0.978270i	$0.566478\pi$
$812$	0	0
$813$	−5504.00	−0.237434
$814$	34965.0	1.50556
$815$	0	0
$816$	−7668.00	−0.328963
$817$	−34606.0	−1.48190
$818$	32610.0	1.39387
$819$	0	0
$820$	0	0
$821$	−10938.0	−0.464968	−0.232484	−	0.972600i	$-0.574685\pi$
$821$	−10938.0	−0.464968	−0.232484	+	0.972600i	$0.574685\pi$
$822$	360.000	0.0152755
$823$	−11540.0	−0.488772	−0.244386	−	0.969678i	$-0.578586\pi$
$823$	−11540.0	−0.488772	−0.244386	+	0.969678i	$0.578586\pi$
$824$	31836.0	1.34595
$825$	0	0
$826$	0	0
$827$	18762.0	0.788898	0.394449	−	0.918918i	$-0.370935\pi$
$827$	18762.0	0.788898	0.394449	+	0.918918i	$0.370935\pi$
$828$	1587.00	0.0666088
$829$	−39610.0	−1.65948	−0.829742	−	0.558147i	$-0.811512\pi$
$829$	−39610.0	−1.65948	−0.829742	+	0.558147i	$0.811512\pi$
$830$	0	0
$831$	9380.00	0.391563
$832$	−25547.0	−1.06452
$833$	0	0
$834$	10248.0	0.425491
$835$	0	0
$836$	5445.00	0.225262
$837$	8800.00	0.363408
$838$	29187.0	1.20316
$839$	39162.0	1.61147	0.805734	−	0.592277i	$-0.201771\pi$
$839$	39162.0	1.61147	0.805734	+	0.592277i	$0.201771\pi$
$840$	0	0
$841$	1855.00	0.0760589
$842$	37650.0	1.54098
$843$	15642.0	0.639074
$844$	−3625.00	−0.147841
$845$	0	0
$846$	−3105.00	−0.126185
$847$	0	0
$848$	42387.0	1.71648
$849$	1316.00	0.0531979
$850$	0	0
$851$	−17871.0	−0.719871
$852$	96.0000	0.00386022
$853$	11527.0	0.462693	0.231346	−	0.972871i	$-0.425687\pi$
$853$	11527.0	0.462693	0.231346	+	0.972871i	$0.425687\pi$
$854$	0	0
$855$	0	0
$856$	15372.0	0.613790
$857$	41826.0	1.66715	0.833576	−	0.552405i	$-0.186290\pi$
$857$	41826.0	1.66715	0.833576	+	0.552405i	$0.186290\pi$
$858$	−15930.0	−0.633848
$859$	35192.0	1.39783	0.698915	−	0.715205i	$-0.253667\pi$
$859$	35192.0	1.39783	0.698915	+	0.715205i	$0.253667\pi$
$860$	0	0
$861$	0	0
$862$	−8964.00	−0.354194
$863$	9063.00	0.357483	0.178742	−	0.983896i	$-0.442797\pi$
$863$	9063.00	0.357483	0.178742	+	0.983896i	$0.442797\pi$
$864$	−4500.00	−0.177191
$865$	0	0
$866$	49848.0	1.95601
$867$	−3994.00	−0.156451
$868$	0	0
$869$	−35190.0	−1.37369
$870$	0	0
$871$	−16520.0	−0.642662
$872$	−33600.0	−1.30486
$873$	20746.0	0.804291
$874$	−25047.0	−0.969368
$875$	0	0
$876$	−1336.00	−0.0515288
$877$	−28439.0	−1.09500	−0.547501	−	0.836805i	$-0.684421\pi$
$877$	−28439.0	−1.09500	−0.547501	+	0.836805i	$0.684421\pi$
$878$	−22038.0	−0.847092
$879$	11994.0	0.460236
$880$	0	0
$881$	−9303.00	−0.355762	−0.177881	−	0.984052i	$-0.556924\pi$
$881$	−9303.00	−0.355762	−0.177881	+	0.984052i	$0.556924\pi$
$882$	0	0
$883$	14728.0	0.561310	0.280655	−	0.959809i	$-0.409448\pi$
$883$	14728.0	0.561310	0.280655	+	0.959809i	$0.409448\pi$
$884$	−3186.00	−0.121218
$885$	0	0
$886$	36.0000	0.00136506
$887$	17016.0	0.644128	0.322064	−	0.946718i	$-0.395623\pi$
$887$	17016.0	0.644128	0.322064	+	0.946718i	$0.395623\pi$
$888$	10878.0	0.411083
$889$	0	0
$890$	0	0
$891$	−18945.0	−0.712325
$892$	4960.00	0.186181
$893$	5445.00	0.204043
$894$	6516.00	0.243767
$895$	0	0
$896$	0	0
$897$	8142.00	0.303070
$898$	−29007.0	−1.07792
$899$	14256.0	0.528881
$900$	0	0
$901$	−32238.0	−1.19201
$902$	26325.0	0.971759
$903$	0	0
$904$	29232.0	1.07549
$905$	0	0
$906$	17196.0	0.630573
$907$	24922.0	0.912372	0.456186	−	0.889884i	$-0.349215\pi$
$907$	24922.0	0.912372	0.456186	+	0.889884i	$0.349215\pi$
$908$	1500.00	0.0548230
$909$	−15732.0	−0.574035
$910$	0	0
$911$	30714.0	1.11701	0.558507	−	0.829500i	$-0.311374\pi$
$911$	30714.0	1.11701	0.558507	+	0.829500i	$0.311374\pi$
$912$	17182.0	0.623852
$913$	34560.0	1.25276
$914$	−28902.0	−1.04594
$915$	0	0
$916$	6092.00	0.219744
$917$	0	0
$918$	16200.0	0.582440
$919$	17426.0	0.625496	0.312748	−	0.949836i	$-0.398750\pi$
$919$	17426.0	0.625496	0.312748	+	0.949836i	$0.398750\pi$
$920$	0	0
$921$	12452.0	0.445502
$922$	1026.00	0.0366481
$923$	−2832.00	−0.100993
$924$	0	0
$925$	0	0
$926$	7233.00	0.256686
$927$	−34868.0	−1.23540
$928$	−7290.00	−0.257873
$929$	26649.0	0.941147	0.470573	−	0.882361i	$-0.344047\pi$
$929$	26649.0	0.941147	0.470573	+	0.882361i	$0.344047\pi$
$930$	0	0
$931$	0	0
$932$	−138.000	−0.00485015
$933$	9360.00	0.328438
$934$	−3618.00	−0.126750
$935$	0	0
$936$	28497.0	0.995143
$937$	−27686.0	−0.965274	−0.482637	−	0.875820i	$-0.660321\pi$
$937$	−27686.0	−0.965274	−0.482637	+	0.875820i	$0.660321\pi$
$938$	0	0
$939$	−2056.00	−0.0714537
$940$	0	0
$941$	−17808.0	−0.616923	−0.308461	−	0.951237i	$-0.599814\pi$
$941$	−17808.0	−0.616923	−0.308461	+	0.951237i	$0.599814\pi$
$942$	−1374.00	−0.0475237
$943$	−13455.0	−0.464640
$944$	25560.0	0.881258
$945$	0	0
$946$	38610.0	1.32698
$947$	6906.00	0.236974	0.118487	−	0.992956i	$-0.462196\pi$
$947$	6906.00	0.236974	0.118487	+	0.992956i	$0.462196\pi$
$948$	1564.00	0.0535827
$949$	39412.0	1.34812
$950$	0	0
$951$	−17244.0	−0.587986
$952$	0	0
$953$	20940.0	0.711766	0.355883	−	0.934530i	$-0.384180\pi$
$953$	20940.0	0.711766	0.355883	+	0.934530i	$0.384180\pi$
$954$	−41193.0	−1.39798
$955$	0	0
$956$	−5502.00	−0.186137
$957$	14580.0	0.492481
$958$	1296.00	0.0437076
$959$	0	0
$960$	0	0
$961$	−22047.0	−0.740056
$962$	45843.0	1.53642
$963$	−16836.0	−0.563377
$964$	3551.00	0.118641
$965$	0	0
$966$	0	0
$967$	−9176.00	−0.305150	−0.152575	−	0.988292i	$-0.548757\pi$
$967$	−9176.00	−0.305150	−0.152575	+	0.988292i	$0.548757\pi$
$968$	14574.0	0.483911
$969$	−13068.0	−0.433235
$970$	0	0
$971$	29763.0	0.983666	0.491833	−	0.870689i	$-0.336327\pi$
$971$	29763.0	0.983666	0.491833	+	0.870689i	$0.336327\pi$
$972$	3542.00	0.116882
$973$	0	0
$974$	−35688.0	−1.17404
$975$	0	0
$976$	−27832.0	−0.912788
$977$	38490.0	1.26039	0.630197	−	0.776436i	$-0.282974\pi$
$977$	38490.0	1.26039	0.630197	+	0.776436i	$0.282974\pi$
$978$	−7368.00	−0.240903
$979$	53730.0	1.75405
$980$	0	0
$981$	36800.0	1.19769
$982$	36828.0	1.19677
$983$	12609.0	0.409120	0.204560	−	0.978854i	$-0.434424\pi$
$983$	12609.0	0.409120	0.204560	+	0.978854i	$0.434424\pi$
$984$	8190.00	0.265333
$985$	0	0
$986$	26244.0	0.847646
$987$	0	0
$988$	7139.00	0.229880
$989$	−19734.0	−0.634484
$990$	0	0
$991$	19820.0	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	19820.0	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	−3960.00	−0.126744
$993$	−3998.00	−0.127767
$994$	0	0
$995$	0	0
$996$	−1536.00	−0.0488655
$997$	−46034.0	−1.46230	−0.731149	−	0.682218i	$-0.761016\pi$
$997$	−46034.0	−1.46230	−0.731149	+	0.682218i	$0.761016\pi$
$998$	32628.0	1.03489
$999$	−25900.0	−0.820260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1225.4.a.b.1.1		1
5.4	even	2		245.4.a.e.1.1		1
7.2	even	3		175.4.e.b.151.1		2
7.4	even	3		175.4.e.b.51.1		2
7.6	odd	2		1225.4.a.a.1.1		1
15.14	odd	2		2205.4.a.e.1.1		1
35.2	odd	12		175.4.k.b.74.1		4
35.4	even	6		35.4.e.a.16.1	yes	2
35.9	even	6		35.4.e.a.11.1	✓	2
35.18	odd	12		175.4.k.b.149.1		4
35.19	odd	6		245.4.e.a.116.1		2
35.23	odd	12		175.4.k.b.74.2		4
35.24	odd	6		245.4.e.a.226.1		2
35.32	odd	12		175.4.k.b.149.2		4
35.34	odd	2		245.4.a.f.1.1		1
105.44	odd	6		315.4.j.b.46.1		2
105.74	odd	6		315.4.j.b.226.1		2
105.104	even	2		2205.4.a.g.1.1		1
140.39	odd	6		560.4.q.b.401.1		2
140.79	odd	6		560.4.q.b.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.a.11.1	✓	2	35.9	even	6
35.4.e.a.16.1	yes	2	35.4	even	6
175.4.e.b.51.1		2	7.4	even	3
175.4.e.b.151.1		2	7.2	even	3
175.4.k.b.74.1		4	35.2	odd	12
175.4.k.b.74.2		4	35.23	odd	12
175.4.k.b.149.1		4	35.18	odd	12
175.4.k.b.149.2		4	35.32	odd	12
245.4.a.e.1.1		1	5.4	even	2
245.4.a.f.1.1		1	35.34	odd	2
245.4.e.a.116.1		2	35.19	odd	6
245.4.e.a.226.1		2	35.24	odd	6
315.4.j.b.46.1		2	105.44	odd	6
315.4.j.b.226.1		2	105.74	odd	6
560.4.q.b.81.1		2	140.79	odd	6
560.4.q.b.401.1		2	140.39	odd	6
1225.4.a.a.1.1		1	7.6	odd	2
1225.4.a.b.1.1		1	1.1	even	1	trivial
2205.4.a.e.1.1		1	15.14	odd	2
2205.4.a.g.1.1		1	105.104	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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