LMFDB - Embedded newform 819.2.o.h.757.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(568,819)] 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("819.568"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,0,-5,14,0,4,12,0,11,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.59066497296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$1.37054 + 2.37385i$ of defining polynomial
Character	$\chi$	$=$	819.757
Dual form			819.2.o.h.568.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37054 - 2.37385i) q^{2} +(-2.75677 + 4.77486i) q^{4} -0.741082 q^{5} +(0.500000 - 0.866025i) q^{7} +9.63087 q^{8} +(1.01568 + 1.75921i) q^{10} +(-0.682410 - 1.18197i) q^{11} +(0.301907 - 3.59289i) q^{13} -2.74108 q^{14} +(-7.68598 - 13.3125i) q^{16} +(-2.07436 + 3.59289i) q^{17} +(-3.63303 + 6.29259i) q^{19} +(2.04299 - 3.53856i) q^{20} +(-1.87054 + 3.23987i) q^{22} +(-1.16673 - 2.02083i) q^{23} -4.45080 q^{25} +(-8.94274 + 4.20752i) q^{26} +(2.75677 + 4.77486i) q^{28} +(-0.203815 - 0.353017i) q^{29} -2.77245 q^{31} +(-11.4370 + 19.8095i) q^{32} +11.3720 q^{34} +(-0.370541 + 0.641796i) q^{35} +(3.05295 + 5.28787i) q^{37} +19.9169 q^{38} -7.13727 q^{40} +(0.627306 + 1.08653i) q^{41} +(0.870541 - 1.50782i) q^{43} +7.52497 q^{44} +(-3.19809 + 5.53926i) q^{46} +5.85843 q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.10000 + 10.5655i) q^{50} +(16.3232 + 11.3463i) q^{52} -4.56778 q^{53} +(0.505722 + 0.875935i) q^{55} +(4.81544 - 8.34058i) q^{56} +(-0.558672 + 0.967649i) q^{58} +(-5.49213 + 9.51264i) q^{59} +(-3.26249 + 5.65079i) q^{61} +(3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(-0.223738 + 2.66263i) q^{65} +(6.87983 + 11.9162i) q^{67} +(-11.4370 - 19.8095i) q^{68} +2.03137 q^{70} +(-2.40763 + 4.17014i) q^{71} +6.06987 q^{73} +(8.36839 - 14.4945i) q^{74} +(-20.0308 - 34.6944i) q^{76} -1.36482 q^{77} -9.12582 q^{79} +(5.69594 + 9.86566i) q^{80} +(1.71950 - 2.97826i) q^{82} -11.7368 q^{83} +(1.53727 - 2.66263i) q^{85} -4.77245 q^{86} +(-6.57220 - 11.3834i) q^{88} +(-0.880503 - 1.52508i) q^{89} +(-2.96058 - 2.05790i) q^{91} +12.8656 q^{92} +(-8.02921 - 13.9070i) q^{94} +(2.69237 - 4.66332i) q^{95} +(-4.76691 + 8.25652i) q^{97} +(-1.37054 + 2.37385i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29}+ \cdots - q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.37054	−	2.37385i	−0.969119	−	1.67856i	−0.698116	−	0.715984i	$-0.745978\pi$
$2$	−1.37054	−	2.37385i	−0.969119	−	1.67856i	−0.271003	−	0.962579i	$-0.587355\pi$
$3$		0			0
$3$		0			0
$4$	−2.75677	+	4.77486i	−1.37838	+	2.38743i
$5$	−0.741082			−0.331422			−0.165711	−	0.986174i	$-0.552992\pi$
$5$	−0.741082			−0.331422			−0.165711	+	0.986174i	$0.552992\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	9.63087			3.40503
$9$		0			0
$10$	1.01568	+	1.75921i	0.321187	+	0.556313i
$11$	−0.682410	−	1.18197i	−0.205754	−	0.356377i	0.744619	−	0.667490i	$-0.232631\pi$
$11$	−0.682410	−	1.18197i	−0.205754	−	0.356377i	−0.950373	+	0.311113i	$0.899298\pi$
$12$		0			0
$13$	0.301907	−	3.59289i	0.0837339	−	0.996488i
$13$	0.301907	−	3.59289i	0.0837339	−	0.996488i
$14$	−2.74108			−0.732585
$15$		0			0
$16$	−7.68598	−	13.3125i	−1.92149	−	3.32813i
$17$	−2.07436	+	3.59289i	−0.503105	+	0.871404i	0.496888	+	0.867814i	$0.334476\pi$
$17$	−2.07436	+	3.59289i	−0.503105	+	0.871404i	−0.999994	+	0.00358919i	$0.998858\pi$
$18$		0			0
$19$	−3.63303	+	6.29259i	−0.833474	+	1.44362i	0.0617933	+	0.998089i	$0.480318\pi$
$19$	−3.63303	+	6.29259i	−0.833474	+	1.44362i	−0.895267	+	0.445530i	$0.853015\pi$
$20$	2.04299	−	3.53856i	0.456826	−	0.791246i
$21$		0			0
$22$	−1.87054	+	3.23987i	−0.398801	+	0.690743i
$23$	−1.16673	−	2.02083i	−0.243279	−	0.421372i	0.718367	−	0.695664i	$-0.244890\pi$
$23$	−1.16673	−	2.02083i	−0.243279	−	0.421372i	−0.961646	+	0.274292i	$0.911556\pi$
$24$		0			0
$25$	−4.45080			−0.890159
$26$	−8.94274	+	4.20752i	−1.75382	+	0.825163i
$27$		0			0
$28$	2.75677	+	4.77486i	0.520980	+	0.902363i
$29$	−0.203815	−	0.353017i	−0.0378474	−	0.0655536i	0.846481	−	0.532419i	$-0.178717\pi$
$29$	−0.203815	−	0.353017i	−0.0378474	−	0.0655536i	−0.884329	+	0.466865i	$0.845383\pi$
$30$		0			0
$31$	−2.77245			−0.497946			−0.248973	−	0.968510i	$-0.580093\pi$
$31$	−2.77245			−0.497946			−0.248973	+	0.968510i	$0.580093\pi$
$32$	−11.4370	+	19.8095i	−2.02180	+	3.50186i
$33$		0			0
$34$	11.3720			1.95027
$35$	−0.370541	+	0.641796i	−0.0626329	+	0.108483i
$36$		0			0
$37$	3.05295	+	5.28787i	0.501902	+	0.869320i	0.999998	+	0.00219764i	$0.000699531\pi$
$37$	3.05295	+	5.28787i	0.501902	+	0.869320i	−0.498096	+	0.867122i	$0.665967\pi$
$38$	19.9169			3.23094
$39$		0			0
$40$	−7.13727			−1.12850
$41$	0.627306	+	1.08653i	0.0979688	+	0.169687i	0.910844	−	0.412751i	$-0.135432\pi$
$41$	0.627306	+	1.08653i	0.0979688	+	0.169687i	−0.812875	+	0.582438i	$0.802099\pi$
$42$		0			0
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	−0.791982	−	0.610545i	$-0.790951\pi$
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	0.924738	+	0.380604i	$0.124284\pi$
$44$	7.52497			1.13443
$45$		0			0
$46$	−3.19809	+	5.53926i	−0.471533	+	0.816719i
$47$	5.85843			0.854539			0.427270	−	0.904124i	$-0.359475\pi$
$47$	5.85843			0.854539			0.427270	+	0.904124i	$0.359475\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	6.10000	+	10.5655i	0.862670	+	1.49419i
$51$		0			0
$52$	16.3232	+	11.3463i	2.26363	+	1.57345i
$53$	−4.56778			−0.627433			−0.313717	−	0.949517i	$-0.601574\pi$
$53$	−4.56778			−0.627433			−0.313717	+	0.949517i	$0.601574\pi$
$54$		0			0
$55$	0.505722	+	0.875935i	0.0681915	+	0.118111i
$56$	4.81544	−	8.34058i	0.643490	−	1.11456i
$57$		0			0
$58$	−0.558672	+	0.967649i	−0.0733573	+	0.127059i
$59$	−5.49213	+	9.51264i	−0.715014	+	1.23844i	0.247940	+	0.968775i	$0.420246\pi$
$59$	−5.49213	+	9.51264i	−0.715014	+	1.23844i	−0.962954	+	0.269665i	$0.913087\pi$
$60$		0			0
$61$	−3.26249	+	5.65079i	−0.417719	+	0.723510i	−0.995710	−	0.0925333i	$-0.970504\pi$
$61$	−3.26249	+	5.65079i	−0.417719	+	0.723510i	0.577991	+	0.816043i	$0.303837\pi$
$62$	3.79975	+	6.58137i	0.482569	+	0.835834i
$63$		0			0
$64$	31.9557			3.99446
$65$	−0.223738	+	2.66263i	−0.0277513	+	0.330258i
$66$		0			0
$67$	6.87983	+	11.9162i	0.840505	+	1.45580i	0.889468	+	0.456997i	$0.151075\pi$
$67$	6.87983	+	11.9162i	0.840505	+	1.45580i	−0.0489630	+	0.998801i	$0.515592\pi$
$68$	−11.4370	−	19.8095i	−1.38694	−	2.40226i
$69$		0			0
$70$	2.03137			0.242795
$71$	−2.40763	+	4.17014i	−0.285733	+	0.494904i	−0.972787	−	0.231703i	$-0.925570\pi$
$71$	−2.40763	+	4.17014i	−0.285733	+	0.494904i	0.687054	+	0.726607i	$0.258904\pi$
$72$		0			0
$73$	6.06987			0.710425			0.355212	−	0.934786i	$-0.384409\pi$
$73$	6.06987			0.710425			0.355212	+	0.934786i	$0.384409\pi$
$74$	8.36839	−	14.4945i	0.972805	−	1.68495i
$75$		0			0
$76$	−20.0308	−	34.6944i	−2.29769	−	3.97972i
$77$	−1.36482			−0.155536
$78$		0			0
$79$	−9.12582			−1.02674			−0.513368	−	0.858169i	$-0.671602\pi$
$79$	−9.12582			−1.02674			−0.513368	+	0.858169i	$0.671602\pi$
$80$	5.69594	+	9.86566i	0.636825	+	1.10301i
$81$		0			0
$82$	1.71950	−	2.97826i	0.189887	−	0.328894i
$83$	−11.7368			−1.28828			−0.644139	−	0.764908i	$-0.722784\pi$
$83$	−11.7368			−1.28828			−0.644139	+	0.764908i	$0.722784\pi$
$84$		0			0
$85$	1.53727	−	2.66263i	0.166740	−	0.288802i
$86$	−4.77245			−0.514626
$87$		0			0
$88$	−6.57220	−	11.3834i	−0.700599	−	1.21347i
$89$	−0.880503	−	1.52508i	−0.0933331	−	0.161658i	0.815579	−	0.578646i	$-0.196419\pi$
$89$	−0.880503	−	1.52508i	−0.0933331	−	0.161658i	−0.908912	+	0.416989i	$0.863085\pi$
$90$		0			0
$91$	−2.96058	−	2.05790i	−0.310353	−	0.215727i
$92$	12.8656			1.34133
$93$		0			0
$94$	−8.02921	−	13.9070i	−0.828150	−	1.43440i
$95$	2.69237	−	4.66332i	0.276231	−	0.478447i
$96$		0			0
$97$	−4.76691	+	8.25652i	−0.484006	+	0.838323i	−0.999831	−	0.0183708i	$-0.994152\pi$
$97$	−4.76691	+	8.25652i	−0.484006	+	0.838323i	0.515825	+	0.856694i	$0.327485\pi$
$98$	−1.37054	+	2.37385i	−0.138446	+	0.239795i
$99$		0			0
$100$	12.2698	−	21.2519i	1.22698	−	2.12519i
$101$	−3.74680	−	6.48965i	−0.372821	−	0.645745i	0.617177	−	0.786824i	$-0.288276\pi$
$101$	−3.74680	−	6.48965i	−0.372821	−	0.645745i	−0.989998	+	0.141079i	$0.954943\pi$
$102$		0			0
$103$	2.80848			0.276728			0.138364	−	0.990381i	$-0.455816\pi$
$103$	2.80848			0.276728			0.138364	+	0.990381i	$0.455816\pi$
$104$	2.90763	−	34.6027i	0.285116	−	3.39307i
$105$		0			0
$106$	6.26033	+	10.8432i	0.608057	+	1.05319i
$107$	0.743235	+	1.28732i	0.0718512	+	0.124450i	0.899713	−	0.436483i	$-0.143776\pi$
$107$	0.743235	+	1.28732i	0.0718512	+	0.124450i	−0.827861	+	0.560933i	$0.810443\pi$
$108$		0			0
$109$	2.87121			0.275012			0.137506	−	0.990501i	$-0.456091\pi$
$109$	2.87121			0.275012			0.137506	+	0.990501i	$0.456091\pi$
$110$	1.38622	−	2.40101i	0.132171	−	0.228927i
$111$		0			0
$112$	−15.3720			−1.45251
$113$	−6.20972	+	10.7555i	−0.584161	+	1.01180i	0.410819	+	0.911717i	$0.365243\pi$
$113$	−6.20972	+	10.7555i	−0.584161	+	1.01180i	−0.994979	+	0.100079i	$0.968090\pi$
$114$		0			0
$115$	0.864640	+	1.49760i	0.0806281	+	0.139652i
$116$	2.24747			0.208673
$117$		0			0
$118$	30.1087			2.77173
$119$	2.07436	+	3.59289i	0.190156	+	0.329360i
$120$		0			0
$121$	4.56863	−	7.91311i	0.415330	−	0.719373i
$122$	17.8855			1.61928
$123$		0			0
$124$	7.64299	−	13.2380i	0.686361	−	1.18881i
$125$	7.00382			0.626440
$126$		0			0
$127$	−2.71526	−	4.70296i	−0.240940	−	0.417321i	0.720042	−	0.693930i	$-0.244122\pi$
$127$	−2.71526	−	4.70296i	−0.240940	−	0.417321i	−0.960982	+	0.276610i	$0.910789\pi$
$128$	−20.9226	−	36.2390i	−1.84931	−	3.20310i
$129$		0			0
$130$	6.62731	−	3.11812i	0.581253	−	0.273477i
$131$	11.3220			0.989209			0.494604	−	0.869118i	$-0.335313\pi$
$131$	11.3220			0.989209			0.494604	+	0.869118i	$0.335313\pi$
$132$		0			0
$133$	3.63303	+	6.29259i	0.315023	+	0.545637i
$134$	18.8582	−	32.6633i	1.62910	−	2.82168i
$135$		0			0
$136$	−19.9779	+	34.6027i	−1.71309	+	2.96715i
$137$	−6.98771	+	12.1031i	−0.597000	+	1.03403i	0.396261	+	0.918138i	$0.370307\pi$
$137$	−6.98771	+	12.1031i	−0.597000	+	1.03403i	−0.993261	+	0.115897i	$0.963026\pi$
$138$		0			0
$139$	−5.21544	+	9.03340i	−0.442368	+	0.766203i	−0.997865	−	0.0653153i	$-0.979195\pi$
$139$	−5.21544	+	9.03340i	−0.442368	+	0.766203i	0.555497	+	0.831518i	$0.312528\pi$
$140$	−2.04299	−	3.53856i	−0.172664	−	0.299063i
$141$		0			0
$142$	13.1990			1.10764
$143$	−4.45271	+	2.09498i	−0.372354	+	0.175191i
$144$		0			0
$145$	0.151043	+	0.261615i	0.0125435	+	0.0217259i
$146$	−8.31901	−	14.4089i	−0.688486	−	1.19249i
$147$		0			0
$148$	−33.6651			−2.76725
$149$	4.08216	−	7.07052i	0.334424	−	0.579239i	−0.648950	−	0.760831i	$-0.724792\pi$
$149$	4.08216	−	7.07052i	0.334424	−	0.579239i	0.983374	+	0.181592i	$0.0581249\pi$
$150$		0			0
$151$	−2.46188			−0.200345			−0.100173	−	0.994970i	$-0.531939\pi$
$151$	−2.46188			−0.200345			−0.100173	+	0.994970i	$0.531939\pi$
$152$	−34.9892	+	60.6031i	−2.83800	+	4.91556i
$153$		0			0
$154$	1.87054	+	3.23987i	0.150732	+	0.261076i
$155$	2.05461			0.165030
$156$		0			0
$157$	−12.9198			−1.03111			−0.515557	−	0.856855i	$-0.672415\pi$
$157$	−12.9198			−1.03111			−0.515557	+	0.856855i	$0.672415\pi$
$158$	12.5073	+	21.6633i	0.995029	+	1.72344i
$159$		0			0
$160$	8.47577	−	14.6805i	0.670069	−	1.16059i
$161$	−2.33345			−0.183902
$162$		0			0
$163$	3.01371	−	5.21990i	0.236052	−	0.408854i	−0.723526	−	0.690297i	$-0.757480\pi$
$163$	3.01371	−	5.21990i	0.236052	−	0.408854i	0.959578	+	0.281443i	$0.0908131\pi$
$164$	−6.91734			−0.540154
$165$		0			0
$166$	16.0857	+	27.8613i	1.24850	+	2.16246i
$167$	3.82558	+	6.62610i	0.296032	+	0.512743i	0.975224	−	0.221218i	$-0.0710031\pi$
$167$	3.82558	+	6.62610i	0.296032	+	0.512743i	−0.679192	+	0.733960i	$0.737670\pi$
$168$		0			0
$169$	−12.8177	−	2.16944i	−0.985977	−	0.166880i
$170$	−8.42755			−0.646364
$171$		0			0
$172$	4.79975	+	8.31342i	0.365978	+	0.633892i
$173$	−0.0822298	+	0.142426i	−0.00625182	+	0.0108285i	−0.869134	−	0.494576i	$-0.835323\pi$
$173$	−0.0822298	+	0.142426i	−0.00625182	+	0.0108285i	0.862883	+	0.505404i	$0.168657\pi$
$174$		0			0
$175$	−2.22540	+	3.85450i	−0.168224	+	0.291373i
$176$	−10.4900	+	18.1692i	−0.790711	+	1.36955i
$177$		0			0
$178$	−2.41353	+	4.18036i	−0.180902	+	0.313331i
$179$	0.384316	+	0.665655i	0.0287252	+	0.0497534i	0.880031	−	0.474917i	$-0.157522\pi$
$179$	0.384316	+	0.665655i	0.0287252	+	0.0497534i	−0.851305	+	0.524670i	$0.824189\pi$
$180$		0			0
$181$	−9.92152			−0.737461			−0.368730	−	0.929536i	$-0.620207\pi$
$181$	−9.92152			−0.737461			−0.368730	+	0.929536i	$0.620207\pi$
$182$	−0.827552	+	9.84840i	−0.0613422	+	0.730012i
$183$		0			0
$184$	−11.2366	−	19.4624i	−0.828373	−	1.43478i
$185$	−2.26249	−	3.91874i	−0.166341	−	0.288112i
$186$		0			0
$187$	5.66224			0.414064
$188$	−16.1503	+	27.9732i	−1.17788	+	2.04015i
$189$		0			0
$190$	−14.7600			−1.07080
$191$	4.94847	−	8.57099i	0.358058	−	0.620175i	−0.629578	−	0.776937i	$-0.716772\pi$
$191$	4.94847	−	8.57099i	0.358058	−	0.620175i	0.987636	+	0.156762i	$0.0501055\pi$
$192$		0			0
$193$	−4.35037	−	7.53507i	−0.313147	−	0.542386i	0.665895	−	0.746045i	$-0.268050\pi$
$193$	−4.35037	−	7.53507i	−0.313147	−	0.542386i	−0.979042	+	0.203659i	$0.934716\pi$
$194$	26.1330			1.87624
$195$		0			0
$196$	5.51353			0.393824
$197$	−13.0093	−	22.5328i	−0.926874	−	1.60539i	−0.788520	−	0.615009i	$-0.789152\pi$
$197$	−13.0093	−	22.5328i	−0.926874	−	1.60539i	−0.138354	−	0.990383i	$-0.544181\pi$
$198$		0			0
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	−0.987820	−	0.155603i	$-0.950268\pi$
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	0.628666	+	0.777675i	$0.283601\pi$
$200$	−42.8651			−3.03102
$201$		0			0
$202$	−10.2703	+	17.7887i	−0.722615	+	1.25161i
$203$	−0.407629			−0.0286099
$204$		0			0
$205$	−0.464885	−	0.805205i	−0.0324690	−	0.0562380i
$206$	−3.84914	−	6.66690i	−0.268182	−	0.464505i
$207$		0			0
$208$	−50.1508	+	23.5957i	−3.47733	+	1.63607i
$209$	9.91685			0.685963
$210$		0			0
$211$	−8.33911	−	14.4438i	−0.574088	−	0.994349i	−0.996140	−	0.0877779i	$-0.972023\pi$
$211$	−8.33911	−	14.4438i	−0.574088	−	0.994349i	0.422052	−	0.906572i	$-0.361310\pi$
$212$	12.5923	−	21.8105i	0.864843	−	1.49795i
$213$		0			0
$214$	2.03727	−	3.52865i	0.139265	−	0.241214i
$215$	−0.645142	+	1.11742i	−0.0439983	+	0.0762074i
$216$		0			0
$217$	−1.38622	+	2.40101i	−0.0941030	+	0.162991i
$218$	−3.93511	−	6.81582i	−0.266520	−	0.461625i
$219$		0			0
$220$	−5.57662			−0.375976
$221$	12.2826	+	8.53765i	0.826216	+	0.574304i
$222$		0			0
$223$	−0.535180	−	0.926959i	−0.0358383	−	0.0620738i	0.847550	−	0.530716i	$-0.178077\pi$
$223$	−0.535180	−	0.926959i	−0.0358383	−	0.0620738i	−0.883388	+	0.468642i	$0.844743\pi$
$224$	11.4370	+	19.8095i	0.764168	+	1.32358i
$225$		0			0
$226$	34.0427			2.26449
$227$	−12.2332	+	21.1885i	−0.811947	+	1.40633i	0.0995534	+	0.995032i	$0.468259\pi$
$227$	−12.2332	+	21.1885i	−0.811947	+	1.40633i	−0.911500	+	0.411300i	$0.865075\pi$
$228$		0			0
$229$	4.72964			0.312543			0.156272	−	0.987714i	$-0.450052\pi$
$229$	4.72964			0.312543			0.156272	+	0.987714i	$0.450052\pi$
$230$	2.37005	−	4.10505i	0.156276	−	0.270679i
$231$		0			0
$232$	−1.96291	−	3.39986i	−0.128871	−	0.223212i
$233$	−20.5507			−1.34632			−0.673160	−	0.739497i	$-0.735064\pi$
$233$	−20.5507			−1.34632			−0.673160	+	0.739497i	$0.735064\pi$
$234$		0			0
$235$	−4.34157			−0.283213
$236$	−30.2810	−	52.4482i	−1.97113	−	3.41409i
$237$		0			0
$238$	5.68598	−	9.84840i	0.368567	−	0.638377i
$239$	−6.25461			−0.404577			−0.202289	−	0.979326i	$-0.564838\pi$
$239$	−6.25461			−0.404577			−0.202289	+	0.979326i	$0.564838\pi$
$240$		0			0
$241$	6.07220	−	10.5174i	0.391145	−	0.677483i	−0.601456	−	0.798906i	$-0.705412\pi$
$241$	6.07220	−	10.5174i	0.391145	−	0.677483i	0.992601	+	0.121423i	$0.0387458\pi$
$242$	−25.0460			−1.61002
$243$		0			0
$244$	−17.9878	−	31.1558i	−1.15155	−	1.99455i
$245$	0.370541	+	0.641796i	0.0236730	+	0.0410028i
$246$		0			0
$247$	21.5117	+	14.9528i	1.36876	+	0.951427i
$248$	−26.7011			−1.69552
$249$		0			0
$250$	−9.59902	−	16.6260i	−0.607095	−	1.05152i
$251$	−3.15719	+	5.46842i	−0.199280	+	0.345163i	−0.948295	−	0.317390i	$-0.897194\pi$
$251$	−3.15719	+	5.46842i	−0.199280	+	0.345163i	0.749015	+	0.662553i	$0.230527\pi$
$252$		0			0
$253$	−1.59237	+	2.75807i	−0.100112	+	0.173398i
$254$	−7.44274	+	12.8912i	−0.466999	+	0.808866i
$255$		0			0
$256$	−25.3948	+	43.9850i	−1.58717	+	2.74907i
$257$	12.1781	+	21.0931i	0.759649	+	1.31575i	0.943030	+	0.332709i	$0.107963\pi$
$257$	12.1781	+	21.0931i	0.759649	+	1.31575i	−0.183380	+	0.983042i	$0.558704\pi$
$258$		0			0
$259$	6.10590			0.379402
$260$	−12.0969	−	8.40855i	−0.750216	−	0.521476i
$261$		0			0
$262$	−15.5173	−	26.8767i	−0.958661	−	1.66045i
$263$	−4.78955	−	8.29574i	−0.295336	−	0.511537i	0.679727	−	0.733465i	$-0.262098\pi$
$263$	−4.78955	−	8.29574i	−0.295336	−	0.511537i	−0.975063	+	0.221928i	$0.928765\pi$
$264$		0			0
$265$	3.38510			0.207945
$266$	9.95843	−	17.2485i	0.610590	−	1.05757i
$267$		0			0
$268$	−75.8643			−4.63415
$269$	14.6995	−	25.4603i	0.896245	−	1.55234i	0.0639886	−	0.997951i	$-0.479618\pi$
$269$	14.6995	−	25.4603i	0.896245	−	1.55234i	0.832256	−	0.554391i	$-0.187049\pi$
$270$		0			0
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	0.870551	−	0.492078i	$-0.163763\pi$
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	−0.861428	+	0.507880i	$0.830429\pi$
$272$	63.7738			3.86686
$273$		0			0
$274$	38.3078			2.31426
$275$	3.03727	+	5.26070i	0.183154	+	0.317232i
$276$		0			0
$277$	16.3855	−	28.3805i	0.984509	−	1.70522i	0.340408	−	0.940278i	$-0.389435\pi$
$277$	16.3855	−	28.3805i	0.984509	−	1.70522i	0.644100	−	0.764941i	$-0.277232\pi$
$278$	28.5919			1.71483
$279$		0			0
$280$	−3.56863	+	6.18106i	−0.213267	+	0.369389i
$281$	−4.29482			−0.256207			−0.128104	−	0.991761i	$-0.540889\pi$
$281$	−4.29482			−0.256207			−0.128104	+	0.991761i	$0.540889\pi$
$282$		0			0
$283$	10.5501	+	18.2734i	0.627140	+	1.08624i	0.988123	+	0.153666i	$0.0491079\pi$
$283$	10.5501	+	18.2734i	0.627140	+	1.08624i	−0.360983	+	0.932572i	$0.617559\pi$
$284$	−13.2745	−	22.9922i	−0.787699	−	1.36433i
$285$		0			0
$286$	11.0758	+	7.69879i	0.654924	+	0.455239i
$287$	1.25461			0.0740574
$288$		0			0
$289$	−0.105901	−	0.183427i	−0.00622950	−	0.0107898i
$290$	0.414022	−	0.717107i	0.0243122	−	0.0421100i
$291$		0			0
$292$	−16.7332	+	28.9828i	−0.979237	+	1.69609i
$293$	8.88192	−	15.3839i	0.518887	−	0.898739i	−0.480872	−	0.876791i	$-0.659680\pi$
$293$	8.88192	−	15.3839i	0.518887	−	0.898739i	0.999759	−	0.0219482i	$-0.00698688\pi$
$294$		0			0
$295$	4.07012	−	7.04965i	0.236971	−	0.410446i
$296$	29.4026	+	50.9268i	1.70899	+	2.96006i
$297$		0			0
$298$	−22.3791			−1.29639
$299$	−7.61286	+	3.58182i	−0.440263	+	0.207142i
$300$		0			0
$301$	−0.870541	−	1.50782i	−0.0501771	−	0.0869094i
$302$	3.37411	+	5.84413i	0.194158	+	0.336292i
$303$		0			0
$304$	111.693			6.40606
$305$	2.41777	−	4.18770i	0.138441	−	0.239787i
$306$		0			0
$307$	18.0156			1.02821			0.514103	−	0.857729i	$-0.328125\pi$
$307$	18.0156			1.02821			0.514103	+	0.857729i	$0.328125\pi$
$308$	3.76249	−	6.51682i	0.214388	−	0.371330i
$309$		0			0
$310$	−2.81593	−	4.87733i	−0.159934	−	0.277014i
$311$	−17.2545			−0.978412			−0.489206	−	0.872168i	$-0.662713\pi$
$311$	−17.2545			−0.978412			−0.489206	+	0.872168i	$0.662713\pi$
$312$		0			0
$313$	6.81526			0.385221			0.192611	−	0.981275i	$-0.438305\pi$
$313$	6.81526			0.385221			0.192611	+	0.981275i	$0.438305\pi$
$314$	17.7071	+	30.6697i	0.999272	+	1.73079i
$315$		0			0
$316$	25.1578	−	43.5745i	1.41523	−	2.45126i
$317$	25.0770			1.40847			0.704233	−	0.709969i	$-0.251291\pi$
$317$	25.0770			1.40847			0.704233	+	0.709969i	$0.251291\pi$
$318$		0			0
$319$	−0.278170	+	0.481805i	−0.0155745	+	0.0269759i
$320$	−23.6818			−1.32385
$321$		0			0
$322$	3.19809	+	5.53926i	0.178223	+	0.308691i
$323$	−15.0724	−	26.1061i	−0.838650	−	1.45258i
$324$		0			0
$325$	−1.34373	+	15.9912i	−0.0745366	+	0.887033i
$326$	−16.5217			−0.915050
$327$		0			0
$328$	6.04151	+	10.4642i	0.333586	+	0.577789i
$329$	2.92921	−	5.07355i	0.161493	−	0.279714i
$330$		0			0
$331$	1.49767	−	2.59404i	0.0823193	−	0.142581i	−0.821926	−	0.569594i	$-0.807101\pi$
$331$	1.49767	−	2.59404i	0.0823193	−	0.142581i	0.904246	+	0.427012i	$0.140434\pi$
$332$	32.3555	−	56.0414i	1.77574	−	3.07567i
$333$		0			0
$334$	10.4862	−	18.1627i	0.573781	−	0.993817i
$335$	−5.09852	−	8.83089i	−0.278562	−	0.482483i
$336$		0			0
$337$	−29.4888			−1.60636			−0.803179	−	0.595738i	$-0.796860\pi$
$337$	−29.4888			−1.60636			−0.803179	+	0.595738i	$0.796860\pi$
$338$	12.4173	+	33.4006i	0.675411	+	1.81675i
$339$		0			0
$340$	8.47577	+	14.6805i	0.459663	+	0.796160i
$341$	1.89195	+	3.27695i	0.102455	+	0.177457i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	8.38407	−	14.5216i	0.452039	−	0.782954i
$345$		0			0
$346$	0.450797			0.0242350
$347$	−2.99343	+	5.18477i	−0.160696	+	0.278333i	−0.935118	−	0.354336i	$-0.884707\pi$
$347$	−2.99343	+	5.18477i	−0.160696	+	0.278333i	0.774423	+	0.632668i	$0.218040\pi$
$348$		0			0
$349$	15.1681	+	26.2719i	0.811929	+	1.40630i	0.911513	+	0.411272i	$0.134915\pi$
$349$	15.1681	+	26.2719i	0.811929	+	1.40630i	−0.0995840	+	0.995029i	$0.531751\pi$
$350$	12.2000			0.652117
$351$		0			0
$352$	31.2189			1.66398
$353$	−14.3031	−	24.7738i	−0.761280	−	1.31857i	−0.942191	−	0.335075i	$-0.891238\pi$
$353$	−14.3031	−	24.7738i	−0.761280	−	1.31857i	0.180912	−	0.983499i	$-0.442095\pi$
$354$		0			0
$355$	1.78425	−	3.09041i	0.0946982	−	0.164022i
$356$	9.70936			0.514595
$357$		0			0
$358$	1.05344	−	1.82462i	0.0556762	−	0.0964340i
$359$	−23.4618			−1.23826			−0.619132	−	0.785287i	$-0.712515\pi$
$359$	−23.4618			−1.23826			−0.619132	+	0.785287i	$0.712515\pi$
$360$		0			0
$361$	−16.8978	−	29.2678i	−0.889357	−	1.54041i
$362$	13.5978	+	23.5522i	0.714687	+	1.23787i
$363$		0			0
$364$	17.9878	−	8.46319i	0.942818	−	0.443592i
$365$	−4.49827			−0.235450
$366$		0			0
$367$	−18.2598	−	31.6270i	−0.953156	−	1.65091i	−0.738533	−	0.674218i	$-0.764481\pi$
$367$	−18.2598	−	31.6270i	−0.953156	−	1.65091i	−0.214623	−	0.976697i	$-0.568852\pi$
$368$	−17.9349	+	31.0641i	−0.934920	+	1.61933i
$369$		0			0
$370$	−6.20166	+	10.7416i	−0.322409	+	0.558429i
$371$	−2.28389	+	3.95582i	−0.118574	+	0.205376i
$372$		0			0
$373$	6.52491	−	11.3015i	0.337847	−	0.585168i	−0.646181	−	0.763185i	$-0.723635\pi$
$373$	6.52491	−	11.3015i	0.337847	−	0.585168i	0.984028	+	0.178017i	$0.0569680\pi$
$374$	−7.76033	−	13.4413i	−0.401277	−	0.695033i
$375$		0			0
$376$	56.4218			2.90973
$377$	−1.32988	+	0.625705i	−0.0684925	+	0.0322254i
$378$		0			0
$379$	−15.3018	−	26.5036i	−0.786003	−	1.36140i	−0.928398	−	0.371587i	$-0.878814\pi$
$379$	−15.3018	−	26.5036i	−0.786003	−	1.36140i	0.142395	−	0.989810i	$-0.454520\pi$
$380$	14.8445	+	25.7114i	0.761505	+	1.31897i
$381$		0			0
$382$	−27.1283			−1.38800
$383$	−2.44299	+	4.23138i	−0.124831	+	0.216213i	−0.921667	−	0.387982i	$-0.873172\pi$
$383$	−2.44299	+	4.23138i	−0.124831	+	0.216213i	0.796836	+	0.604196i	$0.206505\pi$
$384$		0			0
$385$	1.01144			0.0515479
$386$	−11.9247	+	20.6542i	−0.606953	+	1.05127i
$387$		0			0
$388$	−26.2825	−	45.5226i	−1.33429	−	2.31106i
$389$	1.85425			0.0940143			0.0470072	−	0.998895i	$-0.485032\pi$
$389$	1.85425			0.0940143			0.0470072	+	0.998895i	$0.485032\pi$
$390$		0			0
$391$	9.68082			0.489580
$392$	−4.81544	−	8.34058i	−0.243216	−	0.421263i
$393$		0			0
$394$	−35.6595	+	61.7641i	−1.79650	+	3.11163i
$395$	6.76298			0.340283
$396$		0			0
$397$	−10.7567	+	18.6312i	−0.539863	+	0.935071i	0.459048	+	0.888412i	$0.348191\pi$
$397$	−10.7567	+	18.6312i	−0.539863	+	0.935071i	−0.998911	+	0.0466590i	$0.985143\pi$
$398$	27.7753			1.39225
$399$		0			0
$400$	34.2087	+	59.2513i	1.71044	+	2.96256i
$401$	−7.28266	−	12.6139i	−0.363678	−	0.629910i	0.624885	−	0.780717i	$-0.285146\pi$
$401$	−7.28266	−	12.6139i	−0.363678	−	0.629910i	−0.988563	+	0.150808i	$0.951813\pi$
$402$		0			0
$403$	−0.837022	+	9.96110i	−0.0416950	+	0.496198i
$404$	41.3162			2.05556
$405$		0			0
$406$	0.558672	+	0.967649i	0.0277264	+	0.0480236i
$407$	4.16673	−	7.21698i	0.206537	−	0.357733i
$408$		0			0
$409$	11.0645	−	19.1643i	0.547105	−	0.947613i	−0.451366	−	0.892339i	$-0.649063\pi$
$409$	11.0645	−	19.1643i	0.547105	−	0.947613i	0.998471	−	0.0552745i	$-0.0176034\pi$
$410$	−1.27429	+	2.20713i	−0.0629326	+	0.109003i
$411$		0			0
$412$	−7.74232	+	13.4101i	−0.381437	+	0.660668i
$413$	5.49213	+	9.51264i	0.270250	+	0.468086i
$414$		0			0
$415$	8.69791			0.426964
$416$	67.7204	+	47.0726i	3.32027	+	2.30792i
$417$		0			0
$418$	−13.5915	−	23.5411i	−0.664780	−	1.15143i
$419$	1.68795	+	2.92362i	0.0824618	+	0.142828i	0.904307	−	0.426883i	$-0.140388\pi$
$419$	1.68795	+	2.92362i	0.0824618	+	0.142828i	−0.821845	+	0.569711i	$0.807055\pi$
$420$		0			0
$421$	−25.1101			−1.22379			−0.611895	−	0.790939i	$-0.709593\pi$
$421$	−25.1101			−1.22379			−0.611895	+	0.790939i	$0.709593\pi$
$422$	−22.8582	+	39.5915i	−1.11272	+	1.92729i
$423$		0			0
$424$	−43.9917			−2.13643
$425$	9.23254	−	15.9912i	0.447844	−	0.775688i
$426$		0			0
$427$	3.26249	+	5.65079i	0.157883	+	0.273461i
$428$	−8.19570			−0.396154
$429$		0			0
$430$	3.53678			0.170558
$431$	5.39742	+	9.34861i	0.259985	+	0.450307i	0.966238	−	0.257653i	$-0.0829491\pi$
$431$	5.39742	+	9.34861i	0.259985	+	0.450307i	−0.706253	+	0.707960i	$0.749616\pi$
$432$		0			0
$433$	7.25910	−	12.5731i	0.348850	−	0.604226i	−0.637195	−	0.770702i	$-0.719906\pi$
$433$	7.25910	−	12.5731i	0.348850	−	0.604226i	0.986045	+	0.166476i	$0.0532389\pi$
$434$	7.59951			0.364788
$435$		0			0
$436$	−7.91526	+	13.7096i	−0.379072	+	0.656572i
$437$	16.9550			0.811068
$438$		0			0
$439$	7.21544	+	12.4975i	0.344374	+	0.596473i	0.985240	−	0.171180i	$-0.0547578\pi$
$439$	7.21544	+	12.4975i	0.344374	+	0.596473i	−0.640866	+	0.767653i	$0.721425\pi$
$440$	4.87054	+	8.43602i	0.232194	+	0.402172i
$441$		0			0
$442$	3.43327	−	40.8582i	0.163304	−	1.94343i
$443$	30.2430			1.43689			0.718445	−	0.695584i	$-0.244854\pi$
$443$	30.2430			1.43689			0.718445	+	0.695584i	$0.244854\pi$
$444$		0			0
$445$	0.652525	+	1.13021i	0.0309326	+	0.0535769i
$446$	−1.46697	+	2.54087i	−0.0694632	+	0.120314i
$447$		0			0
$448$	15.9779	−	27.6745i	0.754883	−	1.30750i
$449$	15.6380	−	27.0858i	0.738003	−	1.27826i	−0.215390	−	0.976528i	$-0.569102\pi$
$449$	15.6380	−	27.0858i	0.738003	−	1.27826i	0.953393	−	0.301731i	$-0.0975645\pi$
$450$		0			0
$451$	0.856160	−	1.48291i	0.0403150	−	0.0698276i
$452$	−34.2375	−	59.3010i	−1.61039	−	2.78928i
$453$		0			0
$454$	67.0645			3.14749
$455$	2.19403	+	1.52508i	0.102858	+	0.0714966i
$456$		0			0
$457$	−10.3233	−	17.8805i	−0.482904	−	0.836415i	0.516903	−	0.856044i	$-0.327085\pi$
$457$	−10.3233	−	17.8805i	−0.482904	−	0.836415i	−0.999807	+	0.0196293i	$0.993751\pi$
$458$	−6.48216	−	11.2274i	−0.302892	−	0.524624i
$459$		0			0
$460$	−9.53444			−0.444545
$461$	13.6480	−	23.6391i	0.635653	−	1.10098i	−0.350724	−	0.936479i	$-0.614064\pi$
$461$	13.6480	−	23.6391i	0.635653	−	1.10098i	0.986376	−	0.164504i	$-0.0526022\pi$
$462$		0			0
$463$	5.65977			0.263032			0.131516	−	0.991314i	$-0.458016\pi$
$463$	5.65977			0.263032			0.131516	+	0.991314i	$0.458016\pi$
$464$	−3.13303	+	5.42656i	−0.145447	+	0.251922i
$465$		0			0
$466$	28.1656	+	48.7842i	1.30474	+	2.25988i
$467$	−42.2145			−1.95345			−0.976727	−	0.214486i	$-0.931192\pi$
$467$	−42.2145			−1.95345			−0.976727	+	0.214486i	$0.931192\pi$
$468$		0			0
$469$	13.7597			0.635362
$470$	5.95031	+	10.3062i	0.274467	+	0.475391i
$471$		0			0
$472$	−52.8940	+	91.6151i	−2.43464	+	4.21692i
$473$	−2.37626			−0.109261
$474$		0			0
$475$	16.1699	−	28.0070i	0.741925	−	1.28505i
$476$	−22.8740			−1.04843
$477$		0			0
$478$	8.57220	+	14.8475i	0.392083	+	0.679108i
$479$	16.2658	+	28.1732i	0.743204	+	1.28727i	0.951029	+	0.309101i	$0.100028\pi$
$479$	16.2658	+	28.1732i	0.743204	+	1.28727i	−0.207825	+	0.978166i	$0.566639\pi$
$480$		0			0
$481$	19.9204	−	9.37247i	0.908293	−	0.427348i
$482$	−33.2888			−1.51626
$483$		0			0
$484$	25.1893	+	43.6292i	1.14497	+	1.98314i
$485$	3.53267	−	6.11876i	0.160410	−	0.277839i
$486$		0			0
$487$	−13.4291	+	23.2600i	−0.608533	+	1.05401i	0.382950	+	0.923769i	$0.374908\pi$
$487$	−13.4291	+	23.2600i	−0.608533	+	1.05401i	−0.991482	+	0.130240i	$0.958425\pi$
$488$	−31.4206	+	54.4221i	−1.42234	+	2.46357i
$489$		0			0
$490$	1.01568	−	1.75921i	0.0458839	−	0.0794732i
$491$	21.8439	+	37.8348i	0.985802	+	1.70746i	0.638317	+	0.769774i	$0.279631\pi$
$491$	21.8439	+	37.8348i	0.985802	+	1.70746i	0.347485	+	0.937685i	$0.387036\pi$
$492$		0			0
$493$	1.69113			0.0761649
$494$	6.01304	−	71.5590i	0.270539	−	3.21959i
$495$		0			0
$496$	21.3090	+	36.9082i	0.956801	+	1.65723i
$497$	2.40763	+	4.17014i	0.107997	+	0.187056i
$498$		0			0
$499$	−18.1020			−0.810355			−0.405177	−	0.914238i	$-0.632790\pi$
$499$	−18.1020			−0.810355			−0.405177	+	0.914238i	$0.632790\pi$
$500$	−19.3079	+	33.4422i	−0.863474	+	1.49558i
$501$		0			0
$502$	17.3082			0.772505
$503$	−14.2077	+	24.6085i	−0.633492	+	1.09724i	0.353341	+	0.935495i	$0.385046\pi$
$503$	−14.2077	+	24.6085i	−0.633492	+	1.09724i	−0.986833	+	0.161745i	$0.948288\pi$
$504$		0			0
$505$	2.77669	+	4.80937i	0.123561	+	0.214014i
$506$	8.72964			0.388080
$507$		0			0
$508$	29.9413			1.32843
$509$	8.73956	+	15.1374i	0.387374	+	0.670952i	0.992095	−	0.125485i	$-0.0400488\pi$
$509$	8.73956	+	15.1374i	0.387374	+	0.670952i	−0.604721	+	0.796437i	$0.706715\pi$
$510$		0			0
$511$	3.03494	−	5.25666i	0.134258	−	0.232541i
$512$	55.5280			2.45402
$513$		0			0
$514$	33.3812	−	57.8179i	1.47238	−	2.55024i
$515$	−2.08131			−0.0917136
$516$		0			0
$517$	−3.99785	−	6.92447i	−0.175825	−	0.304538i
$518$	−8.36839	−	14.4945i	−0.367686	−	0.636851i
$519$		0			0
$520$	−2.15479	+	25.6434i	−0.0944939	+	1.12454i
$521$	−19.3087			−0.845931			−0.422966	−	0.906146i	$-0.639011\pi$
$521$	−19.3087			−0.845931			−0.422966	+	0.906146i	$0.639011\pi$
$522$		0			0
$523$	5.01144	+	8.68007i	0.219135	+	0.379553i	0.954544	−	0.298071i	$-0.0963431\pi$
$523$	5.01144	+	8.68007i	0.219135	+	0.379553i	−0.735409	+	0.677624i	$0.763010\pi$
$524$	−31.2121	+	54.0610i	−1.36351	+	2.36167i
$525$		0			0
$526$	−13.1285	+	22.7393i	−0.572432	+	0.991481i
$527$	5.75104	−	9.96110i	0.250519	−	0.433912i
$528$		0			0
$529$	8.77750	−	15.2031i	0.381630	−	0.661003i
$530$	−4.63942	−	8.03571i	−0.201524	−	0.349049i
$531$		0			0
$532$	−40.0616			−1.73689
$533$	4.09316	−	1.92581i	0.177294	−	0.0834162i
$534$		0			0
$535$	−0.550798	−	0.954010i	−0.0238131	−	0.0412454i
$536$	66.2588	+	114.764i	2.86194	+	4.95703i
$537$		0			0
$538$	−80.5851			−3.47427
$539$	−0.682410	+	1.18197i	−0.0293935	+	0.0509110i
$540$		0			0
$541$	17.6153			0.757339			0.378670	−	0.925532i	$-0.376382\pi$
$541$	17.6153			0.757339			0.378670	+	0.925532i	$0.376382\pi$
$542$	0.411690	−	0.713067i	0.0176836	−	0.0306289i
$543$		0			0
$544$	−47.4489	−	82.1839i	−2.03435	−	3.52361i
$545$	−2.12780			−0.0911451
$546$		0			0
$547$	2.98425			0.127597			0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425			0.127597			0.0637987	+	0.997963i	$0.479678\pi$
$548$	−38.5269	−	66.7306i	−1.64579	−	2.85059i
$549$		0			0
$550$	8.32540	−	14.4200i	0.354996	−	0.614871i
$551$	2.96185			0.126179
$552$		0			0
$553$	−4.56291	+	7.90320i	−0.194035	+	0.336078i
$554$	−89.8279			−3.81642
$555$		0			0
$556$	−28.7555	−	49.8059i	−1.21950	−	2.11224i
$557$	3.62798	+	6.28384i	0.153722	+	0.266255i	0.932593	−	0.360930i	$-0.117541\pi$
$557$	3.62798	+	6.28384i	0.153722	+	0.266255i	−0.778871	+	0.627184i	$0.784207\pi$
$558$		0			0
$559$	−5.15461	−	3.58298i	−0.218017	−	0.151544i
$560$	11.3919			0.481395
$561$		0			0
$562$	5.88622	+	10.1952i	0.248295	+	0.430060i
$563$	2.13967	−	3.70601i	0.0901762	−	0.156190i	−0.817409	−	0.576058i	$-0.804590\pi$
$563$	2.13967	−	3.70601i	0.0901762	−	0.156190i	0.907585	+	0.419868i	$0.137924\pi$
$564$		0			0
$565$	4.60191	−	7.97074i	0.193604	−	0.335332i
$566$	28.9188	−	50.0888i	1.21555	−	2.10539i
$567$		0			0
$568$	−23.1876	+	40.1621i	−0.972929	+	1.68516i
$569$	−9.88131	−	17.1149i	−0.414246	−	0.717495i	0.581103	−	0.813830i	$-0.302621\pi$
$569$	−9.88131	−	17.1149i	−0.414246	−	0.717495i	−0.995349	+	0.0963347i	$0.969288\pi$
$570$		0			0
$571$	−19.9236			−0.833778			−0.416889	−	0.908957i	$-0.636880\pi$
$571$	−19.9236			−0.833778			−0.416889	+	0.908957i	$0.636880\pi$
$572$	2.27184	−	27.0364i	0.0949905	−	1.13045i
$573$		0			0
$574$	−1.71950	−	2.97826i	−0.0717704	−	0.124310i
$575$	5.19286	+	8.99430i	0.216557	+	0.375088i
$576$		0			0
$577$	−28.7300			−1.19605			−0.598023	−	0.801479i	$-0.704047\pi$
$577$	−28.7300			−1.19605			−0.598023	+	0.801479i	$0.704047\pi$
$578$	−0.290284	+	0.502787i	−0.0120742	+	0.0209132i
$579$		0			0
$580$	−1.66556			−0.0691587
$581$	−5.86839	+	10.1643i	−0.243462	+	0.421688i
$582$		0			0
$583$	3.11710	+	5.39897i	0.129097	+	0.223603i
$584$	58.4582			2.41902
$585$		0			0
$586$	−48.6921			−2.01145
$587$	15.7694	+	27.3134i	0.650872	+	1.12734i	0.982912	+	0.184078i	$0.0589299\pi$
$587$	15.7694	+	27.3134i	0.650872	+	1.12734i	−0.332040	+	0.943265i	$0.607737\pi$
$588$		0			0
$589$	10.0724	−	17.4459i	0.415025	−	0.718845i
$590$	−22.3130			−0.918613
$591$		0			0
$592$	46.9298	−	81.2848i	1.92880	−	3.34079i
$593$	11.1181			0.456564			0.228282	−	0.973595i	$-0.426689\pi$
$593$	11.1181			0.456564			0.228282	+	0.973595i	$0.426689\pi$
$594$		0			0
$595$	−1.53727	−	2.66263i	−0.0630218	−	0.109157i
$596$	22.5071	+	38.9835i	0.921928	+	1.59683i
$597$		0			0
$598$	18.9364	+	13.1627i	0.774368	+	0.538264i
$599$	7.29572			0.298095			0.149048	−	0.988830i	$-0.452379\pi$
$599$	7.29572			0.298095			0.149048	+	0.988830i	$0.452379\pi$
$600$		0			0
$601$	0.586291	+	1.01548i	0.0239153	+	0.0414225i	0.877735	−	0.479146i	$-0.159053\pi$
$601$	0.586291	+	1.01548i	0.0239153	+	0.0414225i	−0.853820	+	0.520568i	$0.825720\pi$
$602$	−2.38622	+	4.13306i	−0.0972552	+	0.168451i
$603$		0			0
$604$	6.78683	−	11.7551i	0.276152	−	0.478310i
$605$	−3.38573	+	5.86426i	−0.137650	+	0.238416i
$606$		0			0
$607$	−0.316919	+	0.548920i	−0.0128633	+	0.0222800i	−0.872385	−	0.488819i	$-0.837428\pi$
$607$	−0.316919	+	0.548920i	−0.0128633	+	0.0222800i	0.859522	+	0.511099i	$0.170761\pi$
$608$	−83.1020	−	143.937i	−3.37023	−	5.83741i
$609$		0			0
$610$	−13.2546			−0.536664
$611$	1.76870	−	21.0487i	0.0715540	−	0.851538i
$612$		0			0
$613$	15.4275	+	26.7212i	0.623110	+	1.07926i	0.988903	+	0.148562i	$0.0474646\pi$
$613$	15.4275	+	26.7212i	0.623110	+	1.07926i	−0.365793	+	0.930696i	$0.619202\pi$
$614$	−24.6911	−	42.7663i	−0.996453	−	1.72591i
$615$		0			0
$616$	−13.1444			−0.529603
$617$	16.9105	−	29.2898i	0.680790	−	1.17916i	−0.293951	−	0.955821i	$-0.594970\pi$
$617$	16.9105	−	29.2898i	0.680790	−	1.17916i	0.974740	−	0.223341i	$-0.0716965\pi$
$618$		0			0
$619$	−0.404797			−0.0162702			−0.00813509	−	0.999967i	$-0.502590\pi$
$619$	−0.404797			−0.0162702			−0.00813509	+	0.999967i	$0.502590\pi$
$620$	−5.66408	+	9.81048i	−0.227475	+	0.393998i
$621$		0			0
$622$	23.6480	+	40.9595i	0.948197	+	1.64233i
$623$	−1.76101			−0.0705532
$624$		0			0
$625$	17.0636			0.682543
$626$	−9.34059	−	16.1784i	−0.373325	−	0.646618i
$627$		0			0
$628$	35.6169	−	61.6903i	1.42127	−	2.46171i
$629$	−25.3316			−1.01004
$630$		0			0
$631$	−15.2254	+	26.3712i	−0.606114	+	1.04982i	0.385761	+	0.922599i	$0.373939\pi$
$631$	−15.2254	+	26.3712i	−0.606114	+	1.04982i	−0.991874	+	0.127221i	$0.959394\pi$
$632$	−87.8897			−3.49606
$633$		0			0
$634$	−34.3691	−	59.5290i	−1.36497	−	2.36420i
$635$	2.01223	+	3.48528i	0.0798529	+	0.138309i
$636$		0			0
$637$	−3.26249	+	1.53499i	−0.129264	+	0.0608183i
$638$	1.52497			0.0603743
$639$		0			0
$640$	15.5053	+	26.8560i	0.612903	+	1.06158i
$641$	4.82282	−	8.35337i	0.190490	−	0.329938i	−0.754923	−	0.655814i	$-0.772326\pi$
$641$	4.82282	−	8.35337i	0.190490	−	0.329938i	0.945413	+	0.325875i	$0.105659\pi$
$642$		0			0
$643$	−4.06648	+	7.04335i	−0.160366	+	0.277763i	−0.935000	−	0.354647i	$-0.884601\pi$
$643$	−4.06648	+	7.04335i	−0.160366	+	0.277763i	0.774634	+	0.632410i	$0.217934\pi$
$644$	6.43278	−	11.1419i	0.253487	−	0.439053i
$645$		0			0
$646$	−41.3146	+	71.5590i	−1.62550	+	2.81545i
$647$	−5.76136	−	9.97898i	−0.226503	−	0.392314i	0.730267	−	0.683162i	$-0.239396\pi$
$647$	−5.76136	−	9.97898i	−0.226503	−	0.392314i	−0.956769	+	0.290848i	$0.906063\pi$
$648$		0			0
$649$	14.9915			0.588469
$650$	39.8023	−	18.7268i	1.56118	−	0.734526i
$651$		0			0
$652$	16.6162	+	28.7801i	0.650740	+	1.12711i
$653$	21.2020	+	36.7229i	0.829697	+	1.43708i	0.898276	+	0.439431i	$0.144820\pi$
$653$	21.2020	+	36.7229i	0.829697	+	1.43708i	−0.0685797	+	0.997646i	$0.521847\pi$
$654$		0			0
$655$	−8.39054			−0.327845
$656$	9.64292	−	16.7020i	0.376493	−	0.652105i
$657$		0			0
$658$	−16.0584			−0.626023
$659$	−1.25044	+	2.16582i	−0.0487101	+	0.0843684i	−0.889352	−	0.457222i	$-0.848844\pi$
$659$	−1.25044	+	2.16582i	−0.0487101	+	0.0843684i	0.840642	+	0.541591i	$0.182178\pi$
$660$		0			0
$661$	−7.41968	−	12.8513i	−0.288592	−	0.499856i	0.684882	−	0.728654i	$-0.259854\pi$
$661$	−7.41968	−	12.8513i	−0.288592	−	0.499856i	−0.973474	+	0.228798i	$0.926520\pi$
$662$	−8.21046			−0.319109
$663$		0			0
$664$	−113.035			−4.38663
$665$	−2.69237	−	4.66332i	−0.104406	−	0.180836i
$666$		0			0
$667$	−0.475592	+	0.823749i	−0.0184150	+	0.0318957i
$668$	−42.1849			−1.63218
$669$		0			0
$670$	−13.9755	+	24.2062i	−0.539919	+	0.935167i
$671$	8.90541			0.343790
$672$		0			0
$673$	−19.8046	−	34.3025i	−0.763410	−	1.32226i	−0.941083	−	0.338175i	$-0.890190\pi$
$673$	−19.8046	−	34.3025i	−0.763410	−	1.32226i	0.177674	−	0.984089i	$-0.443143\pi$
$674$	40.4156	+	70.0019i	1.55675	+	2.69637i
$675$		0			0
$676$	45.6942	−	55.2221i	1.75747	−	2.12393i
$677$	−17.0321			−0.654596			−0.327298	−	0.944921i	$-0.606138\pi$
$677$	−17.0321			−0.654596			−0.327298	+	0.944921i	$0.606138\pi$
$678$		0			0
$679$	4.76691	+	8.25652i	0.182937	+	0.316856i
$680$	14.8052	−	25.6434i	0.567755	−	0.983380i
$681$		0			0
$682$	5.18598	−	8.98238i	0.198581	−	0.343953i
$683$	16.4456	−	28.4846i	0.629272	−	1.08993i	−0.358426	−	0.933558i	$-0.616686\pi$
$683$	16.4456	−	28.4846i	0.629272	−	1.08993i	0.987698	−	0.156374i	$-0.0499804\pi$
$684$		0			0
$685$	5.17846	−	8.96936i	0.197859	−	0.342702i
$686$	1.37054	+	2.37385i	0.0523275	+	0.0906339i
$687$		0			0
$688$	−26.7638			−1.02036
$689$	−1.37905	+	16.4115i	−0.0525375	+	0.625230i
$690$		0			0
$691$	11.8961	+	20.6047i	0.452550	+	0.783839i	0.998544	−	0.0539500i	$-0.0171812\pi$
$691$	11.8961	+	20.6047i	0.452550	+	0.783839i	−0.545994	+	0.837789i	$0.683848\pi$
$692$	−0.453377	−	0.785272i	−0.0172348	−	0.0298515i
$693$		0			0
$694$	16.4105			0.622933
$695$	3.86507	−	6.69449i	0.146610	−	0.253937i
$696$		0			0
$697$	−5.20502			−0.197154
$698$	41.5769	−	72.0134i	1.57371	−	2.72575i
$699$		0			0
$700$	−12.2698	−	21.2519i	−0.463755	−	0.803247i
$701$	−29.7796			−1.12476			−0.562380	−	0.826879i	$-0.690114\pi$
$701$	−29.7796			−1.12476			−0.562380	+	0.826879i	$0.690114\pi$
$702$		0			0
$703$	−44.3658			−1.67329
$704$	−21.8069	−	37.7706i	−0.821878	−	1.42353i
$705$		0			0
$706$	−39.2061	+	67.9069i	−1.47554	+	2.55571i
$707$	−7.49361			−0.281826
$708$		0			0
$709$	−5.96518	+	10.3320i	−0.224027	+	0.388026i	−0.956027	−	0.293278i	$-0.905254\pi$
$709$	−5.96518	+	10.3320i	−0.224027	+	0.388026i	0.732000	+	0.681305i	$0.238587\pi$
$710$	−9.78155			−0.367095
$711$		0			0
$712$	−8.48001	−	14.6878i	−0.317802	−	0.550449i
$713$	3.23469	+	5.60265i	0.121140	+	0.209821i
$714$		0			0
$715$	3.29982	−	1.55255i	0.123406	−	0.0580621i
$716$	−4.23788			−0.158377
$717$		0			0
$718$	32.1553	+	55.6946i	1.20002	+	2.07850i
$719$	16.1819	−	28.0279i	0.603484	−	1.04526i	−0.388805	−	0.921320i	$-0.627112\pi$
$719$	16.1819	−	28.0279i	0.603484	−	1.04526i	0.992289	−	0.123945i	$-0.0395545\pi$
$720$		0			0
$721$	1.40424	−	2.43221i	0.0522966	−	0.0905804i
$722$	−46.3182	+	80.2255i	−1.72379	+	2.98568i
$723$		0			0
$724$	27.3513	−	47.3738i	1.01650	−	1.76063i
$725$	0.907137	+	1.57121i	0.0336902	+	0.0583532i
$726$		0			0
$727$	−31.4897			−1.16789			−0.583943	−	0.811794i	$-0.698491\pi$
$727$	−31.4897			−1.16789			−0.583943	+	0.811794i	$0.698491\pi$
$728$	−28.5130	−	19.8194i	−1.05676	−	0.734556i
$729$		0			0
$730$	6.16507	+	10.6782i	0.228179	+	0.395218i
$731$	3.61162	+	6.25551i	0.133581	+	0.231369i
$732$		0			0
$733$	2.66224			0.0983321			0.0491661	−	0.998791i	$-0.484344\pi$
$733$	2.66224			0.0983321			0.0491661	+	0.998791i	$0.484344\pi$
$734$	−50.0517	+	86.6921i	−1.84744	+	3.19986i
$735$		0			0
$736$	53.3755			1.96745
$737$	9.38973	−	16.2635i	0.345875	−	0.599073i
$738$		0			0
$739$	17.7914	+	30.8156i	0.654467	+	1.13357i	0.982027	+	0.188739i	$0.0604402\pi$
$739$	17.7914	+	30.8156i	0.654467	+	1.13357i	−0.327560	+	0.944830i	$0.606226\pi$
$740$	24.9486			0.917128
$741$		0			0
$742$	12.5207			0.459648
$743$	12.1203	+	20.9929i	0.444650	+	0.770156i	0.998028	−	0.0627740i	$-0.0199947\pi$
$743$	12.1203	+	20.9929i	0.444650	+	0.770156i	−0.553378	+	0.832930i	$0.686661\pi$
$744$		0			0
$745$	−3.02522	+	5.23983i	−0.110835	+	0.191973i
$746$	−35.7706			−1.30966
$747$		0			0
$748$	−15.6095	+	27.0364i	−0.570739	+	0.988549i
$749$	1.48647			0.0543144
$750$		0			0
$751$	14.5705	+	25.2368i	0.531684	+	0.920904i	0.999316	+	0.0369807i	$0.0117740\pi$
$751$	14.5705	+	25.2368i	0.531684	+	0.920904i	−0.467632	+	0.883923i	$0.654893\pi$
$752$	−45.0277	−	77.9903i	−1.64199	−	2.84401i
$753$		0			0
$754$	3.30799	+	2.29939i	0.120470	+	0.0837388i
$755$	1.82446			0.0663988
$756$		0			0
$757$	2.49495	+	4.32138i	0.0906805	+	0.157063i	0.907798	−	0.419408i	$-0.137762\pi$
$757$	2.49495	+	4.32138i	0.0906805	+	0.157063i	−0.817117	+	0.576472i	$0.804429\pi$
$758$	−41.9436	+	72.6485i	−1.52346	+	2.63871i
$759$		0			0
$760$	25.9299	−	44.9119i	0.940576	−	1.62913i
$761$	−5.91858	+	10.2513i	−0.214548	+	0.371609i	−0.953133	−	0.302552i	$-0.902161\pi$
$761$	−5.91858	+	10.2513i	−0.214548	+	0.371609i	0.738584	+	0.674161i	$0.235495\pi$
$762$		0			0
$763$	1.43561	−	2.48654i	0.0519724	−	0.0900189i
$764$	27.2835	+	47.2564i	0.987083	+	1.70968i
$765$		0			0
$766$	13.3929			0.483904
$767$	32.5198	+	22.6045i	1.17422	+	0.816202i
$768$		0			0
$769$	17.9092	+	31.0196i	0.645821	+	1.11859i	0.984111	+	0.177553i	$0.0568180\pi$
$769$	17.9092	+	31.0196i	0.645821	+	1.11859i	−0.338291	+	0.941042i	$0.609849\pi$
$770$	−1.38622	−	2.40101i	−0.0499561	−	0.0865264i
$771$		0			0
$772$	47.9718			1.72654
$773$	−9.97669	+	17.2801i	−0.358837	+	0.621523i	−0.987767	−	0.155939i	$-0.950160\pi$
$773$	−9.97669	+	17.2801i	−0.358837	+	0.621523i	0.628930	+	0.777462i	$0.283493\pi$
$774$		0			0
$775$	12.3396			0.443252
$776$	−45.9095	+	79.5176i	−1.64805	+	2.85451i
$777$		0			0
$778$	−2.54133	−	4.40171i	−0.0911110	−	0.157809i
$779$	−9.11608			−0.326618
$780$		0			0
$781$	6.57196			0.235163
$782$	−13.2680	−	22.9808i	−0.474461	−	0.821791i
$783$		0			0
$784$	−7.68598	+	13.3125i	−0.274499	+	0.475447i
$785$	9.57464			0.341734
$786$		0			0
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	−0.889868	−	0.456219i	$-0.849203\pi$
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	0.840031	+	0.542539i	$0.182537\pi$
$788$	143.454			5.11035
$789$		0			0
$790$	−9.26895	−	16.0543i	−0.329774	−	0.571186i
$791$	6.20972	+	10.7555i	0.220792	+	0.382423i
$792$		0			0
$793$	19.3177	+	13.4278i	0.685992	+	0.476834i
$794$	58.9700			2.09277
$795$		0			0
$796$	−27.9342	−	48.3835i	−0.990101	−	1.71491i
$797$	0.842809	−	1.45979i	0.0298538	−	0.0517083i	−0.850712	−	0.525631i	$-0.823829\pi$
$797$	0.842809	−	1.45979i	0.0298538	−	0.0517083i	0.880566	+	0.473923i	$0.157162\pi$
$798$		0			0
$799$	−12.1525	+	21.0487i	−0.429923	+	0.744649i
$800$	50.9039	−	88.1681i	1.79972	−	3.11721i
$801$		0			0
$802$	−19.9624	+	34.5758i	−0.704895	+	1.22091i
$803$	−4.14214	−	7.17439i	−0.146173	−	0.253179i
$804$		0			0
$805$	1.72928			0.0609491
$806$	24.7933	−	11.6651i	0.873307	−	0.410887i
$807$		0			0
$808$	−36.0850	−	62.5010i	−1.26947	−	2.19878i
$809$	−21.7186	−	37.6177i	−0.763585	−	1.32257i	−0.940992	−	0.338430i	$-0.890104\pi$
$809$	−21.7186	−	37.6177i	−0.763585	−	1.32257i	0.177407	−	0.984138i	$-0.443229\pi$
$810$		0			0
$811$	5.60812			0.196928			0.0984639	−	0.995141i	$-0.468607\pi$
$811$	5.60812			0.196928			0.0984639	+	0.995141i	$0.468607\pi$
$812$	1.12374	−	1.94637i	0.0394355	−	0.0683042i
$813$		0			0
$814$	−22.8427			−0.800635
$815$	−2.23341	+	3.86837i	−0.0782328	+	0.135503i
$816$		0			0
$817$	6.32540	+	10.9559i	0.221298	+	0.383299i
$818$	−60.6574			−2.12084
$819$		0			0
$820$	5.12632			0.179019
$821$	−11.9724	−	20.7368i	−0.417839	−	0.723718i	0.577883	−	0.816120i	$-0.303879\pi$
$821$	−11.9724	−	20.7368i	−0.417839	−	0.723718i	−0.995722	+	0.0924014i	$0.970546\pi$
$822$		0			0
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	0.372810	+	0.927908i	$0.378394\pi$
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	−0.989997	+	0.141091i	$0.954939\pi$
$824$	27.0481			0.942266
$825$		0			0
$826$	15.0544	−	26.0749i	0.523808	−	0.907263i
$827$	16.1563			0.561811			0.280905	−	0.959735i	$-0.409365\pi$
$827$	16.1563			0.561811			0.280905	+	0.959735i	$0.409365\pi$
$828$		0			0
$829$	26.3505	+	45.6404i	0.915190	+	1.58516i	0.806623	+	0.591067i	$0.201293\pi$
$829$	26.3505	+	45.6404i	0.915190	+	1.58516i	0.108568	+	0.994089i	$0.465374\pi$
$830$	−11.9208	−	20.6475i	−0.413779	−	0.716686i
$831$		0			0
$832$	9.64766	−	114.813i	0.334472	−	3.98044i
$833$	4.14871			0.143744
$834$		0			0
$835$	−2.83507	−	4.91048i	−0.0981116	−	0.169934i
$836$	−27.3384	+	47.3516i	−0.945520	+	1.63769i
$837$		0			0
$838$	4.62681	−	8.01388i	0.159831	−	0.276835i
$839$	−11.2169	+	19.4283i	−0.387251	+	0.670738i	−0.992079	−	0.125618i	$-0.959909\pi$
$839$	−11.2169	+	19.4283i	−0.387251	+	0.670738i	0.604828	+	0.796356i	$0.293242\pi$
$840$		0			0
$841$	14.4169	−	24.9708i	0.497135	−	0.861063i
$842$	34.4144	+	59.6075i	1.18600	+	2.05421i
$843$		0			0
$844$	91.9559			3.16525
$845$	9.49897	+	1.60773i	0.326774	+	0.0553076i
$846$		0			0
$847$	−4.56863	−	7.91311i	−0.156980	−	0.271898i
$848$	35.1079	+	60.8086i	1.20561	+	2.08818i
$849$		0			0
$850$	−50.6143			−1.73606
$851$	7.12392	−	12.3390i	0.244205	−	0.422975i
$852$		0			0
$853$	30.8521			1.05635			0.528177	−	0.849134i	$-0.322876\pi$
$853$	30.8521			1.05635			0.528177	+	0.849134i	$0.322876\pi$
$854$	8.94274	−	15.4893i	0.306014	−	0.530032i
$855$		0			0
$856$	7.15800	+	12.3980i	0.244655	+	0.423756i
$857$	−26.7400			−0.913420			−0.456710	−	0.889616i	$-0.650972\pi$
$857$	−26.7400			−0.913420			−0.456710	+	0.889616i	$0.650972\pi$
$858$		0			0
$859$	−5.15804			−0.175990			−0.0879950	−	0.996121i	$-0.528046\pi$
$859$	−5.15804			−0.175990			−0.0879950	+	0.996121i	$0.528046\pi$
$860$	−3.55701	−	6.16092i	−0.121293	−	0.210086i
$861$		0			0
$862$	14.7948	−	25.6253i	0.503912	−	0.872801i
$863$	−8.16814			−0.278047			−0.139023	−	0.990289i	$-0.544396\pi$
$863$	−8.16814			−0.278047			−0.139023	+	0.990289i	$0.544396\pi$
$864$		0			0
$865$	0.0609391	−	0.105550i	0.00207199	−	0.00358879i
$866$	−39.7956			−1.35231
$867$		0			0
$868$	−7.64299	−	13.2380i	−0.259420	−	0.449329i
$869$	6.22755	+	10.7864i	0.211255	+	0.365905i
$870$		0			0
$871$	44.8907	−	21.1209i	1.52106	−	0.715654i
$872$	27.6523			0.936425
$873$		0			0
$874$	−23.2375	−	40.2486i	−0.786021	−	1.36143i
$875$	3.50191	−	6.06548i	0.118386	−	0.205051i
$876$		0			0
$877$	−7.80922	+	13.5260i	−0.263699	+	0.456740i	−0.967222	−	0.253933i	$-0.918276\pi$
$877$	−7.80922	+	13.5260i	−0.263699	+	0.456740i	0.703523	+	0.710672i	$0.251609\pi$
$878$	19.7781	−	34.2567i	0.667479	−	1.15611i
$879$		0			0
$880$	7.77393	−	13.4648i	0.262059	−	0.453900i
$881$	−23.2188	−	40.2161i	−0.782260	−	1.35491i	−0.930622	−	0.365981i	$-0.880734\pi$
$881$	−23.2188	−	40.2161i	−0.782260	−	1.35491i	0.148362	−	0.988933i	$-0.452600\pi$
$882$		0			0
$883$	15.6588			0.526960			0.263480	−	0.964665i	$-0.415130\pi$
$883$	15.6588			0.526960			0.263480	+	0.964665i	$0.415130\pi$
$884$	−74.6263	+	35.1113i	−2.50995	+	1.18092i
$885$		0			0
$886$	−41.4493	−	71.7923i	−1.39252	−	2.41191i
$887$	15.7554	+	27.2891i	0.529013	+	0.916278i	0.999428	+	0.0338320i	$0.0107711\pi$
$887$	15.7554	+	27.2891i	0.529013	+	0.916278i	−0.470414	+	0.882446i	$0.655896\pi$
$888$		0			0
$889$	−5.43052			−0.182134
$890$	1.78862	−	3.09799i	0.0599548	−	0.103845i
$891$		0			0
$892$	5.90146			0.197596
$893$	−21.2838	+	36.8647i	−0.712236	+	1.23363i
$894$		0			0
$895$	−0.284810	−	0.493305i	−0.00952015	−	0.0164894i
$896$	−41.8452			−1.39795
$897$		0			0
$898$	−85.7301			−2.86085
$899$	0.565065	+	0.978722i	0.0188460	+	0.0326422i
$900$		0			0
$901$	9.47521	−	16.4115i	0.315665	−	0.546748i
$902$	−4.69361			−0.156280
$903$		0			0
$904$	−59.8050	+	103.585i	−1.98908	+	3.44520i
$905$	7.35266			0.244411
$906$		0			0
$907$	0.373996	+	0.647780i	0.0124183	+	0.0215092i	0.872168	−	0.489207i	$-0.162714\pi$
$907$	0.373996	+	0.647780i	0.0124183	+	0.0215092i	−0.859749	+	0.510716i	$0.829380\pi$
$908$	−67.4482	−	116.824i	−2.23835	−	3.87693i
$909$		0			0
$910$	0.613284	−	7.29847i	0.0203302	−	0.241942i
$911$	−24.9000			−0.824973			−0.412486	−	0.910964i	$-0.635340\pi$
$911$	−24.9000			−0.824973			−0.412486	+	0.910964i	$0.635340\pi$
$912$		0			0
$913$	8.00929	+	13.8725i	0.265069	+	0.459113i
$914$	−28.2970	+	49.0119i	−0.935983	+	1.62117i
$915$		0			0
$916$	−13.0385	+	22.5834i	−0.430804	+	0.746175i
$917$	5.66100	−	9.80515i	0.186943	−	0.323795i
$918$		0			0
$919$	−0.293247	+	0.507919i	−0.00967334	+	0.0167547i	−0.870822	−	0.491599i	$-0.836412\pi$
$919$	−0.293247	+	0.507919i	−0.00967334	+	0.0167547i	0.861148	+	0.508354i	$0.169746\pi$
$920$	8.32724	+	14.4232i	0.274541	+	0.475519i
$921$		0			0
$922$	−74.8208			−2.46409
$923$	14.2560	+	9.90934i	0.469240	+	0.326170i
$924$		0			0
$925$	−13.5881	−	23.5352i	−0.446773	−	0.773833i
$926$	−7.75694	−	13.4354i	−0.254909	−	0.441515i
$927$		0			0
$928$	9.32412			0.306079
$929$	−25.0975	+	43.4701i	−0.823421	+	1.42621i	0.0796986	+	0.996819i	$0.474604\pi$
$929$	−25.0975	+	43.4701i	−0.823421	+	1.42621i	−0.903120	+	0.429388i	$0.858729\pi$
$930$		0			0
$931$	7.26606			0.238135
$932$	56.6534	−	98.1266i	1.85574	−	3.21424i
$933$		0			0
$934$	57.8567	+	100.211i	1.89313	+	3.27900i
$935$	−4.19619			−0.137230
$936$		0			0
$937$	22.7130			0.742003			0.371001	−	0.928632i	$-0.379015\pi$
$937$	22.7130			0.742003			0.371001	+	0.928632i	$0.379015\pi$
$938$	−18.8582	−	32.6633i	−0.615741	−	1.06650i
$939$		0			0
$940$	11.9687	−	20.7304i	0.390376	−	0.676151i
$941$	49.8734			1.62583			0.812914	−	0.582384i	$-0.197880\pi$
$941$	49.8734			1.62583			0.812914	+	0.582384i	$0.197880\pi$
$942$		0			0
$943$	1.46379	−	2.53536i	0.0476675	−	0.0825626i
$944$	168.849			5.49558
$945$		0			0
$946$	3.25677	+	5.64088i	0.105887	+	0.183401i
$947$	0.133207	+	0.230722i	0.00432865	+	0.00749745i	0.868182	−	0.496247i	$-0.165289\pi$
$947$	0.133207	+	0.230722i	0.00432865	+	0.00749745i	−0.863853	+	0.503744i	$0.831955\pi$
$948$		0			0
$949$	1.83254	−	21.8084i	0.0594867	−	0.707930i
$950$	−88.6459			−2.87605
$951$		0			0
$952$	19.9779	+	34.6027i	0.647486	+	1.12148i
$953$	3.91014	−	6.77257i	0.126662	−	0.219385i	−0.795719	−	0.605665i	$-0.792907\pi$
$953$	3.91014	−	6.77257i	0.126662	−	0.219385i	0.922381	+	0.386281i	$0.126240\pi$
$954$		0			0
$955$	−3.66722	+	6.35181i	−0.118668	+	0.205540i
$956$	17.2425	−	29.8649i	0.557662	−	0.965899i
$957$		0			0
$958$	44.5859	−	77.2251i	1.44051	−	2.49503i
$959$	6.98771	+	12.1031i	0.225645	+	0.390828i
$960$		0			0
$961$	−23.3135			−0.752049
$962$	−49.5506	−	34.4427i	−1.59757	−	1.11048i
$963$		0			0
$964$	33.4793	+	57.9878i	1.07829	+	1.86766i
$965$	3.22398	+	5.58410i	0.103784	+	0.179759i
$966$		0			0
$967$	39.8224			1.28060			0.640301	−	0.768124i	$-0.278810\pi$
$967$	39.8224			1.28060			0.640301	+	0.768124i	$0.278810\pi$
$968$	43.9999	−	76.2101i	1.41421	−	2.44949i
$969$		0			0
$970$	−19.3667			−0.621826
$971$	−22.9648	+	39.7761i	−0.736974	+	1.27648i	0.216878	+	0.976199i	$0.430413\pi$
$971$	−22.9648	+	39.7761i	−0.736974	+	1.27648i	−0.953852	+	0.300278i	$0.902921\pi$
$972$		0			0
$973$	5.21544	+	9.03340i	0.167199	+	0.289598i
$974$	73.6208			2.35896
$975$		0			0
$976$	100.302			3.21058
$977$	−14.3314	−	24.8227i	−0.458501	−	0.794147i	0.540381	−	0.841420i	$-0.318280\pi$
$977$	−14.3314	−	24.8227i	−0.458501	−	0.794147i	−0.998882	+	0.0472734i	$0.984947\pi$
$978$		0			0
$979$	−1.20173	+	2.08145i	−0.0384074	+	0.0665235i
$980$	−4.08598			−0.130522
$981$		0			0
$982$	59.8760	−	103.708i	1.91072	−	3.30946i
$983$	46.1200			1.47100			0.735500	−	0.677524i	$-0.236947\pi$
$983$	46.1200			1.47100			0.735500	+	0.677524i	$0.236947\pi$
$984$		0			0
$985$	9.64095	+	16.6986i	0.307186	+	0.532062i
$986$	−2.31777	−	4.01449i	−0.0738128	−	0.127848i
$987$		0			0
$988$	−130.700	+	61.4940i	−4.15814	+	1.95638i
$989$	−4.06273			−0.129187
$990$		0			0
$991$	−18.9124	−	32.7573i	−0.600773	−	1.04057i	−0.992704	−	0.120575i	$-0.961526\pi$
$991$	−18.9124	−	32.7573i	−0.600773	−	1.04057i	0.391931	−	0.919995i	$-0.371807\pi$
$992$	31.7086	−	54.9208i	1.00675	−	1.74374i
$993$		0			0
$994$	6.59951	−	11.4307i	0.209324	−	0.362559i
$995$	3.75468	−	6.50329i	0.119031	−	0.206168i
$996$		0			0
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	0.383952	+	0.923353i	$0.374563\pi$
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	−0.991623	+	0.129164i	$0.958771\pi$
$998$	24.8095	+	42.9713i	0.785330	+	1.36023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.h.757.1		8
3.2	odd	2		91.2.f.c.29.4	yes	8
12.11	even	2		1456.2.s.q.1121.3		8
13.9	even	3	inner	819.2.o.h.568.1		8
21.2	odd	6		637.2.g.k.263.4		8
21.5	even	6		637.2.g.j.263.4		8
21.11	odd	6		637.2.h.h.471.1		8
21.17	even	6		637.2.h.i.471.1		8
21.20	even	2		637.2.f.i.393.4		8
39.2	even	12		1183.2.c.g.337.8		8
39.11	even	12		1183.2.c.g.337.1		8
39.23	odd	6		1183.2.a.l.1.4		4
39.29	odd	6		1183.2.a.k.1.1		4
39.35	odd	6		91.2.f.c.22.4	✓	8
156.35	even	6		1456.2.s.q.113.3		8
273.62	even	6		8281.2.a.bt.1.4		4
273.74	odd	6		637.2.g.k.373.4		8
273.146	even	6		8281.2.a.bp.1.1		4
273.152	even	6		637.2.h.i.165.1		8
273.191	odd	6		637.2.h.h.165.1		8
273.230	even	6		637.2.f.i.295.4		8
273.269	even	6		637.2.g.j.373.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	39.35	odd	6
91.2.f.c.29.4	yes	8	3.2	odd	2
637.2.f.i.295.4		8	273.230	even	6
637.2.f.i.393.4		8	21.20	even	2
637.2.g.j.263.4		8	21.5	even	6
637.2.g.j.373.4		8	273.269	even	6
637.2.g.k.263.4		8	21.2	odd	6
637.2.g.k.373.4		8	273.74	odd	6
637.2.h.h.165.1		8	273.191	odd	6
637.2.h.h.471.1		8	21.11	odd	6
637.2.h.i.165.1		8	273.152	even	6
637.2.h.i.471.1		8	21.17	even	6
819.2.o.h.568.1		8	13.9	even	3	inner
819.2.o.h.757.1		8	1.1	even	1	trivial
1183.2.a.k.1.1		4	39.29	odd	6
1183.2.a.l.1.4		4	39.23	odd	6
1183.2.c.g.337.1		8	39.11	even	12
1183.2.c.g.337.8		8	39.2	even	12
1456.2.s.q.113.3		8	156.35	even	6
1456.2.s.q.1121.3		8	12.11	even	2
8281.2.a.bp.1.1		4	273.146	even	6
8281.2.a.bt.1.4		4	273.62	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37054 - 2.37385i) q^{2} +(-2.75677 + 4.77486i) q^{4} -0.741082 q^{5} +(0.500000 - 0.866025i) q^{7} +9.63087 q^{8} +(1.01568 + 1.75921i) q^{10} +(-0.682410 - 1.18197i) q^{11} +(0.301907 - 3.59289i) q^{13} -2.74108 q^{14} +(-7.68598 - 13.3125i) q^{16} +(-2.07436 + 3.59289i) q^{17} +(-3.63303 + 6.29259i) q^{19} +(2.04299 - 3.53856i) q^{20} +(-1.87054 + 3.23987i) q^{22} +(-1.16673 - 2.02083i) q^{23} -4.45080 q^{25} +(-8.94274 + 4.20752i) q^{26} +(2.75677 + 4.77486i) q^{28} +(-0.203815 - 0.353017i) q^{29} -2.77245 q^{31} +(-11.4370 + 19.8095i) q^{32} +11.3720 q^{34} +(-0.370541 + 0.641796i) q^{35} +(3.05295 + 5.28787i) q^{37} +19.9169 q^{38} -7.13727 q^{40} +(0.627306 + 1.08653i) q^{41} +(0.870541 - 1.50782i) q^{43} +7.52497 q^{44} +(-3.19809 + 5.53926i) q^{46} +5.85843 q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.10000 + 10.5655i) q^{50} +(16.3232 + 11.3463i) q^{52} -4.56778 q^{53} +(0.505722 + 0.875935i) q^{55} +(4.81544 - 8.34058i) q^{56} +(-0.558672 + 0.967649i) q^{58} +(-5.49213 + 9.51264i) q^{59} +(-3.26249 + 5.65079i) q^{61} +(3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(-0.223738 + 2.66263i) q^{65} +(6.87983 + 11.9162i) q^{67} +(-11.4370 - 19.8095i) q^{68} +2.03137 q^{70} +(-2.40763 + 4.17014i) q^{71} +6.06987 q^{73} +(8.36839 - 14.4945i) q^{74} +(-20.0308 - 34.6944i) q^{76} -1.36482 q^{77} -9.12582 q^{79} +(5.69594 + 9.86566i) q^{80} +(1.71950 - 2.97826i) q^{82} -11.7368 q^{83} +(1.53727 - 2.66263i) q^{85} -4.77245 q^{86} +(-6.57220 - 11.3834i) q^{88} +(-0.880503 - 1.52508i) q^{89} +(-2.96058 - 2.05790i) q^{91} +12.8656 q^{92} +(-8.02921 - 13.9070i) q^{94} +(2.69237 - 4.66332i) q^{95} +(-4.76691 + 8.25652i) q^{97} +(-1.37054 + 2.37385i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29}+ \cdots - q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more