LMFDB - Embedded newform 570.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +2.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} +1.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} -2.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} -1.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} -8.00000 q^{41} -2.00000 q^{42} -6.00000 q^{43} +2.00000 q^{44} +1.00000 q^{45} +4.00000 q^{46} -12.0000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} +4.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{55} -2.00000 q^{56} -1.00000 q^{57} +1.00000 q^{60} +2.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +2.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} +4.00000 q^{69} -2.00000 q^{70} -8.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +8.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -4.00000 q^{77} +4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} +4.00000 q^{83} -2.00000 q^{84} -2.00000 q^{85} -6.00000 q^{86} +2.00000 q^{88} +1.00000 q^{90} -8.00000 q^{91} +4.00000 q^{92} -8.00000 q^{93} -12.0000 q^{94} -1.00000 q^{95} +1.00000 q^{96} -12.0000 q^{97} -3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.00000	−0.534522
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	2.00000	0.426401
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	1.00000	0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	2.00000	0.348155
$34$	−2.00000	−0.342997
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−1.00000	−0.162221
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−2.00000	−0.308607
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	2.00000	0.301511
$45$	1.00000	0.149071
$46$	4.00000	0.589768
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	−2.00000	−0.280056
$52$	4.00000	0.554700
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	2.00000	0.269680
$56$	−2.00000	−0.267261
$57$	−1.00000	−0.132453
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	2.00000	0.246183
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−2.00000	−0.242536
$69$	4.00000	0.481543
$70$	−2.00000	−0.239046
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	8.00000	0.929981
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	−4.00000	−0.455842
$78$	4.00000	0.452911
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−8.00000	−0.883452
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.00000	−0.218218
$85$	−2.00000	−0.216930
$86$	−6.00000	−0.646997
$87$	0	0
$88$	2.00000	0.213201
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	1.00000	0.105409
$91$	−8.00000	−0.838628
$92$	4.00000	0.417029
$93$	−8.00000	−0.829561
$94$	−12.0000	−1.23771
$95$	−1.00000	−0.102598
$96$	1.00000	0.102062
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−3.00000	−0.303046
$99$	2.00000	0.201008
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−2.00000	−0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	4.00000	0.392232
$105$	−2.00000	−0.195180
$106$	−6.00000	−0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	2.00000	0.190693
$111$	8.00000	0.759326
$112$	−2.00000	−0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−1.00000	−0.0936586
$115$	4.00000	0.373002
$116$	0	0
$117$	4.00000	0.369800
$118$	0	0
$119$	4.00000	0.366679
$120$	1.00000	0.0912871
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	−8.00000	−0.721336
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	−2.00000	−0.178174
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	−6.00000	−0.528271
$130$	4.00000	0.350823
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	2.00000	0.174078
$133$	2.00000	0.173422
$134$	8.00000	0.691095
$135$	1.00000	0.0860663
$136$	−2.00000	−0.171499
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	4.00000	0.340503
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	−2.00000	−0.169031
$141$	−12.0000	−1.01058
$142$	−8.00000	−0.671345
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	0	0
$146$	14.0000	1.15865
$147$	−3.00000	−0.247436
$148$	8.00000	0.657596
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	1.00000	0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	−2.00000	−0.161690
$154$	−4.00000	−0.322329
$155$	−8.00000	−0.642575
$156$	4.00000	0.320256
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	−6.00000	−0.475831
$160$	1.00000	0.0790569
$161$	−8.00000	−0.630488
$162$	1.00000	0.0785674
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	−8.00000	−0.624695
$165$	2.00000	0.155700
$166$	4.00000	0.310460
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−2.00000	−0.154303
$169$	3.00000	0.230769
$170$	−2.00000	−0.153393
$171$	−1.00000	−0.0764719
$172$	−6.00000	−0.457496
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	2.00000	0.150756
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	1.00000	0.0745356
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−8.00000	−0.592999
$183$	2.00000	0.147844
$184$	4.00000	0.294884
$185$	8.00000	0.588172
$186$	−8.00000	−0.586588
$187$	−4.00000	−0.292509
$188$	−12.0000	−0.875190
$189$	−2.00000	−0.145479
$190$	−1.00000	−0.0725476
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.00000	0.0721688
$193$	24.0000	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$194$	−12.0000	−0.861550
$195$	4.00000	0.286446
$196$	−3.00000	−0.214286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	2.00000	0.142134
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	1.00000	0.0707107
$201$	8.00000	0.564276
$202$	2.00000	0.140720
$203$	0	0
$204$	−2.00000	−0.140028
$205$	−8.00000	−0.558744
$206$	4.00000	0.278693
$207$	4.00000	0.278019
$208$	4.00000	0.277350
$209$	−2.00000	−0.138343
$210$	−2.00000	−0.138013
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−6.00000	−0.412082
$213$	−8.00000	−0.548151
$214$	−12.0000	−0.820303
$215$	−6.00000	−0.409197
$216$	1.00000	0.0680414
$217$	16.0000	1.08615
$218$	10.0000	0.677285
$219$	14.0000	0.946032
$220$	2.00000	0.134840
$221$	−8.00000	−0.538138
$222$	8.00000	0.536925
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−2.00000	−0.133631
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−1.00000	−0.0662266
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	4.00000	0.263752
$231$	−4.00000	−0.263181
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.00000	0.261488
$235$	−12.0000	−0.782794
$236$	0	0
$237$	0	0
$238$	4.00000	0.259281
$239$	10.0000	0.646846	0.323423	−	0.946254i	$-0.395166\pi$
$239$	10.0000	0.646846	0.323423	+	0.946254i	$0.395166\pi$
$240$	1.00000	0.0645497
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−3.00000	−0.191663
$246$	−8.00000	−0.510061
$247$	−4.00000	−0.254514
$248$	−8.00000	−0.508001
$249$	4.00000	0.253490
$250$	1.00000	0.0632456
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	−2.00000	−0.125988
$253$	8.00000	0.502956
$254$	8.00000	0.501965
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	−6.00000	−0.373544
$259$	−16.0000	−0.994192
$260$	4.00000	0.248069
$261$	0	0
$262$	−18.0000	−1.11204
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	2.00000	0.123091
$265$	−6.00000	−0.368577
$266$	2.00000	0.122628
$267$	0	0
$268$	8.00000	0.488678
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	1.00000	0.0608581
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	−2.00000	−0.121268
$273$	−8.00000	−0.484182
$274$	−22.0000	−1.32907
$275$	2.00000	0.120605
$276$	4.00000	0.240772
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	−2.00000	−0.119523
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	−12.0000	−0.714590
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−8.00000	−0.474713
$285$	−1.00000	−0.0592349
$286$	8.00000	0.473050
$287$	16.0000	0.944450
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−12.0000	−0.703452
$292$	14.0000	0.819288
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	8.00000	0.464991
$297$	2.00000	0.116052
$298$	10.0000	0.579284
$299$	16.0000	0.925304
$300$	1.00000	0.0577350
$301$	12.0000	0.691669
$302$	−8.00000	−0.460348
$303$	2.00000	0.114897
$304$	−1.00000	−0.0573539
$305$	2.00000	0.114520
$306$	−2.00000	−0.114332
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	−4.00000	−0.227921
$309$	4.00000	0.227552
$310$	−8.00000	−0.454369
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	4.00000	0.226455
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	18.0000	1.01580
$315$	−2.00000	−0.112687
$316$	0	0
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	−8.00000	−0.445823
$323$	2.00000	0.111283
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	14.0000	0.775388
$327$	10.0000	0.553001
$328$	−8.00000	−0.441726
$329$	24.0000	1.32316
$330$	2.00000	0.110096
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	4.00000	0.219529
$333$	8.00000	0.438397
$334$	8.00000	0.437741
$335$	8.00000	0.437087
$336$	−2.00000	−0.109109
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	3.00000	0.163178
$339$	−6.00000	−0.325875
$340$	−2.00000	−0.108465
$341$	−16.0000	−0.866449
$342$	−1.00000	−0.0540738
$343$	20.0000	1.07990
$344$	−6.00000	−0.323498
$345$	4.00000	0.215353
$346$	14.0000	0.752645
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	−2.00000	−0.106904
$351$	4.00000	0.213504
$352$	2.00000	0.106600
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	0	0
$357$	4.00000	0.211702
$358$	0	0
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	1.00000	0.0527046
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	−7.00000	−0.367405
$364$	−8.00000	−0.419314
$365$	14.0000	0.732793
$366$	2.00000	0.104542
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	4.00000	0.208514
$369$	−8.00000	−0.416463
$370$	8.00000	0.415900
$371$	12.0000	0.623009
$372$	−8.00000	−0.414781
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	−4.00000	−0.206835
$375$	1.00000	0.0516398
$376$	−12.0000	−0.618853
$377$	0	0
$378$	−2.00000	−0.102869
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	−1.00000	−0.0512989
$381$	8.00000	0.409852
$382$	−18.0000	−0.920960
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	−4.00000	−0.203859
$386$	24.0000	1.22157
$387$	−6.00000	−0.304997
$388$	−12.0000	−0.609208
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	4.00000	0.202548
$391$	−8.00000	−0.404577
$392$	−3.00000	−0.151523
$393$	−18.0000	−0.907980
$394$	18.0000	0.906827
$395$	0	0
$396$	2.00000	0.100504
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−20.0000	−1.00251
$399$	2.00000	0.100125
$400$	1.00000	0.0500000
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	8.00000	0.399004
$403$	−32.0000	−1.59403
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	0	0
$407$	16.0000	0.793091
$408$	−2.00000	−0.0990148
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	−8.00000	−0.395092
$411$	−22.0000	−1.08518
$412$	4.00000	0.197066
$413$	0	0
$414$	4.00000	0.196589
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	0	0
$418$	−2.00000	−0.0978232
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	−2.00000	−0.0975900
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	12.0000	0.584151
$423$	−12.0000	−0.583460
$424$	−6.00000	−0.291386
$425$	−2.00000	−0.0970143
$426$	−8.00000	−0.387601
$427$	−4.00000	−0.193574
$428$	−12.0000	−0.580042
$429$	8.00000	0.386244
$430$	−6.00000	−0.289346
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	10.0000	0.478913
$437$	−4.00000	−0.191346
$438$	14.0000	0.668946
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	2.00000	0.0953463
$441$	−3.00000	−0.142857
$442$	−8.00000	−0.380521
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	4.00000	0.189405
$447$	10.0000	0.472984
$448$	−2.00000	−0.0944911
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	1.00000	0.0471405
$451$	−16.0000	−0.753411
$452$	−6.00000	−0.282216
$453$	−8.00000	−0.375873
$454$	−12.0000	−0.563188
$455$	−8.00000	−0.375046
$456$	−1.00000	−0.0468293
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	10.0000	0.467269
$459$	−2.00000	−0.0933520
$460$	4.00000	0.186501
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	−4.00000	−0.186097
$463$	−6.00000	−0.278844	−0.139422	−	0.990233i	$-0.544524\pi$
$463$	−6.00000	−0.278844	−0.139422	+	0.990233i	$0.544524\pi$
$464$	0	0
$465$	−8.00000	−0.370991
$466$	−6.00000	−0.277945
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	4.00000	0.184900
$469$	−16.0000	−0.738811
$470$	−12.0000	−0.553519
$471$	18.0000	0.829396
$472$	0	0
$473$	−12.0000	−0.551761
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	4.00000	0.183340
$477$	−6.00000	−0.274721
$478$	10.0000	0.457389
$479$	−10.0000	−0.456912	−0.228456	−	0.973554i	$-0.573368\pi$
$479$	−10.0000	−0.456912	−0.228456	+	0.973554i	$0.573368\pi$
$480$	1.00000	0.0456435
$481$	32.0000	1.45907
$482$	2.00000	0.0910975
$483$	−8.00000	−0.364013
$484$	−7.00000	−0.318182
$485$	−12.0000	−0.544892
$486$	1.00000	0.0453609
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	2.00000	0.0905357
$489$	14.0000	0.633102
$490$	−3.00000	−0.135526
$491$	22.0000	0.992846	0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000	0.992846	0.496423	+	0.868081i	$0.334646\pi$
$492$	−8.00000	−0.360668
$493$	0	0
$494$	−4.00000	−0.179969
$495$	2.00000	0.0898933
$496$	−8.00000	−0.359211
$497$	16.0000	0.717698
$498$	4.00000	0.179244
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	1.00000	0.0447214
$501$	8.00000	0.357414
$502$	2.00000	0.0892644
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−2.00000	−0.0890871
$505$	2.00000	0.0889988
$506$	8.00000	0.355643
$507$	3.00000	0.133235
$508$	8.00000	0.354943
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	−2.00000	−0.0885615
$511$	−28.0000	−1.23865
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	18.0000	0.793946
$515$	4.00000	0.176261
$516$	−6.00000	−0.264135
$517$	−24.0000	−1.05552
$518$	−16.0000	−0.703000
$519$	14.0000	0.614532
$520$	4.00000	0.175412
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−18.0000	−0.786334
$525$	−2.00000	−0.0872872
$526$	24.0000	1.04645
$527$	16.0000	0.696971
$528$	2.00000	0.0870388
$529$	−7.00000	−0.304348
$530$	−6.00000	−0.260623
$531$	0	0
$532$	2.00000	0.0867110
$533$	−32.0000	−1.38607
$534$	0	0
$535$	−12.0000	−0.518805
$536$	8.00000	0.345547
$537$	0	0
$538$	0	0
$539$	−6.00000	−0.258438
$540$	1.00000	0.0430331
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	12.0000	0.515444
$543$	2.00000	0.0858282
$544$	−2.00000	−0.0857493
$545$	10.0000	0.428353
$546$	−8.00000	−0.342368
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−22.0000	−0.939793
$549$	2.00000	0.0853579
$550$	2.00000	0.0852803
$551$	0	0
$552$	4.00000	0.170251
$553$	0	0
$554$	18.0000	0.764747
$555$	8.00000	0.339581
$556$	0	0
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	−8.00000	−0.338667
$559$	−24.0000	−1.01509
$560$	−2.00000	−0.0845154
$561$	−4.00000	−0.168880
$562$	12.0000	0.506189
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	−12.0000	−0.505291
$565$	−6.00000	−0.252422
$566$	14.0000	0.588464
$567$	−2.00000	−0.0839921
$568$	−8.00000	−0.335673
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	−1.00000	−0.0418854
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	8.00000	0.334497
$573$	−18.0000	−0.751961
$574$	16.0000	0.667827
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	−13.0000	−0.540729
$579$	24.0000	0.997406
$580$	0	0
$581$	−8.00000	−0.331896
$582$	−12.0000	−0.497416
$583$	−12.0000	−0.496989
$584$	14.0000	0.579324
$585$	4.00000	0.165380
$586$	14.0000	0.578335
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	−3.00000	−0.123718
$589$	8.00000	0.329634
$590$	0	0
$591$	18.0000	0.740421
$592$	8.00000	0.328798
$593$	−46.0000	−1.88899	−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000	−1.88899	−0.944497	+	0.328521i	$0.893450\pi$
$594$	2.00000	0.0820610
$595$	4.00000	0.163984
$596$	10.0000	0.409616
$597$	−20.0000	−0.818546
$598$	16.0000	0.654289
$599$	20.0000	0.817178	0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000	0.817178	0.408589	+	0.912719i	$0.366021\pi$
$600$	1.00000	0.0408248
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	12.0000	0.489083
$603$	8.00000	0.325785
$604$	−8.00000	−0.325515
$605$	−7.00000	−0.284590
$606$	2.00000	0.0812444
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	2.00000	0.0809776
$611$	−48.0000	−1.94187
$612$	−2.00000	−0.0808452
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	−32.0000	−1.29141
$615$	−8.00000	−0.322591
$616$	−4.00000	−0.161165
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	4.00000	0.160904
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	−8.00000	−0.321288
$621$	4.00000	0.160514
$622$	−18.0000	−0.721734
$623$	0	0
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	−2.00000	−0.0798723
$628$	18.0000	0.718278
$629$	−16.0000	−0.637962
$630$	−2.00000	−0.0796819
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	0	0
$633$	12.0000	0.476957
$634$	18.0000	0.714871
$635$	8.00000	0.317470
$636$	−6.00000	−0.237915
$637$	−12.0000	−0.475457
$638$	0	0
$639$	−8.00000	−0.316475
$640$	1.00000	0.0395285
$641$	32.0000	1.26392	0.631962	−	0.774999i	$-0.282250\pi$
$641$	32.0000	1.26392	0.631962	+	0.774999i	$0.282250\pi$
$642$	−12.0000	−0.473602
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	−8.00000	−0.315244
$645$	−6.00000	−0.236250
$646$	2.00000	0.0786889
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	4.00000	0.156893
$651$	16.0000	0.627089
$652$	14.0000	0.548282
$653$	−46.0000	−1.80012	−0.900060	−	0.435767i	$-0.856477\pi$
$653$	−46.0000	−1.80012	−0.900060	+	0.435767i	$0.856477\pi$
$654$	10.0000	0.391031
$655$	−18.0000	−0.703318
$656$	−8.00000	−0.312348
$657$	14.0000	0.546192
$658$	24.0000	0.935617
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	2.00000	0.0778499
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	12.0000	0.466393
$663$	−8.00000	−0.310694
$664$	4.00000	0.155230
$665$	2.00000	0.0775567
$666$	8.00000	0.309994
$667$	0	0
$668$	8.00000	0.309529
$669$	4.00000	0.154649
$670$	8.00000	0.309067
$671$	4.00000	0.154418
$672$	−2.00000	−0.0771517
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	28.0000	1.07852
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−6.00000	−0.230429
$679$	24.0000	0.921035
$680$	−2.00000	−0.0766965
$681$	−12.0000	−0.459841
$682$	−16.0000	−0.612672
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−1.00000	−0.0382360
$685$	−22.0000	−0.840577
$686$	20.0000	0.763604
$687$	10.0000	0.381524
$688$	−6.00000	−0.228748
$689$	−24.0000	−0.914327
$690$	4.00000	0.152277
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	14.0000	0.532200
$693$	−4.00000	−0.151947
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	16.0000	0.606043
$698$	−10.0000	−0.378506
$699$	−6.00000	−0.226941
$700$	−2.00000	−0.0755929
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	4.00000	0.150970
$703$	−8.00000	−0.301726
$704$	2.00000	0.0753778
$705$	−12.0000	−0.451946
$706$	−6.00000	−0.225813
$707$	−4.00000	−0.150435
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	0	0
$713$	−32.0000	−1.19841
$714$	4.00000	0.149696
$715$	8.00000	0.299183
$716$	0	0
$717$	10.0000	0.373457
$718$	−10.0000	−0.373197
$719$	50.0000	1.86469	0.932343	−	0.361576i	$-0.117761\pi$
$719$	50.0000	1.86469	0.932343	+	0.361576i	$0.117761\pi$
$720$	1.00000	0.0372678
$721$	−8.00000	−0.297936
$722$	1.00000	0.0372161
$723$	2.00000	0.0743808
$724$	2.00000	0.0743294
$725$	0	0
$726$	−7.00000	−0.259794
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	12.0000	0.443836
$732$	2.00000	0.0739221
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	18.0000	0.664392
$735$	−3.00000	−0.110657
$736$	4.00000	0.147442
$737$	16.0000	0.589368
$738$	−8.00000	−0.294484
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	8.00000	0.294086
$741$	−4.00000	−0.146944
$742$	12.0000	0.440534
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−8.00000	−0.293294
$745$	10.0000	0.366372
$746$	−36.0000	−1.31805
$747$	4.00000	0.146352
$748$	−4.00000	−0.146254
$749$	24.0000	0.876941
$750$	1.00000	0.0365148
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	−12.0000	−0.437595
$753$	2.00000	0.0728841
$754$	0	0
$755$	−8.00000	−0.291150
$756$	−2.00000	−0.0727393
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−20.0000	−0.726433
$759$	8.00000	0.290382
$760$	−1.00000	−0.0362738
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	8.00000	0.289809
$763$	−20.0000	−0.724049
$764$	−18.0000	−0.651217
$765$	−2.00000	−0.0723102
$766$	24.0000	0.867155
$767$	0	0
$768$	1.00000	0.0360844
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	−4.00000	−0.144150
$771$	18.0000	0.648254
$772$	24.0000	0.863779
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	−6.00000	−0.215666
$775$	−8.00000	−0.287368
$776$	−12.0000	−0.430775
$777$	−16.0000	−0.573997
$778$	30.0000	1.07555
$779$	8.00000	0.286630
$780$	4.00000	0.143223
$781$	−16.0000	−0.572525
$782$	−8.00000	−0.286079
$783$	0	0
$784$	−3.00000	−0.107143
$785$	18.0000	0.642448
$786$	−18.0000	−0.642039
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	18.0000	0.641223
$789$	24.0000	0.854423
$790$	0	0
$791$	12.0000	0.426671
$792$	2.00000	0.0710669
$793$	8.00000	0.284088
$794$	−22.0000	−0.780751
$795$	−6.00000	−0.212798
$796$	−20.0000	−0.708881
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	2.00000	0.0707992
$799$	24.0000	0.849059
$800$	1.00000	0.0353553
$801$	0	0
$802$	12.0000	0.423735
$803$	28.0000	0.988099
$804$	8.00000	0.282138
$805$	−8.00000	−0.281963
$806$	−32.0000	−1.12715
$807$	0	0
$808$	2.00000	0.0703598
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	1.00000	0.0351364
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	0	0
$813$	12.0000	0.420858
$814$	16.0000	0.560800
$815$	14.0000	0.490399
$816$	−2.00000	−0.0700140
$817$	6.00000	0.209913
$818$	30.0000	1.04893
$819$	−8.00000	−0.279543
$820$	−8.00000	−0.279372
$821$	−38.0000	−1.32621	−0.663105	−	0.748527i	$-0.730762\pi$
$821$	−38.0000	−1.32621	−0.663105	+	0.748527i	$0.730762\pi$
$822$	−22.0000	−0.767338
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	4.00000	0.139347
$825$	2.00000	0.0696311
$826$	0	0
$827$	28.0000	0.973655	0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000	0.973655	0.486828	+	0.873498i	$0.338154\pi$
$828$	4.00000	0.139010
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	4.00000	0.138842
$831$	18.0000	0.624413
$832$	4.00000	0.138675
$833$	6.00000	0.207888
$834$	0	0
$835$	8.00000	0.276851
$836$	−2.00000	−0.0691714
$837$	−8.00000	−0.276520
$838$	−30.0000	−1.03633
$839$	−40.0000	−1.38095	−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000	−1.38095	−0.690477	+	0.723355i	$0.742599\pi$
$840$	−2.00000	−0.0690066
$841$	−29.0000	−1.00000
$842$	22.0000	0.758170
$843$	12.0000	0.413302
$844$	12.0000	0.413057
$845$	3.00000	0.103203
$846$	−12.0000	−0.412568
$847$	14.0000	0.481046
$848$	−6.00000	−0.206041
$849$	14.0000	0.480479
$850$	−2.00000	−0.0685994
$851$	32.0000	1.09695
$852$	−8.00000	−0.274075
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	−4.00000	−0.136877
$855$	−1.00000	−0.0341993
$856$	−12.0000	−0.410152
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	8.00000	0.273115
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−6.00000	−0.204598
$861$	16.0000	0.545279
$862$	12.0000	0.408722
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	1.00000	0.0340207
$865$	14.0000	0.476014
$866$	−16.0000	−0.543702
$867$	−13.0000	−0.441503
$868$	16.0000	0.543075
$869$	0	0
$870$	0	0
$871$	32.0000	1.08428
$872$	10.0000	0.338643
$873$	−12.0000	−0.406138
$874$	−4.00000	−0.135302
$875$	−2.00000	−0.0676123
$876$	14.0000	0.473016
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	−40.0000	−1.34993
$879$	14.0000	0.472208
$880$	2.00000	0.0674200
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	−3.00000	−0.101015
$883$	−26.0000	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	24.0000	0.806296
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	8.00000	0.268462
$889$	−16.0000	−0.536623
$890$	0	0
$891$	2.00000	0.0670025
$892$	4.00000	0.133930
$893$	12.0000	0.401565
$894$	10.0000	0.334450
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	16.0000	0.534224
$898$	0	0
$899$	0	0
$900$	1.00000	0.0333333
$901$	12.0000	0.399778
$902$	−16.0000	−0.532742
$903$	12.0000	0.399335
$904$	−6.00000	−0.199557
$905$	2.00000	0.0664822
$906$	−8.00000	−0.265782
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−12.0000	−0.398234
$909$	2.00000	0.0663358
$910$	−8.00000	−0.265197
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	−1.00000	−0.0331133
$913$	8.00000	0.264761
$914$	18.0000	0.595387
$915$	2.00000	0.0661180
$916$	10.0000	0.330409
$917$	36.0000	1.18882
$918$	−2.00000	−0.0660098
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	4.00000	0.131876
$921$	−32.0000	−1.05444
$922$	2.00000	0.0658665
$923$	−32.0000	−1.05329
$924$	−4.00000	−0.131590
$925$	8.00000	0.263038
$926$	−6.00000	−0.197172
$927$	4.00000	0.131377
$928$	0	0
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	−8.00000	−0.262330
$931$	3.00000	0.0983210
$932$	−6.00000	−0.196537
$933$	−18.0000	−0.589294
$934$	8.00000	0.261768
$935$	−4.00000	−0.130814
$936$	4.00000	0.130744
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−16.0000	−0.522419
$939$	−6.00000	−0.195803
$940$	−12.0000	−0.391397
$941$	−8.00000	−0.260793	−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000	−0.260793	−0.130396	+	0.991462i	$0.541625\pi$
$942$	18.0000	0.586472
$943$	−32.0000	−1.04206
$944$	0	0
$945$	−2.00000	−0.0650600
$946$	−12.0000	−0.390154
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	0	0
$949$	56.0000	1.81784
$950$	−1.00000	−0.0324443
$951$	18.0000	0.583690
$952$	4.00000	0.129641
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	−6.00000	−0.194257
$955$	−18.0000	−0.582466
$956$	10.0000	0.323423
$957$	0	0
$958$	−10.0000	−0.323085
$959$	44.0000	1.42083
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	32.0000	1.03172
$963$	−12.0000	−0.386695
$964$	2.00000	0.0644157
$965$	24.0000	0.772587
$966$	−8.00000	−0.257396
$967$	58.0000	1.86515	0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000	1.86515	0.932577	+	0.360971i	$0.117555\pi$
$968$	−7.00000	−0.224989
$969$	2.00000	0.0642493
$970$	−12.0000	−0.385297
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	28.0000	0.897178
$975$	4.00000	0.128103
$976$	2.00000	0.0640184
$977$	38.0000	1.21573	0.607864	−	0.794041i	$-0.292027\pi$
$977$	38.0000	1.21573	0.607864	+	0.794041i	$0.292027\pi$
$978$	14.0000	0.447671
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	10.0000	0.319275
$982$	22.0000	0.702048
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	−8.00000	−0.255031
$985$	18.0000	0.573528
$986$	0	0
$987$	24.0000	0.763928
$988$	−4.00000	−0.127257
$989$	−24.0000	−0.763156
$990$	2.00000	0.0635642
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	−8.00000	−0.254000
$993$	12.0000	0.380808
$994$	16.0000	0.507489
$995$	−20.0000	−0.634043
$996$	4.00000	0.126745
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	−40.0000	−1.26618
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.a.l.1.1	✓	1
3.2	odd	2		1710.2.a.b.1.1		1
4.3	odd	2		4560.2.a.o.1.1		1
5.2	odd	4		2850.2.d.q.799.2		2
5.3	odd	4		2850.2.d.q.799.1		2
5.4	even	2		2850.2.a.e.1.1		1
15.14	odd	2		8550.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.l.1.1	✓	1	1.1	even	1	trivial
1710.2.a.b.1.1		1	3.2	odd	2
2850.2.a.e.1.1		1	5.4	even	2
2850.2.d.q.799.1		2	5.3	odd	4
2850.2.d.q.799.2		2	5.2	odd	4
4560.2.a.o.1.1		1	4.3	odd	2
8550.2.a.bf.1.1		1	15.14	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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