LMFDB - Embedded newform 118.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [118,2,Mod(1,118)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(118, 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("118.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 118 = 2 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	118.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:	$0.942234743851$
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	$\chi$	$=$	118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +2.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} -3.00000 q^{13} -3.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} -2.00000 q^{20} -6.00000 q^{21} -1.00000 q^{22} +4.00000 q^{23} +2.00000 q^{24} -1.00000 q^{25} -3.00000 q^{26} -4.00000 q^{27} -3.00000 q^{28} +4.00000 q^{29} -4.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} +7.00000 q^{34} +6.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} +4.00000 q^{38} -6.00000 q^{39} -2.00000 q^{40} -11.0000 q^{41} -6.00000 q^{42} +9.00000 q^{43} -1.00000 q^{44} -2.00000 q^{45} +4.00000 q^{46} +10.0000 q^{47} +2.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +14.0000 q^{51} -3.00000 q^{52} -4.00000 q^{54} +2.00000 q^{55} -3.00000 q^{56} +8.00000 q^{57} +4.00000 q^{58} -1.00000 q^{59} -4.00000 q^{60} -2.00000 q^{61} -4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} -2.00000 q^{66} +4.00000 q^{67} +7.00000 q^{68} +8.00000 q^{69} +6.00000 q^{70} +9.00000 q^{71} +1.00000 q^{72} -14.0000 q^{73} -7.00000 q^{74} -2.00000 q^{75} +4.00000 q^{76} +3.00000 q^{77} -6.00000 q^{78} +11.0000 q^{79} -2.00000 q^{80} -11.0000 q^{81} -11.0000 q^{82} -13.0000 q^{83} -6.00000 q^{84} -14.0000 q^{85} +9.00000 q^{86} +8.00000 q^{87} -1.00000 q^{88} +18.0000 q^{89} -2.00000 q^{90} +9.00000 q^{91} +4.00000 q^{92} -8.00000 q^{93} +10.0000 q^{94} -8.00000 q^{95} +2.00000 q^{96} +2.00000 q^{97} +2.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$3$	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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	2.00000	0.816497
$7$	−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
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	2.00000	0.577350
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−3.00000	−0.801784
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	−0.447214
$21$	−6.00000	−1.30931
$22$	−1.00000	−0.213201
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	2.00000	0.408248
$25$	−1.00000	−0.200000
$26$	−3.00000	−0.588348
$27$	−4.00000	−0.769800
$28$	−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	$0.378881\pi$
$30$	−4.00000	−0.730297
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	7.00000	1.20049
$35$	6.00000	1.01419
$36$	1.00000	0.166667
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	4.00000	0.648886
$39$	−6.00000	−0.960769
$40$	−2.00000	−0.316228
$41$	−11.0000	−1.71791	−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000	−1.71791	−0.858956	+	0.512050i	$0.828886\pi$
$42$	−6.00000	−0.925820
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−1.00000	−0.150756
$45$	−2.00000	−0.298142
$46$	4.00000	0.589768
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	2.00000	0.288675
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	14.0000	1.96039
$52$	−3.00000	−0.416025
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−4.00000	−0.544331
$55$	2.00000	0.269680
$56$	−3.00000	−0.400892
$57$	8.00000	1.05963
$58$	4.00000	0.525226
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.00000	−0.516398
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−4.00000	−0.508001
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	−2.00000	−0.246183
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	7.00000	0.848875
$69$	8.00000	0.963087
$70$	6.00000	0.717137
$71$	9.00000	1.06810	0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000	1.06810	0.534052	+	0.845452i	$0.320669\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−7.00000	−0.813733
$75$	−2.00000	−0.230940
$76$	4.00000	0.458831
$77$	3.00000	0.341882
$78$	−6.00000	−0.679366
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	−2.00000	−0.223607
$81$	−11.0000	−1.22222
$82$	−11.0000	−1.21475
$83$	−13.0000	−1.42694	−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000	−1.42694	−0.713468	+	0.700688i	$0.752876\pi$
$84$	−6.00000	−0.654654
$85$	−14.0000	−1.51851
$86$	9.00000	0.970495
$87$	8.00000	0.857690
$88$	−1.00000	−0.106600
$89$	18.0000	1.90800	0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000	1.90800	0.953998	+	0.299813i	$0.0969242\pi$
$90$	−2.00000	−0.210819
$91$	9.00000	0.943456
$92$	4.00000	0.417029
$93$	−8.00000	−0.829561
$94$	10.0000	1.03142
$95$	−8.00000	−0.820783
$96$	2.00000	0.204124
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	2.00000	0.202031
$99$	−1.00000	−0.100504
$100$	−1.00000	−0.100000
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	14.0000	1.38621
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	−3.00000	−0.294174
$105$	12.0000	1.17108
$106$	0	0
$107$	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
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	2.00000	0.190693
$111$	−14.0000	−1.32882
$112$	−3.00000	−0.283473
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	8.00000	0.749269
$115$	−8.00000	−0.746004
$116$	4.00000	0.371391
$117$	−3.00000	−0.277350
$118$	−1.00000	−0.0920575
$119$	−21.0000	−1.92507
$120$	−4.00000	−0.365148
$121$	−10.0000	−0.909091
$122$	−2.00000	−0.181071
$123$	−22.0000	−1.98367
$124$	−4.00000	−0.359211
$125$	12.0000	1.07331
$126$	−3.00000	−0.267261
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	18.0000	1.58481
$130$	6.00000	0.526235
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−2.00000	−0.174078
$133$	−12.0000	−1.04053
$134$	4.00000	0.345547
$135$	8.00000	0.688530
$136$	7.00000	0.600245
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	8.00000	0.681005
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	6.00000	0.507093
$141$	20.0000	1.68430
$142$	9.00000	0.755263
$143$	3.00000	0.250873
$144$	1.00000	0.0833333
$145$	−8.00000	−0.664364
$146$	−14.0000	−1.15865
$147$	4.00000	0.329914
$148$	−7.00000	−0.575396
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	−2.00000	−0.163299
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	4.00000	0.324443
$153$	7.00000	0.565916
$154$	3.00000	0.241747
$155$	8.00000	0.642575
$156$	−6.00000	−0.480384
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	11.0000	0.875113
$159$	0	0
$160$	−2.00000	−0.158114
$161$	−12.0000	−0.945732
$162$	−11.0000	−0.864242
$163$	22.0000	1.72317	0.861586	−	0.507611i	$-0.169471\pi$
$163$	22.0000	1.72317	0.861586	+	0.507611i	$0.169471\pi$
$164$	−11.0000	−0.858956
$165$	4.00000	0.311400
$166$	−13.0000	−1.00900
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−6.00000	−0.462910
$169$	−4.00000	−0.307692
$170$	−14.0000	−1.07375
$171$	4.00000	0.305888
$172$	9.00000	0.686244
$173$	−11.0000	−0.836315	−0.418157	−	0.908375i	$-0.637324\pi$
$173$	−11.0000	−0.836315	−0.418157	+	0.908375i	$0.637324\pi$
$174$	8.00000	0.606478
$175$	3.00000	0.226779
$176$	−1.00000	−0.0753778
$177$	−2.00000	−0.150329
$178$	18.0000	1.34916
$179$	−7.00000	−0.523205	−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000	−0.523205	−0.261602	+	0.965176i	$0.584251\pi$
$180$	−2.00000	−0.149071
$181$	−4.00000	−0.297318	−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000	−0.297318	−0.148659	+	0.988889i	$0.547496\pi$
$182$	9.00000	0.667124
$183$	−4.00000	−0.295689
$184$	4.00000	0.294884
$185$	14.0000	1.02930
$186$	−8.00000	−0.586588
$187$	−7.00000	−0.511891
$188$	10.0000	0.729325
$189$	12.0000	0.872872
$190$	−8.00000	−0.580381
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	2.00000	0.144338
$193$	25.0000	1.79954	0.899770	−	0.436365i	$-0.143734\pi$
$193$	25.0000	1.79954	0.899770	+	0.436365i	$0.143734\pi$
$194$	2.00000	0.143592
$195$	12.0000	0.859338
$196$	2.00000	0.142857
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	−1.00000	−0.0710669
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	8.00000	0.564276
$202$	−9.00000	−0.633238
$203$	−12.0000	−0.842235
$204$	14.0000	0.980196
$205$	22.0000	1.53655
$206$	−10.0000	−0.696733
$207$	4.00000	0.278019
$208$	−3.00000	−0.208013
$209$	−4.00000	−0.276686
$210$	12.0000	0.828079
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	0	0
$213$	18.0000	1.23334
$214$	6.00000	0.410152
$215$	−18.0000	−1.22759
$216$	−4.00000	−0.272166
$217$	12.0000	0.814613
$218$	−14.0000	−0.948200
$219$	−28.0000	−1.89206
$220$	2.00000	0.134840
$221$	−21.0000	−1.41261
$222$	−14.0000	−0.939618
$223$	21.0000	1.40626	0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000	1.40626	0.703132	+	0.711059i	$0.251784\pi$
$224$	−3.00000	−0.200446
$225$	−1.00000	−0.0666667
$226$	8.00000	0.532152
$227$	−25.0000	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$227$	−25.0000	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$228$	8.00000	0.529813
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	−8.00000	−0.527504
$231$	6.00000	0.394771
$232$	4.00000	0.262613
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	−3.00000	−0.196116
$235$	−20.0000	−1.30466
$236$	−1.00000	−0.0650945
$237$	22.0000	1.42905
$238$	−21.0000	−1.36123
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−4.00000	−0.258199
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	−10.0000	−0.642824
$243$	−10.0000	−0.641500
$244$	−2.00000	−0.128037
$245$	−4.00000	−0.255551
$246$	−22.0000	−1.40267
$247$	−12.0000	−0.763542
$248$	−4.00000	−0.254000
$249$	−26.0000	−1.64768
$250$	12.0000	0.758947
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	−3.00000	−0.188982
$253$	−4.00000	−0.251478
$254$	−8.00000	−0.501965
$255$	−28.0000	−1.75343
$256$	1.00000	0.0625000
$257$	9.00000	0.561405	0.280702	−	0.959795i	$-0.409433\pi$
$257$	9.00000	0.561405	0.280702	+	0.959795i	$0.409433\pi$
$258$	18.0000	1.12063
$259$	21.0000	1.30488
$260$	6.00000	0.372104
$261$	4.00000	0.247594
$262$	−12.0000	−0.741362
$263$	3.00000	0.184988	0.0924940	−	0.995713i	$-0.470516\pi$
$263$	3.00000	0.184988	0.0924940	+	0.995713i	$0.470516\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	−12.0000	−0.735767
$267$	36.0000	2.20316
$268$	4.00000	0.244339
$269$	−19.0000	−1.15845	−0.579225	−	0.815168i	$-0.696645\pi$
$269$	−19.0000	−1.15845	−0.579225	+	0.815168i	$0.696645\pi$
$270$	8.00000	0.486864
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	7.00000	0.424437
$273$	18.0000	1.08941
$274$	9.00000	0.543710
$275$	1.00000	0.0603023
$276$	8.00000	0.481543
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	−10.0000	−0.599760
$279$	−4.00000	−0.239474
$280$	6.00000	0.358569
$281$	−1.00000	−0.0596550	−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000	−0.0596550	−0.0298275	+	0.999555i	$0.509496\pi$
$282$	20.0000	1.19098
$283$	−19.0000	−1.12943	−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000	−1.12943	−0.564716	+	0.825285i	$0.691014\pi$
$284$	9.00000	0.534052
$285$	−16.0000	−0.947758
$286$	3.00000	0.177394
$287$	33.0000	1.94793
$288$	1.00000	0.0589256
$289$	32.0000	1.88235
$290$	−8.00000	−0.469776
$291$	4.00000	0.234484
$292$	−14.0000	−0.819288
$293$	−8.00000	−0.467365	−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000	−0.467365	−0.233682	+	0.972313i	$0.575078\pi$
$294$	4.00000	0.233285
$295$	2.00000	0.116445
$296$	−7.00000	−0.406867
$297$	4.00000	0.232104
$298$	−5.00000	−0.289642
$299$	−12.0000	−0.693978
$300$	−2.00000	−0.115470
$301$	−27.0000	−1.55625
$302$	2.00000	0.115087
$303$	−18.0000	−1.03407
$304$	4.00000	0.229416
$305$	4.00000	0.229039
$306$	7.00000	0.400163
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	3.00000	0.170941
$309$	−20.0000	−1.13776
$310$	8.00000	0.454369
$311$	−5.00000	−0.283524	−0.141762	−	0.989901i	$-0.545277\pi$
$311$	−5.00000	−0.283524	−0.141762	+	0.989901i	$0.545277\pi$
$312$	−6.00000	−0.339683
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	18.0000	1.01580
$315$	6.00000	0.338062
$316$	11.0000	0.618798
$317$	16.0000	0.898650	0.449325	−	0.893368i	$-0.351665\pi$
$317$	16.0000	0.898650	0.449325	+	0.893368i	$0.351665\pi$
$318$	0	0
$319$	−4.00000	−0.223957
$320$	−2.00000	−0.111803
$321$	12.0000	0.669775
$322$	−12.0000	−0.668734
$323$	28.0000	1.55796
$324$	−11.0000	−0.611111
$325$	3.00000	0.166410
$326$	22.0000	1.21847
$327$	−28.0000	−1.54840
$328$	−11.0000	−0.607373
$329$	−30.0000	−1.65395
$330$	4.00000	0.220193
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−13.0000	−0.713468
$333$	−7.00000	−0.383598
$334$	12.0000	0.656611
$335$	−8.00000	−0.437087
$336$	−6.00000	−0.327327
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	−4.00000	−0.217571
$339$	16.0000	0.869001
$340$	−14.0000	−0.759257
$341$	4.00000	0.216612
$342$	4.00000	0.216295
$343$	15.0000	0.809924
$344$	9.00000	0.485247
$345$	−16.0000	−0.861411
$346$	−11.0000	−0.591364
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	8.00000	0.428845
$349$	1.00000	0.0535288	0.0267644	−	0.999642i	$-0.491480\pi$
$349$	1.00000	0.0535288	0.0267644	+	0.999642i	$0.491480\pi$
$350$	3.00000	0.160357
$351$	12.0000	0.640513
$352$	−1.00000	−0.0533002
$353$	22.0000	1.17094	0.585471	−	0.810693i	$-0.300910\pi$
$353$	22.0000	1.17094	0.585471	+	0.810693i	$0.300910\pi$
$354$	−2.00000	−0.106299
$355$	−18.0000	−0.955341
$356$	18.0000	0.953998
$357$	−42.0000	−2.22288
$358$	−7.00000	−0.369961
$359$	27.0000	1.42501	0.712503	−	0.701669i	$-0.247562\pi$
$359$	27.0000	1.42501	0.712503	+	0.701669i	$0.247562\pi$
$360$	−2.00000	−0.105409
$361$	−3.00000	−0.157895
$362$	−4.00000	−0.210235
$363$	−20.0000	−1.04973
$364$	9.00000	0.471728
$365$	28.0000	1.46559
$366$	−4.00000	−0.209083
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	4.00000	0.208514
$369$	−11.0000	−0.572637
$370$	14.0000	0.727825
$371$	0	0
$372$	−8.00000	−0.414781
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−7.00000	−0.361961
$375$	24.0000	1.23935
$376$	10.0000	0.515711
$377$	−12.0000	−0.618031
$378$	12.0000	0.617213
$379$	14.0000	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$380$	−8.00000	−0.410391
$381$	−16.0000	−0.819705
$382$	6.00000	0.306987
$383$	−25.0000	−1.27744	−0.638720	−	0.769439i	$-0.720536\pi$
$383$	−25.0000	−1.27744	−0.638720	+	0.769439i	$0.720536\pi$
$384$	2.00000	0.102062
$385$	−6.00000	−0.305788
$386$	25.0000	1.27247
$387$	9.00000	0.457496
$388$	2.00000	0.101535
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	12.0000	0.607644
$391$	28.0000	1.41602
$392$	2.00000	0.101015
$393$	−24.0000	−1.21064
$394$	−12.0000	−0.604551
$395$	−22.0000	−1.10694
$396$	−1.00000	−0.0502519
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	16.0000	0.802008
$399$	−24.0000	−1.20150
$400$	−1.00000	−0.0500000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	8.00000	0.399004
$403$	12.0000	0.597763
$404$	−9.00000	−0.447767
$405$	22.0000	1.09319
$406$	−12.0000	−0.595550
$407$	7.00000	0.346977
$408$	14.0000	0.693103
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	22.0000	1.08650
$411$	18.0000	0.887875
$412$	−10.0000	−0.492665
$413$	3.00000	0.147620
$414$	4.00000	0.196589
$415$	26.0000	1.27629
$416$	−3.00000	−0.147087
$417$	−20.0000	−0.979404
$418$	−4.00000	−0.195646
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	12.0000	0.585540
$421$	−11.0000	−0.536107	−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000	−0.536107	−0.268054	+	0.963404i	$0.586380\pi$
$422$	−5.00000	−0.243396
$423$	10.0000	0.486217
$424$	0	0
$425$	−7.00000	−0.339550
$426$	18.0000	0.872103
$427$	6.00000	0.290360
$428$	6.00000	0.290021
$429$	6.00000	0.289683
$430$	−18.0000	−0.868037
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	−4.00000	−0.192450
$433$	13.0000	0.624740	0.312370	−	0.949960i	$-0.398877\pi$
$433$	13.0000	0.624740	0.312370	+	0.949960i	$0.398877\pi$
$434$	12.0000	0.576018
$435$	−16.0000	−0.767141
$436$	−14.0000	−0.670478
$437$	16.0000	0.765384
$438$	−28.0000	−1.33789
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	2.00000	0.0953463
$441$	2.00000	0.0952381
$442$	−21.0000	−0.998868
$443$	9.00000	0.427603	0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000	0.427603	0.213801	+	0.976877i	$0.431415\pi$
$444$	−14.0000	−0.664411
$445$	−36.0000	−1.70656
$446$	21.0000	0.994379
$447$	−10.0000	−0.472984
$448$	−3.00000	−0.141737
$449$	−25.0000	−1.17982	−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000	−1.17982	−0.589911	+	0.807468i	$0.700837\pi$
$450$	−1.00000	−0.0471405
$451$	11.0000	0.517970
$452$	8.00000	0.376288
$453$	4.00000	0.187936
$454$	−25.0000	−1.17331
$455$	−18.0000	−0.843853
$456$	8.00000	0.374634
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−13.0000	−0.607450
$459$	−28.0000	−1.30693
$460$	−8.00000	−0.373002
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	6.00000	0.279145
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	4.00000	0.185695
$465$	16.0000	0.741982
$466$	0	0
$467$	1.00000	0.0462745	0.0231372	−	0.999732i	$-0.492635\pi$
$467$	1.00000	0.0462745	0.0231372	+	0.999732i	$0.492635\pi$
$468$	−3.00000	−0.138675
$469$	−12.0000	−0.554109
$470$	−20.0000	−0.922531
$471$	36.0000	1.65879
$472$	−1.00000	−0.0460287
$473$	−9.00000	−0.413820
$474$	22.0000	1.01049
$475$	−4.00000	−0.183533
$476$	−21.0000	−0.962533
$477$	0	0
$478$	8.00000	0.365911
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	−4.00000	−0.182574
$481$	21.0000	0.957518
$482$	−25.0000	−1.13872
$483$	−24.0000	−1.09204
$484$	−10.0000	−0.454545
$485$	−4.00000	−0.181631
$486$	−10.0000	−0.453609
$487$	−29.0000	−1.31412	−0.657058	−	0.753840i	$-0.728199\pi$
$487$	−29.0000	−1.31412	−0.657058	+	0.753840i	$0.728199\pi$
$488$	−2.00000	−0.0905357
$489$	44.0000	1.98975
$490$	−4.00000	−0.180702
$491$	10.0000	0.451294	0.225647	−	0.974209i	$-0.427550\pi$
$491$	10.0000	0.451294	0.225647	+	0.974209i	$0.427550\pi$
$492$	−22.0000	−0.991837
$493$	28.0000	1.26106
$494$	−12.0000	−0.539906
$495$	2.00000	0.0898933
$496$	−4.00000	−0.179605
$497$	−27.0000	−1.21112
$498$	−26.0000	−1.16509
$499$	−18.0000	−0.805791	−0.402895	−	0.915246i	$-0.631996\pi$
$499$	−18.0000	−0.805791	−0.402895	+	0.915246i	$0.631996\pi$
$500$	12.0000	0.536656
$501$	24.0000	1.07224
$502$	−2.00000	−0.0892644
$503$	30.0000	1.33763	0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000	1.33763	0.668817	+	0.743427i	$0.266801\pi$
$504$	−3.00000	−0.133631
$505$	18.0000	0.800989
$506$	−4.00000	−0.177822
$507$	−8.00000	−0.355292
$508$	−8.00000	−0.354943
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	−28.0000	−1.23986
$511$	42.0000	1.85797
$512$	1.00000	0.0441942
$513$	−16.0000	−0.706417
$514$	9.00000	0.396973
$515$	20.0000	0.881305
$516$	18.0000	0.792406
$517$	−10.0000	−0.439799
$518$	21.0000	0.922687
$519$	−22.0000	−0.965693
$520$	6.00000	0.263117
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	4.00000	0.175075
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	−12.0000	−0.524222
$525$	6.00000	0.261861
$526$	3.00000	0.130806
$527$	−28.0000	−1.21970
$528$	−2.00000	−0.0870388
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−1.00000	−0.0433963
$532$	−12.0000	−0.520266
$533$	33.0000	1.42939
$534$	36.0000	1.55787
$535$	−12.0000	−0.518805
$536$	4.00000	0.172774
$537$	−14.0000	−0.604145
$538$	−19.0000	−0.819148
$539$	−2.00000	−0.0861461
$540$	8.00000	0.344265
$541$	−43.0000	−1.84871	−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000	−1.84871	−0.924357	+	0.381528i	$0.875398\pi$
$542$	−1.00000	−0.0429537
$543$	−8.00000	−0.343313
$544$	7.00000	0.300123
$545$	28.0000	1.19939
$546$	18.0000	0.770329
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	9.00000	0.384461
$549$	−2.00000	−0.0853579
$550$	1.00000	0.0426401
$551$	16.0000	0.681623
$552$	8.00000	0.340503
$553$	−33.0000	−1.40330
$554$	18.0000	0.764747
$555$	28.0000	1.18853
$556$	−10.0000	−0.424094
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	−4.00000	−0.169334
$559$	−27.0000	−1.14198
$560$	6.00000	0.253546
$561$	−14.0000	−0.591080
$562$	−1.00000	−0.0421825
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	20.0000	0.842152
$565$	−16.0000	−0.673125
$566$	−19.0000	−0.798630
$567$	33.0000	1.38587
$568$	9.00000	0.377632
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	−16.0000	−0.670166
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	3.00000	0.125436
$573$	12.0000	0.501307
$574$	33.0000	1.37739
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−19.0000	−0.790980	−0.395490	−	0.918470i	$-0.629425\pi$
$577$	−19.0000	−0.790980	−0.395490	+	0.918470i	$0.629425\pi$
$578$	32.0000	1.33102
$579$	50.0000	2.07793
$580$	−8.00000	−0.332182
$581$	39.0000	1.61799
$582$	4.00000	0.165805
$583$	0	0
$584$	−14.0000	−0.579324
$585$	6.00000	0.248069
$586$	−8.00000	−0.330477
$587$	−15.0000	−0.619116	−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000	−0.619116	−0.309558	+	0.950881i	$0.600181\pi$
$588$	4.00000	0.164957
$589$	−16.0000	−0.659269
$590$	2.00000	0.0823387
$591$	−24.0000	−0.987228
$592$	−7.00000	−0.287698
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	4.00000	0.164122
$595$	42.0000	1.72183
$596$	−5.00000	−0.204808
$597$	32.0000	1.30967
$598$	−12.0000	−0.490716
$599$	27.0000	1.10319	0.551595	−	0.834112i	$-0.314019\pi$
$599$	27.0000	1.10319	0.551595	+	0.834112i	$0.314019\pi$
$600$	−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	$0.434621\pi$
$602$	−27.0000	−1.10044
$603$	4.00000	0.162893
$604$	2.00000	0.0813788
$605$	20.0000	0.813116
$606$	−18.0000	−0.731200
$607$	−21.0000	−0.852364	−0.426182	−	0.904638i	$-0.640142\pi$
$607$	−21.0000	−0.852364	−0.426182	+	0.904638i	$0.640142\pi$
$608$	4.00000	0.162221
$609$	−24.0000	−0.972529
$610$	4.00000	0.161955
$611$	−30.0000	−1.21367
$612$	7.00000	0.282958
$613$	5.00000	0.201948	0.100974	−	0.994889i	$-0.467804\pi$
$613$	5.00000	0.201948	0.100974	+	0.994889i	$0.467804\pi$
$614$	28.0000	1.12999
$615$	44.0000	1.77425
$616$	3.00000	0.120873
$617$	−31.0000	−1.24801	−0.624007	−	0.781419i	$-0.714496\pi$
$617$	−31.0000	−1.24801	−0.624007	+	0.781419i	$0.714496\pi$
$618$	−20.0000	−0.804518
$619$	−16.0000	−0.643094	−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000	−0.643094	−0.321547	+	0.946894i	$0.604203\pi$
$620$	8.00000	0.321288
$621$	−16.0000	−0.642058
$622$	−5.00000	−0.200482
$623$	−54.0000	−2.16346
$624$	−6.00000	−0.240192
$625$	−19.0000	−0.760000
$626$	18.0000	0.719425
$627$	−8.00000	−0.319489
$628$	18.0000	0.718278
$629$	−49.0000	−1.95376
$630$	6.00000	0.239046
$631$	11.0000	0.437903	0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000	0.437903	0.218952	+	0.975736i	$0.429736\pi$
$632$	11.0000	0.437557
$633$	−10.0000	−0.397464
$634$	16.0000	0.635441
$635$	16.0000	0.634941
$636$	0	0
$637$	−6.00000	−0.237729
$638$	−4.00000	−0.158362
$639$	9.00000	0.356034
$640$	−2.00000	−0.0790569
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000	0.473602
$643$	46.0000	1.81406	0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000	1.81406	0.907031	+	0.421063i	$0.138343\pi$
$644$	−12.0000	−0.472866
$645$	−36.0000	−1.41750
$646$	28.0000	1.10165
$647$	20.0000	0.786281	0.393141	−	0.919478i	$-0.371389\pi$
$647$	20.0000	0.786281	0.393141	+	0.919478i	$0.371389\pi$
$648$	−11.0000	−0.432121
$649$	1.00000	0.0392534
$650$	3.00000	0.117670
$651$	24.0000	0.940634
$652$	22.0000	0.861586
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	−28.0000	−1.09489
$655$	24.0000	0.937758
$656$	−11.0000	−0.429478
$657$	−14.0000	−0.546192
$658$	−30.0000	−1.16952
$659$	−28.0000	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$660$	4.00000	0.155700
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	−12.0000	−0.466393
$663$	−42.0000	−1.63114
$664$	−13.0000	−0.504498
$665$	24.0000	0.930680
$666$	−7.00000	−0.271244
$667$	16.0000	0.619522
$668$	12.0000	0.464294
$669$	42.0000	1.62381
$670$	−8.00000	−0.309067
$671$	2.00000	0.0772091
$672$	−6.00000	−0.231455
$673$	−18.0000	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$674$	22.0000	0.847408
$675$	4.00000	0.153960
$676$	−4.00000	−0.153846
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	16.0000	0.614476
$679$	−6.00000	−0.230259
$680$	−14.0000	−0.536875
$681$	−50.0000	−1.91600
$682$	4.00000	0.153168
$683$	37.0000	1.41577	0.707883	−	0.706330i	$-0.249650\pi$
$683$	37.0000	1.41577	0.707883	+	0.706330i	$0.249650\pi$
$684$	4.00000	0.152944
$685$	−18.0000	−0.687745
$686$	15.0000	0.572703
$687$	−26.0000	−0.991962
$688$	9.00000	0.343122
$689$	0	0
$690$	−16.0000	−0.609110
$691$	−29.0000	−1.10321	−0.551606	−	0.834105i	$-0.685985\pi$
$691$	−29.0000	−1.10321	−0.551606	+	0.834105i	$0.685985\pi$
$692$	−11.0000	−0.418157
$693$	3.00000	0.113961
$694$	−4.00000	−0.151838
$695$	20.0000	0.758643
$696$	8.00000	0.303239
$697$	−77.0000	−2.91658
$698$	1.00000	0.0378506
$699$	0	0
$700$	3.00000	0.113389
$701$	27.0000	1.01978	0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000	1.01978	0.509888	+	0.860241i	$0.329687\pi$
$702$	12.0000	0.452911
$703$	−28.0000	−1.05604
$704$	−1.00000	−0.0376889
$705$	−40.0000	−1.50649
$706$	22.0000	0.827981
$707$	27.0000	1.01544
$708$	−2.00000	−0.0751646
$709$	52.0000	1.95290	0.976450	−	0.215742i	$-0.0692169\pi$
$709$	52.0000	1.95290	0.976450	+	0.215742i	$0.0692169\pi$
$710$	−18.0000	−0.675528
$711$	11.0000	0.412532
$712$	18.0000	0.674579
$713$	−16.0000	−0.599205
$714$	−42.0000	−1.57181
$715$	−6.00000	−0.224387
$716$	−7.00000	−0.261602
$717$	16.0000	0.597531
$718$	27.0000	1.00763
$719$	−14.0000	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$719$	−14.0000	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$720$	−2.00000	−0.0745356
$721$	30.0000	1.11726
$722$	−3.00000	−0.111648
$723$	−50.0000	−1.85952
$724$	−4.00000	−0.148659
$725$	−4.00000	−0.148556
$726$	−20.0000	−0.742270
$727$	−23.0000	−0.853023	−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000	−0.853023	−0.426511	+	0.904482i	$0.640258\pi$
$728$	9.00000	0.333562
$729$	13.0000	0.481481
$730$	28.0000	1.03633
$731$	63.0000	2.33014
$732$	−4.00000	−0.147844
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	−32.0000	−1.18114
$735$	−8.00000	−0.295084
$736$	4.00000	0.147442
$737$	−4.00000	−0.147342
$738$	−11.0000	−0.404916
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	14.0000	0.514650
$741$	−24.0000	−0.881662
$742$	0	0
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	−8.00000	−0.293294
$745$	10.0000	0.366372
$746$	10.0000	0.366126
$747$	−13.0000	−0.475645
$748$	−7.00000	−0.255945
$749$	−18.0000	−0.657706
$750$	24.0000	0.876356
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	10.0000	0.364662
$753$	−4.00000	−0.145768
$754$	−12.0000	−0.437014
$755$	−4.00000	−0.145575
$756$	12.0000	0.436436
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	14.0000	0.508503
$759$	−8.00000	−0.290382
$760$	−8.00000	−0.290191
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	−16.0000	−0.579619
$763$	42.0000	1.52050
$764$	6.00000	0.217072
$765$	−14.0000	−0.506171
$766$	−25.0000	−0.903287
$767$	3.00000	0.108324
$768$	2.00000	0.0721688
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	−6.00000	−0.216225
$771$	18.0000	0.648254
$772$	25.0000	0.899770
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	9.00000	0.323498
$775$	4.00000	0.143684
$776$	2.00000	0.0717958
$777$	42.0000	1.50674
$778$	−4.00000	−0.143407
$779$	−44.0000	−1.57646
$780$	12.0000	0.429669
$781$	−9.00000	−0.322045
$782$	28.0000	1.00128
$783$	−16.0000	−0.571793
$784$	2.00000	0.0714286
$785$	−36.0000	−1.28490
$786$	−24.0000	−0.856052
$787$	−12.0000	−0.427754	−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000	−0.427754	−0.213877	+	0.976861i	$0.568609\pi$
$788$	−12.0000	−0.427482
$789$	6.00000	0.213606
$790$	−22.0000	−0.782725
$791$	−24.0000	−0.853342
$792$	−1.00000	−0.0355335
$793$	6.00000	0.213066
$794$	−14.0000	−0.496841
$795$	0	0
$796$	16.0000	0.567105
$797$	23.0000	0.814702	0.407351	−	0.913272i	$-0.366453\pi$
$797$	23.0000	0.814702	0.407351	+	0.913272i	$0.366453\pi$
$798$	−24.0000	−0.849591
$799$	70.0000	2.47642
$800$	−1.00000	−0.0353553
$801$	18.0000	0.635999
$802$	6.00000	0.211867
$803$	14.0000	0.494049
$804$	8.00000	0.282138
$805$	24.0000	0.845889
$806$	12.0000	0.422682
$807$	−38.0000	−1.33766
$808$	−9.00000	−0.316619
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	22.0000	0.773001
$811$	9.00000	0.316033	0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000	0.316033	0.158016	+	0.987436i	$0.449490\pi$
$812$	−12.0000	−0.421117
$813$	−2.00000	−0.0701431
$814$	7.00000	0.245350
$815$	−44.0000	−1.54125
$816$	14.0000	0.490098
$817$	36.0000	1.25948
$818$	−14.0000	−0.489499
$819$	9.00000	0.314485
$820$	22.0000	0.768273
$821$	25.0000	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$822$	18.0000	0.627822
$823$	−14.0000	−0.488009	−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000	−0.488009	−0.244005	+	0.969774i	$0.578461\pi$
$824$	−10.0000	−0.348367
$825$	2.00000	0.0696311
$826$	3.00000	0.104383
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	4.00000	0.139010
$829$	4.00000	0.138926	0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000	0.138926	0.0694629	+	0.997585i	$0.477871\pi$
$830$	26.0000	0.902473
$831$	36.0000	1.24883
$832$	−3.00000	−0.104006
$833$	14.0000	0.485071
$834$	−20.0000	−0.692543
$835$	−24.0000	−0.830554
$836$	−4.00000	−0.138343
$837$	16.0000	0.553041
$838$	−3.00000	−0.103633
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	12.0000	0.414039
$841$	−13.0000	−0.448276
$842$	−11.0000	−0.379085
$843$	−2.00000	−0.0688837
$844$	−5.00000	−0.172107
$845$	8.00000	0.275208
$846$	10.0000	0.343807
$847$	30.0000	1.03081
$848$	0	0
$849$	−38.0000	−1.30416
$850$	−7.00000	−0.240098
$851$	−28.0000	−0.959828
$852$	18.0000	0.616670
$853$	54.0000	1.84892	0.924462	−	0.381273i	$-0.124514\pi$
$853$	54.0000	1.84892	0.924462	+	0.381273i	$0.124514\pi$
$854$	6.00000	0.205316
$855$	−8.00000	−0.273594
$856$	6.00000	0.205076
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	6.00000	0.204837
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−18.0000	−0.613795
$861$	66.0000	2.24927
$862$	12.0000	0.408722
$863$	−14.0000	−0.476566	−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000	−0.476566	−0.238283	+	0.971196i	$0.576585\pi$
$864$	−4.00000	−0.136083
$865$	22.0000	0.748022
$866$	13.0000	0.441758
$867$	64.0000	2.17355
$868$	12.0000	0.407307
$869$	−11.0000	−0.373149
$870$	−16.0000	−0.542451
$871$	−12.0000	−0.406604
$872$	−14.0000	−0.474100
$873$	2.00000	0.0676897
$874$	16.0000	0.541208
$875$	−36.0000	−1.21702
$876$	−28.0000	−0.946032
$877$	20.0000	0.675352	0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000	0.675352	0.337676	+	0.941262i	$0.390359\pi$
$878$	35.0000	1.18119
$879$	−16.0000	−0.539667
$880$	2.00000	0.0674200
$881$	8.00000	0.269527	0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000	0.269527	0.134763	+	0.990878i	$0.456973\pi$
$882$	2.00000	0.0673435
$883$	−34.0000	−1.14419	−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000	−1.14419	−0.572096	+	0.820187i	$0.693869\pi$
$884$	−21.0000	−0.706306
$885$	4.00000	0.134459
$886$	9.00000	0.302361
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	−14.0000	−0.469809
$889$	24.0000	0.804934
$890$	−36.0000	−1.20672
$891$	11.0000	0.368514
$892$	21.0000	0.703132
$893$	40.0000	1.33855
$894$	−10.0000	−0.334450
$895$	14.0000	0.467968
$896$	−3.00000	−0.100223
$897$	−24.0000	−0.801337
$898$	−25.0000	−0.834261
$899$	−16.0000	−0.533630
$900$	−1.00000	−0.0333333
$901$	0	0
$902$	11.0000	0.366260
$903$	−54.0000	−1.79701
$904$	8.00000	0.266076
$905$	8.00000	0.265929
$906$	4.00000	0.132891
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	−25.0000	−0.829654
$909$	−9.00000	−0.298511
$910$	−18.0000	−0.596694
$911$	17.0000	0.563235	0.281618	−	0.959527i	$-0.409129\pi$
$911$	17.0000	0.563235	0.281618	+	0.959527i	$0.409129\pi$
$912$	8.00000	0.264906
$913$	13.0000	0.430237
$914$	−10.0000	−0.330771
$915$	8.00000	0.264472
$916$	−13.0000	−0.429532
$917$	36.0000	1.18882
$918$	−28.0000	−0.924138
$919$	38.0000	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$920$	−8.00000	−0.263752
$921$	56.0000	1.84526
$922$	−18.0000	−0.592798
$923$	−27.0000	−0.888716
$924$	6.00000	0.197386
$925$	7.00000	0.230159
$926$	6.00000	0.197172
$927$	−10.0000	−0.328443
$928$	4.00000	0.131306
$929$	−40.0000	−1.31236	−0.656179	−	0.754606i	$-0.727828\pi$
$929$	−40.0000	−1.31236	−0.656179	+	0.754606i	$0.727828\pi$
$930$	16.0000	0.524661
$931$	8.00000	0.262189
$932$	0	0
$933$	−10.0000	−0.327385
$934$	1.00000	0.0327210
$935$	14.0000	0.457849
$936$	−3.00000	−0.0980581
$937$	−40.0000	−1.30674	−0.653372	−	0.757037i	$-0.726646\pi$
$937$	−40.0000	−1.30674	−0.653372	+	0.757037i	$0.726646\pi$
$938$	−12.0000	−0.391814
$939$	36.0000	1.17482
$940$	−20.0000	−0.652328
$941$	−2.00000	−0.0651981	−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000	−0.0651981	−0.0325991	+	0.999469i	$0.510378\pi$
$942$	36.0000	1.17294
$943$	−44.0000	−1.43284
$944$	−1.00000	−0.0325472
$945$	−24.0000	−0.780720
$946$	−9.00000	−0.292615
$947$	10.0000	0.324956	0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000	0.324956	0.162478	+	0.986712i	$0.448051\pi$
$948$	22.0000	0.714527
$949$	42.0000	1.36338
$950$	−4.00000	−0.129777
$951$	32.0000	1.03767
$952$	−21.0000	−0.680614
$953$	31.0000	1.00419	0.502094	−	0.864813i	$-0.332563\pi$
$953$	31.0000	1.00419	0.502094	+	0.864813i	$0.332563\pi$
$954$	0	0
$955$	−12.0000	−0.388311
$956$	8.00000	0.258738
$957$	−8.00000	−0.258603
$958$	−32.0000	−1.03387
$959$	−27.0000	−0.871875
$960$	−4.00000	−0.129099
$961$	−15.0000	−0.483871
$962$	21.0000	0.677067
$963$	6.00000	0.193347
$964$	−25.0000	−0.805196
$965$	−50.0000	−1.60956
$966$	−24.0000	−0.772187
$967$	−30.0000	−0.964735	−0.482367	−	0.875969i	$-0.660223\pi$
$967$	−30.0000	−0.964735	−0.482367	+	0.875969i	$0.660223\pi$
$968$	−10.0000	−0.321412
$969$	56.0000	1.79898
$970$	−4.00000	−0.128432
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	−10.0000	−0.320750
$973$	30.0000	0.961756
$974$	−29.0000	−0.929220
$975$	6.00000	0.192154
$976$	−2.00000	−0.0640184
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	44.0000	1.40696
$979$	−18.0000	−0.575282
$980$	−4.00000	−0.127775
$981$	−14.0000	−0.446986
$982$	10.0000	0.319113
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	−22.0000	−0.701334
$985$	24.0000	0.764704
$986$	28.0000	0.891702
$987$	−60.0000	−1.90982
$988$	−12.0000	−0.381771
$989$	36.0000	1.14473
$990$	2.00000	0.0635642
$991$	−24.0000	−0.762385	−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000	−0.762385	−0.381193	+	0.924496i	$0.624487\pi$
$992$	−4.00000	−0.127000
$993$	−24.0000	−0.761617
$994$	−27.0000	−0.856388
$995$	−32.0000	−1.01447
$996$	−26.0000	−0.823842
$997$	−52.0000	−1.64686	−0.823428	−	0.567420i	$-0.807941\pi$
$997$	−52.0000	−1.64686	−0.823428	+	0.567420i	$0.807941\pi$
$998$	−18.0000	−0.569780
$999$	28.0000	0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	118.2.a.d.1.1	✓	1
3.2	odd	2		1062.2.a.e.1.1		1
4.3	odd	2		944.2.a.b.1.1		1
5.2	odd	4		2950.2.c.m.1299.2		2
5.3	odd	4		2950.2.c.m.1299.1		2
5.4	even	2		2950.2.a.b.1.1		1
7.6	odd	2		5782.2.a.e.1.1		1
8.3	odd	2		3776.2.a.w.1.1		1
8.5	even	2		3776.2.a.f.1.1		1
12.11	even	2		8496.2.a.t.1.1		1
59.58	odd	2		6962.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
118.2.a.d.1.1	✓	1	1.1	even	1	trivial
944.2.a.b.1.1		1	4.3	odd	2
1062.2.a.e.1.1		1	3.2	odd	2
2950.2.a.b.1.1		1	5.4	even	2
2950.2.c.m.1299.1		2	5.3	odd	4
2950.2.c.m.1299.2		2	5.2	odd	4
3776.2.a.f.1.1		1	8.5	even	2
3776.2.a.w.1.1		1	8.3	odd	2
5782.2.a.e.1.1		1	7.6	odd	2
6962.2.a.e.1.1		1	59.58	odd	2
8496.2.a.t.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:	\( N \)	\(=\)	\( 118 = 2 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	118.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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