LMFDB - Embedded newform 786.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [786,2,Mod(1,786)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(786, 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("786.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 786 = 2 \cdot 3 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	786.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:	$6.27624159887$
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	$\chi$	$=$	786.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{10} -1.00000 q^{12} +6.00000 q^{13} -4.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +4.00000 q^{20} +4.00000 q^{21} +4.00000 q^{23} -1.00000 q^{24} +11.0000 q^{25} +6.00000 q^{26} -1.00000 q^{27} -4.00000 q^{28} -6.00000 q^{29} -4.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} -16.0000 q^{35} +1.00000 q^{36} -8.00000 q^{37} +4.00000 q^{38} -6.00000 q^{39} +4.00000 q^{40} +6.00000 q^{41} +4.00000 q^{42} +12.0000 q^{43} +4.00000 q^{45} +4.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} +11.0000 q^{50} +2.00000 q^{51} +6.00000 q^{52} +12.0000 q^{53} -1.00000 q^{54} -4.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} -4.00000 q^{60} -6.00000 q^{61} -2.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +24.0000 q^{65} -12.0000 q^{67} -2.00000 q^{68} -4.00000 q^{69} -16.0000 q^{70} +4.00000 q^{71} +1.00000 q^{72} -14.0000 q^{73} -8.00000 q^{74} -11.0000 q^{75} +4.00000 q^{76} -6.00000 q^{78} +10.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +4.00000 q^{83} +4.00000 q^{84} -8.00000 q^{85} +12.0000 q^{86} +6.00000 q^{87} +10.0000 q^{89} +4.00000 q^{90} -24.0000 q^{91} +4.00000 q^{92} +2.00000 q^{93} -8.00000 q^{94} +16.0000 q^{95} -1.00000 q^{96} +6.00000 q^{97} +9.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	−1.00000	−0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.00000	1.26491
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	−4.00000	−1.06904
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	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	$0.348268\pi$
$20$	4.00000	0.894427
$21$	4.00000	0.872872
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−1.00000	−0.204124
$25$	11.0000	2.20000
$26$	6.00000	1.17670
$27$	−1.00000	−0.192450
$28$	−4.00000	−0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−4.00000	−0.730297
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−16.0000	−2.70449
$36$	1.00000	0.166667
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	4.00000	0.648886
$39$	−6.00000	−0.960769
$40$	4.00000	0.632456
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.00000	0.617213
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	0	0
$45$	4.00000	0.596285
$46$	4.00000	0.589768
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	11.0000	1.55563
$51$	2.00000	0.280056
$52$	6.00000	0.832050
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−4.00000	−0.534522
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−4.00000	−0.516398
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−2.00000	−0.254000
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	24.0000	2.97683
$66$	0	0
$67$	−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
$69$	−4.00000	−0.481543
$70$	−16.0000	−1.91237
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	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	$0.805631\pi$
$74$	−8.00000	−0.929981
$75$	−11.0000	−1.27017
$76$	4.00000	0.458831
$77$	0	0
$78$	−6.00000	−0.679366
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	4.00000	0.436436
$85$	−8.00000	−0.867722
$86$	12.0000	1.29399
$87$	6.00000	0.643268
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	4.00000	0.421637
$91$	−24.0000	−2.51588
$92$	4.00000	0.417029
$93$	2.00000	0.207390
$94$	−8.00000	−0.825137
$95$	16.0000	1.64157
$96$	−1.00000	−0.102062
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	11.0000	1.10000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	2.00000	0.198030
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	6.00000	0.588348
$105$	16.0000	1.56144
$106$	12.0000	1.16554
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−1.00000	−0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−4.00000	−0.377964
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−4.00000	−0.374634
$115$	16.0000	1.49201
$116$	−6.00000	−0.557086
$117$	6.00000	0.554700
$118$	−8.00000	−0.736460
$119$	8.00000	0.733359
$120$	−4.00000	−0.365148
$121$	−11.0000	−1.00000
$122$	−6.00000	−0.543214
$123$	−6.00000	−0.541002
$124$	−2.00000	−0.179605
$125$	24.0000	2.14663
$126$	−4.00000	−0.356348
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	1.00000	0.0883883
$129$	−12.0000	−1.05654
$130$	24.0000	2.10494
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0	0
$133$	−16.0000	−1.38738
$134$	−12.0000	−1.03664
$135$	−4.00000	−0.344265
$136$	−2.00000	−0.171499
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−4.00000	−0.340503
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	−16.0000	−1.35225
$141$	8.00000	0.673722
$142$	4.00000	0.335673
$143$	0	0
$144$	1.00000	0.0833333
$145$	−24.0000	−1.99309
$146$	−14.0000	−1.15865
$147$	−9.00000	−0.742307
$148$	−8.00000	−0.657596
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−11.0000	−0.898146
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	4.00000	0.324443
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−6.00000	−0.480384
$157$	−16.0000	−1.27694	−0.638470	−	0.769647i	$-0.720432\pi$
$157$	−16.0000	−1.27694	−0.638470	+	0.769647i	$0.720432\pi$
$158$	10.0000	0.795557
$159$	−12.0000	−0.951662
$160$	4.00000	0.316228
$161$	−16.0000	−1.26098
$162$	1.00000	0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	4.00000	0.310460
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	4.00000	0.308607
$169$	23.0000	1.76923
$170$	−8.00000	−0.613572
$171$	4.00000	0.305888
$172$	12.0000	0.914991
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	6.00000	0.454859
$175$	−44.0000	−3.32609
$176$	0	0
$177$	8.00000	0.601317
$178$	10.0000	0.749532
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	4.00000	0.298142
$181$	8.00000	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$182$	−24.0000	−1.77900
$183$	6.00000	0.443533
$184$	4.00000	0.294884
$185$	−32.0000	−2.35269
$186$	2.00000	0.146647
$187$	0	0
$188$	−8.00000	−0.583460
$189$	4.00000	0.290957
$190$	16.0000	1.16076
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	−1.00000	−0.0721688
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	6.00000	0.430775
$195$	−24.0000	−1.71868
$196$	9.00000	0.642857
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	11.0000	0.777817
$201$	12.0000	0.846415
$202$	−4.00000	−0.281439
$203$	24.0000	1.68447
$204$	2.00000	0.140028
$205$	24.0000	1.67623
$206$	−14.0000	−0.975426
$207$	4.00000	0.278019
$208$	6.00000	0.416025
$209$	0	0
$210$	16.0000	1.10410
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	12.0000	0.824163
$213$	−4.00000	−0.274075
$214$	−12.0000	−0.820303
$215$	48.0000	3.27357
$216$	−1.00000	−0.0680414
$217$	8.00000	0.543075
$218$	−10.0000	−0.677285
$219$	14.0000	0.946032
$220$	0	0
$221$	−12.0000	−0.807207
$222$	8.00000	0.536925
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	−4.00000	−0.267261
$225$	11.0000	0.733333
$226$	−14.0000	−0.931266
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−4.00000	−0.264906
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	16.0000	1.05501
$231$	0	0
$232$	−6.00000	−0.393919
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	6.00000	0.392232
$235$	−32.0000	−2.08745
$236$	−8.00000	−0.520756
$237$	−10.0000	−0.649570
$238$	8.00000	0.518563
$239$	14.0000	0.905585	0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000	0.905585	0.452792	+	0.891616i	$0.350428\pi$
$240$	−4.00000	−0.258199
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−11.0000	−0.707107
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	36.0000	2.29996
$246$	−6.00000	−0.382546
$247$	24.0000	1.52708
$248$	−2.00000	−0.127000
$249$	−4.00000	−0.253490
$250$	24.0000	1.51789
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	−6.00000	−0.376473
$255$	8.00000	0.500979
$256$	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	$0.356166\pi$
$258$	−12.0000	−0.747087
$259$	32.0000	1.98838
$260$	24.0000	1.48842
$261$	−6.00000	−0.371391
$262$	−1.00000	−0.0617802
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	48.0000	2.94862
$266$	−16.0000	−0.981023
$267$	−10.0000	−0.611990
$268$	−12.0000	−0.733017
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	−4.00000	−0.243432
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	−2.00000	−0.121268
$273$	24.0000	1.45255
$274$	2.00000	0.120824
$275$	0	0
$276$	−4.00000	−0.240772
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	0	0
$279$	−2.00000	−0.119737
$280$	−16.0000	−0.956183
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	8.00000	0.476393
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	4.00000	0.237356
$285$	−16.0000	−0.947758
$286$	0	0
$287$	−24.0000	−1.41668
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−24.0000	−1.40933
$291$	−6.00000	−0.351726
$292$	−14.0000	−0.819288
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	−9.00000	−0.524891
$295$	−32.0000	−1.86311
$296$	−8.00000	−0.464991
$297$	0	0
$298$	−6.00000	−0.347571
$299$	24.0000	1.38796
$300$	−11.0000	−0.635085
$301$	−48.0000	−2.76667
$302$	12.0000	0.690522
$303$	4.00000	0.229794
$304$	4.00000	0.229416
$305$	−24.0000	−1.37424
$306$	−2.00000	−0.114332
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	14.0000	0.796432
$310$	−8.00000	−0.454369
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	−6.00000	−0.339683
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−16.0000	−0.902932
$315$	−16.0000	−0.901498
$316$	10.0000	0.562544
$317$	24.0000	1.34797	0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000	1.34797	0.673987	+	0.738743i	$0.264580\pi$
$318$	−12.0000	−0.672927
$319$	0	0
$320$	4.00000	0.223607
$321$	12.0000	0.669775
$322$	−16.0000	−0.891645
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	66.0000	3.66102
$326$	−16.0000	−0.886158
$327$	10.0000	0.553001
$328$	6.00000	0.331295
$329$	32.0000	1.76422
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	4.00000	0.219529
$333$	−8.00000	−0.438397
$334$	6.00000	0.328305
$335$	−48.0000	−2.62252
$336$	4.00000	0.218218
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	23.0000	1.25104
$339$	14.0000	0.760376
$340$	−8.00000	−0.433861
$341$	0	0
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	12.0000	0.646997
$345$	−16.0000	−0.861411
$346$	−14.0000	−0.752645
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	6.00000	0.321634
$349$	24.0000	1.28469	0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000	1.28469	0.642345	+	0.766415i	$0.277962\pi$
$350$	−44.0000	−2.35190
$351$	−6.00000	−0.320256
$352$	0	0
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	8.00000	0.425195
$355$	16.0000	0.849192
$356$	10.0000	0.529999
$357$	−8.00000	−0.423405
$358$	−16.0000	−0.845626
$359$	4.00000	0.211112	0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000	0.211112	0.105556	+	0.994413i	$0.466338\pi$
$360$	4.00000	0.210819
$361$	−3.00000	−0.157895
$362$	8.00000	0.420471
$363$	11.0000	0.577350
$364$	−24.0000	−1.25794
$365$	−56.0000	−2.93117
$366$	6.00000	0.313625
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	4.00000	0.208514
$369$	6.00000	0.312348
$370$	−32.0000	−1.66360
$371$	−48.0000	−2.49204
$372$	2.00000	0.103695
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	0	0
$375$	−24.0000	−1.23935
$376$	−8.00000	−0.412568
$377$	−36.0000	−1.85409
$378$	4.00000	0.205738
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	16.0000	0.820783
$381$	6.00000	0.307389
$382$	10.0000	0.511645
$383$	−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
$385$	0	0
$386$	−2.00000	−0.101797
$387$	12.0000	0.609994
$388$	6.00000	0.304604
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	−24.0000	−1.21529
$391$	−8.00000	−0.404577
$392$	9.00000	0.454569
$393$	1.00000	0.0504433
$394$	−18.0000	−0.906827
$395$	40.0000	2.01262
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−14.0000	−0.701757
$399$	16.0000	0.801002
$400$	11.0000	0.550000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	12.0000	0.598506
$403$	−12.0000	−0.597763
$404$	−4.00000	−0.199007
$405$	4.00000	0.198762
$406$	24.0000	1.19110
$407$	0	0
$408$	2.00000	0.0990148
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	24.0000	1.18528
$411$	−2.00000	−0.0986527
$412$	−14.0000	−0.689730
$413$	32.0000	1.57462
$414$	4.00000	0.196589
$415$	16.0000	0.785409
$416$	6.00000	0.294174
$417$	0	0
$418$	0	0
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	16.0000	0.780720
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	20.0000	0.973585
$423$	−8.00000	−0.388973
$424$	12.0000	0.582772
$425$	−22.0000	−1.06716
$426$	−4.00000	−0.193801
$427$	24.0000	1.16144
$428$	−12.0000	−0.580042
$429$	0	0
$430$	48.0000	2.31477
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	−1.00000	−0.0481125
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	8.00000	0.384012
$435$	24.0000	1.15071
$436$	−10.0000	−0.478913
$437$	16.0000	0.765384
$438$	14.0000	0.668946
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	−12.0000	−0.570782
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	8.00000	0.379663
$445$	40.0000	1.89618
$446$	−10.0000	−0.473514
$447$	6.00000	0.283790
$448$	−4.00000	−0.188982
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	11.0000	0.518545
$451$	0	0
$452$	−14.0000	−0.658505
$453$	−12.0000	−0.563809
$454$	12.0000	0.563188
$455$	−96.0000	−4.50055
$456$	−4.00000	−0.187317
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−4.00000	−0.186908
$459$	2.00000	0.0933520
$460$	16.0000	0.746004
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	10.0000	0.464739	0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000	0.464739	0.232370	+	0.972628i	$0.425352\pi$
$464$	−6.00000	−0.278543
$465$	8.00000	0.370991
$466$	2.00000	0.0926482
$467$	16.0000	0.740392	0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000	0.740392	0.370196	+	0.928954i	$0.379291\pi$
$468$	6.00000	0.277350
$469$	48.0000	2.21643
$470$	−32.0000	−1.47605
$471$	16.0000	0.737241
$472$	−8.00000	−0.368230
$473$	0	0
$474$	−10.0000	−0.459315
$475$	44.0000	2.01886
$476$	8.00000	0.366679
$477$	12.0000	0.549442
$478$	14.0000	0.640345
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	−4.00000	−0.182574
$481$	−48.0000	−2.18861
$482$	−10.0000	−0.455488
$483$	16.0000	0.728025
$484$	−11.0000	−0.500000
$485$	24.0000	1.08978
$486$	−1.00000	−0.0453609
$487$	−44.0000	−1.99383	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−44.0000	−1.99383	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	−6.00000	−0.271607
$489$	16.0000	0.723545
$490$	36.0000	1.62631
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	−6.00000	−0.270501
$493$	12.0000	0.540453
$494$	24.0000	1.07981
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	−16.0000	−0.717698
$498$	−4.00000	−0.179244
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	24.0000	1.07331
$501$	−6.00000	−0.268060
$502$	−4.00000	−0.178529
$503$	−32.0000	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$504$	−4.00000	−0.178174
$505$	−16.0000	−0.711991
$506$	0	0
$507$	−23.0000	−1.02147
$508$	−6.00000	−0.266207
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	8.00000	0.354246
$511$	56.0000	2.47729
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	14.0000	0.617514
$515$	−56.0000	−2.46765
$516$	−12.0000	−0.528271
$517$	0	0
$518$	32.0000	1.40600
$519$	14.0000	0.614532
$520$	24.0000	1.05247
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	−6.00000	−0.262613
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−1.00000	−0.0436852
$525$	44.0000	1.92032
$526$	−6.00000	−0.261612
$527$	4.00000	0.174243
$528$	0	0
$529$	−7.00000	−0.304348
$530$	48.0000	2.08499
$531$	−8.00000	−0.347170
$532$	−16.0000	−0.693688
$533$	36.0000	1.55933
$534$	−10.0000	−0.432742
$535$	−48.0000	−2.07522
$536$	−12.0000	−0.518321
$537$	16.0000	0.690451
$538$	16.0000	0.689809
$539$	0	0
$540$	−4.00000	−0.172133
$541$	40.0000	1.71973	0.859867	−	0.510518i	$-0.170546\pi$
$541$	40.0000	1.71973	0.859867	+	0.510518i	$0.170546\pi$
$542$	28.0000	1.20270
$543$	−8.00000	−0.343313
$544$	−2.00000	−0.0857493
$545$	−40.0000	−1.71341
$546$	24.0000	1.02711
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	2.00000	0.0854358
$549$	−6.00000	−0.256074
$550$	0	0
$551$	−24.0000	−1.02243
$552$	−4.00000	−0.170251
$553$	−40.0000	−1.70097
$554$	−18.0000	−0.764747
$555$	32.0000	1.35832
$556$	0	0
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−2.00000	−0.0846668
$559$	72.0000	3.04528
$560$	−16.0000	−0.676123
$561$	0	0
$562$	26.0000	1.09674
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	8.00000	0.336861
$565$	−56.0000	−2.35594
$566$	4.00000	0.168133
$567$	−4.00000	−0.167984
$568$	4.00000	0.167836
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	−16.0000	−0.670166
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	−10.0000	−0.417756
$574$	−24.0000	−1.00174
$575$	44.0000	1.83493
$576$	1.00000	0.0416667
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−13.0000	−0.540729
$579$	2.00000	0.0831172
$580$	−24.0000	−0.996546
$581$	−16.0000	−0.663792
$582$	−6.00000	−0.248708
$583$	0	0
$584$	−14.0000	−0.579324
$585$	24.0000	0.992278
$586$	26.0000	1.07405
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−9.00000	−0.371154
$589$	−8.00000	−0.329634
$590$	−32.0000	−1.31742
$591$	18.0000	0.740421
$592$	−8.00000	−0.328798
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	32.0000	1.31187
$596$	−6.00000	−0.245770
$597$	14.0000	0.572982
$598$	24.0000	0.981433
$599$	−42.0000	−1.71607	−0.858037	−	0.513588i	$-0.828316\pi$
$599$	−42.0000	−1.71607	−0.858037	+	0.513588i	$0.828316\pi$
$600$	−11.0000	−0.449073
$601$	38.0000	1.55005	0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000	1.55005	0.775026	+	0.631929i	$0.217737\pi$
$602$	−48.0000	−1.95633
$603$	−12.0000	−0.488678
$604$	12.0000	0.488273
$605$	−44.0000	−1.78885
$606$	4.00000	0.162489
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	4.00000	0.162221
$609$	−24.0000	−0.972529
$610$	−24.0000	−0.971732
$611$	−48.0000	−1.94187
$612$	−2.00000	−0.0808452
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	28.0000	1.12999
$615$	−24.0000	−0.967773
$616$	0	0
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	14.0000	0.563163
$619$	−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
$621$	−4.00000	−0.160514
$622$	30.0000	1.20289
$623$	−40.0000	−1.60257
$624$	−6.00000	−0.240192
$625$	41.0000	1.64000
$626$	−10.0000	−0.399680
$627$	0	0
$628$	−16.0000	−0.638470
$629$	16.0000	0.637962
$630$	−16.0000	−0.637455
$631$	−28.0000	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$632$	10.0000	0.397779
$633$	−20.0000	−0.794929
$634$	24.0000	0.953162
$635$	−24.0000	−0.952411
$636$	−12.0000	−0.475831
$637$	54.0000	2.13956
$638$	0	0
$639$	4.00000	0.158238
$640$	4.00000	0.158114
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	12.0000	0.473602
$643$	24.0000	0.946468	0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000	0.946468	0.473234	+	0.880937i	$0.343087\pi$
$644$	−16.0000	−0.630488
$645$	−48.0000	−1.89000
$646$	−8.00000	−0.314756
$647$	26.0000	1.02217	0.511083	−	0.859532i	$-0.329245\pi$
$647$	26.0000	1.02217	0.511083	+	0.859532i	$0.329245\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	66.0000	2.58873
$651$	−8.00000	−0.313545
$652$	−16.0000	−0.626608
$653$	28.0000	1.09572	0.547862	−	0.836569i	$-0.315442\pi$
$653$	28.0000	1.09572	0.547862	+	0.836569i	$0.315442\pi$
$654$	10.0000	0.391031
$655$	−4.00000	−0.156293
$656$	6.00000	0.234261
$657$	−14.0000	−0.546192
$658$	32.0000	1.24749
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	−8.00000	−0.310929
$663$	12.0000	0.466041
$664$	4.00000	0.155230
$665$	−64.0000	−2.48181
$666$	−8.00000	−0.309994
$667$	−24.0000	−0.929284
$668$	6.00000	0.232147
$669$	10.0000	0.386622
$670$	−48.0000	−1.85440
$671$	0	0
$672$	4.00000	0.154303
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	−14.0000	−0.539260
$675$	−11.0000	−0.423390
$676$	23.0000	0.884615
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	14.0000	0.537667
$679$	−24.0000	−0.921035
$680$	−8.00000	−0.306786
$681$	−12.0000	−0.459841
$682$	0	0
$683$	44.0000	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$684$	4.00000	0.152944
$685$	8.00000	0.305664
$686$	−8.00000	−0.305441
$687$	4.00000	0.152610
$688$	12.0000	0.457496
$689$	72.0000	2.74298
$690$	−16.0000	−0.609110
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	6.00000	0.227429
$697$	−12.0000	−0.454532
$698$	24.0000	0.908413
$699$	−2.00000	−0.0756469
$700$	−44.0000	−1.66304
$701$	20.0000	0.755390	0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000	0.755390	0.377695	+	0.925930i	$0.376717\pi$
$702$	−6.00000	−0.226455
$703$	−32.0000	−1.20690
$704$	0	0
$705$	32.0000	1.20519
$706$	−14.0000	−0.526897
$707$	16.0000	0.601742
$708$	8.00000	0.300658
$709$	12.0000	0.450669	0.225335	−	0.974281i	$-0.427652\pi$
$709$	12.0000	0.450669	0.225335	+	0.974281i	$0.427652\pi$
$710$	16.0000	0.600469
$711$	10.0000	0.375029
$712$	10.0000	0.374766
$713$	−8.00000	−0.299602
$714$	−8.00000	−0.299392
$715$	0	0
$716$	−16.0000	−0.597948
$717$	−14.0000	−0.522840
$718$	4.00000	0.149279
$719$	−34.0000	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$720$	4.00000	0.149071
$721$	56.0000	2.08555
$722$	−3.00000	−0.111648
$723$	10.0000	0.371904
$724$	8.00000	0.297318
$725$	−66.0000	−2.45118
$726$	11.0000	0.408248
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−24.0000	−0.889499
$729$	1.00000	0.0370370
$730$	−56.0000	−2.07265
$731$	−24.0000	−0.887672
$732$	6.00000	0.221766
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	−8.00000	−0.295285
$735$	−36.0000	−1.32788
$736$	4.00000	0.147442
$737$	0	0
$738$	6.00000	0.220863
$739$	−52.0000	−1.91285	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000	−1.91285	−0.956425	+	0.291977i	$0.905687\pi$
$740$	−32.0000	−1.17634
$741$	−24.0000	−0.881662
$742$	−48.0000	−1.76214
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	2.00000	0.0733236
$745$	−24.0000	−0.879292
$746$	−32.0000	−1.17160
$747$	4.00000	0.146352
$748$	0	0
$749$	48.0000	1.75388
$750$	−24.0000	−0.876356
$751$	22.0000	0.802791	0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000	0.802791	0.401396	+	0.915905i	$0.368525\pi$
$752$	−8.00000	−0.291730
$753$	4.00000	0.145768
$754$	−36.0000	−1.31104
$755$	48.0000	1.74690
$756$	4.00000	0.145479
$757$	−50.0000	−1.81728	−0.908640	−	0.417579i	$-0.862879\pi$
$757$	−50.0000	−1.81728	−0.908640	+	0.417579i	$0.862879\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	16.0000	0.580381
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	6.00000	0.217357
$763$	40.0000	1.44810
$764$	10.0000	0.361787
$765$	−8.00000	−0.289241
$766$	−6.00000	−0.216789
$767$	−48.0000	−1.73318
$768$	−1.00000	−0.0360844
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	−2.00000	−0.0719816
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	12.0000	0.431331
$775$	−22.0000	−0.790263
$776$	6.00000	0.215387
$777$	−32.0000	−1.14799
$778$	30.0000	1.07555
$779$	24.0000	0.859889
$780$	−24.0000	−0.859338
$781$	0	0
$782$	−8.00000	−0.286079
$783$	6.00000	0.214423
$784$	9.00000	0.321429
$785$	−64.0000	−2.28426
$786$	1.00000	0.0356688
$787$	20.0000	0.712923	0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000	0.712923	0.356462	+	0.934310i	$0.383983\pi$
$788$	−18.0000	−0.641223
$789$	6.00000	0.213606
$790$	40.0000	1.42314
$791$	56.0000	1.99113
$792$	0	0
$793$	−36.0000	−1.27840
$794$	−2.00000	−0.0709773
$795$	−48.0000	−1.70238
$796$	−14.0000	−0.496217
$797$	24.0000	0.850124	0.425062	−	0.905164i	$-0.360252\pi$
$797$	24.0000	0.850124	0.425062	+	0.905164i	$0.360252\pi$
$798$	16.0000	0.566394
$799$	16.0000	0.566039
$800$	11.0000	0.388909
$801$	10.0000	0.353333
$802$	−14.0000	−0.494357
$803$	0	0
$804$	12.0000	0.423207
$805$	−64.0000	−2.25570
$806$	−12.0000	−0.422682
$807$	−16.0000	−0.563227
$808$	−4.00000	−0.140720
$809$	38.0000	1.33601	0.668004	−	0.744157i	$-0.267149\pi$
$809$	38.0000	1.33601	0.668004	+	0.744157i	$0.267149\pi$
$810$	4.00000	0.140546
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	24.0000	0.842235
$813$	−28.0000	−0.982003
$814$	0	0
$815$	−64.0000	−2.24182
$816$	2.00000	0.0700140
$817$	48.0000	1.67931
$818$	26.0000	0.909069
$819$	−24.0000	−0.838628
$820$	24.0000	0.838116
$821$	−16.0000	−0.558404	−0.279202	−	0.960232i	$-0.590070\pi$
$821$	−16.0000	−0.558404	−0.279202	+	0.960232i	$0.590070\pi$
$822$	−2.00000	−0.0697580
$823$	38.0000	1.32460	0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000	1.32460	0.662298	+	0.749240i	$0.269581\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	32.0000	1.11342
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	4.00000	0.139010
$829$	−6.00000	−0.208389	−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000	−0.208389	−0.104194	+	0.994557i	$0.533226\pi$
$830$	16.0000	0.555368
$831$	18.0000	0.624413
$832$	6.00000	0.208013
$833$	−18.0000	−0.623663
$834$	0	0
$835$	24.0000	0.830554
$836$	0	0
$837$	2.00000	0.0691301
$838$	36.0000	1.24360
$839$	22.0000	0.759524	0.379762	−	0.925084i	$-0.376006\pi$
$839$	22.0000	0.759524	0.379762	+	0.925084i	$0.376006\pi$
$840$	16.0000	0.552052
$841$	7.00000	0.241379
$842$	−6.00000	−0.206774
$843$	−26.0000	−0.895488
$844$	20.0000	0.688428
$845$	92.0000	3.16490
$846$	−8.00000	−0.275046
$847$	44.0000	1.51186
$848$	12.0000	0.412082
$849$	−4.00000	−0.137280
$850$	−22.0000	−0.754594
$851$	−32.0000	−1.09695
$852$	−4.00000	−0.137038
$853$	−44.0000	−1.50653	−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000	−1.50653	−0.753266	+	0.657716i	$0.771523\pi$
$854$	24.0000	0.821263
$855$	16.0000	0.547188
$856$	−12.0000	−0.410152
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	0	0
$859$	−32.0000	−1.09183	−0.545913	−	0.837842i	$-0.683817\pi$
$859$	−32.0000	−1.09183	−0.545913	+	0.837842i	$0.683817\pi$
$860$	48.0000	1.63679
$861$	24.0000	0.817918
$862$	−14.0000	−0.476842
$863$	−22.0000	−0.748889	−0.374444	−	0.927249i	$-0.622167\pi$
$863$	−22.0000	−0.748889	−0.374444	+	0.927249i	$0.622167\pi$
$864$	−1.00000	−0.0340207
$865$	−56.0000	−1.90406
$866$	−18.0000	−0.611665
$867$	13.0000	0.441503
$868$	8.00000	0.271538
$869$	0	0
$870$	24.0000	0.813676
$871$	−72.0000	−2.43963
$872$	−10.0000	−0.338643
$873$	6.00000	0.203069
$874$	16.0000	0.541208
$875$	−96.0000	−3.24539
$876$	14.0000	0.473016
$877$	−54.0000	−1.82345	−0.911725	−	0.410801i	$-0.865249\pi$
$877$	−54.0000	−1.82345	−0.911725	+	0.410801i	$0.865249\pi$
$878$	4.00000	0.134993
$879$	−26.0000	−0.876958
$880$	0	0
$881$	−50.0000	−1.68454	−0.842271	−	0.539054i	$-0.818782\pi$
$881$	−50.0000	−1.68454	−0.842271	+	0.539054i	$0.818782\pi$
$882$	9.00000	0.303046
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	−12.0000	−0.403604
$885$	32.0000	1.07567
$886$	36.0000	1.20944
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	8.00000	0.268462
$889$	24.0000	0.804934
$890$	40.0000	1.34080
$891$	0	0
$892$	−10.0000	−0.334825
$893$	−32.0000	−1.07084
$894$	6.00000	0.200670
$895$	−64.0000	−2.13928
$896$	−4.00000	−0.133631
$897$	−24.0000	−0.801337
$898$	14.0000	0.467186
$899$	12.0000	0.400222
$900$	11.0000	0.366667
$901$	−24.0000	−0.799556
$902$	0	0
$903$	48.0000	1.59734
$904$	−14.0000	−0.465633
$905$	32.0000	1.06372
$906$	−12.0000	−0.398673
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	12.0000	0.398234
$909$	−4.00000	−0.132672
$910$	−96.0000	−3.18237
$911$	−14.0000	−0.463841	−0.231920	−	0.972735i	$-0.574501\pi$
$911$	−14.0000	−0.463841	−0.231920	+	0.972735i	$0.574501\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	−10.0000	−0.330771
$915$	24.0000	0.793416
$916$	−4.00000	−0.132164
$917$	4.00000	0.132092
$918$	2.00000	0.0660098
$919$	22.0000	0.725713	0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000	0.725713	0.362857	+	0.931845i	$0.381802\pi$
$920$	16.0000	0.527504
$921$	−28.0000	−0.922631
$922$	6.00000	0.197599
$923$	24.0000	0.789970
$924$	0	0
$925$	−88.0000	−2.89342
$926$	10.0000	0.328620
$927$	−14.0000	−0.459820
$928$	−6.00000	−0.196960
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	8.00000	0.262330
$931$	36.0000	1.17985
$932$	2.00000	0.0655122
$933$	−30.0000	−0.982156
$934$	16.0000	0.523536
$935$	0	0
$936$	6.00000	0.196116
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	48.0000	1.56726
$939$	10.0000	0.326338
$940$	−32.0000	−1.04372
$941$	38.0000	1.23876	0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000	1.23876	0.619382	+	0.785090i	$0.287383\pi$
$942$	16.0000	0.521308
$943$	24.0000	0.781548
$944$	−8.00000	−0.260378
$945$	16.0000	0.520480
$946$	0	0
$947$	20.0000	0.649913	0.324956	−	0.945729i	$-0.394650\pi$
$947$	20.0000	0.649913	0.324956	+	0.945729i	$0.394650\pi$
$948$	−10.0000	−0.324785
$949$	−84.0000	−2.72676
$950$	44.0000	1.42755
$951$	−24.0000	−0.778253
$952$	8.00000	0.259281
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	12.0000	0.388514
$955$	40.0000	1.29437
$956$	14.0000	0.452792
$957$	0	0
$958$	−12.0000	−0.387702
$959$	−8.00000	−0.258333
$960$	−4.00000	−0.129099
$961$	−27.0000	−0.870968
$962$	−48.0000	−1.54758
$963$	−12.0000	−0.386695
$964$	−10.0000	−0.322078
$965$	−8.00000	−0.257529
$966$	16.0000	0.514792
$967$	6.00000	0.192947	0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000	0.192947	0.0964735	+	0.995336i	$0.469244\pi$
$968$	−11.0000	−0.353553
$969$	8.00000	0.256997
$970$	24.0000	0.770594
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−44.0000	−1.40985
$975$	−66.0000	−2.11369
$976$	−6.00000	−0.192055
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	16.0000	0.511624
$979$	0	0
$980$	36.0000	1.14998
$981$	−10.0000	−0.319275
$982$	−12.0000	−0.382935
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	−6.00000	−0.191273
$985$	−72.0000	−2.29411
$986$	12.0000	0.382158
$987$	−32.0000	−1.01857
$988$	24.0000	0.763542
$989$	48.0000	1.52631
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	−2.00000	−0.0635001
$993$	8.00000	0.253872
$994$	−16.0000	−0.507489
$995$	−56.0000	−1.77532
$996$	−4.00000	−0.126745
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−20.0000	−0.633089
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	786.2.a.k.1.1	✓	1
3.2	odd	2		2358.2.a.a.1.1		1
4.3	odd	2		6288.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
786.2.a.k.1.1	✓	1	1.1	even	1	trivial
2358.2.a.a.1.1		1	3.2	odd	2
6288.2.a.r.1.1		1	4.3	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:	\( N \)	\(=\)	\( 786 = 2 \cdot 3 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	786.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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