LMFDB - Embedded newform 7803.2.a.cg.1.17

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)

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);

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")

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			1.17
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)

$f(q)$	$=$	$q+1.27156 q^{2} -0.383141 q^{4} +1.88026 q^{5} -0.231288 q^{7} -3.03030 q^{8} +2.39086 q^{10} +3.42484 q^{11} +5.14809 q^{13} -0.294096 q^{14} -3.08692 q^{16} +7.16225 q^{19} -0.720403 q^{20} +4.35488 q^{22} +2.39597 q^{23} -1.46463 q^{25} +6.54609 q^{26} +0.0886158 q^{28} +4.71564 q^{29} -4.64813 q^{31} +2.13540 q^{32} -0.434881 q^{35} -4.22375 q^{37} +9.10722 q^{38} -5.69775 q^{40} -0.157955 q^{41} +8.98677 q^{43} -1.31220 q^{44} +3.04662 q^{46} -8.05136 q^{47} -6.94651 q^{49} -1.86236 q^{50} -1.97244 q^{52} -1.37171 q^{53} +6.43958 q^{55} +0.700872 q^{56} +5.99621 q^{58} +6.47064 q^{59} -12.9905 q^{61} -5.91036 q^{62} +8.88913 q^{64} +9.67973 q^{65} -0.781257 q^{67} -0.552976 q^{70} +7.87370 q^{71} +2.97354 q^{73} -5.37075 q^{74} -2.74415 q^{76} -0.792124 q^{77} +11.0702 q^{79} -5.80421 q^{80} -0.200850 q^{82} -3.34474 q^{83} +11.4272 q^{86} -10.3783 q^{88} -16.6262 q^{89} -1.19069 q^{91} -0.917994 q^{92} -10.2378 q^{94} +13.4669 q^{95} +15.6356 q^{97} -8.83288 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.27156	0.899127	0.449564	−	0.893248i	$-0.351580\pi$
$2$	1.27156	0.899127	0.449564	+	0.893248i	$0.351580\pi$
$3$	0	0
$3$	0	0
$4$	−0.383141	−0.191570
$5$	1.88026	0.840877	0.420439	−	0.907321i	$-0.361876\pi$
$5$	1.88026	0.840877	0.420439	+	0.907321i	$0.361876\pi$
$6$	0	0
$7$	−0.231288	−0.0874186	−0.0437093	−	0.999044i	$-0.513918\pi$
$7$	−0.231288	−0.0874186	−0.0437093	+	0.999044i	$0.513918\pi$
$8$	−3.03030	−1.07137
$9$	0	0
$10$	2.39086	0.756055
$11$	3.42484	1.03263	0.516314	−	0.856399i	$-0.327304\pi$
$11$	3.42484	1.03263	0.516314	+	0.856399i	$0.327304\pi$
$12$	0	0
$13$	5.14809	1.42782	0.713911	−	0.700236i	$-0.246922\pi$
$13$	5.14809	1.42782	0.713911	+	0.700236i	$0.246922\pi$
$14$	−0.294096	−0.0786004
$15$	0	0
$16$	−3.08692	−0.771730
$17$	0	0
$17$	0	0
$18$	0	0
$19$	7.16225	1.64313	0.821567	−	0.570113i	$-0.193100\pi$
$19$	7.16225	1.64313	0.821567	+	0.570113i	$0.193100\pi$
$20$	−0.720403	−0.161087
$21$	0	0
$22$	4.35488	0.928464
$23$	2.39597	0.499595	0.249797	−	0.968298i	$-0.419636\pi$
$23$	2.39597	0.499595	0.249797	+	0.968298i	$0.419636\pi$
$24$	0	0
$25$	−1.46463	−0.292926
$26$	6.54609	1.28379
$27$	0	0
$28$	0.0886158	0.0167468
$29$	4.71564	0.875673	0.437836	−	0.899055i	$-0.355745\pi$
$29$	4.71564	0.875673	0.437836	+	0.899055i	$0.355745\pi$
$30$	0	0
$31$	−4.64813	−0.834828	−0.417414	−	0.908716i	$-0.637064\pi$
$31$	−4.64813	−0.834828	−0.417414	+	0.908716i	$0.637064\pi$
$32$	2.13540	0.377489
$33$	0	0
$34$	0	0
$35$	−0.434881	−0.0735083
$36$	0	0
$37$	−4.22375	−0.694381	−0.347191	−	0.937795i	$-0.612864\pi$
$37$	−4.22375	−0.694381	−0.347191	+	0.937795i	$0.612864\pi$
$38$	9.10722	1.47739
$39$	0	0
$40$	−5.69775	−0.900893
$41$	−0.157955	−0.0246685	−0.0123343	−	0.999924i	$-0.503926\pi$
$41$	−0.157955	−0.0246685	−0.0123343	+	0.999924i	$0.503926\pi$
$42$	0	0
$43$	8.98677	1.37047	0.685235	−	0.728322i	$-0.259700\pi$
$43$	8.98677	1.37047	0.685235	+	0.728322i	$0.259700\pi$
$44$	−1.31220	−0.197821
$45$	0	0
$46$	3.04662	0.449199
$47$	−8.05136	−1.17441	−0.587206	−	0.809437i	$-0.699772\pi$
$47$	−8.05136	−1.17441	−0.587206	+	0.809437i	$0.699772\pi$
$48$	0	0
$49$	−6.94651	−0.992358
$50$	−1.86236	−0.263378
$51$	0	0
$52$	−1.97244	−0.273528
$53$	−1.37171	−0.188419	−0.0942095	−	0.995552i	$-0.530032\pi$
$53$	−1.37171	−0.188419	−0.0942095	+	0.995552i	$0.530032\pi$
$54$	0	0
$55$	6.43958	0.868313
$56$	0.700872	0.0936579
$57$	0	0
$58$	5.99621	0.787341
$59$	6.47064	0.842405	0.421203	−	0.906967i	$-0.361608\pi$
$59$	6.47064	0.842405	0.421203	+	0.906967i	$0.361608\pi$
$60$	0	0
$61$	−12.9905	−1.66326	−0.831629	−	0.555332i	$-0.812591\pi$
$61$	−12.9905	−1.66326	−0.831629	+	0.555332i	$0.812591\pi$
$62$	−5.91036	−0.750617
$63$	0	0
$64$	8.88913	1.11114
$65$	9.67973	1.20062
$66$	0	0
$67$	−0.781257	−0.0954458	−0.0477229	−	0.998861i	$-0.515196\pi$
$67$	−0.781257	−0.0954458	−0.0477229	+	0.998861i	$0.515196\pi$
$68$	0	0
$69$	0	0
$70$	−0.552976	−0.0660933
$71$	7.87370	0.934436	0.467218	−	0.884142i	$-0.345256\pi$
$71$	7.87370	0.934436	0.467218	+	0.884142i	$0.345256\pi$
$72$	0	0
$73$	2.97354	0.348027	0.174013	−	0.984743i	$-0.444326\pi$
$73$	2.97354	0.348027	0.174013	+	0.984743i	$0.444326\pi$
$74$	−5.37075	−0.624337
$75$	0	0
$76$	−2.74415	−0.314776
$77$	−0.792124	−0.0902709
$78$	0	0
$79$	11.0702	1.24550	0.622750	−	0.782421i	$-0.286015\pi$
$79$	11.0702	1.24550	0.622750	+	0.782421i	$0.286015\pi$
$80$	−5.80421	−0.648930
$81$	0	0
$82$	−0.200850	−0.0221801
$83$	−3.34474	−0.367133	−0.183566	−	0.983007i	$-0.558764\pi$
$83$	−3.34474	−0.367133	−0.183566	+	0.983007i	$0.558764\pi$
$84$	0	0
$85$	0	0
$86$	11.4272	1.23223
$87$	0	0
$88$	−10.3783	−1.10633
$89$	−16.6262	−1.76237	−0.881187	−	0.472767i	$-0.843255\pi$
$89$	−16.6262	−1.76237	−0.881187	+	0.472767i	$0.843255\pi$
$90$	0	0
$91$	−1.19069	−0.124818
$92$	−0.917994	−0.0957075
$93$	0	0
$94$	−10.2378	−1.05595
$95$	13.4669	1.38167
$96$	0	0
$97$	15.6356	1.58756	0.793779	−	0.608206i	$-0.208110\pi$
$97$	15.6356	1.58756	0.793779	+	0.608206i	$0.208110\pi$
$98$	−8.83288	−0.892256
$99$	0	0
$100$	0.561159	0.0561159
$101$	0.195673	0.0194702	0.00973509	−	0.999953i	$-0.496901\pi$
$101$	0.195673	0.0194702	0.00973509	+	0.999953i	$0.496901\pi$
$102$	0	0
$103$	−0.355474	−0.0350259	−0.0175129	−	0.999847i	$-0.505575\pi$
$103$	−0.355474	−0.0350259	−0.0175129	+	0.999847i	$0.505575\pi$
$104$	−15.6003	−1.52973
$105$	0	0
$106$	−1.74421	−0.169413
$107$	10.0649	0.973013	0.486507	−	0.873677i	$-0.338271\pi$
$107$	10.0649	0.973013	0.486507	+	0.873677i	$0.338271\pi$
$108$	0	0
$109$	10.2939	0.985976	0.492988	−	0.870036i	$-0.335905\pi$
$109$	10.2939	0.985976	0.492988	+	0.870036i	$0.335905\pi$
$110$	8.18830	0.780724
$111$	0	0
$112$	0.713967	0.0674636
$113$	−14.5799	−1.37156	−0.685780	−	0.727808i	$-0.740539\pi$
$113$	−14.5799	−1.37156	−0.685780	+	0.727808i	$0.740539\pi$
$114$	0	0
$115$	4.50505	0.420098
$116$	−1.80675	−0.167753
$117$	0	0
$118$	8.22779	0.757429
$119$	0	0
$120$	0	0
$121$	0.729533	0.0663211
$122$	−16.5181	−1.49548
$123$	0	0
$124$	1.78089	0.159928
$125$	−12.1552	−1.08719
$126$	0	0
$127$	−3.06420	−0.271904	−0.135952	−	0.990715i	$-0.543409\pi$
$127$	−3.06420	−0.271904	−0.135952	+	0.990715i	$0.543409\pi$
$128$	7.03224	0.621568
$129$	0	0
$130$	12.3083	1.07951
$131$	7.50146	0.655406	0.327703	−	0.944781i	$-0.393726\pi$
$131$	7.50146	0.655406	0.327703	+	0.944781i	$0.393726\pi$
$132$	0	0
$133$	−1.65654	−0.143640
$134$	−0.993414	−0.0858179
$135$	0	0
$136$	0	0
$137$	9.35686	0.799411	0.399705	−	0.916644i	$-0.369112\pi$
$137$	9.35686	0.799411	0.399705	+	0.916644i	$0.369112\pi$
$138$	0	0
$139$	5.07571	0.430516	0.215258	−	0.976557i	$-0.430941\pi$
$139$	5.07571	0.430516	0.215258	+	0.976557i	$0.430941\pi$
$140$	0.166621	0.0140820
$141$	0	0
$142$	10.0119	0.840177
$143$	17.6314	1.47441
$144$	0	0
$145$	8.86662	0.736333
$146$	3.78103	0.312920
$147$	0	0
$148$	1.61829	0.133023
$149$	3.54068	0.290063	0.145032	−	0.989427i	$-0.453672\pi$
$149$	3.54068	0.290063	0.145032	+	0.989427i	$0.453672\pi$
$150$	0	0
$151$	−12.4560	−1.01366	−0.506829	−	0.862047i	$-0.669182\pi$
$151$	−12.4560	−1.01366	−0.506829	+	0.862047i	$0.669182\pi$
$152$	−21.7038	−1.76041
$153$	0	0
$154$	−1.00723	−0.0811650
$155$	−8.73968	−0.701988
$156$	0	0
$157$	11.6965	0.933485	0.466742	−	0.884393i	$-0.345428\pi$
$157$	11.6965	0.933485	0.466742	+	0.884393i	$0.345428\pi$
$158$	14.0765	1.11986
$159$	0	0
$160$	4.01511	0.317422
$161$	−0.554159	−0.0436739
$162$	0	0
$163$	15.7122	1.23068	0.615338	−	0.788263i	$-0.289019\pi$
$163$	15.7122	1.23068	0.615338	+	0.788263i	$0.289019\pi$
$164$	0.0605192	0.00472575
$165$	0	0
$166$	−4.25303	−0.330099
$167$	−5.17428	−0.400398	−0.200199	−	0.979755i	$-0.564159\pi$
$167$	−5.17428	−0.400398	−0.200199	+	0.979755i	$0.564159\pi$
$168$	0	0
$169$	13.5028	1.03868
$170$	0	0
$171$	0	0
$172$	−3.44320	−0.262541
$173$	18.1521	1.38008	0.690039	−	0.723772i	$-0.257593\pi$
$173$	18.1521	1.38008	0.690039	+	0.723772i	$0.257593\pi$
$174$	0	0
$175$	0.338751	0.0256072
$176$	−10.5722	−0.796911
$177$	0	0
$178$	−21.1412	−1.58460
$179$	8.82243	0.659419	0.329710	−	0.944082i	$-0.393049\pi$
$179$	8.82243	0.659419	0.329710	+	0.944082i	$0.393049\pi$
$180$	0	0
$181$	23.1721	1.72237	0.861184	−	0.508293i	$-0.169723\pi$
$181$	23.1721	1.72237	0.861184	+	0.508293i	$0.169723\pi$
$182$	−1.51403	−0.112227
$183$	0	0
$184$	−7.26052	−0.535252
$185$	−7.94175	−0.583889
$186$	0	0
$187$	0	0
$188$	3.08481	0.224983
$189$	0	0
$190$	17.1239	1.24230
$191$	25.4613	1.84231	0.921157	−	0.389191i	$-0.127245\pi$
$191$	25.4613	1.84231	0.921157	+	0.389191i	$0.127245\pi$
$192$	0	0
$193$	8.15435	0.586963	0.293481	−	0.955965i	$-0.405186\pi$
$193$	8.15435	0.586963	0.293481	+	0.955965i	$0.405186\pi$
$194$	19.8816	1.42742
$195$	0	0
$196$	2.66149	0.190106
$197$	−14.2837	−1.01767	−0.508836	−	0.860864i	$-0.669924\pi$
$197$	−14.2837	−1.01767	−0.508836	+	0.860864i	$0.669924\pi$
$198$	0	0
$199$	0.538435	0.0381686	0.0190843	−	0.999818i	$-0.493925\pi$
$199$	0.538435	0.0381686	0.0190843	+	0.999818i	$0.493925\pi$
$200$	4.43827	0.313833
$201$	0	0
$202$	0.248809	0.0175062
$203$	−1.09067	−0.0765501
$204$	0	0
$205$	−0.296997	−0.0207432
$206$	−0.452006	−0.0314927
$207$	0	0
$208$	−15.8917	−1.10189
$209$	24.5296	1.69675
$210$	0	0
$211$	3.41620	0.235181	0.117591	−	0.993062i	$-0.462483\pi$
$211$	3.41620	0.235181	0.117591	+	0.993062i	$0.462483\pi$
$212$	0.525559	0.0360955
$213$	0	0
$214$	12.7981	0.874863
$215$	16.8974	1.15240
$216$	0	0
$217$	1.07506	0.0729795
$218$	13.0893	0.886518
$219$	0	0
$220$	−2.46727	−0.166343
$221$	0	0
$222$	0	0
$223$	−20.1879	−1.35188	−0.675941	−	0.736956i	$-0.736263\pi$
$223$	−20.1879	−1.35188	−0.675941	+	0.736956i	$0.736263\pi$
$224$	−0.493893	−0.0329996
$225$	0	0
$226$	−18.5392	−1.23321
$227$	−1.44153	−0.0956779	−0.0478390	−	0.998855i	$-0.515233\pi$
$227$	−1.44153	−0.0956779	−0.0478390	+	0.998855i	$0.515233\pi$
$228$	0	0
$229$	−10.5245	−0.695480	−0.347740	−	0.937591i	$-0.613051\pi$
$229$	−10.5245	−0.695480	−0.347740	+	0.937591i	$0.613051\pi$
$230$	5.72843	0.377721
$231$	0	0
$232$	−14.2898	−0.938172
$233$	13.4456	0.880852	0.440426	−	0.897789i	$-0.354828\pi$
$233$	13.4456	0.880852	0.440426	+	0.897789i	$0.354828\pi$
$234$	0	0
$235$	−15.1386	−0.987536
$236$	−2.47916	−0.161380
$237$	0	0
$238$	0	0
$239$	17.3220	1.12047	0.560233	−	0.828335i	$-0.310712\pi$
$239$	17.3220	1.12047	0.560233	+	0.828335i	$0.310712\pi$
$240$	0	0
$241$	−14.8368	−0.955722	−0.477861	−	0.878435i	$-0.658588\pi$
$241$	−14.8368	−0.955722	−0.477861	+	0.878435i	$0.658588\pi$
$242$	0.927643	0.0596311
$243$	0	0
$244$	4.97717	0.318631
$245$	−13.0612	−0.834451
$246$	0	0
$247$	36.8719	2.34610
$248$	14.0852	0.894412
$249$	0	0
$250$	−15.4560	−0.977524
$251$	−28.1651	−1.77776	−0.888882	−	0.458136i	$-0.848517\pi$
$251$	−28.1651	−1.77776	−0.888882	+	0.458136i	$0.848517\pi$
$252$	0	0
$253$	8.20582	0.515896
$254$	−3.89631	−0.244476
$255$	0	0
$256$	−8.83636	−0.552273
$257$	4.45435	0.277855	0.138927	−	0.990303i	$-0.455635\pi$
$257$	4.45435	0.277855	0.138927	+	0.990303i	$0.455635\pi$
$258$	0	0
$259$	0.976903	0.0607018
$260$	−3.70870	−0.230004
$261$	0	0
$262$	9.53854	0.589293
$263$	−17.4190	−1.07410	−0.537050	−	0.843551i	$-0.680461\pi$
$263$	−17.4190	−1.07410	−0.537050	+	0.843551i	$0.680461\pi$
$264$	0	0
$265$	−2.57917	−0.158437
$266$	−2.10639	−0.129151
$267$	0	0
$268$	0.299332	0.0182846
$269$	21.6846	1.32213	0.661066	−	0.750328i	$-0.270104\pi$
$269$	21.6846	1.32213	0.661066	+	0.750328i	$0.270104\pi$
$270$	0	0
$271$	−27.4783	−1.66919	−0.834593	−	0.550866i	$-0.814297\pi$
$271$	−27.4783	−1.66919	−0.834593	+	0.550866i	$0.814297\pi$
$272$	0	0
$273$	0	0
$274$	11.8978	0.718772
$275$	−5.01612	−0.302484
$276$	0	0
$277$	25.4864	1.53133	0.765664	−	0.643240i	$-0.222410\pi$
$277$	25.4864	1.53133	0.765664	+	0.643240i	$0.222410\pi$
$278$	6.45405	0.387088
$279$	0	0
$280$	1.31782	0.0787548
$281$	21.5893	1.28791	0.643955	−	0.765063i	$-0.277292\pi$
$281$	21.5893	1.28791	0.643955	+	0.765063i	$0.277292\pi$
$282$	0	0
$283$	8.65063	0.514227	0.257113	−	0.966381i	$-0.417229\pi$
$283$	8.65063	0.514227	0.257113	+	0.966381i	$0.417229\pi$
$284$	−3.01673	−0.179010
$285$	0	0
$286$	22.4193	1.32568
$287$	0.0365332	0.00215649
$288$	0	0
$289$	0	0
$290$	11.2744	0.662057
$291$	0	0
$292$	−1.13928	−0.0666716
$293$	15.4778	0.904222	0.452111	−	0.891962i	$-0.350671\pi$
$293$	15.4778	0.904222	0.452111	+	0.891962i	$0.350671\pi$
$294$	0	0
$295$	12.1665	0.708359
$296$	12.7992	0.743941
$297$	0	0
$298$	4.50217	0.260804
$299$	12.3347	0.713332
$300$	0	0
$301$	−2.07853	−0.119804
$302$	−15.8386	−0.911407
$303$	0	0
$304$	−22.1093	−1.26806
$305$	−24.4254	−1.39860
$306$	0	0
$307$	−31.1421	−1.77737	−0.888687	−	0.458514i	$-0.848382\pi$
$307$	−31.1421	−1.77737	−0.888687	+	0.458514i	$0.848382\pi$
$308$	0.303495	0.0172932
$309$	0	0
$310$	−11.1130	−0.631176
$311$	29.5655	1.67650	0.838252	−	0.545283i	$-0.183578\pi$
$311$	29.5655	1.67650	0.838252	+	0.545283i	$0.183578\pi$
$312$	0	0
$313$	−13.4364	−0.759468	−0.379734	−	0.925096i	$-0.623984\pi$
$313$	−13.4364	−0.759468	−0.379734	+	0.925096i	$0.623984\pi$
$314$	14.8728	0.839321
$315$	0	0
$316$	−4.24146	−0.238601
$317$	0.407831	0.0229061	0.0114530	−	0.999934i	$-0.496354\pi$
$317$	0.407831	0.0229061	0.0114530	+	0.999934i	$0.496354\pi$
$318$	0	0
$319$	16.1503	0.904244
$320$	16.7139	0.934333
$321$	0	0
$322$	−0.704645	−0.0392684
$323$	0	0
$324$	0	0
$325$	−7.54004	−0.418246
$326$	19.9790	1.10653
$327$	0	0
$328$	0.478653	0.0264292
$329$	1.86218	0.102665
$330$	0	0
$331$	−8.25686	−0.453838	−0.226919	−	0.973914i	$-0.572865\pi$
$331$	−8.25686	−0.453838	−0.226919	+	0.973914i	$0.572865\pi$
$332$	1.28151	0.0703317
$333$	0	0
$334$	−6.57940	−0.360009
$335$	−1.46897	−0.0802582
$336$	0	0
$337$	23.7049	1.29129	0.645643	−	0.763640i	$-0.276590\pi$
$337$	23.7049	1.29129	0.645643	+	0.763640i	$0.276590\pi$
$338$	17.1696	0.933902
$339$	0	0
$340$	0	0
$341$	−15.9191	−0.862067
$342$	0	0
$343$	3.22566	0.174169
$344$	−27.2326	−1.46828
$345$	0	0
$346$	23.0814	1.24087
$347$	−29.7545	−1.59731	−0.798653	−	0.601792i	$-0.794453\pi$
$347$	−29.7545	−1.59731	−0.798653	+	0.601792i	$0.794453\pi$
$348$	0	0
$349$	−18.5714	−0.994105	−0.497053	−	0.867720i	$-0.665584\pi$
$349$	−18.5714	−0.994105	−0.497053	+	0.867720i	$0.665584\pi$
$350$	0.430741	0.0230241
$351$	0	0
$352$	7.31341	0.389806
$353$	−32.4661	−1.72800	−0.863999	−	0.503494i	$-0.832047\pi$
$353$	−32.4661	−1.72800	−0.863999	+	0.503494i	$0.832047\pi$
$354$	0	0
$355$	14.8046	0.785746
$356$	6.37018	0.337619
$357$	0	0
$358$	11.2182	0.592902
$359$	−30.9584	−1.63392	−0.816962	−	0.576692i	$-0.804343\pi$
$359$	−30.9584	−1.63392	−0.816962	+	0.576692i	$0.804343\pi$
$360$	0	0
$361$	32.2978	1.69989
$362$	29.4647	1.54863
$363$	0	0
$364$	0.456202	0.0239115
$365$	5.59102	0.292647
$366$	0	0
$367$	−3.73792	−0.195118	−0.0975589	−	0.995230i	$-0.531103\pi$
$367$	−3.73792	−0.195118	−0.0975589	+	0.995230i	$0.531103\pi$
$368$	−7.39618	−0.385552
$369$	0	0
$370$	−10.0984	−0.524991
$371$	0.317260	0.0164713
$372$	0	0
$373$	14.3295	0.741954	0.370977	−	0.928642i	$-0.379023\pi$
$373$	14.3295	0.741954	0.370977	+	0.928642i	$0.379023\pi$
$374$	0	0
$375$	0	0
$376$	24.3981	1.25823
$377$	24.2765	1.25030
$378$	0	0
$379$	−16.3486	−0.839769	−0.419884	−	0.907578i	$-0.637929\pi$
$379$	−16.3486	−0.839769	−0.419884	+	0.907578i	$0.637929\pi$
$380$	−5.15971	−0.264688
$381$	0	0
$382$	32.3755	1.65647
$383$	11.4346	0.584279	0.292139	−	0.956376i	$-0.405633\pi$
$383$	11.4346	0.584279	0.292139	+	0.956376i	$0.405633\pi$
$384$	0	0
$385$	−1.48940	−0.0759067
$386$	10.3687	0.527754
$387$	0	0
$388$	−5.99065	−0.304129
$389$	36.2589	1.83840	0.919198	−	0.393795i	$-0.128838\pi$
$389$	36.2589	1.83840	0.919198	+	0.393795i	$0.128838\pi$
$390$	0	0
$391$	0	0
$392$	21.0500	1.06319
$393$	0	0
$394$	−18.1625	−0.915016
$395$	20.8149	1.04731
$396$	0	0
$397$	−21.1987	−1.06393	−0.531966	−	0.846766i	$-0.678547\pi$
$397$	−21.1987	−1.06393	−0.531966	+	0.846766i	$0.678547\pi$
$398$	0.684651	0.0343185
$399$	0	0
$400$	4.52120	0.226060
$401$	−7.74570	−0.386802	−0.193401	−	0.981120i	$-0.561952\pi$
$401$	−7.74570	−0.386802	−0.193401	+	0.981120i	$0.561952\pi$
$402$	0	0
$403$	−23.9290	−1.19199
$404$	−0.0749703	−0.00372991
$405$	0	0
$406$	−1.38685	−0.0688283
$407$	−14.4657	−0.717037
$408$	0	0
$409$	−18.6180	−0.920599	−0.460300	−	0.887764i	$-0.652258\pi$
$409$	−18.6180	−0.920599	−0.460300	+	0.887764i	$0.652258\pi$
$410$	−0.377649	−0.0186508
$411$	0	0
$412$	0.136197	0.00670992
$413$	−1.49658	−0.0736419
$414$	0	0
$415$	−6.28897	−0.308713
$416$	10.9932	0.538988
$417$	0	0
$418$	31.1908	1.52559
$419$	−30.9529	−1.51215	−0.756073	−	0.654487i	$-0.772885\pi$
$419$	−30.9529	−1.51215	−0.756073	+	0.654487i	$0.772885\pi$
$420$	0	0
$421$	−12.6804	−0.618004	−0.309002	−	0.951061i	$-0.599995\pi$
$421$	−12.6804	−0.618004	−0.309002	+	0.951061i	$0.599995\pi$
$422$	4.34390	0.211458
$423$	0	0
$424$	4.15670	0.201867
$425$	0	0
$426$	0	0
$427$	3.00453	0.145400
$428$	−3.85628	−0.186400
$429$	0	0
$430$	21.4861	1.03615
$431$	−4.38639	−0.211285	−0.105642	−	0.994404i	$-0.533690\pi$
$431$	−4.38639	−0.211285	−0.105642	+	0.994404i	$0.533690\pi$
$432$	0	0
$433$	23.7292	1.14035	0.570175	−	0.821523i	$-0.306875\pi$
$433$	23.7292	1.14035	0.570175	+	0.821523i	$0.306875\pi$
$434$	1.36699	0.0656178
$435$	0	0
$436$	−3.94401	−0.188884
$437$	17.1606	0.820901
$438$	0	0
$439$	16.0889	0.767884	0.383942	−	0.923357i	$-0.374566\pi$
$439$	16.0889	0.767884	0.383942	+	0.923357i	$0.374566\pi$
$440$	−19.5139	−0.930288
$441$	0	0
$442$	0	0
$443$	−1.22288	−0.0581009	−0.0290505	−	0.999578i	$-0.509248\pi$
$443$	−1.22288	−0.0581009	−0.0290505	+	0.999578i	$0.509248\pi$
$444$	0	0
$445$	−31.2616	−1.48194
$446$	−25.6701	−1.21551
$447$	0	0
$448$	−2.05595	−0.0971344
$449$	23.4697	1.10760	0.553802	−	0.832649i	$-0.313177\pi$
$449$	23.4697	1.10760	0.553802	+	0.832649i	$0.313177\pi$
$450$	0	0
$451$	−0.540972	−0.0254734
$452$	5.58615	0.262750
$453$	0	0
$454$	−1.83299	−0.0860266
$455$	−2.23880	−0.104957
$456$	0	0
$457$	−38.6263	−1.80686	−0.903431	−	0.428734i	$-0.858960\pi$
$457$	−38.6263	−1.80686	−0.903431	+	0.428734i	$0.858960\pi$
$458$	−13.3825	−0.625325
$459$	0	0
$460$	−1.72607	−0.0804783
$461$	17.9331	0.835227	0.417613	−	0.908625i	$-0.362867\pi$
$461$	17.9331	0.835227	0.417613	+	0.908625i	$0.362867\pi$
$462$	0	0
$463$	−9.71279	−0.451392	−0.225696	−	0.974198i	$-0.572466\pi$
$463$	−9.71279	−0.451392	−0.225696	+	0.974198i	$0.572466\pi$
$464$	−14.5568	−0.675783
$465$	0	0
$466$	17.0969	0.791998
$467$	33.6249	1.55597	0.777987	−	0.628281i	$-0.216241\pi$
$467$	33.6249	1.55597	0.777987	+	0.628281i	$0.216241\pi$
$468$	0	0
$469$	0.180695	0.00834374
$470$	−19.2497	−0.887921
$471$	0	0
$472$	−19.6080	−0.902530
$473$	30.7782	1.41519
$474$	0	0
$475$	−10.4900	−0.481316
$476$	0	0
$477$	0	0
$478$	22.0259	1.00744
$479$	−29.2755	−1.33763	−0.668815	−	0.743429i	$-0.733198\pi$
$479$	−29.2755	−1.33763	−0.668815	+	0.743429i	$0.733198\pi$
$480$	0	0
$481$	−21.7443	−0.991453
$482$	−18.8659	−0.859316
$483$	0	0
$484$	−0.279514	−0.0127052
$485$	29.3990	1.33494
$486$	0	0
$487$	−27.3459	−1.23916	−0.619580	−	0.784934i	$-0.712697\pi$
$487$	−27.3459	−1.23916	−0.619580	+	0.784934i	$0.712697\pi$
$488$	39.3650	1.78197
$489$	0	0
$490$	−16.6081	−0.750278
$491$	−0.811216	−0.0366097	−0.0183048	−	0.999832i	$-0.505827\pi$
$491$	−0.811216	−0.0366097	−0.0183048	+	0.999832i	$0.505827\pi$
$492$	0	0
$493$	0	0
$494$	46.8847	2.10944
$495$	0	0
$496$	14.3484	0.644262
$497$	−1.82109	−0.0816871
$498$	0	0
$499$	−28.5393	−1.27759	−0.638797	−	0.769375i	$-0.720568\pi$
$499$	−28.5393	−1.27759	−0.638797	+	0.769375i	$0.720568\pi$
$500$	4.65714	0.208274
$501$	0	0
$502$	−35.8135	−1.59844
$503$	−7.74450	−0.345310	−0.172655	−	0.984982i	$-0.555235\pi$
$503$	−7.74450	−0.345310	−0.172655	+	0.984982i	$0.555235\pi$
$504$	0	0
$505$	0.367916	0.0163720
$506$	10.4342	0.463856
$507$	0	0
$508$	1.17402	0.0520887
$509$	24.2954	1.07687	0.538437	−	0.842666i	$-0.319015\pi$
$509$	24.2954	1.07687	0.538437	+	0.842666i	$0.319015\pi$
$510$	0	0
$511$	−0.687744	−0.0304240
$512$	−25.3004	−1.11813
$513$	0	0
$514$	5.66396	0.249827
$515$	−0.668383	−0.0294525
$516$	0	0
$517$	−27.5746	−1.21273
$518$	1.24219	0.0545786
$519$	0	0
$520$	−29.3325	−1.28632
$521$	38.3077	1.67829	0.839146	−	0.543906i	$-0.183055\pi$
$521$	38.3077	1.67829	0.839146	+	0.543906i	$0.183055\pi$
$522$	0	0
$523$	34.6641	1.51576	0.757878	−	0.652397i	$-0.226236\pi$
$523$	34.6641	1.51576	0.757878	+	0.652397i	$0.226236\pi$
$524$	−2.87412	−0.125556
$525$	0	0
$526$	−22.1492	−0.965752
$527$	0	0
$528$	0	0
$529$	−17.2593	−0.750405
$530$	−3.27957	−0.142455
$531$	0	0
$532$	0.634689	0.0275172
$533$	−0.813168	−0.0352222
$534$	0	0
$535$	18.9247	0.818184
$536$	2.36745	0.102258
$537$	0	0
$538$	27.5732	1.18876
$539$	−23.7907	−1.02474
$540$	0	0
$541$	−4.75440	−0.204407	−0.102204	−	0.994763i	$-0.532589\pi$
$541$	−4.75440	−0.204407	−0.102204	+	0.994763i	$0.532589\pi$
$542$	−34.9402	−1.50081
$543$	0	0
$544$	0	0
$545$	19.3552	0.829084
$546$	0	0
$547$	19.4361	0.831026	0.415513	−	0.909587i	$-0.363602\pi$
$547$	19.4361	0.831026	0.415513	+	0.909587i	$0.363602\pi$
$548$	−3.58499	−0.153143
$549$	0	0
$550$	−6.37829	−0.271971
$551$	33.7746	1.43885
$552$	0	0
$553$	−2.56041	−0.108880
$554$	32.4074	1.37686
$555$	0	0
$556$	−1.94471	−0.0824741
$557$	9.95386	0.421759	0.210879	−	0.977512i	$-0.432367\pi$
$557$	9.95386	0.421759	0.210879	+	0.977512i	$0.432367\pi$
$558$	0	0
$559$	46.2646	1.95679
$560$	1.34244	0.0567286
$561$	0	0
$562$	27.4521	1.15800
$563$	7.12091	0.300111	0.150055	−	0.988678i	$-0.452055\pi$
$563$	7.12091	0.300111	0.150055	+	0.988678i	$0.452055\pi$
$564$	0	0
$565$	−27.4140	−1.15331
$566$	10.9998	0.462355
$567$	0	0
$568$	−23.8597	−1.00113
$569$	−24.5270	−1.02822	−0.514112	−	0.857723i	$-0.671879\pi$
$569$	−24.5270	−1.02822	−0.514112	+	0.857723i	$0.671879\pi$
$570$	0	0
$571$	−35.2798	−1.47641	−0.738207	−	0.674575i	$-0.764327\pi$
$571$	−35.2798	−1.47641	−0.738207	+	0.674575i	$0.764327\pi$
$572$	−6.75530	−0.282453
$573$	0	0
$574$	0.0464541	0.00193895
$575$	−3.50921	−0.146344
$576$	0	0
$577$	3.41354	0.142108	0.0710538	−	0.997472i	$-0.477364\pi$
$577$	3.41354	0.142108	0.0710538	+	0.997472i	$0.477364\pi$
$578$	0	0
$579$	0	0
$580$	−3.39716	−0.141060
$581$	0.773597	0.0320942
$582$	0	0
$583$	−4.69789	−0.194567
$584$	−9.01072	−0.372866
$585$	0	0
$586$	19.6809	0.813010
$587$	−16.5308	−0.682300	−0.341150	−	0.940009i	$-0.610816\pi$
$587$	−16.5308	−0.682300	−0.341150	+	0.940009i	$0.610816\pi$
$588$	0	0
$589$	−33.2910	−1.37173
$590$	15.4704	0.636905
$591$	0	0
$592$	13.0384	0.535875
$593$	−8.17470	−0.335695	−0.167847	−	0.985813i	$-0.553682\pi$
$593$	−8.17470	−0.335695	−0.167847	+	0.985813i	$0.553682\pi$
$594$	0	0
$595$	0	0
$596$	−1.35658	−0.0555676
$597$	0	0
$598$	15.6842	0.641376
$599$	31.5073	1.28735	0.643676	−	0.765298i	$-0.277408\pi$
$599$	31.5073	1.28735	0.643676	+	0.765298i	$0.277408\pi$
$600$	0	0
$601$	4.40664	0.179751	0.0898754	−	0.995953i	$-0.471353\pi$
$601$	4.40664	0.179751	0.0898754	+	0.995953i	$0.471353\pi$
$602$	−2.64297	−0.107719
$603$	0	0
$604$	4.77241	0.194187
$605$	1.37171	0.0557679
$606$	0	0
$607$	37.1701	1.50869	0.754344	−	0.656480i	$-0.227955\pi$
$607$	37.1701	1.50869	0.754344	+	0.656480i	$0.227955\pi$
$608$	15.2943	0.620265
$609$	0	0
$610$	−31.0583	−1.25751
$611$	−41.4491	−1.67685
$612$	0	0
$613$	1.50892	0.0609449	0.0304724	−	0.999536i	$-0.490299\pi$
$613$	1.50892	0.0609449	0.0304724	+	0.999536i	$0.490299\pi$
$614$	−39.5990	−1.59809
$615$	0	0
$616$	2.40037	0.0967138
$617$	41.5179	1.67145	0.835724	−	0.549150i	$-0.185048\pi$
$617$	41.5179	1.67145	0.835724	+	0.549150i	$0.185048\pi$
$618$	0	0
$619$	−32.4630	−1.30480	−0.652398	−	0.757876i	$-0.726237\pi$
$619$	−32.4630	−1.30480	−0.652398	+	0.757876i	$0.726237\pi$
$620$	3.34853	0.134480
$621$	0	0
$622$	37.5942	1.50739
$623$	3.84544	0.154064
$624$	0	0
$625$	−15.5317	−0.621269
$626$	−17.0851	−0.682858
$627$	0	0
$628$	−4.48142	−0.178828
$629$	0	0
$630$	0	0
$631$	−11.6257	−0.462814	−0.231407	−	0.972857i	$-0.574333\pi$
$631$	−11.6257	−0.462814	−0.231407	+	0.972857i	$0.574333\pi$
$632$	−33.5462	−1.33439
$633$	0	0
$634$	0.518581	0.0205955
$635$	−5.76149	−0.228638
$636$	0	0
$637$	−35.7612	−1.41691
$638$	20.5361	0.813031
$639$	0	0
$640$	13.2224	0.522662
$641$	−14.2439	−0.562600	−0.281300	−	0.959620i	$-0.590766\pi$
$641$	−14.2439	−0.562600	−0.281300	+	0.959620i	$0.590766\pi$
$642$	0	0
$643$	−26.4280	−1.04222	−0.521110	−	0.853490i	$-0.674482\pi$
$643$	−26.4280	−1.04222	−0.521110	+	0.853490i	$0.674482\pi$
$644$	0.212321	0.00836662
$645$	0	0
$646$	0	0
$647$	−9.88070	−0.388451	−0.194225	−	0.980957i	$-0.562219\pi$
$647$	−9.88070	−0.388451	−0.194225	+	0.980957i	$0.562219\pi$
$648$	0	0
$649$	22.1609	0.869892
$650$	−9.58759	−0.376056
$651$	0	0
$652$	−6.01999	−0.235761
$653$	−2.06379	−0.0807625	−0.0403812	−	0.999184i	$-0.512857\pi$
$653$	−2.06379	−0.0807625	−0.0403812	+	0.999184i	$0.512857\pi$
$654$	0	0
$655$	14.1047	0.551116
$656$	0.487596	0.0190374
$657$	0	0
$658$	2.36787	0.0923093
$659$	−21.3928	−0.833343	−0.416672	−	0.909057i	$-0.636804\pi$
$659$	−21.3928	−0.833343	−0.416672	+	0.909057i	$0.636804\pi$
$660$	0	0
$661$	24.2883	0.944707	0.472354	−	0.881409i	$-0.343405\pi$
$661$	24.2883	0.944707	0.472354	+	0.881409i	$0.343405\pi$
$662$	−10.4991	−0.408058
$663$	0	0
$664$	10.1356	0.393336
$665$	−3.11473	−0.120784
$666$	0	0
$667$	11.2985	0.437481
$668$	1.98248	0.0767043
$669$	0	0
$670$	−1.86787	−0.0721623
$671$	−44.4902	−1.71753
$672$	0	0
$673$	−35.2471	−1.35868	−0.679338	−	0.733825i	$-0.737733\pi$
$673$	−35.2471	−1.35868	−0.679338	+	0.733825i	$0.737733\pi$
$674$	30.1421	1.16103
$675$	0	0
$676$	−5.17347	−0.198980
$677$	−1.38936	−0.0533974	−0.0266987	−	0.999644i	$-0.508499\pi$
$677$	−1.38936	−0.0533974	−0.0266987	+	0.999644i	$0.508499\pi$
$678$	0	0
$679$	−3.61633	−0.138782
$680$	0	0
$681$	0	0
$682$	−20.2420	−0.775108
$683$	31.8369	1.21821	0.609103	−	0.793091i	$-0.291530\pi$
$683$	31.8369	1.21821	0.609103	+	0.793091i	$0.291530\pi$
$684$	0	0
$685$	17.5933	0.672206
$686$	4.10161	0.156600
$687$	0	0
$688$	−27.7414	−1.05763
$689$	−7.06169	−0.269029
$690$	0	0
$691$	−17.5280	−0.666797	−0.333399	−	0.942786i	$-0.608196\pi$
$691$	−17.5280	−0.666797	−0.333399	+	0.942786i	$0.608196\pi$
$692$	−6.95481	−0.264382
$693$	0	0
$694$	−37.8346	−1.43618
$695$	9.54364	0.362011
$696$	0	0
$697$	0	0
$698$	−23.6146	−0.893827
$699$	0	0
$700$	−0.129789	−0.00490557
$701$	−26.4148	−0.997674	−0.498837	−	0.866696i	$-0.666239\pi$
$701$	−26.4148	−0.997674	−0.498837	+	0.866696i	$0.666239\pi$
$702$	0	0
$703$	−30.2516	−1.14096
$704$	30.4439	1.14740
$705$	0	0
$706$	−41.2825	−1.55369
$707$	−0.0452568	−0.00170206
$708$	0	0
$709$	11.3649	0.426816	0.213408	−	0.976963i	$-0.431544\pi$
$709$	11.3649	0.426816	0.213408	+	0.976963i	$0.431544\pi$
$710$	18.8249	0.706485
$711$	0	0
$712$	50.3824	1.88816
$713$	−11.1368	−0.417076
$714$	0	0
$715$	33.1515	1.23980
$716$	−3.38023	−0.126325
$717$	0	0
$718$	−39.3654	−1.46910
$719$	−15.3875	−0.573856	−0.286928	−	0.957952i	$-0.592634\pi$
$719$	−15.3875	−0.573856	−0.286928	+	0.957952i	$0.592634\pi$
$720$	0	0
$721$	0.0822168	0.00306191
$722$	41.0686	1.52841
$723$	0	0
$724$	−8.87818	−0.329955
$725$	−6.90667	−0.256507
$726$	0	0
$727$	−43.0876	−1.59803	−0.799015	−	0.601311i	$-0.794645\pi$
$727$	−43.0876	−1.59803	−0.799015	+	0.601311i	$0.794645\pi$
$728$	3.60815	0.133727
$729$	0	0
$730$	7.10931	0.263127
$731$	0	0
$732$	0	0
$733$	−24.1471	−0.891892	−0.445946	−	0.895060i	$-0.647133\pi$
$733$	−24.1471	−0.891892	−0.445946	+	0.895060i	$0.647133\pi$
$734$	−4.75298	−0.175436
$735$	0	0
$736$	5.11637	0.188592
$737$	−2.67568	−0.0985600
$738$	0	0
$739$	0.996882	0.0366709	0.0183354	−	0.999832i	$-0.494163\pi$
$739$	0.996882	0.0366709	0.0183354	+	0.999832i	$0.494163\pi$
$740$	3.04281	0.111856
$741$	0	0
$742$	0.403415	0.0148098
$743$	−32.5845	−1.19541	−0.597705	−	0.801716i	$-0.703921\pi$
$743$	−32.5845	−1.19541	−0.597705	+	0.801716i	$0.703921\pi$
$744$	0	0
$745$	6.65739	0.243908
$746$	18.2208	0.667111
$747$	0	0
$748$	0	0
$749$	−2.32790	−0.0850594
$750$	0	0
$751$	35.0544	1.27915	0.639576	−	0.768728i	$-0.279110\pi$
$751$	35.0544	1.27915	0.639576	+	0.768728i	$0.279110\pi$
$752$	24.8539	0.906330
$753$	0	0
$754$	30.8690	1.12418
$755$	−23.4206	−0.852361
$756$	0	0
$757$	−7.14147	−0.259561	−0.129781	−	0.991543i	$-0.541427\pi$
$757$	−7.14147	−0.259561	−0.129781	+	0.991543i	$0.541427\pi$
$758$	−20.7881	−0.755059
$759$	0	0
$760$	−40.8087	−1.48029
$761$	−13.7182	−0.497283	−0.248641	−	0.968596i	$-0.579984\pi$
$761$	−13.7182	−0.497283	−0.248641	+	0.968596i	$0.579984\pi$
$762$	0	0
$763$	−2.38085	−0.0861926
$764$	−9.75526	−0.352933
$765$	0	0
$766$	14.5397	0.525341
$767$	33.3114	1.20280
$768$	0	0
$769$	15.2265	0.549081	0.274540	−	0.961576i	$-0.411474\pi$
$769$	15.2265	0.549081	0.274540	+	0.961576i	$0.411474\pi$
$770$	−1.89386	−0.0682498
$771$	0	0
$772$	−3.12426	−0.112445
$773$	−22.8305	−0.821156	−0.410578	−	0.911825i	$-0.634673\pi$
$773$	−22.8305	−0.821156	−0.410578	+	0.911825i	$0.634673\pi$
$774$	0	0
$775$	6.80778	0.244543
$776$	−47.3807	−1.70087
$777$	0	0
$778$	46.1052	1.65295
$779$	−1.13132	−0.0405336
$780$	0	0
$781$	26.9662	0.964925
$782$	0	0
$783$	0	0
$784$	21.4433	0.765833
$785$	21.9925	0.784946
$786$	0	0
$787$	−2.73917	−0.0976410	−0.0488205	−	0.998808i	$-0.515546\pi$
$787$	−2.73917	−0.0976410	−0.0488205	+	0.998808i	$0.515546\pi$
$788$	5.47267	0.194956
$789$	0	0
$790$	26.4674	0.941667
$791$	3.37215	0.119900
$792$	0	0
$793$	−66.8760	−2.37484
$794$	−26.9554	−0.956611
$795$	0	0
$796$	−0.206296	−0.00731198
$797$	5.79845	0.205392	0.102696	−	0.994713i	$-0.467253\pi$
$797$	5.79845	0.205392	0.102696	+	0.994713i	$0.467253\pi$
$798$	0	0
$799$	0	0
$800$	−3.12757	−0.110576
$801$	0	0
$802$	−9.84910	−0.347784
$803$	10.1839	0.359382
$804$	0	0
$805$	−1.04196	−0.0367243
$806$	−30.4270	−1.07175
$807$	0	0
$808$	−0.592948	−0.0208598
$809$	19.3287	0.679561	0.339781	−	0.940505i	$-0.389647\pi$
$809$	19.3287	0.679561	0.339781	+	0.940505i	$0.389647\pi$
$810$	0	0
$811$	7.32574	0.257242	0.128621	−	0.991694i	$-0.458945\pi$
$811$	7.32574	0.257242	0.128621	+	0.991694i	$0.458945\pi$
$812$	0.417880	0.0146647
$813$	0	0
$814$	−18.3940	−0.644708
$815$	29.5430	1.03485
$816$	0	0
$817$	64.3655	2.25186
$818$	−23.6738	−0.827736
$819$	0	0
$820$	0.113792	0.00397378
$821$	5.19508	0.181310	0.0906548	−	0.995882i	$-0.471104\pi$
$821$	5.19508	0.181310	0.0906548	+	0.995882i	$0.471104\pi$
$822$	0	0
$823$	23.0057	0.801928	0.400964	−	0.916094i	$-0.368675\pi$
$823$	23.0057	0.801928	0.400964	+	0.916094i	$0.368675\pi$
$824$	1.07719	0.0375258
$825$	0	0
$826$	−1.90299	−0.0662134
$827$	−17.9679	−0.624806	−0.312403	−	0.949950i	$-0.601134\pi$
$827$	−17.9679	−0.624806	−0.312403	+	0.949950i	$0.601134\pi$
$828$	0	0
$829$	−9.11808	−0.316684	−0.158342	−	0.987384i	$-0.550615\pi$
$829$	−9.11808	−0.316684	−0.158342	+	0.987384i	$0.550615\pi$
$830$	−7.99679	−0.277573
$831$	0	0
$832$	45.7620	1.58651
$833$	0	0
$834$	0	0
$835$	−9.72898	−0.336685
$836$	−9.39828	−0.325046
$837$	0	0
$838$	−39.3584	−1.35961
$839$	24.8846	0.859113	0.429556	−	0.903040i	$-0.358670\pi$
$839$	24.8846	0.859113	0.429556	+	0.903040i	$0.358670\pi$
$840$	0	0
$841$	−6.76272	−0.233197
$842$	−16.1238	−0.555665
$843$	0	0
$844$	−1.30889	−0.0450537
$845$	25.3887	0.873399
$846$	0	0
$847$	−0.168732	−0.00579770
$848$	4.23437	0.145409
$849$	0	0
$850$	0	0
$851$	−10.1200	−0.346909
$852$	0	0
$853$	−57.7204	−1.97631	−0.988154	−	0.153468i	$-0.950956\pi$
$853$	−57.7204	−1.97631	−0.988154	+	0.153468i	$0.950956\pi$
$854$	3.82044	0.130733
$855$	0	0
$856$	−30.4998	−1.04246
$857$	−12.1845	−0.416216	−0.208108	−	0.978106i	$-0.566731\pi$
$857$	−12.1845	−0.416216	−0.208108	+	0.978106i	$0.566731\pi$
$858$	0	0
$859$	−32.7974	−1.11903	−0.559517	−	0.828819i	$-0.689013\pi$
$859$	−32.7974	−1.11903	−0.559517	+	0.828819i	$0.689013\pi$
$860$	−6.47410	−0.220765
$861$	0	0
$862$	−5.57755	−0.189972
$863$	−34.6709	−1.18021	−0.590106	−	0.807326i	$-0.700914\pi$
$863$	−34.6709	−1.18021	−0.590106	+	0.807326i	$0.700914\pi$
$864$	0	0
$865$	34.1306	1.16048
$866$	30.1730	1.02532
$867$	0	0
$868$	−0.411897	−0.0139807
$869$	37.9138	1.28614
$870$	0	0
$871$	−4.02198	−0.136280
$872$	−31.1936	−1.05635
$873$	0	0
$874$	21.8206	0.738094
$875$	2.81134	0.0950408
$876$	0	0
$877$	30.9770	1.04602	0.523009	−	0.852327i	$-0.324809\pi$
$877$	30.9770	1.04602	0.523009	+	0.852327i	$0.324809\pi$
$878$	20.4580	0.690425
$879$	0	0
$880$	−19.8785	−0.670104
$881$	33.4295	1.12627	0.563135	−	0.826365i	$-0.309595\pi$
$881$	33.4295	1.12627	0.563135	+	0.826365i	$0.309595\pi$
$882$	0	0
$883$	−18.2136	−0.612938	−0.306469	−	0.951881i	$-0.599148\pi$
$883$	−18.2136	−0.612938	−0.306469	+	0.951881i	$0.599148\pi$
$884$	0	0
$885$	0	0
$886$	−1.55497	−0.0522401
$887$	56.2425	1.88844	0.944220	−	0.329316i	$-0.106818\pi$
$887$	56.2425	1.88844	0.944220	+	0.329316i	$0.106818\pi$
$888$	0	0
$889$	0.708712	0.0237694
$890$	−39.7509	−1.33245
$891$	0	0
$892$	7.73481	0.258980
$893$	−57.6659	−1.92972
$894$	0	0
$895$	16.5884	0.554490
$896$	−1.62647	−0.0543366
$897$	0	0
$898$	29.8431	0.995876
$899$	−21.9189	−0.731036
$900$	0	0
$901$	0	0
$902$	−0.687878	−0.0229038
$903$	0	0
$904$	44.1815	1.46945
$905$	43.5695	1.44830
$906$	0	0
$907$	9.52095	0.316138	0.158069	−	0.987428i	$-0.449473\pi$
$907$	9.52095	0.316138	0.158069	+	0.987428i	$0.449473\pi$
$908$	0.552310	0.0183291
$909$	0	0
$910$	−2.84677	−0.0943695
$911$	−14.9716	−0.496030	−0.248015	−	0.968756i	$-0.579778\pi$
$911$	−14.9716	−0.496030	−0.248015	+	0.968756i	$0.579778\pi$
$912$	0	0
$913$	−11.4552	−0.379112
$914$	−49.1155	−1.62460
$915$	0	0
$916$	4.03237	0.133233
$917$	−1.73500	−0.0572946
$918$	0	0
$919$	−12.5474	−0.413900	−0.206950	−	0.978352i	$-0.566354\pi$
$919$	−12.5474	−0.413900	−0.206950	+	0.978352i	$0.566354\pi$
$920$	−13.6516	−0.450081
$921$	0	0
$922$	22.8030	0.750975
$923$	40.5345	1.33421
$924$	0	0
$925$	6.18623	0.203402
$926$	−12.3504	−0.405859
$927$	0	0
$928$	10.0698	0.330557
$929$	1.77458	0.0582220	0.0291110	−	0.999576i	$-0.490732\pi$
$929$	1.77458	0.0582220	0.0291110	+	0.999576i	$0.490732\pi$
$930$	0	0
$931$	−49.7526	−1.63058
$932$	−5.15156	−0.168745
$933$	0	0
$934$	42.7560	1.39902
$935$	0	0
$936$	0	0
$937$	26.5081	0.865982	0.432991	−	0.901398i	$-0.357458\pi$
$937$	26.5081	0.865982	0.432991	+	0.901398i	$0.357458\pi$
$938$	0.229765	0.00750208
$939$	0	0
$940$	5.80023	0.189183
$941$	32.9345	1.07364	0.536818	−	0.843698i	$-0.319626\pi$
$941$	32.9345	1.07364	0.536818	+	0.843698i	$0.319626\pi$
$942$	0	0
$943$	−0.378457	−0.0123243
$944$	−19.9744	−0.650110
$945$	0	0
$946$	39.1363	1.27243
$947$	8.19278	0.266230	0.133115	−	0.991101i	$-0.457502\pi$
$947$	8.19278	0.266230	0.133115	+	0.991101i	$0.457502\pi$
$948$	0	0
$949$	15.3080	0.496920
$950$	−13.3387	−0.432764
$951$	0	0
$952$	0	0
$953$	−17.5763	−0.569353	−0.284676	−	0.958624i	$-0.591886\pi$
$953$	−17.5763	−0.569353	−0.284676	+	0.958624i	$0.591886\pi$
$954$	0	0
$955$	47.8738	1.54916
$956$	−6.63675	−0.214648
$957$	0	0
$958$	−37.2254	−1.20270
$959$	−2.16413	−0.0698833
$960$	0	0
$961$	−9.39493	−0.303062
$962$	−27.6491	−0.891442
$963$	0	0
$964$	5.68458	0.183088
$965$	15.3323	0.493564
$966$	0	0
$967$	41.2137	1.32534	0.662671	−	0.748910i	$-0.269423\pi$
$967$	41.2137	1.32534	0.662671	+	0.748910i	$0.269423\pi$
$968$	−2.21070	−0.0710547
$969$	0	0
$970$	37.3826	1.20028
$971$	58.4141	1.87460	0.937298	−	0.348529i	$-0.113319\pi$
$971$	58.4141	1.87460	0.937298	+	0.348529i	$0.113319\pi$
$972$	0	0
$973$	−1.17395	−0.0376351
$974$	−34.7719	−1.11416
$975$	0	0
$976$	40.1005	1.28359
$977$	47.8936	1.53225	0.766126	−	0.642691i	$-0.222182\pi$
$977$	47.8936	1.53225	0.766126	+	0.642691i	$0.222182\pi$
$978$	0	0
$979$	−56.9421	−1.81988
$980$	5.00429	0.159856
$981$	0	0
$982$	−1.03151	−0.0329167
$983$	−5.58236	−0.178050	−0.0890248	−	0.996029i	$-0.528375\pi$
$983$	−5.58236	−0.178050	−0.0890248	+	0.996029i	$0.528375\pi$
$984$	0	0
$985$	−26.8570	−0.855736
$986$	0	0
$987$	0	0
$988$	−14.1271	−0.449444
$989$	21.5320	0.684679
$990$	0	0
$991$	−60.1849	−1.91184	−0.955918	−	0.293635i	$-0.905135\pi$
$991$	−60.1849	−1.91184	−0.955918	+	0.293635i	$0.905135\pi$
$992$	−9.92562	−0.315139
$993$	0	0
$994$	−2.31562	−0.0734471
$995$	1.01240	0.0320951
$996$	0	0
$997$	−37.9195	−1.20092	−0.600461	−	0.799654i	$-0.705016\pi$
$997$	−37.9195	−1.20092	−0.600461	+	0.799654i	$0.705016\pi$
$998$	−36.2894	−1.14872
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7803.2.a.cg.1.17		24
3.2	odd	2		7803.2.a.cd.1.8		24
17.3	odd	16		459.2.l.a.298.9	yes	48
17.6	odd	16		459.2.l.a.325.9	yes	48
17.16	even	2		7803.2.a.cd.1.17		24
51.20	even	16		459.2.l.a.298.4	✓	48
51.23	even	16		459.2.l.a.325.4	yes	48
51.50	odd	2	inner	7803.2.a.cg.1.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.298.4	✓	48	51.20	even	16
459.2.l.a.298.9	yes	48	17.3	odd	16
459.2.l.a.325.4	yes	48	51.23	even	16
459.2.l.a.325.9	yes	48	17.6	odd	16
7803.2.a.cd.1.8		24	3.2	odd	2
7803.2.a.cd.1.17		24	17.16	even	2
7803.2.a.cg.1.8		24	51.50	odd	2	inner
7803.2.a.cg.1.17		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)

\(f(q)\)	\(=\)	\(q+1.27156 q^{2} -0.383141 q^{4} +1.88026 q^{5} -0.231288 q^{7} -3.03030 q^{8} +2.39086 q^{10} +3.42484 q^{11} +5.14809 q^{13} -0.294096 q^{14} -3.08692 q^{16} +7.16225 q^{19} -0.720403 q^{20} +4.35488 q^{22} +2.39597 q^{23} -1.46463 q^{25} +6.54609 q^{26} +0.0886158 q^{28} +4.71564 q^{29} -4.64813 q^{31} +2.13540 q^{32} -0.434881 q^{35} -4.22375 q^{37} +9.10722 q^{38} -5.69775 q^{40} -0.157955 q^{41} +8.98677 q^{43} -1.31220 q^{44} +3.04662 q^{46} -8.05136 q^{47} -6.94651 q^{49} -1.86236 q^{50} -1.97244 q^{52} -1.37171 q^{53} +6.43958 q^{55} +0.700872 q^{56} +5.99621 q^{58} +6.47064 q^{59} -12.9905 q^{61} -5.91036 q^{62} +8.88913 q^{64} +9.67973 q^{65} -0.781257 q^{67} -0.552976 q^{70} +7.87370 q^{71} +2.97354 q^{73} -5.37075 q^{74} -2.74415 q^{76} -0.792124 q^{77} +11.0702 q^{79} -5.80421 q^{80} -0.200850 q^{82} -3.34474 q^{83} +11.4272 q^{86} -10.3783 q^{88} -16.6262 q^{89} -1.19069 q^{91} -0.917994 q^{92} -10.2378 q^{94} +13.4669 q^{95} +15.6356 q^{97} -8.83288 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 20 q^{5} + 8 q^{11} + 4 q^{13} + 16 q^{14} + 24 q^{16} + 4 q^{19} + 48 q^{20} + 36 q^{23} + 28 q^{25} + 64 q^{29} + 36 q^{41} + 4 q^{43} + 16 q^{44} + 24 q^{49} + 16 q^{52} + 20 q^{55}+ \cdots - 12 q^{95}+O(q^{100}) \) 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

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