LMFDB - Embedded newform 794.2.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [794,2,Mod(1,794)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("794.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(794, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 794 = 2 \cdot 397 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	794.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$6.34012192049$
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	$\chi$	$=$	794.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} -3.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} +2.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} +5.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} -2.00000 q^{36} -8.00000 q^{37} -3.00000 q^{38} -1.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -11.0000 q^{43} -4.00000 q^{44} +2.00000 q^{45} +2.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -4.00000 q^{50} +6.00000 q^{51} +1.00000 q^{52} +3.00000 q^{53} +5.00000 q^{54} +4.00000 q^{55} +3.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} +4.00000 q^{66} -8.00000 q^{67} -6.00000 q^{68} -2.00000 q^{69} +9.00000 q^{71} -2.00000 q^{72} -10.0000 q^{73} -8.00000 q^{74} +4.00000 q^{75} -3.00000 q^{76} -1.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +11.0000 q^{83} +6.00000 q^{85} -11.0000 q^{86} -6.00000 q^{87} -4.00000 q^{88} -2.00000 q^{89} +2.00000 q^{90} +2.00000 q^{92} +2.00000 q^{93} +6.00000 q^{94} +3.00000 q^{95} -1.00000 q^{96} +13.0000 q^{97} -7.00000 q^{98} +8.00000 q^{99} +O(q^{100})\)

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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−2.00000	−0.471405
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	1.00000	0.196116
$27$	5.00000	0.962250
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	−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
$33$	4.00000	0.696311
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−3.00000	−0.486664
$39$	−1.00000	−0.160128
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	−11.0000	−1.67748	−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000	−1.67748	−0.838742	+	0.544529i	$0.816708\pi$
$44$	−4.00000	−0.603023
$45$	2.00000	0.298142
$46$	2.00000	0.294884
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	−4.00000	−0.565685
$51$	6.00000	0.840168
$52$	1.00000	0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	5.00000	0.680414
$55$	4.00000	0.539360
$56$	0	0
$57$	3.00000	0.397360
$58$	6.00000	0.787839
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	4.00000	0.492366
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−6.00000	−0.727607
$69$	−2.00000	−0.240772
$70$	0	0
$71$	9.00000	1.06810	0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000	1.06810	0.534052	+	0.845452i	$0.320669\pi$
$72$	−2.00000	−0.235702
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−8.00000	−0.929981
$75$	4.00000	0.461880
$76$	−3.00000	−0.344124
$77$	0	0
$78$	−1.00000	−0.113228
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	11.0000	1.20741	0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000	1.20741	0.603703	+	0.797209i	$0.293691\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	−11.0000	−1.18616
$87$	−6.00000	−0.643268
$88$	−4.00000	−0.426401
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	2.00000	0.210819
$91$	0	0
$92$	2.00000	0.208514
$93$	2.00000	0.207390
$94$	6.00000	0.618853
$95$	3.00000	0.307794
$96$	−1.00000	−0.102062
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	−7.00000	−0.707107
$99$	8.00000	0.804030
$100$	−4.00000	−0.400000
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	6.00000	0.594089
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	3.00000	0.291386
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	5.00000	0.481125
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	4.00000	0.381385
$111$	8.00000	0.759326
$112$	0	0
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	3.00000	0.280976
$115$	−2.00000	−0.186501
$116$	6.00000	0.557086
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	1.00000	0.0912871
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	2.00000	0.180334
$124$	−2.00000	−0.179605
$125$	9.00000	0.804984
$126$	0	0
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	1.00000	0.0883883
$129$	11.0000	0.968496
$130$	−1.00000	−0.0877058
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	−8.00000	−0.691095
$135$	−5.00000	−0.430331
$136$	−6.00000	−0.514496
$137$	−19.0000	−1.62328	−0.811640	−	0.584158i	$-0.801425\pi$
$137$	−19.0000	−1.62328	−0.811640	+	0.584158i	$0.801425\pi$
$138$	−2.00000	−0.170251
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	9.00000	0.755263
$143$	−4.00000	−0.334497
$144$	−2.00000	−0.166667
$145$	−6.00000	−0.498273
$146$	−10.0000	−0.827606
$147$	7.00000	0.577350
$148$	−8.00000	−0.657596
$149$	21.0000	1.72039	0.860194	−	0.509968i	$-0.170343\pi$
$149$	21.0000	1.72039	0.860194	+	0.509968i	$0.170343\pi$
$150$	4.00000	0.326599
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−3.00000	−0.243332
$153$	12.0000	0.970143
$154$	0	0
$155$	2.00000	0.160644
$156$	−1.00000	−0.0800641
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	0	0
$159$	−3.00000	−0.237915
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−2.00000	−0.156174
$165$	−4.00000	−0.311400
$166$	11.0000	0.853766
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	6.00000	0.460179
$171$	6.00000	0.458831
$172$	−11.0000	−0.838742
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−4.00000	−0.300658
$178$	−2.00000	−0.149906
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	2.00000	0.149071
$181$	−23.0000	−1.70958	−0.854788	−	0.518977i	$-0.826313\pi$
$181$	−23.0000	−1.70958	−0.854788	+	0.518977i	$0.826313\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	2.00000	0.147442
$185$	8.00000	0.588172
$186$	2.00000	0.146647
$187$	24.0000	1.75505
$188$	6.00000	0.437595
$189$	0	0
$190$	3.00000	0.217643
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	13.0000	0.933346
$195$	1.00000	0.0716115
$196$	−7.00000	−0.500000
$197$	−17.0000	−1.21120	−0.605600	−	0.795769i	$-0.707067\pi$
$197$	−17.0000	−1.21120	−0.605600	+	0.795769i	$0.707067\pi$
$198$	8.00000	0.568535
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	−4.00000	−0.282843
$201$	8.00000	0.564276
$202$	−3.00000	−0.211079
$203$	0	0
$204$	6.00000	0.420084
$205$	2.00000	0.139686
$206$	7.00000	0.487713
$207$	−4.00000	−0.278019
$208$	1.00000	0.0693375
$209$	12.0000	0.830057
$210$	0	0
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	3.00000	0.206041
$213$	−9.00000	−0.616670
$214$	3.00000	0.205076
$215$	11.0000	0.750194
$216$	5.00000	0.340207
$217$	0	0
$218$	−1.00000	−0.0677285
$219$	10.0000	0.675737
$220$	4.00000	0.269680
$221$	−6.00000	−0.403604
$222$	8.00000	0.536925
$223$	3.00000	0.200895	0.100447	−	0.994942i	$-0.467973\pi$
$223$	3.00000	0.200895	0.100447	+	0.994942i	$0.467973\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	−10.0000	−0.665190
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	3.00000	0.198680
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	−2.00000	−0.131876
$231$	0	0
$232$	6.00000	0.393919
$233$	−12.0000	−0.786146	−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000	−0.786146	−0.393073	+	0.919507i	$0.628588\pi$
$234$	−2.00000	−0.130744
$235$	−6.00000	−0.391397
$236$	4.00000	0.260378
$237$	0	0
$238$	0	0
$239$	5.00000	0.323423	0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000	0.323423	0.161712	+	0.986838i	$0.448299\pi$
$240$	1.00000	0.0645497
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	5.00000	0.321412
$243$	−16.0000	−1.02640
$244$	2.00000	0.128037
$245$	7.00000	0.447214
$246$	2.00000	0.127515
$247$	−3.00000	−0.190885
$248$	−2.00000	−0.127000
$249$	−11.0000	−0.697097
$250$	9.00000	0.569210
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	18.0000	1.12942
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−9.00000	−0.561405	−0.280702	−	0.959795i	$-0.590567\pi$
$257$	−9.00000	−0.561405	−0.280702	+	0.959795i	$0.590567\pi$
$258$	11.0000	0.684830
$259$	0	0
$260$	−1.00000	−0.0620174
$261$	−12.0000	−0.742781
$262$	0	0
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	4.00000	0.246183
$265$	−3.00000	−0.184289
$266$	0	0
$267$	2.00000	0.122398
$268$	−8.00000	−0.488678
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−5.00000	−0.304290
$271$	−26.0000	−1.57939	−0.789694	−	0.613501i	$-0.789761\pi$
$271$	−26.0000	−1.57939	−0.789694	+	0.613501i	$0.789761\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	−19.0000	−1.14783
$275$	16.0000	0.964836
$276$	−2.00000	−0.120386
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	0	0
$279$	4.00000	0.239474
$280$	0	0
$281$	−29.0000	−1.72999	−0.864997	−	0.501776i	$-0.832680\pi$
$281$	−29.0000	−1.72999	−0.864997	+	0.501776i	$0.832680\pi$
$282$	−6.00000	−0.357295
$283$	−10.0000	−0.594438	−0.297219	−	0.954809i	$-0.596059\pi$
$283$	−10.0000	−0.594438	−0.297219	+	0.954809i	$0.596059\pi$
$284$	9.00000	0.534052
$285$	−3.00000	−0.177705
$286$	−4.00000	−0.236525
$287$	0	0
$288$	−2.00000	−0.117851
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	−13.0000	−0.762073
$292$	−10.0000	−0.585206
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	7.00000	0.408248
$295$	−4.00000	−0.232889
$296$	−8.00000	−0.464991
$297$	−20.0000	−1.16052
$298$	21.0000	1.21650
$299$	2.00000	0.115663
$300$	4.00000	0.230940
$301$	0	0
$302$	0	0
$303$	3.00000	0.172345
$304$	−3.00000	−0.172062
$305$	−2.00000	−0.114520
$306$	12.0000	0.685994
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	0	0
$309$	−7.00000	−0.398216
$310$	2.00000	0.113592
$311$	5.00000	0.283524	0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000	0.283524	0.141762	+	0.989901i	$0.454723\pi$
$312$	−1.00000	−0.0566139
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	5.00000	0.282166
$315$	0	0
$316$	0	0
$317$	−27.0000	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	−3.00000	−0.168232
$319$	−24.0000	−1.34374
$320$	−1.00000	−0.0559017
$321$	−3.00000	−0.167444
$322$	0	0
$323$	18.0000	1.00155
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	4.00000	0.221540
$327$	1.00000	0.0553001
$328$	−2.00000	−0.110432
$329$	0	0
$330$	−4.00000	−0.220193
$331$	6.00000	0.329790	0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000	0.329790	0.164895	+	0.986311i	$0.447272\pi$
$332$	11.0000	0.603703
$333$	16.0000	0.876795
$334$	−14.0000	−0.766046
$335$	8.00000	0.437087
$336$	0	0
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	−12.0000	−0.652714
$339$	10.0000	0.543125
$340$	6.00000	0.325396
$341$	8.00000	0.433224
$342$	6.00000	0.324443
$343$	0	0
$344$	−11.0000	−0.593080
$345$	2.00000	0.107676
$346$	24.0000	1.29025
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	−6.00000	−0.321634
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	−4.00000	−0.213201
$353$	31.0000	1.64996	0.824982	−	0.565159i	$-0.191185\pi$
$353$	31.0000	1.64996	0.824982	+	0.565159i	$0.191185\pi$
$354$	−4.00000	−0.212598
$355$	−9.00000	−0.477670
$356$	−2.00000	−0.106000
$357$	0	0
$358$	−3.00000	−0.158555
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	2.00000	0.105409
$361$	−10.0000	−0.526316
$362$	−23.0000	−1.20885
$363$	−5.00000	−0.262432
$364$	0	0
$365$	10.0000	0.523424
$366$	−2.00000	−0.104542
$367$	−24.0000	−1.25279	−0.626395	−	0.779506i	$-0.715470\pi$
$367$	−24.0000	−1.25279	−0.626395	+	0.779506i	$0.715470\pi$
$368$	2.00000	0.104257
$369$	4.00000	0.208232
$370$	8.00000	0.415900
$371$	0	0
$372$	2.00000	0.103695
$373$	−13.0000	−0.673114	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000	−0.673114	−0.336557	+	0.941663i	$0.609263\pi$
$374$	24.0000	1.24101
$375$	−9.00000	−0.464758
$376$	6.00000	0.309426
$377$	6.00000	0.309016
$378$	0	0
$379$	10.0000	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	3.00000	0.153897
$381$	−18.0000	−0.922168
$382$	0	0
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−16.0000	−0.814379
$387$	22.0000	1.11832
$388$	13.0000	0.659975
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	1.00000	0.0506370
$391$	−12.0000	−0.606866
$392$	−7.00000	−0.353553
$393$	0	0
$394$	−17.0000	−0.856448
$395$	0	0
$396$	8.00000	0.402015
$397$	1.00000	0.0501886
$397$	1.00000	0.0501886
$398$	7.00000	0.350878
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	8.00000	0.399004
$403$	−2.00000	−0.0996271
$404$	−3.00000	−0.149256
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	32.0000	1.58618
$408$	6.00000	0.297044
$409$	27.0000	1.33506	0.667532	−	0.744581i	$-0.267351\pi$
$409$	27.0000	1.33506	0.667532	+	0.744581i	$0.267351\pi$
$410$	2.00000	0.0987730
$411$	19.0000	0.937201
$412$	7.00000	0.344865
$413$	0	0
$414$	−4.00000	−0.196589
$415$	−11.0000	−0.539969
$416$	1.00000	0.0490290
$417$	0	0
$418$	12.0000	0.586939
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−14.0000	−0.681509
$423$	−12.0000	−0.583460
$424$	3.00000	0.145693
$425$	24.0000	1.16417
$426$	−9.00000	−0.436051
$427$	0	0
$428$	3.00000	0.145010
$429$	4.00000	0.193122
$430$	11.0000	0.530467
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	5.00000	0.240563
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−1.00000	−0.0478913
$437$	−6.00000	−0.287019
$438$	10.0000	0.477818
$439$	−36.0000	−1.71819	−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000	−1.71819	−0.859093	+	0.511819i	$0.828972\pi$
$440$	4.00000	0.190693
$441$	14.0000	0.666667
$442$	−6.00000	−0.285391
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	8.00000	0.379663
$445$	2.00000	0.0948091
$446$	3.00000	0.142054
$447$	−21.0000	−0.993266
$448$	0	0
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	8.00000	0.377124
$451$	8.00000	0.376705
$452$	−10.0000	−0.470360
$453$	0	0
$454$	24.0000	1.12638
$455$	0	0
$456$	3.00000	0.140488
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	14.0000	0.654177
$459$	−30.0000	−1.40028
$460$	−2.00000	−0.0932505
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	31.0000	1.44069	0.720346	−	0.693615i	$-0.243983\pi$
$463$	31.0000	1.44069	0.720346	+	0.693615i	$0.243983\pi$
$464$	6.00000	0.278543
$465$	−2.00000	−0.0927478
$466$	−12.0000	−0.555889
$467$	2.00000	0.0925490	0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000	0.0925490	0.0462745	+	0.998929i	$0.485265\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	−6.00000	−0.276759
$471$	−5.00000	−0.230388
$472$	4.00000	0.184115
$473$	44.0000	2.02312
$474$	0	0
$475$	12.0000	0.550598
$476$	0	0
$477$	−6.00000	−0.274721
$478$	5.00000	0.228695
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	1.00000	0.0456435
$481$	−8.00000	−0.364769
$482$	−26.0000	−1.18427
$483$	0	0
$484$	5.00000	0.227273
$485$	−13.0000	−0.590300
$486$	−16.0000	−0.725775
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	2.00000	0.0905357
$489$	−4.00000	−0.180886
$490$	7.00000	0.316228
$491$	−40.0000	−1.80517	−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000	−1.80517	−0.902587	+	0.430507i	$0.858335\pi$
$492$	2.00000	0.0901670
$493$	−36.0000	−1.62136
$494$	−3.00000	−0.134976
$495$	−8.00000	−0.359573
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−11.0000	−0.492922
$499$	−11.0000	−0.492428	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−11.0000	−0.492428	−0.246214	+	0.969216i	$0.579187\pi$
$500$	9.00000	0.402492
$501$	14.0000	0.625474
$502$	8.00000	0.357057
$503$	20.0000	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$504$	0	0
$505$	3.00000	0.133498
$506$	−8.00000	−0.355643
$507$	12.0000	0.532939
$508$	18.0000	0.798621
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	−6.00000	−0.265684
$511$	0	0
$512$	1.00000	0.0441942
$513$	−15.0000	−0.662266
$514$	−9.00000	−0.396973
$515$	−7.00000	−0.308457
$516$	11.0000	0.484248
$517$	−24.0000	−1.05552
$518$	0	0
$519$	−24.0000	−1.05348
$520$	−1.00000	−0.0438529
$521$	1.00000	0.0438108	0.0219054	−	0.999760i	$-0.493027\pi$
$521$	1.00000	0.0438108	0.0219054	+	0.999760i	$0.493027\pi$
$522$	−12.0000	−0.525226
$523$	−13.0000	−0.568450	−0.284225	−	0.958758i	$-0.591736\pi$
$523$	−13.0000	−0.568450	−0.284225	+	0.958758i	$0.591736\pi$
$524$	0	0
$525$	0	0
$526$	−9.00000	−0.392419
$527$	12.0000	0.522728
$528$	4.00000	0.174078
$529$	−19.0000	−0.826087
$530$	−3.00000	−0.130312
$531$	−8.00000	−0.347170
$532$	0	0
$533$	−2.00000	−0.0866296
$534$	2.00000	0.0865485
$535$	−3.00000	−0.129701
$536$	−8.00000	−0.345547
$537$	3.00000	0.129460
$538$	−18.0000	−0.776035
$539$	28.0000	1.20605
$540$	−5.00000	−0.215166
$541$	8.00000	0.343947	0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000	0.343947	0.171973	+	0.985102i	$0.444986\pi$
$542$	−26.0000	−1.11680
$543$	23.0000	0.987024
$544$	−6.00000	−0.257248
$545$	1.00000	0.0428353
$546$	0	0
$547$	10.0000	0.427569	0.213785	−	0.976881i	$-0.431421\pi$
$547$	10.0000	0.427569	0.213785	+	0.976881i	$0.431421\pi$
$548$	−19.0000	−0.811640
$549$	−4.00000	−0.170716
$550$	16.0000	0.682242
$551$	−18.0000	−0.766826
$552$	−2.00000	−0.0851257
$553$	0	0
$554$	18.0000	0.764747
$555$	−8.00000	−0.339581
$556$	0	0
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	4.00000	0.169334
$559$	−11.0000	−0.465250
$560$	0	0
$561$	−24.0000	−1.01328
$562$	−29.0000	−1.22329
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	−6.00000	−0.252646
$565$	10.0000	0.420703
$566$	−10.0000	−0.420331
$567$	0	0
$568$	9.00000	0.377632
$569$	5.00000	0.209611	0.104805	−	0.994493i	$-0.466578\pi$
$569$	5.00000	0.209611	0.104805	+	0.994493i	$0.466578\pi$
$570$	−3.00000	−0.125656
$571$	−30.0000	−1.25546	−0.627730	−	0.778431i	$-0.716016\pi$
$571$	−30.0000	−1.25546	−0.627730	+	0.778431i	$0.716016\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	0	0
$575$	−8.00000	−0.333623
$576$	−2.00000	−0.0833333
$577$	−32.0000	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$578$	19.0000	0.790296
$579$	16.0000	0.664937
$580$	−6.00000	−0.249136
$581$	0	0
$582$	−13.0000	−0.538867
$583$	−12.0000	−0.496989
$584$	−10.0000	−0.413803
$585$	2.00000	0.0826898
$586$	−18.0000	−0.743573
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	7.00000	0.288675
$589$	6.00000	0.247226
$590$	−4.00000	−0.164677
$591$	17.0000	0.699287
$592$	−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	$0.254026\pi$
$594$	−20.0000	−0.820610
$595$	0	0
$596$	21.0000	0.860194
$597$	−7.00000	−0.286491
$598$	2.00000	0.0817861
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	4.00000	0.163299
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	16.0000	0.651570
$604$	0	0
$605$	−5.00000	−0.203279
$606$	3.00000	0.121867
$607$	−13.0000	−0.527654	−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000	−0.527654	−0.263827	+	0.964570i	$0.584985\pi$
$608$	−3.00000	−0.121666
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	6.00000	0.242734
$612$	12.0000	0.485071
$613$	41.0000	1.65597	0.827987	−	0.560747i	$-0.189486\pi$
$613$	41.0000	1.65597	0.827987	+	0.560747i	$0.189486\pi$
$614$	23.0000	0.928204
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	−7.00000	−0.281581
$619$	2.00000	0.0803868	0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000	0.0803868	0.0401934	+	0.999192i	$0.487203\pi$
$620$	2.00000	0.0803219
$621$	10.0000	0.401286
$622$	5.00000	0.200482
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	11.0000	0.440000
$626$	−18.0000	−0.719425
$627$	−12.0000	−0.479234
$628$	5.00000	0.199522
$629$	48.0000	1.91389
$630$	0	0
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	0	0
$633$	14.0000	0.556450
$634$	−27.0000	−1.07231
$635$	−18.0000	−0.714308
$636$	−3.00000	−0.118958
$637$	−7.00000	−0.277350
$638$	−24.0000	−0.950169
$639$	−18.0000	−0.712069
$640$	−1.00000	−0.0395285
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	−3.00000	−0.118401
$643$	−25.0000	−0.985904	−0.492952	−	0.870057i	$-0.664082\pi$
$643$	−25.0000	−0.985904	−0.492952	+	0.870057i	$0.664082\pi$
$644$	0	0
$645$	−11.0000	−0.433125
$646$	18.0000	0.708201
$647$	18.0000	0.707653	0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000	0.707653	0.353827	+	0.935311i	$0.384880\pi$
$648$	1.00000	0.0392837
$649$	−16.0000	−0.628055
$650$	−4.00000	−0.156893
$651$	0	0
$652$	4.00000	0.156652
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	1.00000	0.0391031
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	20.0000	0.780274
$658$	0	0
$659$	44.0000	1.71400	0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000	1.71400	0.856998	+	0.515319i	$0.172327\pi$
$660$	−4.00000	−0.155700
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	6.00000	0.233197
$663$	6.00000	0.233021
$664$	11.0000	0.426883
$665$	0	0
$666$	16.0000	0.619987
$667$	12.0000	0.464642
$668$	−14.0000	−0.541676
$669$	−3.00000	−0.115987
$670$	8.00000	0.309067
$671$	−8.00000	−0.308837
$672$	0	0
$673$	−35.0000	−1.34915	−0.674575	−	0.738206i	$-0.735673\pi$
$673$	−35.0000	−1.34915	−0.674575	+	0.738206i	$0.735673\pi$
$674$	−6.00000	−0.231111
$675$	−20.0000	−0.769800
$676$	−12.0000	−0.461538
$677$	15.0000	0.576497	0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000	0.576497	0.288248	+	0.957556i	$0.406927\pi$
$678$	10.0000	0.384048
$679$	0	0
$680$	6.00000	0.230089
$681$	−24.0000	−0.919682
$682$	8.00000	0.306336
$683$	41.0000	1.56882	0.784411	−	0.620242i	$-0.212966\pi$
$683$	41.0000	1.56882	0.784411	+	0.620242i	$0.212966\pi$
$684$	6.00000	0.229416
$685$	19.0000	0.725953
$686$	0	0
$687$	−14.0000	−0.534133
$688$	−11.0000	−0.419371
$689$	3.00000	0.114291
$690$	2.00000	0.0761387
$691$	−16.0000	−0.608669	−0.304334	−	0.952565i	$-0.598434\pi$
$691$	−16.0000	−0.608669	−0.304334	+	0.952565i	$0.598434\pi$
$692$	24.0000	0.912343
$693$	0	0
$694$	30.0000	1.13878
$695$	0	0
$696$	−6.00000	−0.227429
$697$	12.0000	0.454532
$698$	26.0000	0.984115
$699$	12.0000	0.453882
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	5.00000	0.188713
$703$	24.0000	0.905177
$704$	−4.00000	−0.150756
$705$	6.00000	0.225973
$706$	31.0000	1.16670
$707$	0	0
$708$	−4.00000	−0.150329
$709$	12.0000	0.450669	0.225335	−	0.974281i	$-0.427652\pi$
$709$	12.0000	0.450669	0.225335	+	0.974281i	$0.427652\pi$
$710$	−9.00000	−0.337764
$711$	0	0
$712$	−2.00000	−0.0749532
$713$	−4.00000	−0.149801
$714$	0	0
$715$	4.00000	0.149592
$716$	−3.00000	−0.112115
$717$	−5.00000	−0.186728
$718$	−21.0000	−0.783713
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−10.0000	−0.372161
$723$	26.0000	0.966950
$724$	−23.0000	−0.854788
$725$	−24.0000	−0.891338
$726$	−5.00000	−0.185567
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	10.0000	0.370117
$731$	66.0000	2.44110
$732$	−2.00000	−0.0739221
$733$	38.0000	1.40356	0.701781	−	0.712393i	$-0.252388\pi$
$733$	38.0000	1.40356	0.701781	+	0.712393i	$0.252388\pi$
$734$	−24.0000	−0.885856
$735$	−7.00000	−0.258199
$736$	2.00000	0.0737210
$737$	32.0000	1.17874
$738$	4.00000	0.147242
$739$	−38.0000	−1.39785	−0.698926	−	0.715194i	$-0.746338\pi$
$739$	−38.0000	−1.39785	−0.698926	+	0.715194i	$0.746338\pi$
$740$	8.00000	0.294086
$741$	3.00000	0.110208
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	2.00000	0.0733236
$745$	−21.0000	−0.769380
$746$	−13.0000	−0.475964
$747$	−22.0000	−0.804938
$748$	24.0000	0.877527
$749$	0	0
$750$	−9.00000	−0.328634
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	6.00000	0.218797
$753$	−8.00000	−0.291536
$754$	6.00000	0.218507
$755$	0	0
$756$	0	0
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	10.0000	0.363216
$759$	8.00000	0.290382
$760$	3.00000	0.108821
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	−18.0000	−0.652071
$763$	0	0
$764$	0	0
$765$	−12.0000	−0.433861
$766$	−10.0000	−0.361315
$767$	4.00000	0.144432
$768$	−1.00000	−0.0360844
$769$	7.00000	0.252426	0.126213	−	0.992003i	$-0.459718\pi$
$769$	7.00000	0.252426	0.126213	+	0.992003i	$0.459718\pi$
$770$	0	0
$771$	9.00000	0.324127
$772$	−16.0000	−0.575853
$773$	19.0000	0.683383	0.341691	−	0.939812i	$-0.389000\pi$
$773$	19.0000	0.683383	0.341691	+	0.939812i	$0.389000\pi$
$774$	22.0000	0.790774
$775$	8.00000	0.287368
$776$	13.0000	0.466673
$777$	0	0
$778$	−10.0000	−0.358517
$779$	6.00000	0.214972
$780$	1.00000	0.0358057
$781$	−36.0000	−1.28818
$782$	−12.0000	−0.429119
$783$	30.0000	1.07211
$784$	−7.00000	−0.250000
$785$	−5.00000	−0.178458
$786$	0	0
$787$	−10.0000	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$787$	−10.0000	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$788$	−17.0000	−0.605600
$789$	9.00000	0.320408
$790$	0	0
$791$	0	0
$792$	8.00000	0.284268
$793$	2.00000	0.0710221
$794$	1.00000	0.0354887
$795$	3.00000	0.106399
$796$	7.00000	0.248108
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	−4.00000	−0.141421
$801$	4.00000	0.141333
$802$	−27.0000	−0.953403
$803$	40.0000	1.41157
$804$	8.00000	0.282138
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	18.0000	0.633630
$808$	−3.00000	−0.105540
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	−1.00000	−0.0351364
$811$	−4.00000	−0.140459	−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000	−0.140459	−0.0702295	+	0.997531i	$0.522373\pi$
$812$	0	0
$813$	26.0000	0.911860
$814$	32.0000	1.12160
$815$	−4.00000	−0.140114
$816$	6.00000	0.210042
$817$	33.0000	1.15452
$818$	27.0000	0.944033
$819$	0	0
$820$	2.00000	0.0698430
$821$	20.0000	0.698005	0.349002	−	0.937122i	$-0.386521\pi$
$821$	20.0000	0.698005	0.349002	+	0.937122i	$0.386521\pi$
$822$	19.0000	0.662701
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	7.00000	0.243857
$825$	−16.0000	−0.557048
$826$	0	0
$827$	−27.0000	−0.938882	−0.469441	−	0.882964i	$-0.655545\pi$
$827$	−27.0000	−0.938882	−0.469441	+	0.882964i	$0.655545\pi$
$828$	−4.00000	−0.139010
$829$	48.0000	1.66711	0.833554	−	0.552437i	$-0.186302\pi$
$829$	48.0000	1.66711	0.833554	+	0.552437i	$0.186302\pi$
$830$	−11.0000	−0.381816
$831$	−18.0000	−0.624413
$832$	1.00000	0.0346688
$833$	42.0000	1.45521
$834$	0	0
$835$	14.0000	0.484490
$836$	12.0000	0.415029
$837$	−10.0000	−0.345651
$838$	−12.0000	−0.414533
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−22.0000	−0.758170
$843$	29.0000	0.998813
$844$	−14.0000	−0.481900
$845$	12.0000	0.412813
$846$	−12.0000	−0.412568
$847$	0	0
$848$	3.00000	0.103020
$849$	10.0000	0.343199
$850$	24.0000	0.823193
$851$	−16.0000	−0.548473
$852$	−9.00000	−0.308335
$853$	−21.0000	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$854$	0	0
$855$	−6.00000	−0.205196
$856$	3.00000	0.102538
$857$	4.00000	0.136637	0.0683187	−	0.997664i	$-0.478237\pi$
$857$	4.00000	0.136637	0.0683187	+	0.997664i	$0.478237\pi$
$858$	4.00000	0.136558
$859$	23.0000	0.784750	0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000	0.784750	0.392375	+	0.919805i	$0.371654\pi$
$860$	11.0000	0.375097
$861$	0	0
$862$	−30.0000	−1.02180
$863$	32.0000	1.08929	0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000	1.08929	0.544646	+	0.838666i	$0.316664\pi$
$864$	5.00000	0.170103
$865$	−24.0000	−0.816024
$866$	14.0000	0.475739
$867$	−19.0000	−0.645274
$868$	0	0
$869$	0	0
$870$	6.00000	0.203419
$871$	−8.00000	−0.271070
$872$	−1.00000	−0.0338643
$873$	−26.0000	−0.879967
$874$	−6.00000	−0.202953
$875$	0	0
$876$	10.0000	0.337869
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	−36.0000	−1.21494
$879$	18.0000	0.607125
$880$	4.00000	0.134840
$881$	3.00000	0.101073	0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000	0.101073	0.0505363	+	0.998722i	$0.483907\pi$
$882$	14.0000	0.471405
$883$	50.0000	1.68263	0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000	1.68263	0.841317	+	0.540542i	$0.181781\pi$
$884$	−6.00000	−0.201802
$885$	4.00000	0.134459
$886$	−6.00000	−0.201574
$887$	−30.0000	−1.00730	−0.503651	−	0.863907i	$-0.668010\pi$
$887$	−30.0000	−1.00730	−0.503651	+	0.863907i	$0.668010\pi$
$888$	8.00000	0.268462
$889$	0	0
$890$	2.00000	0.0670402
$891$	−4.00000	−0.134005
$892$	3.00000	0.100447
$893$	−18.0000	−0.602347
$894$	−21.0000	−0.702345
$895$	3.00000	0.100279
$896$	0	0
$897$	−2.00000	−0.0667781
$898$	−12.0000	−0.400445
$899$	−12.0000	−0.400222
$900$	8.00000	0.266667
$901$	−18.0000	−0.599667
$902$	8.00000	0.266371
$903$	0	0
$904$	−10.0000	−0.332595
$905$	23.0000	0.764546
$906$	0	0
$907$	−52.0000	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$908$	24.0000	0.796468
$909$	6.00000	0.199007
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	3.00000	0.0993399
$913$	−44.0000	−1.45619
$914$	2.00000	0.0661541
$915$	2.00000	0.0661180
$916$	14.0000	0.462573
$917$	0	0
$918$	−30.0000	−0.990148
$919$	−51.0000	−1.68233	−0.841167	−	0.540775i	$-0.818131\pi$
$919$	−51.0000	−1.68233	−0.841167	+	0.540775i	$0.818131\pi$
$920$	−2.00000	−0.0659380
$921$	−23.0000	−0.757876
$922$	−18.0000	−0.592798
$923$	9.00000	0.296239
$924$	0	0
$925$	32.0000	1.05215
$926$	31.0000	1.01872
$927$	−14.0000	−0.459820
$928$	6.00000	0.196960
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	−2.00000	−0.0655826
$931$	21.0000	0.688247
$932$	−12.0000	−0.393073
$933$	−5.00000	−0.163693
$934$	2.00000	0.0654420
$935$	−24.0000	−0.784884
$936$	−2.00000	−0.0653720
$937$	46.0000	1.50275	0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000	1.50275	0.751377	+	0.659873i	$0.229390\pi$
$938$	0	0
$939$	18.0000	0.587408
$940$	−6.00000	−0.195698
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	−5.00000	−0.162909
$943$	−4.00000	−0.130258
$944$	4.00000	0.130189
$945$	0	0
$946$	44.0000	1.43056
$947$	30.0000	0.974869	0.487435	−	0.873160i	$-0.337933\pi$
$947$	30.0000	0.974869	0.487435	+	0.873160i	$0.337933\pi$
$948$	0	0
$949$	−10.0000	−0.324614
$950$	12.0000	0.389331
$951$	27.0000	0.875535
$952$	0	0
$953$	−48.0000	−1.55487	−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000	−1.55487	−0.777436	+	0.628962i	$0.783480\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	5.00000	0.161712
$957$	24.0000	0.775810
$958$	0	0
$959$	0	0
$960$	1.00000	0.0322749
$961$	−27.0000	−0.870968
$962$	−8.00000	−0.257930
$963$	−6.00000	−0.193347
$964$	−26.0000	−0.837404
$965$	16.0000	0.515058
$966$	0	0
$967$	36.0000	1.15768	0.578841	−	0.815440i	$-0.303505\pi$
$967$	36.0000	1.15768	0.578841	+	0.815440i	$0.303505\pi$
$968$	5.00000	0.160706
$969$	−18.0000	−0.578243
$970$	−13.0000	−0.417405
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	−16.0000	−0.513200
$973$	0	0
$974$	28.0000	0.897178
$975$	4.00000	0.128103
$976$	2.00000	0.0640184
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	−4.00000	−0.127906
$979$	8.00000	0.255681
$980$	7.00000	0.223607
$981$	2.00000	0.0638551
$982$	−40.0000	−1.27645
$983$	3.00000	0.0956851	0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000	0.0956851	0.0478426	+	0.998855i	$0.484765\pi$
$984$	2.00000	0.0637577
$985$	17.0000	0.541665
$986$	−36.0000	−1.14647
$987$	0	0
$988$	−3.00000	−0.0954427
$989$	−22.0000	−0.699559
$990$	−8.00000	−0.254257
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	−2.00000	−0.0635001
$993$	−6.00000	−0.190404
$994$	0	0
$995$	−7.00000	−0.221915
$996$	−11.0000	−0.348548
$997$	3.00000	0.0950110	0.0475055	−	0.998871i	$-0.484873\pi$
$997$	3.00000	0.0950110	0.0475055	+	0.998871i	$0.484873\pi$
$998$	−11.0000	−0.348199
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	794.2.a.c.1.1	✓	1
3.2	odd	2		7146.2.a.f.1.1		1
4.3	odd	2		6352.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
794.2.a.c.1.1	✓	1	1.1	even	1	trivial
6352.2.a.b.1.1		1	4.3	odd	2
7146.2.a.f.1.1		1	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 794 = 2 \cdot 397 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	794.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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