LMFDB - Embedded newform 5610.2.a.bh.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5610,2,Mod(1,5610)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5610.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5610, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,1,1,-1,1,0,1,1,-1,1,1,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5610.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} +1.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} -6.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -8.00000 q^{46} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -6.00000 q^{58} -8.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +1.00000 q^{66} +12.0000 q^{67} +1.00000 q^{68} -8.00000 q^{69} +8.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -6.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} -1.00000 q^{85} -8.00000 q^{86} -6.00000 q^{87} +1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} -8.00000 q^{92} -4.00000 q^{93} +1.00000 q^{96} -6.00000 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	−6.00000	−0.960769
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−8.00000	−1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−6.00000	−0.832050
$53$	−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
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−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	$0.459132\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	1.00000	0.123091
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	1.00000	0.121268
$69$	−8.00000	−0.963087
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.00000	0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	2.00000	0.232495
$75$	1.00000	0.115470
$76$	0	0
$77$	0	0
$78$	−6.00000	−0.679366
$79$	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
$82$	2.00000	0.220863
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	−8.00000	−0.862662
$87$	−6.00000	−0.643268
$88$	1.00000	0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−8.00000	−0.834058
$93$	−4.00000	−0.414781
$94$	0	0
$95$	0	0
$96$	1.00000	0.102062
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	−7.00000	−0.707107
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	1.00000	0.0990148
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−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
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	0	0
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	8.00000	0.746004
$116$	−6.00000	−0.557086
$117$	−6.00000	−0.554700
$118$	−8.00000	−0.736460
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	2.00000	0.180334
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	6.00000	0.526235
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	12.0000	1.03664
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−8.00000	−0.681005
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	0	0
$142$	8.00000	0.671345
$143$	−6.00000	−0.501745
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	−2.00000	−0.165521
$147$	−7.00000	−0.577350
$148$	2.00000	0.164399
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	1.00000	0.0816497
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	0	0
$153$	1.00000	0.0808452
$154$	0	0
$155$	4.00000	0.321288
$156$	−6.00000	−0.480384
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	0	0
$159$	−6.00000	−0.475831
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	−1.00000	−0.0778499
$166$	12.0000	0.931381
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	−8.00000	−0.609994
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	1.00000	0.0753778
$177$	−8.00000	−0.601317
$178$	2.00000	0.149906
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−1.00000	−0.0745356
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	−8.00000	−0.589768
$185$	−2.00000	−0.147043
$186$	−4.00000	−0.293294
$187$	1.00000	0.0731272
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	1.00000	0.0721688
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	−6.00000	−0.430775
$195$	6.00000	0.429669
$196$	−7.00000	−0.500000
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	1.00000	0.0710669
$199$	12.0000	0.850657	0.425329	−	0.905039i	$-0.360158\pi$
$199$	12.0000	0.850657	0.425329	+	0.905039i	$0.360158\pi$
$200$	1.00000	0.0707107
$201$	12.0000	0.846415
$202$	−2.00000	−0.140720
$203$	0	0
$204$	1.00000	0.0700140
$205$	−2.00000	−0.139686
$206$	−8.00000	−0.557386
$207$	−8.00000	−0.556038
$208$	−6.00000	−0.416025
$209$	0	0
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−6.00000	−0.412082
$213$	8.00000	0.548151
$214$	−12.0000	−0.820303
$215$	8.00000	0.545595
$216$	1.00000	0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	−2.00000	−0.135147
$220$	−1.00000	−0.0674200
$221$	−6.00000	−0.403604
$222$	2.00000	0.134231
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−10.0000	−0.665190
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	7.00000	0.447214
$246$	2.00000	0.127515
$247$	0	0
$248$	−4.00000	−0.254000
$249$	12.0000	0.760469
$250$	−1.00000	−0.0632456
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	−16.0000	−1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	6.00000	0.372104
$261$	−6.00000	−0.371391
$262$	4.00000	0.247121
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	1.00000	0.0615457
$265$	6.00000	0.368577
$266$	0	0
$267$	2.00000	0.122398
$268$	12.0000	0.733017
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	−1.00000	−0.0608581
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	2.00000	0.120824
$275$	1.00000	0.0603023
$276$	−8.00000	−0.481543
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	4.00000	0.239904
$279$	−4.00000	−0.239474
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	−6.00000	−0.354787
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	−6.00000	−0.351726
$292$	−2.00000	−0.117041
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	−7.00000	−0.408248
$295$	8.00000	0.465778
$296$	2.00000	0.116248
$297$	1.00000	0.0580259
$298$	−2.00000	−0.115857
$299$	48.0000	2.77591
$300$	1.00000	0.0577350
$301$	0	0
$302$	16.0000	0.920697
$303$	−2.00000	−0.114897
$304$	0	0
$305$	−2.00000	−0.114520
$306$	1.00000	0.0571662
$307$	−24.0000	−1.36975	−0.684876	−	0.728659i	$-0.740144\pi$
$307$	−24.0000	−1.36975	−0.684876	+	0.728659i	$0.740144\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	4.00000	0.227185
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	−6.00000	−0.339683
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−2.00000	−0.112867
$315$	0	0
$316$	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
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−6.00000	−0.332820
$326$	−4.00000	−0.221540
$327$	2.00000	0.110600
$328$	2.00000	0.110432
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	12.0000	0.658586
$333$	2.00000	0.109599
$334$	4.00000	0.218870
$335$	−12.0000	−0.655630
$336$	0	0
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	23.0000	1.25104
$339$	−10.0000	−0.543125
$340$	−1.00000	−0.0542326
$341$	−4.00000	−0.216612
$342$	0	0
$343$	0	0
$344$	−8.00000	−0.431331
$345$	8.00000	0.430706
$346$	2.00000	0.107521
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	−6.00000	−0.321634
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	1.00000	0.0533002
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	−8.00000	−0.425195
$355$	−8.00000	−0.424596
$356$	2.00000	0.106000
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	−6.00000	−0.315353
$363$	1.00000	0.0524864
$364$	0	0
$365$	2.00000	0.104685
$366$	2.00000	0.104542
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	−8.00000	−0.417029
$369$	2.00000	0.104116
$370$	−2.00000	−0.103975
$371$	0	0
$372$	−4.00000	−0.207390
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	36.0000	1.85409
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	−24.0000	−1.22795
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	6.00000	0.305392
$387$	−8.00000	−0.406663
$388$	−6.00000	−0.304604
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	6.00000	0.303822
$391$	−8.00000	−0.404577
$392$	−7.00000	−0.353553
$393$	4.00000	0.201773
$394$	2.00000	0.100759
$395$	0	0
$396$	1.00000	0.0502519
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	12.0000	0.601506
$399$	0	0
$400$	1.00000	0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	12.0000	0.598506
$403$	24.0000	1.19553
$404$	−2.00000	−0.0995037
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	2.00000	0.0991363
$408$	1.00000	0.0495074
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	−2.00000	−0.0987730
$411$	2.00000	0.0986527
$412$	−8.00000	−0.394132
$413$	0	0
$414$	−8.00000	−0.393179
$415$	−12.0000	−0.589057
$416$	−6.00000	−0.294174
$417$	4.00000	0.195881
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−6.00000	−0.291386
$425$	1.00000	0.0485071
$426$	8.00000	0.387601
$427$	0	0
$428$	−12.0000	−0.580042
$429$	−6.00000	−0.289683
$430$	8.00000	0.385794
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	1.00000	0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	2.00000	0.0957826
$437$	0	0
$438$	−2.00000	−0.0955637
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	−1.00000	−0.0476731
$441$	−7.00000	−0.333333
$442$	−6.00000	−0.285391
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	2.00000	0.0949158
$445$	−2.00000	−0.0948091
$446$	−24.0000	−1.13643
$447$	−2.00000	−0.0945968
$448$	0	0
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	1.00000	0.0471405
$451$	2.00000	0.0941763
$452$	−10.0000	−0.470360
$453$	16.0000	0.751746
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−2.00000	−0.0934539
$459$	1.00000	0.0466760
$460$	8.00000	0.373002
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−6.00000	−0.278543
$465$	4.00000	0.185496
$466$	−6.00000	−0.277945
$467$	−32.0000	−1.48078	−0.740392	−	0.672176i	$-0.765360\pi$
$467$	−32.0000	−1.48078	−0.740392	+	0.672176i	$0.765360\pi$
$468$	−6.00000	−0.277350
$469$	0	0
$470$	0	0
$471$	−2.00000	−0.0921551
$472$	−8.00000	−0.368230
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−6.00000	−0.274721
$478$	0	0
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	−1.00000	−0.0456435
$481$	−12.0000	−0.547153
$482$	14.0000	0.637683
$483$	0	0
$484$	1.00000	0.0454545
$485$	6.00000	0.272446
$486$	1.00000	0.0453609
$487$	12.0000	0.543772	0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000	0.543772	0.271886	+	0.962329i	$0.412353\pi$
$488$	2.00000	0.0905357
$489$	−4.00000	−0.180886
$490$	7.00000	0.316228
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	2.00000	0.0901670
$493$	−6.00000	−0.270226
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	−4.00000	−0.179605
$497$	0	0
$498$	12.0000	0.537733
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−1.00000	−0.0447214
$501$	4.00000	0.178707
$502$	−8.00000	−0.357057
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	−8.00000	−0.355643
$507$	23.0000	1.02147
$508$	−16.0000	−0.709885
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	−1.00000	−0.0442807
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	8.00000	0.352522
$516$	−8.00000	−0.352180
$517$	0	0
$518$	0	0
$519$	2.00000	0.0877903
$520$	6.00000	0.263117
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	−6.00000	−0.262613
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−8.00000	−0.348817
$527$	−4.00000	−0.174243
$528$	1.00000	0.0435194
$529$	41.0000	1.78261
$530$	6.00000	0.260623
$531$	−8.00000	−0.347170
$532$	0	0
$533$	−12.0000	−0.519778
$534$	2.00000	0.0865485
$535$	12.0000	0.518805
$536$	12.0000	0.518321
$537$	0	0
$538$	18.0000	0.776035
$539$	−7.00000	−0.301511
$540$	−1.00000	−0.0430331
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−16.0000	−0.687259
$543$	−6.00000	−0.257485
$544$	1.00000	0.0428746
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	2.00000	0.0854358
$549$	2.00000	0.0853579
$550$	1.00000	0.0426401
$551$	0	0
$552$	−8.00000	−0.340503
$553$	0	0
$554$	−22.0000	−0.934690
$555$	−2.00000	−0.0848953
$556$	4.00000	0.169638
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	−4.00000	−0.169334
$559$	48.0000	2.03018
$560$	0	0
$561$	1.00000	0.0422200
$562$	26.0000	1.09674
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	10.0000	0.420703
$566$	−4.00000	−0.168133
$567$	0	0
$568$	8.00000	0.335673
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−6.00000	−0.250873
$573$	−24.0000	−1.00261
$574$	0	0
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	1.00000	0.0415945
$579$	6.00000	0.249351
$580$	6.00000	0.249136
$581$	0	0
$582$	−6.00000	−0.248708
$583$	−6.00000	−0.248495
$584$	−2.00000	−0.0827606
$585$	6.00000	0.248069
$586$	22.0000	0.908812
$587$	40.0000	1.65098	0.825488	−	0.564419i	$-0.190900\pi$
$587$	40.0000	1.65098	0.825488	+	0.564419i	$0.190900\pi$
$588$	−7.00000	−0.288675
$589$	0	0
$590$	8.00000	0.329355
$591$	2.00000	0.0822690
$592$	2.00000	0.0821995
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	12.0000	0.491127
$598$	48.0000	1.96287
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	1.00000	0.0408248
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	16.0000	0.651031
$605$	−1.00000	−0.0406558
$606$	−2.00000	−0.0812444
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	0	0
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	1.00000	0.0404226
$613$	10.0000	0.403896	0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000	0.403896	0.201948	+	0.979396i	$0.435273\pi$
$614$	−24.0000	−0.968561
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	−8.00000	−0.321807
$619$	36.0000	1.44696	0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000	1.44696	0.723481	+	0.690344i	$0.242541\pi$
$620$	4.00000	0.160644
$621$	−8.00000	−0.321029
$622$	0	0
$623$	0	0
$624$	−6.00000	−0.240192
$625$	1.00000	0.0400000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	2.00000	0.0797452
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	0	0
$633$	−20.0000	−0.794929
$634$	18.0000	0.714871
$635$	16.0000	0.634941
$636$	−6.00000	−0.237915
$637$	42.0000	1.66410
$638$	−6.00000	−0.237542
$639$	8.00000	0.316475
$640$	−1.00000	−0.0395285
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	−12.0000	−0.473602
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	0	0
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	1.00000	0.0392837
$649$	−8.00000	−0.314027
$650$	−6.00000	−0.235339
$651$	0	0
$652$	−4.00000	−0.156652
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	2.00000	0.0782062
$655$	−4.00000	−0.156293
$656$	2.00000	0.0780869
$657$	−2.00000	−0.0780274
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	−1.00000	−0.0389249
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	28.0000	1.08825
$663$	−6.00000	−0.233021
$664$	12.0000	0.465690
$665$	0	0
$666$	2.00000	0.0774984
$667$	48.0000	1.85857
$668$	4.00000	0.154765
$669$	−24.0000	−0.927894
$670$	−12.0000	−0.463600
$671$	2.00000	0.0772091
$672$	0	0
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	6.00000	0.231111
$675$	1.00000	0.0384900
$676$	23.0000	0.884615
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−10.0000	−0.384048
$679$	0	0
$680$	−1.00000	−0.0383482
$681$	12.0000	0.459841
$682$	−4.00000	−0.153168
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	−2.00000	−0.0764161
$686$	0	0
$687$	−2.00000	−0.0763048
$688$	−8.00000	−0.304997
$689$	36.0000	1.37149
$690$	8.00000	0.304555
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	20.0000	0.759190
$695$	−4.00000	−0.151729
$696$	−6.00000	−0.227429
$697$	2.00000	0.0757554
$698$	26.0000	0.984115
$699$	−6.00000	−0.226941
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	−6.00000	−0.226455
$703$	0	0
$704$	1.00000	0.0376889
$705$	0	0
$706$	10.0000	0.376355
$707$	0	0
$708$	−8.00000	−0.300658
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	2.00000	0.0749532
$713$	32.0000	1.19841
$714$	0	0
$715$	6.00000	0.224387
$716$	0	0
$717$	0	0
$718$	0	0
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−19.0000	−0.707107
$723$	14.0000	0.520666
$724$	−6.00000	−0.222988
$725$	−6.00000	−0.222834
$726$	1.00000	0.0371135
$727$	−48.0000	−1.78022	−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000	−1.78022	−0.890111	+	0.455744i	$0.849373\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	−8.00000	−0.295891
$732$	2.00000	0.0739221
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	−28.0000	−1.03350
$735$	7.00000	0.258199
$736$	−8.00000	−0.294884
$737$	12.0000	0.442026
$738$	2.00000	0.0736210
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	−4.00000	−0.146647
$745$	2.00000	0.0732743
$746$	−14.0000	−0.512576
$747$	12.0000	0.439057
$748$	1.00000	0.0365636
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	28.0000	1.02173	0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000	1.02173	0.510867	+	0.859660i	$0.329324\pi$
$752$	0	0
$753$	−8.00000	−0.291536
$754$	36.0000	1.31104
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	−4.00000	−0.145287
$759$	−8.00000	−0.290382
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	−16.0000	−0.579619
$763$	0	0
$764$	−24.0000	−0.868290
$765$	−1.00000	−0.0361551
$766$	8.00000	0.289052
$767$	48.0000	1.73318
$768$	1.00000	0.0360844
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	6.00000	0.215945
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	−8.00000	−0.287554
$775$	−4.00000	−0.143684
$776$	−6.00000	−0.215387
$777$	0	0
$778$	−22.0000	−0.788738
$779$	0	0
$780$	6.00000	0.214834
$781$	8.00000	0.286263
$782$	−8.00000	−0.286079
$783$	−6.00000	−0.214423
$784$	−7.00000	−0.250000
$785$	2.00000	0.0713831
$786$	4.00000	0.142675
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	2.00000	0.0712470
$789$	−8.00000	−0.284808
$790$	0	0
$791$	0	0
$792$	1.00000	0.0355335
$793$	−12.0000	−0.426132
$794$	10.0000	0.354887
$795$	6.00000	0.212798
$796$	12.0000	0.425329
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	2.00000	0.0706665
$802$	22.0000	0.776847
$803$	−2.00000	−0.0705785
$804$	12.0000	0.423207
$805$	0	0
$806$	24.0000	0.845364
$807$	18.0000	0.633630
$808$	−2.00000	−0.0703598
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	−1.00000	−0.0351364
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	0	0
$813$	−16.0000	−0.561144
$814$	2.00000	0.0701000
$815$	4.00000	0.140114
$816$	1.00000	0.0350070
$817$	0	0
$818$	−14.0000	−0.489499
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	2.00000	0.0697580
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−8.00000	−0.278693
$825$	1.00000	0.0348155
$826$	0	0
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	−8.00000	−0.278019
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−12.0000	−0.416526
$831$	−22.0000	−0.763172
$832$	−6.00000	−0.208013
$833$	−7.00000	−0.242536
$834$	4.00000	0.138509
$835$	−4.00000	−0.138426
$836$	0	0
$837$	−4.00000	−0.138260
$838$	−4.00000	−0.138178
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−18.0000	−0.620321
$843$	26.0000	0.895488
$844$	−20.0000	−0.688428
$845$	−23.0000	−0.791224
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	−4.00000	−0.137280
$850$	1.00000	0.0342997
$851$	−16.0000	−0.548473
$852$	8.00000	0.274075
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	0	0
$855$	0	0
$856$	−12.0000	−0.410152
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	−6.00000	−0.204837
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	−20.0000	−0.681203
$863$	−32.0000	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$864$	1.00000	0.0340207
$865$	−2.00000	−0.0680020
$866$	2.00000	0.0679628
$867$	1.00000	0.0339618
$868$	0	0
$869$	0	0
$870$	6.00000	0.203419
$871$	−72.0000	−2.43963
$872$	2.00000	0.0677285
$873$	−6.00000	−0.203069
$874$	0	0
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	−16.0000	−0.539974
$879$	22.0000	0.742042
$880$	−1.00000	−0.0337100
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	−7.00000	−0.235702
$883$	−28.0000	−0.942275	−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000	−0.942275	−0.471138	+	0.882060i	$0.656156\pi$
$884$	−6.00000	−0.201802
$885$	8.00000	0.268917
$886$	24.0000	0.806296
$887$	44.0000	1.47738	0.738688	−	0.674048i	$-0.235446\pi$
$887$	44.0000	1.47738	0.738688	+	0.674048i	$0.235446\pi$
$888$	2.00000	0.0671156
$889$	0	0
$890$	−2.00000	−0.0670402
$891$	1.00000	0.0335013
$892$	−24.0000	−0.803579
$893$	0	0
$894$	−2.00000	−0.0668900
$895$	0	0
$896$	0	0
$897$	48.0000	1.60267
$898$	−2.00000	−0.0667409
$899$	24.0000	0.800445
$900$	1.00000	0.0333333
$901$	−6.00000	−0.199889
$902$	2.00000	0.0665927
$903$	0	0
$904$	−10.0000	−0.332595
$905$	6.00000	0.199447
$906$	16.0000	0.531564
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	12.0000	0.398234
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	10.0000	0.330771
$915$	−2.00000	−0.0661180
$916$	−2.00000	−0.0660819
$917$	0	0
$918$	1.00000	0.0330049
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	8.00000	0.263752
$921$	−24.0000	−0.790827
$922$	14.0000	0.461065
$923$	−48.0000	−1.57994
$924$	0	0
$925$	2.00000	0.0657596
$926$	8.00000	0.262896
$927$	−8.00000	−0.262754
$928$	−6.00000	−0.196960
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	4.00000	0.131165
$931$	0	0
$932$	−6.00000	−0.196537
$933$	0	0
$934$	−32.0000	−1.04707
$935$	−1.00000	−0.0327035
$936$	−6.00000	−0.196116
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	−14.0000	−0.456873
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−2.00000	−0.0651635
$943$	−16.0000	−0.521032
$944$	−8.00000	−0.260378
$945$	0	0
$946$	−8.00000	−0.260102
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	−6.00000	−0.194257
$955$	24.0000	0.776622
$956$	0	0
$957$	−6.00000	−0.193952
$958$	12.0000	0.387702
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	−12.0000	−0.386896
$963$	−12.0000	−0.386695
$964$	14.0000	0.450910
$965$	−6.00000	−0.193147
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	6.00000	0.192648
$971$	−8.00000	−0.256732	−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000	−0.256732	−0.128366	+	0.991727i	$0.540973\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	12.0000	0.384505
$975$	−6.00000	−0.192154
$976$	2.00000	0.0640184
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	−4.00000	−0.127906
$979$	2.00000	0.0639203
$980$	7.00000	0.223607
$981$	2.00000	0.0638551
$982$	36.0000	1.14881
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	2.00000	0.0637577
$985$	−2.00000	−0.0637253
$986$	−6.00000	−0.191079
$987$	0	0
$988$	0	0
$989$	64.0000	2.03508
$990$	−1.00000	−0.0317821
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	−4.00000	−0.127000
$993$	28.0000	0.888553
$994$	0	0
$995$	−12.0000	−0.380426
$996$	12.0000	0.380235
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	−28.0000	−0.886325
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bh.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bh.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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