LMFDB - Embedded newform 7803.2.a.cg.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7803,2,Mod(1,7803)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7803, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7803.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 7803 = 3^{3} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7803.a (trivial)

Newform invariants

comment:select newform

sage:traces = [24,0,0,24,20,0,0,0,0,0,8,0,4,16,0,24,0,0,4,48,0,0,36,0,28,0, 0,0,64,0,0,0,0,0,0,0,0,0,0,0,36,0,4,16,0,0,0,0,24,0,0,16,0,0,20,80,0,0, 0,0,0,-16,0,-24,72,0,16,0,0,-48,72,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(73)] == traces)

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

Self dual:	yes
Analytic conductor:	$62.3072686972$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 459)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	7803.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.313123 q^{2} -1.90195 q^{4} -0.0595634 q^{5} +2.67689 q^{7} -1.22179 q^{8} -0.0186507 q^{10} -5.42825 q^{11} -0.468997 q^{13} +0.838195 q^{14} +3.42134 q^{16} -6.86939 q^{19} +0.113287 q^{20} -1.69971 q^{22} -5.26114 q^{23} -4.99645 q^{25} -0.146854 q^{26} -5.09133 q^{28} +2.40874 q^{29} +3.15540 q^{31} +3.51488 q^{32} -0.159445 q^{35} -7.50219 q^{37} -2.15096 q^{38} +0.0727740 q^{40} +2.22712 q^{41} -4.51587 q^{43} +10.3243 q^{44} -1.64738 q^{46} +9.24764 q^{47} +0.165753 q^{49} -1.56450 q^{50} +0.892011 q^{52} +12.9263 q^{53} +0.323325 q^{55} -3.27060 q^{56} +0.754230 q^{58} +9.43019 q^{59} -1.82014 q^{61} +0.988026 q^{62} -5.74209 q^{64} +0.0279351 q^{65} -3.18673 q^{67} -0.0499258 q^{70} -4.32016 q^{71} +11.9409 q^{73} -2.34910 q^{74} +13.0653 q^{76} -14.5308 q^{77} +10.6746 q^{79} -0.203787 q^{80} +0.697360 q^{82} +8.70940 q^{83} -1.41402 q^{86} +6.63217 q^{88} -15.9437 q^{89} -1.25545 q^{91} +10.0065 q^{92} +2.89564 q^{94} +0.409164 q^{95} -3.48884 q^{97} +0.0519011 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 20 q^{5} + 8 q^{11} + 4 q^{13} + 16 q^{14} + 24 q^{16} + 4 q^{19} + 48 q^{20} + 36 q^{23} + 28 q^{25} + 64 q^{29} + 36 q^{41} + 4 q^{43} + 16 q^{44} + 24 q^{49} + 16 q^{52} + 20 q^{55}+ \cdots - 12 q^{95}+O(q^{100}) $ 24 * q + 24 * q^4 + 20 * q^5 + 8 * q^11 + 4 * q^13 + 16 * q^14 + 24 * q^16 + 4 * q^19 + 48 * q^20 + 36 * q^23 + 28 * q^25 + 64 * q^29 + 36 * q^41 + 4 * q^43 + 16 * q^44 + 24 * q^49 + 16 * q^52 + 20 * q^55 + 80 * q^56 - 16 * q^62 - 24 * q^64 + 72 * q^65 + 16 * q^67 - 48 * q^70 + 72 * q^71 + 80 * q^74 - 40 * q^76 + 104 * q^80 + 144 * q^92 - 72 * q^94 - 12 * q^95

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 $

$2$	0.313123	0.221411	0.110706	−	0.993853i	$-0.464689\pi$
$2$	0.313123	0.221411	0.110706	+	0.993853i	$0.464689\pi$
$3$	0	0
$3$	0	0
$4$	−1.90195	−0.950977
$5$	−0.0595634	−0.0266376	−0.0133188	−	0.999911i	$-0.504240\pi$
$5$	−0.0595634	−0.0266376	−0.0133188	+	0.999911i	$0.504240\pi$
$6$	0	0
$7$	2.67689	1.01177	0.505885	−	0.862601i	$-0.331166\pi$
$7$	2.67689	1.01177	0.505885	+	0.862601i	$0.331166\pi$
$8$	−1.22179	−0.431968
$9$	0	0
$10$	−0.0186507	−0.00589786
$11$	−5.42825	−1.63668	−0.818339	−	0.574736i	$-0.805105\pi$
$11$	−5.42825	−1.63668	−0.818339	+	0.574736i	$0.805105\pi$
$12$	0	0
$13$	−0.468997	−0.130076	−0.0650382	−	0.997883i	$-0.520717\pi$
$13$	−0.468997	−0.130076	−0.0650382	+	0.997883i	$0.520717\pi$
$14$	0.838195	0.224017
$15$	0	0
$16$	3.42134	0.855335
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−6.86939	−1.57595	−0.787973	−	0.615710i	$-0.788869\pi$
$19$	−6.86939	−1.57595	−0.787973	+	0.615710i	$0.788869\pi$
$20$	0.113287	0.0253317
$21$	0	0
$22$	−1.69971	−0.362378
$23$	−5.26114	−1.09702	−0.548512	−	0.836143i	$-0.684806\pi$
$23$	−5.26114	−1.09702	−0.548512	+	0.836143i	$0.684806\pi$
$24$	0	0
$25$	−4.99645	−0.999290
$26$	−0.146854	−0.0288003
$27$	0	0
$28$	−5.09133	−0.962170
$29$	2.40874	0.447291	0.223646	−	0.974670i	$-0.428204\pi$
$29$	2.40874	0.447291	0.223646	+	0.974670i	$0.428204\pi$
$30$	0	0
$31$	3.15540	0.566726	0.283363	−	0.959013i	$-0.408550\pi$
$31$	3.15540	0.566726	0.283363	+	0.959013i	$0.408550\pi$
$32$	3.51488	0.621348
$33$	0	0
$34$	0	0
$35$	−0.159445	−0.0269511
$36$	0	0
$37$	−7.50219	−1.23335	−0.616676	−	0.787217i	$-0.711521\pi$
$37$	−7.50219	−1.23335	−0.616676	+	0.787217i	$0.711521\pi$
$38$	−2.15096	−0.348932
$39$	0	0
$40$	0.0727740	0.0115066
$41$	2.22712	0.347817	0.173909	−	0.984762i	$-0.444360\pi$
$41$	2.22712	0.347817	0.173909	+	0.984762i	$0.444360\pi$
$42$	0	0
$43$	−4.51587	−0.688664	−0.344332	−	0.938848i	$-0.611895\pi$
$43$	−4.51587	−0.688664	−0.344332	+	0.938848i	$0.611895\pi$
$44$	10.3243	1.55644
$45$	0	0
$46$	−1.64738	−0.242893
$47$	9.24764	1.34891	0.674453	−	0.738317i	$-0.264379\pi$
$47$	9.24764	1.34891	0.674453	+	0.738317i	$0.264379\pi$
$48$	0	0
$49$	0.165753	0.0236791
$50$	−1.56450	−0.221254
$51$	0	0
$52$	0.892011	0.123700
$53$	12.9263	1.77557	0.887784	−	0.460260i	$-0.152244\pi$
$53$	12.9263	1.77557	0.887784	+	0.460260i	$0.152244\pi$
$54$	0	0
$55$	0.323325	0.0435971
$56$	−3.27060	−0.437052
$57$	0	0
$58$	0.754230	0.0990353
$59$	9.43019	1.22771	0.613853	−	0.789421i	$-0.289619\pi$
$59$	9.43019	1.22771	0.613853	+	0.789421i	$0.289619\pi$
$60$	0	0
$61$	−1.82014	−0.233045	−0.116522	−	0.993188i	$-0.537175\pi$
$61$	−1.82014	−0.233045	−0.116522	+	0.993188i	$0.537175\pi$
$62$	0.988026	0.125479
$63$	0	0
$64$	−5.74209	−0.717761
$65$	0.0279351	0.00346492
$66$	0	0
$67$	−3.18673	−0.389321	−0.194661	−	0.980871i	$-0.562361\pi$
$67$	−3.18673	−0.389321	−0.194661	+	0.980871i	$0.562361\pi$
$68$	0	0
$69$	0	0
$70$	−0.0499258	−0.00596727
$71$	−4.32016	−0.512708	−0.256354	−	0.966583i	$-0.582521\pi$
$71$	−4.32016	−0.512708	−0.256354	+	0.966583i	$0.582521\pi$
$72$	0	0
$73$	11.9409	1.39757	0.698786	−	0.715331i	$-0.253724\pi$
$73$	11.9409	1.39757	0.698786	+	0.715331i	$0.253724\pi$
$74$	−2.34910	−0.273078
$75$	0	0
$76$	13.0653	1.49869
$77$	−14.5308	−1.65594
$78$	0	0
$79$	10.6746	1.20098	0.600491	−	0.799631i	$-0.294972\pi$
$79$	10.6746	1.20098	0.600491	+	0.799631i	$0.294972\pi$
$80$	−0.203787	−0.0227840
$81$	0	0
$82$	0.697360	0.0770106
$83$	8.70940	0.955981	0.477990	−	0.878365i	$-0.341365\pi$
$83$	8.70940	0.955981	0.477990	+	0.878365i	$0.341365\pi$
$84$	0	0
$85$	0	0
$86$	−1.41402	−0.152478
$87$	0	0
$88$	6.63217	0.706992
$89$	−15.9437	−1.69003	−0.845017	−	0.534740i	$-0.820410\pi$
$89$	−15.9437	−1.69003	−0.845017	+	0.534740i	$0.820410\pi$
$90$	0	0
$91$	−1.25545	−0.131607
$92$	10.0065	1.04324
$93$	0	0
$94$	2.89564	0.298663
$95$	0.409164	0.0419794
$96$	0	0
$97$	−3.48884	−0.354238	−0.177119	−	0.984189i	$-0.556678\pi$
$97$	−3.48884	−0.354238	−0.177119	+	0.984189i	$0.556678\pi$
$98$	0.0519011	0.00524280
$99$	0	0
$100$	9.50302	0.950302
$101$	4.40807	0.438619	0.219310	−	0.975655i	$-0.429620\pi$
$101$	4.40807	0.438619	0.219310	+	0.975655i	$0.429620\pi$
$102$	0	0
$103$	0.977534	0.0963192	0.0481596	−	0.998840i	$-0.484664\pi$
$103$	0.977534	0.0963192	0.0481596	+	0.998840i	$0.484664\pi$
$104$	0.573016	0.0561888
$105$	0	0
$106$	4.04752	0.393130
$107$	17.5401	1.69567	0.847834	−	0.530261i	$-0.177906\pi$
$107$	17.5401	1.69567	0.847834	+	0.530261i	$0.177906\pi$
$108$	0	0
$109$	−11.5439	−1.10570	−0.552851	−	0.833280i	$-0.686460\pi$
$109$	−11.5439	−1.10570	−0.552851	+	0.833280i	$0.686460\pi$
$110$	0.101240	0.00965289
$111$	0	0
$112$	9.15856	0.865402
$113$	−4.55658	−0.428647	−0.214323	−	0.976763i	$-0.568755\pi$
$113$	−4.55658	−0.428647	−0.214323	+	0.976763i	$0.568755\pi$
$114$	0	0
$115$	0.313372	0.0292221
$116$	−4.58131	−0.425364
$117$	0	0
$118$	2.95280	0.271828
$119$	0	0
$120$	0	0
$121$	18.4658	1.67871
$122$	−0.569926	−0.0515987
$123$	0	0
$124$	−6.00142	−0.538944
$125$	0.595423	0.0532563
$126$	0	0
$127$	−5.54664	−0.492184	−0.246092	−	0.969246i	$-0.579147\pi$
$127$	−5.54664	−0.492184	−0.246092	+	0.969246i	$0.579147\pi$
$128$	−8.82773	−0.780269
$129$	0	0
$130$	0.00874710	0.000767172 0
$131$	−6.29120	−0.549665	−0.274832	−	0.961492i	$-0.588622\pi$
$131$	−6.29120	−0.549665	−0.274832	+	0.961492i	$0.588622\pi$
$132$	0	0
$133$	−18.3886	−1.59450
$134$	−0.997837	−0.0862000
$135$	0	0
$136$	0	0
$137$	−8.44606	−0.721595	−0.360798	−	0.932644i	$-0.617495\pi$
$137$	−8.44606	−0.721595	−0.360798	+	0.932644i	$0.617495\pi$
$138$	0	0
$139$	5.53570	0.469532	0.234766	−	0.972052i	$-0.424568\pi$
$139$	5.53570	0.469532	0.234766	+	0.972052i	$0.424568\pi$
$140$	0.303257	0.0256299
$141$	0	0
$142$	−1.35274	−0.113519
$143$	2.54583	0.212893
$144$	0	0
$145$	−0.143473	−0.0119148
$146$	3.73895	0.309438
$147$	0	0
$148$	14.2688	1.17289
$149$	22.6720	1.85736	0.928680	−	0.370882i	$-0.120945\pi$
$149$	22.6720	1.85736	0.928680	+	0.370882i	$0.120945\pi$
$150$	0	0
$151$	−12.7231	−1.03539	−0.517696	−	0.855565i	$-0.673210\pi$
$151$	−12.7231	−1.03539	−0.517696	+	0.855565i	$0.673210\pi$
$152$	8.39295	0.680758
$153$	0	0
$154$	−4.54993	−0.366644
$155$	−0.187946	−0.0150962
$156$	0	0
$157$	2.50104	0.199605	0.0998023	−	0.995007i	$-0.468179\pi$
$157$	2.50104	0.199605	0.0998023	+	0.995007i	$0.468179\pi$
$158$	3.34245	0.265911
$159$	0	0
$160$	−0.209358	−0.0165512
$161$	−14.0835	−1.10994
$162$	0	0
$163$	−10.7483	−0.841870	−0.420935	−	0.907091i	$-0.638298\pi$
$163$	−10.7483	−0.841870	−0.420935	+	0.907091i	$0.638298\pi$
$164$	−4.23587	−0.330766
$165$	0	0
$166$	2.72711	0.211665
$167$	9.22508	0.713858	0.356929	−	0.934131i	$-0.383824\pi$
$167$	9.22508	0.713858	0.356929	+	0.934131i	$0.383824\pi$
$168$	0	0
$169$	−12.7800	−0.983080
$170$	0	0
$171$	0	0
$172$	8.58899	0.654904
$173$	1.58189	0.120269	0.0601345	−	0.998190i	$-0.480847\pi$
$173$	1.58189	0.120269	0.0601345	+	0.998190i	$0.480847\pi$
$174$	0	0
$175$	−13.3750	−1.01105
$176$	−18.5719	−1.39991
$177$	0	0
$178$	−4.99235	−0.374192
$179$	−6.65124	−0.497137	−0.248569	−	0.968614i	$-0.579960\pi$
$179$	−6.65124	−0.497137	−0.248569	+	0.968614i	$0.579960\pi$
$180$	0	0
$181$	17.0736	1.26907	0.634534	−	0.772895i	$-0.281192\pi$
$181$	17.0736	1.26907	0.634534	+	0.772895i	$0.281192\pi$
$182$	−0.393111	−0.0291393
$183$	0	0
$184$	6.42801	0.473879
$185$	0.446856	0.0328535
$186$	0	0
$187$	0	0
$188$	−17.5886	−1.28278
$189$	0	0
$190$	0.128119	0.00929470
$191$	4.76822	0.345016	0.172508	−	0.985008i	$-0.444813\pi$
$191$	4.76822	0.345016	0.172508	+	0.985008i	$0.444813\pi$
$192$	0	0
$193$	7.73014	0.556427	0.278214	−	0.960519i	$-0.410258\pi$
$193$	7.73014	0.556427	0.278214	+	0.960519i	$0.410258\pi$
$194$	−1.09243	−0.0784321
$195$	0	0
$196$	−0.315255	−0.0225182
$197$	1.90035	0.135395	0.0676973	−	0.997706i	$-0.478435\pi$
$197$	1.90035	0.135395	0.0676973	+	0.997706i	$0.478435\pi$
$198$	0	0
$199$	8.57114	0.607592	0.303796	−	0.952737i	$-0.401746\pi$
$199$	8.57114	0.607592	0.303796	+	0.952737i	$0.401746\pi$
$200$	6.10461	0.431661
$201$	0	0
$202$	1.38027	0.0971151
$203$	6.44793	0.452556
$204$	0	0
$205$	−0.132655	−0.00926501
$206$	0.306088	0.0213261
$207$	0	0
$208$	−1.60460	−0.111259
$209$	37.2887	2.57932
$210$	0	0
$211$	19.7013	1.35629	0.678147	−	0.734926i	$-0.262783\pi$
$211$	19.7013	1.35629	0.678147	+	0.734926i	$0.262783\pi$
$212$	−24.5853	−1.68852
$213$	0	0
$214$	5.49221	0.375440
$215$	0.268981	0.0183444
$216$	0	0
$217$	8.44666	0.573397
$218$	−3.61465	−0.244815
$219$	0	0
$220$	−0.614949	−0.0414599
$221$	0	0
$222$	0	0
$223$	−21.4095	−1.43368	−0.716842	−	0.697235i	$-0.754413\pi$
$223$	−21.4095	−1.43368	−0.716842	+	0.697235i	$0.754413\pi$
$224$	9.40895	0.628662
$225$	0	0
$226$	−1.42677	−0.0949071
$227$	−8.17670	−0.542707	−0.271353	−	0.962480i	$-0.587471\pi$
$227$	−8.17670	−0.542707	−0.271353	+	0.962480i	$0.587471\pi$
$228$	0	0
$229$	20.4392	1.35066	0.675329	−	0.737517i	$-0.264002\pi$
$229$	20.4392	1.35066	0.675329	+	0.737517i	$0.264002\pi$
$230$	0.0981238	0.00647009
$231$	0	0
$232$	−2.94297	−0.193216
$233$	14.8774	0.974653	0.487326	−	0.873220i	$-0.337972\pi$
$233$	14.8774	0.974653	0.487326	+	0.873220i	$0.337972\pi$
$234$	0	0
$235$	−0.550821	−0.0359316
$236$	−17.9358	−1.16752
$237$	0	0
$238$	0	0
$239$	−21.0979	−1.36471	−0.682356	−	0.731020i	$-0.739045\pi$
$239$	−21.0979	−1.36471	−0.682356	+	0.731020i	$0.739045\pi$
$240$	0	0
$241$	11.6366	0.749579	0.374790	−	0.927110i	$-0.377715\pi$
$241$	11.6366	0.749579	0.374790	+	0.927110i	$0.377715\pi$
$242$	5.78207	0.371686
$243$	0	0
$244$	3.46182	0.221620
$245$	−0.00987284	−0.000630753 0
$246$	0	0
$247$	3.22172	0.204993
$248$	−3.85523	−0.244808
$249$	0	0
$250$	0.186440	0.0117915
$251$	25.8214	1.62983	0.814915	−	0.579580i	$-0.196784\pi$
$251$	25.8214	1.62983	0.814915	+	0.579580i	$0.196784\pi$
$252$	0	0
$253$	28.5588	1.79547
$254$	−1.73678	−0.108975
$255$	0	0
$256$	8.72002	0.545001
$257$	12.5634	0.783683	0.391842	−	0.920033i	$-0.371838\pi$
$257$	12.5634	0.783683	0.391842	+	0.920033i	$0.371838\pi$
$258$	0	0
$259$	−20.0825	−1.24787
$260$	−0.0531312	−0.00329506
$261$	0	0
$262$	−1.96992	−0.121702
$263$	−6.42202	−0.395999	−0.197999	−	0.980202i	$-0.563444\pi$
$263$	−6.42202	−0.395999	−0.197999	+	0.980202i	$0.563444\pi$
$264$	0	0
$265$	−0.769937	−0.0472968
$266$	−5.75789	−0.353039
$267$	0	0
$268$	6.06102	0.370236
$269$	24.9360	1.52038	0.760188	−	0.649703i	$-0.225107\pi$
$269$	24.9360	1.52038	0.760188	+	0.649703i	$0.225107\pi$
$270$	0	0
$271$	8.88651	0.539817	0.269909	−	0.962886i	$-0.413007\pi$
$271$	8.88651	0.539817	0.269909	+	0.962886i	$0.413007\pi$
$272$	0	0
$273$	0	0
$274$	−2.64465	−0.159769
$275$	27.1220	1.63552
$276$	0	0
$277$	13.8281	0.830853	0.415426	−	0.909627i	$-0.363632\pi$
$277$	13.8281	0.830853	0.415426	+	0.909627i	$0.363632\pi$
$278$	1.73335	0.103960
$279$	0	0
$280$	0.194808	0.0116420
$281$	−16.9209	−1.00941	−0.504707	−	0.863290i	$-0.668400\pi$
$281$	−16.9209	−1.00941	−0.504707	+	0.863290i	$0.668400\pi$
$282$	0	0
$283$	−25.2209	−1.49923	−0.749614	−	0.661875i	$-0.769761\pi$
$283$	−25.2209	−1.49923	−0.749614	+	0.661875i	$0.769761\pi$
$284$	8.21674	0.487574
$285$	0	0
$286$	0.797157	0.0471369
$287$	5.96175	0.351911
$288$	0	0
$289$	0	0
$290$	−0.0449246	−0.00263806
$291$	0	0
$292$	−22.7110	−1.32906
$293$	1.93377	0.112972	0.0564859	−	0.998403i	$-0.482010\pi$
$293$	1.93377	0.112972	0.0564859	+	0.998403i	$0.482010\pi$
$294$	0	0
$295$	−0.561694	−0.0327031
$296$	9.16609	0.532768
$297$	0	0
$298$	7.09910	0.411240
$299$	2.46746	0.142697
$300$	0	0
$301$	−12.0885	−0.696770
$302$	−3.98389	−0.229247
$303$	0	0
$304$	−23.5025	−1.34796
$305$	0.108414	0.00620775
$306$	0	0
$307$	−0.791215	−0.0451570	−0.0225785	−	0.999745i	$-0.507188\pi$
$307$	−0.791215	−0.0451570	−0.0225785	+	0.999745i	$0.507188\pi$
$308$	27.6370	1.57476
$309$	0	0
$310$	−0.0588503	−0.00334247
$311$	31.0352	1.75985	0.879923	−	0.475115i	$-0.157594\pi$
$311$	31.0352	1.75985	0.879923	+	0.475115i	$0.157594\pi$
$312$	0	0
$313$	9.18268	0.519036	0.259518	−	0.965738i	$-0.416436\pi$
$313$	9.18268	0.519036	0.259518	+	0.965738i	$0.416436\pi$
$314$	0.783132	0.0441947
$315$	0	0
$316$	−20.3025	−1.14211
$317$	20.0230	1.12461	0.562303	−	0.826931i	$-0.309915\pi$
$317$	20.0230	1.12461	0.562303	+	0.826931i	$0.309915\pi$
$318$	0	0
$319$	−13.0752	−0.732072
$320$	0.342019	0.0191194
$321$	0	0
$322$	−4.40987	−0.245752
$323$	0	0
$324$	0	0
$325$	2.34332	0.129984
$326$	−3.36553	−0.186399
$327$	0	0
$328$	−2.72107	−0.150246
$329$	24.7549	1.36478
$330$	0	0
$331$	−24.6835	−1.35673	−0.678363	−	0.734727i	$-0.737310\pi$
$331$	−24.6835	−1.35673	−0.678363	+	0.734727i	$0.737310\pi$
$332$	−16.5649	−0.909116
$333$	0	0
$334$	2.88858	0.158056
$335$	0.189813	0.0103706
$336$	0	0
$337$	27.5408	1.50024	0.750121	−	0.661301i	$-0.229995\pi$
$337$	27.5408	1.50024	0.750121	+	0.661301i	$0.229995\pi$
$338$	−4.00172	−0.217665
$339$	0	0
$340$	0	0
$341$	−17.1283	−0.927548
$342$	0	0
$343$	−18.2945	−0.987812
$344$	5.51745	0.297481
$345$	0	0
$346$	0.495326	0.0266289
$347$	23.0283	1.23622	0.618111	−	0.786091i	$-0.287898\pi$
$347$	23.0283	1.23622	0.618111	+	0.786091i	$0.287898\pi$
$348$	0	0
$349$	−19.0768	−1.02116	−0.510580	−	0.859830i	$-0.670569\pi$
$349$	−19.0768	−1.02116	−0.510580	+	0.859830i	$0.670569\pi$
$350$	−4.18800	−0.223858
$351$	0	0
$352$	−19.0796	−1.01695
$353$	−7.27281	−0.387093	−0.193546	−	0.981091i	$-0.561999\pi$
$353$	−7.27281	−0.387093	−0.193546	+	0.981091i	$0.561999\pi$
$354$	0	0
$355$	0.257323	0.0136573
$356$	30.3243	1.60718
$357$	0	0
$358$	−2.08265	−0.110072
$359$	−26.5753	−1.40259	−0.701296	−	0.712870i	$-0.747395\pi$
$359$	−26.5753	−1.40259	−0.701296	+	0.712870i	$0.747395\pi$
$360$	0	0
$361$	28.1885	1.48361
$362$	5.34612	0.280986
$363$	0	0
$364$	2.38782	0.125156
$365$	−0.711239	−0.0372279
$366$	0	0
$367$	29.2010	1.52428	0.762139	−	0.647414i	$-0.224149\pi$
$367$	29.2010	1.52428	0.762139	+	0.647414i	$0.224149\pi$
$368$	−18.0002	−0.938323
$369$	0	0
$370$	0.139921	0.00727413
$371$	34.6024	1.79647
$372$	0	0
$373$	16.7965	0.869689	0.434844	−	0.900506i	$-0.356803\pi$
$373$	16.7965	0.869689	0.434844	+	0.900506i	$0.356803\pi$
$374$	0	0
$375$	0	0
$376$	−11.2987	−0.582684
$377$	−1.12969	−0.0581821
$378$	0	0
$379$	9.67958	0.497206	0.248603	−	0.968605i	$-0.420028\pi$
$379$	9.67958	0.497206	0.248603	+	0.968605i	$0.420028\pi$
$380$	−0.778212	−0.0399214
$381$	0	0
$382$	1.49304	0.0763904
$383$	−5.22295	−0.266880	−0.133440	−	0.991057i	$-0.542602\pi$
$383$	−5.22295	−0.266880	−0.133440	+	0.991057i	$0.542602\pi$
$384$	0	0
$385$	0.865506	0.0441103
$386$	2.42048	0.123199
$387$	0	0
$388$	6.63561	0.336872
$389$	−1.34027	−0.0679545	−0.0339772	−	0.999423i	$-0.510817\pi$
$389$	−1.34027	−0.0679545	−0.0339772	+	0.999423i	$0.510817\pi$
$390$	0	0
$391$	0	0
$392$	−0.202516	−0.0102286
$393$	0	0
$394$	0.595043	0.0299778
$395$	−0.635814	−0.0319913
$396$	0	0
$397$	12.8974	0.647301	0.323650	−	0.946177i	$-0.395090\pi$
$397$	12.8974	0.647301	0.323650	+	0.946177i	$0.395090\pi$
$398$	2.68382	0.134528
$399$	0	0
$400$	−17.0946	−0.854728
$401$	12.5291	0.625676	0.312838	−	0.949807i	$-0.398720\pi$
$401$	12.5291	0.625676	0.312838	+	0.949807i	$0.398720\pi$
$402$	0	0
$403$	−1.47987	−0.0737177
$404$	−8.38395	−0.417117
$405$	0	0
$406$	2.01899	0.100201
$407$	40.7237	2.01860
$408$	0	0
$409$	−0.156286	−0.00772787	−0.00386393	−	0.999993i	$-0.501230\pi$
$409$	−0.156286	−0.00772787	−0.00386393	+	0.999993i	$0.501230\pi$
$410$	−0.0415372	−0.00205138
$411$	0	0
$412$	−1.85922	−0.0915974
$413$	25.2436	1.24216
$414$	0	0
$415$	−0.518762	−0.0254650
$416$	−1.64847	−0.0808228
$417$	0	0
$418$	11.6759	0.571089
$419$	26.5208	1.29563	0.647814	−	0.761799i	$-0.275683\pi$
$419$	26.5208	1.29563	0.647814	+	0.761799i	$0.275683\pi$
$420$	0	0
$421$	−26.6269	−1.29772	−0.648859	−	0.760909i	$-0.724753\pi$
$421$	−26.6269	−1.29772	−0.648859	+	0.760909i	$0.724753\pi$
$422$	6.16893	0.300299
$423$	0	0
$424$	−15.7933	−0.766988
$425$	0	0
$426$	0	0
$427$	−4.87231	−0.235788
$428$	−33.3605	−1.61254
$429$	0	0
$430$	0.0842240	0.00406164
$431$	−31.8546	−1.53438	−0.767191	−	0.641419i	$-0.778346\pi$
$431$	−31.8546	−1.53438	−0.767191	+	0.641419i	$0.778346\pi$
$432$	0	0
$433$	34.1585	1.64155	0.820776	−	0.571249i	$-0.193541\pi$
$433$	34.1585	1.64155	0.820776	+	0.571249i	$0.193541\pi$
$434$	2.64484	0.126956
$435$	0	0
$436$	21.9559	1.05150
$437$	36.1408	1.72885
$438$	0	0
$439$	−29.6909	−1.41707	−0.708534	−	0.705677i	$-0.750643\pi$
$439$	−29.6909	−1.41707	−0.708534	+	0.705677i	$0.750643\pi$
$440$	−0.395035	−0.0188326
$441$	0	0
$442$	0	0
$443$	−15.6384	−0.743002	−0.371501	−	0.928432i	$-0.621157\pi$
$443$	−15.6384	−0.743002	−0.371501	+	0.928432i	$0.621157\pi$
$444$	0	0
$445$	0.949664	0.0450184
$446$	−6.70379	−0.317434
$447$	0	0
$448$	−15.3710	−0.726210
$449$	−8.43301	−0.397978	−0.198989	−	0.980002i	$-0.563766\pi$
$449$	−8.43301	−0.397978	−0.198989	+	0.980002i	$0.563766\pi$
$450$	0	0
$451$	−12.0893	−0.569265
$452$	8.66640	0.407633
$453$	0	0
$454$	−2.56031	−0.120161
$455$	0.0747792	0.00350570
$456$	0	0
$457$	−23.8380	−1.11509	−0.557547	−	0.830145i	$-0.688257\pi$
$457$	−23.8380	−1.11509	−0.557547	+	0.830145i	$0.688257\pi$
$458$	6.39996	0.299051
$459$	0	0
$460$	−0.596019	−0.0277895
$461$	−3.64094	−0.169576	−0.0847878	−	0.996399i	$-0.527021\pi$
$461$	−3.64094	−0.169576	−0.0847878	+	0.996399i	$0.527021\pi$
$462$	0	0
$463$	−20.7505	−0.964359	−0.482180	−	0.876072i	$-0.660155\pi$
$463$	−20.7505	−0.964359	−0.482180	+	0.876072i	$0.660155\pi$
$464$	8.24111	0.382584
$465$	0	0
$466$	4.65846	0.215799
$467$	36.2856	1.67910	0.839549	−	0.543284i	$-0.182819\pi$
$467$	36.2856	1.67910	0.839549	+	0.543284i	$0.182819\pi$
$468$	0	0
$469$	−8.53054	−0.393904
$470$	−0.172475	−0.00795566
$471$	0	0
$472$	−11.5217	−0.530329
$473$	24.5133	1.12712
$474$	0	0
$475$	34.3226	1.57483
$476$	0	0
$477$	0	0
$478$	−6.60624	−0.302162
$479$	25.3038	1.15616	0.578079	−	0.815981i	$-0.303802\pi$
$479$	25.3038	1.15616	0.578079	+	0.815981i	$0.303802\pi$
$480$	0	0
$481$	3.51850	0.160430
$482$	3.64368	0.165965
$483$	0	0
$484$	−35.1212	−1.59642
$485$	0.207807	0.00943603
$486$	0	0
$487$	−20.6946	−0.937763	−0.468881	−	0.883261i	$-0.655343\pi$
$487$	−20.6946	−0.937763	−0.468881	+	0.883261i	$0.655343\pi$
$488$	2.22383	0.100668
$489$	0	0
$490$	−0.00309141	−0.000139656 0
$491$	−16.5956	−0.748949	−0.374474	−	0.927237i	$-0.622177\pi$
$491$	−16.5956	−0.748949	−0.374474	+	0.927237i	$0.622177\pi$
$492$	0	0
$493$	0	0
$494$	1.00879	0.0453878
$495$	0	0
$496$	10.7957	0.484741
$497$	−11.5646	−0.518743
$498$	0	0
$499$	−28.5717	−1.27905	−0.639523	−	0.768772i	$-0.720868\pi$
$499$	−28.5717	−1.27905	−0.639523	+	0.768772i	$0.720868\pi$
$500$	−1.13247	−0.0506455
$501$	0	0
$502$	8.08525	0.360862
$503$	−11.9774	−0.534044	−0.267022	−	0.963690i	$-0.586040\pi$
$503$	−11.9774	−0.534044	−0.267022	+	0.963690i	$0.586040\pi$
$504$	0	0
$505$	−0.262560	−0.0116838
$506$	8.94240	0.397538
$507$	0	0
$508$	10.5494	0.468056
$509$	24.8636	1.10206	0.551031	−	0.834485i	$-0.314235\pi$
$509$	24.8636	1.10206	0.551031	+	0.834485i	$0.314235\pi$
$510$	0	0
$511$	31.9644	1.41402
$512$	20.3859	0.900938
$513$	0	0
$514$	3.93388	0.173516
$515$	−0.0582253	−0.00256571
$516$	0	0
$517$	−50.1984	−2.20773
$518$	−6.28830	−0.276292
$519$	0	0
$520$	−0.0341308	−0.00149673
$521$	−25.5726	−1.12036	−0.560178	−	0.828373i	$-0.689267\pi$
$521$	−25.5726	−1.12036	−0.560178	+	0.828373i	$0.689267\pi$
$522$	0	0
$523$	15.9637	0.698043	0.349022	−	0.937115i	$-0.386514\pi$
$523$	15.9637	0.698043	0.349022	+	0.937115i	$0.386514\pi$
$524$	11.9656	0.522719
$525$	0	0
$526$	−2.01088	−0.0876784
$527$	0	0
$528$	0	0
$529$	4.67963	0.203462
$530$	−0.241085	−0.0104720
$531$	0	0
$532$	34.9743	1.51633
$533$	−1.04451	−0.0452428
$534$	0	0
$535$	−1.04475	−0.0451685
$536$	3.89351	0.168174
$537$	0	0
$538$	7.80803	0.336628
$539$	−0.899750	−0.0387550
$540$	0	0
$541$	24.4814	1.05254	0.526268	−	0.850319i	$-0.323591\pi$
$541$	24.4814	1.05254	0.526268	+	0.850319i	$0.323591\pi$
$542$	2.78257	0.119521
$543$	0	0
$544$	0	0
$545$	0.687593	0.0294532
$546$	0	0
$547$	37.3240	1.59586	0.797929	−	0.602752i	$-0.205929\pi$
$547$	37.3240	1.59586	0.797929	+	0.602752i	$0.205929\pi$
$548$	16.0640	0.686221
$549$	0	0
$550$	8.49250	0.362121
$551$	−16.5466	−0.704907
$552$	0	0
$553$	28.5747	1.21512
$554$	4.32990	0.183960
$555$	0	0
$556$	−10.5287	−0.446514
$557$	13.6266	0.577378	0.288689	−	0.957423i	$-0.406781\pi$
$557$	13.6266	0.577378	0.288689	+	0.957423i	$0.406781\pi$
$558$	0	0
$559$	2.11793	0.0895789
$560$	−0.545515	−0.0230522
$561$	0	0
$562$	−5.29831	−0.223496
$563$	38.6768	1.63003	0.815017	−	0.579437i	$-0.196727\pi$
$563$	38.6768	1.63003	0.815017	+	0.579437i	$0.196727\pi$
$564$	0	0
$565$	0.271405	0.0114181
$566$	−7.89724	−0.331946
$567$	0	0
$568$	5.27832	0.221473
$569$	−11.7660	−0.493257	−0.246629	−	0.969110i	$-0.579323\pi$
$569$	−11.7660	−0.493257	−0.246629	+	0.969110i	$0.579323\pi$
$570$	0	0
$571$	−12.8135	−0.536230	−0.268115	−	0.963387i	$-0.586401\pi$
$571$	−12.8135	−0.536230	−0.268115	+	0.963387i	$0.586401\pi$
$572$	−4.84205	−0.202456
$573$	0	0
$574$	1.86676	0.0779170
$575$	26.2871	1.09625
$576$	0	0
$577$	−30.7966	−1.28208	−0.641040	−	0.767508i	$-0.721497\pi$
$577$	−30.7966	−1.28208	−0.641040	+	0.767508i	$0.721497\pi$
$578$	0	0
$579$	0	0
$580$	0.272879	0.0113307
$581$	23.3141	0.967233
$582$	0	0
$583$	−70.1673	−2.90603
$584$	−14.5892	−0.603706
$585$	0	0
$586$	0.605506	0.0250132
$587$	18.8429	0.777731	0.388865	−	0.921295i	$-0.372867\pi$
$587$	18.8429	0.777731	0.388865	+	0.921295i	$0.372867\pi$
$588$	0	0
$589$	−21.6757	−0.893130
$590$	−0.175879	−0.00724083
$591$	0	0
$592$	−25.6675	−1.05493
$593$	−28.3421	−1.16387	−0.581936	−	0.813235i	$-0.697705\pi$
$593$	−28.3421	−1.16387	−0.581936	+	0.813235i	$0.697705\pi$
$594$	0	0
$595$	0	0
$596$	−43.1210	−1.76631
$597$	0	0
$598$	0.772617	0.0315947
$599$	−20.3955	−0.833339	−0.416669	−	0.909058i	$-0.636803\pi$
$599$	−20.3955	−0.833339	−0.416669	+	0.909058i	$0.636803\pi$
$600$	0	0
$601$	−26.9498	−1.09931	−0.549653	−	0.835393i	$-0.685240\pi$
$601$	−26.9498	−1.09931	−0.549653	+	0.835393i	$0.685240\pi$
$602$	−3.78518	−0.154273
$603$	0	0
$604$	24.1988	0.984634
$605$	−1.09989	−0.0447169
$606$	0	0
$607$	37.1072	1.50613	0.753067	−	0.657944i	$-0.228574\pi$
$607$	37.1072	1.50613	0.753067	+	0.657944i	$0.228574\pi$
$608$	−24.1451	−0.979211
$609$	0	0
$610$	0.0339468	0.00137446
$611$	−4.33711	−0.175461
$612$	0	0
$613$	−43.2999	−1.74887	−0.874433	−	0.485147i	$-0.838766\pi$
$613$	−43.2999	−1.74887	−0.874433	+	0.485147i	$0.838766\pi$
$614$	−0.247747	−0.00999827
$615$	0	0
$616$	17.7536	0.715314
$617$	−5.84686	−0.235386	−0.117693	−	0.993050i	$-0.537550\pi$
$617$	−5.84686	−0.235386	−0.117693	+	0.993050i	$0.537550\pi$
$618$	0	0
$619$	4.58413	0.184252	0.0921259	−	0.995747i	$-0.470634\pi$
$619$	4.58413	0.184252	0.0921259	+	0.995747i	$0.470634\pi$
$620$	0.357465	0.0143562
$621$	0	0
$622$	9.71783	0.389650
$623$	−42.6797	−1.70993
$624$	0	0
$625$	24.9468	0.997872
$626$	2.87530	0.114920
$627$	0	0
$628$	−4.75686	−0.189819
$629$	0	0
$630$	0	0
$631$	42.2599	1.68234	0.841170	−	0.540771i	$-0.181868\pi$
$631$	42.2599	1.68234	0.841170	+	0.540771i	$0.181868\pi$
$632$	−13.0421	−0.518786
$633$	0	0
$634$	6.26967	0.249000
$635$	0.330377	0.0131106
$636$	0	0
$637$	−0.0777378	−0.00308009
$638$	−4.09415	−0.162089
$639$	0	0
$640$	0.525810	0.0207845
$641$	36.7738	1.45248	0.726239	−	0.687442i	$-0.241266\pi$
$641$	36.7738	1.45248	0.726239	+	0.687442i	$0.241266\pi$
$642$	0	0
$643$	−21.9041	−0.863812	−0.431906	−	0.901919i	$-0.642159\pi$
$643$	−21.9041	−0.863812	−0.431906	+	0.901919i	$0.642159\pi$
$644$	26.7862	1.05552
$645$	0	0
$646$	0	0
$647$	13.3204	0.523681	0.261840	−	0.965111i	$-0.415671\pi$
$647$	13.3204	0.523681	0.261840	+	0.965111i	$0.415671\pi$
$648$	0	0
$649$	−51.1894	−2.00936
$650$	0.733747	0.0287799
$651$	0	0
$652$	20.4427	0.800599
$653$	10.2684	0.401832	0.200916	−	0.979608i	$-0.435608\pi$
$653$	10.2684	0.401832	0.200916	+	0.979608i	$0.435608\pi$
$654$	0	0
$655$	0.374726	0.0146417
$656$	7.61972	0.297500
$657$	0	0
$658$	7.75133	0.302178
$659$	22.3839	0.871954	0.435977	−	0.899958i	$-0.356403\pi$
$659$	22.3839	0.871954	0.435977	+	0.899958i	$0.356403\pi$
$660$	0	0
$661$	31.3766	1.22041	0.610204	−	0.792245i	$-0.291088\pi$
$661$	31.3766	1.22041	0.610204	+	0.792245i	$0.291088\pi$
$662$	−7.72895	−0.300394
$663$	0	0
$664$	−10.6411	−0.412953
$665$	1.09529	0.0424735
$666$	0	0
$667$	−12.6727	−0.490690
$668$	−17.5457	−0.678863
$669$	0	0
$670$	0.0594346	0.00229616
$671$	9.88015	0.381419
$672$	0	0
$673$	−9.91808	−0.382314	−0.191157	−	0.981559i	$-0.561224\pi$
$673$	−9.91808	−0.382314	−0.191157	+	0.981559i	$0.561224\pi$
$674$	8.62363	0.332170
$675$	0	0
$676$	24.3071	0.934887
$677$	−1.21290	−0.0466157	−0.0233078	−	0.999728i	$-0.507420\pi$
$677$	−1.21290	−0.0466157	−0.0233078	+	0.999728i	$0.507420\pi$
$678$	0	0
$679$	−9.33924	−0.358407
$680$	0	0
$681$	0	0
$682$	−5.36325	−0.205369
$683$	30.8740	1.18136	0.590681	−	0.806905i	$-0.298859\pi$
$683$	30.8740	1.18136	0.590681	+	0.806905i	$0.298859\pi$
$684$	0	0
$685$	0.503076	0.0192216
$686$	−5.72843	−0.218713
$687$	0	0
$688$	−15.4503	−0.589038
$689$	−6.06241	−0.230959
$690$	0	0
$691$	25.7685	0.980281	0.490140	−	0.871643i	$-0.336945\pi$
$691$	25.7685	0.980281	0.490140	+	0.871643i	$0.336945\pi$
$692$	−3.00869	−0.114373
$693$	0	0
$694$	7.21067	0.273713
$695$	−0.329726	−0.0125072
$696$	0	0
$697$	0	0
$698$	−5.97339	−0.226096
$699$	0	0
$700$	25.4386	0.961488
$701$	25.4354	0.960683	0.480342	−	0.877081i	$-0.340513\pi$
$701$	25.4354	0.960683	0.480342	+	0.877081i	$0.340513\pi$
$702$	0	0
$703$	51.5354	1.94370
$704$	31.1695	1.17474
$705$	0	0
$706$	−2.27728	−0.0857066
$707$	11.7999	0.443782
$708$	0	0
$709$	40.1810	1.50903	0.754515	−	0.656283i	$-0.227872\pi$
$709$	40.1810	1.50903	0.754515	+	0.656283i	$0.227872\pi$
$710$	0.0805737	0.00302388
$711$	0	0
$712$	19.4799	0.730040
$713$	−16.6010	−0.621712
$714$	0	0
$715$	−0.151638	−0.00567096
$716$	12.6504	0.472766
$717$	0	0
$718$	−8.32133	−0.310549
$719$	19.9051	0.742334	0.371167	−	0.928566i	$-0.378958\pi$
$719$	19.9051	0.742334	0.371167	+	0.928566i	$0.378958\pi$
$720$	0	0
$721$	2.61675	0.0974529
$722$	8.82645	0.328487
$723$	0	0
$724$	−32.4732	−1.20686
$725$	−12.0351	−0.446974
$726$	0	0
$727$	3.61240	0.133977	0.0669883	−	0.997754i	$-0.478661\pi$
$727$	3.61240	0.133977	0.0669883	+	0.997754i	$0.478661\pi$
$728$	1.53390	0.0568502
$729$	0	0
$730$	−0.222705	−0.00824267
$731$	0	0
$732$	0	0
$733$	8.52916	0.315032	0.157516	−	0.987516i	$-0.449651\pi$
$733$	8.52916	0.315032	0.157516	+	0.987516i	$0.449651\pi$
$734$	9.14347	0.337492
$735$	0	0
$736$	−18.4923	−0.681634
$737$	17.2984	0.637193
$738$	0	0
$739$	22.1784	0.815846	0.407923	−	0.913016i	$-0.366253\pi$
$739$	22.1784	0.815846	0.407923	+	0.913016i	$0.366253\pi$
$740$	−0.849900	−0.0312429
$741$	0	0
$742$	10.8348	0.397758
$743$	−25.8967	−0.950057	−0.475029	−	0.879970i	$-0.657562\pi$
$743$	−25.8967	−0.950057	−0.475029	+	0.879970i	$0.657562\pi$
$744$	0	0
$745$	−1.35042	−0.0494756
$746$	5.25935	0.192559
$747$	0	0
$748$	0	0
$749$	46.9530	1.71563
$750$	0	0
$751$	4.24257	0.154813	0.0774067	−	0.997000i	$-0.475336\pi$
$751$	4.24257	0.154813	0.0774067	+	0.997000i	$0.475336\pi$
$752$	31.6393	1.15377
$753$	0	0
$754$	−0.353732	−0.0128821
$755$	0.757832	0.0275803
$756$	0	0
$757$	7.87822	0.286339	0.143169	−	0.989698i	$-0.454271\pi$
$757$	7.87822	0.286339	0.143169	+	0.989698i	$0.454271\pi$
$758$	3.03089	0.110087
$759$	0	0
$760$	−0.499913	−0.0181337
$761$	45.9699	1.66641	0.833205	−	0.552965i	$-0.186504\pi$
$761$	45.9699	1.66641	0.833205	+	0.552965i	$0.186504\pi$
$762$	0	0
$763$	−30.9017	−1.11872
$764$	−9.06893	−0.328102
$765$	0	0
$766$	−1.63542	−0.0590903
$767$	−4.42273	−0.159695
$768$	0	0
$769$	17.5627	0.633328	0.316664	−	0.948538i	$-0.397437\pi$
$769$	17.5627	0.633328	0.316664	+	0.948538i	$0.397437\pi$
$770$	0.271009	0.00976650
$771$	0	0
$772$	−14.7024	−0.529150
$773$	−17.5276	−0.630422	−0.315211	−	0.949022i	$-0.602075\pi$
$773$	−17.5276	−0.630422	−0.315211	+	0.949022i	$0.602075\pi$
$774$	0	0
$775$	−15.7658	−0.566324
$776$	4.26262	0.153019
$777$	0	0
$778$	−0.419669	−0.0150459
$779$	−15.2989	−0.548141
$780$	0	0
$781$	23.4509	0.839138
$782$	0	0
$783$	0	0
$784$	0.567098	0.0202535
$785$	−0.148971	−0.00531699
$786$	0	0
$787$	32.0204	1.14141	0.570703	−	0.821157i	$-0.306671\pi$
$787$	32.0204	1.14141	0.570703	+	0.821157i	$0.306671\pi$
$788$	−3.61438	−0.128757
$789$	0	0
$790$	−0.199088	−0.00708322
$791$	−12.1975	−0.433692
$792$	0	0
$793$	0.853639	0.0303136
$794$	4.03846	0.143320
$795$	0	0
$796$	−16.3019	−0.577806
$797$	−5.33744	−0.189062	−0.0945310	−	0.995522i	$-0.530135\pi$
$797$	−5.33744	−0.189062	−0.0945310	+	0.995522i	$0.530135\pi$
$798$	0	0
$799$	0	0
$800$	−17.5619	−0.620908
$801$	0	0
$802$	3.92316	0.138532
$803$	−64.8179	−2.28737
$804$	0	0
$805$	0.838863	0.0295660
$806$	−0.463381	−0.0163219
$807$	0	0
$808$	−5.38573	−0.189469
$809$	40.5854	1.42691	0.713454	−	0.700702i	$-0.247130\pi$
$809$	40.5854	1.42691	0.713454	+	0.700702i	$0.247130\pi$
$810$	0	0
$811$	−21.6764	−0.761161	−0.380581	−	0.924748i	$-0.624276\pi$
$811$	−21.6764	−0.761161	−0.380581	+	0.924748i	$0.624276\pi$
$812$	−12.2637	−0.430371
$813$	0	0
$814$	12.7515	0.446940
$815$	0.640204	0.0224254
$816$	0	0
$817$	31.0213	1.08530
$818$	−0.0489368	−0.00171104
$819$	0	0
$820$	0.252303	0.00881081
$821$	−3.03504	−0.105924	−0.0529619	−	0.998597i	$-0.516866\pi$
$821$	−3.03504	−0.105924	−0.0529619	+	0.998597i	$0.516866\pi$
$822$	0	0
$823$	−6.08315	−0.212045	−0.106023	−	0.994364i	$-0.533812\pi$
$823$	−6.08315	−0.212045	−0.106023	+	0.994364i	$0.533812\pi$
$824$	−1.19434	−0.0416068
$825$	0	0
$826$	7.90434	0.275027
$827$	22.8467	0.794456	0.397228	−	0.917720i	$-0.369972\pi$
$827$	22.8467	0.794456	0.397228	+	0.917720i	$0.369972\pi$
$828$	0	0
$829$	5.37918	0.186827	0.0934133	−	0.995627i	$-0.470222\pi$
$829$	5.37918	0.186827	0.0934133	+	0.995627i	$0.470222\pi$
$830$	−0.162436	−0.00563823
$831$	0	0
$832$	2.69302	0.0933638
$833$	0	0
$834$	0	0
$835$	−0.549478	−0.0190155
$836$	−70.9215	−2.45287
$837$	0	0
$838$	8.30427	0.286866
$839$	−1.52790	−0.0527490	−0.0263745	−	0.999652i	$-0.508396\pi$
$839$	−1.52790	−0.0527490	−0.0263745	+	0.999652i	$0.508396\pi$
$840$	0	0
$841$	−23.1980	−0.799930
$842$	−8.33749	−0.287329
$843$	0	0
$844$	−37.4710	−1.28981
$845$	0.761223	0.0261869
$846$	0	0
$847$	49.4311	1.69847
$848$	44.2254	1.51870
$849$	0	0
$850$	0	0
$851$	39.4701	1.35302
$852$	0	0
$853$	21.3280	0.730257	0.365129	−	0.930957i	$-0.381025\pi$
$853$	21.3280	0.730257	0.365129	+	0.930957i	$0.381025\pi$
$854$	−1.52563	−0.0522060
$855$	0	0
$856$	−21.4304	−0.732474
$857$	−4.61715	−0.157719	−0.0788595	−	0.996886i	$-0.525128\pi$
$857$	−4.61715	−0.157719	−0.0788595	+	0.996886i	$0.525128\pi$
$858$	0	0
$859$	37.1599	1.26788	0.633939	−	0.773383i	$-0.281437\pi$
$859$	37.1599	1.26788	0.633939	+	0.773383i	$0.281437\pi$
$860$	−0.511590	−0.0174451
$861$	0	0
$862$	−9.97439	−0.339729
$863$	−32.4840	−1.10577	−0.552884	−	0.833258i	$-0.686473\pi$
$863$	−32.4840	−1.10577	−0.552884	+	0.833258i	$0.686473\pi$
$864$	0	0
$865$	−0.0942229	−0.00320368
$866$	10.6958	0.363458
$867$	0	0
$868$	−16.0652	−0.545287
$869$	−57.9442	−1.96562
$870$	0	0
$871$	1.49457	0.0506415
$872$	14.1042	0.477628
$873$	0	0
$874$	11.3165	0.382787
$875$	1.59388	0.0538831
$876$	0	0
$877$	2.78388	0.0940050	0.0470025	−	0.998895i	$-0.485033\pi$
$877$	2.78388	0.0940050	0.0470025	+	0.998895i	$0.485033\pi$
$878$	−9.29688	−0.313754
$879$	0	0
$880$	1.10620	0.0372901
$881$	−50.9155	−1.71539	−0.857694	−	0.514161i	$-0.828103\pi$
$881$	−50.9155	−1.71539	−0.857694	+	0.514161i	$0.828103\pi$
$882$	0	0
$883$	−36.5258	−1.22919	−0.614596	−	0.788842i	$-0.710681\pi$
$883$	−36.5258	−1.22919	−0.614596	+	0.788842i	$0.710681\pi$
$884$	0	0
$885$	0	0
$886$	−4.89673	−0.164509
$887$	−26.1442	−0.877835	−0.438918	−	0.898527i	$-0.644638\pi$
$887$	−26.1442	−0.877835	−0.438918	+	0.898527i	$0.644638\pi$
$888$	0	0
$889$	−14.8477	−0.497978
$890$	0.297361	0.00996757
$891$	0	0
$892$	40.7198	1.36340
$893$	−63.5256	−2.12580
$894$	0	0
$895$	0.396171	0.0132425
$896$	−23.6309	−0.789453
$897$	0	0
$898$	−2.64056	−0.0881168
$899$	7.60053	0.253492
$900$	0	0
$901$	0	0
$902$	−3.78544	−0.126041
$903$	0	0
$904$	5.56718	0.185162
$905$	−1.01696	−0.0338049
$906$	0	0
$907$	−47.6037	−1.58065	−0.790327	−	0.612686i	$-0.790089\pi$
$907$	−47.6037	−1.58065	−0.790327	+	0.612686i	$0.790089\pi$
$908$	15.5517	0.516102
$909$	0	0
$910$	0.0234151	0.000776201 0
$911$	−36.3037	−1.20280	−0.601398	−	0.798949i	$-0.705389\pi$
$911$	−36.3037	−1.20280	−0.601398	+	0.798949i	$0.705389\pi$
$912$	0	0
$913$	−47.2767	−1.56463
$914$	−7.46421	−0.246894
$915$	0	0
$916$	−38.8744	−1.28444
$917$	−16.8409	−0.556135
$918$	0	0
$919$	−1.14473	−0.0377611	−0.0188806	−	0.999822i	$-0.506010\pi$
$919$	−1.14473	−0.0377611	−0.0188806	+	0.999822i	$0.506010\pi$
$920$	−0.382874	−0.0126230
$921$	0	0
$922$	−1.14006	−0.0375459
$923$	2.02614	0.0666912
$924$	0	0
$925$	37.4843	1.23248
$926$	−6.49746	−0.213520
$927$	0	0
$928$	8.46642	0.277924
$929$	44.2349	1.45130	0.725649	−	0.688065i	$-0.241540\pi$
$929$	44.2349	1.45130	0.725649	+	0.688065i	$0.241540\pi$
$930$	0	0
$931$	−1.13862	−0.0373169
$932$	−28.2962	−0.926873
$933$	0	0
$934$	11.3618	0.371771
$935$	0	0
$936$	0	0
$937$	4.81714	0.157369	0.0786846	−	0.996900i	$-0.474928\pi$
$937$	4.81714	0.157369	0.0786846	+	0.996900i	$0.474928\pi$
$938$	−2.67110	−0.0872146
$939$	0	0
$940$	1.04764	0.0341701
$941$	−50.4375	−1.64422	−0.822108	−	0.569331i	$-0.807202\pi$
$941$	−50.4375	−1.64422	−0.822108	+	0.569331i	$0.807202\pi$
$942$	0	0
$943$	−11.7172	−0.381564
$944$	32.2639	1.05010
$945$	0	0
$946$	7.67566	0.249557
$947$	−22.9599	−0.746097	−0.373049	−	0.927812i	$-0.621688\pi$
$947$	−22.9599	−0.746097	−0.373049	+	0.927812i	$0.621688\pi$
$948$	0	0
$949$	−5.60023	−0.181791
$950$	10.7472	0.348684
$951$	0	0
$952$	0	0
$953$	22.2611	0.721108	0.360554	−	0.932738i	$-0.382588\pi$
$953$	22.2611	0.721108	0.360554	+	0.932738i	$0.382588\pi$
$954$	0	0
$955$	−0.284011	−0.00919040
$956$	40.1273	1.29781
$957$	0	0
$958$	7.92318	0.255986
$959$	−22.6092	−0.730089
$960$	0	0
$961$	−21.0435	−0.678821
$962$	1.10172	0.0355210
$963$	0	0
$964$	−22.1323	−0.712833
$965$	−0.460434	−0.0148219
$966$	0	0
$967$	−40.5446	−1.30383	−0.651913	−	0.758294i	$-0.726033\pi$
$967$	−40.5446	−1.30383	−0.651913	+	0.758294i	$0.726033\pi$
$968$	−22.5614	−0.725150
$969$	0	0
$970$	0.0650691	0.00208924
$971$	7.46199	0.239467	0.119733	−	0.992806i	$-0.461796\pi$
$971$	7.46199	0.239467	0.119733	+	0.992806i	$0.461796\pi$
$972$	0	0
$973$	14.8185	0.475059
$974$	−6.47995	−0.207631
$975$	0	0
$976$	−6.22731	−0.199331
$977$	1.73790	0.0556002	0.0278001	−	0.999614i	$-0.491150\pi$
$977$	1.73790	0.0556002	0.0278001	+	0.999614i	$0.491150\pi$
$978$	0	0
$979$	86.5466	2.76604
$980$	0.0187777	0.000599831 0
$981$	0	0
$982$	−5.19645	−0.165826
$983$	−54.0188	−1.72293	−0.861466	−	0.507815i	$-0.830454\pi$
$983$	−54.0188	−1.72293	−0.861466	+	0.507815i	$0.830454\pi$
$984$	0	0
$985$	−0.113192	−0.00360658
$986$	0	0
$987$	0	0
$988$	−6.12757	−0.194944
$989$	23.7587	0.755481
$990$	0	0
$991$	−6.96503	−0.221251	−0.110626	−	0.993862i	$-0.535285\pi$
$991$	−6.96503	−0.221251	−0.110626	+	0.993862i	$0.535285\pi$
$992$	11.0908	0.352135
$993$	0	0
$994$	−3.62113	−0.114855
$995$	−0.510526	−0.0161848
$996$	0	0
$997$	−46.6989	−1.47897	−0.739484	−	0.673174i	$-0.764930\pi$
$997$	−46.6989	−1.47897	−0.739484	+	0.673174i	$0.764930\pi$
$998$	−8.94645	−0.283195
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7803.2.a.cg.1.14		24
3.2	odd	2		7803.2.a.cd.1.11		24
17.11	odd	16		459.2.l.a.325.7	yes	48
17.14	odd	16		459.2.l.a.298.7	yes	48
17.16	even	2		7803.2.a.cd.1.14		24
51.11	even	16		459.2.l.a.325.6	yes	48
51.14	even	16		459.2.l.a.298.6	✓	48
51.50	odd	2	inner	7803.2.a.cg.1.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.298.6	✓	48	51.14	even	16
459.2.l.a.298.7	yes	48	17.14	odd	16
459.2.l.a.325.6	yes	48	51.11	even	16
459.2.l.a.325.7	yes	48	17.11	odd	16
7803.2.a.cd.1.11		24	3.2	odd	2
7803.2.a.cd.1.14		24	17.16	even	2
7803.2.a.cg.1.11		24	51.50	odd	2	inner
7803.2.a.cg.1.14		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7803 = 3^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7803.a (trivial)

\(f(q)\)	\(=\)	\(q+0.313123 q^{2} -1.90195 q^{4} -0.0595634 q^{5} +2.67689 q^{7} -1.22179 q^{8} -0.0186507 q^{10} -5.42825 q^{11} -0.468997 q^{13} +0.838195 q^{14} +3.42134 q^{16} -6.86939 q^{19} +0.113287 q^{20} -1.69971 q^{22} -5.26114 q^{23} -4.99645 q^{25} -0.146854 q^{26} -5.09133 q^{28} +2.40874 q^{29} +3.15540 q^{31} +3.51488 q^{32} -0.159445 q^{35} -7.50219 q^{37} -2.15096 q^{38} +0.0727740 q^{40} +2.22712 q^{41} -4.51587 q^{43} +10.3243 q^{44} -1.64738 q^{46} +9.24764 q^{47} +0.165753 q^{49} -1.56450 q^{50} +0.892011 q^{52} +12.9263 q^{53} +0.323325 q^{55} -3.27060 q^{56} +0.754230 q^{58} +9.43019 q^{59} -1.82014 q^{61} +0.988026 q^{62} -5.74209 q^{64} +0.0279351 q^{65} -3.18673 q^{67} -0.0499258 q^{70} -4.32016 q^{71} +11.9409 q^{73} -2.34910 q^{74} +13.0653 q^{76} -14.5308 q^{77} +10.6746 q^{79} -0.203787 q^{80} +0.697360 q^{82} +8.70940 q^{83} -1.41402 q^{86} +6.63217 q^{88} -15.9437 q^{89} -1.25545 q^{91} +10.0065 q^{92} +2.89564 q^{94} +0.409164 q^{95} -3.48884 q^{97} +0.0519011 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 20 q^{5} + 8 q^{11} + 4 q^{13} + 16 q^{14} + 24 q^{16} + 4 q^{19} + 48 q^{20} + 36 q^{23} + 28 q^{25} + 64 q^{29} + 36 q^{41} + 4 q^{43} + 16 q^{44} + 24 q^{49} + 16 q^{52} + 20 q^{55}+ \cdots - 12 q^{95}+O(q^{100}) \) 24 * q + 24 * q^4 + 20 * q^5 + 8 * q^11 + 4 * q^13 + 16 * q^14 + 24 * q^16 + 4 * q^19 + 48 * q^20 + 36 * q^23 + 28 * q^25 + 64 * q^29 + 36 * q^41 + 4 * q^43 + 16 * q^44 + 24 * q^49 + 16 * q^52 + 20 * q^55 + 80 * q^56 - 16 * q^62 - 24 * q^64 + 72 * q^65 + 16 * q^67 - 48 * q^70 + 72 * q^71 + 80 * q^74 - 40 * q^76 + 104 * q^80 + 144 * q^92 - 72 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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