LMFDB - Embedded newform 819.2.bm.e.478.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.2
Root			$-1.18541 - 0.771231i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.e.550.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54246i q^{2} -0.379188 q^{4} +(-1.27069 - 0.733632i) q^{5} +(2.63491 + 0.239300i) q^{7} -2.50004i q^{8} +O(q^{10})$	\(q-1.54246i q^{2} -0.379188 q^{4} +(-1.27069 - 0.733632i) q^{5} +(2.63491 + 0.239300i) q^{7} -2.50004i q^{8} +(-1.13160 + 1.95999i) q^{10} +(1.93300 + 1.11602i) q^{11} +(3.57691 - 0.453537i) q^{13} +(0.369112 - 4.06424i) q^{14} -4.61459 q^{16} +2.52122 q^{17} +(-0.829287 + 0.478789i) q^{19} +(0.481830 + 0.278185i) q^{20} +(1.72142 - 2.98158i) q^{22} +2.64900 q^{23} +(-1.42357 - 2.46569i) q^{25} +(-0.699564 - 5.51725i) q^{26} +(-0.999126 - 0.0907399i) q^{28} +(0.728078 + 1.26107i) q^{29} +(-2.89114 + 1.66920i) q^{31} +2.11775i q^{32} -3.88889i q^{34} +(-3.17259 - 2.23713i) q^{35} -7.41040i q^{37} +(0.738514 + 1.27914i) q^{38} +(-1.83411 + 3.17677i) q^{40} +(-3.52497 + 2.03514i) q^{41} +(3.00991 - 5.21332i) q^{43} +(-0.732971 - 0.423181i) q^{44} -4.08598i q^{46} +(-9.05536 - 5.22812i) q^{47} +(6.88547 + 1.26107i) q^{49} +(-3.80323 + 2.19580i) q^{50} +(-1.35632 + 0.171976i) q^{52} +(-1.74412 - 3.02090i) q^{53} +(-1.63749 - 2.83622i) q^{55} +(0.598261 - 6.58737i) q^{56} +(1.94515 - 1.12303i) q^{58} +0.767344i q^{59} +(6.05695 + 10.4909i) q^{61} +(2.57468 + 4.45947i) q^{62} -5.96263 q^{64} +(-4.87787 - 2.04783i) q^{65} +(-8.35667 - 4.82473i) q^{67} -0.956018 q^{68} +(-3.45069 + 4.89359i) q^{70} +(2.50519 + 1.44637i) q^{71} +(11.3623 - 6.56004i) q^{73} -11.4303 q^{74} +(0.314456 - 0.181551i) q^{76} +(4.82621 + 3.40317i) q^{77} +(-1.88401 + 3.26320i) q^{79} +(5.86371 + 3.38541i) q^{80} +(3.13913 + 5.43712i) q^{82} +3.89258i q^{83} +(-3.20369 - 1.84965i) q^{85} +(-8.04135 - 4.64268i) q^{86} +(2.79009 - 4.83258i) q^{88} +10.1478i q^{89} +(9.53336 - 0.339072i) q^{91} -1.00447 q^{92} +(-8.06417 + 13.9676i) q^{94} +1.40502 q^{95} +(-5.44296 - 3.14250i) q^{97} +(1.94515 - 10.6206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.54246i		−	1.09069i	−0.838213	−	0.545343i	$-0.816400\pi$
$2$		−	1.54246i		−	1.09069i	0.838213	−	0.545343i	$-0.183600\pi$
$3$		0			0
$3$		0			0
$4$	−0.379188			−0.189594
$5$	−1.27069	−	0.733632i	−0.568269	−	0.328090i	0.188189	−	0.982133i	$-0.439738\pi$
$5$	−1.27069	−	0.733632i	−0.568269	−	0.328090i	−0.756458	+	0.654043i	$0.773072\pi$
$6$		0			0
$7$	2.63491	+	0.239300i	0.995901	+	0.0904471i
$7$	2.63491	+	0.239300i	0.995901	+	0.0904471i
$8$		−	2.50004i		−	0.883898i
$9$		0			0
$10$	−1.13160	+	1.95999i	−0.357843	+	0.619803i
$11$	1.93300	+	1.11602i	0.582822	+	0.336492i	0.762254	−	0.647278i	$-0.224093\pi$
$11$	1.93300	+	1.11602i	0.582822	+	0.336492i	−0.179432	+	0.983770i	$0.557426\pi$
$12$		0			0
$13$	3.57691	−	0.453537i	0.992057	−	0.125789i
$13$	3.57691	−	0.453537i	0.992057	−	0.125789i
$14$	0.369112	−	4.06424i	0.0986493	−	1.08621i
$15$		0			0
$16$	−4.61459			−1.15365
$17$	2.52122			0.611487			0.305743	−	0.952114i	$-0.401095\pi$
$17$	2.52122			0.611487			0.305743	+	0.952114i	$0.401095\pi$
$18$		0			0
$19$	−0.829287	+	0.478789i	−0.190252	+	0.109842i	−0.592100	−	0.805864i	$-0.701701\pi$
$19$	−0.829287	+	0.478789i	−0.190252	+	0.109842i	0.401849	+	0.915706i	$0.368368\pi$
$20$	0.481830	+	0.278185i	0.107740	+	0.0622040i
$21$		0			0
$22$	1.72142	−	2.98158i	0.367007	−	0.635675i
$23$	2.64900			0.552355			0.276178	−	0.961107i	$-0.410932\pi$
$23$	2.64900			0.552355			0.276178	+	0.961107i	$0.410932\pi$
$24$		0			0
$25$	−1.42357	−	2.46569i	−0.284713	−	0.493138i
$26$	−0.699564	−	5.51725i	−0.137196	−	1.08202i
$27$		0			0
$28$	−0.999126	−	0.0907399i	−0.188817	−	0.0171482i
$29$	0.728078	+	1.26107i	0.135201	+	0.234175i	0.925674	−	0.378322i	$-0.123499\pi$
$29$	0.728078	+	1.26107i	0.135201	+	0.234175i	−0.790473	+	0.612496i	$0.790165\pi$
$30$		0			0
$31$	−2.89114	+	1.66920i	−0.519264	+	0.299797i	−0.736633	−	0.676292i	$-0.763586\pi$
$31$	−2.89114	+	1.66920i	−0.519264	+	0.299797i	0.217369	+	0.976089i	$0.430252\pi$
$32$			2.11775i			0.374369i
$33$		0			0
$34$		−	3.88889i		−	0.666939i
$35$	−3.17259	−	2.23713i	−0.536265	−	0.378144i
$36$		0			0
$37$		−	7.41040i		−	1.21826i	−0.793070	−	0.609131i	$-0.791518\pi$
$37$		−	7.41040i		−	1.21826i	0.793070	−	0.609131i	$-0.208482\pi$
$38$	0.738514	+	1.27914i	0.119803	+	0.207505i
$39$		0			0
$40$	−1.83411	+	3.17677i	−0.289998	+	0.502292i
$41$	−3.52497	+	2.03514i	−0.550507	+	0.317835i	−0.749327	−	0.662201i	$-0.769623\pi$
$41$	−3.52497	+	2.03514i	−0.550507	+	0.317835i	0.198819	+	0.980036i	$0.436289\pi$
$42$		0			0
$43$	3.00991	−	5.21332i	0.459008	−	0.795024i	−0.539901	−	0.841728i	$-0.681538\pi$
$43$	3.00991	−	5.21332i	0.459008	−	0.795024i	0.998909	+	0.0467040i	$0.0148718\pi$
$44$	−0.732971	−	0.423181i	−0.110500	−	0.0637970i
$45$		0			0
$46$		−	4.08598i		−	0.602446i
$47$	−9.05536	−	5.22812i	−1.32086	−	0.762599i	−0.336995	−	0.941507i	$-0.609410\pi$
$47$	−9.05536	−	5.22812i	−1.32086	−	0.762599i	−0.983866	+	0.178907i	$0.942744\pi$
$48$		0			0
$49$	6.88547	+	1.26107i	0.983639	+	0.180153i
$50$	−3.80323	+	2.19580i	−0.537859	+	0.310533i
$51$		0			0
$52$	−1.35632	+	0.171976i	−0.188088	+	0.0238488i
$53$	−1.74412	−	3.02090i	−0.239573	−	0.414953i	0.721019	−	0.692916i	$-0.243674\pi$
$53$	−1.74412	−	3.02090i	−0.239573	−	0.414953i	−0.960592	+	0.277963i	$0.910341\pi$
$54$		0			0
$55$	−1.63749	−	2.83622i	−0.220800	−	0.382436i
$56$	0.598261	−	6.58737i	0.0799459	−	0.880275i
$57$		0			0
$58$	1.94515	−	1.12303i	0.255411	−	0.147461i
$59$			0.767344i			0.0998997i	0.998752	+	0.0499499i	$0.0159062\pi$
$59$			0.767344i			0.0998997i	−0.998752	+	0.0499499i	$0.984094\pi$
$60$		0			0
$61$	6.05695	+	10.4909i	0.775513	+	1.34323i	0.934506	+	0.355948i	$0.115842\pi$
$61$	6.05695	+	10.4909i	0.775513	+	1.34323i	−0.158993	+	0.987280i	$0.550825\pi$
$62$	2.57468	+	4.45947i	0.326984	+	0.566354i
$63$		0			0
$64$	−5.96263			−0.745329
$65$	−4.87787	−	2.04783i	−0.605025	−	0.254003i
$66$		0			0
$67$	−8.35667	−	4.82473i	−1.02093	−	0.589434i	−0.106557	−	0.994307i	$-0.533983\pi$
$67$	−8.35667	−	4.82473i	−1.02093	−	0.589434i	−0.914373	+	0.404872i	$0.867316\pi$
$68$	−0.956018			−0.115934
$69$		0			0
$70$	−3.45069	+	4.89359i	−0.412436	+	0.584896i
$71$	2.50519	+	1.44637i	0.297311	+	0.171652i	0.641234	−	0.767345i	$-0.278423\pi$
$71$	2.50519	+	1.44637i	0.297311	+	0.171652i	−0.343923	+	0.938998i	$0.611756\pi$
$72$		0			0
$73$	11.3623	−	6.56004i	1.32986	−	0.767795i	0.344582	−	0.938756i	$-0.388021\pi$
$73$	11.3623	−	6.56004i	1.32986	−	0.767795i	0.985278	+	0.170962i	$0.0546874\pi$
$74$	−11.4303			−1.32874
$75$		0			0
$76$	0.314456	−	0.181551i	0.0360706	−	0.0208254i
$77$	4.82621	+	3.40317i	0.549998	+	0.387828i
$78$		0			0
$79$	−1.88401	+	3.26320i	−0.211968	+	0.367139i	−0.952330	−	0.305069i	$-0.901321\pi$
$79$	−1.88401	+	3.26320i	−0.211968	+	0.367139i	0.740362	+	0.672208i	$0.234654\pi$
$80$	5.86371	+	3.38541i	0.655583	+	0.378501i
$81$		0			0
$82$	3.13913	+	5.43712i	0.346658	+	0.600430i
$83$			3.89258i			0.427266i	0.976914	+	0.213633i	$0.0685296\pi$
$83$			3.89258i			0.427266i	−0.976914	+	0.213633i	$0.931470\pi$
$84$		0			0
$85$	−3.20369	−	1.84965i	−0.347489	−	0.200623i
$86$	−8.04135	−	4.64268i	−0.867121	−	0.500633i
$87$		0			0
$88$	2.79009	−	4.83258i	0.297425	−	0.515155i
$89$			10.1478i			1.07567i	0.843051	+	0.537834i	$0.180757\pi$
$89$			10.1478i			1.07567i	−0.843051	+	0.537834i	$0.819243\pi$
$90$		0			0
$91$	9.53336	−	0.339072i	0.999368	−	0.0355444i
$92$	−1.00447			−0.104723
$93$		0			0
$94$	−8.06417	+	13.9676i	−0.831756	+	1.44064i
$95$	1.40502			0.144152
$96$		0			0
$97$	−5.44296	−	3.14250i	−0.552649	−	0.319072i	0.197541	−	0.980295i	$-0.436705\pi$
$97$	−5.44296	−	3.14250i	−0.552649	−	0.319072i	−0.750190	+	0.661223i	$0.770038\pi$
$98$	1.94515	−	10.6206i	0.196490	−	1.07284i
$99$		0			0
$100$	0.539800	+	0.934961i	0.0539800	+	0.0934961i
$101$	1.30339	−	2.25754i	0.129692	−	0.224634i	−0.793865	−	0.608094i	$-0.791934\pi$
$101$	1.30339	−	2.25754i	0.129692	−	0.224634i	0.923557	+	0.383460i	$0.125268\pi$
$102$		0			0
$103$	−6.25199	+	10.8288i	−0.616027	+	1.06699i	0.374176	+	0.927358i	$0.377926\pi$
$103$	−6.25199	+	10.8288i	−0.616027	+	1.06699i	−0.990203	+	0.139633i	$0.955408\pi$
$104$	−1.13386	−	8.94243i	−0.111184	−	0.876877i
$105$		0			0
$106$	−4.65963	+	2.69024i	−0.452583	+	0.261299i
$107$	18.2516			1.76445			0.882227	−	0.470825i	$-0.156044\pi$
$107$	18.2516			1.76445			0.882227	+	0.470825i	$0.156044\pi$
$108$		0			0
$109$	−1.37903	+	0.796181i	−0.132087	+	0.0762603i	−0.564587	−	0.825373i	$-0.690965\pi$
$109$	−1.37903	+	0.796181i	−0.132087	+	0.0762603i	0.432501	+	0.901634i	$0.357631\pi$
$110$	−4.37477	+	2.52577i	−0.417118	+	0.240823i
$111$		0			0
$112$	−12.1590	−	1.10427i	−1.14892	−	0.104344i
$113$	−10.1371	+	17.5580i	−0.953617	+	1.65171i	−0.216115	+	0.976368i	$0.569339\pi$
$113$	−10.1371	+	17.5580i	−0.953617	+	1.65171i	−0.737502	+	0.675345i	$0.763995\pi$
$114$		0			0
$115$	−3.36606	−	1.94339i	−0.313886	−	0.181222i
$116$	−0.276079	−	0.478182i	−0.0256333	−	0.0443981i
$117$		0			0
$118$	1.18360			0.108959
$119$	6.64319	+	0.603330i	0.608980	+	0.0553072i
$120$		0			0
$121$	−3.00900	−	5.21175i	−0.273546	−	0.473795i
$122$	16.1819	−	9.34261i	1.46504	−	0.845840i
$123$		0			0
$124$	1.09629	−	0.632941i	0.0984494	−	0.0568398i
$125$			11.5138i			1.02983i
$126$		0			0
$127$	2.15084	+	3.72537i	0.190856	+	0.330573i	0.945534	−	0.325523i	$-0.105540\pi$
$127$	2.15084	+	3.72537i	0.190856	+	0.330573i	−0.754678	+	0.656095i	$0.772207\pi$
$128$			13.4326i			1.18729i
$129$		0			0
$130$	−3.15871	+	7.52393i	−0.277037	+	0.659892i
$131$	−7.41308	+	12.8398i	−0.647684	+	1.12182i	0.335990	+	0.941865i	$0.390929\pi$
$131$	−7.41308	+	12.8398i	−0.647684	+	1.12182i	−0.983675	+	0.179957i	$0.942404\pi$
$132$		0			0
$133$	−2.29967	+	1.06312i	−0.199407	+	0.0921839i
$134$	−7.44196	+	12.8898i	−0.642887	+	1.11351i
$135$		0			0
$136$		−	6.30316i		−	0.540492i
$137$		−	5.17843i		−	0.442423i	−0.975226	−	0.221211i	$-0.928999\pi$
$137$		−	5.17843i		−	0.442423i	0.975226	−	0.221211i	$-0.0710011\pi$
$138$		0			0
$139$	−10.3510	+	17.9284i	−0.877959	+	1.52067i	−0.0243815	+	0.999703i	$0.507762\pi$
$139$	−10.3510	+	17.9284i	−0.877959	+	1.52067i	−0.853577	+	0.520966i	$0.825572\pi$
$140$	1.20301	+	0.848293i	0.101673	+	0.0716938i
$141$		0			0
$142$	2.23097	−	3.86415i	0.187219	−	0.324272i
$143$	7.42033	+	3.11521i	0.620519	+	0.260507i
$144$		0			0
$145$		−	2.13657i		−	0.177432i
$146$	−10.1186	−	17.5259i	−0.837422	−	1.45046i
$147$		0			0
$148$			2.80994i			0.230975i
$149$	15.2801	−	8.82198i	1.25180	−	0.722725i	0.280331	−	0.959904i	$-0.409556\pi$
$149$	15.2801	−	8.82198i	1.25180	−	0.722725i	0.971466	+	0.237178i	$0.0762226\pi$
$150$		0			0
$151$	13.1219	−	7.57592i	1.06784	−	0.616520i	0.140252	−	0.990116i	$-0.455209\pi$
$151$	13.1219	−	7.57592i	1.06784	−	0.616520i	0.927591	+	0.373596i	$0.121875\pi$
$152$	1.19699	+	2.07325i	0.0970889	+	0.168163i
$153$		0			0
$154$	5.24927	−	7.44425i	0.422998	−	0.599875i
$155$	4.89832			0.393442
$156$		0			0
$157$	8.38350	+	14.5206i	0.669076	+	1.15887i	0.978163	+	0.207840i	$0.0666433\pi$
$157$	8.38350	+	14.5206i	0.669076	+	1.15887i	−0.309087	+	0.951034i	$0.600023\pi$
$158$	5.03337	+	2.90602i	0.400433	+	0.231190i
$159$		0			0
$160$	1.55365	−	2.69100i	0.122827	−	0.212743i
$161$	6.97988	+	0.633907i	0.550091	+	0.0499589i
$162$		0			0
$163$	−13.9910	+	8.07769i	−1.09586	+	0.632693i	−0.935130	−	0.354306i	$-0.884717\pi$
$163$	−13.9910	+	8.07769i	−1.09586	+	0.632693i	−0.160727	+	0.986999i	$0.551384\pi$
$164$	1.33663	−	0.771701i	0.104373	−	0.0602597i
$165$		0			0
$166$	6.00415			0.466012
$167$	17.1116	−	9.87941i	1.32414	−	0.764492i	0.339752	−	0.940515i	$-0.389657\pi$
$167$	17.1116	−	9.87941i	1.32414	−	0.764492i	0.984386	+	0.176023i	$0.0563234\pi$
$168$		0			0
$169$	12.5886	−	3.24453i	0.968354	−	0.249579i
$170$	−2.85302	+	4.94157i	−0.218816	+	0.379001i
$171$		0			0
$172$	−1.14132	+	1.97683i	−0.0870251	+	0.150732i
$173$	0.817014	+	1.41511i	0.0621164	+	0.107589i	0.895411	−	0.445240i	$-0.146882\pi$
$173$	0.817014	+	1.41511i	0.0621164	+	0.107589i	−0.833295	+	0.552829i	$0.813548\pi$
$174$		0			0
$175$	−3.16093	−	6.83753i	−0.238944	−	0.516868i
$176$	−8.92001	−	5.14997i	−0.672371	−	0.388194i
$177$		0			0
$178$	15.6526			1.17322
$179$	8.73157	−	15.1235i	0.652628	−	1.13038i	−0.329855	−	0.944032i	$-0.607000\pi$
$179$	8.73157	−	15.1235i	0.652628	−	1.13038i	0.982483	−	0.186353i	$-0.0596668\pi$
$180$		0			0
$181$	−0.848669			−0.0630811			−0.0315405	−	0.999502i	$-0.510041\pi$
$181$	−0.848669			−0.0630811			−0.0315405	+	0.999502i	$0.510041\pi$
$182$	−0.523005	−	14.7048i	−0.0387677	−	1.09000i
$183$		0			0
$184$		−	6.62261i		−	0.488225i
$185$	−5.43651	+	9.41631i	−0.399700	+	0.692301i
$186$		0			0
$187$	4.87353	+	2.81373i	0.356388	+	0.205761i
$188$	3.43369	+	1.98244i	0.250427	+	0.144584i
$189$		0			0
$190$		−	2.16719i		−	0.157225i
$191$	−13.6803	−	23.6950i	−0.989875	−	1.71451i	−0.617865	−	0.786284i	$-0.712002\pi$
$191$	−13.6803	−	23.6950i	−0.989875	−	1.71451i	−0.372010	−	0.928229i	$-0.621331\pi$
$192$		0			0
$193$	10.2145	+	5.89736i	0.735258	+	0.424501i	0.820342	−	0.571873i	$-0.193783\pi$
$193$	10.2145	+	5.89736i	0.735258	+	0.424501i	−0.0850849	+	0.996374i	$0.527116\pi$
$194$	−4.84718	+	8.39556i	−0.348007	+	0.602766i
$195$		0			0
$196$	−2.61089	−	0.478182i	−0.186492	−	0.0341559i
$197$	−7.28644	+	4.20683i	−0.519137	+	0.299724i	−0.736582	−	0.676349i	$-0.763561\pi$
$197$	−7.28644	+	4.20683i	−0.519137	+	0.299724i	0.217444	+	0.976073i	$0.430228\pi$
$198$		0			0
$199$	−5.06886			−0.359322			−0.179661	−	0.983729i	$-0.557500\pi$
$199$	−5.06886			−0.359322			−0.179661	+	0.983729i	$0.557500\pi$
$200$	−6.16433	+	3.55898i	−0.435884	+	0.251658i
$201$		0			0
$202$	−3.48217	−	2.01043i	−0.245005	−	0.141454i
$203$	1.61664	+	3.49703i	0.113466	+	0.245443i
$204$		0			0
$205$	5.97218			0.417115
$206$	16.7030	+	9.64346i	1.16375	+	0.671892i
$207$		0			0
$208$	−16.5060	+	2.09289i	−1.14448	+	0.145116i
$209$	−2.13735			−0.147844
$210$		0			0
$211$	10.2926	+	17.8273i	0.708570	+	1.22728i	0.965388	+	0.260820i	$0.0839928\pi$
$211$	10.2926	+	17.8273i	0.708570	+	1.22728i	−0.256817	+	0.966460i	$0.582674\pi$
$212$	0.661349	+	1.14549i	0.0454217	+	0.0786726i
$213$		0			0
$214$		−	28.1525i		−	1.92446i
$215$	−7.64932	+	4.41634i	−0.521680	+	0.301192i
$216$		0			0
$217$	−8.01732	+	3.70634i	−0.544251	+	0.251603i
$218$	1.22808	+	2.12709i	0.0831760	+	0.144065i
$219$		0			0
$220$	0.620919	+	1.07546i	0.0418623	+	0.0725077i
$221$	9.01820	−	1.14347i	0.606630	−	0.0769180i
$222$		0			0
$223$	7.09390	−	4.09566i	0.475042	−	0.274266i	−0.243306	−	0.969950i	$-0.578232\pi$
$223$	7.09390	−	4.09566i	0.475042	−	0.274266i	0.718348	+	0.695684i	$0.244898\pi$
$224$	−0.506779	+	5.58008i	−0.0338606	+	0.372835i
$225$		0			0
$226$	27.0825	+	15.6361i	1.80150	+	1.04010i
$227$			22.8768i			1.51839i	0.650865	+	0.759193i	$0.274406\pi$
$227$			22.8768i			1.51839i	−0.650865	+	0.759193i	$0.725594\pi$
$228$		0			0
$229$	−12.3924	−	7.15476i	−0.818913	−	0.472800i	0.0311285	−	0.999515i	$-0.490090\pi$
$229$	−12.3924	−	7.15476i	−0.818913	−	0.472800i	−0.850041	+	0.526716i	$0.823423\pi$
$230$	−2.99761	+	5.19201i	−0.197657	+	0.342351i
$231$		0			0
$232$	3.15272	−	1.82023i	0.206986	−	0.119504i
$233$	−5.03403	+	8.71920i	−0.329790	+	0.571213i	−0.982470	−	0.186420i	$-0.940311\pi$
$233$	−5.03403	+	8.71920i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$234$		0			0
$235$	7.67103	+	13.2866i	0.500403	+	0.866723i
$236$		−	0.290968i		−	0.0189404i
$237$		0			0
$238$	0.930613	−	10.2469i	0.0603227	−	0.664206i
$239$			27.8817i			1.80351i	0.432242	+	0.901757i	$0.357722\pi$
$239$			27.8817i			1.80351i	−0.432242	+	0.901757i	$0.642278\pi$
$240$		0			0
$241$		−	12.1304i		−	0.781390i	−0.920520	−	0.390695i	$-0.872235\pi$
$241$		−	12.1304i		−	0.781390i	0.920520	−	0.390695i	$-0.127765\pi$
$242$	−8.03892	+	4.64127i	−0.516762	+	0.298352i
$243$		0			0
$244$	−2.29672	−	3.97804i	−0.147033	−	0.254668i
$245$	−7.82413	−	6.65383i	−0.499865	−	0.425098i
$246$		0			0
$247$	−2.74914	+	2.08870i	−0.174924	+	0.132901i
$248$	4.17307	+	7.22796i	0.264990	+	0.458976i
$249$		0			0
$250$	17.7596			1.12322
$251$	5.86315	−	10.1553i	0.370079	−	0.640995i	−0.619499	−	0.784998i	$-0.712664\pi$
$251$	5.86315	−	10.1553i	0.370079	−	0.640995i	0.989577	+	0.144003i	$0.0459974\pi$
$252$		0			0
$253$	5.12052	+	2.95634i	0.321925	+	0.185863i
$254$	5.74624	−	3.31759i	0.360551	−	0.208164i
$255$		0			0
$256$	8.79407			0.549629
$257$	22.4611			1.40108			0.700541	−	0.713612i	$-0.252942\pi$
$257$	22.4611			1.40108			0.700541	+	0.713612i	$0.252942\pi$
$258$		0			0
$259$	1.77331	−	19.5257i	0.110188	−	1.21327i
$260$	1.84963	+	0.776515i	0.114709	+	0.0481574i
$261$		0			0
$262$	19.8050	+	11.4344i	1.22355	+	0.706420i
$263$	−7.07387	+	12.2523i	−0.436194	+	0.755510i	−0.997392	−	0.0721716i	$-0.977007\pi$
$263$	−7.07387	+	12.2523i	−0.436194	+	0.755510i	0.561199	+	0.827681i	$0.310340\pi$
$264$		0			0
$265$			5.11817i			0.314406i
$266$	1.63982	+	3.54715i	0.100544	+	0.217490i
$267$		0			0
$268$	3.16875	+	1.82948i	0.193562	+	0.111753i
$269$	−12.7409			−0.776829			−0.388415	−	0.921485i	$-0.626977\pi$
$269$	−12.7409			−0.776829			−0.388415	+	0.921485i	$0.626977\pi$
$270$		0			0
$271$			3.75688i			0.228214i	0.993468	+	0.114107i	$0.0364007\pi$
$271$			3.75688i			0.228214i	−0.993468	+	0.114107i	$0.963599\pi$
$272$	−11.6344			−0.705440
$273$		0			0
$274$	−7.98752			−0.482544
$275$		−	6.35491i		−	0.383216i
$276$		0			0
$277$	4.92202			0.295736			0.147868	−	0.989007i	$-0.452759\pi$
$277$	4.92202			0.295736			0.147868	+	0.989007i	$0.452759\pi$
$278$	27.6539	+	15.9660i	1.65857	+	0.957577i
$279$		0			0
$280$	−5.59291	+	7.93160i	−0.334240	+	0.474003i
$281$		−	21.9099i		−	1.30703i	−0.756912	−	0.653516i	$-0.773293\pi$
$281$		−	21.9099i		−	1.30703i	0.756912	−	0.653516i	$-0.226707\pi$
$282$		0			0
$283$	−15.2086	+	26.3420i	−0.904055	+	1.56587i	−0.0818746	+	0.996643i	$0.526091\pi$
$283$	−15.2086	+	26.3420i	−0.904055	+	1.56587i	−0.822181	+	0.569227i	$0.807243\pi$
$284$	−0.949937	−	0.548446i	−0.0563684	−	0.0325443i
$285$		0			0
$286$	4.80510	−	11.4456i	0.284131	−	0.676791i
$287$	−9.77497	+	4.51888i	−0.576998	+	0.266741i
$288$		0			0
$289$	−10.6434			−0.626084
$290$	−3.29557			−0.193523
$291$		0			0
$292$	−4.30846	+	2.48749i	−0.252134	+	0.145569i
$293$	9.06140	+	5.23160i	0.529372	+	0.305633i	0.740761	−	0.671769i	$-0.234465\pi$
$293$	9.06140	+	5.23160i	0.529372	+	0.305633i	−0.211388	+	0.977402i	$0.567798\pi$
$294$		0			0
$295$	0.562949	−	0.975056i	0.0327761	−	0.0567699i
$296$	−18.5263			−1.07682
$297$		0			0
$298$	−13.6076	−	23.5690i	−0.788266	−	1.36532i
$299$	9.47525	−	1.20142i	0.547968	−	0.0694800i
$300$		0			0
$301$	9.17839	−	13.0163i	0.529034	−	0.750250i
$302$	−11.6856	−	20.2400i	−0.672429	−	1.16468i
$303$		0			0
$304$	3.82682	−	2.20942i	0.219483	−	0.126719i
$305$		−	17.7743i		−	1.01775i
$306$		0			0
$307$		−	11.2995i		−	0.644896i	−0.946587	−	0.322448i	$-0.895494\pi$
$307$		−	11.2995i		−	0.644896i	0.946587	−	0.322448i	$-0.104506\pi$
$308$	−1.83004	−	1.29044i	−0.104276	−	0.0735298i
$309$		0			0
$310$		−	7.55547i		−	0.429122i
$311$	3.38424	+	5.86168i	0.191903	+	0.332385i	0.945881	−	0.324514i	$-0.105201\pi$
$311$	3.38424	+	5.86168i	0.191903	+	0.332385i	−0.753978	+	0.656900i	$0.771868\pi$
$312$		0			0
$313$	1.36847	−	2.37027i	0.0773507	−	0.133975i	−0.824755	−	0.565490i	$-0.808687\pi$
$313$	1.36847	−	2.37027i	0.0773507	−	0.133975i	0.902106	+	0.431514i	$0.142021\pi$
$314$	22.3975	−	12.9312i	1.26397	−	0.729751i
$315$		0			0
$316$	0.714395	−	1.23737i	0.0401879	−	0.0696074i
$317$	13.0303	+	7.52306i	0.731856	+	0.422537i	0.819101	−	0.573650i	$-0.194473\pi$
$317$	13.0303	+	7.52306i	0.731856	+	0.422537i	−0.0872447	+	0.996187i	$0.527806\pi$
$318$		0			0
$319$			3.25020i			0.181976i
$320$	7.57665	+	4.37438i	0.423548	+	0.244535i
$321$		0			0
$322$	0.977778	−	10.7662i	0.0544894	−	0.599976i
$323$	−2.09082	+	1.20713i	−0.116336	+	0.0671668i
$324$		0			0
$325$	−6.21026	−	8.17392i	−0.344483	−	0.453408i
$326$	12.4595	+	21.5805i	0.690069	+	1.19523i
$327$		0			0
$328$	5.08793	+	8.81256i	0.280934	+	0.486592i
$329$	−22.6090	−	15.9426i	−1.24647	−	0.878941i
$330$		0			0
$331$	4.99837	−	2.88581i	0.274735	−	0.158619i	−0.356302	−	0.934371i	$-0.615963\pi$
$331$	4.99837	−	2.88581i	0.274735	−	0.158619i	0.631038	+	0.775752i	$0.282629\pi$
$332$		−	1.47602i		−	0.0810071i
$333$		0			0
$334$	−15.2386	−	26.3941i	−0.833820	−	1.44422i
$335$	7.07915	+	12.2615i	0.386775	+	0.669915i
$336$		0			0
$337$	−26.5503			−1.44628			−0.723142	−	0.690699i	$-0.757303\pi$
$337$	−26.5503			−1.44628			−0.723142	+	0.690699i	$0.757303\pi$
$338$	−5.00456	−	19.4174i	−0.272212	−	1.05617i
$339$		0			0
$340$	1.21480	+	0.701366i	0.0658819	+	0.0380369i
$341$	−7.45143			−0.403518
$342$		0			0
$343$	17.8408	+	4.97049i	0.963313	+	0.268381i
$344$	−13.0335	−	7.52491i	−0.702720	−	0.405716i
$345$		0			0
$346$	2.18275	−	1.26021i	0.117345	−	0.0677494i
$347$	11.9494			0.641478			0.320739	−	0.947168i	$-0.396069\pi$
$347$	11.9494			0.641478			0.320739	+	0.947168i	$0.396069\pi$
$348$		0			0
$349$	−30.8266	+	17.7977i	−1.65011	+	0.952692i	−0.673086	+	0.739564i	$0.735032\pi$
$349$	−30.8266	+	17.7977i	−1.65011	+	0.952692i	−0.977024	+	0.213127i	$0.931635\pi$
$350$	−10.5466	+	4.87561i	−0.563741	+	0.260612i
$351$		0			0
$352$	−2.36345	+	4.09362i	−0.125972	+	0.218191i
$353$	−28.4860	−	16.4464i	−1.51615	−	0.875352i	−0.999820	−	0.0189653i	$-0.993963\pi$
$353$	−28.4860	−	16.4464i	−1.51615	−	0.875352i	−0.516335	−	0.856387i	$-0.672704\pi$
$354$		0			0
$355$	−2.12221	−	3.67577i	−0.112635	−	0.195090i
$356$		−	3.84794i		−	0.203940i
$357$		0			0
$358$	−23.3274	−	13.4681i	−1.23289	−	0.711812i
$359$	−9.62271	−	5.55567i	−0.507867	−	0.293217i	0.224089	−	0.974569i	$-0.428059\pi$
$359$	−9.62271	−	5.55567i	−0.507867	−	0.293217i	−0.731956	+	0.681351i	$0.761393\pi$
$360$		0			0
$361$	−9.04152	+	15.6604i	−0.475870	+	0.824230i
$362$			1.30904i			0.0688016i
$363$		0			0
$364$	−3.61494	+	0.128572i	−0.189474	+	0.00673900i
$365$	−19.2506			−1.00762
$366$		0			0
$367$	4.16652	−	7.21663i	0.217491	−	0.376705i	−0.736550	−	0.676384i	$-0.763546\pi$
$367$	4.16652	−	7.21663i	0.217491	−	0.376705i	0.954040	+	0.299679i	$0.0968795\pi$
$368$	−12.2241			−0.637224
$369$		0			0
$370$	14.5243	+	8.38560i	0.755082	+	0.435947i
$371$	−3.87269	−	8.37716i	−0.201060	−	0.434921i
$372$		0			0
$373$	−6.37494	−	11.0417i	−0.330082	−	0.571718i	0.652446	−	0.757835i	$-0.273743\pi$
$373$	−6.37494	−	11.0417i	−0.330082	−	0.571718i	−0.982528	+	0.186117i	$0.940410\pi$
$374$	4.34008	−	7.51723i	0.224420	−	0.388707i
$375$		0			0
$376$	−13.0705	+	22.6388i	−0.674060	+	1.16751i
$377$	3.17621	+	4.18052i	0.163583	+	0.215308i
$378$		0			0
$379$	−27.6640	+	15.9718i	−1.42100	+	0.820416i	−0.996385	−	0.0849569i	$-0.972925\pi$
$379$	−27.6640	+	15.9718i	−1.42100	+	0.820416i	−0.424617	+	0.905373i	$0.639591\pi$
$380$	−0.532767			−0.0273304
$381$		0			0
$382$	−36.5487	+	21.1014i	−1.86999	+	1.07964i
$383$	−14.7030	+	8.48876i	−0.751286	+	0.433755i	−0.826158	−	0.563438i	$-0.809478\pi$
$383$	−14.7030	+	8.48876i	−0.751286	+	0.433755i	0.0748724	+	0.997193i	$0.476145\pi$
$384$		0			0
$385$	−3.63594	−	7.86504i	−0.185304	−	0.400840i
$386$	9.09645	−	15.7555i	0.462997	−	0.801934i
$387$		0			0
$388$	2.06391	+	1.19160i	0.104779	+	0.0604942i
$389$	−0.862649	−	1.49415i	−0.0437381	−	0.0757565i	0.843328	−	0.537400i	$-0.180593\pi$
$389$	−0.862649	−	1.49415i	−0.0437381	−	0.0757565i	−0.887066	+	0.461643i	$0.847260\pi$
$390$		0			0
$391$	6.67873			0.337758
$392$	3.15272	−	17.2140i	0.159237	−	0.869436i
$393$		0			0
$394$	6.48887	+	11.2391i	0.326905	+	0.566215i
$395$	4.78798	−	2.76434i	0.240910	−	0.139089i
$396$		0			0
$397$	2.69264	−	1.55459i	0.135140	−	0.0780229i	−0.430906	−	0.902397i	$-0.641806\pi$
$397$	2.69264	−	1.55459i	0.135140	−	0.0780229i	0.566046	+	0.824374i	$0.308473\pi$
$398$			7.81853i			0.391907i
$399$		0			0
$400$	6.56918	+	11.3782i	0.328459	+	0.568908i
$401$		−	30.5453i		−	1.52536i	−0.646777	−	0.762679i	$-0.723883\pi$
$401$		−	30.5453i		−	1.52536i	0.646777	−	0.762679i	$-0.276117\pi$
$402$		0			0
$403$	−9.58431	+	7.28182i	−0.477428	+	0.362733i
$404$	−0.494231	+	0.856034i	−0.0245889	+	0.0425893i
$405$		0			0
$406$	5.39403	−	2.49361i	0.267701	−	0.123756i
$407$	8.27014	−	14.3243i	0.409936	−	0.710029i
$408$		0			0
$409$			7.34845i			0.363357i	0.983358	+	0.181679i	$0.0581531\pi$
$409$			7.34845i			0.363357i	−0.983358	+	0.181679i	$0.941847\pi$
$410$		−	9.21185i		−	0.454941i
$411$		0			0
$412$	2.37068	−	4.10614i	0.116795	−	0.202295i
$413$	−0.183626	+	2.02188i	−0.00903564	+	0.0994903i
$414$		0			0
$415$	2.85572	−	4.94625i	0.140182	−	0.242802i
$416$	0.960479	+	7.57502i	0.0470914	+	0.371396i
$417$		0			0
$418$			3.29678i			0.161251i
$419$	−5.78350	−	10.0173i	−0.282542	−	0.489378i	0.689468	−	0.724316i	$-0.257844\pi$
$419$	−5.78350	−	10.0173i	−0.282542	−	0.489378i	−0.972010	+	0.234938i	$0.924511\pi$
$420$		0			0
$421$			7.57918i			0.369386i	0.982796	+	0.184693i	$0.0591291\pi$
$421$			7.57918i			0.369386i	−0.982796	+	0.184693i	$0.940871\pi$
$422$	27.4979	−	15.8759i	1.33858	−	0.772827i
$423$		0			0
$424$	−7.55238	+	4.36037i	−0.366776	+	0.211758i
$425$	−3.58913	−	6.21656i	−0.174098	−	0.301547i
$426$		0			0
$427$	13.4490	+	29.0921i	0.650843	+	1.40787i
$428$	−6.92081			−0.334530
$429$		0			0
$430$	6.81203	+	11.7988i	0.328505	+	0.568988i
$431$	2.14410	+	1.23790i	0.103278	+	0.0596274i	0.550749	−	0.834671i	$-0.314342\pi$
$431$	2.14410	+	1.23790i	0.103278	+	0.0596274i	−0.447471	+	0.894298i	$0.647675\pi$
$432$		0			0
$433$	0.513211	−	0.888908i	0.0246634	−	0.0427182i	−0.853430	−	0.521207i	$-0.825482\pi$
$433$	0.513211	−	0.888908i	0.0246634	−	0.0427182i	0.878094	+	0.478489i	$0.158815\pi$
$434$	5.71688	+	12.3664i	0.274419	+	0.593607i
$435$		0			0
$436$	0.522910	−	0.301902i	0.0250429	−	0.0144585i
$437$	−2.19678	+	1.26831i	−0.105086	+	0.0606717i
$438$		0			0
$439$	−9.07569			−0.433159			−0.216580	−	0.976265i	$-0.569490\pi$
$439$	−9.07569			−0.433159			−0.216580	+	0.976265i	$0.569490\pi$
$440$	−7.09067	+	4.09380i	−0.338035	+	0.195164i
$441$		0			0
$442$	−1.76376	−	13.9102i	−0.0838933	−	0.661642i
$443$	−12.9878	+	22.4955i	−0.617069	+	1.06879i	0.372949	+	0.927852i	$0.378347\pi$
$443$	−12.9878	+	22.4955i	−0.617069	+	1.06879i	−0.990018	+	0.140943i	$0.954987\pi$
$444$		0			0
$445$	7.44478	−	12.8947i	0.352916	−	0.611269i
$446$	−6.31740	−	10.9421i	−0.299138	−	0.518122i
$447$		0			0
$448$	−15.7110	−	1.42686i	−0.742274	−	0.0674128i
$449$	−27.6762	−	15.9789i	−1.30612	−	0.754089i	−0.324674	−	0.945826i	$-0.605255\pi$
$449$	−27.6762	−	15.9789i	−1.30612	−	0.754089i	−0.981446	+	0.191737i	$0.938588\pi$
$450$		0			0
$451$	−9.08502			−0.427797
$452$	3.84386	−	6.65777i	0.180800	−	0.313155i
$453$		0			0
$454$	35.2866			1.65608
$455$	−12.3627	−	6.56313i	−0.579572	−	0.307684i
$456$		0			0
$457$		−	41.1453i		−	1.92470i	−0.271817	−	0.962349i	$-0.587624\pi$
$457$		−	41.1453i		−	1.92470i	0.271817	−	0.962349i	$-0.412376\pi$
$458$	−11.0359	+	19.1148i	−0.515675	+	0.893176i
$459$		0			0
$460$	1.27637	+	0.736912i	0.0595110	+	0.0343587i
$461$	−5.19415	−	2.99884i	−0.241916	−	0.139670i	0.374141	−	0.927372i	$-0.377938\pi$
$461$	−5.19415	−	2.99884i	−0.241916	−	0.139670i	−0.616057	+	0.787702i	$0.711271\pi$
$462$		0			0
$463$			27.1770i			1.26302i	0.775367	+	0.631511i	$0.217565\pi$
$463$			27.1770i			1.26302i	−0.775367	+	0.631511i	$0.782435\pi$
$464$	−3.35979	−	5.81932i	−0.155974	−	0.270155i
$465$		0			0
$466$	13.4490	+	7.76480i	0.623014	+	0.359697i
$467$	−2.29607	+	3.97690i	−0.106249	+	0.184029i	−0.914248	−	0.405155i	$-0.867217\pi$
$467$	−2.29607	+	3.97690i	−0.106249	+	0.184029i	0.807999	+	0.589184i	$0.200551\pi$
$468$		0			0
$469$	−20.8645	−	14.7125i	−0.963433	−	0.679359i
$470$	20.4941	−	11.8323i	0.945322	−	0.545782i
$471$		0			0
$472$	1.91839			0.0883011
$473$	11.6363	−	6.71824i	0.535039	−	0.308905i
$474$		0			0
$475$	2.36109	+	1.36318i	0.108334	+	0.0625469i
$476$	−2.51902	−	0.228776i	−0.115459	−	0.0104859i
$477$		0			0
$478$	43.0064			1.96707
$479$	7.37621	+	4.25866i	0.337028	+	0.194583i	0.658957	−	0.752181i	$-0.270998\pi$
$479$	7.37621	+	4.25866i	0.337028	+	0.194583i	−0.321929	+	0.946764i	$0.604331\pi$
$480$		0			0
$481$	−3.36089	−	26.5063i	−0.153243	−	1.20859i
$482$	−18.7107			−0.852250
$483$		0			0
$484$	1.14098	+	1.97623i	0.0518627	+	0.0898288i
$485$	4.61087	+	7.98626i	0.209369	+	0.362638i
$486$		0			0
$487$			6.53675i			0.296208i	0.988972	+	0.148104i	$0.0473171\pi$
$487$			6.53675i			0.296208i	−0.988972	+	0.148104i	$0.952683\pi$
$488$	26.2278	−	15.1426i	1.18728	−	0.685474i
$489$		0			0
$490$	−10.2633	+	12.0684i	−0.463648	+	0.545195i
$491$	18.2580	+	31.6237i	0.823970	+	1.42716i	0.902704	+	0.430263i	$0.141579\pi$
$491$	18.2580	+	31.6237i	0.823970	+	1.42716i	−0.0787336	+	0.996896i	$0.525088\pi$
$492$		0			0
$493$	1.83565	+	3.17944i	0.0826734	+	0.143195i
$494$	3.22174	+	4.24044i	0.144953	+	0.190787i
$495$		0			0
$496$	13.3414	−	7.70268i	0.599048	−	0.345860i
$497$	6.25481	+	4.41054i	0.280567	+	0.197840i
$498$		0			0
$499$	−19.5923	−	11.3116i	−0.877070	−	0.506377i	−0.00737889	−	0.999973i	$-0.502349\pi$
$499$	−19.5923	−	11.3116i	−0.877070	−	0.506377i	−0.869691	+	0.493596i	$0.835682\pi$
$500$		−	4.36591i		−	0.195249i
$501$		0			0
$502$	−15.6641	−	9.04368i	−0.699124	−	0.403639i
$503$	6.05831	−	10.4933i	0.270127	−	0.467873i	−0.698767	−	0.715349i	$-0.746268\pi$
$503$	6.05831	−	10.4933i	0.270127	−	0.467873i	0.968894	+	0.247476i	$0.0796011\pi$
$504$		0			0
$505$	−3.31241	+	1.91242i	−0.147400	+	0.0851017i
$506$	4.56004	−	7.89821i	0.202718	−	0.351118i
$507$		0			0
$508$	−0.815574	−	1.41262i	−0.0361852	−	0.0626747i
$509$		−	18.6029i		−	0.824561i	−0.911057	−	0.412280i	$-0.864732\pi$
$509$		−	18.6029i		−	0.824561i	0.911057	−	0.412280i	$-0.135268\pi$
$510$		0			0
$511$	31.5085	−	14.5661i	1.39385	−	0.644366i
$512$			13.3008i			0.587816i
$513$		0			0
$514$		−	34.6453i		−	1.52814i
$515$	15.8887	−	9.17333i	0.700139	−	0.404225i
$516$		0			0
$517$	−11.6694	−	20.2119i	−0.513218	−	0.888919i
$518$	−30.1177	−	2.73526i	−1.32329	−	0.120181i
$519$		0			0
$520$	−5.11967	+	12.1949i	−0.224512	+	0.534781i
$521$	−2.14960	−	3.72321i	−0.0941756	−	0.163117i	0.815089	−	0.579336i	$-0.196688\pi$
$521$	−2.14960	−	3.72321i	−0.0941756	−	0.163117i	−0.909264	+	0.416219i	$0.863355\pi$
$522$		0			0
$523$	6.23463			0.272622			0.136311	−	0.990666i	$-0.456475\pi$
$523$	6.23463			0.272622			0.136311	+	0.990666i	$0.456475\pi$
$524$	2.81095	−	4.86872i	0.122797	−	0.212691i
$525$		0			0
$526$	18.8987	+	10.9112i	0.824023	+	0.475750i
$527$	−7.28921	+	4.20843i	−0.317523	+	0.183322i
$528$		0			0
$529$	−15.9828			−0.694904
$530$	7.89458			0.342918
$531$		0			0
$532$	0.872008	−	0.403121i	0.0378063	−	0.0174775i
$533$	−11.6855	+	8.87822i	−0.506154	+	0.384558i
$534$		0			0
$535$	−23.1922	−	13.3900i	−1.00268	−	0.578900i
$536$	−12.0620	+	20.8920i	−0.521000	+	0.902398i
$537$		0			0
$538$			19.6524i			0.847276i
$539$	11.9022	+	10.1220i	0.512666	+	0.435984i
$540$		0			0
$541$	−4.56161	−	2.63365i	−0.196119	−	0.113229i	0.398725	−	0.917071i	$-0.369453\pi$
$541$	−4.56161	−	2.63365i	−0.196119	−	0.113229i	−0.594844	+	0.803841i	$0.702786\pi$
$542$	5.79485			0.248910
$543$		0			0
$544$			5.33933i			0.228922i
$545$	2.33642			0.100081
$546$		0			0
$547$	3.35409			0.143411			0.0717053	−	0.997426i	$-0.477156\pi$
$547$	3.35409			0.143411			0.0717053	+	0.997426i	$0.477156\pi$
$548$			1.96360i			0.0838808i
$549$		0			0
$550$	−9.80221			−0.417968
$551$	−1.20757	−	0.697192i	−0.0514443	−	0.0297014i
$552$		0			0
$553$	−5.74508	+	8.14739i	−0.244306	+	0.346462i
$554$		−	7.59203i		−	0.322555i
$555$		0			0
$556$	3.92497	−	6.79825i	0.166456	−	0.288310i
$557$	6.93267	+	4.00258i	0.293747	+	0.169595i	0.639630	−	0.768683i	$-0.279087\pi$
$557$	6.93267	+	4.00258i	0.293747	+	0.169595i	−0.345884	+	0.938277i	$0.612421\pi$
$558$		0			0
$559$	8.40176	−	20.0127i	0.355357	−	0.846447i
$560$	14.6402	+	10.3234i	0.618661	+	0.436245i
$561$		0			0
$562$	−33.7951			−1.42556
$563$	34.6065			1.45849			0.729246	−	0.684252i	$-0.239871\pi$
$563$	34.6065			1.45849			0.729246	+	0.684252i	$0.239871\pi$
$564$		0			0
$565$	25.7622	−	14.8738i	1.08382	−	0.625745i
$566$	40.6315	+	23.4586i	1.70787	+	0.986040i
$567$		0			0
$568$	3.61598	−	6.26306i	0.151723	−	0.262792i
$569$	4.76640			0.199818			0.0999089	−	0.994997i	$-0.468145\pi$
$569$	4.76640			0.199818			0.0999089	+	0.994997i	$0.468145\pi$
$570$		0			0
$571$	17.3388	+	30.0317i	0.725607	+	1.25679i	0.958724	+	0.284339i	$0.0917741\pi$
$571$	17.3388	+	30.0317i	0.725607	+	1.25679i	−0.233117	+	0.972449i	$0.574893\pi$
$572$	−2.81370	−	1.18125i	−0.117647	−	0.0493906i
$573$		0			0
$574$	6.97020	+	15.0775i	0.290930	+	0.629323i
$575$	−3.77103	−	6.53162i	−0.157263	−	0.272387i
$576$		0			0
$577$	33.2462	−	19.1947i	1.38406	−	0.799085i	0.391419	−	0.920213i	$-0.371984\pi$
$577$	33.2462	−	19.1947i	1.38406	−	0.799085i	0.992637	+	0.121128i	$0.0386510\pi$
$578$			16.4171i			0.682861i
$579$		0			0
$580$			0.810161i			0.0336401i
$581$	−0.931495	+	10.2566i	−0.0386449	+	0.425514i
$582$		0			0
$583$		−	7.78588i		−	0.322458i
$584$	−16.4004	−	28.4063i	−0.678652	−	1.17546i
$585$		0			0
$586$	8.06954	−	13.9769i	0.333350	−	0.577379i
$587$	−13.2140	+	7.62912i	−0.545401	+	0.314887i	−0.747265	−	0.664526i	$-0.768633\pi$
$587$	−13.2140	+	7.62912i	−0.545401	+	0.314887i	0.201864	+	0.979414i	$0.435300\pi$
$588$		0			0
$589$	1.59839	−	2.76849i	0.0658605	−	0.114074i
$590$	−1.50399	−	0.868327i	−0.0619181	−	0.0357484i
$591$		0			0
$592$			34.1960i			1.40545i
$593$	−36.2229	−	20.9133i	−1.48750	−	0.858807i	−0.487599	−	0.873068i	$-0.662127\pi$
$593$	−36.2229	−	20.9133i	−1.48750	−	0.858807i	−0.999898	+	0.0142607i	$0.995461\pi$
$594$		0			0
$595$	−7.99880	−	5.64030i	−0.327919	−	0.231230i
$596$	−5.79404	+	3.34519i	−0.237333	+	0.137024i
$597$		0			0
$598$	−1.85315	−	14.6152i	−0.0757808	−	0.597660i
$599$	21.7048	+	37.5937i	0.886832	+	1.53604i	0.843599	+	0.536973i	$0.180432\pi$
$599$	21.7048	+	37.5937i	0.886832	+	1.53604i	0.0432328	+	0.999065i	$0.486234\pi$
$600$		0			0
$601$	−12.1988	−	21.1289i	−0.497599	−	0.861866i	0.502398	−	0.864637i	$-0.332451\pi$
$601$	−12.1988	−	21.1289i	−0.497599	−	0.861866i	−0.999996	+	0.00277068i	$0.999118\pi$
$602$	−20.0772	−	14.1573i	−0.818286	−	0.577009i
$603$		0			0
$604$	−4.97566	+	2.87270i	−0.202457	+	0.116889i
$605$			8.83001i			0.358991i
$606$		0			0
$607$	−0.234017	−	0.405330i	−0.00949847	−	0.0164518i	0.861237	−	0.508203i	$-0.169690\pi$
$607$	−0.234017	−	0.405330i	−0.00949847	−	0.0164518i	−0.870736	+	0.491752i	$0.836357\pi$
$608$	−1.01396	−	1.75623i	−0.0411214	−	0.0712243i
$609$		0			0
$610$	−27.4162			−1.11005
$611$	−34.7614	−	14.5936i	−1.40630	−	0.590393i
$612$		0			0
$613$	29.7884	+	17.1983i	1.20314	+	0.694635i	0.961253	−	0.275669i	$-0.0888994\pi$
$613$	29.7884	+	17.1983i	1.20314	+	0.694635i	0.241890	+	0.970304i	$0.422233\pi$
$614$	−17.4290			−0.703378
$615$		0			0
$616$	8.50807	−	12.0657i	0.342800	−	0.486142i
$617$	−8.47087	−	4.89066i	−0.341024	−	0.196890i	0.319701	−	0.947519i	$-0.396418\pi$
$617$	−8.47087	−	4.89066i	−0.341024	−	0.196890i	−0.660725	+	0.750628i	$0.729751\pi$
$618$		0			0
$619$	18.7382	−	10.8185i	0.753152	−	0.434833i	−0.0736794	−	0.997282i	$-0.523474\pi$
$619$	18.7382	−	10.8185i	0.753152	−	0.434833i	0.826832	+	0.562449i	$0.190141\pi$
$620$	−1.85738			−0.0745943
$621$		0			0
$622$	9.04142	−	5.22006i	0.362528	−	0.209305i
$623$	−2.42838	+	26.7386i	−0.0972910	+	1.07126i
$624$		0			0
$625$	1.32907	−	2.30202i	0.0531630	−	0.0920810i
$626$	−3.65605	−	2.11082i	−0.146125	−	0.0843653i
$627$		0			0
$628$	−3.17892	−	5.50606i	−0.126853	−	0.219716i
$629$		−	18.6833i		−	0.744951i
$630$		0			0
$631$	−12.0447	−	6.95404i	−0.479494	−	0.276836i	0.240712	−	0.970597i	$-0.422619\pi$
$631$	−12.0447	−	6.95404i	−0.479494	−	0.276836i	−0.720206	+	0.693761i	$0.755953\pi$
$632$	8.15814	+	4.71010i	0.324513	+	0.187358i
$633$		0			0
$634$	11.6040	−	20.0988i	0.460855	−	0.798225i
$635$		−	6.31171i		−	0.250472i
$636$		0			0
$637$	25.2007	+	1.38792i	0.998487	+	0.0549912i
$638$	5.01330			0.198479
$639$		0			0
$640$	9.85462	−	17.0687i	0.389538	−	0.674700i
$641$	23.6700			0.934908			0.467454	−	0.884017i	$-0.345171\pi$
$641$	23.6700			0.934908			0.467454	+	0.884017i	$0.345171\pi$
$642$		0			0
$643$	19.6315	+	11.3342i	0.774190	+	0.446979i	0.834367	−	0.551209i	$-0.185833\pi$
$643$	19.6315	+	11.3342i	0.774190	+	0.446979i	−0.0601776	+	0.998188i	$0.519167\pi$
$644$	−2.64669	−	0.240370i	−0.104294	−	0.00947191i
$645$		0			0
$646$	1.86196	+	3.22501i	0.0732578	+	0.126886i
$647$	−11.7855	+	20.4131i	−0.463336	+	0.802521i	−0.999125	−	0.0418310i	$-0.986681\pi$
$647$	−11.7855	+	20.4131i	−0.463336	+	0.802521i	0.535789	+	0.844352i	$0.320014\pi$
$648$		0			0
$649$	−0.856371	+	1.48328i	−0.0336155	+	0.0582237i
$650$	−12.6080	+	9.57909i	−0.494525	+	0.375723i
$651$		0			0
$652$	5.30521	−	3.06296i	0.207768	−	0.119955i
$653$	−8.91076			−0.348705			−0.174353	−	0.984683i	$-0.555783\pi$
$653$	−8.91076			−0.348705			−0.174353	+	0.984683i	$0.555783\pi$
$654$		0			0
$655$	18.8394	−	10.8770i	0.736118	−	0.424998i
$656$	16.2663	−	9.39134i	0.635092	−	0.366670i
$657$		0			0
$658$	−24.5908	+	34.8734i	−0.958648	+	1.35951i
$659$	4.92457	−	8.52960i	0.191834	−	0.332266i	−0.754024	−	0.656847i	$-0.771890\pi$
$659$	4.92457	−	8.52960i	0.191834	−	0.332266i	0.945858	+	0.324581i	$0.105223\pi$
$660$		0			0
$661$	−0.385266	−	0.222433i	−0.0149851	−	0.00865166i	0.492489	−	0.870319i	$-0.336087\pi$
$661$	−0.385266	−	0.222433i	−0.0149851	−	0.00865166i	−0.507474	+	0.861667i	$0.669421\pi$
$662$	−4.45125	−	7.70980i	−0.173003	−	0.299650i
$663$		0			0
$664$	9.73159			0.377659
$665$	3.70210	+	0.336222i	0.143561	+	0.0130381i
$666$		0			0
$667$	1.92868	+	3.34057i	0.0746788	+	0.129348i
$668$	−6.48853	+	3.74616i	−0.251049	+	0.144943i
$669$		0			0
$670$	18.9128	−	10.9193i	0.730666	−	0.421850i
$671$			27.0387i			1.04382i
$672$		0			0
$673$	2.77793	+	4.81152i	0.107081	+	0.185470i	0.914587	−	0.404390i	$-0.132516\pi$
$673$	2.77793	+	4.81152i	0.107081	+	0.185470i	−0.807505	+	0.589860i	$0.799183\pi$
$674$			40.9528i			1.57744i
$675$		0			0
$676$	−4.77345	+	1.23029i	−0.183594	+	0.0473187i
$677$	−4.65253	+	8.05842i	−0.178811	+	0.309710i	−0.941474	−	0.337087i	$-0.890558\pi$
$677$	−4.65253	+	8.05842i	−0.178811	+	0.309710i	0.762662	+	0.646797i	$0.223892\pi$
$678$		0			0
$679$	−13.5897	−	9.58269i	−0.521525	−	0.367750i
$680$	−4.62420	+	8.00935i	−0.177330	+	0.307145i
$681$		0			0
$682$			11.4936i			0.440111i
$683$		−	21.8103i		−	0.834549i	−0.908780	−	0.417275i	$-0.862985\pi$
$683$		−	21.8103i		−	0.834549i	0.908780	−	0.417275i	$-0.137015\pi$
$684$		0			0
$685$	−3.79906	+	6.58017i	−0.145155	+	0.251415i
$686$	7.66680	−	27.5188i	0.292720	−	1.05067i
$687$		0			0
$688$	−13.8895	+	24.0574i	−0.529533	+	0.917178i
$689$	−7.60865	−	10.0145i	−0.289866	−	0.381521i
$690$		0			0
$691$		−	8.12516i		−	0.309096i	−0.987985	−	0.154548i	$-0.950608\pi$
$691$		−	8.12516i		−	0.309096i	0.987985	−	0.154548i	$-0.0493921\pi$
$692$	−0.309802	−	0.536593i	−0.0117769	−	0.0203982i
$693$		0			0
$694$		−	18.4315i		−	0.699650i
$695$	26.3057	−	15.1876i	0.997834	−	0.576100i
$696$		0			0
$697$	−8.88723	+	5.13104i	−0.336628	+	0.194352i
$698$	27.4523	+	47.5489i	1.03909	+	1.79975i
$699$		0			0
$700$	1.19859	+	2.59271i	0.0453023	+	0.0979952i
$701$	28.5599			1.07869			0.539347	−	0.842084i	$-0.318671\pi$
$701$	28.5599			1.07869			0.539347	+	0.842084i	$0.318671\pi$
$702$		0			0
$703$	3.54802	+	6.14535i	0.133816	+	0.231776i
$704$	−11.5258	−	6.65441i	−0.434394	−	0.250798i
$705$		0			0
$706$	−25.3679	+	43.9385i	−0.954734	+	1.65365i
$707$	3.97455	−	5.63651i	0.149478	−	0.211983i
$708$		0			0
$709$	30.8663	−	17.8207i	1.15921	−	0.669269i	0.208094	−	0.978109i	$-0.433274\pi$
$709$	30.8663	−	17.8207i	1.15921	−	0.669269i	0.951114	+	0.308840i	$0.0999408\pi$
$710$	−5.66973	+	3.27342i	−0.212781	+	0.122849i
$711$		0			0
$712$	25.3700			0.950780
$713$	−7.65864	+	4.42172i	−0.286818	+	0.165595i
$714$		0			0
$715$	−7.14351	−	9.40226i	−0.267152	−	0.351625i
$716$	−3.31091	+	5.73466i	−0.123734	+	0.214314i
$717$		0			0
$718$	−8.56941	+	14.8427i	−0.319808	+	0.553923i
$719$	7.54188	+	13.0629i	0.281265	+	0.487165i	0.971696	−	0.236233i	$-0.0759128\pi$
$719$	7.54188	+	13.0629i	0.281265	+	0.487165i	−0.690432	+	0.723397i	$0.742579\pi$
$720$		0			0
$721$	−19.0648	+	27.0367i	−0.710009	+	1.00690i
$722$	24.1555	+	13.9462i	0.898976	+	0.519024i
$723$		0			0
$724$	0.321805			0.0119598
$725$	2.07294	−	3.59043i	0.0769870	−	0.133345i
$726$		0			0
$727$	40.1445			1.48888			0.744439	−	0.667690i	$-0.232717\pi$
$727$	40.1445			1.48888			0.744439	+	0.667690i	$0.232717\pi$
$728$	−0.847692	−	23.8338i	−0.0314176	−	0.883339i
$729$		0			0
$730$			29.6934i			1.09900i
$731$	7.58867	−	13.1440i	0.280677	−	0.486147i
$732$		0			0
$733$	24.3833	+	14.0777i	0.900619	+	0.519973i	0.877401	−	0.479758i	$-0.159275\pi$
$733$	24.3833	+	14.0777i	0.900619	+	0.519973i	0.0232181	+	0.999730i	$0.492609\pi$
$734$	−11.1314	−	6.42670i	−0.410866	−	0.237214i
$735$		0			0
$736$			5.60993i			0.206785i
$737$	−10.7690	−	18.6524i	−0.396680	−	0.687070i
$738$		0			0
$739$	20.2757	+	11.7062i	0.745855	+	0.430619i	0.824194	−	0.566307i	$-0.191628\pi$
$739$	20.2757	+	11.7062i	0.745855	+	0.430619i	−0.0783395	+	0.996927i	$0.524962\pi$
$740$	2.06146	−	3.57055i	0.0757808	−	0.131256i
$741$		0			0
$742$	−12.9215	+	5.97347i	−0.474362	+	0.219293i
$743$	−27.8733	+	16.0926i	−1.02257	+	0.590382i	−0.914848	−	0.403799i	$-0.867689\pi$
$743$	−27.8733	+	16.0926i	−1.02257	+	0.590382i	−0.107723	+	0.994181i	$0.534356\pi$
$744$		0			0
$745$	−25.8884			−0.948476
$746$	−17.0314	+	9.83310i	−0.623565	+	0.360015i
$747$		0			0
$748$	−1.84798	−	1.06693i	−0.0675690	−	0.0390110i
$749$	48.0914	+	4.36763i	1.75722	+	0.159590i
$750$		0			0
$751$	17.2533			0.629583			0.314791	−	0.949161i	$-0.398065\pi$
$751$	17.2533			0.629583			0.314791	+	0.949161i	$0.398065\pi$
$752$	41.7868	+	24.1256i	1.52381	+	0.879771i
$753$		0			0
$754$	6.44830	−	4.89919i	0.234833	−	0.178418i
$755$	−22.2318			−0.809097
$756$		0			0
$757$	0.137120	+	0.237499i	0.00498371	+	0.00863204i	0.868507	−	0.495678i	$-0.165080\pi$
$757$	0.137120	+	0.237499i	0.00498371	+	0.00863204i	−0.863523	+	0.504310i	$0.831747\pi$
$758$	24.6359	+	42.6706i	0.894816	+	1.54987i
$759$		0			0
$760$		−	3.51261i		−	0.127416i
$761$	0.726332	−	0.419348i	0.0263295	−	0.0152013i	−0.486777	−	0.873526i	$-0.661828\pi$
$761$	0.726332	−	0.419348i	0.0263295	−	0.0152013i	0.513107	+	0.858325i	$0.328494\pi$
$762$		0			0
$763$	−3.82413	+	1.76786i	−0.138443	+	0.0640009i
$764$	5.18742	+	8.98488i	0.187674	+	0.325062i
$765$		0			0
$766$	13.0936	+	22.6787i	0.473090	+	0.819416i
$767$	0.348019	+	2.74472i	0.0125662	+	0.0991062i
$768$		0			0
$769$	−19.0211	+	10.9818i	−0.685918	+	0.396015i	−0.802081	−	0.597215i	$-0.796274\pi$
$769$	−19.0211	+	10.9818i	−0.685918	+	0.396015i	0.116163	+	0.993230i	$0.462941\pi$
$770$	−12.1315	+	5.60829i	−0.437190	+	0.202109i
$771$		0			0
$772$	−3.87323	−	2.23621i	−0.139401	−	0.0804829i
$773$		−	53.2366i		−	1.91479i	−0.288787	−	0.957394i	$-0.593252\pi$
$773$		−	53.2366i		−	1.91479i	0.288787	−	0.957394i	$-0.406748\pi$
$774$		0			0
$775$	8.23146	+	4.75244i	0.295683	+	0.170713i
$776$	−7.85636	+	13.6076i	−0.282027	+	0.488485i
$777$		0			0
$778$	−2.30467	+	1.33060i	−0.0826265	+	0.0477044i
$779$	1.94881	−	3.37543i	0.0698232	−	0.120937i
$780$		0			0
$781$	3.22835	+	5.59167i	0.115519	+	0.200086i
$782$		−	10.3017i		−	0.368387i
$783$		0			0
$784$	−31.7736	−	5.81932i	−1.13477	−	0.207833i
$785$		−	24.6016i		−	0.878069i
$786$		0			0
$787$		−	18.3408i		−	0.653780i	−0.945062	−	0.326890i	$-0.893999\pi$
$787$		−	18.3408i		−	0.653780i	0.945062	−	0.326890i	$-0.106001\pi$
$788$	2.76293	−	1.59518i	0.0984254	−	0.0568259i
$789$		0			0
$790$	−4.26389	−	7.38528i	−0.151702	−	0.262756i
$791$	−30.9119	+	43.8378i	−1.09910	+	1.55869i
$792$		0			0
$793$	26.4232	+	34.7781i	0.938316	+	1.23501i
$794$	−2.39790	−	4.15329i	−0.0850984	−	0.147395i
$795$		0			0
$796$	1.92205			0.0681254
$797$	14.8967	−	25.8018i	0.527667	−	0.913945i	−0.471813	−	0.881698i	$-0.656400\pi$
$797$	14.8967	−	25.8018i	0.527667	−	0.913945i	0.999480	−	0.0322469i	$-0.0102663\pi$
$798$		0			0
$799$	−22.8306	−	13.1813i	−0.807688	−	0.466319i
$800$	5.22172	−	3.01476i	0.184616	−	0.106588i
$801$		0			0
$802$	−47.1149			−1.66369
$803$	29.2845			1.03343
$804$		0			0
$805$	−8.40419	−	5.92616i	−0.296209	−	0.208870i
$806$	11.2319	+	14.7834i	0.395628	+	0.520724i
$807$		0			0
$808$	−5.64395	−	3.25853i	−0.198553	−	0.114635i
$809$	−13.0496	+	22.6026i	−0.458799	+	0.794663i	−0.998898	−	0.0469383i	$-0.985054\pi$
$809$	−13.0496	+	22.6026i	−0.458799	+	0.794663i	0.540099	+	0.841602i	$0.318387\pi$
$810$		0			0
$811$		−	29.8679i		−	1.04880i	−0.851471	−	0.524402i	$-0.824289\pi$
$811$		−	29.8679i		−	1.04880i	0.851471	−	0.524402i	$-0.175711\pi$
$812$	−0.613013	−	1.32603i	−0.0215125	−	0.0465346i
$813$		0			0
$814$	−22.0947	−	12.7564i	−0.774419	−	0.447111i
$815$	23.7042			0.830322
$816$		0			0
$817$			5.76446i			0.201673i
$818$	11.3347			0.396308
$819$		0			0
$820$	−2.26458			−0.0790825
$821$			46.8412i			1.63477i	0.576093	+	0.817384i	$0.304577\pi$
$821$			46.8412i			1.63477i	−0.576093	+	0.817384i	$0.695423\pi$
$822$		0			0
$823$	17.8744			0.623062			0.311531	−	0.950236i	$-0.399158\pi$
$823$	17.8744			0.623062			0.311531	+	0.950236i	$0.399158\pi$
$824$	27.0724	+	15.6302i	0.943111	+	0.544505i
$825$		0			0
$826$	3.11867	+	0.283236i	0.108513	+	0.00985503i
$827$		−	23.3454i		−	0.811799i	−0.913918	−	0.405899i	$-0.866958\pi$
$827$		−	23.3454i		−	0.811799i	0.913918	−	0.405899i	$-0.133042\pi$
$828$		0			0
$829$	−27.8730	+	48.2775i	−0.968071	+	1.67675i	−0.266943	+	0.963712i	$0.586014\pi$
$829$	−27.8730	+	48.2775i	−0.968071	+	1.67675i	−0.701128	+	0.713036i	$0.747320\pi$
$830$	−7.62940	−	4.40484i	−0.264820	−	0.152894i
$831$		0			0
$832$	−21.3278	+	2.70428i	−0.739409	+	0.0937539i
$833$	17.3598	+	3.17944i	0.601482	+	0.110161i
$834$		0			0
$835$	−28.9914			−1.00329
$836$	0.810458			0.0280303
$837$		0			0
$838$	−15.4513	+	8.92083i	−0.533757	+	0.308165i
$839$	16.1000	+	9.29535i	0.555834	+	0.320911i	0.751472	−	0.659765i	$-0.229344\pi$
$839$	16.1000	+	9.29535i	0.555834	+	0.320911i	−0.195638	+	0.980676i	$0.562678\pi$
$840$		0			0
$841$	13.4398	−	23.2784i	0.463442	−	0.802704i
$842$	11.6906			0.402884
$843$		0			0
$844$	−3.90282	−	6.75989i	−0.134341	−	0.232685i
$845$	−18.3765	−	5.11263i	−0.632170	−	0.175880i
$846$		0			0
$847$	−6.68127	−	14.4525i	−0.229571	−	0.496595i
$848$	8.04840	+	13.9402i	0.276383	+	0.478710i
$849$		0			0
$850$	−9.58880	+	5.53610i	−0.328893	+	0.189887i
$851$		−	19.6302i		−	0.672913i
$852$		0			0
$853$			31.4429i			1.07659i	0.842758	+	0.538293i	$0.180931\pi$
$853$			31.4429i			1.07659i	−0.842758	+	0.538293i	$0.819069\pi$
$854$	44.8734	−	20.7446i	1.53554	−	0.709865i
$855$		0			0
$856$		−	45.6298i		−	1.55960i
$857$	−28.3523	−	49.1076i	−0.968495	−	1.67748i	−0.699916	−	0.714225i	$-0.746779\pi$
$857$	−28.3523	−	49.1076i	−0.968495	−	1.67748i	−0.268579	−	0.963258i	$-0.586554\pi$
$858$		0			0
$859$	−0.915541	+	1.58576i	−0.0312379	+	0.0541056i	−0.881222	−	0.472703i	$-0.843278\pi$
$859$	−0.915541	+	1.58576i	−0.0312379	+	0.0541056i	0.849984	+	0.526809i	$0.176612\pi$
$860$	2.90053	−	1.67462i	0.0989074	−	0.0571042i
$861$		0			0
$862$	1.90941	−	3.30719i	0.0650347	−	0.112643i
$863$	−19.2517	−	11.1150i	−0.655336	−	0.378358i	0.135162	−	0.990824i	$-0.456845\pi$
$863$	−19.2517	−	11.1150i	−0.655336	−	0.378358i	−0.790497	+	0.612465i	$0.790178\pi$
$864$		0			0
$865$		−	2.39755i		−	0.0815192i
$866$	−1.37111	−	0.791609i	−0.0465921	−	0.0269000i
$867$		0			0
$868$	3.04008	−	1.40540i	0.103187	−	0.0477024i
$869$	−7.28359	+	4.20518i	−0.247079	+	0.142651i
$870$		0			0
$871$	−32.0793	−	13.4676i	−1.08697	−	0.456331i
$872$	1.99048	+	3.44762i	0.0674063	+	0.116751i
$873$		0			0
$874$	1.95633	+	3.38845i	0.0661737	+	0.114616i
$875$	−2.75526	+	30.3379i	−0.0931449	+	1.02561i
$876$		0			0
$877$	−19.4370	+	11.2220i	−0.656341	+	0.378939i	−0.790881	−	0.611969i	$-0.790378\pi$
$877$	−19.4370	+	11.2220i	−0.656341	+	0.378939i	0.134540	+	0.990908i	$0.457044\pi$
$878$			13.9989i			0.472440i
$879$		0			0
$880$	7.55637	+	13.0880i	0.254725	+	0.441197i
$881$	−16.2431	−	28.1338i	−0.547242	−	0.947852i	−0.998462	−	0.0554388i	$-0.982344\pi$
$881$	−16.2431	−	28.1338i	−0.547242	−	0.947852i	0.451220	−	0.892413i	$-0.350989\pi$
$882$		0			0
$883$	16.1468			0.543383			0.271691	−	0.962384i	$-0.412417\pi$
$883$	16.1468			0.543383			0.271691	+	0.962384i	$0.412417\pi$
$884$	−3.41959	+	0.433590i	−0.115013	+	0.0145832i
$885$		0			0
$886$	34.6985	+	20.0332i	1.16572	+	0.673028i
$887$	−11.9870			−0.402484			−0.201242	−	0.979542i	$-0.564498\pi$
$887$	−11.9870			−0.402484			−0.201242	+	0.979542i	$0.564498\pi$
$888$		0			0
$889$	4.77579	+	10.3307i	0.160175	+	0.346480i
$890$	−19.8896	−	11.4833i	−0.666702	−	0.384921i
$891$		0			0
$892$	−2.68992	+	1.55303i	−0.0900653	+	0.0519992i
$893$	10.0127			0.335061
$894$		0			0
$895$	−22.1902	+	12.8115i	−0.741737	+	0.428242i
$896$	−3.21444	+	35.3938i	−0.107387	+	1.18242i
$897$		0			0
$898$	−24.6468	+	42.6895i	−0.822474	+	1.42457i
$899$	−4.20995	−	2.43062i	−0.140410	−	0.0810656i
$900$		0			0
$901$	−4.39731	−	7.61637i	−0.146496	−	0.253738i
$902$			14.0133i			0.466592i
$903$		0			0
$904$	43.8956	+	25.3431i	1.45995	+	0.842900i
$905$	1.07839	+	0.622611i	0.0358470	+	0.0206963i
$906$		0			0
$907$	8.39927	−	14.5480i	0.278893	−	0.483057i	−0.692217	−	0.721690i	$-0.743366\pi$
$907$	8.39927	−	14.5480i	0.278893	−	0.483057i	0.971110	+	0.238632i	$0.0766991\pi$
$908$		−	8.67462i		−	0.287877i
$909$		0			0
$910$	−10.1234	+	19.0690i	−0.335587	+	0.632130i
$911$	−18.7103			−0.619899			−0.309949	−	0.950753i	$-0.600312\pi$
$911$	−18.7103			−0.619899			−0.309949	+	0.950753i	$0.600312\pi$
$912$		0			0
$913$	−4.34419	+	7.52435i	−0.143772	+	0.249020i
$914$	−63.4651			−2.09924
$915$		0			0
$916$	4.69905	+	2.71300i	0.155261	+	0.0896400i
$917$	−22.6054	+	32.0578i	−0.746495	+	1.05864i
$918$		0			0
$919$	6.74748	+	11.6870i	0.222579	+	0.385518i	0.955590	−	0.294698i	$-0.0952192\pi$
$919$	6.74748	+	11.6870i	0.222579	+	0.385518i	−0.733011	+	0.680216i	$0.761886\pi$
$920$	−4.85856	+	8.41528i	−0.160182	+	0.277443i
$921$		0			0
$922$	−4.62560	+	8.01177i	−0.152336	+	0.263854i
$923$	9.61681	+	4.03734i	0.316541	+	0.132891i
$924$		0			0
$925$	−18.2718	+	10.5492i	−0.600771	+	0.346856i
$926$	41.9195			1.37756
$927$		0			0
$928$	−2.67063	+	1.54189i	−0.0876678	+	0.0506150i
$929$	20.1751	−	11.6481i	0.661924	−	0.382162i	−0.131086	−	0.991371i	$-0.541846\pi$
$929$	20.1751	−	11.6481i	0.661924	−	0.382162i	0.793010	+	0.609209i	$0.208513\pi$
$930$		0			0
$931$	−6.31382	+	2.25090i	−0.206927	+	0.0737703i
$932$	1.90884	−	3.30622i	0.0625263	−	0.108299i
$933$		0			0
$934$	6.13422	+	3.54160i	0.200718	+	0.115885i
$935$	−4.12849	−	7.15075i	−0.135016	−	0.233855i
$936$		0			0
$937$	−46.4351			−1.51697			−0.758484	−	0.651692i	$-0.774060\pi$
$937$	−46.4351			−1.51697			−0.758484	+	0.651692i	$0.774060\pi$
$938$	−22.6934	+	32.1827i	−0.740966	+	1.05080i
$939$		0			0
$940$	−2.90876	−	5.03813i	−0.0948734	−	0.164326i
$941$	25.5347	−	14.7424i	0.832406	−	0.480590i	−0.0222695	−	0.999752i	$-0.507089\pi$
$941$	25.5347	−	14.7424i	0.832406	−	0.480590i	0.854676	+	0.519162i	$0.173756\pi$
$942$		0			0
$943$	−9.33764	+	5.39109i	−0.304075	+	0.175558i
$944$		−	3.54098i		−	0.115249i
$945$		0			0
$946$	−10.3626	−	17.9486i	−0.336918	−	0.583559i
$947$			39.9526i			1.29828i	0.760667	+	0.649142i	$0.224872\pi$
$947$			39.9526i			1.29828i	−0.760667	+	0.649142i	$0.775128\pi$
$948$		0			0
$949$	37.6668	−	28.6179i	1.22272	−	0.928977i
$950$	2.10265	−	3.64189i	0.0682189	−	0.118159i
$951$		0			0
$952$	1.50835	−	16.6082i	0.0488859	−	0.538276i
$953$	−1.93532	+	3.35208i	−0.0626913	+	0.108584i	−0.895668	−	0.444724i	$-0.853302\pi$
$953$	−1.93532	+	3.35208i	−0.0626913	+	0.108584i	0.832976	+	0.553309i	$0.186635\pi$
$954$		0			0
$955$			40.1454i			1.29907i
$956$		−	10.5724i		−	0.341936i
$957$		0			0
$958$	6.56882	−	11.3775i	0.212229	−	0.367591i
$959$	1.23920	−	13.6447i	0.0400158	−	0.440609i
$960$		0			0
$961$	−9.92754	+	17.1950i	−0.320243	+	0.554678i
$962$	−40.8850	+	5.18404i	−1.31819	+	0.167140i
$963$		0			0
$964$			4.59972i			0.148147i
$965$	−8.65298	−	14.9874i	−0.278549	−	0.482462i
$966$		0			0
$967$		−	29.8554i		−	0.960086i	−0.877245	−	0.480043i	$-0.840621\pi$
$967$		−	29.8554i		−	0.960086i	0.877245	−	0.480043i	$-0.159379\pi$
$968$	−13.0296	+	7.52263i	−0.418787	+	0.241787i
$969$		0			0
$970$	12.3185	−	7.11209i	0.395523	−	0.228356i
$971$	−23.2584	−	40.2847i	−0.746397	−	1.29280i	−0.949539	−	0.313649i	$-0.898449\pi$
$971$	−23.2584	−	40.2847i	−0.746397	−	1.29280i	0.203142	−	0.979149i	$-0.434885\pi$
$972$		0			0
$973$	−31.5642	+	44.7627i	−1.01190	+	1.43503i
$974$	10.0827			0.323070
$975$		0			0
$976$	−27.9504	−	48.4114i	−0.894669	−	1.54961i
$977$	−2.04067	−	1.17818i	−0.0652867	−	0.0376933i	0.467001	−	0.884257i	$-0.345334\pi$
$977$	−2.04067	−	1.17818i	−0.0652867	−	0.0376933i	−0.532288	+	0.846563i	$0.678668\pi$
$978$		0			0
$979$	−11.3252	+	19.6158i	−0.361954	+	0.626923i
$980$	2.96682	+	2.52305i	0.0947715	+	0.0805960i
$981$		0			0
$982$	48.7784	−	28.1622i	1.55658	−	0.898692i
$983$	−24.9474	+	14.4034i	−0.795697	+	0.459396i	−0.841964	−	0.539533i	$-0.818601\pi$
$983$	−24.9474	+	14.4034i	−0.795697	+	0.459396i	0.0462672	+	0.998929i	$0.485267\pi$
$984$		0			0
$985$	12.3451			0.393346
$986$	4.90416	−	2.83142i	0.156180	−	0.0901707i
$987$		0			0
$988$	1.04244	−	0.792010i	0.0331645	−	0.0251972i
$989$	7.97327	−	13.8101i	0.253535	−	0.439136i
$990$		0			0
$991$	22.4345	−	38.8576i	0.712654	−	1.23435i	−0.251203	−	0.967934i	$-0.580826\pi$
$991$	22.4345	−	38.8576i	0.712654	−	1.23435i	0.963857	−	0.266419i	$-0.0858404\pi$
$992$	−3.53495	−	6.12272i	−0.112235	−	0.194396i
$993$		0			0
$994$	6.80309	−	9.64781i	0.215781	−	0.306010i
$995$	6.44095	+	3.71868i	0.204192	+	0.117890i
$996$		0			0
$997$	29.0851			0.921136			0.460568	−	0.887624i	$-0.347646\pi$
$997$	29.0851			0.921136			0.460568	+	0.887624i	$0.347646\pi$
$998$	−17.4477	+	30.2203i	−0.552298	+	0.956607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.e.478.2		12
3.2	odd	2		273.2.t.c.205.5	yes	12
7.4	even	3		819.2.do.f.361.5		12
13.4	even	6		819.2.do.f.667.5		12
21.11	odd	6		273.2.bl.c.88.2	yes	12
39.17	odd	6		273.2.bl.c.121.2	yes	12
91.4	even	6	inner	819.2.bm.e.550.5		12
273.95	odd	6		273.2.t.c.4.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.2	✓	12	273.95	odd	6
273.2.t.c.205.5	yes	12	3.2	odd	2
273.2.bl.c.88.2	yes	12	21.11	odd	6
273.2.bl.c.121.2	yes	12	39.17	odd	6
819.2.bm.e.478.2		12	1.1	even	1	trivial
819.2.bm.e.550.5		12	91.4	even	6	inner
819.2.do.f.361.5		12	7.4	even	3
819.2.do.f.667.5		12	13.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.54246i q^{2} -0.379188 q^{4} +(-1.27069 - 0.733632i) q^{5} +(2.63491 + 0.239300i) q^{7} -2.50004i q^{8} +O(q^{10})\)	\(q-1.54246i q^{2} -0.379188 q^{4} +(-1.27069 - 0.733632i) q^{5} +(2.63491 + 0.239300i) q^{7} -2.50004i q^{8} +(-1.13160 + 1.95999i) q^{10} +(1.93300 + 1.11602i) q^{11} +(3.57691 - 0.453537i) q^{13} +(0.369112 - 4.06424i) q^{14} -4.61459 q^{16} +2.52122 q^{17} +(-0.829287 + 0.478789i) q^{19} +(0.481830 + 0.278185i) q^{20} +(1.72142 - 2.98158i) q^{22} +2.64900 q^{23} +(-1.42357 - 2.46569i) q^{25} +(-0.699564 - 5.51725i) q^{26} +(-0.999126 - 0.0907399i) q^{28} +(0.728078 + 1.26107i) q^{29} +(-2.89114 + 1.66920i) q^{31} +2.11775i q^{32} -3.88889i q^{34} +(-3.17259 - 2.23713i) q^{35} -7.41040i q^{37} +(0.738514 + 1.27914i) q^{38} +(-1.83411 + 3.17677i) q^{40} +(-3.52497 + 2.03514i) q^{41} +(3.00991 - 5.21332i) q^{43} +(-0.732971 - 0.423181i) q^{44} -4.08598i q^{46} +(-9.05536 - 5.22812i) q^{47} +(6.88547 + 1.26107i) q^{49} +(-3.80323 + 2.19580i) q^{50} +(-1.35632 + 0.171976i) q^{52} +(-1.74412 - 3.02090i) q^{53} +(-1.63749 - 2.83622i) q^{55} +(0.598261 - 6.58737i) q^{56} +(1.94515 - 1.12303i) q^{58} +0.767344i q^{59} +(6.05695 + 10.4909i) q^{61} +(2.57468 + 4.45947i) q^{62} -5.96263 q^{64} +(-4.87787 - 2.04783i) q^{65} +(-8.35667 - 4.82473i) q^{67} -0.956018 q^{68} +(-3.45069 + 4.89359i) q^{70} +(2.50519 + 1.44637i) q^{71} +(11.3623 - 6.56004i) q^{73} -11.4303 q^{74} +(0.314456 - 0.181551i) q^{76} +(4.82621 + 3.40317i) q^{77} +(-1.88401 + 3.26320i) q^{79} +(5.86371 + 3.38541i) q^{80} +(3.13913 + 5.43712i) q^{82} +3.89258i q^{83} +(-3.20369 - 1.84965i) q^{85} +(-8.04135 - 4.64268i) q^{86} +(2.79009 - 4.83258i) q^{88} +10.1478i q^{89} +(9.53336 - 0.339072i) q^{91} -1.00447 q^{92} +(-8.06417 + 13.9676i) q^{94} +1.40502 q^{95} +(-5.44296 - 3.14250i) q^{97} +(1.94515 - 10.6206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more