LMFDB - Embedded newform 765.2.bh.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(19,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 4, 7]))

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

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

chi := DirichletCharacter("765.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bh (of order $8$, degree $4$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	765.19
Dual form			765.2.bh.b.604.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.672981 - 0.672981i) q^{2} +1.09419i q^{4} +(0.973741 + 2.01292i) q^{5} +(-0.492777 - 0.204115i) q^{7} +(2.08233 + 2.08233i) q^{8} +(2.00996 + 0.699345i) q^{10} +(-4.31906 - 1.78902i) q^{11} +3.92573 q^{13} +(-0.468995 + 0.194264i) q^{14} +0.614355 q^{16} +(4.03088 + 0.867192i) q^{17} +(0.708548 + 0.708548i) q^{19} +(-2.20252 + 1.06546i) q^{20} +(-4.11062 + 1.70268i) q^{22} +(-2.19587 + 5.30129i) q^{23} +(-3.10366 + 3.92012i) q^{25} +(2.64194 - 2.64194i) q^{26} +(0.223341 - 0.539193i) q^{28} +(3.17120 + 7.65596i) q^{29} +(-2.29036 + 0.948699i) q^{31} +(-3.75122 + 3.75122i) q^{32} +(3.29631 - 2.12910i) q^{34} +(-0.0689710 - 1.19067i) q^{35} +(1.56660 + 3.78211i) q^{37} +0.953679 q^{38} +(-2.16391 + 6.21921i) q^{40} +(0.311708 - 0.752530i) q^{41} +(-4.55216 - 4.55216i) q^{43} +(1.95753 - 4.72589i) q^{44} +(2.08989 + 5.04545i) q^{46} +1.70505 q^{47} +(-4.74858 - 4.74858i) q^{49} +(0.549461 + 4.72687i) q^{50} +4.29551i q^{52} +(5.77230 - 5.77230i) q^{53} +(-0.604514 - 10.4359i) q^{55} +(-0.601090 - 1.45116i) q^{56} +(7.28648 + 3.01816i) q^{58} +(4.28304 - 4.28304i) q^{59} +(-0.432837 + 1.04496i) q^{61} +(-0.902914 + 2.17983i) q^{62} +6.27771i q^{64} +(3.82265 + 7.90217i) q^{65} -7.68603i q^{67} +(-0.948875 + 4.41056i) q^{68} +(-0.847716 - 0.754884i) q^{70} +(-6.41424 + 2.65686i) q^{71} +(11.1662 - 4.62521i) q^{73} +(3.59958 + 1.49100i) q^{74} +(-0.775289 + 0.775289i) q^{76} +(1.76317 + 1.76317i) q^{77} +(-1.36830 - 0.566769i) q^{79} +(0.598223 + 1.23664i) q^{80} +(-0.296665 - 0.716212i) q^{82} +(11.4464 - 11.4464i) q^{83} +(2.17945 + 8.95824i) q^{85} -6.12703 q^{86} +(-5.26841 - 12.7191i) q^{88} -12.0717i q^{89} +(-1.93451 - 0.801300i) q^{91} +(-5.80064 - 2.40270i) q^{92} +(1.14747 - 1.14747i) q^{94} +(-0.736305 + 2.11619i) q^{95} +(-0.210684 + 0.0872680i) q^{97} -6.39141 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) $ 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.672981	−	0.672981i	0.475869	−	0.475869i	−0.427938	−	0.903808i	$-0.640760\pi$
$2$	0.672981	−	0.672981i	0.475869	−	0.475869i	0.903808	+	0.427938i	$0.140760\pi$
$3$		0			0
$3$		0			0
$4$			1.09419i			0.547097i
$5$	0.973741	+	2.01292i	0.435470	+	0.900203i
$5$	0.973741	+	2.01292i	0.435470	+	0.900203i
$6$		0			0
$7$	−0.492777	−	0.204115i	−0.186252	−	0.0771481i	0.287608	−	0.957748i	$-0.407140\pi$
$7$	−0.492777	−	0.204115i	−0.186252	−	0.0771481i	−0.473860	+	0.880600i	$0.657140\pi$
$8$	2.08233	+	2.08233i	0.736216	+	0.736216i
$9$		0			0
$10$	2.00996	+	0.699345i	0.635606	+	0.221152i
$11$	−4.31906	−	1.78902i	−1.30225	−	0.539408i	−0.379634	−	0.925137i	$-0.623950\pi$
$11$	−4.31906	−	1.78902i	−1.30225	−	0.539408i	−0.922612	+	0.385728i	$0.873950\pi$
$12$		0			0
$13$	3.92573			1.08880			0.544401	−	0.838825i	$-0.316757\pi$
$13$	3.92573			1.08880			0.544401	+	0.838825i	$0.316757\pi$
$14$	−0.468995	+	0.194264i	−0.125344	+	0.0519192i
$15$		0			0
$16$	0.614355			0.153589
$17$	4.03088	+	0.867192i	0.977632	+	0.210325i
$17$	4.03088	+	0.867192i	0.977632	+	0.210325i
$18$		0			0
$19$	0.708548	+	0.708548i	0.162552	+	0.162552i	0.783696	−	0.621144i	$-0.213332\pi$
$19$	0.708548	+	0.708548i	0.162552	+	0.162552i	−0.621144	+	0.783696i	$0.713332\pi$
$20$	−2.20252	+	1.06546i	−0.492498	+	0.238244i
$21$		0			0
$22$	−4.11062	+	1.70268i	−0.876387	+	0.363012i
$23$	−2.19587	+	5.30129i	−0.457870	+	1.10540i	0.511388	+	0.859350i	$0.329132\pi$
$23$	−2.19587	+	5.30129i	−0.457870	+	1.10540i	−0.969258	+	0.246046i	$0.920868\pi$
$24$		0			0
$25$	−3.10366	+	3.92012i	−0.620731	+	0.784023i
$26$	2.64194	−	2.64194i	0.518128	−	0.518128i
$27$		0			0
$28$	0.223341	−	0.539193i	0.0422075	−	0.101898i
$29$	3.17120	+	7.65596i	0.588878	+	1.42168i	0.884576	+	0.466395i	$0.154448\pi$
$29$	3.17120	+	7.65596i	0.588878	+	1.42168i	−0.295699	+	0.955281i	$0.595552\pi$
$30$		0			0
$31$	−2.29036	+	0.948699i	−0.411361	+	0.170391i	−0.578760	−	0.815498i	$-0.696463\pi$
$31$	−2.29036	+	0.948699i	−0.411361	+	0.170391i	0.167399	+	0.985889i	$0.446463\pi$
$32$	−3.75122	+	3.75122i	−0.663128	+	0.663128i
$33$		0			0
$34$	3.29631	−	2.12910i	0.565312	−	0.365138i
$35$	−0.0689710	−	1.19067i	−0.0116582	−	0.201260i
$36$		0			0
$37$	1.56660	+	3.78211i	0.257548	+	0.621775i	0.998775	−	0.0494786i	$-0.0157560\pi$
$37$	1.56660	+	3.78211i	0.257548	+	0.621775i	−0.741227	+	0.671254i	$0.765756\pi$
$38$	0.953679			0.154707
$39$		0			0
$40$	−2.16391	+	6.21921i	−0.342144	+	0.983344i
$41$	0.311708	−	0.752530i	0.0486806	−	0.117525i	−0.897669	−	0.440671i	$-0.854740\pi$
$41$	0.311708	−	0.752530i	0.0486806	−	0.117525i	0.946349	+	0.323146i	$0.104740\pi$
$42$		0			0
$43$	−4.55216	−	4.55216i	−0.694197	−	0.694197i	0.268955	−	0.963153i	$-0.413322\pi$
$43$	−4.55216	−	4.55216i	−0.694197	−	0.694197i	−0.963153	+	0.268955i	$0.913322\pi$
$44$	1.95753	−	4.72589i	0.295108	−	0.712455i
$45$		0			0
$46$	2.08989	+	5.04545i	0.308138	+	0.743911i
$47$	1.70505			0.248707			0.124354	−	0.992238i	$-0.460314\pi$
$47$	1.70505			0.248707			0.124354	+	0.992238i	$0.460314\pi$
$48$		0			0
$49$	−4.74858	−	4.74858i	−0.678369	−	0.678369i
$50$	0.549461	+	4.72687i	0.0777056	+	0.668480i
$51$		0			0
$52$			4.29551i			0.595680i
$53$	5.77230	−	5.77230i	0.792887	−	0.792887i	−0.189076	−	0.981962i	$-0.560549\pi$
$53$	5.77230	−	5.77230i	0.792887	−	0.792887i	0.981962	+	0.189076i	$0.0605492\pi$
$54$		0			0
$55$	−0.604514	−	10.4359i	−0.0815126	−	1.40718i
$56$	−0.601090	−	1.45116i	−0.0803240	−	0.193919i
$57$		0			0
$58$	7.28648	+	3.01816i	0.956761	+	0.396304i
$59$	4.28304	−	4.28304i	0.557605	−	0.557605i	−0.371020	−	0.928625i	$-0.620992\pi$
$59$	4.28304	−	4.28304i	0.557605	−	0.557605i	0.928625	+	0.371020i	$0.120992\pi$
$60$		0			0
$61$	−0.432837	+	1.04496i	−0.0554192	+	0.133794i	−0.949164	−	0.314782i	$-0.898069\pi$
$61$	−0.432837	+	1.04496i	−0.0554192	+	0.133794i	0.893745	+	0.448576i	$0.148069\pi$
$62$	−0.902914	+	2.17983i	−0.114670	+	0.276838i
$63$		0			0
$64$			6.27771i			0.784713i
$65$	3.82265	+	7.90217i	0.474141	+	0.980143i
$66$		0			0
$67$		−	7.68603i		−	0.938998i	−0.882933	−	0.469499i	$-0.844435\pi$
$67$		−	7.68603i		−	0.938998i	0.882933	−	0.469499i	$-0.155565\pi$
$68$	−0.948875	+	4.41056i	−0.115068	+	0.534859i
$69$		0			0
$70$	−0.847716	−	0.754884i	−0.101321	−	0.0902259i
$71$	−6.41424	+	2.65686i	−0.761230	+	0.315312i	−0.729314	−	0.684179i	$-0.760161\pi$
$71$	−6.41424	+	2.65686i	−0.761230	+	0.315312i	−0.0319156	+	0.999491i	$0.510161\pi$
$72$		0			0
$73$	11.1662	−	4.62521i	1.30691	−	0.541340i	0.382929	−	0.923778i	$-0.374915\pi$
$73$	11.1662	−	4.62521i	1.30691	−	0.541340i	0.923981	+	0.382438i	$0.124915\pi$
$74$	3.59958	+	1.49100i	0.418443	+	0.173325i
$75$		0			0
$76$	−0.775289	+	0.775289i	−0.0889317	+	0.0889317i
$77$	1.76317	+	1.76317i	0.200932	+	0.200932i
$78$		0			0
$79$	−1.36830	−	0.566769i	−0.153946	−	0.0637666i	0.304380	−	0.952551i	$-0.401551\pi$
$79$	−1.36830	−	0.566769i	−0.153946	−	0.0637666i	−0.458326	+	0.888784i	$0.651551\pi$
$80$	0.598223	+	1.23664i	0.0668833	+	0.138261i
$81$		0			0
$82$	−0.296665	−	0.716212i	−0.0327611	−	0.0790924i
$83$	11.4464	−	11.4464i	1.25640	−	1.25640i	0.303606	−	0.952798i	$-0.401810\pi$
$83$	11.4464	−	11.4464i	1.25640	−	1.25640i	0.952798	−	0.303606i	$-0.0981905\pi$
$84$		0			0
$85$	2.17945	+	8.95824i	0.236394	+	0.971657i
$86$	−6.12703			−0.660694
$87$		0			0
$88$	−5.26841	−	12.7191i	−0.561614	−	1.35586i
$89$		−	12.0717i		−	1.27960i	−0.768542	−	0.639800i	$-0.779017\pi$
$89$		−	12.0717i		−	1.27960i	0.768542	−	0.639800i	$-0.220983\pi$
$90$		0			0
$91$	−1.93451	−	0.801300i	−0.202792	−	0.0839991i
$92$	−5.80064	−	2.40270i	−0.604758	−	0.250499i
$93$		0			0
$94$	1.14747	−	1.14747i	0.118352	−	0.118352i
$95$	−0.736305	+	2.11619i	−0.0755433	+	0.217117i
$96$		0			0
$97$	−0.210684	+	0.0872680i	−0.0213917	+	0.00886072i	−0.393354	−	0.919387i	$-0.628685\pi$
$97$	−0.210684	+	0.0872680i	−0.0213917	+	0.00886072i	0.371962	+	0.928248i	$0.378685\pi$
$98$	−6.39141			−0.645630
$99$		0			0
$100$	−4.28936	−	3.39600i	−0.428936	−	0.339600i
$101$	6.66539			0.663231			0.331616	−	0.943415i	$-0.392406\pi$
$101$	6.66539			0.663231			0.331616	+	0.943415i	$0.392406\pi$
$102$		0			0
$103$		−	0.350456i		−	0.0345315i	−0.999851	−	0.0172657i	$-0.994504\pi$
$103$		−	0.350456i		−	0.0345315i	0.999851	−	0.0172657i	$-0.00549613\pi$
$104$	8.17468	+	8.17468i	0.801594	+	0.801594i
$105$		0			0
$106$		−	7.76930i		−	0.754621i
$107$	−7.20512	+	2.98446i	−0.696545	+	0.288518i	−0.702724	−	0.711463i	$-0.748033\pi$
$107$	−7.20512	+	2.98446i	−0.696545	+	0.288518i	0.00617913	+	0.999981i	$0.498033\pi$
$108$		0			0
$109$	4.66038	−	11.2511i	0.446383	−	1.07766i	−0.527284	−	0.849689i	$-0.676790\pi$
$109$	4.66038	−	11.2511i	0.446383	−	1.07766i	0.973667	−	0.227975i	$-0.0732104\pi$
$110$	−7.43002	−	6.61637i	−0.708425	−	0.630846i
$111$		0			0
$112$	−0.302740	−	0.125399i	−0.0286062	−	0.0118491i
$113$	6.84161	−	16.5171i	0.643604	−	1.55380i	−0.178179	−	0.983998i	$-0.557020\pi$
$113$	6.84161	−	16.5171i	0.643604	−	1.55380i	0.821783	−	0.569800i	$-0.192980\pi$
$114$		0			0
$115$	−12.8093	+	0.741990i	−1.19447	+	0.0691910i
$116$	−8.37710	+	3.46991i	−0.777794	+	0.322173i
$117$		0			0
$118$		−	5.76481i		−	0.530694i
$119$	−1.80932	−	1.25009i	−0.165860	−	0.114596i
$120$		0			0
$121$	7.67557	+	7.67557i	0.697779	+	0.697779i
$122$	0.411948	+	0.994531i	0.0372960	+	0.0900406i
$123$		0			0
$124$	−1.03806	−	2.50610i	−0.0932205	−	0.225054i
$125$	−10.9130	−	2.43022i	−0.976090	−	0.217366i
$126$		0			0
$127$	8.76596	+	8.76596i	0.777853	+	0.777853i	0.979465	−	0.201612i	$-0.0646181\pi$
$127$	8.76596	+	8.76596i	0.777853	+	0.777853i	−0.201612	+	0.979465i	$0.564618\pi$
$128$	−3.27766	−	3.27766i	−0.289707	−	0.289707i
$129$		0			0
$130$	7.89058	+	2.74544i	0.692049	+	0.240791i
$131$	3.83884	+	9.26779i	0.335401	+	0.809730i	0.998145	+	0.0608839i	$0.0193919\pi$
$131$	3.83884	+	9.26779i	0.335401	+	0.809730i	−0.662744	+	0.748846i	$0.730608\pi$
$132$		0			0
$133$	−0.204531	−	0.493781i	−0.0177351	−	0.0428163i
$134$	−5.17255	−	5.17255i	−0.446841	−	0.446841i
$135$		0			0
$136$	6.58785	+	10.1994i	0.564903	+	0.874593i
$137$		−	3.06808i		−	0.262124i	−0.991374	−	0.131062i	$-0.958161\pi$
$137$		−	3.06808i		−	0.262124i	0.991374	−	0.131062i	$-0.0418386\pi$
$138$		0			0
$139$	11.3389	−	4.69672i	0.961753	−	0.398371i	0.154117	−	0.988053i	$-0.450747\pi$
$139$	11.3389	−	4.69672i	0.961753	−	0.398371i	0.807636	+	0.589682i	$0.200747\pi$
$140$	1.30283	−	0.0754676i	0.110109	−	0.00637817i
$141$		0			0
$142$	−2.52864	+	6.10468i	−0.212199	+	0.512293i
$143$	−16.9555	−	7.02320i	−1.41789	−	0.587309i
$144$		0			0
$145$	−12.3229	+	13.8383i	−1.02336	+	1.14921i
$146$	4.40199	−	10.6274i	0.364312	−	0.879526i
$147$		0			0
$148$	−4.13836	+	1.71417i	−0.340171	+	0.140904i
$149$			5.46544i			0.447747i	0.974618	+	0.223873i	$0.0718702\pi$
$149$			5.46544i			0.447747i	−0.974618	+	0.223873i	$0.928130\pi$
$150$		0			0
$151$	3.54105	+	3.54105i	0.288167	+	0.288167i	0.836355	−	0.548188i	$-0.184682\pi$
$151$	3.54105	+	3.54105i	0.288167	+	0.288167i	−0.548188	+	0.836355i	$0.684682\pi$
$152$			2.95087i			0.239347i
$153$		0			0
$154$	2.37316			0.191235
$155$	−4.13987	−	3.68652i	−0.332522	−	0.296108i
$156$		0			0
$157$	−10.9442			−0.873443			−0.436721	−	0.899597i	$-0.643860\pi$
$157$	−10.9442			−0.873443			−0.436721	+	0.899597i	$0.643860\pi$
$158$	−1.30227	+	0.539417i	−0.103603	+	0.0429137i
$159$		0			0
$160$	−11.2036	−	3.89817i	−0.885722	−	0.308177i
$161$	2.16414	−	2.16414i	0.170558	−	0.170558i
$162$		0			0
$163$	6.82704	+	2.82785i	0.534735	+	0.221495i	0.633676	−	0.773599i	$-0.281545\pi$
$163$	6.82704	+	2.82785i	0.534735	+	0.221495i	−0.0989404	+	0.995093i	$0.531545\pi$
$164$	0.823413	+	0.341069i	0.0642978	+	0.0266330i
$165$		0			0
$166$		−	15.4064i		−	1.19577i
$167$	−7.46152	−	18.0137i	−0.577390	−	1.39394i	−0.895147	−	0.445770i	$-0.852930\pi$
$167$	−7.46152	−	18.0137i	−0.577390	−	1.39394i	0.317758	−	0.948172i	$-0.397070\pi$
$168$		0			0
$169$	2.41138			0.185491
$170$	7.49545	+	4.56200i	0.574875	+	0.349889i
$171$		0			0
$172$	4.98094	−	4.98094i	0.379793	−	0.379793i
$173$	5.08958	+	12.2873i	0.386954	+	0.934189i	0.990582	+	0.136923i	$0.0437212\pi$
$173$	5.08958	+	12.2873i	0.386954	+	0.934189i	−0.603628	+	0.797266i	$0.706279\pi$
$174$		0			0
$175$	2.32956	−	1.29824i	0.176098	−	0.0981377i
$176$	−2.65344	−	1.09909i	−0.200011	−	0.0828471i
$177$		0			0
$178$	−8.12404	−	8.12404i	−0.608922	−	0.608922i
$179$	−7.18598	+	7.18598i	−0.537105	+	0.537105i	−0.922678	−	0.385572i	$-0.874004\pi$
$179$	−7.18598	+	7.18598i	−0.537105	+	0.537105i	0.385572	+	0.922678i	$0.374004\pi$
$180$		0			0
$181$	−18.1259	−	7.50798i	−1.34728	−	0.558064i	−0.411750	−	0.911297i	$-0.635082\pi$
$181$	−18.1259	−	7.50798i	−1.34728	−	0.558064i	−0.935535	+	0.353233i	$0.885082\pi$
$182$	−1.84115	+	0.762628i	−0.136475	+	0.0565298i
$183$		0			0
$184$	−15.6116	+	6.46653i	−1.15090	+	0.476719i
$185$	−6.08761	+	6.83624i	−0.447570	+	0.502610i
$186$		0			0
$187$	−15.8582	−	10.9568i	−1.15967	−	0.801238i
$188$			1.86566i			0.136067i
$189$		0			0
$190$	0.928636	+	1.91968i	0.0673704	+	0.139268i
$191$			8.81287i			0.637677i	0.947809	+	0.318838i	$0.103293\pi$
$191$			8.81287i			0.637677i	−0.947809	+	0.318838i	$0.896707\pi$
$192$		0			0
$193$	5.91720	−	14.2854i	0.425930	−	1.02829i	−0.554636	−	0.832093i	$-0.687142\pi$
$193$	5.91720	−	14.2854i	0.425930	−	1.02829i	0.980566	−	0.196192i	$-0.0628575\pi$
$194$	−0.0830564	+	0.200516i	−0.00596310	+	0.0143962i
$195$		0			0
$196$	5.19587	−	5.19587i	0.371133	−	0.371133i
$197$	−0.212628	−	0.0880736i	−0.0151491	−	0.00627498i	0.375096	−	0.926986i	$-0.377610\pi$
$197$	−0.212628	−	0.0880736i	−0.0151491	−	0.00627498i	−0.390245	+	0.920711i	$0.627610\pi$
$198$		0			0
$199$	8.21298	+	19.8279i	0.582203	+	1.40556i	0.890812	+	0.454372i	$0.150136\pi$
$199$	8.21298	+	19.8279i	0.582203	+	1.40556i	−0.308609	+	0.951189i	$0.599864\pi$
$200$	−14.6258	+	1.70014i	−1.03420	+	0.120218i
$201$		0			0
$202$	4.48568	−	4.48568i	0.315611	−	0.315611i
$203$		−	4.41997i		−	0.310221i
$204$		0			0
$205$	1.81830	−	0.105327i	0.126996	−	0.00735637i
$206$	−0.235850	−	0.235850i	−0.0164325	−	0.0164325i
$207$		0			0
$208$	2.41179			0.167228
$209$	−1.79266	−	4.32787i	−0.124001	−	0.299365i
$210$		0			0
$211$	−5.94870	+	14.3614i	−0.409525	+	0.988682i	0.575738	+	0.817635i	$0.304715\pi$
$211$	−5.94870	+	14.3614i	−0.409525	+	0.988682i	−0.985263	+	0.171047i	$0.945285\pi$
$212$	6.31601	+	6.31601i	0.433786	+	0.433786i
$213$		0			0
$214$	−2.84042	+	6.85739i	−0.194167	+	0.468761i
$215$	4.73048	−	13.5957i	0.322616	−	0.927221i
$216$		0			0
$217$	1.32228			0.0897622
$218$	−4.43546	−	10.7081i	−0.300407	−	0.725247i
$219$		0			0
$220$	11.4189	−	0.661455i	0.769865	−	0.0445953i
$221$	15.8242	+	3.40436i	1.06445	+	0.229002i
$222$		0			0
$223$	0.756286	−	0.756286i	0.0506447	−	0.0506447i	−0.681331	−	0.731976i	$-0.738599\pi$
$223$	0.756286	−	0.756286i	0.0506447	−	0.0506447i	0.731976	+	0.681331i	$0.238599\pi$
$224$	2.61419	−	1.08283i	0.174668	−	0.0723498i
$225$		0			0
$226$	−6.51143	−	15.7200i	−0.433134	−	1.04568i
$227$	−0.791349	+	1.91049i	−0.0525237	+	0.126803i	−0.947963	−	0.318380i	$-0.896861\pi$
$227$	−0.791349	+	1.91049i	−0.0525237	+	0.126803i	0.895440	+	0.445183i	$0.146861\pi$
$228$		0			0
$229$	−9.06042	+	9.06042i	−0.598730	+	0.598730i	−0.939974	−	0.341245i	$-0.889151\pi$
$229$	−9.06042	+	9.06042i	−0.598730	+	0.598730i	0.341245	+	0.939974i	$0.389151\pi$
$230$	−8.12105	+	9.11974i	−0.535486	+	0.601338i
$231$		0			0
$232$	−9.33876	+	22.5458i	−0.613120	+	1.48020i
$233$	5.99035	−	2.48129i	0.392441	−	0.162554i	−0.177732	−	0.984079i	$-0.556876\pi$
$233$	5.99035	−	2.48129i	0.392441	−	0.162554i	0.570173	+	0.821524i	$0.306876\pi$
$234$		0			0
$235$	1.66028	+	3.43212i	0.108305	+	0.223887i
$236$	4.68648	+	4.68648i	0.305064	+	0.305064i
$237$		0			0
$238$	−2.05892	+	0.376346i	−0.133460	+	0.0243949i
$239$	−1.26828			−0.0820381			−0.0410190	−	0.999158i	$-0.513060\pi$
$239$	−1.26828			−0.0820381			−0.0410190	+	0.999158i	$0.513060\pi$
$240$		0			0
$241$	−2.30585	+	0.955116i	−0.148533	+	0.0615244i	−0.455712	−	0.890127i	$-0.650615\pi$
$241$	−2.30585	+	0.955116i	−0.148533	+	0.0615244i	0.307178	+	0.951652i	$0.400615\pi$
$242$	10.3310			0.664103
$243$		0			0
$244$	−1.14339	−	0.473608i	−0.0731981	−	0.0303196i
$245$	4.93461	−	14.1824i	0.315260	−	0.906079i
$246$		0			0
$247$	2.78157	+	2.78157i	0.176987	+	0.176987i
$248$	−6.74480	−	2.79379i	−0.428296	−	0.177406i
$249$		0			0
$250$	−8.97975	+	5.70876i	−0.567929	+	0.361054i
$251$		−	17.3565i		−	1.09553i	−0.836632	−	0.547765i	$-0.815479\pi$
$251$		−	17.3565i		−	1.09553i	0.836632	−	0.547765i	$-0.184521\pi$
$252$		0			0
$253$	18.9682	−	18.9682i	1.19252	−	1.19252i
$254$	11.7987			0.740313
$255$		0			0
$256$	−16.9670			−1.06044
$257$	10.9991	−	10.9991i	0.686105	−	0.686105i	−0.275264	−	0.961369i	$-0.588765\pi$
$257$	10.9991	−	10.9991i	0.686105	−	0.686105i	0.961369	+	0.275264i	$0.0887653\pi$
$258$		0			0
$259$		−	2.18350i		−	0.135676i
$260$	−8.64650	+	4.18271i	−0.536233	+	0.259401i
$261$		0			0
$262$	8.82051	+	3.65358i	0.544933	+	0.225719i
$263$	6.39290	+	6.39290i	0.394203	+	0.394203i	0.876183	−	0.481979i	$-0.160082\pi$
$263$	6.39290	+	6.39290i	0.394203	+	0.394203i	−0.481979	+	0.876183i	$0.660082\pi$
$264$		0			0
$265$	17.2399	+	5.99843i	1.05904	+	0.368481i
$266$	−0.469951	−	0.194660i	−0.0288145	−	0.0119354i
$267$		0			0
$268$	8.41000			0.513723
$269$	2.79002	−	1.15566i	0.170110	−	0.0704620i	−0.296003	−	0.955187i	$-0.595654\pi$
$269$	2.79002	−	1.15566i	0.170110	−	0.0704620i	0.466113	+	0.884725i	$0.345654\pi$
$270$		0			0
$271$	13.1638			0.799642			0.399821	−	0.916593i	$-0.369072\pi$
$271$	13.1638			0.799642			0.399821	+	0.916593i	$0.369072\pi$
$272$	2.47639	+	0.532764i	0.150153	+	0.0323035i
$273$		0			0
$274$	−2.06476	−	2.06476i	−0.124737	−	0.124737i
$275$	20.4180	−	11.3787i	1.23125	−	0.686164i
$276$		0			0
$277$	−3.74298	+	1.55039i	−0.224894	+	0.0931540i	−0.492285	−	0.870434i	$-0.663838\pi$
$277$	−3.74298	+	1.55039i	−0.224894	+	0.0931540i	0.267392	+	0.963588i	$0.413838\pi$
$278$	4.47006	−	10.7917i	0.268096	−	0.647241i
$279$		0			0
$280$	2.33576	−	2.62300i	0.139588	−	0.156754i
$281$	−10.0869	+	10.0869i	−0.601731	+	0.601731i	−0.940772	−	0.339041i	$-0.889898\pi$
$281$	−10.0869	+	10.0869i	−0.601731	+	0.601731i	0.339041	+	0.940772i	$0.389898\pi$
$282$		0			0
$283$	2.13312	−	5.14980i	0.126801	−	0.306124i	−0.847712	−	0.530457i	$-0.822020\pi$
$283$	2.13312	−	5.14980i	0.126801	−	0.306124i	0.974513	+	0.224333i	$0.0720203\pi$
$284$	−2.90712	−	7.01841i	−0.172506	−	0.416466i
$285$		0			0
$286$	−16.1372	+	6.68425i	−0.954213	+	0.395248i
$287$	−0.307205	+	0.307205i	−0.0181337	+	0.0181337i
$288$		0			0
$289$	15.4960	+	6.99109i	0.911527	+	0.411241i
$290$	1.01984	+	17.6060i	0.0598873	+	1.03386i
$291$		0			0
$292$	5.06088	+	12.2180i	0.296165	+	0.715006i
$293$	1.97120			0.115159			0.0575795	−	0.998341i	$-0.481662\pi$
$293$	1.97120			0.115159			0.0575795	+	0.998341i	$0.481662\pi$
$294$		0			0
$295$	12.7920	+	4.45083i	0.744778	+	0.259137i
$296$	−4.61343	+	11.1378i	−0.268150	+	0.647372i
$297$		0			0
$298$	3.67814	+	3.67814i	0.213069	+	0.213069i
$299$	−8.62039	+	20.8115i	−0.498530	+	1.20356i
$300$		0			0
$301$	1.31403	+	3.17236i	0.0757396	+	0.182852i
$302$	4.76612			0.274260
$303$		0			0
$304$	0.435300	+	0.435300i	0.0249662	+	0.0249662i
$305$	−2.52489	+	0.146257i	−0.144575	+	0.00837466i
$306$		0			0
$307$			1.69613i			0.0968034i	0.998828	+	0.0484017i	$0.0154128\pi$
$307$			1.69613i			0.0968034i	−0.998828	+	0.0484017i	$0.984587\pi$
$308$	−1.92925	+	1.92925i	−0.109929	+	0.109929i
$309$		0			0
$310$	−5.26701	+	0.305097i	−0.299146	+	0.0173284i
$311$	−4.16844	−	10.0635i	−0.236371	−	0.570649i	0.760531	−	0.649301i	$-0.224938\pi$
$311$	−4.16844	−	10.0635i	−0.236371	−	0.570649i	−0.996902	+	0.0786518i	$0.974938\pi$
$312$		0			0
$313$	−24.2903	−	10.0614i	−1.37297	−	0.568702i	−0.430377	−	0.902649i	$-0.641619\pi$
$313$	−24.2903	−	10.0614i	−1.37297	−	0.568702i	−0.942592	+	0.333947i	$0.891619\pi$
$314$	−7.36524	+	7.36524i	−0.415645	+	0.415645i
$315$		0			0
$316$	0.620155	−	1.49719i	0.0348865	−	0.0842234i
$317$	−9.57139	+	23.1074i	−0.537583	+	1.29784i	0.388823	+	0.921313i	$0.372882\pi$
$317$	−9.57139	+	23.1074i	−0.537583	+	1.29784i	−0.926406	+	0.376527i	$0.877118\pi$
$318$		0			0
$319$		−	38.7399i		−	2.16902i
$320$	−12.6365	+	6.11286i	−0.706401	+	0.341719i
$321$		0			0
$322$		−	2.91286i		−	0.162327i
$323$	2.24162	+	3.47052i	0.124727	+	0.193105i
$324$		0			0
$325$	−12.1841	+	15.3893i	−0.675854	+	0.853646i
$326$	6.49756	−	2.69138i	0.359867	−	0.149062i
$327$		0			0
$328$	2.21610	−	0.917938i	0.122364	−	0.0506847i
$329$	−0.840209	−	0.348026i	−0.0463222	−	0.0191873i
$330$		0			0
$331$	22.8306	−	22.8306i	1.25488	−	1.25488i	0.301376	−	0.953505i	$-0.402554\pi$
$331$	22.8306	−	22.8306i	1.25488	−	1.25488i	0.953505	−	0.301376i	$-0.0974458\pi$
$332$	12.5245	+	12.5245i	0.687374	+	0.687374i
$333$		0			0
$334$	−17.1443	−	7.10142i	−0.938097	−	0.388572i
$335$	15.4713	−	7.48420i	0.845289	−	0.408906i
$336$		0			0
$337$	−4.92267	−	11.8844i	−0.268155	−	0.647383i	0.731242	−	0.682119i	$-0.238941\pi$
$337$	−4.92267	−	11.8844i	−0.268155	−	0.647383i	−0.999397	+	0.0347353i	$0.988941\pi$
$338$	1.62281	−	1.62281i	0.0882693	−	0.0882693i
$339$		0			0
$340$	−9.80204	+	2.38474i	−0.531590	+	0.129330i
$341$	11.5895			0.627604
$342$		0			0
$343$	2.79954	+	6.75868i	0.151161	+	0.364934i
$344$		−	18.9582i		−	1.02216i
$345$		0			0
$346$	11.6943	+	4.84395i	0.628691	+	0.260412i
$347$	−24.8871	−	10.3086i	−1.33601	−	0.553394i	−0.403647	−	0.914915i	$-0.632257\pi$
$347$	−24.8871	−	10.3086i	−1.33601	−	0.553394i	−0.932364	+	0.361521i	$0.882257\pi$
$348$		0			0
$349$	−10.1253	+	10.1253i	−0.541995	+	0.541995i	−0.924113	−	0.382119i	$-0.875195\pi$
$349$	−10.1253	+	10.1253i	−0.541995	+	0.541995i	0.382119	+	0.924113i	$0.375195\pi$
$350$	0.694061	−	2.44144i	0.0370991	−	0.130501i
$351$		0			0
$352$	22.9127	−	9.49076i	1.22125	−	0.505859i
$353$	−1.65351			−0.0880076			−0.0440038	−	0.999031i	$-0.514011\pi$
$353$	−1.65351			−0.0880076			−0.0440038	+	0.999031i	$0.514011\pi$
$354$		0			0
$355$	−11.5938	−	10.3242i	−0.615338	−	0.547953i
$356$	13.2088			0.700065
$357$		0			0
$358$			9.67206i			0.511184i
$359$	−12.2781	−	12.2781i	−0.648012	−	0.648012i	0.304500	−	0.952512i	$-0.401511\pi$
$359$	−12.2781	−	12.2781i	−0.648012	−	0.648012i	−0.952512	+	0.304500i	$0.901511\pi$
$360$		0			0
$361$		−	17.9959i		−	0.947154i
$362$	−17.2511	+	7.14564i	−0.906697	+	0.375566i
$363$		0			0
$364$	0.876777	−	2.11673i	0.0459556	−	0.110947i
$365$	20.1832	+	17.9730i	1.05644	+	0.940748i
$366$		0			0
$367$	−8.84242	−	3.66265i	−0.461571	−	0.191189i	0.139766	−	0.990185i	$-0.455365\pi$
$367$	−8.84242	−	3.66265i	−0.461571	−	0.191189i	−0.601337	+	0.798996i	$0.705365\pi$
$368$	−1.34904	+	3.25688i	−0.0703237	+	0.169776i
$369$		0			0
$370$	0.503812	+	8.69750i	0.0261919	+	0.452162i
$371$	−4.02267	+	1.66624i	−0.208846	+	0.0865070i
$372$		0			0
$373$		−	14.4236i		−	0.746828i	−0.927665	−	0.373414i	$-0.878187\pi$
$373$		−	14.4236i		−	0.746828i	0.927665	−	0.373414i	$-0.121813\pi$
$374$	−18.0460	+	3.29858i	−0.933134	+	0.170565i
$375$		0			0
$376$	3.55049	+	3.55049i	0.183102	+	0.183102i
$377$	12.4493	+	30.0553i	0.641172	+	1.54793i
$378$		0			0
$379$	3.64196	+	8.79246i	0.187075	+	0.451638i	0.989394	−	0.145257i	$-0.0464008\pi$
$379$	3.64196	+	8.79246i	0.187075	+	0.451638i	−0.802319	+	0.596895i	$0.796401\pi$
$380$	−2.31552	−	0.805660i	−0.118784	−	0.0413295i
$381$		0			0
$382$	5.93089	+	5.93089i	0.303451	+	0.303451i
$383$	19.6401	+	19.6401i	1.00356	+	1.00356i	0.999994	+	0.00356842i	$0.00113586\pi$
$383$	19.6401	+	19.6401i	1.00356	+	1.00356i	0.00356842	+	0.999994i	$0.498864\pi$
$384$		0			0
$385$	−1.83224	+	5.26598i	−0.0933796	+	0.268379i
$386$	−5.63163	−	13.5960i	−0.286643	−	0.692016i
$387$		0			0
$388$	−0.0954881	−	0.230529i	−0.00484767	−	0.0117033i
$389$	−14.8835	−	14.8835i	−0.754624	−	0.754624i	0.220715	−	0.975338i	$-0.429161\pi$
$389$	−14.8835	−	14.8835i	−0.754624	−	0.754624i	−0.975338	+	0.220715i	$0.929161\pi$
$390$		0			0
$391$	−13.4485	+	19.4646i	−0.680121	+	0.984369i
$392$		−	19.7763i		−	0.998852i
$393$		0			0
$394$	−0.202367	+	0.0838230i	−0.0101951	+	0.00422294i
$395$	−0.191513	−	3.30616i	−0.00963607	−	0.166351i
$396$		0			0
$397$	−11.3468	+	27.3935i	−0.569478	+	1.37484i	0.332518	+	0.943097i	$0.392102\pi$
$397$	−11.3468	+	27.3935i	−0.569478	+	1.37484i	−0.901996	+	0.431744i	$0.857898\pi$
$398$	18.8710	+	7.81661i	0.945916	+	0.391811i
$399$		0			0
$400$	−1.90675	+	2.40834i	−0.0953374	+	0.120417i
$401$	−6.33937	+	15.3046i	−0.316573	+	0.764275i	0.682858	+	0.730551i	$0.260737\pi$
$401$	−6.33937	+	15.3046i	−0.316573	+	0.764275i	−0.999431	+	0.0337238i	$0.989263\pi$
$402$		0			0
$403$	−8.99135	+	3.72434i	−0.447891	+	0.185523i
$404$			7.29322i			0.362851i
$405$		0			0
$406$	−2.97455	−	2.97455i	−0.147625	−	0.147625i
$407$		−	19.1379i		−	0.948629i
$408$		0			0
$409$	19.3593			0.957257			0.478629	−	0.878017i	$-0.341134\pi$
$409$	19.3593			0.957257			0.478629	+	0.878017i	$0.341134\pi$
$410$	1.15280	−	1.29457i	0.0569327	−	0.0639341i
$411$		0			0
$412$	0.383467			0.0188921
$413$	−2.98482	+	1.23635i	−0.146873	+	0.0608369i
$414$		0			0
$415$	34.1864	+	11.8948i	1.67814	+	0.583892i
$416$	−14.7263	+	14.7263i	−0.722015	+	0.722015i
$417$		0			0
$418$	−4.11900	−	1.70615i	−0.201467	−	0.0834503i
$419$	13.3054	+	5.51126i	0.650009	+	0.269243i	0.683228	−	0.730205i	$-0.260576\pi$
$419$	13.3054	+	5.51126i	0.650009	+	0.269243i	−0.0332183	+	0.999448i	$0.510576\pi$
$420$		0			0
$421$		−	26.7439i		−	1.30342i	−0.758468	−	0.651710i	$-0.774052\pi$
$421$		−	26.7439i		−	1.30342i	0.758468	−	0.651710i	$-0.225948\pi$
$422$	5.66161	+	13.6683i	0.275603	+	0.665364i
$423$		0			0
$424$	24.0397			1.16747
$425$	−15.9100	+	13.1100i	−0.771746	+	0.635931i
$426$		0			0
$427$	0.426584	−	0.426584i	0.0206439	−	0.0206439i
$428$	−3.26557	−	7.88379i	−0.157847	−	0.381077i
$429$		0			0
$430$	−5.96614	−	12.3332i	−0.287713	−	0.594759i
$431$	26.4399	+	10.9518i	1.27356	+	0.527527i	0.914046	−	0.405611i	$-0.132941\pi$
$431$	26.4399	+	10.9518i	1.27356	+	0.527527i	0.359518	+	0.933138i	$0.382941\pi$
$432$		0			0
$433$	25.5919	+	25.5919i	1.22987	+	1.22987i	0.964013	+	0.265855i	$0.0856542\pi$
$433$	25.5919	+	25.5919i	1.22987	+	1.22987i	0.265855	+	0.964013i	$0.414346\pi$
$434$	0.889869	−	0.889869i	0.0427151	−	0.0427151i
$435$		0			0
$436$	12.3109	+	5.09935i	0.589586	+	0.244215i
$437$	−5.31210	+	2.20034i	−0.254112	+	0.105257i
$438$		0			0
$439$	−29.9716	+	12.4146i	−1.43047	+	0.592519i	−0.957467	−	0.288544i	$-0.906829\pi$
$439$	−29.9716	+	12.4146i	−1.43047	+	0.592519i	−0.473000	+	0.881063i	$0.656829\pi$
$440$	20.4723	−	22.9899i	0.975980	−	1.09600i
$441$		0			0
$442$	12.9404	−	8.35828i	0.615513	−	0.397563i
$443$		−	1.88468i		−	0.0895437i	−0.998997	−	0.0447719i	$-0.985744\pi$
$443$		−	1.88468i		−	0.0895437i	0.998997	−	0.0447719i	$-0.0142561\pi$
$444$		0			0
$445$	24.2994	−	11.7547i	1.15190	−	0.557228i
$446$		−	1.01793i		−	0.0482005i
$447$		0			0
$448$	1.28137	−	3.09351i	0.0605391	−	0.146154i
$449$	0.766010	−	1.84931i	0.0361503	−	0.0872745i	−0.904773	−	0.425894i	$-0.859960\pi$
$449$	0.766010	−	1.84931i	0.0361503	−	0.0872745i	0.940924	+	0.338619i	$0.109960\pi$
$450$		0			0
$451$	−2.69258	+	2.69258i	−0.126788	+	0.126788i
$452$	18.0729	+	7.48604i	0.850078	+	0.352114i
$453$		0			0
$454$	0.753158	+	1.81828i	0.0353474	+	0.0853363i
$455$	−0.270762	−	4.67426i	−0.0126935	−	0.219133i
$456$		0			0
$457$	−12.4863	+	12.4863i	−0.584086	+	0.584086i	−0.936023	−	0.351938i	$-0.885523\pi$
$457$	−12.4863	+	12.4863i	−0.584086	+	0.584086i	0.351938	+	0.936023i	$0.385523\pi$
$458$			12.1950i			0.569834i
$459$		0			0
$460$	−0.811881	−	14.0158i	−0.0378541	−	0.653490i
$461$	22.5151	+	22.5151i	1.04863	+	1.04863i	0.998755	+	0.0498792i	$0.0158836\pi$
$461$	22.5151	+	22.5151i	1.04863	+	1.04863i	0.0498792	+	0.998755i	$0.484116\pi$
$462$		0			0
$463$	15.7977			0.734179			0.367090	−	0.930186i	$-0.380354\pi$
$463$	15.7977			0.734179			0.367090	+	0.930186i	$0.380354\pi$
$464$	1.94825	+	4.70348i	0.0904450	+	0.218354i
$465$		0			0
$466$	2.36154	−	5.70125i	0.109396	−	0.264105i
$467$	−6.26872	−	6.26872i	−0.290082	−	0.290082i	0.547031	−	0.837112i	$-0.315758\pi$
$467$	−6.26872	−	6.26872i	−0.290082	−	0.290082i	−0.837112	+	0.547031i	$0.815758\pi$
$468$		0			0
$469$	−1.56883	+	3.78750i	−0.0724419	+	0.174890i
$470$	3.42709	+	1.19242i	0.158080	+	0.0550022i
$471$		0			0
$472$	17.8374			0.821035
$473$	11.5172	+	27.8049i	0.529560	+	1.27847i
$474$		0			0
$475$	−4.97668	+	0.578501i	−0.228346	+	0.0265434i
$476$	1.36784	−	1.97974i	0.0626950	−	0.0907413i
$477$		0			0
$478$	−0.853527	+	0.853527i	−0.0390394	+	0.0390394i
$479$	−11.0031	+	4.55765i	−0.502746	+	0.208244i	−0.619619	−	0.784903i	$-0.712713\pi$
$479$	−11.0031	+	4.55765i	−0.502746	+	0.208244i	0.116873	+	0.993147i	$0.462713\pi$
$480$		0			0
$481$	6.15006	+	14.8476i	0.280419	+	0.676991i
$482$	−0.909021	+	2.19457i	−0.0414048	+	0.0999600i
$483$		0			0
$484$	−8.39855	+	8.39855i	−0.381752	+	0.381752i
$485$	−0.380814	−	0.339112i	−0.0172919	−	0.0153983i
$486$		0			0
$487$	10.2467	−	24.7378i	0.464324	−	1.12098i	−0.502281	−	0.864704i	$-0.667506\pi$
$487$	10.2467	−	24.7378i	0.464324	−	1.12098i	0.966605	−	0.256272i	$-0.0824942\pi$
$488$	−3.07727	+	1.27465i	−0.139302	+	0.0577006i
$489$		0			0
$490$	−6.22358	−	12.8654i	−0.281153	−	0.581198i
$491$	−16.3477	−	16.3477i	−0.737761	−	0.737761i	0.234383	−	0.972144i	$-0.424693\pi$
$491$	−16.3477	−	16.3477i	−0.737761	−	0.737761i	−0.972144	+	0.234383i	$0.924693\pi$
$492$		0			0
$493$	6.14355	+	33.6103i	0.276691	+	1.51373i
$494$	3.74389			0.168446
$495$		0			0
$496$	−1.40710	+	0.582838i	−0.0631805	+	0.0261702i
$497$	3.70309			0.166106
$498$		0			0
$499$	4.58831	+	1.90054i	0.205401	+	0.0850799i	0.483012	−	0.875614i	$-0.339543\pi$
$499$	4.58831	+	1.90054i	0.205401	+	0.0850799i	−0.277611	+	0.960694i	$0.589543\pi$
$500$	2.65913	−	11.9410i	0.118920	−	0.534016i
$501$		0			0
$502$	−11.6806	−	11.6806i	−0.521330	−	0.521330i
$503$	−21.6009	−	8.94738i	−0.963136	−	0.398944i	−0.154983	−	0.987917i	$-0.549532\pi$
$503$	−21.6009	−	8.94738i	−0.963136	−	0.398944i	−0.808153	+	0.588973i	$0.799532\pi$
$504$		0			0
$505$	6.49036	+	13.4169i	0.288817	+	0.597043i
$506$		−	25.5305i		−	1.13497i
$507$		0			0
$508$	−9.59165	+	9.59165i	−0.425561	+	0.425561i
$509$	−23.9562			−1.06184			−0.530921	−	0.847422i	$-0.678154\pi$
$509$	−23.9562			−1.06184			−0.530921	+	0.847422i	$0.678154\pi$
$510$		0			0
$511$	−6.44654			−0.285178
$512$	−4.86316	+	4.86316i	−0.214924	+	0.214924i
$513$		0			0
$514$		−	14.8044i		−	0.652993i
$515$	0.705439	−	0.341254i	0.0310853	−	0.0150374i
$516$		0			0
$517$	−7.36423	−	3.05036i	−0.323878	−	0.134155i
$518$	−1.46946	−	1.46946i	−0.0645642	−	0.0645642i
$519$		0			0
$520$	−8.49492	+	24.4150i	−0.372527	+	1.07067i
$521$	−7.00747	−	2.90259i	−0.307003	−	0.127165i	0.223863	−	0.974621i	$-0.428133\pi$
$521$	−7.00747	−	2.90259i	−0.307003	−	0.127165i	−0.530866	+	0.847456i	$0.678133\pi$
$522$		0			0
$523$	−17.3848			−0.760185			−0.380093	−	0.924948i	$-0.624108\pi$
$523$	−17.3848			−0.760185			−0.380093	+	0.924948i	$0.624108\pi$
$524$	−10.1407	+	4.20044i	−0.443001	+	0.183497i
$525$		0			0
$526$	8.60461			0.375179
$527$	−10.0549	+	1.83791i	−0.437997	+	0.0800605i
$528$		0			0
$529$	−7.01842	−	7.01842i	−0.305149	−	0.305149i
$530$	15.6389	−	7.56528i	0.679312	−	0.328615i
$531$		0			0
$532$	0.540292	−	0.223796i	0.0234246	−	0.00970280i
$533$	1.22368	−	2.95423i	0.0530036	−	0.127962i
$534$		0			0
$535$	−13.0234	−	11.5972i	−0.563050	−	0.501391i
$536$	16.0049	−	16.0049i	0.691305	−	0.691305i
$537$		0			0
$538$	1.09989	−	2.65537i	0.0474196	−	0.114481i
$539$	12.0141	+	29.0047i	0.517486	+	1.24932i
$540$		0			0
$541$	−20.5428	+	8.50911i	−0.883204	+	0.365835i	−0.777739	−	0.628588i	$-0.783633\pi$
$541$	−20.5428	+	8.50911i	−0.883204	+	0.365835i	−0.105466	+	0.994423i	$0.533633\pi$
$542$	8.85896	−	8.85896i	0.380525	−	0.380525i
$543$		0			0
$544$	−18.3737	+	11.8677i	−0.787767	+	0.508822i
$545$	27.1856	−	1.57475i	1.16450	−	0.0674551i
$546$		0			0
$547$	−15.3797	−	37.1299i	−0.657589	−	1.58756i	−0.801517	−	0.597972i	$-0.795974\pi$
$547$	−15.3797	−	37.1299i	−0.657589	−	1.58756i	0.143929	−	0.989588i	$-0.454026\pi$
$548$	3.35707			0.143407
$549$		0			0
$550$	6.08328	−	21.3986i	0.259392	−	0.912441i
$551$	−3.17767	+	7.67157i	−0.135373	+	0.326820i
$552$		0			0
$553$	0.558581	+	0.558581i	0.0237533	+	0.0237533i
$554$	−1.47557	+	3.56234i	−0.0626909	+	0.151349i
$555$		0			0
$556$	5.13912	+	12.4069i	0.217947	+	0.526172i
$557$	6.44000			0.272872			0.136436	−	0.990649i	$-0.456435\pi$
$557$	6.44000			0.272872			0.136436	+	0.990649i	$0.456435\pi$
$558$		0			0
$559$	−17.8705	−	17.8705i	−0.755844	−	0.755844i
$560$	−0.0423727	−	0.731496i	−0.00179057	−	0.0309113i
$561$		0			0
$562$			13.5765i			0.572691i
$563$	−14.0594	+	14.0594i	−0.592532	+	0.592532i	−0.938315	−	0.345782i	$-0.887614\pi$
$563$	−14.0594	+	14.0594i	−0.592532	+	0.592532i	0.345782	+	0.938315i	$0.387614\pi$
$564$		0			0
$565$	39.9095	−	2.31180i	1.67900	−	0.0972582i
$566$	−2.03017	−	4.90127i	−0.0853345	−	0.206016i
$567$		0			0
$568$	−18.8891	−	7.82410i	−0.792567	−	0.328292i
$569$	−4.57941	+	4.57941i	−0.191979	+	0.191979i	−0.796551	−	0.604572i	$-0.793344\pi$
$569$	−4.57941	+	4.57941i	−0.191979	+	0.191979i	0.604572	+	0.796551i	$0.293344\pi$
$570$		0			0
$571$	−14.0045	+	33.8098i	−0.586069	+	1.41490i	0.301164	+	0.953572i	$0.402625\pi$
$571$	−14.0045	+	33.8098i	−0.586069	+	1.41490i	−0.887232	+	0.461323i	$0.847375\pi$
$572$	7.68473	−	18.5526i	0.321315	−	0.775723i
$573$		0			0
$574$			0.413486i			0.0172586i
$575$	−13.9665	−	25.0615i	−0.582442	−	1.04513i
$576$		0			0
$577$			19.2887i			0.802999i	0.915859	+	0.401500i	$0.131511\pi$
$577$			19.2887i			0.802999i	−0.915859	+	0.401500i	$0.868489\pi$
$578$	15.1334	−	5.72361i	0.629465	−	0.238071i
$579$		0			0
$580$	−15.1418	−	13.4836i	−0.628727	−	0.559876i
$581$	−7.97688	+	3.30413i	−0.330937	+	0.137079i
$582$		0			0
$583$	−35.2577	+	14.6042i	−1.46022	+	0.604845i
$584$	32.8831	+	13.6206i	1.36071	+	0.563625i
$585$		0			0
$586$	1.32658	−	1.32658i	0.0548006	−	0.0548006i
$587$	−12.6487	−	12.6487i	−0.522068	−	0.522068i	0.396127	−	0.918196i	$-0.370354\pi$
$587$	−12.6487	−	12.6487i	−0.522068	−	0.522068i	−0.918196	+	0.396127i	$0.870354\pi$
$588$		0			0
$589$	−2.29503	−	0.950633i	−0.0945651	−	0.0391702i
$590$	11.6041	−	5.61343i	0.477732	−	0.231101i
$591$		0			0
$592$	0.962450	+	2.32356i	0.0395565	+	0.0954977i
$593$	−15.9962	+	15.9962i	−0.656884	+	0.656884i	−0.954642	−	0.297757i	$-0.903761\pi$
$593$	−15.9962	+	15.9962i	−0.656884	+	0.656884i	0.297757	+	0.954642i	$0.403761\pi$
$594$		0			0
$595$	0.754528	−	4.85927i	0.0309326	−	0.199210i
$596$	−5.98025			−0.244961
$597$		0			0
$598$	8.20436	+	19.8071i	0.335501	+	0.809972i
$599$		−	17.4019i		−	0.711023i	−0.934672	−	0.355511i	$-0.884307\pi$
$599$		−	17.4019i		−	0.711023i	0.934672	−	0.355511i	$-0.115693\pi$
$600$		0			0
$601$	19.9088	+	8.24649i	0.812096	+	0.336381i	0.749790	−	0.661676i	$-0.230155\pi$
$601$	19.9088	+	8.24649i	0.812096	+	0.336381i	0.0623060	+	0.998057i	$0.480155\pi$
$602$	3.01926	+	1.25062i	0.123056	+	0.0509713i
$603$		0			0
$604$	−3.87460	+	3.87460i	−0.157655	+	0.157655i
$605$	−7.97625	+	22.9243i	−0.324281	+	0.932005i
$606$		0			0
$607$	14.8391	−	6.14655i	0.602300	−	0.249481i	−0.0606323	−	0.998160i	$-0.519312\pi$
$607$	14.8391	−	6.14655i	0.602300	−	0.249481i	0.662932	+	0.748679i	$0.269312\pi$
$608$	−5.31584			−0.215586
$609$		0			0
$610$	−1.60078	+	1.79763i	−0.0648135	+	0.0727840i
$611$	6.69358			0.270793
$612$		0			0
$613$			15.6440i			0.631855i	0.948783	+	0.315928i	$0.102316\pi$
$613$			15.6440i			0.631855i	−0.948783	+	0.315928i	$0.897684\pi$
$614$	1.14147	+	1.14147i	0.0460658	+	0.0460658i
$615$		0			0
$616$			7.34301i			0.295858i
$617$	21.6389	−	8.96313i	0.871150	−	0.360842i	0.0980919	−	0.995177i	$-0.468726\pi$
$617$	21.6389	−	8.96313i	0.871150	−	0.360842i	0.773058	+	0.634335i	$0.218726\pi$
$618$		0			0
$619$	11.0559	−	26.6912i	0.444372	−	1.07281i	−0.530026	−	0.847981i	$-0.677818\pi$
$619$	11.0559	−	26.6912i	0.444372	−	1.07281i	0.974398	−	0.224828i	$-0.0721821\pi$
$620$	4.03376	−	4.52982i	0.162000	−	0.181922i
$621$		0			0
$622$	−9.57783	−	3.96727i	−0.384036	−	0.159073i
$623$	−2.46402	+	5.94866i	−0.0987187	+	0.238328i
$624$		0			0
$625$	−5.73462	−	24.3334i	−0.229385	−	0.973336i
$626$	−23.1180	+	9.57580i	−0.923982	+	0.382726i
$627$		0			0
$628$		−	11.9751i		−	0.477858i
$629$	3.03497	+	16.6038i	0.121012	+	0.662036i
$630$		0			0
$631$	29.7914	+	29.7914i	1.18598	+	1.18598i	0.978169	+	0.207809i	$0.0666332\pi$
$631$	29.7914	+	29.7914i	1.18598	+	1.18598i	0.207809	+	0.978169i	$0.433367\pi$
$632$	−1.66906	−	4.02946i	−0.0663916	−	0.160284i
$633$		0			0
$634$	9.10946	+	21.9922i	0.361783	+	0.873421i
$635$	−9.10936	+	26.1809i	−0.361494	+	1.03896i
$636$		0			0
$637$	−18.6417	−	18.6417i	−0.738610	−	0.738610i
$638$	−26.0712	−	26.0712i	−1.03217	−	1.03217i
$639$		0			0
$640$	3.40606	−	9.78924i	0.134636	−	0.386954i
$641$	−7.27533	−	17.5642i	−0.287358	−	0.693744i	0.712611	−	0.701559i	$-0.247512\pi$
$641$	−7.27533	−	17.5642i	−0.287358	−	0.693744i	−0.999969	+	0.00781522i	$0.997512\pi$
$642$		0			0
$643$	7.78340	+	18.7908i	0.306947	+	0.741036i	0.999801	+	0.0199581i	$0.00635327\pi$
$643$	7.78340	+	18.7908i	0.306947	+	0.741036i	−0.692853	+	0.721078i	$0.743647\pi$
$644$	2.36799	+	2.36799i	0.0933119	+	0.0933119i
$645$		0			0
$646$	3.84416	+	0.827023i	0.151247	+	0.0325388i
$647$			16.7736i			0.659440i	0.944079	+	0.329720i	$0.106954\pi$
$647$			16.7736i			0.659440i	−0.944079	+	0.329720i	$0.893046\pi$
$648$		0			0
$649$	−26.1612	+	10.8363i	−1.02692	+	0.425362i
$650$	2.15704	+	18.5564i	0.0846060	+	0.727842i
$651$		0			0
$652$	−3.09422	+	7.47010i	−0.121179	+	0.292552i
$653$	−6.18810	−	2.56320i	−0.242159	−	0.100306i	0.258303	−	0.966064i	$-0.416837\pi$
$653$	−6.18810	−	2.56320i	−0.242159	−	0.100306i	−0.500462	+	0.865758i	$0.666837\pi$
$654$		0			0
$655$	−14.9172	+	16.7517i	−0.582865	+	0.654543i
$656$	0.191500	−	0.462321i	0.00747680	−	0.0180506i
$657$		0			0
$658$	−0.799660	+	0.331230i	−0.0311740	+	0.0129127i
$659$		−	36.0525i		−	1.40440i	−0.711978	−	0.702202i	$-0.752200\pi$
$659$		−	36.0525i		−	1.40440i	0.711978	−	0.702202i	$-0.247800\pi$
$660$		0			0
$661$	−31.6304	−	31.6304i	−1.23028	−	1.23028i	−0.963855	−	0.266427i	$-0.914157\pi$
$661$	−31.6304	−	31.6304i	−1.23028	−	1.23028i	−0.266427	−	0.963855i	$-0.585843\pi$
$662$		−	30.7291i		−	1.19432i
$663$		0			0
$664$	47.6704			1.84997
$665$	0.794780	−	0.892518i	0.0308202	−	0.0346104i
$666$		0			0
$667$	−47.5501			−1.84115
$668$	19.7105	−	8.16434i	0.762621	−	0.315888i
$669$		0			0
$670$	5.37519	−	15.4486i	0.207662	−	0.596833i
$671$	3.73891	−	3.73891i	0.144339	−	0.144339i
$672$		0			0
$673$	−4.56264	−	1.88991i	−0.175877	−	0.0728506i	0.293007	−	0.956110i	$-0.405344\pi$
$673$	−4.56264	−	1.88991i	−0.175877	−	0.0728506i	−0.468884	+	0.883260i	$0.655344\pi$
$674$	−11.3108	−	4.68510i	−0.435677	−	0.180463i
$675$		0			0
$676$			2.63851i			0.101481i
$677$	−10.8899	−	26.2906i	−0.418534	−	1.01043i	−0.982773	−	0.184819i	$-0.940830\pi$
$677$	−10.8899	−	26.2906i	−0.418534	−	1.01043i	0.564238	−	0.825612i	$-0.309170\pi$
$678$		0			0
$679$	0.121633			0.00466783
$680$	−14.1157	+	23.1924i	−0.541312	+	0.889387i
$681$		0			0
$682$	7.79949	−	7.79949i	0.298658	−	0.298658i
$683$	−12.5401	−	30.2745i	−0.479835	−	1.15842i	−0.959686	−	0.281073i	$-0.909310\pi$
$683$	−12.5401	−	30.2745i	−0.479835	−	1.15842i	0.479852	−	0.877350i	$-0.340690\pi$
$684$		0			0
$685$	6.17578	−	2.98751i	0.235964	−	0.114147i
$686$	6.43250	+	2.66443i	0.245594	+	0.101728i
$687$		0			0
$688$	−2.79664	−	2.79664i	−0.106621	−	0.106621i
$689$	22.6605	−	22.6605i	0.863297	−	0.863297i
$690$		0			0
$691$	6.13856	+	2.54268i	0.233522	+	0.0967279i	0.496376	−	0.868108i	$-0.334664\pi$
$691$	6.13856	+	2.54268i	0.233522	+	0.0967279i	−0.262854	+	0.964836i	$0.584664\pi$
$692$	−13.4447	+	5.56898i	−0.511091	+	0.211701i
$693$		0			0
$694$	−23.6860	+	9.81108i	−0.899110	+	0.372423i
$695$	20.4953	+	18.2508i	0.777429	+	0.692294i
$696$		0			0
$697$	1.90905	−	2.76305i	0.0723103	−	0.104658i
$698$			13.6283i			0.515837i
$699$		0			0
$700$	1.42052	+	2.54899i	0.0536908	+	0.0963428i
$701$			24.2220i			0.914852i	0.889248	+	0.457426i	$0.151228\pi$
$701$			24.2220i			0.914852i	−0.889248	+	0.457426i	$0.848772\pi$
$702$		0			0
$703$	−1.56980	+	3.78982i	−0.0592060	+	0.142936i
$704$	11.2309	−	27.1138i	0.423281	−	1.02189i
$705$		0			0
$706$	−1.11278	+	1.11278i	−0.0418801	+	0.0418801i
$707$	−3.28455	−	1.36050i	−0.123528	−	0.0511670i
$708$		0			0
$709$	0.466820	+	1.12700i	0.0175318	+	0.0423255i	0.932403	−	0.361420i	$-0.117708\pi$
$709$	0.466820	+	1.12700i	0.0175318	+	0.0423255i	−0.914871	+	0.403746i	$0.867708\pi$
$710$	−14.7504	+	0.854435i	−0.553574	+	0.0320664i
$711$		0			0
$712$	25.1373	−	25.1373i	0.942062	−	0.942062i
$713$		−	14.2251i		−	0.532734i
$714$		0			0
$715$	−2.37316	−	40.9687i	−0.0887511	−	1.53214i
$716$	−7.86285	−	7.86285i	−0.293849	−	0.293849i
$717$		0			0
$718$	−16.5258			−0.616738
$719$	6.74904	+	16.2936i	0.251697	+	0.607650i	0.998341	−	0.0575735i	$-0.0183364\pi$
$719$	6.74904	+	16.2936i	0.251697	+	0.607650i	−0.746645	+	0.665223i	$0.768336\pi$
$720$		0			0
$721$	−0.0715333	+	0.172697i	−0.00266404	+	0.00643156i
$722$	−12.1109	−	12.1109i	−0.450721	−	0.450721i
$723$		0			0
$724$	8.21518	−	19.8332i	0.305315	−	0.737095i
$725$	−39.8546	−	11.3300i	−1.48016	−	0.420786i
$726$		0			0
$727$	11.3177			0.419751			0.209876	−	0.977728i	$-0.432694\pi$
$727$	11.3177			0.419751			0.209876	+	0.977728i	$0.432694\pi$
$728$	−2.35972	−	5.69687i	−0.0874570	−	0.211140i
$729$		0			0
$730$	25.6784	−	1.48745i	0.950399	−	0.0550529i
$731$	−14.4016	−	22.2968i	−0.532662	−	0.824676i
$732$		0			0
$733$	1.79642	−	1.79642i	0.0663522	−	0.0663522i	−0.673152	−	0.739504i	$-0.735060\pi$
$733$	1.79642	−	1.79642i	0.0663522	−	0.0663522i	0.739504	+	0.673152i	$0.235060\pi$
$734$	−8.41568	+	3.48589i	−0.310628	+	0.128666i
$735$		0			0
$736$	−11.6491	−	28.1235i	−0.429393	−	1.03665i
$737$	−13.7504	+	33.1965i	−0.506503	+	1.22281i
$738$		0			0
$739$	12.6407	−	12.6407i	0.464997	−	0.464997i	−0.435292	−	0.900289i	$-0.643355\pi$
$739$	12.6407	−	12.6407i	0.464997	−	0.464997i	0.900289	+	0.435292i	$0.143355\pi$
$740$	−7.48016	−	6.66102i	−0.274976	−	0.244864i
$741$		0			0
$742$	−1.58583	+	3.82853i	−0.0582176	+	0.140550i
$743$	−11.0414	+	4.57351i	−0.405071	+	0.167786i	−0.575910	−	0.817513i	$-0.695352\pi$
$743$	−11.0414	+	4.57351i	−0.405071	+	0.167786i	0.170839	+	0.985299i	$0.445352\pi$
$744$		0			0
$745$	−11.0015	+	5.32193i	−0.403063	+	0.194980i
$746$	−9.70683	−	9.70683i	−0.355392	−	0.355392i
$747$		0			0
$748$	11.9888	−	17.3519i	0.438354	−	0.634450i
$749$	4.15968			0.151992
$750$		0			0
$751$	24.7061	−	10.2336i	0.901537	−	0.373429i	0.116726	−	0.993164i	$-0.462760\pi$
$751$	24.7061	−	10.2336i	0.901537	−	0.373429i	0.784811	+	0.619735i	$0.212760\pi$
$752$	1.04751			0.0381987
$753$		0			0
$754$	28.6048	+	11.8485i	1.04172	+	0.431496i
$755$	−3.67977	+	10.5759i	−0.133921	+	0.384897i
$756$		0			0
$757$	0.179229	+	0.179229i	0.00651419	+	0.00651419i	0.710356	−	0.703842i	$-0.248534\pi$
$757$	0.179229	+	0.179229i	0.00651419	+	0.00651419i	−0.703842	+	0.710356i	$0.748534\pi$
$758$	8.36813	+	3.46619i	0.303944	+	0.125898i
$759$		0			0
$760$	−5.93985	+	2.87338i	−0.215461	+	0.104228i
$761$		−	32.3234i		−	1.17172i	−0.810412	−	0.585860i	$-0.800757\pi$
$761$		−	32.3234i		−	1.17172i	0.810412	−	0.585860i	$-0.199243\pi$
$762$		0			0
$763$	−4.59305	+	4.59305i	−0.166279	+	0.166279i
$764$	−9.64298			−0.348871
$765$		0			0
$766$	26.4348			0.955129
$767$	16.8141	−	16.8141i	0.607121	−	0.607121i
$768$		0			0
$769$			7.23844i			0.261025i	0.991447	+	0.130512i	$0.0416622\pi$
$769$			7.23844i			0.261025i	−0.991447	+	0.130512i	$0.958338\pi$
$770$	2.31084	+	4.77697i	0.0832770	+	0.172150i
$771$		0			0
$772$	15.6310	+	6.47456i	0.562571	+	0.233025i
$773$	5.84658	+	5.84658i	0.210287	+	0.210287i	0.804389	−	0.594102i	$-0.202493\pi$
$773$	5.84658	+	5.84658i	0.210287	+	0.210287i	−0.594102	+	0.804389i	$0.702493\pi$
$774$		0			0
$775$	3.38949	−	11.9229i	0.121754	−	0.428284i
$776$	−0.620435	−	0.256992i	−0.0222723	−	0.00922549i
$777$		0			0
$778$	−20.0326			−0.718205
$779$	0.754064	−	0.312344i	0.0270172	−	0.0111909i
$780$		0			0
$781$	32.4567			1.16139
$782$	4.04873	+	22.1499i	0.144782	+	0.792080i
$783$		0			0
$784$	−2.91732	−	2.91732i	−0.104190	−	0.104190i
$785$	−10.6568	−	22.0298i	−0.380358	−	0.786276i
$786$		0			0
$787$	9.85358	−	4.08149i	0.351242	−	0.145489i	−0.200085	−	0.979779i	$-0.564122\pi$
$787$	9.85358	−	4.08149i	0.351242	−	0.145489i	0.551327	+	0.834289i	$0.314122\pi$
$788$	0.0963695	−	0.232657i	0.00343302	−	0.00828805i
$789$		0			0
$790$	−2.35387	−	2.09610i	−0.0837469	−	0.0745759i
$791$	−6.74277	+	6.74277i	−0.239745	+	0.239745i
$792$		0			0
$793$	−1.69920	+	4.10224i	−0.0603405	+	0.145675i
$794$	10.7992	+	26.0715i	0.383248	+	0.925242i
$795$		0			0
$796$	−21.6955	+	8.98658i	−0.768978	+	0.318521i
$797$	−16.0429	+	16.0429i	−0.568269	+	0.568269i	−0.931643	−	0.363374i	$-0.881625\pi$
$797$	−16.0429	+	16.0429i	−0.568269	+	0.568269i	0.363374	+	0.931643i	$0.381625\pi$
$798$		0			0
$799$	6.87286	+	1.47861i	0.243144	+	0.0523093i
$800$	−3.06271	−	26.3477i	−0.108283	−	0.931532i
$801$		0			0
$802$	6.03342	+	14.5660i	0.213048	+	0.514342i
$803$	−56.5023			−1.99392
$804$		0			0
$805$	6.46356	+	2.24892i	0.227810	+	0.0792641i
$806$	−3.54460	+	8.55742i	−0.124853	+	0.301422i
$807$		0			0
$808$	13.8796	+	13.8796i	0.488281	+	0.488281i
$809$	−7.24370	+	17.4878i	−0.254675	+	0.614840i	−0.998570	−	0.0534567i	$-0.982976\pi$
$809$	−7.24370	+	17.4878i	−0.254675	+	0.614840i	0.743895	+	0.668296i	$0.232976\pi$
$810$		0			0
$811$	−10.8154	−	26.1106i	−0.379779	−	0.916867i	−0.992007	−	0.126186i	$-0.959726\pi$
$811$	−10.8154	−	26.1106i	−0.379779	−	0.916867i	0.612228	−	0.790681i	$-0.290274\pi$
$812$	4.83630			0.169721
$813$		0			0
$814$	−12.8794	−	12.8794i	−0.451423	−	0.451423i
$815$	0.955541	+	16.4959i	0.0334711	+	0.577825i
$816$		0			0
$817$		−	6.45084i		−	0.225686i
$818$	13.0285	−	13.0285i	0.455530	−	0.455530i
$819$		0			0
$820$	0.115248	+	1.98957i	0.00402464	+	0.0694789i
$821$	−5.59227	−	13.5009i	−0.195172	−	0.471186i	0.795750	−	0.605625i	$-0.207077\pi$
$821$	−5.59227	−	13.5009i	−0.195172	−	0.471186i	−0.990922	+	0.134439i	$0.957077\pi$
$822$		0			0
$823$	−17.9968	−	7.45453i	−0.627330	−	0.259848i	0.0462883	−	0.998928i	$-0.485261\pi$
$823$	−17.9968	−	7.45453i	−0.627330	−	0.259848i	−0.673618	+	0.739080i	$0.735261\pi$
$824$	0.729767	−	0.729767i	0.0254226	−	0.0254226i
$825$		0			0
$826$	−1.17668	+	2.84076i	−0.0409420	+	0.0988428i
$827$	3.73464	−	9.01621i	0.129866	−	0.313524i	−0.845550	−	0.533896i	$-0.820727\pi$
$827$	3.73464	−	9.01621i	0.129866	−	0.313524i	0.975416	+	0.220372i	$0.0707272\pi$
$828$		0			0
$829$		−	5.96301i		−	0.207104i	−0.994624	−	0.103552i	$-0.966979\pi$
$829$		−	5.96301i		−	0.207104i	0.994624	−	0.103552i	$-0.0330208\pi$
$830$	31.0118	−	15.0018i	1.07643	−	0.520721i
$831$		0			0
$832$			24.6446i			0.854398i
$833$	−15.0230	−	23.2589i	−0.520517	−	0.805873i
$834$		0			0
$835$	28.9945	−	32.5601i	1.00340	−	1.12679i
$836$	4.73552	−	1.96152i	0.163782	−	0.0678405i
$837$		0			0
$838$	12.6632	−	5.24528i	0.437444	−	0.181195i
$839$	20.9048	+	8.65906i	0.721715	+	0.298944i	0.713142	−	0.701019i	$-0.247271\pi$
$839$	20.9048	+	8.65906i	0.721715	+	0.298944i	0.00857233	+	0.999963i	$0.497271\pi$
$840$		0			0
$841$	−28.0511	+	28.0511i	−0.967281	+	0.967281i
$842$	−17.9982	−	17.9982i	−0.620258	−	0.620258i
$843$		0			0
$844$	−15.7142	−	6.50903i	−0.540904	−	0.224050i
$845$	2.34806	+	4.85390i	0.0807757	+	0.166979i
$846$		0			0
$847$	−2.21564	−	5.34904i	−0.0761304	−	0.183795i
$848$	3.54624	−	3.54624i	0.121779	−	0.121779i
$849$		0			0
$850$	−1.88429	+	19.5299i	−0.0646305	+	0.669870i
$851$	−23.4901			−0.805232
$852$		0			0
$853$	2.53060	+	6.10940i	0.0866459	+	0.209182i	0.961263	−	0.275632i	$-0.0888872\pi$
$853$	2.53060	+	6.10940i	0.0866459	+	0.209182i	−0.874617	+	0.484814i	$0.838887\pi$
$854$		−	0.574166i		−	0.0196476i
$855$		0			0
$856$	−21.2181	−	8.78882i	−0.725219	−	0.300396i
$857$	25.2501	+	10.4589i	0.862526	+	0.357270i	0.769695	−	0.638412i	$-0.220408\pi$
$857$	25.2501	+	10.4589i	0.862526	+	0.357270i	0.0928314	+	0.995682i	$0.470408\pi$
$858$		0			0
$859$	−10.0721	+	10.0721i	−0.343654	+	0.343654i	−0.857739	−	0.514085i	$-0.828132\pi$
$859$	−10.0721	+	10.0721i	−0.343654	+	0.343654i	0.514085	+	0.857739i	$0.328132\pi$
$860$	14.8763	+	5.17606i	0.507279	+	0.176502i
$861$		0			0
$862$	25.1639	−	10.4232i	0.857084	−	0.355016i
$863$	31.4670			1.07115			0.535574	−	0.844488i	$-0.320095\pi$
$863$	31.4670			1.07115			0.535574	+	0.844488i	$0.320095\pi$
$864$		0			0
$865$	−19.7774	+	22.2096i	−0.672453	+	0.755148i
$866$	34.4457			1.17051
$867$		0			0
$868$			1.44683i			0.0491086i
$869$	4.89583	+	4.89583i	0.166080	+	0.166080i
$870$		0			0
$871$		−	30.1733i		−	1.02238i
$872$	33.1331	−	13.7242i	1.12203	−	0.464759i
$873$		0			0
$874$	−2.09415	+	5.05573i	−0.0708358	+	0.171013i
$875$	4.88164	+	3.42506i	0.165029	+	0.115788i
$876$		0			0
$877$	−5.14819	−	2.13245i	−0.173842	−	0.0720078i	0.294065	−	0.955785i	$-0.404992\pi$
$877$	−5.14819	−	2.13245i	−0.173842	−	0.0720078i	−0.467907	+	0.883778i	$0.654992\pi$
$878$	−11.8155	+	28.5251i	−0.398754	+	0.962677i
$879$		0			0
$880$	−0.371386	−	6.41138i	−0.0125194	−	0.216128i
$881$	−29.7926	+	12.3405i	−1.00374	+	0.415762i	−0.823167	−	0.567800i	$-0.807795\pi$
$881$	−29.7926	+	12.3405i	−1.00374	+	0.415762i	−0.180572	+	0.983562i	$0.557795\pi$
$882$		0			0
$883$			38.2240i			1.28634i	0.765724	+	0.643169i	$0.222381\pi$
$883$			38.2240i			1.28634i	−0.765724	+	0.643169i	$0.777619\pi$
$884$	−3.72503	+	17.3147i	−0.125286	+	0.582356i
$885$		0			0
$886$	−1.26835	−	1.26835i	−0.0426111	−	0.0426111i
$887$	−2.37088	−	5.72381i	−0.0796063	−	0.192187i	0.879065	−	0.476701i	$-0.158168\pi$
$887$	−2.37088	−	5.72381i	−0.0796063	−	0.192187i	−0.958672	+	0.284515i	$0.908168\pi$
$888$		0			0
$889$	−2.53040	−	6.10892i	−0.0848668	−	0.204887i
$890$	8.44229	−	24.2637i	0.282986	−	0.813321i
$891$		0			0
$892$	0.827523	+	0.827523i	0.0277075	+	0.0277075i
$893$	1.20811	+	1.20811i	0.0404279	+	0.0404279i
$894$		0			0
$895$	−21.4621	−	7.46749i	−0.717397	−	0.249611i
$896$	0.946134	+	2.28417i	0.0316081	+	0.0763088i
$897$		0			0
$898$	−0.729042	−	1.76006i	−0.0243284	−	0.0587340i
$899$	−14.5264	−	14.5264i	−0.484483	−	0.484483i
$900$		0			0
$901$	28.2731	−	18.2618i	0.941915	−	0.608387i
$902$			3.62410i			0.120669i
$903$		0			0
$904$	48.6406	−	20.1476i	1.61776	−	0.670099i
$905$	−2.53697	−	43.7967i	−0.0843317	−	1.45585i
$906$		0			0
$907$	4.14501	−	10.0069i	0.137633	−	0.332275i	−0.840002	−	0.542583i	$-0.817447\pi$
$907$	4.14501	−	10.0069i	0.137633	−	0.332275i	0.977635	+	0.210307i	$0.0674465\pi$
$908$	−2.09044	−	0.865889i	−0.0693737	−	0.0287355i
$909$		0			0
$910$	−3.32791	−	2.96347i	−0.110319	−	0.0982381i
$911$	15.0373	−	36.3032i	0.498207	−	1.20278i	−0.452241	−	0.891896i	$-0.649375\pi$
$911$	15.0373	−	36.3032i	0.498207	−	1.20278i	0.950448	−	0.310882i	$-0.100625\pi$
$912$		0			0
$913$	−69.9154	+	28.9599i	−2.31386	+	0.958433i
$914$			16.8061i			0.555897i
$915$		0			0
$916$	−9.91385	−	9.91385i	−0.327563	−	0.327563i
$917$		−	5.35051i		−	0.176689i
$918$		0			0
$919$	−48.2620			−1.59202			−0.796008	−	0.605286i	$-0.793059\pi$
$919$	−48.2620			−1.59202			−0.796008	+	0.605286i	$0.793059\pi$
$920$	−28.2182	−	25.1281i	−0.930327	−	0.828448i
$921$		0			0
$922$	30.3045			0.998026
$923$	−25.1806	+	10.4301i	−0.828829	+	0.343312i
$924$		0			0
$925$	−19.6885	−	5.59712i	−0.647354	−	0.184032i
$926$	10.6315	−	10.6315i	0.349374	−	0.349374i
$927$		0			0
$928$	−40.6151	−	16.8233i	−1.33325	−	0.552252i
$929$	−21.5317	−	8.91871i	−0.706431	−	0.292613i	0.000395678	−	1.00000i	$-0.499874\pi$
$929$	−21.5317	−	8.91871i	−0.706431	−	0.292613i	−0.706827	+	0.707387i	$0.749874\pi$
$930$		0			0
$931$		−	6.72920i		−	0.220541i
$932$	2.71501	+	6.55460i	0.0889330	+	0.214703i
$933$		0			0
$934$	−8.43745			−0.276082
$935$	6.61325	−	42.5903i	0.216276	−	1.39285i
$936$		0			0
$937$	6.87594	−	6.87594i	0.224627	−	0.224627i	−0.585816	−	0.810444i	$-0.699226\pi$
$937$	6.87594	−	6.87594i	0.224627	−	0.224627i	0.810444	+	0.585816i	$0.199226\pi$
$938$	1.49312	+	3.60471i	0.0487520	+	0.117698i
$939$		0			0
$940$	−3.75541	+	1.81667i	−0.122488	+	0.0592531i
$941$	−13.0919	−	5.42286i	−0.426785	−	0.176780i	0.158943	−	0.987288i	$-0.449191\pi$
$941$	−13.0919	−	5.42286i	−0.426785	−	0.176780i	−0.585728	+	0.810508i	$0.699191\pi$
$942$		0			0
$943$	3.30491	+	3.30491i	0.107623	+	0.107623i
$944$	2.63131	−	2.63131i	0.0856418	−	0.0856418i
$945$		0			0
$946$	26.4630	+	10.9613i	0.860387	+	0.356384i
$947$	−35.5574	+	14.7284i	−1.15546	+	0.478607i	−0.876361	−	0.481655i	$-0.840036\pi$
$947$	−35.5574	+	14.7284i	−1.15546	+	0.478607i	−0.279099	+	0.960262i	$0.590036\pi$
$948$		0			0
$949$	43.8357	−	18.1573i	1.42297	−	0.589412i
$950$	−2.95989	+	3.73853i	−0.0960316	+	0.121294i
$951$		0			0
$952$	−1.16449	−	6.37071i	−0.0377412	−	0.206476i
$953$			37.7984i			1.22441i	0.790698	+	0.612206i	$0.209718\pi$
$953$			37.7984i			1.22441i	−0.790698	+	0.612206i	$0.790282\pi$
$954$		0			0
$955$	−17.7396	+	8.58145i	−0.574039	+	0.277689i
$956$		−	1.38774i		−	0.0448828i
$957$		0			0
$958$	−4.33769	+	10.4721i	−0.140145	+	0.338339i
$959$	−0.626240	+	1.51188i	−0.0202223	+	0.0488210i
$960$		0			0
$961$	−17.5746	+	17.5746i	−0.566922	+	0.566922i
$962$	14.1310	+	5.85325i	0.455602	+	0.188716i
$963$		0			0
$964$	−1.04508	−	2.52305i	−0.0336598	−	0.0812620i
$965$	34.5171	−	1.99944i	1.11115	−	0.0643643i
$966$		0			0
$967$	3.39288	−	3.39288i	0.109108	−	0.109108i	−0.650445	−	0.759553i	$-0.725418\pi$
$967$	3.39288	−	3.39288i	0.109108	−	0.109108i	0.759553	+	0.650445i	$0.225418\pi$
$968$			31.9662i			1.02743i
$969$		0			0
$970$	−0.484497	+	0.0280650i	−0.0155563	+	0.000901113i
$971$	25.8080	+	25.8080i	0.828217	+	0.828217i	0.987270	−	0.159053i	$-0.0508442\pi$
$971$	25.8080	+	25.8080i	0.828217	+	0.828217i	−0.159053	+	0.987270i	$0.550844\pi$
$972$		0			0
$973$	−6.54621			−0.209862
$974$	−9.75221	−	23.5439i	−0.312481	−	0.754396i
$975$		0			0
$976$	−0.265916	+	0.641978i	−0.00851176	+	0.0205492i
$977$	−44.0684	−	44.0684i	−1.40987	−	1.40987i	−0.760303	−	0.649569i	$-0.774949\pi$
$977$	−44.0684	−	44.0684i	−1.40987	−	1.40987i	−0.649569	−	0.760303i	$-0.725051\pi$
$978$		0			0
$979$	−21.5965	+	52.1385i	−0.690227	+	1.66635i
$980$	15.5183	+	5.39941i	0.495713	+	0.172478i
$981$		0			0
$982$	−22.0034			−0.702156
$983$	15.3732	+	37.1141i	0.490328	+	1.18376i	0.954553	+	0.298040i	$0.0963329\pi$
$983$	15.3732	+	37.1141i	0.490328	+	1.18376i	−0.464225	+	0.885717i	$0.653667\pi$
$984$		0			0
$985$	−0.0297603	−	0.513764i	−0.000948243	−	0.0163699i
$986$	26.7536	+	18.4846i	0.852008	+	0.588670i
$987$		0			0
$988$	−3.04358	+	3.04358i	−0.0968291	+	0.0968291i
$989$	34.1282	−	14.1364i	1.08521	−	0.449511i
$990$		0			0
$991$	9.59778	+	23.1711i	0.304883	+	0.736054i	0.999855	+	0.0170168i	$0.00541686\pi$
$991$	9.59778	+	23.1711i	0.304883	+	0.736054i	−0.694972	+	0.719037i	$0.744583\pi$
$992$	5.03287	−	12.1504i	0.159794	−	0.385776i
$993$		0			0
$994$	2.49211	−	2.49211i	0.0790449	−	0.0790449i
$995$	−31.9145	+	35.8392i	−1.01176	+	1.13618i
$996$		0			0
$997$	14.2988	−	34.5204i	0.452848	−	1.09327i	−0.518387	−	0.855146i	$-0.673467\pi$
$997$	14.2988	−	34.5204i	0.452848	−	1.09327i	0.971235	−	0.238125i	$-0.0765327\pi$
$998$	4.36687	−	1.80882i	0.138231	−	0.0572571i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bh.b.19.5		24
3.2	odd	2		85.2.m.a.19.2	yes	24
5.4	even	2	inner	765.2.bh.b.19.2		24
15.2	even	4		425.2.m.e.376.2		24
15.8	even	4		425.2.m.e.376.5		24
15.14	odd	2		85.2.m.a.19.5	yes	24
17.9	even	8	inner	765.2.bh.b.604.2		24
51.14	even	16		1445.2.b.i.579.17		24
51.20	even	16		1445.2.b.i.579.18		24
51.26	odd	8		85.2.m.a.9.5	yes	24
85.9	even	8	inner	765.2.bh.b.604.5		24
255.14	even	16		1445.2.b.i.579.8		24
255.77	even	8		425.2.m.e.26.2		24
255.122	odd	16		7225.2.a.by.1.8		24
255.128	even	8		425.2.m.e.26.5		24
255.167	odd	16		7225.2.a.by.1.7		24
255.173	odd	16		7225.2.a.by.1.17		24
255.179	odd	8		85.2.m.a.9.2	✓	24
255.218	odd	16		7225.2.a.by.1.18		24
255.224	even	16		1445.2.b.i.579.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.2	✓	24	255.179	odd	8
85.2.m.a.9.5	yes	24	51.26	odd	8
85.2.m.a.19.2	yes	24	3.2	odd	2
85.2.m.a.19.5	yes	24	15.14	odd	2
425.2.m.e.26.2		24	255.77	even	8
425.2.m.e.26.5		24	255.128	even	8
425.2.m.e.376.2		24	15.2	even	4
425.2.m.e.376.5		24	15.8	even	4
765.2.bh.b.19.2		24	5.4	even	2	inner
765.2.bh.b.19.5		24	1.1	even	1	trivial
765.2.bh.b.604.2		24	17.9	even	8	inner
765.2.bh.b.604.5		24	85.9	even	8	inner
1445.2.b.i.579.7		24	255.224	even	16
1445.2.b.i.579.8		24	255.14	even	16
1445.2.b.i.579.17		24	51.14	even	16
1445.2.b.i.579.18		24	51.20	even	16
7225.2.a.by.1.7		24	255.167	odd	16
7225.2.a.by.1.8		24	255.122	odd	16
7225.2.a.by.1.17		24	255.173	odd	16
7225.2.a.by.1.18		24	255.218	odd	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bh (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.672981 - 0.672981i) q^{2} +1.09419i q^{4} +(0.973741 + 2.01292i) q^{5} +(-0.492777 - 0.204115i) q^{7} +(2.08233 + 2.08233i) q^{8} +(2.00996 + 0.699345i) q^{10} +(-4.31906 - 1.78902i) q^{11} +3.92573 q^{13} +(-0.468995 + 0.194264i) q^{14} +0.614355 q^{16} +(4.03088 + 0.867192i) q^{17} +(0.708548 + 0.708548i) q^{19} +(-2.20252 + 1.06546i) q^{20} +(-4.11062 + 1.70268i) q^{22} +(-2.19587 + 5.30129i) q^{23} +(-3.10366 + 3.92012i) q^{25} +(2.64194 - 2.64194i) q^{26} +(0.223341 - 0.539193i) q^{28} +(3.17120 + 7.65596i) q^{29} +(-2.29036 + 0.948699i) q^{31} +(-3.75122 + 3.75122i) q^{32} +(3.29631 - 2.12910i) q^{34} +(-0.0689710 - 1.19067i) q^{35} +(1.56660 + 3.78211i) q^{37} +0.953679 q^{38} +(-2.16391 + 6.21921i) q^{40} +(0.311708 - 0.752530i) q^{41} +(-4.55216 - 4.55216i) q^{43} +(1.95753 - 4.72589i) q^{44} +(2.08989 + 5.04545i) q^{46} +1.70505 q^{47} +(-4.74858 - 4.74858i) q^{49} +(0.549461 + 4.72687i) q^{50} +4.29551i q^{52} +(5.77230 - 5.77230i) q^{53} +(-0.604514 - 10.4359i) q^{55} +(-0.601090 - 1.45116i) q^{56} +(7.28648 + 3.01816i) q^{58} +(4.28304 - 4.28304i) q^{59} +(-0.432837 + 1.04496i) q^{61} +(-0.902914 + 2.17983i) q^{62} +6.27771i q^{64} +(3.82265 + 7.90217i) q^{65} -7.68603i q^{67} +(-0.948875 + 4.41056i) q^{68} +(-0.847716 - 0.754884i) q^{70} +(-6.41424 + 2.65686i) q^{71} +(11.1662 - 4.62521i) q^{73} +(3.59958 + 1.49100i) q^{74} +(-0.775289 + 0.775289i) q^{76} +(1.76317 + 1.76317i) q^{77} +(-1.36830 - 0.566769i) q^{79} +(0.598223 + 1.23664i) q^{80} +(-0.296665 - 0.716212i) q^{82} +(11.4464 - 11.4464i) q^{83} +(2.17945 + 8.95824i) q^{85} -6.12703 q^{86} +(-5.26841 - 12.7191i) q^{88} -12.0717i q^{89} +(-1.93451 - 0.801300i) q^{91} +(-5.80064 - 2.40270i) q^{92} +(1.14747 - 1.14747i) q^{94} +(-0.736305 + 2.11619i) q^{95} +(-0.210684 + 0.0872680i) q^{97} -6.39141 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) \) 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

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