LMFDB - Embedded newform 7803.2.a.ca.1.13

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 = [15,6,0,12,3,0,-3,18,0,0,-6,0,-3,-3,0,6,0,0,-3,-6,0,12,3,0,6, -24,0,-9,6,0,0,42,0,0,33,0,0,36,0,-15,0,0,-3,18,0,-12,24,0,18,42,0,-12, 48,0,-3,15,0,12,18,0,0,-63,0,30,-24,0,12,0,0,51,21,0,18] 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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 3 x^{13} + 76 x^{12} - 69 x^{11} - 354 x^{10} + 523 x^{9} + 720 x^{8} - 1437 x^{7} + \cdots - 51 $ x^15 - 6x^14 - 3x^13 + 76x^12 - 69x^11 - 354x^10 + 523x^9 + 720x^8 - 1437x^7 - 529x^6 + 1752x^5 - 111x^4 - 902x^3 + 258x^2 + 135x - 51
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.32100$ of defining polynomial
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)

$f(q)$	$=$	$q+2.32100 q^{2} +3.38702 q^{4} +3.93643 q^{5} +4.64937 q^{7} +3.21926 q^{8} +9.13644 q^{10} +3.08721 q^{11} -3.71402 q^{13} +10.7912 q^{14} +0.697859 q^{16} -5.38802 q^{19} +13.3328 q^{20} +7.16540 q^{22} -3.50014 q^{23} +10.4955 q^{25} -8.62022 q^{26} +15.7475 q^{28} -0.595460 q^{29} -4.02969 q^{31} -4.81880 q^{32} +18.3019 q^{35} +1.09685 q^{37} -12.5056 q^{38} +12.6724 q^{40} -2.62337 q^{41} +7.81087 q^{43} +10.4564 q^{44} -8.12381 q^{46} -2.55512 q^{47} +14.6167 q^{49} +24.3600 q^{50} -12.5795 q^{52} +12.9031 q^{53} +12.1526 q^{55} +14.9676 q^{56} -1.38206 q^{58} -8.06452 q^{59} -2.27876 q^{61} -9.35288 q^{62} -12.5801 q^{64} -14.6200 q^{65} +10.1892 q^{67} +42.4787 q^{70} +11.5168 q^{71} +13.9430 q^{73} +2.54579 q^{74} -18.2493 q^{76} +14.3536 q^{77} -0.886611 q^{79} +2.74707 q^{80} -6.08883 q^{82} -7.23859 q^{83} +18.1290 q^{86} +9.93855 q^{88} -7.65382 q^{89} -17.2679 q^{91} -11.8550 q^{92} -5.93042 q^{94} -21.2096 q^{95} -0.528318 q^{97} +33.9252 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 6 q^{2} + 12 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} - 6 q^{11} - 3 q^{13} - 3 q^{14} + 6 q^{16} - 3 q^{19} - 6 q^{20} + 12 q^{22} + 3 q^{23} + 6 q^{25} - 24 q^{26} - 9 q^{28} + 6 q^{29} + 42 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) $ 15 * q + 6 * q^2 + 12 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 - 6 * q^11 - 3 * q^13 - 3 * q^14 + 6 * q^16 - 3 * q^19 - 6 * q^20 + 12 * q^22 + 3 * q^23 + 6 * q^25 - 24 * q^26 - 9 * q^28 + 6 * q^29 + 42 * q^32 + 33 * q^35 + 36 * q^38 - 15 * q^40 - 3 * q^43 + 18 * q^44 - 12 * q^46 + 24 * q^47 + 18 * q^49 + 42 * q^50 - 12 * q^52 + 48 * q^53 - 3 * q^55 + 15 * q^56 + 12 * q^58 + 18 * q^59 - 63 * q^62 + 30 * q^64 - 24 * q^65 + 12 * q^67 + 51 * q^70 + 21 * q^71 + 18 * q^73 + 48 * q^74 + 60 * q^76 + 54 * q^77 + 39 * q^79 - 6 * q^80 - 39 * q^82 + 51 * q^83 + 48 * q^86 + 48 * q^88 + 36 * q^89 - 9 * q^91 + 3 * q^92 + 36 * q^94 - 39 * q^95 - 3 * q^97 + 15 * q^98

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 $

$2$	2.32100	1.64119	0.820596	−	0.571509i	$-0.193642\pi$
$2$	2.32100	1.64119	0.820596	+	0.571509i	$0.193642\pi$
$3$	0	0
$3$	0	0
$4$	3.38702	1.69351
$5$	3.93643	1.76043	0.880213	−	0.474579i	$-0.157400\pi$
$5$	3.93643	1.76043	0.880213	+	0.474579i	$0.157400\pi$
$6$	0	0
$7$	4.64937	1.75730	0.878649	−	0.477468i	$-0.158445\pi$
$7$	4.64937	1.75730	0.878649	+	0.477468i	$0.158445\pi$
$8$	3.21926	1.13818
$9$	0	0
$10$	9.13644	2.88920
$11$	3.08721	0.930829	0.465415	−	0.885093i	$-0.345905\pi$
$11$	3.08721	0.930829	0.465415	+	0.885093i	$0.345905\pi$
$12$	0	0
$13$	−3.71402	−1.03008	−0.515042	−	0.857165i	$-0.672224\pi$
$13$	−3.71402	−1.03008	−0.515042	+	0.857165i	$0.672224\pi$
$14$	10.7912	2.88406
$15$	0	0
$16$	0.697859	0.174465
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−5.38802	−1.23610	−0.618049	−	0.786140i	$-0.712077\pi$
$19$	−5.38802	−1.23610	−0.618049	+	0.786140i	$0.712077\pi$
$20$	13.3328	2.98130
$21$	0	0
$22$	7.16540	1.52767
$23$	−3.50014	−0.729830	−0.364915	−	0.931041i	$-0.618902\pi$
$23$	−3.50014	−0.729830	−0.364915	+	0.931041i	$0.618902\pi$
$24$	0	0
$25$	10.4955	2.09910
$26$	−8.62022	−1.69056
$27$	0	0
$28$	15.7475	2.97600
$29$	−0.595460	−0.110574	−0.0552871	−	0.998471i	$-0.517607\pi$
$29$	−0.595460	−0.110574	−0.0552871	+	0.998471i	$0.517607\pi$
$30$	0	0
$31$	−4.02969	−0.723753	−0.361877	−	0.932226i	$-0.617864\pi$
$31$	−4.02969	−0.723753	−0.361877	+	0.932226i	$0.617864\pi$
$32$	−4.81880	−0.851852
$33$	0	0
$34$	0	0
$35$	18.3019	3.09359
$36$	0	0
$37$	1.09685	0.180322	0.0901608	−	0.995927i	$-0.471262\pi$
$37$	1.09685	0.180322	0.0901608	+	0.995927i	$0.471262\pi$
$38$	−12.5056	−2.02867
$39$	0	0
$40$	12.6724	2.00368
$41$	−2.62337	−0.409702	−0.204851	−	0.978793i	$-0.565671\pi$
$41$	−2.62337	−0.409702	−0.204851	+	0.978793i	$0.565671\pi$
$42$	0	0
$43$	7.81087	1.19115	0.595573	−	0.803301i	$-0.296925\pi$
$43$	7.81087	1.19115	0.595573	+	0.803301i	$0.296925\pi$
$44$	10.4564	1.57637
$45$	0	0
$46$	−8.12381	−1.19779
$47$	−2.55512	−0.372703	−0.186351	−	0.982483i	$-0.559666\pi$
$47$	−2.55512	−0.372703	−0.186351	+	0.982483i	$0.559666\pi$
$48$	0	0
$49$	14.6167	2.08810
$50$	24.3600	3.44503
$51$	0	0
$52$	−12.5795	−1.74446
$53$	12.9031	1.77238	0.886189	−	0.463325i	$-0.153344\pi$
$53$	12.9031	1.77238	0.886189	+	0.463325i	$0.153344\pi$
$54$	0	0
$55$	12.1526	1.63866
$56$	14.9676	2.00012
$57$	0	0
$58$	−1.38206	−0.181473
$59$	−8.06452	−1.04991	−0.524956	−	0.851130i	$-0.675918\pi$
$59$	−8.06452	−1.04991	−0.524956	+	0.851130i	$0.675918\pi$
$60$	0	0
$61$	−2.27876	−0.291766	−0.145883	−	0.989302i	$-0.546602\pi$
$61$	−2.27876	−0.291766	−0.145883	+	0.989302i	$0.546602\pi$
$62$	−9.35288	−1.18782
$63$	0	0
$64$	−12.5801	−1.57252
$65$	−14.6200	−1.81339
$66$	0	0
$67$	10.1892	1.24481	0.622404	−	0.782696i	$-0.286156\pi$
$67$	10.1892	1.24481	0.622404	+	0.782696i	$0.286156\pi$
$68$	0	0
$69$	0	0
$70$	42.4787	5.07718
$71$	11.5168	1.36679	0.683395	−	0.730049i	$-0.260503\pi$
$71$	11.5168	1.36679	0.683395	+	0.730049i	$0.260503\pi$
$72$	0	0
$73$	13.9430	1.63191	0.815955	−	0.578115i	$-0.196212\pi$
$73$	13.9430	1.63191	0.815955	+	0.578115i	$0.196212\pi$
$74$	2.54579	0.295942
$75$	0	0
$76$	−18.2493	−2.09334
$77$	14.3536	1.63574
$78$	0	0
$79$	−0.886611	−0.0997515	−0.0498758	−	0.998755i	$-0.515883\pi$
$79$	−0.886611	−0.0997515	−0.0498758	+	0.998755i	$0.515883\pi$
$80$	2.74707	0.307132
$81$	0	0
$82$	−6.08883	−0.672399
$83$	−7.23859	−0.794539	−0.397269	−	0.917702i	$-0.630042\pi$
$83$	−7.23859	−0.794539	−0.397269	+	0.917702i	$0.630042\pi$
$84$	0	0
$85$	0	0
$86$	18.1290	1.95490
$87$	0	0
$88$	9.93855	1.05945
$89$	−7.65382	−0.811303	−0.405652	−	0.914028i	$-0.632955\pi$
$89$	−7.65382	−0.811303	−0.405652	+	0.914028i	$0.632955\pi$
$90$	0	0
$91$	−17.2679	−1.81016
$92$	−11.8550	−1.23597
$93$	0	0
$94$	−5.93042	−0.611676
$95$	−21.2096	−2.17606
$96$	0	0
$97$	−0.528318	−0.0536426	−0.0268213	−	0.999640i	$-0.508539\pi$
$97$	−0.528318	−0.0536426	−0.0268213	+	0.999640i	$0.508539\pi$
$98$	33.9252	3.42696
$99$	0	0
$100$	35.5485	3.55485
$101$	−0.885430	−0.0881036	−0.0440518	−	0.999029i	$-0.514027\pi$
$101$	−0.885430	−0.0881036	−0.0440518	+	0.999029i	$0.514027\pi$
$102$	0	0
$103$	3.98414	0.392569	0.196285	−	0.980547i	$-0.437112\pi$
$103$	3.98414	0.392569	0.196285	+	0.980547i	$0.437112\pi$
$104$	−11.9564	−1.17242
$105$	0	0
$106$	29.9480	2.90881
$107$	7.41940	0.717260	0.358630	−	0.933480i	$-0.383244\pi$
$107$	7.41940	0.717260	0.358630	+	0.933480i	$0.383244\pi$
$108$	0	0
$109$	−11.5916	−1.11027	−0.555135	−	0.831760i	$-0.687334\pi$
$109$	−11.5916	−1.11027	−0.555135	+	0.831760i	$0.687334\pi$
$110$	28.2061	2.68935
$111$	0	0
$112$	3.24461	0.306586
$113$	−3.40454	−0.320272	−0.160136	−	0.987095i	$-0.551193\pi$
$113$	−3.40454	−0.320272	−0.160136	+	0.987095i	$0.551193\pi$
$114$	0	0
$115$	−13.7781	−1.28481
$116$	−2.01683	−0.187258
$117$	0	0
$118$	−18.7177	−1.72311
$119$	0	0
$120$	0	0
$121$	−1.46913	−0.133557
$122$	−5.28900	−0.478844
$123$	0	0
$124$	−13.6486	−1.22568
$125$	21.6327	1.93489
$126$	0	0
$127$	−9.20187	−0.816534	−0.408267	−	0.912862i	$-0.633867\pi$
$127$	−9.20187	−0.816534	−0.408267	+	0.912862i	$0.633867\pi$
$128$	−19.5608	−1.72895
$129$	0	0
$130$	−33.9329	−2.97611
$131$	−7.98259	−0.697442	−0.348721	−	0.937227i	$-0.613384\pi$
$131$	−7.98259	−0.697442	−0.348721	+	0.937227i	$0.613384\pi$
$132$	0	0
$133$	−25.0509	−2.17219
$134$	23.6491	2.04297
$135$	0	0
$136$	0	0
$137$	0.0615045	0.00525468	0.00262734	−	0.999997i	$-0.499164\pi$
$137$	0.0615045	0.00525468	0.00262734	+	0.999997i	$0.499164\pi$
$138$	0	0
$139$	−7.42112	−0.629451	−0.314726	−	0.949183i	$-0.601912\pi$
$139$	−7.42112	−0.629451	−0.314726	+	0.949183i	$0.601912\pi$
$140$	61.9890	5.23903
$141$	0	0
$142$	26.7304	2.24317
$143$	−11.4660	−0.958832
$144$	0	0
$145$	−2.34399	−0.194658
$146$	32.3617	2.67828
$147$	0	0
$148$	3.71506	0.305376
$149$	15.8134	1.29548	0.647741	−	0.761861i	$-0.275714\pi$
$149$	15.8134	1.29548	0.647741	+	0.761861i	$0.275714\pi$
$150$	0	0
$151$	−19.4411	−1.58209	−0.791047	−	0.611755i	$-0.790464\pi$
$151$	−19.4411	−1.58209	−0.791047	+	0.611755i	$0.790464\pi$
$152$	−17.3455	−1.40690
$153$	0	0
$154$	33.3146	2.68457
$155$	−15.8626	−1.27411
$156$	0	0
$157$	−20.5387	−1.63916	−0.819582	−	0.572963i	$-0.805794\pi$
$157$	−20.5387	−1.63916	−0.819582	+	0.572963i	$0.805794\pi$
$158$	−2.05782	−0.163711
$159$	0	0
$160$	−18.9689	−1.49962
$161$	−16.2735	−1.28253
$162$	0	0
$163$	14.9709	1.17261	0.586305	−	0.810090i	$-0.300582\pi$
$163$	14.9709	1.17261	0.586305	+	0.810090i	$0.300582\pi$
$164$	−8.88541	−0.693834
$165$	0	0
$166$	−16.8007	−1.30399
$167$	−22.0028	−1.70262	−0.851312	−	0.524660i	$-0.824193\pi$
$167$	−22.0028	−1.70262	−0.851312	+	0.524660i	$0.824193\pi$
$168$	0	0
$169$	0.793944	0.0610726
$170$	0	0
$171$	0	0
$172$	26.4556	2.01722
$173$	−5.27537	−0.401079	−0.200539	−	0.979686i	$-0.564269\pi$
$173$	−5.27537	−0.401079	−0.200539	+	0.979686i	$0.564269\pi$
$174$	0	0
$175$	48.7975	3.68874
$176$	2.15444	0.162397
$177$	0	0
$178$	−17.7645	−1.33150
$179$	−4.27673	−0.319658	−0.159829	−	0.987145i	$-0.551094\pi$
$179$	−4.27673	−0.319658	−0.159829	+	0.987145i	$0.551094\pi$
$180$	0	0
$181$	7.92258	0.588881	0.294440	−	0.955670i	$-0.404867\pi$
$181$	7.92258	0.588881	0.294440	+	0.955670i	$0.404867\pi$
$182$	−40.0786	−2.97083
$183$	0	0
$184$	−11.2679	−0.830679
$185$	4.31769	0.317443
$186$	0	0
$187$	0	0
$188$	−8.65424	−0.631175
$189$	0	0
$190$	−49.2274	−3.57133
$191$	4.23329	0.306310	0.153155	−	0.988202i	$-0.451057\pi$
$191$	4.23329	0.306310	0.153155	+	0.988202i	$0.451057\pi$
$192$	0	0
$193$	10.9289	0.786680	0.393340	−	0.919393i	$-0.371319\pi$
$193$	10.9289	0.786680	0.393340	+	0.919393i	$0.371319\pi$
$194$	−1.22622	−0.0880377
$195$	0	0
$196$	49.5069	3.53621
$197$	−14.1732	−1.00980	−0.504901	−	0.863177i	$-0.668471\pi$
$197$	−14.1732	−1.00980	−0.504901	+	0.863177i	$0.668471\pi$
$198$	0	0
$199$	−3.33506	−0.236416	−0.118208	−	0.992989i	$-0.537715\pi$
$199$	−3.33506	−0.236416	−0.118208	+	0.992989i	$0.537715\pi$
$200$	33.7878	2.38916
$201$	0	0
$202$	−2.05508	−0.144595
$203$	−2.76852	−0.194312
$204$	0	0
$205$	−10.3267	−0.721250
$206$	9.24717	0.644281
$207$	0	0
$208$	−2.59186	−0.179713
$209$	−16.6340	−1.15060
$210$	0	0
$211$	23.7286	1.63354	0.816772	−	0.576960i	$-0.195761\pi$
$211$	23.7286	1.63354	0.816772	+	0.576960i	$0.195761\pi$
$212$	43.7030	3.00154
$213$	0	0
$214$	17.2204	1.17716
$215$	30.7470	2.09692
$216$	0	0
$217$	−18.7355	−1.27185
$218$	−26.9040	−1.82217
$219$	0	0
$220$	41.1611	2.77508
$221$	0	0
$222$	0	0
$223$	−13.1707	−0.881976	−0.440988	−	0.897513i	$-0.645372\pi$
$223$	−13.1707	−0.881976	−0.440988	+	0.897513i	$0.645372\pi$
$224$	−22.4044	−1.49696
$225$	0	0
$226$	−7.90192	−0.525628
$227$	−18.4376	−1.22374	−0.611872	−	0.790957i	$-0.709583\pi$
$227$	−18.4376	−1.22374	−0.611872	+	0.790957i	$0.709583\pi$
$228$	0	0
$229$	−4.17505	−0.275895	−0.137948	−	0.990440i	$-0.544051\pi$
$229$	−4.17505	−0.275895	−0.137948	+	0.990440i	$0.544051\pi$
$230$	−31.9789	−2.10862
$231$	0	0
$232$	−1.91694	−0.125853
$233$	0.327777	0.0214734	0.0107367	−	0.999942i	$-0.496582\pi$
$233$	0.327777	0.0214734	0.0107367	+	0.999942i	$0.496582\pi$
$234$	0	0
$235$	−10.0581	−0.656115
$236$	−27.3147	−1.77803
$237$	0	0
$238$	0	0
$239$	19.6419	1.27053	0.635265	−	0.772294i	$-0.280891\pi$
$239$	19.6419	1.27053	0.635265	+	0.772294i	$0.280891\pi$
$240$	0	0
$241$	−3.24284	−0.208890	−0.104445	−	0.994531i	$-0.533307\pi$
$241$	−3.24284	−0.208890	−0.104445	+	0.994531i	$0.533307\pi$
$242$	−3.40984	−0.219193
$243$	0	0
$244$	−7.71822	−0.494108
$245$	57.5375	3.67594
$246$	0	0
$247$	20.0112	1.27328
$248$	−12.9726	−0.823762
$249$	0	0
$250$	50.2093	3.17552
$251$	13.8850	0.876416	0.438208	−	0.898874i	$-0.355613\pi$
$251$	13.8850	0.876416	0.438208	+	0.898874i	$0.355613\pi$
$252$	0	0
$253$	−10.8057	−0.679347
$254$	−21.3575	−1.34009
$255$	0	0
$256$	−20.2403	−1.26502
$257$	−17.8327	−1.11238	−0.556188	−	0.831057i	$-0.687736\pi$
$257$	−17.8327	−1.11238	−0.556188	+	0.831057i	$0.687736\pi$
$258$	0	0
$259$	5.09968	0.316879
$260$	−49.5182	−3.07099
$261$	0	0
$262$	−18.5276	−1.14464
$263$	−19.4844	−1.20146	−0.600730	−	0.799452i	$-0.705123\pi$
$263$	−19.4844	−1.20146	−0.600730	+	0.799452i	$0.705123\pi$
$264$	0	0
$265$	50.7922	3.12014
$266$	−58.1431	−3.56498
$267$	0	0
$268$	34.5110	2.10809
$269$	−7.32426	−0.446568	−0.223284	−	0.974753i	$-0.571678\pi$
$269$	−7.32426	−0.446568	−0.223284	+	0.974753i	$0.571678\pi$
$270$	0	0
$271$	22.9249	1.39259	0.696293	−	0.717757i	$-0.254831\pi$
$271$	22.9249	1.39259	0.696293	+	0.717757i	$0.254831\pi$
$272$	0	0
$273$	0	0
$274$	0.142752	0.00862394
$275$	32.4018	1.95390
$276$	0	0
$277$	−17.0248	−1.02292	−0.511460	−	0.859307i	$-0.670895\pi$
$277$	−17.0248	−1.02292	−0.511460	+	0.859307i	$0.670895\pi$
$278$	−17.2244	−1.03305
$279$	0	0
$280$	58.9188	3.52107
$281$	24.2761	1.44819	0.724097	−	0.689699i	$-0.242257\pi$
$281$	24.2761	1.44819	0.724097	+	0.689699i	$0.242257\pi$
$282$	0	0
$283$	−4.16919	−0.247832	−0.123916	−	0.992293i	$-0.539545\pi$
$283$	−4.16919	−0.247832	−0.123916	+	0.992293i	$0.539545\pi$
$284$	39.0076	2.31467
$285$	0	0
$286$	−26.6124	−1.57363
$287$	−12.1970	−0.719968
$288$	0	0
$289$	0	0
$290$	−5.44039	−0.319470
$291$	0	0
$292$	47.2254	2.76366
$293$	15.2384	0.890234	0.445117	−	0.895472i	$-0.353162\pi$
$293$	15.2384	0.890234	0.445117	+	0.895472i	$0.353162\pi$
$294$	0	0
$295$	−31.7454	−1.84829
$296$	3.53106	0.205239
$297$	0	0
$298$	36.7027	2.12613
$299$	12.9996	0.751786
$300$	0	0
$301$	36.3156	2.09320
$302$	−45.1227	−2.59652
$303$	0	0
$304$	−3.76008	−0.215655
$305$	−8.97020	−0.513632
$306$	0	0
$307$	−20.6037	−1.17591	−0.587957	−	0.808892i	$-0.700068\pi$
$307$	−20.6037	−1.17591	−0.587957	+	0.808892i	$0.700068\pi$
$308$	48.6159	2.77015
$309$	0	0
$310$	−36.8170	−2.09106
$311$	−11.7004	−0.663470	−0.331735	−	0.943373i	$-0.607634\pi$
$311$	−11.7004	−0.663470	−0.331735	+	0.943373i	$0.607634\pi$
$312$	0	0
$313$	1.92944	0.109059	0.0545293	−	0.998512i	$-0.482634\pi$
$313$	1.92944	0.109059	0.0545293	+	0.998512i	$0.482634\pi$
$314$	−47.6701	−2.69018
$315$	0	0
$316$	−3.00297	−0.168930
$317$	−35.1090	−1.97192	−0.985958	−	0.166993i	$-0.946594\pi$
$317$	−35.1090	−1.97192	−0.985958	+	0.166993i	$0.946594\pi$
$318$	0	0
$319$	−1.83831	−0.102926
$320$	−49.5208	−2.76830
$321$	0	0
$322$	−37.7706	−2.10488
$323$	0	0
$324$	0	0
$325$	−38.9805	−2.16225
$326$	34.7474	1.92448
$327$	0	0
$328$	−8.44533	−0.466315
$329$	−11.8797	−0.654949
$330$	0	0
$331$	−8.47141	−0.465631	−0.232815	−	0.972521i	$-0.574794\pi$
$331$	−8.47141	−0.465631	−0.232815	+	0.972521i	$0.574794\pi$
$332$	−24.5173	−1.34556
$333$	0	0
$334$	−51.0683	−2.79433
$335$	40.1091	2.19139
$336$	0	0
$337$	−9.19228	−0.500736	−0.250368	−	0.968151i	$-0.580552\pi$
$337$	−9.19228	−0.500736	−0.250368	+	0.968151i	$0.580552\pi$
$338$	1.84274	0.100232
$339$	0	0
$340$	0	0
$341$	−12.4405	−0.673690
$342$	0	0
$343$	35.4127	1.91211
$344$	25.1452	1.35574
$345$	0	0
$346$	−12.2441	−0.658247
$347$	−7.16878	−0.384840	−0.192420	−	0.981313i	$-0.561634\pi$
$347$	−7.16878	−0.384840	−0.192420	+	0.981313i	$0.561634\pi$
$348$	0	0
$349$	−33.4295	−1.78944	−0.894720	−	0.446627i	$-0.852625\pi$
$349$	−33.4295	−1.78944	−0.894720	+	0.446627i	$0.852625\pi$
$350$	113.259	6.05394
$351$	0	0
$352$	−14.8767	−0.792928
$353$	−6.05306	−0.322172	−0.161086	−	0.986940i	$-0.551500\pi$
$353$	−6.05306	−0.322172	−0.161086	+	0.986940i	$0.551500\pi$
$354$	0	0
$355$	45.3350	2.40613
$356$	−25.9236	−1.37395
$357$	0	0
$358$	−9.92627	−0.524620
$359$	14.2698	0.753133	0.376566	−	0.926390i	$-0.377105\pi$
$359$	14.2698	0.753133	0.376566	+	0.926390i	$0.377105\pi$
$360$	0	0
$361$	10.0308	0.527937
$362$	18.3883	0.966466
$363$	0	0
$364$	−58.4866	−3.06553
$365$	54.8859	2.87286
$366$	0	0
$367$	−15.0265	−0.784376	−0.392188	−	0.919885i	$-0.628282\pi$
$367$	−15.0265	−0.784376	−0.392188	+	0.919885i	$0.628282\pi$
$368$	−2.44261	−0.127330
$369$	0	0
$370$	10.0213	0.520984
$371$	59.9913	3.11459
$372$	0	0
$373$	5.28506	0.273650	0.136825	−	0.990595i	$-0.456310\pi$
$373$	5.28506	0.273650	0.136825	+	0.990595i	$0.456310\pi$
$374$	0	0
$375$	0	0
$376$	−8.22561	−0.424203
$377$	2.21155	0.113901
$378$	0	0
$379$	−27.8889	−1.43255	−0.716277	−	0.697816i	$-0.754155\pi$
$379$	−27.8889	−1.43255	−0.716277	+	0.697816i	$0.754155\pi$
$380$	−71.8373	−3.68518
$381$	0	0
$382$	9.82544	0.502713
$383$	−3.76295	−0.192278	−0.0961389	−	0.995368i	$-0.530649\pi$
$383$	−3.76295	−0.192278	−0.0961389	+	0.995368i	$0.530649\pi$
$384$	0	0
$385$	56.5020	2.87961
$386$	25.3659	1.29109
$387$	0	0
$388$	−1.78942	−0.0908442
$389$	26.6607	1.35175	0.675875	−	0.737017i	$-0.263766\pi$
$389$	26.6607	1.35175	0.675875	+	0.737017i	$0.263766\pi$
$390$	0	0
$391$	0	0
$392$	47.0549	2.37663
$393$	0	0
$394$	−32.8960	−1.65728
$395$	−3.49008	−0.175605
$396$	0	0
$397$	1.11129	0.0557740	0.0278870	−	0.999611i	$-0.491122\pi$
$397$	1.11129	0.0557740	0.0278870	+	0.999611i	$0.491122\pi$
$398$	−7.74065	−0.388004
$399$	0	0
$400$	7.32438	0.366219
$401$	−26.5399	−1.32534	−0.662670	−	0.748911i	$-0.730577\pi$
$401$	−26.5399	−1.32534	−0.662670	+	0.748911i	$0.730577\pi$
$402$	0	0
$403$	14.9663	0.745526
$404$	−2.99897	−0.149204
$405$	0	0
$406$	−6.42571	−0.318903
$407$	3.38622	0.167849
$408$	0	0
$409$	35.4537	1.75307	0.876537	−	0.481334i	$-0.159848\pi$
$409$	35.4537	1.75307	0.876537	+	0.481334i	$0.159848\pi$
$410$	−23.9683	−1.18371
$411$	0	0
$412$	13.4944	0.664819
$413$	−37.4950	−1.84501
$414$	0	0
$415$	−28.4942	−1.39873
$416$	17.8971	0.877479
$417$	0	0
$418$	−38.6074	−1.88835
$419$	8.59690	0.419986	0.209993	−	0.977703i	$-0.432656\pi$
$419$	8.59690	0.419986	0.209993	+	0.977703i	$0.432656\pi$
$420$	0	0
$421$	37.2443	1.81518	0.907588	−	0.419861i	$-0.137921\pi$
$421$	37.2443	1.81518	0.907588	+	0.419861i	$0.137921\pi$
$422$	55.0740	2.68096
$423$	0	0
$424$	41.5385	2.01729
$425$	0	0
$426$	0	0
$427$	−10.5948	−0.512719
$428$	25.1296	1.21469
$429$	0	0
$430$	71.3635	3.44146
$431$	30.0833	1.44906	0.724530	−	0.689243i	$-0.242057\pi$
$431$	30.0833	1.44906	0.724530	+	0.689243i	$0.242057\pi$
$432$	0	0
$433$	−33.7489	−1.62187	−0.810934	−	0.585138i	$-0.801040\pi$
$433$	−33.7489	−1.62187	−0.810934	+	0.585138i	$0.801040\pi$
$434$	−43.4850	−2.08735
$435$	0	0
$436$	−39.2609	−1.88025
$437$	18.8589	0.902141
$438$	0	0
$439$	−15.5597	−0.742623	−0.371312	−	0.928508i	$-0.621092\pi$
$439$	−15.5597	−0.742623	−0.371312	+	0.928508i	$0.621092\pi$
$440$	39.1224	1.86509
$441$	0	0
$442$	0	0
$443$	−18.5997	−0.883697	−0.441848	−	0.897090i	$-0.645677\pi$
$443$	−18.5997	−0.883697	−0.441848	+	0.897090i	$0.645677\pi$
$444$	0	0
$445$	−30.1287	−1.42824
$446$	−30.5692	−1.44749
$447$	0	0
$448$	−58.4897	−2.76338
$449$	4.94404	0.233324	0.116662	−	0.993172i	$-0.462781\pi$
$449$	4.94404	0.233324	0.116662	+	0.993172i	$0.462781\pi$
$450$	0	0
$451$	−8.09890	−0.381363
$452$	−11.5312	−0.542384
$453$	0	0
$454$	−42.7935	−2.00840
$455$	−67.9738	−3.18666
$456$	0	0
$457$	17.6650	0.826336	0.413168	−	0.910655i	$-0.364422\pi$
$457$	17.6650	0.826336	0.413168	+	0.910655i	$0.364422\pi$
$458$	−9.69028	−0.452797
$459$	0	0
$460$	−46.6666	−2.17584
$461$	−4.55367	−0.212085	−0.106043	−	0.994362i	$-0.533818\pi$
$461$	−4.55367	−0.212085	−0.106043	+	0.994362i	$0.533818\pi$
$462$	0	0
$463$	−3.82572	−0.177796	−0.0888981	−	0.996041i	$-0.528335\pi$
$463$	−3.82572	−0.177796	−0.0888981	+	0.996041i	$0.528335\pi$
$464$	−0.415547	−0.0192913
$465$	0	0
$466$	0.760768	0.0352419
$467$	15.3172	0.708797	0.354399	−	0.935094i	$-0.384686\pi$
$467$	15.3172	0.708797	0.354399	+	0.935094i	$0.384686\pi$
$468$	0	0
$469$	47.3734	2.18750
$470$	−23.3447	−1.07681
$471$	0	0
$472$	−25.9618	−1.19499
$473$	24.1138	1.10875
$474$	0	0
$475$	−56.5500	−2.59469
$476$	0	0
$477$	0	0
$478$	45.5888	2.08518
$479$	−9.47219	−0.432795	−0.216398	−	0.976305i	$-0.569431\pi$
$479$	−9.47219	−0.432795	−0.216398	+	0.976305i	$0.569431\pi$
$480$	0	0
$481$	−4.07373	−0.185746
$482$	−7.52662	−0.342828
$483$	0	0
$484$	−4.97596	−0.226180
$485$	−2.07969	−0.0944338
$486$	0	0
$487$	36.5055	1.65422	0.827112	−	0.562037i	$-0.189982\pi$
$487$	36.5055	1.65422	0.827112	+	0.562037i	$0.189982\pi$
$488$	−7.33594	−0.332082
$489$	0	0
$490$	133.544	6.03292
$491$	5.20074	0.234706	0.117353	−	0.993090i	$-0.462559\pi$
$491$	5.20074	0.234706	0.117353	+	0.993090i	$0.462559\pi$
$492$	0	0
$493$	0	0
$494$	46.4460	2.08970
$495$	0	0
$496$	−2.81215	−0.126269
$497$	53.5458	2.40186
$498$	0	0
$499$	−7.74769	−0.346834	−0.173417	−	0.984848i	$-0.555481\pi$
$499$	−7.74769	−0.346834	−0.173417	+	0.984848i	$0.555481\pi$
$500$	73.2703	3.27675
$501$	0	0
$502$	32.2271	1.43837
$503$	31.6182	1.40979	0.704893	−	0.709314i	$-0.250995\pi$
$503$	31.6182	1.40979	0.704893	+	0.709314i	$0.250995\pi$
$504$	0	0
$505$	−3.48544	−0.155100
$506$	−25.0799	−1.11494
$507$	0	0
$508$	−31.1669	−1.38281
$509$	15.1531	0.671648	0.335824	−	0.941925i	$-0.390985\pi$
$509$	15.1531	0.671648	0.335824	+	0.941925i	$0.390985\pi$
$510$	0	0
$511$	64.8264	2.86775
$512$	−7.85603	−0.347191
$513$	0	0
$514$	−41.3897	−1.82562
$515$	15.6833	0.691089
$516$	0	0
$517$	−7.88820	−0.346922
$518$	11.8363	0.520059
$519$	0	0
$520$	−47.0656	−2.06396
$521$	−0.696974	−0.0305350	−0.0152675	−	0.999883i	$-0.504860\pi$
$521$	−0.696974	−0.0305350	−0.0152675	+	0.999883i	$0.504860\pi$
$522$	0	0
$523$	2.66391	0.116484	0.0582422	−	0.998302i	$-0.481450\pi$
$523$	2.66391	0.116484	0.0582422	+	0.998302i	$0.481450\pi$
$524$	−27.0372	−1.18113
$525$	0	0
$526$	−45.2232	−1.97183
$527$	0	0
$528$	0	0
$529$	−10.7490	−0.467348
$530$	117.888	5.12075
$531$	0	0
$532$	−84.8480	−3.67863
$533$	9.74326	0.422027
$534$	0	0
$535$	29.2060	1.26268
$536$	32.8017	1.41682
$537$	0	0
$538$	−16.9996	−0.732904
$539$	45.1247	1.94366
$540$	0	0
$541$	38.3164	1.64735	0.823676	−	0.567061i	$-0.191920\pi$
$541$	38.3164	1.64735	0.823676	+	0.567061i	$0.191920\pi$
$542$	53.2085	2.28550
$543$	0	0
$544$	0	0
$545$	−45.6294	−1.95455
$546$	0	0
$547$	−46.0911	−1.97071	−0.985356	−	0.170509i	$-0.945459\pi$
$547$	−46.0911	−1.97071	−0.985356	+	0.170509i	$0.945459\pi$
$548$	0.208317	0.00889886
$549$	0	0
$550$	75.2045	3.20673
$551$	3.20835	0.136680
$552$	0	0
$553$	−4.12218	−0.175293
$554$	−39.5144	−1.67881
$555$	0	0
$556$	−25.1355	−1.06598
$557$	40.8208	1.72963	0.864817	−	0.502088i	$-0.167435\pi$
$557$	40.8208	1.72963	0.864817	+	0.502088i	$0.167435\pi$
$558$	0	0
$559$	−29.0097	−1.22698
$560$	12.7722	0.539723
$561$	0	0
$562$	56.3448	2.37676
$563$	13.3274	0.561682	0.280841	−	0.959754i	$-0.409387\pi$
$563$	13.3274	0.561682	0.280841	+	0.959754i	$0.409387\pi$
$564$	0	0
$565$	−13.4017	−0.563815
$566$	−9.67666	−0.406740
$567$	0	0
$568$	37.0756	1.55566
$569$	−43.4276	−1.82058	−0.910290	−	0.413971i	$-0.864141\pi$
$569$	−43.4276	−1.82058	−0.910290	+	0.413971i	$0.864141\pi$
$570$	0	0
$571$	−43.4628	−1.81886	−0.909431	−	0.415854i	$-0.863483\pi$
$571$	−43.4628	−1.81886	−0.909431	+	0.415854i	$0.863483\pi$
$572$	−38.8354	−1.62379
$573$	0	0
$574$	−28.3093	−1.18161
$575$	−36.7358	−1.53199
$576$	0	0
$577$	−14.7233	−0.612940	−0.306470	−	0.951880i	$-0.599148\pi$
$577$	−14.7233	−0.612940	−0.306470	+	0.951880i	$0.599148\pi$
$578$	0	0
$579$	0	0
$580$	−7.93913	−0.329654
$581$	−33.6549	−1.39624
$582$	0	0
$583$	39.8346	1.64978
$584$	44.8864	1.85741
$585$	0	0
$586$	35.3681	1.46104
$587$	1.81698	0.0749947	0.0374973	−	0.999297i	$-0.488061\pi$
$587$	1.81698	0.0749947	0.0374973	+	0.999297i	$0.488061\pi$
$588$	0	0
$589$	21.7120	0.894629
$590$	−73.6810	−3.03340
$591$	0	0
$592$	0.765449	0.0314597
$593$	45.4079	1.86468	0.932340	−	0.361582i	$-0.117763\pi$
$593$	45.4079	1.86468	0.932340	+	0.361582i	$0.117763\pi$
$594$	0	0
$595$	0	0
$596$	53.5602	2.19391
$597$	0	0
$598$	30.1720	1.23383
$599$	18.4863	0.755331	0.377665	−	0.925942i	$-0.376727\pi$
$599$	18.4863	0.755331	0.377665	+	0.925942i	$0.376727\pi$
$600$	0	0
$601$	1.08114	0.0441006	0.0220503	−	0.999757i	$-0.492981\pi$
$601$	1.08114	0.0441006	0.0220503	+	0.999757i	$0.492981\pi$
$602$	84.2884	3.43534
$603$	0	0
$604$	−65.8474	−2.67929
$605$	−5.78312	−0.235117
$606$	0	0
$607$	−10.0572	−0.408210	−0.204105	−	0.978949i	$-0.565428\pi$
$607$	−10.0572	−0.408210	−0.204105	+	0.978949i	$0.565428\pi$
$608$	25.9638	1.05297
$609$	0	0
$610$	−20.8198	−0.842969
$611$	9.48977	0.383915
$612$	0	0
$613$	19.4146	0.784148	0.392074	−	0.919934i	$-0.371758\pi$
$613$	19.4146	0.784148	0.392074	+	0.919934i	$0.371758\pi$
$614$	−47.8210	−1.92990
$615$	0	0
$616$	46.2080	1.86177
$617$	28.5208	1.14820	0.574102	−	0.818784i	$-0.305351\pi$
$617$	28.5208	1.14820	0.574102	+	0.818784i	$0.305351\pi$
$618$	0	0
$619$	37.3006	1.49924	0.749619	−	0.661869i	$-0.230237\pi$
$619$	37.3006	1.49924	0.749619	+	0.661869i	$0.230237\pi$
$620$	−53.7269	−2.15772
$621$	0	0
$622$	−27.1566	−1.08888
$623$	−35.5855	−1.42570
$624$	0	0
$625$	32.6781	1.30712
$626$	4.47823	0.178986
$627$	0	0
$628$	−69.5648	−2.77594
$629$	0	0
$630$	0	0
$631$	−0.834835	−0.0332342	−0.0166171	−	0.999862i	$-0.505290\pi$
$631$	−0.834835	−0.0332342	−0.0166171	+	0.999862i	$0.505290\pi$
$632$	−2.85423	−0.113535
$633$	0	0
$634$	−81.4878	−3.23629
$635$	−36.2226	−1.43745
$636$	0	0
$637$	−54.2866	−2.15091
$638$	−4.26671	−0.168921
$639$	0	0
$640$	−76.9999	−3.04369
$641$	−19.5225	−0.771092	−0.385546	−	0.922689i	$-0.625987\pi$
$641$	−19.5225	−0.771092	−0.385546	+	0.922689i	$0.625987\pi$
$642$	0	0
$643$	−43.8261	−1.72833	−0.864166	−	0.503207i	$-0.832153\pi$
$643$	−43.8261	−1.72833	−0.864166	+	0.503207i	$0.832153\pi$
$644$	−55.1186	−2.17198
$645$	0	0
$646$	0	0
$647$	34.1353	1.34200	0.670999	−	0.741459i	$-0.265866\pi$
$647$	34.1353	1.34200	0.670999	+	0.741459i	$0.265866\pi$
$648$	0	0
$649$	−24.8969	−0.977288
$650$	−90.4736	−3.54867
$651$	0	0
$652$	50.7067	1.98583
$653$	−38.0215	−1.48790	−0.743948	−	0.668237i	$-0.767049\pi$
$653$	−38.0215	−1.48790	−0.743948	+	0.668237i	$0.767049\pi$
$654$	0	0
$655$	−31.4229	−1.22780
$656$	−1.83074	−0.0714785
$657$	0	0
$658$	−27.5727	−1.07490
$659$	−6.44198	−0.250944	−0.125472	−	0.992097i	$-0.540045\pi$
$659$	−6.44198	−0.250944	−0.125472	+	0.992097i	$0.540045\pi$
$660$	0	0
$661$	31.9117	1.24122	0.620611	−	0.784119i	$-0.286885\pi$
$661$	31.9117	1.24122	0.620611	+	0.784119i	$0.286885\pi$
$662$	−19.6621	−0.764189
$663$	0	0
$664$	−23.3029	−0.904330
$665$	−98.6113	−3.82398
$666$	0	0
$667$	2.08419	0.0807004
$668$	−74.5237	−2.88341
$669$	0	0
$670$	93.0930	3.59649
$671$	−7.03502	−0.271584
$672$	0	0
$673$	15.5981	0.601262	0.300631	−	0.953741i	$-0.402803\pi$
$673$	15.5981	0.601262	0.300631	+	0.953741i	$0.402803\pi$
$674$	−21.3352	−0.821803
$675$	0	0
$676$	2.68910	0.103427
$677$	20.2686	0.778987	0.389493	−	0.921029i	$-0.372650\pi$
$677$	20.2686	0.778987	0.389493	+	0.921029i	$0.372650\pi$
$678$	0	0
$679$	−2.45635	−0.0942660
$680$	0	0
$681$	0	0
$682$	−28.8743	−1.10566
$683$	−10.0841	−0.385857	−0.192929	−	0.981213i	$-0.561799\pi$
$683$	−10.0841	−0.385857	−0.192929	+	0.981213i	$0.561799\pi$
$684$	0	0
$685$	0.242108	0.00925048
$686$	82.1928	3.13814
$687$	0	0
$688$	5.45088	0.207813
$689$	−47.9224	−1.82570
$690$	0	0
$691$	9.51230	0.361865	0.180932	−	0.983496i	$-0.442088\pi$
$691$	9.51230	0.361865	0.180932	+	0.983496i	$0.442088\pi$
$692$	−17.8678	−0.679231
$693$	0	0
$694$	−16.6387	−0.631597
$695$	−29.2127	−1.10810
$696$	0	0
$697$	0	0
$698$	−77.5897	−2.93681
$699$	0	0
$700$	165.278	6.24692
$701$	10.7532	0.406143	0.203071	−	0.979164i	$-0.434908\pi$
$701$	10.7532	0.406143	0.203071	+	0.979164i	$0.434908\pi$
$702$	0	0
$703$	−5.90987	−0.222895
$704$	−38.8375	−1.46374
$705$	0	0
$706$	−14.0491	−0.528746
$707$	−4.11669	−0.154824
$708$	0	0
$709$	−19.9245	−0.748280	−0.374140	−	0.927372i	$-0.622062\pi$
$709$	−19.9245	−0.748280	−0.374140	+	0.927372i	$0.622062\pi$
$710$	105.222	3.94893
$711$	0	0
$712$	−24.6397	−0.923410
$713$	14.1045	0.528217
$714$	0	0
$715$	−45.1350	−1.68795
$716$	−14.4854	−0.541343
$717$	0	0
$718$	33.1202	1.23604
$719$	22.8373	0.851689	0.425844	−	0.904796i	$-0.359977\pi$
$719$	22.8373	0.851689	0.425844	+	0.904796i	$0.359977\pi$
$720$	0	0
$721$	18.5238	0.689861
$722$	23.2814	0.866445
$723$	0	0
$724$	26.8339	0.997275
$725$	−6.24965	−0.232106
$726$	0	0
$727$	13.8639	0.514185	0.257092	−	0.966387i	$-0.417236\pi$
$727$	13.8639	0.514185	0.257092	+	0.966387i	$0.417236\pi$
$728$	−55.5898	−2.06030
$729$	0	0
$730$	127.390	4.71491
$731$	0	0
$732$	0	0
$733$	11.5792	0.427688	0.213844	−	0.976868i	$-0.431402\pi$
$733$	11.5792	0.427688	0.213844	+	0.976868i	$0.431402\pi$
$734$	−34.8764	−1.28731
$735$	0	0
$736$	16.8665	0.621707
$737$	31.4562	1.15870
$738$	0	0
$739$	23.4221	0.861596	0.430798	−	0.902448i	$-0.358232\pi$
$739$	23.4221	0.861596	0.430798	+	0.902448i	$0.358232\pi$
$740$	14.6241	0.537592
$741$	0	0
$742$	139.240	5.11165
$743$	−3.11494	−0.114276	−0.0571380	−	0.998366i	$-0.518198\pi$
$743$	−3.11494	−0.114276	−0.0571380	+	0.998366i	$0.518198\pi$
$744$	0	0
$745$	62.2482	2.28060
$746$	12.2666	0.449112
$747$	0	0
$748$	0	0
$749$	34.4956	1.26044
$750$	0	0
$751$	−3.15974	−0.115301	−0.0576503	−	0.998337i	$-0.518361\pi$
$751$	−3.15974	−0.115301	−0.0576503	+	0.998337i	$0.518361\pi$
$752$	−1.78311	−0.0650234
$753$	0	0
$754$	5.13300	0.186933
$755$	−76.5286	−2.78516
$756$	0	0
$757$	−42.9618	−1.56147	−0.780737	−	0.624859i	$-0.785156\pi$
$757$	−42.9618	−1.56147	−0.780737	+	0.624859i	$0.785156\pi$
$758$	−64.7299	−2.35110
$759$	0	0
$760$	−68.2793	−2.47675
$761$	25.8735	0.937913	0.468957	−	0.883221i	$-0.344630\pi$
$761$	25.8735	0.937913	0.468957	+	0.883221i	$0.344630\pi$
$762$	0	0
$763$	−53.8935	−1.95108
$764$	14.3382	0.518739
$765$	0	0
$766$	−8.73379	−0.315565
$767$	29.9518	1.08150
$768$	0	0
$769$	−6.30524	−0.227373	−0.113686	−	0.993517i	$-0.536266\pi$
$769$	−6.30524	−0.227373	−0.113686	+	0.993517i	$0.536266\pi$
$770$	131.141	4.72599
$771$	0	0
$772$	37.0164	1.33225
$773$	15.5761	0.560234	0.280117	−	0.959966i	$-0.409627\pi$
$773$	15.5761	0.560234	0.280117	+	0.959966i	$0.409627\pi$
$774$	0	0
$775$	−42.2936	−1.51923
$776$	−1.70079	−0.0610550
$777$	0	0
$778$	61.8793	2.21848
$779$	14.1348	0.506431
$780$	0	0
$781$	35.5547	1.27225
$782$	0	0
$783$	0	0
$784$	10.2004	0.364299
$785$	−80.8490	−2.88563
$786$	0	0
$787$	32.8050	1.16937	0.584685	−	0.811260i	$-0.301218\pi$
$787$	32.8050	1.16937	0.584685	+	0.811260i	$0.301218\pi$
$788$	−48.0051	−1.71011
$789$	0	0
$790$	−8.10047	−0.288202
$791$	−15.8290	−0.562813
$792$	0	0
$793$	8.46337	0.300543
$794$	2.57930	0.0915359
$795$	0	0
$796$	−11.2959	−0.400373
$797$	52.0620	1.84413	0.922065	−	0.387036i	$-0.126501\pi$
$797$	52.0620	1.84413	0.922065	+	0.387036i	$0.126501\pi$
$798$	0	0
$799$	0	0
$800$	−50.5757	−1.78812
$801$	0	0
$802$	−61.5990	−2.17514
$803$	43.0451	1.51903
$804$	0	0
$805$	−64.0594	−2.25780
$806$	34.7368	1.22355
$807$	0	0
$808$	−2.85043	−0.100278
$809$	33.4067	1.17452	0.587259	−	0.809399i	$-0.300207\pi$
$809$	33.4067	1.17452	0.587259	+	0.809399i	$0.300207\pi$
$810$	0	0
$811$	24.4591	0.858875	0.429437	−	0.903097i	$-0.358712\pi$
$811$	24.4591	0.858875	0.429437	+	0.903097i	$0.358712\pi$
$812$	−9.37701	−0.329069
$813$	0	0
$814$	7.85939	0.275472
$815$	58.9319	2.06429
$816$	0	0
$817$	−42.0851	−1.47237
$818$	82.2879	2.87713
$819$	0	0
$820$	−34.9768	−1.22144
$821$	26.1273	0.911848	0.455924	−	0.890019i	$-0.349309\pi$
$821$	26.1273	0.911848	0.455924	+	0.890019i	$0.349309\pi$
$822$	0	0
$823$	−10.3083	−0.359324	−0.179662	−	0.983728i	$-0.557500\pi$
$823$	−10.3083	−0.359324	−0.179662	+	0.983728i	$0.557500\pi$
$824$	12.8260	0.446815
$825$	0	0
$826$	−87.0256	−3.02801
$827$	21.6599	0.753188	0.376594	−	0.926378i	$-0.377095\pi$
$827$	21.6599	0.753188	0.376594	+	0.926378i	$0.377095\pi$
$828$	0	0
$829$	−5.51045	−0.191386	−0.0956928	−	0.995411i	$-0.530507\pi$
$829$	−5.51045	−0.191386	−0.0956928	+	0.995411i	$0.530507\pi$
$830$	−66.1350	−2.29558
$831$	0	0
$832$	46.7229	1.61982
$833$	0	0
$834$	0	0
$835$	−86.6124	−2.99734
$836$	−56.3396	−1.94854
$837$	0	0
$838$	19.9534	0.689277
$839$	43.0316	1.48561	0.742807	−	0.669505i	$-0.233494\pi$
$839$	43.0316	1.48561	0.742807	+	0.669505i	$0.233494\pi$
$840$	0	0
$841$	−28.6454	−0.987773
$842$	86.4439	2.97905
$843$	0	0
$844$	80.3692	2.76642
$845$	3.12531	0.107514
$846$	0	0
$847$	−6.83052	−0.234699
$848$	9.00454	0.309217
$849$	0	0
$850$	0	0
$851$	−3.83914	−0.131604
$852$	0	0
$853$	34.5345	1.18244	0.591219	−	0.806511i	$-0.298647\pi$
$853$	34.5345	1.18244	0.591219	+	0.806511i	$0.298647\pi$
$854$	−24.5905	−0.841471
$855$	0	0
$856$	23.8850	0.816373
$857$	−46.5077	−1.58867	−0.794336	−	0.607479i	$-0.792181\pi$
$857$	−46.5077	−1.58867	−0.794336	+	0.607479i	$0.792181\pi$
$858$	0	0
$859$	−41.9890	−1.43265	−0.716323	−	0.697768i	$-0.754176\pi$
$859$	−41.9890	−1.43265	−0.716323	+	0.697768i	$0.754176\pi$
$860$	104.141	3.55116
$861$	0	0
$862$	69.8231	2.37818
$863$	−9.52042	−0.324079	−0.162039	−	0.986784i	$-0.551807\pi$
$863$	−9.52042	−0.324079	−0.162039	+	0.986784i	$0.551807\pi$
$864$	0	0
$865$	−20.7661	−0.706070
$866$	−78.3310	−2.66180
$867$	0	0
$868$	−63.4575	−2.15389
$869$	−2.73715	−0.0928516
$870$	0	0
$871$	−37.8429	−1.28226
$872$	−37.3163	−1.26369
$873$	0	0
$874$	43.7713	1.48059
$875$	100.578	3.40017
$876$	0	0
$877$	−23.5649	−0.795729	−0.397865	−	0.917444i	$-0.630249\pi$
$877$	−23.5649	−0.795729	−0.397865	+	0.917444i	$0.630249\pi$
$878$	−36.1140	−1.21879
$879$	0	0
$880$	8.48080	0.285888
$881$	30.3436	1.02230	0.511151	−	0.859491i	$-0.329219\pi$
$881$	30.3436	1.02230	0.511151	+	0.859491i	$0.329219\pi$
$882$	0	0
$883$	−58.1905	−1.95827	−0.979133	−	0.203223i	$-0.934858\pi$
$883$	−58.1905	−1.95827	−0.979133	+	0.203223i	$0.934858\pi$
$884$	0	0
$885$	0	0
$886$	−43.1697	−1.45032
$887$	42.4474	1.42524	0.712622	−	0.701548i	$-0.247507\pi$
$887$	42.4474	1.42524	0.712622	+	0.701548i	$0.247507\pi$
$888$	0	0
$889$	−42.7829	−1.43489
$890$	−69.9287	−2.34401
$891$	0	0
$892$	−44.6095	−1.49364
$893$	13.7670	0.460697
$894$	0	0
$895$	−16.8351	−0.562734
$896$	−90.9456	−3.03828
$897$	0	0
$898$	11.4751	0.382929
$899$	2.39952	0.0800284
$900$	0	0
$901$	0	0
$902$	−18.7975	−0.625889
$903$	0	0
$904$	−10.9601	−0.364528
$905$	31.1867	1.03668
$906$	0	0
$907$	−11.6026	−0.385259	−0.192630	−	0.981272i	$-0.561702\pi$
$907$	−11.6026	−0.385259	−0.192630	+	0.981272i	$0.561702\pi$
$908$	−62.4484	−2.07242
$909$	0	0
$910$	−157.767	−5.22992
$911$	−15.6285	−0.517795	−0.258898	−	0.965905i	$-0.583359\pi$
$911$	−15.6285	−0.517795	−0.258898	+	0.965905i	$0.583359\pi$
$912$	0	0
$913$	−22.3471	−0.739580
$914$	41.0005	1.35618
$915$	0	0
$916$	−14.1410	−0.467231
$917$	−37.1141	−1.22561
$918$	0	0
$919$	0.269292	0.00888313	0.00444157	−	0.999990i	$-0.498586\pi$
$919$	0.269292	0.00888313	0.00444157	+	0.999990i	$0.498586\pi$
$920$	−44.3553	−1.46235
$921$	0	0
$922$	−10.5690	−0.348073
$923$	−42.7736	−1.40791
$924$	0	0
$925$	11.5120	0.378513
$926$	−8.87948	−0.291798
$927$	0	0
$928$	2.86940	0.0941928
$929$	37.9315	1.24449	0.622246	−	0.782822i	$-0.286220\pi$
$929$	37.9315	1.24449	0.622246	+	0.782822i	$0.286220\pi$
$930$	0	0
$931$	−78.7550	−2.58109
$932$	1.11019	0.0363653
$933$	0	0
$934$	35.5512	1.16327
$935$	0	0
$936$	0	0
$937$	−7.31303	−0.238906	−0.119453	−	0.992840i	$-0.538114\pi$
$937$	−7.31303	−0.238906	−0.119453	+	0.992840i	$0.538114\pi$
$938$	109.953	3.59010
$939$	0	0
$940$	−34.0668	−1.11114
$941$	−16.1684	−0.527075	−0.263537	−	0.964649i	$-0.584889\pi$
$941$	−16.1684	−0.527075	−0.263537	+	0.964649i	$0.584889\pi$
$942$	0	0
$943$	9.18218	0.299013
$944$	−5.62790	−0.183172
$945$	0	0
$946$	55.9680	1.81968
$947$	9.92364	0.322475	0.161237	−	0.986916i	$-0.448452\pi$
$947$	9.92364	0.322475	0.161237	+	0.986916i	$0.448452\pi$
$948$	0	0
$949$	−51.7848	−1.68100
$950$	−131.252	−4.25839
$951$	0	0
$952$	0	0
$953$	−7.14877	−0.231571	−0.115786	−	0.993274i	$-0.536939\pi$
$953$	−7.14877	−0.231571	−0.115786	+	0.993274i	$0.536939\pi$
$954$	0	0
$955$	16.6641	0.539236
$956$	66.5276	2.15166
$957$	0	0
$958$	−21.9849	−0.710300
$959$	0.285957	0.00923405
$960$	0	0
$961$	−14.7616	−0.476182
$962$	−9.45512	−0.304845
$963$	0	0
$964$	−10.9836	−0.353757
$965$	43.0209	1.38489
$966$	0	0
$967$	−52.7668	−1.69687	−0.848433	−	0.529303i	$-0.822454\pi$
$967$	−52.7668	−1.69687	−0.848433	+	0.529303i	$0.822454\pi$
$968$	−4.72951	−0.152012
$969$	0	0
$970$	−4.82695	−0.154984
$971$	26.0042	0.834515	0.417258	−	0.908788i	$-0.362991\pi$
$971$	26.0042	0.834515	0.417258	+	0.908788i	$0.362991\pi$
$972$	0	0
$973$	−34.5035	−1.10613
$974$	84.7292	2.71490
$975$	0	0
$976$	−1.59026	−0.0509028
$977$	−36.6925	−1.17390	−0.586949	−	0.809624i	$-0.699671\pi$
$977$	−36.6925	−1.17390	−0.586949	+	0.809624i	$0.699671\pi$
$978$	0	0
$979$	−23.6290	−0.755185
$980$	194.881	6.22524
$981$	0	0
$982$	12.0709	0.385197
$983$	19.6098	0.625455	0.312727	−	0.949843i	$-0.398757\pi$
$983$	19.6098	0.625455	0.312727	+	0.949843i	$0.398757\pi$
$984$	0	0
$985$	−55.7920	−1.77768
$986$	0	0
$987$	0	0
$988$	67.7784	2.15632
$989$	−27.3392	−0.869334
$990$	0	0
$991$	26.0694	0.828121	0.414060	−	0.910249i	$-0.364110\pi$
$991$	26.0694	0.828121	0.414060	+	0.910249i	$0.364110\pi$
$992$	19.4183	0.616530
$993$	0	0
$994$	124.280	3.94191
$995$	−13.1282	−0.416193
$996$	0	0
$997$	−35.8303	−1.13476	−0.567379	−	0.823457i	$-0.692042\pi$
$997$	−35.8303	−1.13476	−0.567379	+	0.823457i	$0.692042\pi$
$998$	−17.9823	−0.569221
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7803.2.a.ca.1.13	yes	15
3.2	odd	2		7803.2.a.bx.1.3	✓	15
17.16	even	2		7803.2.a.bz.1.13	yes	15
51.50	odd	2		7803.2.a.by.1.3	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7803.2.a.bx.1.3	✓	15	3.2	odd	2
7803.2.a.by.1.3	yes	15	51.50	odd	2
7803.2.a.bz.1.13	yes	15	17.16	even	2
7803.2.a.ca.1.13	yes	15	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)

\(f(q)\)	\(=\)	\(q+2.32100 q^{2} +3.38702 q^{4} +3.93643 q^{5} +4.64937 q^{7} +3.21926 q^{8} +9.13644 q^{10} +3.08721 q^{11} -3.71402 q^{13} +10.7912 q^{14} +0.697859 q^{16} -5.38802 q^{19} +13.3328 q^{20} +7.16540 q^{22} -3.50014 q^{23} +10.4955 q^{25} -8.62022 q^{26} +15.7475 q^{28} -0.595460 q^{29} -4.02969 q^{31} -4.81880 q^{32} +18.3019 q^{35} +1.09685 q^{37} -12.5056 q^{38} +12.6724 q^{40} -2.62337 q^{41} +7.81087 q^{43} +10.4564 q^{44} -8.12381 q^{46} -2.55512 q^{47} +14.6167 q^{49} +24.3600 q^{50} -12.5795 q^{52} +12.9031 q^{53} +12.1526 q^{55} +14.9676 q^{56} -1.38206 q^{58} -8.06452 q^{59} -2.27876 q^{61} -9.35288 q^{62} -12.5801 q^{64} -14.6200 q^{65} +10.1892 q^{67} +42.4787 q^{70} +11.5168 q^{71} +13.9430 q^{73} +2.54579 q^{74} -18.2493 q^{76} +14.3536 q^{77} -0.886611 q^{79} +2.74707 q^{80} -6.08883 q^{82} -7.23859 q^{83} +18.1290 q^{86} +9.93855 q^{88} -7.65382 q^{89} -17.2679 q^{91} -11.8550 q^{92} -5.93042 q^{94} -21.2096 q^{95} -0.528318 q^{97} +33.9252 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 6 q^{2} + 12 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} - 6 q^{11} - 3 q^{13} - 3 q^{14} + 6 q^{16} - 3 q^{19} - 6 q^{20} + 12 q^{22} + 3 q^{23} + 6 q^{25} - 24 q^{26} - 9 q^{28} + 6 q^{29} + 42 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) \) 15 * q + 6 * q^2 + 12 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 - 6 * q^11 - 3 * q^13 - 3 * q^14 + 6 * q^16 - 3 * q^19 - 6 * q^20 + 12 * q^22 + 3 * q^23 + 6 * q^25 - 24 * q^26 - 9 * q^28 + 6 * q^29 + 42 * q^32 + 33 * q^35 + 36 * q^38 - 15 * q^40 - 3 * q^43 + 18 * q^44 - 12 * q^46 + 24 * q^47 + 18 * q^49 + 42 * q^50 - 12 * q^52 + 48 * q^53 - 3 * q^55 + 15 * q^56 + 12 * q^58 + 18 * q^59 - 63 * q^62 + 30 * q^64 - 24 * q^65 + 12 * q^67 + 51 * q^70 + 21 * q^71 + 18 * q^73 + 48 * q^74 + 60 * q^76 + 54 * q^77 + 39 * q^79 - 6 * q^80 - 39 * q^82 + 51 * q^83 + 48 * q^86 + 48 * q^88 + 36 * q^89 - 9 * q^91 + 3 * q^92 + 36 * q^94 - 39 * q^95 - 3 * q^97 + 15 * q^98

Introduction

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