LMFDB - Embedded newform 130.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(1,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("130.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.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:	$1.03805522628$
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	$\chi$	$=$	130.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} +2.00000 q^{12} -1.00000 q^{13} -4.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +6.00000 q^{19} -1.00000 q^{20} -8.00000 q^{21} -2.00000 q^{22} +6.00000 q^{23} +2.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.00000 q^{27} -4.00000 q^{28} +2.00000 q^{29} -2.00000 q^{30} -6.00000 q^{31} +1.00000 q^{32} -4.00000 q^{33} +2.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +6.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} -8.00000 q^{42} -10.0000 q^{43} -2.00000 q^{44} -1.00000 q^{45} +6.00000 q^{46} -12.0000 q^{47} +2.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +4.00000 q^{51} -1.00000 q^{52} +2.00000 q^{53} -4.00000 q^{54} +2.00000 q^{55} -4.00000 q^{56} +12.0000 q^{57} +2.00000 q^{58} +10.0000 q^{59} -2.00000 q^{60} +2.00000 q^{61} -6.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -4.00000 q^{66} -12.0000 q^{67} +2.00000 q^{68} +12.0000 q^{69} +4.00000 q^{70} +10.0000 q^{71} +1.00000 q^{72} +10.0000 q^{73} -2.00000 q^{74} +2.00000 q^{75} +6.00000 q^{76} +8.00000 q^{77} -2.00000 q^{78} -4.00000 q^{79} -1.00000 q^{80} -11.0000 q^{81} +10.0000 q^{82} -8.00000 q^{84} -2.00000 q^{85} -10.0000 q^{86} +4.00000 q^{87} -2.00000 q^{88} -14.0000 q^{89} -1.00000 q^{90} +4.00000 q^{91} +6.00000 q^{92} -12.0000 q^{93} -12.0000 q^{94} -6.00000 q^{95} +2.00000 q^{96} +14.0000 q^{97} +9.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.00000	0.816497
$7$	−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
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	2.00000	0.577350
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.00000	−1.06904
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	−1.00000	−0.223607
$21$	−8.00000	−1.74574
$22$	−2.00000	−0.426401
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	2.00000	0.408248
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−4.00000	−0.769800
$28$	−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	$0.440546\pi$
$30$	−2.00000	−0.365148
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	2.00000	0.342997
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	6.00000	0.973329
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−8.00000	−1.23443
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−2.00000	−0.301511
$45$	−1.00000	−0.149071
$46$	6.00000	0.884652
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	2.00000	0.288675
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	4.00000	0.560112
$52$	−1.00000	−0.138675
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−4.00000	−0.544331
$55$	2.00000	0.269680
$56$	−4.00000	−0.534522
$57$	12.0000	1.58944
$58$	2.00000	0.262613
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	−2.00000	−0.258199
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−6.00000	−0.762001
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−4.00000	−0.492366
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	2.00000	0.242536
$69$	12.0000	1.44463
$70$	4.00000	0.478091
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	1.00000	0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−2.00000	−0.232495
$75$	2.00000	0.230940
$76$	6.00000	0.688247
$77$	8.00000	0.911685
$78$	−2.00000	−0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−0.111803
$81$	−11.0000	−1.22222
$82$	10.0000	1.10432
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−8.00000	−0.872872
$85$	−2.00000	−0.216930
$86$	−10.0000	−1.07833
$87$	4.00000	0.428845
$88$	−2.00000	−0.213201
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−1.00000	−0.105409
$91$	4.00000	0.419314
$92$	6.00000	0.625543
$93$	−12.0000	−1.24434
$94$	−12.0000	−1.23771
$95$	−6.00000	−0.615587
$96$	2.00000	0.204124
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	9.00000	0.909137
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	4.00000	0.396059
$103$	−18.0000	−1.77359	−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000	−1.77359	−0.886796	+	0.462160i	$0.847074\pi$
$104$	−1.00000	−0.0980581
$105$	8.00000	0.780720
$106$	2.00000	0.194257
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−4.00000	−0.384900
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	2.00000	0.190693
$111$	−4.00000	−0.379663
$112$	−4.00000	−0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	12.0000	1.12390
$115$	−6.00000	−0.559503
$116$	2.00000	0.185695
$117$	−1.00000	−0.0924500
$118$	10.0000	0.920575
$119$	−8.00000	−0.733359
$120$	−2.00000	−0.182574
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	20.0000	1.80334
$124$	−6.00000	−0.538816
$125$	−1.00000	−0.0894427
$126$	−4.00000	−0.356348
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	1.00000	0.0883883
$129$	−20.0000	−1.76090
$130$	1.00000	0.0877058
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	−4.00000	−0.348155
$133$	−24.0000	−2.08106
$134$	−12.0000	−1.03664
$135$	4.00000	0.344265
$136$	2.00000	0.171499
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	12.0000	1.02151
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	4.00000	0.338062
$141$	−24.0000	−2.02116
$142$	10.0000	0.839181
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	10.0000	0.827606
$147$	18.0000	1.48461
$148$	−2.00000	−0.164399
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	2.00000	0.163299
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	6.00000	0.486664
$153$	2.00000	0.161690
$154$	8.00000	0.644658
$155$	6.00000	0.481932
$156$	−2.00000	−0.160128
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	−4.00000	−0.318223
$159$	4.00000	0.317221
$160$	−1.00000	−0.0790569
$161$	−24.0000	−1.89146
$162$	−11.0000	−0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	10.0000	0.780869
$165$	4.00000	0.311400
$166$	0	0
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	−8.00000	−0.617213
$169$	1.00000	0.0769231
$170$	−2.00000	−0.153393
$171$	6.00000	0.458831
$172$	−10.0000	−0.762493
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	4.00000	0.303239
$175$	−4.00000	−0.302372
$176$	−2.00000	−0.150756
$177$	20.0000	1.50329
$178$	−14.0000	−1.04934
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	−1.00000	−0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	4.00000	0.296500
$183$	4.00000	0.295689
$184$	6.00000	0.442326
$185$	2.00000	0.147043
$186$	−12.0000	−0.879883
$187$	−4.00000	−0.292509
$188$	−12.0000	−0.875190
$189$	16.0000	1.16383
$190$	−6.00000	−0.435286
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	2.00000	0.144338
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	14.0000	1.00514
$195$	2.00000	0.143223
$196$	9.00000	0.642857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	−2.00000	−0.142134
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	1.00000	0.0707107
$201$	−24.0000	−1.69283
$202$	14.0000	0.985037
$203$	−8.00000	−0.561490
$204$	4.00000	0.280056
$205$	−10.0000	−0.698430
$206$	−18.0000	−1.25412
$207$	6.00000	0.417029
$208$	−1.00000	−0.0693375
$209$	−12.0000	−0.830057
$210$	8.00000	0.552052
$211$	28.0000	1.92760	0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000	1.92760	0.963800	+	0.266627i	$0.0859092\pi$
$212$	2.00000	0.137361
$213$	20.0000	1.37038
$214$	6.00000	0.410152
$215$	10.0000	0.681994
$216$	−4.00000	−0.272166
$217$	24.0000	1.62923
$218$	−6.00000	−0.406371
$219$	20.0000	1.35147
$220$	2.00000	0.134840
$221$	−2.00000	−0.134535
$222$	−4.00000	−0.268462
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−4.00000	−0.267261
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	12.0000	0.794719
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−6.00000	−0.395628
$231$	16.0000	1.05272
$232$	2.00000	0.131306
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−1.00000	−0.0653720
$235$	12.0000	0.782794
$236$	10.0000	0.650945
$237$	−8.00000	−0.519656
$238$	−8.00000	−0.518563
$239$	−26.0000	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$240$	−2.00000	−0.129099
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−7.00000	−0.449977
$243$	−10.0000	−0.641500
$244$	2.00000	0.128037
$245$	−9.00000	−0.574989
$246$	20.0000	1.27515
$247$	−6.00000	−0.381771
$248$	−6.00000	−0.381000
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	−4.00000	−0.251976
$253$	−12.0000	−0.754434
$254$	−14.0000	−0.878438
$255$	−4.00000	−0.250490
$256$	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	$0.885208\pi$
$258$	−20.0000	−1.24515
$259$	8.00000	0.497096
$260$	1.00000	0.0620174
$261$	2.00000	0.123797
$262$	4.00000	0.247121
$263$	2.00000	0.123325	0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000	0.123325	0.0616626	+	0.998097i	$0.480360\pi$
$264$	−4.00000	−0.246183
$265$	−2.00000	−0.122859
$266$	−24.0000	−1.47153
$267$	−28.0000	−1.71357
$268$	−12.0000	−0.733017
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	4.00000	0.243432
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	2.00000	0.121268
$273$	8.00000	0.484182
$274$	−18.0000	−1.08742
$275$	−2.00000	−0.120605
$276$	12.0000	0.722315
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−8.00000	−0.479808
$279$	−6.00000	−0.359211
$280$	4.00000	0.239046
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−24.0000	−1.42918
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	10.0000	0.593391
$285$	−12.0000	−0.710819
$286$	2.00000	0.118262
$287$	−40.0000	−2.36113
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−2.00000	−0.117444
$291$	28.0000	1.64139
$292$	10.0000	0.585206
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	18.0000	1.04978
$295$	−10.0000	−0.582223
$296$	−2.00000	−0.116248
$297$	8.00000	0.464207
$298$	2.00000	0.115857
$299$	−6.00000	−0.346989
$300$	2.00000	0.115470
$301$	40.0000	2.30556
$302$	6.00000	0.345261
$303$	28.0000	1.60856
$304$	6.00000	0.344124
$305$	−2.00000	−0.114520
$306$	2.00000	0.114332
$307$	24.0000	1.36975	0.684876	−	0.728659i	$-0.259856\pi$
$307$	24.0000	1.36975	0.684876	+	0.728659i	$0.259856\pi$
$308$	8.00000	0.455842
$309$	−36.0000	−2.04797
$310$	6.00000	0.340777
$311$	−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
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	10.0000	0.564333
$315$	4.00000	0.225374
$316$	−4.00000	−0.225018
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	4.00000	0.224309
$319$	−4.00000	−0.223957
$320$	−1.00000	−0.0559017
$321$	12.0000	0.669775
$322$	−24.0000	−1.33747
$323$	12.0000	0.667698
$324$	−11.0000	−0.611111
$325$	−1.00000	−0.0554700
$326$	−4.00000	−0.221540
$327$	−12.0000	−0.663602
$328$	10.0000	0.552158
$329$	48.0000	2.64633
$330$	4.00000	0.220193
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	0	0
$333$	−2.00000	−0.109599
$334$	20.0000	1.09435
$335$	12.0000	0.655630
$336$	−8.00000	−0.436436
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	1.00000	0.0543928
$339$	4.00000	0.217250
$340$	−2.00000	−0.108465
$341$	12.0000	0.649836
$342$	6.00000	0.324443
$343$	−8.00000	−0.431959
$344$	−10.0000	−0.539164
$345$	−12.0000	−0.646058
$346$	10.0000	0.537603
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	4.00000	0.214423
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−4.00000	−0.213809
$351$	4.00000	0.213504
$352$	−2.00000	−0.106600
$353$	34.0000	1.80964	0.904819	−	0.425797i	$-0.140006\pi$
$353$	34.0000	1.80964	0.904819	+	0.425797i	$0.140006\pi$
$354$	20.0000	1.06299
$355$	−10.0000	−0.530745
$356$	−14.0000	−0.741999
$357$	−16.0000	−0.846810
$358$	−4.00000	−0.211407
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	−1.00000	−0.0527046
$361$	17.0000	0.894737
$362$	10.0000	0.525588
$363$	−14.0000	−0.734809
$364$	4.00000	0.209657
$365$	−10.0000	−0.523424
$366$	4.00000	0.209083
$367$	30.0000	1.56599	0.782994	−	0.622030i	$-0.213692\pi$
$367$	30.0000	1.56599	0.782994	+	0.622030i	$0.213692\pi$
$368$	6.00000	0.312772
$369$	10.0000	0.520579
$370$	2.00000	0.103975
$371$	−8.00000	−0.415339
$372$	−12.0000	−0.622171
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−4.00000	−0.206835
$375$	−2.00000	−0.103280
$376$	−12.0000	−0.618853
$377$	−2.00000	−0.103005
$378$	16.0000	0.822951
$379$	6.00000	0.308199	0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000	0.308199	0.154100	+	0.988055i	$0.450752\pi$
$380$	−6.00000	−0.307794
$381$	−28.0000	−1.43448
$382$	0	0
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	2.00000	0.102062
$385$	−8.00000	−0.407718
$386$	14.0000	0.712581
$387$	−10.0000	−0.508329
$388$	14.0000	0.710742
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	2.00000	0.101274
$391$	12.0000	0.606866
$392$	9.00000	0.454569
$393$	8.00000	0.403547
$394$	−6.00000	−0.302276
$395$	4.00000	0.201262
$396$	−2.00000	−0.100504
$397$	38.0000	1.90717	0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000	1.90717	0.953583	+	0.301131i	$0.0973643\pi$
$398$	0	0
$399$	−48.0000	−2.40301
$400$	1.00000	0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	−24.0000	−1.19701
$403$	6.00000	0.298881
$404$	14.0000	0.696526
$405$	11.0000	0.546594
$406$	−8.00000	−0.397033
$407$	4.00000	0.198273
$408$	4.00000	0.198030
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−10.0000	−0.493865
$411$	−36.0000	−1.77575
$412$	−18.0000	−0.886796
$413$	−40.0000	−1.96827
$414$	6.00000	0.294884
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−16.0000	−0.783523
$418$	−12.0000	−0.586939
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	8.00000	0.390360
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	28.0000	1.36302
$423$	−12.0000	−0.583460
$424$	2.00000	0.0971286
$425$	2.00000	0.0970143
$426$	20.0000	0.969003
$427$	−8.00000	−0.387147
$428$	6.00000	0.290021
$429$	4.00000	0.193122
$430$	10.0000	0.482243
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	−4.00000	−0.192450
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	24.0000	1.15204
$435$	−4.00000	−0.191785
$436$	−6.00000	−0.287348
$437$	36.0000	1.72211
$438$	20.0000	0.955637
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	2.00000	0.0953463
$441$	9.00000	0.428571
$442$	−2.00000	−0.0951303
$443$	−14.0000	−0.665160	−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000	−0.665160	−0.332580	+	0.943075i	$0.607919\pi$
$444$	−4.00000	−0.189832
$445$	14.0000	0.663664
$446$	4.00000	0.189405
$447$	4.00000	0.189194
$448$	−4.00000	−0.188982
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	1.00000	0.0471405
$451$	−20.0000	−0.941763
$452$	2.00000	0.0940721
$453$	12.0000	0.563809
$454$	−4.00000	−0.187729
$455$	−4.00000	−0.187523
$456$	12.0000	0.561951
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	10.0000	0.467269
$459$	−8.00000	−0.373408
$460$	−6.00000	−0.279751
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	16.0000	0.744387
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000	0.0928477
$465$	12.0000	0.556487
$466$	−6.00000	−0.277945
$467$	10.0000	0.462745	0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000	0.462745	0.231372	+	0.972865i	$0.425678\pi$
$468$	−1.00000	−0.0462250
$469$	48.0000	2.21643
$470$	12.0000	0.553519
$471$	20.0000	0.921551
$472$	10.0000	0.460287
$473$	20.0000	0.919601
$474$	−8.00000	−0.367452
$475$	6.00000	0.275299
$476$	−8.00000	−0.366679
$477$	2.00000	0.0915737
$478$	−26.0000	−1.18921
$479$	2.00000	0.0913823	0.0456912	−	0.998956i	$-0.485451\pi$
$479$	2.00000	0.0913823	0.0456912	+	0.998956i	$0.485451\pi$
$480$	−2.00000	−0.0912871
$481$	2.00000	0.0911922
$482$	−22.0000	−1.00207
$483$	−48.0000	−2.18408
$484$	−7.00000	−0.318182
$485$	−14.0000	−0.635707
$486$	−10.0000	−0.453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	2.00000	0.0905357
$489$	−8.00000	−0.361773
$490$	−9.00000	−0.406579
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	20.0000	0.901670
$493$	4.00000	0.180151
$494$	−6.00000	−0.269953
$495$	2.00000	0.0898933
$496$	−6.00000	−0.269408
$497$	−40.0000	−1.79425
$498$	0	0
$499$	38.0000	1.70111	0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000	1.70111	0.850557	+	0.525883i	$0.176265\pi$
$500$	−1.00000	−0.0447214
$501$	40.0000	1.78707
$502$	0	0
$503$	−14.0000	−0.624229	−0.312115	−	0.950044i	$-0.601037\pi$
$503$	−14.0000	−0.624229	−0.312115	+	0.950044i	$0.601037\pi$
$504$	−4.00000	−0.178174
$505$	−14.0000	−0.622992
$506$	−12.0000	−0.533465
$507$	2.00000	0.0888231
$508$	−14.0000	−0.621150
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	−4.00000	−0.177123
$511$	−40.0000	−1.76950
$512$	1.00000	0.0441942
$513$	−24.0000	−1.05963
$514$	−30.0000	−1.32324
$515$	18.0000	0.793175
$516$	−20.0000	−0.880451
$517$	24.0000	1.05552
$518$	8.00000	0.351500
$519$	20.0000	0.877903
$520$	1.00000	0.0438529
$521$	−26.0000	−1.13908	−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000	−1.13908	−0.569540	+	0.821963i	$0.692879\pi$
$522$	2.00000	0.0875376
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	4.00000	0.174741
$525$	−8.00000	−0.349149
$526$	2.00000	0.0872041
$527$	−12.0000	−0.522728
$528$	−4.00000	−0.174078
$529$	13.0000	0.565217
$530$	−2.00000	−0.0868744
$531$	10.0000	0.433963
$532$	−24.0000	−1.04053
$533$	−10.0000	−0.433148
$534$	−28.0000	−1.21168
$535$	−6.00000	−0.259403
$536$	−12.0000	−0.518321
$537$	−8.00000	−0.345225
$538$	6.00000	0.258678
$539$	−18.0000	−0.775315
$540$	4.00000	0.172133
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	−2.00000	−0.0859074
$543$	20.0000	0.858282
$544$	2.00000	0.0857493
$545$	6.00000	0.257012
$546$	8.00000	0.342368
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	−18.0000	−0.768922
$549$	2.00000	0.0853579
$550$	−2.00000	−0.0852803
$551$	12.0000	0.511217
$552$	12.0000	0.510754
$553$	16.0000	0.680389
$554$	2.00000	0.0849719
$555$	4.00000	0.169791
$556$	−8.00000	−0.339276
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	−6.00000	−0.254000
$559$	10.0000	0.422955
$560$	4.00000	0.169031
$561$	−8.00000	−0.337760
$562$	−6.00000	−0.253095
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	−24.0000	−1.01058
$565$	−2.00000	−0.0841406
$566$	14.0000	0.588464
$567$	44.0000	1.84783
$568$	10.0000	0.419591
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−12.0000	−0.502625
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	−40.0000	−1.66957
$575$	6.00000	0.250217
$576$	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	$0.377754\pi$
$578$	−13.0000	−0.540729
$579$	28.0000	1.16364
$580$	−2.00000	−0.0830455
$581$	0	0
$582$	28.0000	1.16064
$583$	−4.00000	−0.165663
$584$	10.0000	0.413803
$585$	1.00000	0.0413449
$586$	22.0000	0.908812
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	18.0000	0.742307
$589$	−36.0000	−1.48335
$590$	−10.0000	−0.411693
$591$	−12.0000	−0.493614
$592$	−2.00000	−0.0821995
$593$	−2.00000	−0.0821302	−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000	−0.0821302	−0.0410651	+	0.999156i	$0.513075\pi$
$594$	8.00000	0.328244
$595$	8.00000	0.327968
$596$	2.00000	0.0819232
$597$	0	0
$598$	−6.00000	−0.245358
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	2.00000	0.0816497
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	40.0000	1.63028
$603$	−12.0000	−0.488678
$604$	6.00000	0.244137
$605$	7.00000	0.284590
$606$	28.0000	1.13742
$607$	−34.0000	−1.38002	−0.690009	−	0.723801i	$-0.742393\pi$
$607$	−34.0000	−1.38002	−0.690009	+	0.723801i	$0.742393\pi$
$608$	6.00000	0.243332
$609$	−16.0000	−0.648353
$610$	−2.00000	−0.0809776
$611$	12.0000	0.485468
$612$	2.00000	0.0808452
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	24.0000	0.968561
$615$	−20.0000	−0.806478
$616$	8.00000	0.322329
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	−36.0000	−1.44813
$619$	−46.0000	−1.84890	−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000	−1.84890	−0.924448	+	0.381308i	$0.875474\pi$
$620$	6.00000	0.240966
$621$	−24.0000	−0.963087
$622$	−12.0000	−0.481156
$623$	56.0000	2.24359
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	−24.0000	−0.958468
$628$	10.0000	0.399043
$629$	−4.00000	−0.159490
$630$	4.00000	0.159364
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	−4.00000	−0.159111
$633$	56.0000	2.22580
$634$	−18.0000	−0.714871
$635$	14.0000	0.555573
$636$	4.00000	0.158610
$637$	−9.00000	−0.356593
$638$	−4.00000	−0.158362
$639$	10.0000	0.395594
$640$	−1.00000	−0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	12.0000	0.473602
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	−24.0000	−0.945732
$645$	20.0000	0.787499
$646$	12.0000	0.472134
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	−11.0000	−0.432121
$649$	−20.0000	−0.785069
$650$	−1.00000	−0.0392232
$651$	48.0000	1.88127
$652$	−4.00000	−0.156652
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	−12.0000	−0.469237
$655$	−4.00000	−0.156293
$656$	10.0000	0.390434
$657$	10.0000	0.390137
$658$	48.0000	1.87123
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	4.00000	0.155700
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	−14.0000	−0.544125
$663$	−4.00000	−0.155347
$664$	0	0
$665$	24.0000	0.930680
$666$	−2.00000	−0.0774984
$667$	12.0000	0.464642
$668$	20.0000	0.773823
$669$	8.00000	0.309298
$670$	12.0000	0.463600
$671$	−4.00000	−0.154418
$672$	−8.00000	−0.308607
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	−22.0000	−0.847408
$675$	−4.00000	−0.153960
$676$	1.00000	0.0384615
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	4.00000	0.153619
$679$	−56.0000	−2.14908
$680$	−2.00000	−0.0766965
$681$	−8.00000	−0.306561
$682$	12.0000	0.459504
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	6.00000	0.229416
$685$	18.0000	0.687745
$686$	−8.00000	−0.305441
$687$	20.0000	0.763048
$688$	−10.0000	−0.381246
$689$	−2.00000	−0.0761939
$690$	−12.0000	−0.456832
$691$	−38.0000	−1.44559	−0.722794	−	0.691063i	$-0.757142\pi$
$691$	−38.0000	−1.44559	−0.722794	+	0.691063i	$0.757142\pi$
$692$	10.0000	0.380143
$693$	8.00000	0.303895
$694$	6.00000	0.227757
$695$	8.00000	0.303457
$696$	4.00000	0.151620
$697$	20.0000	0.757554
$698$	2.00000	0.0757011
$699$	−12.0000	−0.453882
$700$	−4.00000	−0.151186
$701$	38.0000	1.43524	0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000	1.43524	0.717620	+	0.696435i	$0.245231\pi$
$702$	4.00000	0.150970
$703$	−12.0000	−0.452589
$704$	−2.00000	−0.0753778
$705$	24.0000	0.903892
$706$	34.0000	1.27961
$707$	−56.0000	−2.10610
$708$	20.0000	0.751646
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	−10.0000	−0.375293
$711$	−4.00000	−0.150012
$712$	−14.0000	−0.524672
$713$	−36.0000	−1.34821
$714$	−16.0000	−0.598785
$715$	−2.00000	−0.0747958
$716$	−4.00000	−0.149487
$717$	−52.0000	−1.94198
$718$	−6.00000	−0.223918
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	−1.00000	−0.0372678
$721$	72.0000	2.68142
$722$	17.0000	0.632674
$723$	−44.0000	−1.63638
$724$	10.0000	0.371647
$725$	2.00000	0.0742781
$726$	−14.0000	−0.519589
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	4.00000	0.148250
$729$	13.0000	0.481481
$730$	−10.0000	−0.370117
$731$	−20.0000	−0.739727
$732$	4.00000	0.147844
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	30.0000	1.10732
$735$	−18.0000	−0.663940
$736$	6.00000	0.221163
$737$	24.0000	0.884051
$738$	10.0000	0.368105
$739$	42.0000	1.54499	0.772497	−	0.635018i	$-0.219007\pi$
$739$	42.0000	1.54499	0.772497	+	0.635018i	$0.219007\pi$
$740$	2.00000	0.0735215
$741$	−12.0000	−0.440831
$742$	−8.00000	−0.293689
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	−12.0000	−0.439941
$745$	−2.00000	−0.0732743
$746$	−14.0000	−0.512576
$747$	0	0
$748$	−4.00000	−0.146254
$749$	−24.0000	−0.876941
$750$	−2.00000	−0.0730297
$751$	44.0000	1.60558	0.802791	−	0.596260i	$-0.203347\pi$
$751$	44.0000	1.60558	0.802791	+	0.596260i	$0.203347\pi$
$752$	−12.0000	−0.437595
$753$	0	0
$754$	−2.00000	−0.0728357
$755$	−6.00000	−0.218362
$756$	16.0000	0.581914
$757$	18.0000	0.654221	0.327111	−	0.944986i	$-0.393925\pi$
$757$	18.0000	0.654221	0.327111	+	0.944986i	$0.393925\pi$
$758$	6.00000	0.217930
$759$	−24.0000	−0.871145
$760$	−6.00000	−0.217643
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	−28.0000	−1.01433
$763$	24.0000	0.868858
$764$	0	0
$765$	−2.00000	−0.0723102
$766$	12.0000	0.433578
$767$	−10.0000	−0.361079
$768$	2.00000	0.0721688
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	−8.00000	−0.288300
$771$	−60.0000	−2.16085
$772$	14.0000	0.503871
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	−10.0000	−0.359443
$775$	−6.00000	−0.215526
$776$	14.0000	0.502571
$777$	16.0000	0.573997
$778$	−10.0000	−0.358517
$779$	60.0000	2.14972
$780$	2.00000	0.0716115
$781$	−20.0000	−0.715656
$782$	12.0000	0.429119
$783$	−8.00000	−0.285897
$784$	9.00000	0.321429
$785$	−10.0000	−0.356915
$786$	8.00000	0.285351
$787$	−8.00000	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$788$	−6.00000	−0.213741
$789$	4.00000	0.142404
$790$	4.00000	0.142314
$791$	−8.00000	−0.284447
$792$	−2.00000	−0.0710669
$793$	−2.00000	−0.0710221
$794$	38.0000	1.34857
$795$	−4.00000	−0.141865
$796$	0	0
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	−48.0000	−1.69918
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	−14.0000	−0.494666
$802$	−6.00000	−0.211867
$803$	−20.0000	−0.705785
$804$	−24.0000	−0.846415
$805$	24.0000	0.845889
$806$	6.00000	0.211341
$807$	12.0000	0.422420
$808$	14.0000	0.492518
$809$	−34.0000	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$810$	11.0000	0.386501
$811$	−38.0000	−1.33436	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000	−1.33436	−0.667180	+	0.744896i	$0.732499\pi$
$812$	−8.00000	−0.280745
$813$	−4.00000	−0.140286
$814$	4.00000	0.140200
$815$	4.00000	0.140114
$816$	4.00000	0.140028
$817$	−60.0000	−2.09913
$818$	34.0000	1.18878
$819$	4.00000	0.139771
$820$	−10.0000	−0.349215
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	−36.0000	−1.25564
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	−18.0000	−0.627060
$825$	−4.00000	−0.139262
$826$	−40.0000	−1.39178
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	6.00000	0.208514
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	4.00000	0.138758
$832$	−1.00000	−0.0346688
$833$	18.0000	0.623663
$834$	−16.0000	−0.554035
$835$	−20.0000	−0.692129
$836$	−12.0000	−0.415029
$837$	24.0000	0.829561
$838$	16.0000	0.552711
$839$	26.0000	0.897620	0.448810	−	0.893627i	$-0.351848\pi$
$839$	26.0000	0.897620	0.448810	+	0.893627i	$0.351848\pi$
$840$	8.00000	0.276026
$841$	−25.0000	−0.862069
$842$	10.0000	0.344623
$843$	−12.0000	−0.413302
$844$	28.0000	0.963800
$845$	−1.00000	−0.0344010
$846$	−12.0000	−0.412568
$847$	28.0000	0.962091
$848$	2.00000	0.0686803
$849$	28.0000	0.960958
$850$	2.00000	0.0685994
$851$	−12.0000	−0.411355
$852$	20.0000	0.685189
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−8.00000	−0.273754
$855$	−6.00000	−0.205196
$856$	6.00000	0.205076
$857$	−14.0000	−0.478231	−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000	−0.478231	−0.239115	+	0.970991i	$0.576857\pi$
$858$	4.00000	0.136558
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	10.0000	0.340997
$861$	−80.0000	−2.72639
$862$	18.0000	0.613082
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	−4.00000	−0.136083
$865$	−10.0000	−0.340010
$866$	−38.0000	−1.29129
$867$	−26.0000	−0.883006
$868$	24.0000	0.814613
$869$	8.00000	0.271381
$870$	−4.00000	−0.135613
$871$	12.0000	0.406604
$872$	−6.00000	−0.203186
$873$	14.0000	0.473828
$874$	36.0000	1.21772
$875$	4.00000	0.135225
$876$	20.0000	0.675737
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	−32.0000	−1.07995
$879$	44.0000	1.48408
$880$	2.00000	0.0674200
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	9.00000	0.303046
$883$	38.0000	1.27880	0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000	1.27880	0.639401	+	0.768874i	$0.279182\pi$
$884$	−2.00000	−0.0672673
$885$	−20.0000	−0.672293
$886$	−14.0000	−0.470339
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	−4.00000	−0.134231
$889$	56.0000	1.87818
$890$	14.0000	0.469281
$891$	22.0000	0.737028
$892$	4.00000	0.133930
$893$	−72.0000	−2.40939
$894$	4.00000	0.133780
$895$	4.00000	0.133705
$896$	−4.00000	−0.133631
$897$	−12.0000	−0.400668
$898$	−6.00000	−0.200223
$899$	−12.0000	−0.400222
$900$	1.00000	0.0333333
$901$	4.00000	0.133259
$902$	−20.0000	−0.665927
$903$	80.0000	2.66223
$904$	2.00000	0.0665190
$905$	−10.0000	−0.332411
$906$	12.0000	0.398673
$907$	−14.0000	−0.464862	−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000	−0.464862	−0.232431	+	0.972613i	$0.574668\pi$
$908$	−4.00000	−0.132745
$909$	14.0000	0.464351
$910$	−4.00000	−0.132599
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	12.0000	0.397360
$913$	0	0
$914$	−10.0000	−0.330771
$915$	−4.00000	−0.132236
$916$	10.0000	0.330409
$917$	−16.0000	−0.528367
$918$	−8.00000	−0.264039
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	−6.00000	−0.197814
$921$	48.0000	1.58165
$922$	−6.00000	−0.197599
$923$	−10.0000	−0.329154
$924$	16.0000	0.526361
$925$	−2.00000	−0.0657596
$926$	16.0000	0.525793
$927$	−18.0000	−0.591198
$928$	2.00000	0.0656532
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	12.0000	0.393496
$931$	54.0000	1.76978
$932$	−6.00000	−0.196537
$933$	−24.0000	−0.785725
$934$	10.0000	0.327210
$935$	4.00000	0.130814
$936$	−1.00000	−0.0326860
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	48.0000	1.56726
$939$	−12.0000	−0.391605
$940$	12.0000	0.391397
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	20.0000	0.651635
$943$	60.0000	1.95387
$944$	10.0000	0.325472
$945$	−16.0000	−0.520480
$946$	20.0000	0.650256
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	−8.00000	−0.259828
$949$	−10.0000	−0.324614
$950$	6.00000	0.194666
$951$	−36.0000	−1.16738
$952$	−8.00000	−0.259281
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	−26.0000	−0.840900
$957$	−8.00000	−0.258603
$958$	2.00000	0.0646171
$959$	72.0000	2.32500
$960$	−2.00000	−0.0645497
$961$	5.00000	0.161290
$962$	2.00000	0.0644826
$963$	6.00000	0.193347
$964$	−22.0000	−0.708572
$965$	−14.0000	−0.450676
$966$	−48.0000	−1.54437
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	−7.00000	−0.224989
$969$	24.0000	0.770991
$970$	−14.0000	−0.449513
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	−10.0000	−0.320750
$973$	32.0000	1.02587
$974$	−16.0000	−0.512673
$975$	−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	$0.659324\pi$
$978$	−8.00000	−0.255812
$979$	28.0000	0.894884
$980$	−9.00000	−0.287494
$981$	−6.00000	−0.191565
$982$	0	0
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	20.0000	0.637577
$985$	6.00000	0.191176
$986$	4.00000	0.127386
$987$	96.0000	3.05571
$988$	−6.00000	−0.190885
$989$	−60.0000	−1.90789
$990$	2.00000	0.0635642
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	−6.00000	−0.190500
$993$	−28.0000	−0.888553
$994$	−40.0000	−1.26872
$995$	0	0
$996$	0	0
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	38.0000	1.20287
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.a.c.1.1	✓	1
3.2	odd	2		1170.2.a.d.1.1		1
4.3	odd	2		1040.2.a.b.1.1		1
5.2	odd	4		650.2.b.g.599.2		2
5.3	odd	4		650.2.b.g.599.1		2
5.4	even	2		650.2.a.c.1.1		1
7.6	odd	2		6370.2.a.l.1.1		1
8.3	odd	2		4160.2.a.t.1.1		1
8.5	even	2		4160.2.a.c.1.1		1
12.11	even	2		9360.2.a.by.1.1		1
13.2	odd	12		1690.2.l.a.1161.2		4
13.3	even	3		1690.2.e.a.191.1		2
13.4	even	6		1690.2.e.g.991.1		2
13.5	odd	4		1690.2.d.e.1351.1		2
13.6	odd	12		1690.2.l.a.361.1		4
13.7	odd	12		1690.2.l.a.361.2		4
13.8	odd	4		1690.2.d.e.1351.2		2
13.9	even	3		1690.2.e.a.991.1		2
13.10	even	6		1690.2.e.g.191.1		2
13.11	odd	12		1690.2.l.a.1161.1		4
13.12	even	2		1690.2.a.e.1.1		1
15.2	even	4		5850.2.e.u.5149.1		2
15.8	even	4		5850.2.e.u.5149.2		2
15.14	odd	2		5850.2.a.cb.1.1		1
20.19	odd	2		5200.2.a.bd.1.1		1
65.64	even	2		8450.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.c.1.1	✓	1	1.1	even	1	trivial
650.2.a.c.1.1		1	5.4	even	2
650.2.b.g.599.1		2	5.3	odd	4
650.2.b.g.599.2		2	5.2	odd	4
1040.2.a.b.1.1		1	4.3	odd	2
1170.2.a.d.1.1		1	3.2	odd	2
1690.2.a.e.1.1		1	13.12	even	2
1690.2.d.e.1351.1		2	13.5	odd	4
1690.2.d.e.1351.2		2	13.8	odd	4
1690.2.e.a.191.1		2	13.3	even	3
1690.2.e.a.991.1		2	13.9	even	3
1690.2.e.g.191.1		2	13.10	even	6
1690.2.e.g.991.1		2	13.4	even	6
1690.2.l.a.361.1		4	13.6	odd	12
1690.2.l.a.361.2		4	13.7	odd	12
1690.2.l.a.1161.1		4	13.11	odd	12
1690.2.l.a.1161.2		4	13.2	odd	12
4160.2.a.c.1.1		1	8.5	even	2
4160.2.a.t.1.1		1	8.3	odd	2
5200.2.a.bd.1.1		1	20.19	odd	2
5850.2.a.cb.1.1		1	15.14	odd	2
5850.2.e.u.5149.1		2	15.2	even	4
5850.2.e.u.5149.2		2	15.8	even	4
6370.2.a.l.1.1		1	7.6	odd	2
8450.2.a.n.1.1		1	65.64	even	2
9360.2.a.by.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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