LMFDB - Embedded newform 158.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [158,2,Mod(1,158)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(158, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("158.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.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:	$1.26163635194$
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	$\chi$	$=$	158.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +4.00000 q^{11} -1.00000 q^{12} -7.00000 q^{13} +3.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +2.00000 q^{18} -6.00000 q^{19} -1.00000 q^{20} +3.00000 q^{21} -4.00000 q^{22} +6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +7.00000 q^{26} +5.00000 q^{27} -3.00000 q^{28} +4.00000 q^{29} -1.00000 q^{30} +8.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} +4.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} +10.0000 q^{37} +6.00000 q^{38} +7.00000 q^{39} +1.00000 q^{40} -8.00000 q^{41} -3.00000 q^{42} -8.00000 q^{43} +4.00000 q^{44} +2.00000 q^{45} -6.00000 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{50} +4.00000 q^{51} -7.00000 q^{52} +2.00000 q^{53} -5.00000 q^{54} -4.00000 q^{55} +3.00000 q^{56} +6.00000 q^{57} -4.00000 q^{58} +1.00000 q^{59} +1.00000 q^{60} -8.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} +7.00000 q^{65} +4.00000 q^{66} -4.00000 q^{67} -4.00000 q^{68} -6.00000 q^{69} -3.00000 q^{70} -11.0000 q^{71} +2.00000 q^{72} -6.00000 q^{73} -10.0000 q^{74} +4.00000 q^{75} -6.00000 q^{76} -12.0000 q^{77} -7.00000 q^{78} -1.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} +6.00000 q^{83} +3.00000 q^{84} +4.00000 q^{85} +8.00000 q^{86} -4.00000 q^{87} -4.00000 q^{88} -15.0000 q^{89} -2.00000 q^{90} +21.0000 q^{91} +6.00000 q^{92} -8.00000 q^{93} +3.00000 q^{94} +6.00000 q^{95} +1.00000 q^{96} +1.00000 q^{97} -2.00000 q^{98} -8.00000 q^{99} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.00000	0.408248
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	−1.00000	−0.288675
$13$	−7.00000	−1.94145	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000	−1.94145	−0.970725	+	0.240192i	$0.922790\pi$
$14$	3.00000	0.801784
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	2.00000	0.471405
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−1.00000	−0.223607
$21$	3.00000	0.654654
$22$	−4.00000	−0.852803
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	7.00000	1.37281
$27$	5.00000	0.962250
$28$	−3.00000	−0.566947
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	−1.00000	−0.182574
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	4.00000	0.685994
$35$	3.00000	0.507093
$36$	−2.00000	−0.333333
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	6.00000	0.973329
$39$	7.00000	1.12090
$40$	1.00000	0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−3.00000	−0.462910
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	4.00000	0.603023
$45$	2.00000	0.298142
$46$	−6.00000	−0.884652
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	4.00000	0.565685
$51$	4.00000	0.560112
$52$	−7.00000	−0.970725
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−5.00000	−0.680414
$55$	−4.00000	−0.539360
$56$	3.00000	0.400892
$57$	6.00000	0.794719
$58$	−4.00000	−0.525226
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	1.00000	0.129099
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−8.00000	−1.01600
$63$	6.00000	0.755929
$64$	1.00000	0.125000
$65$	7.00000	0.868243
$66$	4.00000	0.492366
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−4.00000	−0.485071
$69$	−6.00000	−0.722315
$70$	−3.00000	−0.358569
$71$	−11.0000	−1.30546	−0.652730	−	0.757591i	$-0.726376\pi$
$71$	−11.0000	−1.30546	−0.652730	+	0.757591i	$0.726376\pi$
$72$	2.00000	0.235702
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−10.0000	−1.16248
$75$	4.00000	0.461880
$76$	−6.00000	−0.688247
$77$	−12.0000	−1.36753
$78$	−7.00000	−0.792594
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	3.00000	0.327327
$85$	4.00000	0.433861
$86$	8.00000	0.862662
$87$	−4.00000	−0.428845
$88$	−4.00000	−0.426401
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	−2.00000	−0.210819
$91$	21.0000	2.20140
$92$	6.00000	0.625543
$93$	−8.00000	−0.829561
$94$	3.00000	0.309426
$95$	6.00000	0.615587
$96$	1.00000	0.102062
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−2.00000	−0.202031
$99$	−8.00000	−0.804030
$100$	−4.00000	−0.400000
$101$	5.00000	0.497519	0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000	0.497519	0.248759	+	0.968565i	$0.419977\pi$
$102$	−4.00000	−0.396059
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	7.00000	0.686406
$105$	−3.00000	−0.292770
$106$	−2.00000	−0.194257
$107$	5.00000	0.483368	0.241684	−	0.970355i	$-0.422300\pi$
$107$	5.00000	0.483368	0.241684	+	0.970355i	$0.422300\pi$
$108$	5.00000	0.481125
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	4.00000	0.381385
$111$	−10.0000	−0.949158
$112$	−3.00000	−0.283473
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	−6.00000	−0.561951
$115$	−6.00000	−0.559503
$116$	4.00000	0.371391
$117$	14.0000	1.29430
$118$	−1.00000	−0.0920575
$119$	12.0000	1.10004
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	0	0
$123$	8.00000	0.721336
$124$	8.00000	0.718421
$125$	9.00000	0.804984
$126$	−6.00000	−0.534522
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	−7.00000	−0.613941
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	−4.00000	−0.348155
$133$	18.0000	1.56080
$134$	4.00000	0.345547
$135$	−5.00000	−0.430331
$136$	4.00000	0.342997
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	6.00000	0.510754
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	3.00000	0.253546
$141$	3.00000	0.252646
$142$	11.0000	0.923099
$143$	−28.0000	−2.34148
$144$	−2.00000	−0.166667
$145$	−4.00000	−0.332182
$146$	6.00000	0.496564
$147$	−2.00000	−0.164957
$148$	10.0000	0.821995
$149$	16.0000	1.31077	0.655386	−	0.755295i	$-0.272506\pi$
$149$	16.0000	1.31077	0.655386	+	0.755295i	$0.272506\pi$
$150$	−4.00000	−0.326599
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	6.00000	0.486664
$153$	8.00000	0.646762
$154$	12.0000	0.966988
$155$	−8.00000	−0.642575
$156$	7.00000	0.560449
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	1.00000	0.0795557
$159$	−2.00000	−0.158610
$160$	1.00000	0.0790569
$161$	−18.0000	−1.41860
$162$	−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	$0.449930\pi$
$164$	−8.00000	−0.624695
$165$	4.00000	0.311400
$166$	−6.00000	−0.465690
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−3.00000	−0.231455
$169$	36.0000	2.76923
$170$	−4.00000	−0.306786
$171$	12.0000	0.917663
$172$	−8.00000	−0.609994
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	4.00000	0.303239
$175$	12.0000	0.907115
$176$	4.00000	0.301511
$177$	−1.00000	−0.0751646
$178$	15.0000	1.12430
$179$	−14.0000	−1.04641	−0.523205	−	0.852207i	$-0.675264\pi$
$179$	−14.0000	−1.04641	−0.523205	+	0.852207i	$0.675264\pi$
$180$	2.00000	0.149071
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	−21.0000	−1.55662
$183$	0	0
$184$	−6.00000	−0.442326
$185$	−10.0000	−0.735215
$186$	8.00000	0.586588
$187$	−16.0000	−1.17004
$188$	−3.00000	−0.218797
$189$	−15.0000	−1.09109
$190$	−6.00000	−0.435286
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	−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	$0.790854\pi$
$194$	−1.00000	−0.0717958
$195$	−7.00000	−0.501280
$196$	2.00000	0.142857
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	8.00000	0.568535
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	4.00000	0.282843
$201$	4.00000	0.282138
$202$	−5.00000	−0.351799
$203$	−12.0000	−0.842235
$204$	4.00000	0.280056
$205$	8.00000	0.558744
$206$	−1.00000	−0.0696733
$207$	−12.0000	−0.834058
$208$	−7.00000	−0.485363
$209$	−24.0000	−1.66011
$210$	3.00000	0.207020
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	2.00000	0.137361
$213$	11.0000	0.753708
$214$	−5.00000	−0.341793
$215$	8.00000	0.545595
$216$	−5.00000	−0.340207
$217$	−24.0000	−1.62923
$218$	14.0000	0.948200
$219$	6.00000	0.405442
$220$	−4.00000	−0.269680
$221$	28.0000	1.88348
$222$	10.0000	0.671156
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	3.00000	0.200446
$225$	8.00000	0.533333
$226$	10.0000	0.665190
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	6.00000	0.397360
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	6.00000	0.395628
$231$	12.0000	0.789542
$232$	−4.00000	−0.262613
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	−14.0000	−0.915209
$235$	3.00000	0.195698
$236$	1.00000	0.0650945
$237$	1.00000	0.0649570
$238$	−12.0000	−0.777844
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.00000	0.0645497
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	−5.00000	−0.321412
$243$	−16.0000	−1.02640
$244$	0	0
$245$	−2.00000	−0.127775
$246$	−8.00000	−0.510061
$247$	42.0000	2.67240
$248$	−8.00000	−0.508001
$249$	−6.00000	−0.380235
$250$	−9.00000	−0.569210
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	6.00000	0.377964
$253$	24.0000	1.50887
$254$	13.0000	0.815693
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	−8.00000	−0.498058
$259$	−30.0000	−1.86411
$260$	7.00000	0.434122
$261$	−8.00000	−0.495188
$262$	−18.0000	−1.11204
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	4.00000	0.246183
$265$	−2.00000	−0.122859
$266$	−18.0000	−1.10365
$267$	15.0000	0.917985
$268$	−4.00000	−0.244339
$269$	−1.00000	−0.0609711	−0.0304855	−	0.999535i	$-0.509705\pi$
$269$	−1.00000	−0.0609711	−0.0304855	+	0.999535i	$0.509705\pi$
$270$	5.00000	0.304290
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−4.00000	−0.242536
$273$	−21.0000	−1.27098
$274$	12.0000	0.724947
$275$	−16.0000	−0.964836
$276$	−6.00000	−0.361158
$277$	13.0000	0.781094	0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000	0.781094	0.390547	+	0.920583i	$0.372286\pi$
$278$	5.00000	0.299880
$279$	−16.0000	−0.957895
$280$	−3.00000	−0.179284
$281$	−9.00000	−0.536895	−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$282$	−3.00000	−0.178647
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	−11.0000	−0.652730
$285$	−6.00000	−0.355409
$286$	28.0000	1.65567
$287$	24.0000	1.41668
$288$	2.00000	0.117851
$289$	−1.00000	−0.0588235
$290$	4.00000	0.234888
$291$	−1.00000	−0.0586210
$292$	−6.00000	−0.351123
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	2.00000	0.116642
$295$	−1.00000	−0.0582223
$296$	−10.0000	−0.581238
$297$	20.0000	1.16052
$298$	−16.0000	−0.926855
$299$	−42.0000	−2.42892
$300$	4.00000	0.230940
$301$	24.0000	1.38334
$302$	4.00000	0.230174
$303$	−5.00000	−0.287242
$304$	−6.00000	−0.344124
$305$	0	0
$306$	−8.00000	−0.457330
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	−12.0000	−0.683763
$309$	−1.00000	−0.0568880
$310$	8.00000	0.454369
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−7.00000	−0.396297
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	0	0
$315$	−6.00000	−0.338062
$316$	−1.00000	−0.0562544
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	2.00000	0.112154
$319$	16.0000	0.895828
$320$	−1.00000	−0.0559017
$321$	−5.00000	−0.279073
$322$	18.0000	1.00310
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	28.0000	1.55316
$326$	−4.00000	−0.221540
$327$	14.0000	0.774202
$328$	8.00000	0.441726
$329$	9.00000	0.496186
$330$	−4.00000	−0.220193
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	6.00000	0.329293
$333$	−20.0000	−1.09599
$334$	−8.00000	−0.437741
$335$	4.00000	0.218543
$336$	3.00000	0.163663
$337$	11.0000	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$338$	−36.0000	−1.95814
$339$	10.0000	0.543125
$340$	4.00000	0.216930
$341$	32.0000	1.73290
$342$	−12.0000	−0.648886
$343$	15.0000	0.809924
$344$	8.00000	0.431331
$345$	6.00000	0.323029
$346$	−14.0000	−0.752645
$347$	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
$349$	−20.0000	−1.07058	−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000	−1.07058	−0.535288	+	0.844670i	$0.679797\pi$
$350$	−12.0000	−0.641427
$351$	−35.0000	−1.86816
$352$	−4.00000	−0.213201
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	1.00000	0.0531494
$355$	11.0000	0.583819
$356$	−15.0000	−0.794998
$357$	−12.0000	−0.635107
$358$	14.0000	0.739923
$359$	−13.0000	−0.686114	−0.343057	−	0.939315i	$-0.611462\pi$
$359$	−13.0000	−0.686114	−0.343057	+	0.939315i	$0.611462\pi$
$360$	−2.00000	−0.105409
$361$	17.0000	0.894737
$362$	6.00000	0.315353
$363$	−5.00000	−0.262432
$364$	21.0000	1.10070
$365$	6.00000	0.314054
$366$	0	0
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	6.00000	0.312772
$369$	16.0000	0.832927
$370$	10.0000	0.519875
$371$	−6.00000	−0.311504
$372$	−8.00000	−0.414781
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	16.0000	0.827340
$375$	−9.00000	−0.464758
$376$	3.00000	0.154713
$377$	−28.0000	−1.44207
$378$	15.0000	0.771517
$379$	−3.00000	−0.154100	−0.0770498	−	0.997027i	$-0.524550\pi$
$379$	−3.00000	−0.154100	−0.0770498	+	0.997027i	$0.524550\pi$
$380$	6.00000	0.307794
$381$	13.0000	0.666010
$382$	−3.00000	−0.153493
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	1.00000	0.0510310
$385$	12.0000	0.611577
$386$	22.0000	1.11977
$387$	16.0000	0.813326
$388$	1.00000	0.0507673
$389$	5.00000	0.253510	0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000	0.253510	0.126755	+	0.991934i	$0.459544\pi$
$390$	7.00000	0.354459
$391$	−24.0000	−1.21373
$392$	−2.00000	−0.101015
$393$	−18.0000	−0.907980
$394$	18.0000	0.906827
$395$	1.00000	0.0503155
$396$	−8.00000	−0.402015
$397$	−19.0000	−0.953583	−0.476791	−	0.879017i	$-0.658200\pi$
$397$	−19.0000	−0.953583	−0.476791	+	0.879017i	$0.658200\pi$
$398$	15.0000	0.751882
$399$	−18.0000	−0.901127
$400$	−4.00000	−0.200000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	−4.00000	−0.199502
$403$	−56.0000	−2.78956
$404$	5.00000	0.248759
$405$	−1.00000	−0.0496904
$406$	12.0000	0.595550
$407$	40.0000	1.98273
$408$	−4.00000	−0.198030
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	−8.00000	−0.395092
$411$	12.0000	0.591916
$412$	1.00000	0.0492665
$413$	−3.00000	−0.147620
$414$	12.0000	0.589768
$415$	−6.00000	−0.294528
$416$	7.00000	0.343203
$417$	5.00000	0.244851
$418$	24.0000	1.17388
$419$	5.00000	0.244266	0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000	0.244266	0.122133	+	0.992514i	$0.461027\pi$
$420$	−3.00000	−0.146385
$421$	−35.0000	−1.70580	−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000	−1.70580	−0.852898	+	0.522078i	$0.825157\pi$
$422$	−20.0000	−0.973585
$423$	6.00000	0.291730
$424$	−2.00000	−0.0971286
$425$	16.0000	0.776114
$426$	−11.0000	−0.532952
$427$	0	0
$428$	5.00000	0.241684
$429$	28.0000	1.35185
$430$	−8.00000	−0.385794
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	5.00000	0.240563
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	24.0000	1.15204
$435$	4.00000	0.191785
$436$	−14.0000	−0.670478
$437$	−36.0000	−1.72211
$438$	−6.00000	−0.286691
$439$	2.00000	0.0954548	0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000	0.0954548	0.0477274	+	0.998860i	$0.484802\pi$
$440$	4.00000	0.190693
$441$	−4.00000	−0.190476
$442$	−28.0000	−1.33182
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−10.0000	−0.474579
$445$	15.0000	0.711068
$446$	10.0000	0.473514
$447$	−16.0000	−0.756774
$448$	−3.00000	−0.141737
$449$	−8.00000	−0.377543	−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000	−0.377543	−0.188772	+	0.982021i	$0.560451\pi$
$450$	−8.00000	−0.377124
$451$	−32.0000	−1.50682
$452$	−10.0000	−0.470360
$453$	4.00000	0.187936
$454$	−4.00000	−0.187729
$455$	−21.0000	−0.984495
$456$	−6.00000	−0.280976
$457$	−37.0000	−1.73079	−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000	−1.73079	−0.865393	+	0.501093i	$0.832931\pi$
$458$	10.0000	0.467269
$459$	−20.0000	−0.933520
$460$	−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	$0.544622\pi$
$462$	−12.0000	−0.558291
$463$	−13.0000	−0.604161	−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000	−0.604161	−0.302081	+	0.953282i	$0.597681\pi$
$464$	4.00000	0.185695
$465$	8.00000	0.370991
$466$	0	0
$467$	18.0000	0.832941	0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000	0.832941	0.416470	+	0.909149i	$0.363267\pi$
$468$	14.0000	0.647150
$469$	12.0000	0.554109
$470$	−3.00000	−0.138380
$471$	0	0
$472$	−1.00000	−0.0460287
$473$	−32.0000	−1.47136
$474$	−1.00000	−0.0459315
$475$	24.0000	1.10120
$476$	12.0000	0.550019
$477$	−4.00000	−0.183147
$478$	6.00000	0.274434
$479$	38.0000	1.73626	0.868132	−	0.496333i	$-0.165321\pi$
$479$	38.0000	1.73626	0.868132	+	0.496333i	$0.165321\pi$
$480$	−1.00000	−0.0456435
$481$	−70.0000	−3.19173
$482$	−17.0000	−0.774329
$483$	18.0000	0.819028
$484$	5.00000	0.227273
$485$	−1.00000	−0.0454077
$486$	16.0000	0.725775
$487$	20.0000	0.906287	0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000	0.906287	0.453143	+	0.891438i	$0.350303\pi$
$488$	0	0
$489$	−4.00000	−0.180886
$490$	2.00000	0.0903508
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	8.00000	0.360668
$493$	−16.0000	−0.720604
$494$	−42.0000	−1.88967
$495$	8.00000	0.359573
$496$	8.00000	0.359211
$497$	33.0000	1.48025
$498$	6.00000	0.268866
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	9.00000	0.402492
$501$	−8.00000	−0.357414
$502$	21.0000	0.937276
$503$	33.0000	1.47140	0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000	1.47140	0.735699	+	0.677309i	$0.236854\pi$
$504$	−6.00000	−0.267261
$505$	−5.00000	−0.222497
$506$	−24.0000	−1.06693
$507$	−36.0000	−1.59882
$508$	−13.0000	−0.576782
$509$	−16.0000	−0.709188	−0.354594	−	0.935020i	$-0.615381\pi$
$509$	−16.0000	−0.709188	−0.354594	+	0.935020i	$0.615381\pi$
$510$	4.00000	0.177123
$511$	18.0000	0.796273
$512$	−1.00000	−0.0441942
$513$	−30.0000	−1.32453
$514$	−14.0000	−0.617514
$515$	−1.00000	−0.0440653
$516$	8.00000	0.352180
$517$	−12.0000	−0.527759
$518$	30.0000	1.31812
$519$	−14.0000	−0.614532
$520$	−7.00000	−0.306970
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	8.00000	0.350150
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	18.0000	0.786334
$525$	−12.0000	−0.523723
$526$	−18.0000	−0.784837
$527$	−32.0000	−1.39394
$528$	−4.00000	−0.174078
$529$	13.0000	0.565217
$530$	2.00000	0.0868744
$531$	−2.00000	−0.0867926
$532$	18.0000	0.780399
$533$	56.0000	2.42563
$534$	−15.0000	−0.649113
$535$	−5.00000	−0.216169
$536$	4.00000	0.172774
$537$	14.0000	0.604145
$538$	1.00000	0.0431131
$539$	8.00000	0.344584
$540$	−5.00000	−0.215166
$541$	25.0000	1.07483	0.537417	−	0.843317i	$-0.319400\pi$
$541$	25.0000	1.07483	0.537417	+	0.843317i	$0.319400\pi$
$542$	8.00000	0.343629
$543$	6.00000	0.257485
$544$	4.00000	0.171499
$545$	14.0000	0.599694
$546$	21.0000	0.898717
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	−12.0000	−0.512615
$549$	0	0
$550$	16.0000	0.682242
$551$	−24.0000	−1.02243
$552$	6.00000	0.255377
$553$	3.00000	0.127573
$554$	−13.0000	−0.552317
$555$	10.0000	0.424476
$556$	−5.00000	−0.212047
$557$	43.0000	1.82197	0.910984	−	0.412441i	$-0.135324\pi$
$557$	43.0000	1.82197	0.910984	+	0.412441i	$0.135324\pi$
$558$	16.0000	0.677334
$559$	56.0000	2.36855
$560$	3.00000	0.126773
$561$	16.0000	0.675521
$562$	9.00000	0.379642
$563$	−32.0000	−1.34864	−0.674320	−	0.738440i	$-0.735563\pi$
$563$	−32.0000	−1.34864	−0.674320	+	0.738440i	$0.735563\pi$
$564$	3.00000	0.126323
$565$	10.0000	0.420703
$566$	−22.0000	−0.924729
$567$	−3.00000	−0.125988
$568$	11.0000	0.461550
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	6.00000	0.251312
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−28.0000	−1.17074
$573$	−3.00000	−0.125327
$574$	−24.0000	−1.00174
$575$	−24.0000	−1.00087
$576$	−2.00000	−0.0833333
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	1.00000	0.0415945
$579$	22.0000	0.914289
$580$	−4.00000	−0.166091
$581$	−18.0000	−0.746766
$582$	1.00000	0.0414513
$583$	8.00000	0.331326
$584$	6.00000	0.248282
$585$	−14.0000	−0.578829
$586$	18.0000	0.743573
$587$	37.0000	1.52715	0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000	1.52715	0.763577	+	0.645717i	$0.223441\pi$
$588$	−2.00000	−0.0824786
$589$	−48.0000	−1.97781
$590$	1.00000	0.0411693
$591$	18.0000	0.740421
$592$	10.0000	0.410997
$593$	27.0000	1.10876	0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000	1.10876	0.554379	+	0.832265i	$0.312956\pi$
$594$	−20.0000	−0.820610
$595$	−12.0000	−0.491952
$596$	16.0000	0.655386
$597$	15.0000	0.613909
$598$	42.0000	1.71751
$599$	38.0000	1.55264	0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000	1.55264	0.776319	+	0.630340i	$0.217085\pi$
$600$	−4.00000	−0.163299
$601$	−12.0000	−0.489490	−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000	−0.489490	−0.244745	+	0.969587i	$0.578704\pi$
$602$	−24.0000	−0.978167
$603$	8.00000	0.325785
$604$	−4.00000	−0.162758
$605$	−5.00000	−0.203279
$606$	5.00000	0.203111
$607$	−9.00000	−0.365299	−0.182649	−	0.983178i	$-0.558467\pi$
$607$	−9.00000	−0.365299	−0.182649	+	0.983178i	$0.558467\pi$
$608$	6.00000	0.243332
$609$	12.0000	0.486265
$610$	0	0
$611$	21.0000	0.849569
$612$	8.00000	0.323381
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	12.0000	0.484281
$615$	−8.00000	−0.322591
$616$	12.0000	0.483494
$617$	9.00000	0.362326	0.181163	−	0.983453i	$-0.442014\pi$
$617$	9.00000	0.362326	0.181163	+	0.983453i	$0.442014\pi$
$618$	1.00000	0.0402259
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	−8.00000	−0.321288
$621$	30.0000	1.20386
$622$	−12.0000	−0.481156
$623$	45.0000	1.80289
$624$	7.00000	0.280224
$625$	11.0000	0.440000
$626$	−14.0000	−0.559553
$627$	24.0000	0.958468
$628$	0	0
$629$	−40.0000	−1.59490
$630$	6.00000	0.239046
$631$	−17.0000	−0.676759	−0.338380	−	0.941010i	$-0.609879\pi$
$631$	−17.0000	−0.676759	−0.338380	+	0.941010i	$0.609879\pi$
$632$	1.00000	0.0397779
$633$	−20.0000	−0.794929
$634$	3.00000	0.119145
$635$	13.0000	0.515889
$636$	−2.00000	−0.0793052
$637$	−14.0000	−0.554700
$638$	−16.0000	−0.633446
$639$	22.0000	0.870307
$640$	1.00000	0.0395285
$641$	3.00000	0.118493	0.0592464	−	0.998243i	$-0.481130\pi$
$641$	3.00000	0.118493	0.0592464	+	0.998243i	$0.481130\pi$
$642$	5.00000	0.197334
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	−18.0000	−0.709299
$645$	−8.00000	−0.315000
$646$	−24.0000	−0.944267
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	−28.0000	−1.09825
$651$	24.0000	0.940634
$652$	4.00000	0.156652
$653$	47.0000	1.83925	0.919626	−	0.392795i	$-0.128492\pi$
$653$	47.0000	1.83925	0.919626	+	0.392795i	$0.128492\pi$
$654$	−14.0000	−0.547443
$655$	−18.0000	−0.703318
$656$	−8.00000	−0.312348
$657$	12.0000	0.468165
$658$	−9.00000	−0.350857
$659$	27.0000	1.05177	0.525885	−	0.850555i	$-0.323734\pi$
$659$	27.0000	1.05177	0.525885	+	0.850555i	$0.323734\pi$
$660$	4.00000	0.155700
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	−8.00000	−0.310929
$663$	−28.0000	−1.08743
$664$	−6.00000	−0.232845
$665$	−18.0000	−0.698010
$666$	20.0000	0.774984
$667$	24.0000	0.929284
$668$	8.00000	0.309529
$669$	10.0000	0.386622
$670$	−4.00000	−0.154533
$671$	0	0
$672$	−3.00000	−0.115728
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	−11.0000	−0.423704
$675$	−20.0000	−0.769800
$676$	36.0000	1.38462
$677$	−21.0000	−0.807096	−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000	−0.807096	−0.403548	+	0.914959i	$0.632223\pi$
$678$	−10.0000	−0.384048
$679$	−3.00000	−0.115129
$680$	−4.00000	−0.153393
$681$	−4.00000	−0.153280
$682$	−32.0000	−1.22534
$683$	−34.0000	−1.30097	−0.650487	−	0.759517i	$-0.725435\pi$
$683$	−34.0000	−1.30097	−0.650487	+	0.759517i	$0.725435\pi$
$684$	12.0000	0.458831
$685$	12.0000	0.458496
$686$	−15.0000	−0.572703
$687$	10.0000	0.381524
$688$	−8.00000	−0.304997
$689$	−14.0000	−0.533358
$690$	−6.00000	−0.228416
$691$	−43.0000	−1.63580	−0.817899	−	0.575362i	$-0.804861\pi$
$691$	−43.0000	−1.63580	−0.817899	+	0.575362i	$0.804861\pi$
$692$	14.0000	0.532200
$693$	24.0000	0.911685
$694$	−6.00000	−0.227757
$695$	5.00000	0.189661
$696$	4.00000	0.151620
$697$	32.0000	1.21209
$698$	20.0000	0.757011
$699$	0	0
$700$	12.0000	0.453557
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	35.0000	1.32099
$703$	−60.0000	−2.26294
$704$	4.00000	0.150756
$705$	−3.00000	−0.112987
$706$	−24.0000	−0.903252
$707$	−15.0000	−0.564133
$708$	−1.00000	−0.0375823
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	−11.0000	−0.412823
$711$	2.00000	0.0750059
$712$	15.0000	0.562149
$713$	48.0000	1.79761
$714$	12.0000	0.449089
$715$	28.0000	1.04714
$716$	−14.0000	−0.523205
$717$	6.00000	0.224074
$718$	13.0000	0.485156
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	2.00000	0.0745356
$721$	−3.00000	−0.111726
$722$	−17.0000	−0.632674
$723$	−17.0000	−0.632237
$724$	−6.00000	−0.222988
$725$	−16.0000	−0.594225
$726$	5.00000	0.185567
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	−21.0000	−0.778312
$729$	13.0000	0.481481
$730$	−6.00000	−0.222070
$731$	32.0000	1.18356
$732$	0	0
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	16.0000	0.590571
$735$	2.00000	0.0737711
$736$	−6.00000	−0.221163
$737$	−16.0000	−0.589368
$738$	−16.0000	−0.588968
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	−10.0000	−0.367607
$741$	−42.0000	−1.54291
$742$	6.00000	0.220267
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	8.00000	0.293294
$745$	−16.0000	−0.586195
$746$	−26.0000	−0.951928
$747$	−12.0000	−0.439057
$748$	−16.0000	−0.585018
$749$	−15.0000	−0.548088
$750$	9.00000	0.328634
$751$	−18.0000	−0.656829	−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000	−0.656829	−0.328415	+	0.944534i	$0.606514\pi$
$752$	−3.00000	−0.109399
$753$	21.0000	0.765283
$754$	28.0000	1.01970
$755$	4.00000	0.145575
$756$	−15.0000	−0.545545
$757$	−7.00000	−0.254419	−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000	−0.254419	−0.127210	+	0.991876i	$0.540602\pi$
$758$	3.00000	0.108965
$759$	−24.0000	−0.871145
$760$	−6.00000	−0.217643
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	−13.0000	−0.470940
$763$	42.0000	1.52050
$764$	3.00000	0.108536
$765$	−8.00000	−0.289241
$766$	6.00000	0.216789
$767$	−7.00000	−0.252755
$768$	−1.00000	−0.0360844
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	−12.0000	−0.432450
$771$	−14.0000	−0.504198
$772$	−22.0000	−0.791797
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	−16.0000	−0.575108
$775$	−32.0000	−1.14947
$776$	−1.00000	−0.0358979
$777$	30.0000	1.07624
$778$	−5.00000	−0.179259
$779$	48.0000	1.71978
$780$	−7.00000	−0.250640
$781$	−44.0000	−1.57444
$782$	24.0000	0.858238
$783$	20.0000	0.714742
$784$	2.00000	0.0714286
$785$	0	0
$786$	18.0000	0.642039
$787$	24.0000	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$788$	−18.0000	−0.641223
$789$	−18.0000	−0.640817
$790$	−1.00000	−0.0355784
$791$	30.0000	1.06668
$792$	8.00000	0.284268
$793$	0	0
$794$	19.0000	0.674285
$795$	2.00000	0.0709327
$796$	−15.0000	−0.531661
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	18.0000	0.637193
$799$	12.0000	0.424529
$800$	4.00000	0.141421
$801$	30.0000	1.06000
$802$	−10.0000	−0.353112
$803$	−24.0000	−0.846942
$804$	4.00000	0.141069
$805$	18.0000	0.634417
$806$	56.0000	1.97252
$807$	1.00000	0.0352017
$808$	−5.00000	−0.175899
$809$	−9.00000	−0.316423	−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000	−0.316423	−0.158212	+	0.987405i	$0.550573\pi$
$810$	1.00000	0.0351364
$811$	−32.0000	−1.12367	−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000	−1.12367	−0.561836	+	0.827249i	$0.689905\pi$
$812$	−12.0000	−0.421117
$813$	8.00000	0.280572
$814$	−40.0000	−1.40200
$815$	−4.00000	−0.140114
$816$	4.00000	0.140028
$817$	48.0000	1.67931
$818$	−22.0000	−0.769212
$819$	−42.0000	−1.46760
$820$	8.00000	0.279372
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−12.0000	−0.418548
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−1.00000	−0.0348367
$825$	16.0000	0.557048
$826$	3.00000	0.104383
$827$	19.0000	0.660695	0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000	0.660695	0.330347	+	0.943859i	$0.392834\pi$
$828$	−12.0000	−0.417029
$829$	16.0000	0.555703	0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000	0.555703	0.277851	+	0.960624i	$0.410378\pi$
$830$	6.00000	0.208263
$831$	−13.0000	−0.450965
$832$	−7.00000	−0.242681
$833$	−8.00000	−0.277184
$834$	−5.00000	−0.173136
$835$	−8.00000	−0.276851
$836$	−24.0000	−0.830057
$837$	40.0000	1.38260
$838$	−5.00000	−0.172722
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	3.00000	0.103510
$841$	−13.0000	−0.448276
$842$	35.0000	1.20618
$843$	9.00000	0.309976
$844$	20.0000	0.688428
$845$	−36.0000	−1.23844
$846$	−6.00000	−0.206284
$847$	−15.0000	−0.515406
$848$	2.00000	0.0686803
$849$	−22.0000	−0.755038
$850$	−16.0000	−0.548795
$851$	60.0000	2.05677
$852$	11.0000	0.376854
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	0	0
$855$	−12.0000	−0.410391
$856$	−5.00000	−0.170896
$857$	−3.00000	−0.102478	−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000	−0.102478	−0.0512390	+	0.998686i	$0.516317\pi$
$858$	−28.0000	−0.955904
$859$	25.0000	0.852989	0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000	0.852989	0.426494	+	0.904490i	$0.359748\pi$
$860$	8.00000	0.272798
$861$	−24.0000	−0.817918
$862$	14.0000	0.476842
$863$	−44.0000	−1.49778	−0.748889	−	0.662696i	$-0.769412\pi$
$863$	−44.0000	−1.49778	−0.748889	+	0.662696i	$0.769412\pi$
$864$	−5.00000	−0.170103
$865$	−14.0000	−0.476014
$866$	11.0000	0.373795
$867$	1.00000	0.0339618
$868$	−24.0000	−0.814613
$869$	−4.00000	−0.135691
$870$	−4.00000	−0.135613
$871$	28.0000	0.948744
$872$	14.0000	0.474100
$873$	−2.00000	−0.0676897
$874$	36.0000	1.21772
$875$	−27.0000	−0.912767
$876$	6.00000	0.202721
$877$	−26.0000	−0.877958	−0.438979	−	0.898497i	$-0.644660\pi$
$877$	−26.0000	−0.877958	−0.438979	+	0.898497i	$0.644660\pi$
$878$	−2.00000	−0.0674967
$879$	18.0000	0.607125
$880$	−4.00000	−0.134840
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	4.00000	0.134687
$883$	−13.0000	−0.437485	−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000	−0.437485	−0.218742	+	0.975783i	$0.570195\pi$
$884$	28.0000	0.941742
$885$	1.00000	0.0336146
$886$	4.00000	0.134383
$887$	−56.0000	−1.88030	−0.940148	−	0.340766i	$-0.889313\pi$
$887$	−56.0000	−1.88030	−0.940148	+	0.340766i	$0.889313\pi$
$888$	10.0000	0.335578
$889$	39.0000	1.30802
$890$	−15.0000	−0.502801
$891$	4.00000	0.134005
$892$	−10.0000	−0.334825
$893$	18.0000	0.602347
$894$	16.0000	0.535120
$895$	14.0000	0.467968
$896$	3.00000	0.100223
$897$	42.0000	1.40234
$898$	8.00000	0.266963
$899$	32.0000	1.06726
$900$	8.00000	0.266667
$901$	−8.00000	−0.266519
$902$	32.0000	1.06548
$903$	−24.0000	−0.798670
$904$	10.0000	0.332595
$905$	6.00000	0.199447
$906$	−4.00000	−0.132891
$907$	−18.0000	−0.597680	−0.298840	−	0.954303i	$-0.596600\pi$
$907$	−18.0000	−0.597680	−0.298840	+	0.954303i	$0.596600\pi$
$908$	4.00000	0.132745
$909$	−10.0000	−0.331679
$910$	21.0000	0.696143
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	6.00000	0.198680
$913$	24.0000	0.794284
$914$	37.0000	1.22385
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−54.0000	−1.78324
$918$	20.0000	0.660098
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	6.00000	0.197814
$921$	12.0000	0.395413
$922$	6.00000	0.197599
$923$	77.0000	2.53449
$924$	12.0000	0.394771
$925$	−40.0000	−1.31519
$926$	13.0000	0.427207
$927$	−2.00000	−0.0656886
$928$	−4.00000	−0.131306
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	−8.00000	−0.262330
$931$	−12.0000	−0.393284
$932$	0	0
$933$	−12.0000	−0.392862
$934$	−18.0000	−0.588978
$935$	16.0000	0.523256
$936$	−14.0000	−0.457604
$937$	−12.0000	−0.392023	−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000	−0.392023	−0.196011	+	0.980602i	$0.562799\pi$
$938$	−12.0000	−0.391814
$939$	−14.0000	−0.456873
$940$	3.00000	0.0978492
$941$	−34.0000	−1.10837	−0.554184	−	0.832394i	$-0.686970\pi$
$941$	−34.0000	−1.10837	−0.554184	+	0.832394i	$0.686970\pi$
$942$	0	0
$943$	−48.0000	−1.56310
$944$	1.00000	0.0325472
$945$	15.0000	0.487950
$946$	32.0000	1.04041
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	1.00000	0.0324785
$949$	42.0000	1.36338
$950$	−24.0000	−0.778663
$951$	3.00000	0.0972817
$952$	−12.0000	−0.388922
$953$	37.0000	1.19855	0.599274	−	0.800544i	$-0.295456\pi$
$953$	37.0000	1.19855	0.599274	+	0.800544i	$0.295456\pi$
$954$	4.00000	0.129505
$955$	−3.00000	−0.0970777
$956$	−6.00000	−0.194054
$957$	−16.0000	−0.517207
$958$	−38.0000	−1.22772
$959$	36.0000	1.16250
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	70.0000	2.25689
$963$	−10.0000	−0.322245
$964$	17.0000	0.547533
$965$	22.0000	0.708205
$966$	−18.0000	−0.579141
$967$	2.00000	0.0643157	0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000	0.0643157	0.0321578	+	0.999483i	$0.489762\pi$
$968$	−5.00000	−0.160706
$969$	−24.0000	−0.770991
$970$	1.00000	0.0321081
$971$	−34.0000	−1.09111	−0.545556	−	0.838074i	$-0.683681\pi$
$971$	−34.0000	−1.09111	−0.545556	+	0.838074i	$0.683681\pi$
$972$	−16.0000	−0.513200
$973$	15.0000	0.480878
$974$	−20.0000	−0.640841
$975$	−28.0000	−0.896718
$976$	0	0
$977$	−34.0000	−1.08776	−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000	−1.08776	−0.543878	+	0.839164i	$0.683045\pi$
$978$	4.00000	0.127906
$979$	−60.0000	−1.91761
$980$	−2.00000	−0.0638877
$981$	28.0000	0.893971
$982$	15.0000	0.478669
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	−8.00000	−0.255031
$985$	18.0000	0.573528
$986$	16.0000	0.509544
$987$	−9.00000	−0.286473
$988$	42.0000	1.33620
$989$	−48.0000	−1.52631
$990$	−8.00000	−0.254257
$991$	29.0000	0.921215	0.460608	−	0.887604i	$-0.347632\pi$
$991$	29.0000	0.921215	0.460608	+	0.887604i	$0.347632\pi$
$992$	−8.00000	−0.254000
$993$	−8.00000	−0.253872
$994$	−33.0000	−1.04670
$995$	15.0000	0.475532
$996$	−6.00000	−0.190117
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	−8.00000	−0.253236
$999$	50.0000	1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.a.a.1.1	✓	1
3.2	odd	2		1422.2.a.h.1.1		1
4.3	odd	2		1264.2.a.e.1.1		1
5.4	even	2		3950.2.a.j.1.1		1
7.6	odd	2		7742.2.a.h.1.1		1
8.3	odd	2		5056.2.a.h.1.1		1
8.5	even	2		5056.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.a.a.1.1	✓	1	1.1	even	1	trivial
1264.2.a.e.1.1		1	4.3	odd	2
1422.2.a.h.1.1		1	3.2	odd	2
3950.2.a.j.1.1		1	5.4	even	2
5056.2.a.h.1.1		1	8.3	odd	2
5056.2.a.o.1.1		1	8.5	even	2
7742.2.a.h.1.1		1	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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