LMFDB - Embedded newform 5610.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} -4.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} -4.00000 q^{21} +1.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +2.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -2.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -4.00000 q^{42} +4.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -8.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} -2.00000 q^{52} -14.0000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{56} +2.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +1.00000 q^{66} -16.0000 q^{67} +1.00000 q^{68} +4.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -6.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} -4.00000 q^{77} -2.00000 q^{78} -8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -12.0000 q^{83} -4.00000 q^{84} -1.00000 q^{85} +4.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} -1.00000 q^{90} +8.00000 q^{91} +4.00000 q^{93} -8.00000 q^{94} +1.00000 q^{96} +6.00000 q^{97} +9.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	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
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−4.00000	−1.06904
$15$	−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
$21$	−4.00000	−0.872872
$22$	1.00000	0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	−0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−4.00000	−0.617213
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−2.00000	−0.277350
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	−4.00000	−0.534522
$57$	0	0
$58$	2.00000	0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−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
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	1.00000	0.123091
$67$	−16.0000	−1.95471	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−16.0000	−1.95471	−0.977356	+	0.211604i	$0.932131\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	4.00000	0.478091
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−6.00000	−0.697486
$75$	1.00000	0.115470
$76$	0	0
$77$	−4.00000	−0.455842
$78$	−2.00000	−0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−4.00000	−0.436436
$85$	−1.00000	−0.108465
$86$	4.00000	0.431331
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−1.00000	−0.105409
$91$	8.00000	0.838628
$92$	0	0
$93$	4.00000	0.414781
$94$	−8.00000	−0.825137
$95$	0	0
$96$	1.00000	0.102062
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	9.00000	0.909137
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	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	$0.628955\pi$
$104$	−2.00000	−0.196116
$105$	4.00000	0.390360
$106$	−14.0000	−1.35980
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	1.00000	0.0962250
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	−1.00000	−0.0953463
$111$	−6.00000	−0.569495
$112$	−4.00000	−0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	0	0
$116$	2.00000	0.185695
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	−4.00000	−0.366679
$120$	−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
$126$	−4.00000	−0.356348
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	4.00000	0.352180
$130$	2.00000	0.175412
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	−16.0000	−1.38219
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	4.00000	0.338062
$141$	−8.00000	−0.673722
$142$	−12.0000	−1.00702
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	−6.00000	−0.496564
$147$	9.00000	0.742307
$148$	−6.00000	−0.493197
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	1.00000	0.0816497
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	1.00000	0.0808452
$154$	−4.00000	−0.322329
$155$	−4.00000	−0.321288
$156$	−2.00000	−0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−8.00000	−0.636446
$159$	−14.0000	−1.11027
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−2.00000	−0.156174
$165$	−1.00000	−0.0778499
$166$	−12.0000	−0.931381
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	−4.00000	−0.308607
$169$	−9.00000	−0.692308
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	4.00000	0.304997
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	2.00000	0.151620
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	4.00000	0.300658
$178$	−6.00000	−0.449719
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−1.00000	−0.0745356
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	8.00000	0.592999
$183$	2.00000	0.147844
$184$	0	0
$185$	6.00000	0.441129
$186$	4.00000	0.293294
$187$	1.00000	0.0731272
$188$	−8.00000	−0.583460
$189$	−4.00000	−0.290957
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	6.00000	0.430775
$195$	2.00000	0.143223
$196$	9.00000	0.642857
$197$	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
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	1.00000	0.0707107
$201$	−16.0000	−1.12855
$202$	−14.0000	−0.985037
$203$	−8.00000	−0.561490
$204$	1.00000	0.0700140
$205$	2.00000	0.139686
$206$	−8.00000	−0.557386
$207$	0	0
$208$	−2.00000	−0.138675
$209$	0	0
$210$	4.00000	0.276026
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−14.0000	−0.961524
$213$	−12.0000	−0.822226
$214$	4.00000	0.273434
$215$	−4.00000	−0.272798
$216$	1.00000	0.0680414
$217$	−16.0000	−1.08615
$218$	−14.0000	−0.948200
$219$	−6.00000	−0.405442
$220$	−1.00000	−0.0674200
$221$	−2.00000	−0.134535
$222$	−6.00000	−0.402694
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	−4.00000	−0.267261
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	28.0000	1.85843	0.929213	−	0.369546i	$-0.120487\pi$
$227$	28.0000	1.85843	0.929213	+	0.369546i	$0.120487\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	−4.00000	−0.263181
$232$	2.00000	0.131306
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−2.00000	−0.130744
$235$	8.00000	0.521862
$236$	4.00000	0.260378
$237$	−8.00000	−0.519656
$238$	−4.00000	−0.259281
$239$	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
$245$	−9.00000	−0.574989
$246$	−2.00000	−0.127515
$247$	0	0
$248$	4.00000	0.254000
$249$	−12.0000	−0.760469
$250$	−1.00000	−0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	16.0000	1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−30.0000	−1.87135	−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000	−1.87135	−0.935674	+	0.352865i	$0.885208\pi$
$258$	4.00000	0.249029
$259$	24.0000	1.49129
$260$	2.00000	0.124035
$261$	2.00000	0.123797
$262$	−20.0000	−1.23560
$263$	−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
$265$	14.0000	0.860013
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−16.0000	−0.977356
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	−1.00000	−0.0608581
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	1.00000	0.0606339
$273$	8.00000	0.484182
$274$	−6.00000	−0.362473
$275$	1.00000	0.0603023
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	20.0000	1.19952
$279$	4.00000	0.239474
$280$	4.00000	0.239046
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	−8.00000	−0.476393
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−2.00000	−0.118262
$287$	8.00000	0.472225
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	6.00000	0.351726
$292$	−6.00000	−0.351123
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	9.00000	0.524891
$295$	−4.00000	−0.232889
$296$	−6.00000	−0.348743
$297$	1.00000	0.0580259
$298$	18.0000	1.04271
$299$	0	0
$300$	1.00000	0.0577350
$301$	−16.0000	−0.922225
$302$	−16.0000	−0.920697
$303$	−14.0000	−0.804279
$304$	0	0
$305$	−2.00000	−0.114520
$306$	1.00000	0.0571662
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−4.00000	−0.227921
$309$	−8.00000	−0.455104
$310$	−4.00000	−0.227185
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	−2.00000	−0.113228
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−14.0000	−0.790066
$315$	4.00000	0.225374
$316$	−8.00000	−0.450035
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	−14.0000	−0.785081
$319$	2.00000	0.111979
$320$	−1.00000	−0.0559017
$321$	4.00000	0.223258
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	4.00000	0.221540
$327$	−14.0000	−0.774202
$328$	−2.00000	−0.110432
$329$	32.0000	1.76422
$330$	−1.00000	−0.0550482
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−12.0000	−0.658586
$333$	−6.00000	−0.328798
$334$	−12.0000	−0.656611
$335$	16.0000	0.874173
$336$	−4.00000	−0.218218
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−9.00000	−0.489535
$339$	6.00000	0.325875
$340$	−1.00000	−0.0542326
$341$	4.00000	0.216612
$342$	0	0
$343$	−8.00000	−0.431959
$344$	4.00000	0.215666
$345$	0	0
$346$	18.0000	0.967686
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	2.00000	0.107211
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	−4.00000	−0.213809
$351$	−2.00000	−0.106752
$352$	1.00000	0.0533002
$353$	2.00000	0.106449	0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000	0.106449	0.0532246	+	0.998583i	$0.483050\pi$
$354$	4.00000	0.212598
$355$	12.0000	0.636894
$356$	−6.00000	−0.317999
$357$	−4.00000	−0.211702
$358$	20.0000	1.05703
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	18.0000	0.946059
$363$	1.00000	0.0524864
$364$	8.00000	0.419314
$365$	6.00000	0.314054
$366$	2.00000	0.104542
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	−2.00000	−0.104116
$370$	6.00000	0.311925
$371$	56.0000	2.90738
$372$	4.00000	0.207390
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	−8.00000	−0.412568
$377$	−4.00000	−0.206010
$378$	−4.00000	−0.205738
$379$	−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
$382$	8.00000	0.409316
$383$	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
$386$	−22.0000	−1.11977
$387$	4.00000	0.203331
$388$	6.00000	0.304604
$389$	38.0000	1.92668	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	38.0000	1.92668	0.963338	+	0.268290i	$0.0864585\pi$
$390$	2.00000	0.101274
$391$	0	0
$392$	9.00000	0.454569
$393$	−20.0000	−1.00887
$394$	2.00000	0.100759
$395$	8.00000	0.402524
$396$	1.00000	0.0502519
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	1.00000	0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	−16.0000	−0.798007
$403$	−8.00000	−0.398508
$404$	−14.0000	−0.696526
$405$	−1.00000	−0.0496904
$406$	−8.00000	−0.397033
$407$	−6.00000	−0.297409
$408$	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
$411$	−6.00000	−0.295958
$412$	−8.00000	−0.394132
$413$	−16.0000	−0.787309
$414$	0	0
$415$	12.0000	0.589057
$416$	−2.00000	−0.0980581
$417$	20.0000	0.979404
$418$	0	0
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	4.00000	0.195180
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	4.00000	0.194717
$423$	−8.00000	−0.388973
$424$	−14.0000	−0.679900
$425$	1.00000	0.0485071
$426$	−12.0000	−0.581402
$427$	−8.00000	−0.387147
$428$	4.00000	0.193347
$429$	−2.00000	−0.0965609
$430$	−4.00000	−0.192897
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	1.00000	0.0481125
$433$	−22.0000	−1.05725	−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000	−1.05725	−0.528626	+	0.848855i	$0.677293\pi$
$434$	−16.0000	−0.768025
$435$	−2.00000	−0.0958927
$436$	−14.0000	−0.670478
$437$	0	0
$438$	−6.00000	−0.286691
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	−1.00000	−0.0476731
$441$	9.00000	0.428571
$442$	−2.00000	−0.0951303
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	−6.00000	−0.284747
$445$	6.00000	0.284427
$446$	−24.0000	−1.13643
$447$	18.0000	0.851371
$448$	−4.00000	−0.188982
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	1.00000	0.0471405
$451$	−2.00000	−0.0941763
$452$	6.00000	0.282216
$453$	−16.0000	−0.751746
$454$	28.0000	1.31411
$455$	−8.00000	−0.375046
$456$	0	0
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	14.0000	0.654177
$459$	1.00000	0.0466760
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	−4.00000	−0.186097
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	2.00000	0.0928477
$465$	−4.00000	−0.185496
$466$	26.0000	1.20443
$467$	24.0000	1.11059	0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000	1.11059	0.555294	+	0.831654i	$0.312606\pi$
$468$	−2.00000	−0.0924500
$469$	64.0000	2.95525
$470$	8.00000	0.369012
$471$	−14.0000	−0.645086
$472$	4.00000	0.184115
$473$	4.00000	0.183920
$474$	−8.00000	−0.367452
$475$	0	0
$476$	−4.00000	−0.183340
$477$	−14.0000	−0.641016
$478$	0	0
$479$	32.0000	1.46212	0.731059	−	0.682315i	$-0.239027\pi$
$479$	32.0000	1.46212	0.731059	+	0.682315i	$0.239027\pi$
$480$	−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
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	2.00000	0.0905357
$489$	4.00000	0.180886
$490$	−9.00000	−0.406579
$491$	−40.0000	−1.80517	−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000	−1.80517	−0.902587	+	0.430507i	$0.858335\pi$
$492$	−2.00000	−0.0901670
$493$	2.00000	0.0900755
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	4.00000	0.179605
$497$	48.0000	2.15309
$498$	−12.0000	−0.537733
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	−1.00000	−0.0447214
$501$	−12.0000	−0.536120
$502$	−12.0000	−0.535586
$503$	20.0000	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$504$	−4.00000	−0.178174
$505$	14.0000	0.622992
$506$	0	0
$507$	−9.00000	−0.399704
$508$	16.0000	0.709885
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	−1.00000	−0.0442807
$511$	24.0000	1.06170
$512$	1.00000	0.0441942
$513$	0	0
$514$	−30.0000	−1.32324
$515$	8.00000	0.352522
$516$	4.00000	0.176090
$517$	−8.00000	−0.351840
$518$	24.0000	1.05450
$519$	18.0000	0.790112
$520$	2.00000	0.0877058
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	2.00000	0.0875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−20.0000	−0.873704
$525$	−4.00000	−0.174574
$526$	−8.00000	−0.348817
$527$	4.00000	0.174243
$528$	1.00000	0.0435194
$529$	−23.0000	−1.00000
$530$	14.0000	0.608121
$531$	4.00000	0.173585
$532$	0	0
$533$	4.00000	0.173259
$534$	−6.00000	−0.259645
$535$	−4.00000	−0.172935
$536$	−16.0000	−0.691095
$537$	20.0000	0.863064
$538$	−30.0000	−1.29339
$539$	9.00000	0.387657
$540$	−1.00000	−0.0430331
$541$	−46.0000	−1.97769	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−46.0000	−1.97769	−0.988847	+	0.148933i	$0.952416\pi$
$542$	16.0000	0.687259
$543$	18.0000	0.772454
$544$	1.00000	0.0428746
$545$	14.0000	0.599694
$546$	8.00000	0.342368
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	−6.00000	−0.256307
$549$	2.00000	0.0853579
$550$	1.00000	0.0426401
$551$	0	0
$552$	0	0
$553$	32.0000	1.36078
$554$	−22.0000	−0.934690
$555$	6.00000	0.254686
$556$	20.0000	0.848189
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	4.00000	0.169334
$559$	−8.00000	−0.338364
$560$	4.00000	0.169031
$561$	1.00000	0.0422200
$562$	18.0000	0.759284
$563$	−28.0000	−1.18006	−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000	−1.18006	−0.590030	+	0.807382i	$0.700884\pi$
$564$	−8.00000	−0.336861
$565$	−6.00000	−0.252422
$566$	4.00000	0.168133
$567$	−4.00000	−0.167984
$568$	−12.0000	−0.503509
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	0	0
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−2.00000	−0.0836242
$573$	8.00000	0.334205
$574$	8.00000	0.333914
$575$	0	0
$576$	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	$0.651411\pi$
$578$	1.00000	0.0415945
$579$	−22.0000	−0.914289
$580$	−2.00000	−0.0830455
$581$	48.0000	1.99138
$582$	6.00000	0.248708
$583$	−14.0000	−0.579821
$584$	−6.00000	−0.248282
$585$	2.00000	0.0826898
$586$	22.0000	0.908812
$587$	−8.00000	−0.330195	−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000	−0.330195	−0.165098	+	0.986277i	$0.552794\pi$
$588$	9.00000	0.371154
$589$	0	0
$590$	−4.00000	−0.164677
$591$	2.00000	0.0822690
$592$	−6.00000	−0.246598
$593$	2.00000	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$594$	1.00000	0.0410305
$595$	4.00000	0.163984
$596$	18.0000	0.737309
$597$	20.0000	0.818546
$598$	0	0
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	1.00000	0.0408248
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	−16.0000	−0.652111
$603$	−16.0000	−0.651570
$604$	−16.0000	−0.651031
$605$	−1.00000	−0.0406558
$606$	−14.0000	−0.568711
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	0	0
$609$	−8.00000	−0.324176
$610$	−2.00000	−0.0809776
$611$	16.0000	0.647291
$612$	1.00000	0.0404226
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	4.00000	0.161427
$615$	2.00000	0.0806478
$616$	−4.00000	−0.161165
$617$	46.0000	1.85189	0.925945	−	0.377658i	$-0.123271\pi$
$617$	46.0000	1.85189	0.925945	+	0.377658i	$0.123271\pi$
$618$	−8.00000	−0.321807
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	−12.0000	−0.481156
$623$	24.0000	0.961540
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−6.00000	−0.239236
$630$	4.00000	0.159364
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	−8.00000	−0.318223
$633$	4.00000	0.158986
$634$	−30.0000	−1.19145
$635$	−16.0000	−0.634941
$636$	−14.0000	−0.555136
$637$	−18.0000	−0.713186
$638$	2.00000	0.0791808
$639$	−12.0000	−0.474713
$640$	−1.00000	−0.0395285
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	4.00000	0.157867
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	0	0
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	−2.00000	−0.0784465
$651$	−16.0000	−0.627089
$652$	4.00000	0.156652
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	−14.0000	−0.547443
$655$	20.0000	0.781465
$656$	−2.00000	−0.0780869
$657$	−6.00000	−0.234082
$658$	32.0000	1.24749
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	−1.00000	−0.0389249
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	−12.0000	−0.466393
$663$	−2.00000	−0.0776736
$664$	−12.0000	−0.465690
$665$	0	0
$666$	−6.00000	−0.232495
$667$	0	0
$668$	−12.0000	−0.464294
$669$	−24.0000	−0.927894
$670$	16.0000	0.618134
$671$	2.00000	0.0772091
$672$	−4.00000	−0.154303
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	18.0000	0.693334
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	6.00000	0.230429
$679$	−24.0000	−0.921035
$680$	−1.00000	−0.0383482
$681$	28.0000	1.07296
$682$	4.00000	0.153168
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	0	0
$685$	6.00000	0.229248
$686$	−8.00000	−0.305441
$687$	14.0000	0.534133
$688$	4.00000	0.152499
$689$	28.0000	1.06672
$690$	0	0
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	18.0000	0.684257
$693$	−4.00000	−0.151947
$694$	20.0000	0.759190
$695$	−20.0000	−0.758643
$696$	2.00000	0.0758098
$697$	−2.00000	−0.0757554
$698$	−22.0000	−0.832712
$699$	26.0000	0.983410
$700$	−4.00000	−0.151186
$701$	−22.0000	−0.830929	−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000	−0.830929	−0.415464	+	0.909610i	$0.636381\pi$
$702$	−2.00000	−0.0754851
$703$	0	0
$704$	1.00000	0.0376889
$705$	8.00000	0.301297
$706$	2.00000	0.0752710
$707$	56.0000	2.10610
$708$	4.00000	0.150329
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	12.0000	0.450352
$711$	−8.00000	−0.300023
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−4.00000	−0.149696
$715$	2.00000	0.0747958
$716$	20.0000	0.747435
$717$	0	0
$718$	24.0000	0.895672
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	−1.00000	−0.0372678
$721$	32.0000	1.19174
$722$	−19.0000	−0.707107
$723$	14.0000	0.520666
$724$	18.0000	0.668965
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	4.00000	0.147945
$732$	2.00000	0.0739221
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	8.00000	0.295285
$735$	−9.00000	−0.331970
$736$	0	0
$737$	−16.0000	−0.589368
$738$	−2.00000	−0.0736210
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	6.00000	0.220564
$741$	0	0
$742$	56.0000	2.05582
$743$	−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
$745$	−18.0000	−0.659469
$746$	−2.00000	−0.0732252
$747$	−12.0000	−0.439057
$748$	1.00000	0.0365636
$749$	−16.0000	−0.584627
$750$	−1.00000	−0.0365148
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−8.00000	−0.291730
$753$	−12.0000	−0.437304
$754$	−4.00000	−0.145671
$755$	16.0000	0.582300
$756$	−4.00000	−0.145479
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	0	0
$761$	−54.0000	−1.95750	−0.978749	−	0.205061i	$-0.934261\pi$
$761$	−54.0000	−1.95750	−0.978749	+	0.205061i	$0.934261\pi$
$762$	16.0000	0.579619
$763$	56.0000	2.02734
$764$	8.00000	0.289430
$765$	−1.00000	−0.0361551
$766$	24.0000	0.867155
$767$	−8.00000	−0.288863
$768$	1.00000	0.0360844
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	4.00000	0.144150
$771$	−30.0000	−1.08042
$772$	−22.0000	−0.791797
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	6.00000	0.215387
$777$	24.0000	0.860995
$778$	38.0000	1.36237
$779$	0	0
$780$	2.00000	0.0716115
$781$	−12.0000	−0.429394
$782$	0	0
$783$	2.00000	0.0714742
$784$	9.00000	0.321429
$785$	14.0000	0.499681
$786$	−20.0000	−0.713376
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	2.00000	0.0712470
$789$	−8.00000	−0.284808
$790$	8.00000	0.284627
$791$	−24.0000	−0.853342
$792$	1.00000	0.0355335
$793$	−4.00000	−0.142044
$794$	2.00000	0.0709773
$795$	14.0000	0.496529
$796$	20.0000	0.708881
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	0	0
$799$	−8.00000	−0.283020
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	10.0000	0.353112
$803$	−6.00000	−0.211735
$804$	−16.0000	−0.564276
$805$	0	0
$806$	−8.00000	−0.281788
$807$	−30.0000	−1.05605
$808$	−14.0000	−0.492518
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	−1.00000	−0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−8.00000	−0.280745
$813$	16.0000	0.561144
$814$	−6.00000	−0.210300
$815$	−4.00000	−0.140114
$816$	1.00000	0.0350070
$817$	0	0
$818$	−14.0000	−0.489499
$819$	8.00000	0.279543
$820$	2.00000	0.0698430
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	−6.00000	−0.209274
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−8.00000	−0.278693
$825$	1.00000	0.0348155
$826$	−16.0000	−0.556711
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	0	0
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	12.0000	0.416526
$831$	−22.0000	−0.763172
$832$	−2.00000	−0.0693375
$833$	9.00000	0.311832
$834$	20.0000	0.692543
$835$	12.0000	0.415277
$836$	0	0
$837$	4.00000	0.138260
$838$	−12.0000	−0.414533
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	4.00000	0.138013
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	18.0000	0.619953
$844$	4.00000	0.137686
$845$	9.00000	0.309609
$846$	−8.00000	−0.275046
$847$	−4.00000	−0.137442
$848$	−14.0000	−0.480762
$849$	4.00000	0.137280
$850$	1.00000	0.0342997
$851$	0	0
$852$	−12.0000	−0.411113
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	4.00000	0.136717
$857$	58.0000	1.98124	0.990621	−	0.136637i	$-0.0436295\pi$
$857$	58.0000	1.98124	0.990621	+	0.136637i	$0.0436295\pi$
$858$	−2.00000	−0.0682789
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−4.00000	−0.136399
$861$	8.00000	0.272639
$862$	8.00000	0.272481
$863$	−56.0000	−1.90626	−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000	−1.90626	−0.953131	+	0.302558i	$0.902160\pi$
$864$	1.00000	0.0340207
$865$	−18.0000	−0.612018
$866$	−22.0000	−0.747590
$867$	1.00000	0.0339618
$868$	−16.0000	−0.543075
$869$	−8.00000	−0.271381
$870$	−2.00000	−0.0678064
$871$	32.0000	1.08428
$872$	−14.0000	−0.474100
$873$	6.00000	0.203069
$874$	0	0
$875$	4.00000	0.135225
$876$	−6.00000	−0.202721
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	−8.00000	−0.269987
$879$	22.0000	0.742042
$880$	−1.00000	−0.0337100
$881$	−38.0000	−1.28025	−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000	−1.28025	−0.640126	+	0.768270i	$0.721118\pi$
$882$	9.00000	0.303046
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	−2.00000	−0.0672673
$885$	−4.00000	−0.134459
$886$	24.0000	0.806296
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	−6.00000	−0.201347
$889$	−64.0000	−2.14649
$890$	6.00000	0.201120
$891$	1.00000	0.0335013
$892$	−24.0000	−0.803579
$893$	0	0
$894$	18.0000	0.602010
$895$	−20.0000	−0.668526
$896$	−4.00000	−0.133631
$897$	0	0
$898$	−14.0000	−0.467186
$899$	8.00000	0.266815
$900$	1.00000	0.0333333
$901$	−14.0000	−0.466408
$902$	−2.00000	−0.0665927
$903$	−16.0000	−0.532447
$904$	6.00000	0.199557
$905$	−18.0000	−0.598340
$906$	−16.0000	−0.531564
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	28.0000	0.929213
$909$	−14.0000	−0.464351
$910$	−8.00000	−0.265197
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	−22.0000	−0.727695
$915$	−2.00000	−0.0661180
$916$	14.0000	0.462573
$917$	80.0000	2.64183
$918$	1.00000	0.0330049
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	−6.00000	−0.197599
$923$	24.0000	0.789970
$924$	−4.00000	−0.131590
$925$	−6.00000	−0.197279
$926$	−24.0000	−0.788689
$927$	−8.00000	−0.262754
$928$	2.00000	0.0656532
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	−4.00000	−0.131165
$931$	0	0
$932$	26.0000	0.851658
$933$	−12.0000	−0.392862
$934$	24.0000	0.785304
$935$	−1.00000	−0.0327035
$936$	−2.00000	−0.0653720
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	64.0000	2.08967
$939$	14.0000	0.456873
$940$	8.00000	0.260931
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−14.0000	−0.456145
$943$	0	0
$944$	4.00000	0.130189
$945$	4.00000	0.130120
$946$	4.00000	0.130051
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	−8.00000	−0.259828
$949$	12.0000	0.389536
$950$	0	0
$951$	−30.0000	−0.972817
$952$	−4.00000	−0.129641
$953$	10.0000	0.323932	0.161966	−	0.986796i	$-0.448217\pi$
$953$	10.0000	0.323932	0.161966	+	0.986796i	$0.448217\pi$
$954$	−14.0000	−0.453267
$955$	−8.00000	−0.258874
$956$	0	0
$957$	2.00000	0.0646508
$958$	32.0000	1.03387
$959$	24.0000	0.775000
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	12.0000	0.386896
$963$	4.00000	0.128898
$964$	14.0000	0.450910
$965$	22.0000	0.708205
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−6.00000	−0.192648
$971$	−4.00000	−0.128366	−0.0641831	−	0.997938i	$-0.520444\pi$
$971$	−4.00000	−0.128366	−0.0641831	+	0.997938i	$0.520444\pi$
$972$	1.00000	0.0320750
$973$	−80.0000	−2.56468
$974$	−8.00000	−0.256337
$975$	−2.00000	−0.0640513
$976$	2.00000	0.0640184
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	4.00000	0.127906
$979$	−6.00000	−0.191761
$980$	−9.00000	−0.287494
$981$	−14.0000	−0.446986
$982$	−40.0000	−1.27645
$983$	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
$986$	2.00000	0.0636930
$987$	32.0000	1.01857
$988$	0	0
$989$	0	0
$990$	−1.00000	−0.0317821
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	4.00000	0.127000
$993$	−12.0000	−0.380808
$994$	48.0000	1.52247
$995$	−20.0000	−0.634043
$996$	−12.0000	−0.380235
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	28.0000	0.886325
$999$	−6.00000	−0.189832

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
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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