LMFDB - Embedded newform 1040.2.bp.b.287.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(287,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))

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

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

chi := DirichletCharacter("1040.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bp (of order $4$, 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.12
Character	$\chi$	$=$	1040.287
Dual form			1040.2.bp.b.703.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.246371 - 0.246371i) q^{3} +(-1.83645 + 1.27572i) q^{5} +(1.16350 - 1.16350i) q^{7} -2.87860i q^{9} +O(q^{10})$	\(q+(-0.246371 - 0.246371i) q^{3} +(-1.83645 + 1.27572i) q^{5} +(1.16350 - 1.16350i) q^{7} -2.87860i q^{9} +4.32359i q^{11} +(-0.707107 + 0.707107i) q^{13} +(0.766746 + 0.138146i) q^{15} +(2.78171 + 2.78171i) q^{17} -5.23058 q^{19} -0.573302 q^{21} +(2.06657 + 2.06657i) q^{23} +(1.74507 - 4.68559i) q^{25} +(-1.44831 + 1.44831i) q^{27} -1.84106i q^{29} +8.65733i q^{31} +(1.06520 - 1.06520i) q^{33} +(-0.652402 + 3.62100i) q^{35} +(3.13131 + 3.13131i) q^{37} +0.348421 q^{39} +12.2790 q^{41} +(-1.55893 - 1.55893i) q^{43} +(3.67230 + 5.28640i) q^{45} +(-8.20963 + 8.20963i) q^{47} +4.29255i q^{49} -1.37066i q^{51} +(-8.76970 + 8.76970i) q^{53} +(-5.51569 - 7.94003i) q^{55} +(1.28866 + 1.28866i) q^{57} +8.70920 q^{59} +2.92139 q^{61} +(-3.34924 - 3.34924i) q^{63} +(0.396493 - 2.20063i) q^{65} +(-10.1942 + 10.1942i) q^{67} -1.01829i q^{69} +8.12141i q^{71} +(1.50787 - 1.50787i) q^{73} +(-1.58432 + 0.724457i) q^{75} +(5.03048 + 5.03048i) q^{77} -1.92670 q^{79} -7.92217 q^{81} +(8.76618 + 8.76618i) q^{83} +(-8.65714 - 1.55977i) q^{85} +(-0.453582 + 0.453582i) q^{87} -8.27235i q^{89} +1.64543i q^{91} +(2.13291 - 2.13291i) q^{93} +(9.60568 - 6.67276i) q^{95} +(-5.37601 - 5.37601i) q^{97} +12.4459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{5}+O(q^{10}) $ 48 * q + 8 * q^5	$ 48 q + 8 q^{5} - 16 q^{17} + 32 q^{21} + 16 q^{25} - 24 q^{33} + 24 q^{37} - 16 q^{41} - 48 q^{45} + 40 q^{53} - 8 q^{57} - 16 q^{61} + 40 q^{73} - 72 q^{77} - 160 q^{81} - 64 q^{85} - 8 q^{93} + 16 q^{97}+O(q^{100}) $ 48 * q + 8 * q^5 - 16 * q^17 + 32 * q^21 + 16 * q^25 - 24 * q^33 + 24 * q^37 - 16 * q^41 - 48 * q^45 + 40 * q^53 - 8 * q^57 - 16 * q^61 + 40 * q^73 - 72 * q^77 - 160 * q^81 - 64 * q^85 - 8 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.246371	−	0.246371i	−0.142242	−	0.142242i	0.632400	−	0.774642i	$-0.282070\pi$
$3$	−0.246371	−	0.246371i	−0.142242	−	0.142242i	−0.774642	+	0.632400i	$0.782070\pi$
$4$		0			0
$5$	−1.83645	+	1.27572i	−0.821284	+	0.570520i
$5$	−1.83645	+	1.27572i	−0.821284	+	0.570520i
$6$		0			0
$7$	1.16350	−	1.16350i	0.439760	−	0.439760i	−0.452171	−	0.891931i	$-0.649350\pi$
$7$	1.16350	−	1.16350i	0.439760	−	0.439760i	0.891931	+	0.452171i	$0.149350\pi$
$8$		0			0
$9$		−	2.87860i		−	0.959534i
$10$		0			0
$11$			4.32359i			1.30361i	0.758386	+	0.651805i	$0.225988\pi$
$11$			4.32359i			1.30361i	−0.758386	+	0.651805i	$0.774012\pi$
$12$		0			0
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$		0			0
$15$	0.766746	+	0.138146i	0.197973	+	0.0356692i
$16$		0			0
$17$	2.78171	+	2.78171i	0.674663	+	0.674663i	0.958787	−	0.284124i	$-0.0917029\pi$
$17$	2.78171	+	2.78171i	0.674663	+	0.674663i	−0.284124	+	0.958787i	$0.591703\pi$
$18$		0			0
$19$	−5.23058			−1.19998			−0.599989	−	0.800008i	$-0.704828\pi$
$19$	−5.23058			−1.19998			−0.599989	+	0.800008i	$0.704828\pi$
$20$		0			0
$21$	−0.573302			−0.125105
$22$		0			0
$23$	2.06657	+	2.06657i	0.430910	+	0.430910i	0.888938	−	0.458028i	$-0.151444\pi$
$23$	2.06657	+	2.06657i	0.430910	+	0.430910i	−0.458028	+	0.888938i	$0.651444\pi$
$24$		0			0
$25$	1.74507	−	4.68559i	0.349014	−	0.937117i
$26$		0			0
$27$	−1.44831	+	1.44831i	−0.278728	+	0.278728i
$28$		0			0
$29$		−	1.84106i		−	0.341876i	−0.985282	−	0.170938i	$-0.945320\pi$
$29$		−	1.84106i		−	0.341876i	0.985282	−	0.170938i	$-0.0546797\pi$
$30$		0			0
$31$			8.65733i			1.55490i	0.628944	+	0.777451i	$0.283488\pi$
$31$			8.65733i			1.55490i	−0.628944	+	0.777451i	$0.716512\pi$
$32$		0			0
$33$	1.06520	−	1.06520i	0.185428	−	0.185428i
$34$		0			0
$35$	−0.652402	+	3.62100i	−0.110276	+	0.612060i
$36$		0			0
$37$	3.13131	+	3.13131i	0.514784	+	0.514784i	0.915989	−	0.401204i	$-0.131408\pi$
$37$	3.13131	+	3.13131i	0.514784	+	0.514784i	−0.401204	+	0.915989i	$0.631408\pi$
$38$		0			0
$39$	0.348421			0.0557919
$40$		0			0
$41$	12.2790			1.91765			0.958825	−	0.283998i	$-0.0916608\pi$
$41$	12.2790			1.91765			0.958825	+	0.283998i	$0.0916608\pi$
$42$		0			0
$43$	−1.55893	−	1.55893i	−0.237735	−	0.237735i	0.578177	−	0.815912i	$-0.303764\pi$
$43$	−1.55893	−	1.55893i	−0.237735	−	0.237735i	−0.815912	+	0.578177i	$0.803764\pi$
$44$		0			0
$45$	3.67230	+	5.28640i	0.547433	+	0.788050i
$46$		0			0
$47$	−8.20963	+	8.20963i	−1.19750	+	1.19750i	−0.222585	+	0.974913i	$0.571449\pi$
$47$	−8.20963	+	8.20963i	−1.19750	+	1.19750i	−0.974913	+	0.222585i	$0.928551\pi$
$48$		0			0
$49$			4.29255i			0.613222i
$50$		0			0
$51$		−	1.37066i		−	0.191931i
$52$		0			0
$53$	−8.76970	+	8.76970i	−1.20461	+	1.20461i	−0.231862	+	0.972749i	$0.574482\pi$
$53$	−8.76970	+	8.76970i	−1.20461	+	1.20461i	−0.972749	+	0.231862i	$0.925518\pi$
$54$		0			0
$55$	−5.51569	−	7.94003i	−0.743736	−	1.07063i
$56$		0			0
$57$	1.28866	+	1.28866i	0.170687	+	0.170687i
$58$		0			0
$59$	8.70920			1.13384			0.566921	−	0.823772i	$-0.308135\pi$
$59$	8.70920			1.13384			0.566921	+	0.823772i	$0.308135\pi$
$60$		0			0
$61$	2.92139			0.374046			0.187023	−	0.982356i	$-0.440116\pi$
$61$	2.92139			0.374046			0.187023	+	0.982356i	$0.440116\pi$
$62$		0			0
$63$	−3.34924	−	3.34924i	−0.421965	−	0.421965i
$64$		0			0
$65$	0.396493	−	2.20063i	0.0491788	−	0.272955i
$66$		0			0
$67$	−10.1942	+	10.1942i	−1.24542	+	1.24542i	−0.287704	+	0.957719i	$0.592892\pi$
$67$	−10.1942	+	10.1942i	−1.24542	+	1.24542i	−0.957719	+	0.287704i	$0.907108\pi$
$68$		0			0
$69$		−	1.01829i		−	0.122587i
$70$		0			0
$71$			8.12141i			0.963834i	0.876217	+	0.481917i	$0.160059\pi$
$71$			8.12141i			0.963834i	−0.876217	+	0.481917i	$0.839941\pi$
$72$		0			0
$73$	1.50787	−	1.50787i	0.176483	−	0.176483i	−0.613338	−	0.789821i	$-0.710174\pi$
$73$	1.50787	−	1.50787i	0.176483	−	0.176483i	0.789821	+	0.613338i	$0.210174\pi$
$74$		0			0
$75$	−1.58432	+	0.724457i	−0.182942	+	0.0836531i
$76$		0			0
$77$	5.03048	+	5.03048i	0.573276	+	0.573276i
$78$		0			0
$79$	−1.92670			−0.216770			−0.108385	−	0.994109i	$-0.534568\pi$
$79$	−1.92670			−0.216770			−0.108385	+	0.994109i	$0.534568\pi$
$80$		0			0
$81$	−7.92217			−0.880241
$82$		0			0
$83$	8.76618	+	8.76618i	0.962213	+	0.962213i	0.999312	−	0.0370982i	$-0.0118114\pi$
$83$	8.76618	+	8.76618i	0.962213	+	0.962213i	−0.0370982	+	0.999312i	$0.511811\pi$
$84$		0			0
$85$	−8.65714	−	1.55977i	−0.938998	−	0.169181i
$86$		0			0
$87$	−0.453582	+	0.453582i	−0.0486291	+	0.0486291i
$88$		0			0
$89$		−	8.27235i		−	0.876867i	−0.898764	−	0.438434i	$-0.855533\pi$
$89$		−	8.27235i		−	0.876867i	0.898764	−	0.438434i	$-0.144467\pi$
$90$		0			0
$91$			1.64543i			0.172488i
$92$		0			0
$93$	2.13291	−	2.13291i	0.221172	−	0.221172i
$94$		0			0
$95$	9.60568	−	6.67276i	0.985522	−	0.684611i
$96$		0			0
$97$	−5.37601	−	5.37601i	−0.545851	−	0.545851i	0.379387	−	0.925238i	$-0.376135\pi$
$97$	−5.37601	−	5.37601i	−0.545851	−	0.545851i	−0.925238	+	0.379387i	$0.876135\pi$
$98$		0			0
$99$	12.4459			1.25086
$100$		0			0
$101$	2.27851			0.226721			0.113360	−	0.993554i	$-0.463839\pi$
$101$	2.27851			0.226721			0.113360	+	0.993554i	$0.463839\pi$
$102$		0			0
$103$	−1.86072	−	1.86072i	−0.183343	−	0.183343i	0.609468	−	0.792811i	$-0.291383\pi$
$103$	−1.86072	−	1.86072i	−0.183343	−	0.183343i	−0.792811	+	0.609468i	$0.791383\pi$
$104$		0			0
$105$	1.05284	−	0.731374i	0.102747	−	0.0713748i
$106$		0			0
$107$	5.49498	−	5.49498i	0.531220	−	0.531220i	−0.389715	−	0.920935i	$-0.627427\pi$
$107$	5.49498	−	5.49498i	0.531220	−	0.531220i	0.920935	+	0.389715i	$0.127427\pi$
$108$		0			0
$109$			4.79311i			0.459097i	0.973297	+	0.229548i	$0.0737249\pi$
$109$			4.79311i			0.459097i	−0.973297	+	0.229548i	$0.926275\pi$
$110$		0			0
$111$		−	1.54292i		−	0.146448i
$112$		0			0
$113$	9.34780	−	9.34780i	0.879367	−	0.879367i	−0.114102	−	0.993469i	$-0.536399\pi$
$113$	9.34780	−	9.34780i	0.879367	−	0.879367i	0.993469	+	0.114102i	$0.0363991\pi$
$114$		0			0
$115$	−6.43152	−	1.15878i	−0.599743	−	0.108057i
$116$		0			0
$117$	2.03548	+	2.03548i	0.188180	+	0.188180i
$118$		0			0
$119$	6.47301			0.593380
$120$		0			0
$121$	−7.69340			−0.699400
$122$		0			0
$123$	−3.02517	−	3.02517i	−0.272771	−	0.272771i
$124$		0			0
$125$	2.77277	+	10.8311i	0.248004	+	0.968759i
$126$		0			0
$127$	−4.11272	+	4.11272i	−0.364945	+	0.364945i	−0.865630	−	0.500685i	$-0.833082\pi$
$127$	−4.11272	+	4.11272i	−0.364945	+	0.364945i	0.500685	+	0.865630i	$0.333082\pi$
$128$		0			0
$129$			0.768150i			0.0676319i
$130$		0			0
$131$		−	6.45388i		−	0.563878i	−0.959432	−	0.281939i	$-0.909022\pi$
$131$		−	6.45388i		−	0.563878i	0.959432	−	0.281939i	$-0.0909776\pi$
$132$		0			0
$133$	−6.08576	+	6.08576i	−0.527702	+	0.527702i
$134$		0			0
$135$	0.812106	−	4.50740i	0.0698950	−	0.387935i
$136$		0			0
$137$	−9.94608	−	9.94608i	−0.849751	−	0.849751i	0.140351	−	0.990102i	$-0.455177\pi$
$137$	−9.94608	−	9.94608i	−0.849751	−	0.849751i	−0.990102	+	0.140351i	$0.955177\pi$
$138$		0			0
$139$	17.9829			1.52529			0.762646	−	0.646816i	$-0.223900\pi$
$139$	17.9829			1.52529			0.762646	+	0.646816i	$0.223900\pi$
$140$		0			0
$141$	4.04522			0.340669
$142$		0			0
$143$	−3.05724	−	3.05724i	−0.255659	−	0.255659i
$144$		0			0
$145$	2.34867	+	3.38100i	0.195047	+	0.280777i
$146$		0			0
$147$	1.05756	−	1.05756i	0.0872260	−	0.0872260i
$148$		0			0
$149$		−	12.5932i		−	1.03167i	−0.856687	−	0.515836i	$-0.827481\pi$
$149$		−	12.5932i		−	1.03167i	0.856687	−	0.515836i	$-0.172519\pi$
$150$		0			0
$151$		−	12.2792i		−	0.999271i	−0.866236	−	0.499635i	$-0.833467\pi$
$151$		−	12.2792i		−	0.999271i	0.866236	−	0.499635i	$-0.166533\pi$
$152$		0			0
$153$	8.00743	−	8.00743i	0.647362	−	0.647362i
$154$		0			0
$155$	−11.0443	−	15.8987i	−0.887102	−	1.27702i
$156$		0			0
$157$	6.32403	+	6.32403i	0.504713	+	0.504713i	0.912899	−	0.408186i	$-0.133839\pi$
$157$	6.32403	+	6.32403i	0.504713	+	0.504713i	−0.408186	+	0.912899i	$0.633839\pi$
$158$		0			0
$159$	4.32119			0.342693
$160$		0			0
$161$	4.80890			0.378994
$162$		0			0
$163$	−15.0315	−	15.0315i	−1.17736	−	1.17736i	−0.980416	−	0.196940i	$-0.936900\pi$
$163$	−15.0315	−	15.0315i	−1.17736	−	1.17736i	−0.196940	−	0.980416i	$-0.563100\pi$
$164$		0			0
$165$	−0.597287	+	3.31509i	−0.0464987	+	0.258080i
$166$		0			0
$167$	−2.09809	+	2.09809i	−0.162355	+	0.162355i	−0.783609	−	0.621254i	$-0.786624\pi$
$167$	−2.09809	+	2.09809i	−0.162355	+	0.162355i	0.621254	+	0.783609i	$0.286624\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$			15.0568i			1.15142i
$172$		0			0
$173$	4.34051	−	4.34051i	0.330003	−	0.330003i	−0.522585	−	0.852587i	$-0.675032\pi$
$173$	4.34051	−	4.34051i	0.330003	−	0.330003i	0.852587	+	0.522585i	$0.175032\pi$
$174$		0			0
$175$	−3.42128	−	7.48205i	−0.258624	−	0.565590i
$176$		0			0
$177$	−2.14569	−	2.14569i	−0.161280	−	0.161280i
$178$		0			0
$179$	3.65104			0.272892			0.136446	−	0.990648i	$-0.456432\pi$
$179$	3.65104			0.272892			0.136446	+	0.990648i	$0.456432\pi$
$180$		0			0
$181$	−10.4658			−0.777919			−0.388959	−	0.921255i	$-0.627165\pi$
$181$	−10.4658			−0.777919			−0.388959	+	0.921255i	$0.627165\pi$
$182$		0			0
$183$	−0.719745	−	0.719745i	−0.0532051	−	0.0532051i
$184$		0			0
$185$	−9.74516	−	1.75580i	−0.716478	−	0.129089i
$186$		0			0
$187$	−12.0269	+	12.0269i	−0.879498	+	0.879498i
$188$		0			0
$189$			3.37022i			0.245147i
$190$		0			0
$191$			22.1096i			1.59979i	0.600139	+	0.799896i	$0.295112\pi$
$191$			22.1096i			1.59979i	−0.600139	+	0.799896i	$0.704888\pi$
$192$		0			0
$193$	−17.3280	+	17.3280i	−1.24730	+	1.24730i	−0.290385	+	0.956910i	$0.593783\pi$
$193$	−17.3280	+	17.3280i	−1.24730	+	1.24730i	−0.956910	+	0.290385i	$0.906217\pi$
$194$		0			0
$195$	−0.639856	+	0.444488i	−0.0458210	+	0.0318304i
$196$		0			0
$197$	−7.75600	−	7.75600i	−0.552592	−	0.552592i	0.374596	−	0.927188i	$-0.377781\pi$
$197$	−7.75600	−	7.75600i	−0.552592	−	0.552592i	−0.927188	+	0.374596i	$0.877781\pi$
$198$		0			0
$199$	−2.10962			−0.149547			−0.0747733	−	0.997201i	$-0.523823\pi$
$199$	−2.10962			−0.149547			−0.0747733	+	0.997201i	$0.523823\pi$
$200$		0			0
$201$	5.02312			0.354303
$202$		0			0
$203$	−2.14206	−	2.14206i	−0.150343	−	0.150343i
$204$		0			0
$205$	−22.5496	+	15.6645i	−1.57493	+	1.09406i
$206$		0			0
$207$	5.94884	−	5.94884i	0.413473	−	0.413473i
$208$		0			0
$209$		−	22.6149i		−	1.56430i
$210$		0			0
$211$		−	25.5279i		−	1.75742i	−0.477360	−	0.878708i	$-0.658406\pi$
$211$		−	25.5279i		−	1.75742i	0.477360	−	0.878708i	$-0.341594\pi$
$212$		0			0
$213$	2.00088	−	2.00088i	0.137098	−	0.137098i
$214$		0			0
$215$	4.85166	+	0.874133i	0.330881	+	0.0596154i
$216$		0			0
$217$	10.0728	+	10.0728i	0.683784	+	0.683784i
$218$		0			0
$219$	−0.742991			−0.0502067
$220$		0			0
$221$	−3.93393			−0.264625
$222$		0			0
$223$	9.30177	+	9.30177i	0.622892	+	0.622892i	0.946270	−	0.323378i	$-0.104818\pi$
$223$	9.30177	+	9.30177i	0.622892	+	0.622892i	−0.323378	+	0.946270i	$0.604818\pi$
$224$		0			0
$225$	−13.4879	−	5.02337i	−0.899196	−	0.334891i
$226$		0			0
$227$	6.62201	−	6.62201i	0.439518	−	0.439518i	−0.452331	−	0.891850i	$-0.649408\pi$
$227$	6.62201	−	6.62201i	0.439518	−	0.439518i	0.891850	+	0.452331i	$0.149408\pi$
$228$		0			0
$229$		−	5.74449i		−	0.379607i	−0.981822	−	0.189803i	$-0.939215\pi$
$229$		−	5.74449i		−	0.379607i	0.981822	−	0.189803i	$-0.0607851\pi$
$230$		0			0
$231$		−	2.47872i		−	0.163088i
$232$		0			0
$233$	−17.5645	+	17.5645i	−1.15069	+	1.15069i	−0.164271	+	0.986415i	$0.552527\pi$
$233$	−17.5645	+	17.5645i	−1.15069	+	1.15069i	−0.986415	+	0.164271i	$0.947473\pi$
$234$		0			0
$235$	4.60335	−	25.5498i	0.300289	−	1.66668i
$236$		0			0
$237$	0.474681	+	0.474681i	0.0308339	+	0.0308339i
$238$		0			0
$239$	5.94145			0.384321			0.192160	−	0.981364i	$-0.438451\pi$
$239$	5.94145			0.384321			0.192160	+	0.981364i	$0.438451\pi$
$240$		0			0
$241$	28.9057			1.86198			0.930989	−	0.365046i	$-0.118947\pi$
$241$	28.9057			1.86198			0.930989	+	0.365046i	$0.118947\pi$
$242$		0			0
$243$	6.29673	+	6.29673i	0.403936	+	0.403936i
$244$		0			0
$245$	−5.47610	−	7.88304i	−0.349855	−	0.503629i
$246$		0			0
$247$	3.69858	−	3.69858i	0.235335	−	0.235335i
$248$		0			0
$249$		−	4.31946i		−	0.273735i
$250$		0			0
$251$			9.63201i			0.607967i	0.952677	+	0.303984i	$0.0983168\pi$
$251$			9.63201i			0.607967i	−0.952677	+	0.303984i	$0.901683\pi$
$252$		0			0
$253$	−8.93501	+	8.93501i	−0.561739	+	0.561739i
$254$		0			0
$255$	1.74858	+	2.51715i	0.109500	+	0.157630i
$256$		0			0
$257$	−1.68617	−	1.68617i	−0.105181	−	0.105181i	0.652558	−	0.757739i	$-0.273696\pi$
$257$	−1.68617	−	1.68617i	−0.105181	−	0.105181i	−0.757739	+	0.652558i	$0.773696\pi$
$258$		0			0
$259$	7.28653			0.452763
$260$		0			0
$261$	−5.29967			−0.328041
$262$		0			0
$263$	−18.1463	−	18.1463i	−1.11895	−	1.11895i	−0.991896	−	0.127050i	$-0.959449\pi$
$263$	−18.1463	−	18.1463i	−1.11895	−	1.11895i	−0.127050	−	0.991896i	$-0.540551\pi$
$264$		0			0
$265$	4.91739	−	27.2928i	0.302073	−	1.67658i
$266$		0			0
$267$	−2.03806	+	2.03806i	−0.124727	+	0.124727i
$268$		0			0
$269$		−	15.0349i		−	0.916697i	−0.888773	−	0.458349i	$-0.848441\pi$
$269$		−	15.0349i		−	0.916697i	0.888773	−	0.458349i	$-0.151559\pi$
$270$		0			0
$271$		−	26.1386i		−	1.58781i	−0.608044	−	0.793903i	$-0.708046\pi$
$271$		−	26.1386i		−	1.58781i	0.608044	−	0.793903i	$-0.291954\pi$
$272$		0			0
$273$	0.405386	−	0.405386i	0.0245351	−	0.0245351i
$274$		0			0
$275$	20.2585	+	7.54496i	1.22164	+	0.454978i
$276$		0			0
$277$	5.93922	+	5.93922i	0.356853	+	0.356853i	0.862652	−	0.505799i	$-0.168802\pi$
$277$	5.93922	+	5.93922i	0.356853	+	0.356853i	−0.505799	+	0.862652i	$0.668802\pi$
$278$		0			0
$279$	24.9210			1.49198
$280$		0			0
$281$	19.1333			1.14140			0.570699	−	0.821159i	$-0.306672\pi$
$281$	19.1333			1.14140			0.570699	+	0.821159i	$0.306672\pi$
$282$		0			0
$283$	−13.8566	−	13.8566i	−0.823691	−	0.823691i	0.162944	−	0.986635i	$-0.447901\pi$
$283$	−13.8566	−	13.8566i	−0.823691	−	0.823691i	−0.986635	+	0.162944i	$0.947901\pi$
$284$		0			0
$285$	−4.01053	−	0.722585i	−0.237563	−	0.0428022i
$286$		0			0
$287$	14.2865	−	14.2865i	0.843306	−	0.843306i
$288$		0			0
$289$		−	1.52421i		−	0.0896597i
$290$		0			0
$291$			2.64898i			0.155286i
$292$		0			0
$293$	−0.640034	+	0.640034i	−0.0373912	+	0.0373912i	−0.725555	−	0.688164i	$-0.758417\pi$
$293$	−0.640034	+	0.640034i	−0.0373912	+	0.0373912i	0.688164	+	0.725555i	$0.258417\pi$
$294$		0			0
$295$	−15.9940	+	11.1105i	−0.931206	+	0.646879i
$296$		0			0
$297$	−6.26191	−	6.26191i	−0.363353	−	0.363353i
$298$		0			0
$299$	−2.92258			−0.169017
$300$		0			0
$301$	−3.62763			−0.209093
$302$		0			0
$303$	−0.561359	−	0.561359i	−0.0322492	−	0.0322492i
$304$		0			0
$305$	−5.36498	+	3.72688i	−0.307198	+	0.213401i
$306$		0			0
$307$	0.455285	−	0.455285i	0.0259845	−	0.0259845i	−0.693995	−	0.719980i	$-0.744151\pi$
$307$	0.455285	−	0.455285i	0.0259845	−	0.0259845i	0.719980	+	0.693995i	$0.244151\pi$
$308$		0			0
$309$			0.916855i			0.0521581i
$310$		0			0
$311$			1.85115i			0.104969i	0.998622	+	0.0524845i	$0.0167140\pi$
$311$			1.85115i			0.104969i	−0.998622	+	0.0524845i	$0.983286\pi$
$312$		0			0
$313$	7.79621	−	7.79621i	0.440668	−	0.440668i	−0.451568	−	0.892236i	$-0.649135\pi$
$313$	7.79621	−	7.79621i	0.440668	−	0.440668i	0.892236	+	0.451568i	$0.149135\pi$
$314$		0			0
$315$	10.4234	+	1.87801i	0.587293	+	0.105814i
$316$		0			0
$317$	23.1131	+	23.1131i	1.29816	+	1.29816i	0.929605	+	0.368558i	$0.120148\pi$
$317$	23.1131	+	23.1131i	1.29816	+	1.29816i	0.368558	+	0.929605i	$0.379852\pi$
$318$		0			0
$319$	7.95997			0.445673
$320$		0			0
$321$	−2.70760			−0.151124
$322$		0			0
$323$	−14.5499	−	14.5499i	−0.809580	−	0.809580i
$324$		0			0
$325$	2.07926	+	4.54716i	0.115337	+	0.252231i
$326$		0			0
$327$	1.18088	−	1.18088i	0.0653029	−	0.0653029i
$328$		0			0
$329$			19.1038i			1.05322i
$330$		0			0
$331$			15.7085i			0.863417i	0.902013	+	0.431708i	$0.142089\pi$
$331$			15.7085i			0.863417i	−0.902013	+	0.431708i	$0.857911\pi$
$332$		0			0
$333$	9.01380	−	9.01380i	0.493953	−	0.493953i
$334$		0			0
$335$	5.71616	−	31.7262i	0.312307	−	1.73338i
$336$		0			0
$337$	−10.2727	−	10.2727i	−0.559591	−	0.559591i	0.369600	−	0.929191i	$-0.379495\pi$
$337$	−10.2727	−	10.2727i	−0.559591	−	0.559591i	−0.929191	+	0.369600i	$0.879495\pi$
$338$		0			0
$339$	−4.60605			−0.250166
$340$		0			0
$341$	−37.4307			−2.02699
$342$		0			0
$343$	13.1388	+	13.1388i	0.709431	+	0.709431i
$344$		0			0
$345$	1.29905	+	1.87003i	0.0699384	+	0.100679i
$346$		0			0
$347$	0.202668	−	0.202668i	0.0108798	−	0.0108798i	−0.701646	−	0.712526i	$-0.747551\pi$
$347$	0.202668	−	0.202668i	0.0108798	−	0.0108798i	0.712526	+	0.701646i	$0.247551\pi$
$348$		0			0
$349$			19.6839i			1.05365i	0.849973	+	0.526827i	$0.176618\pi$
$349$			19.6839i			1.05365i	−0.849973	+	0.526827i	$0.823382\pi$
$350$		0			0
$351$		−	2.04823i		−	0.109326i
$352$		0			0
$353$	−4.65116	+	4.65116i	−0.247556	+	0.247556i	−0.819967	−	0.572411i	$-0.806008\pi$
$353$	−4.65116	+	4.65116i	−0.247556	+	0.247556i	0.572411	+	0.819967i	$0.306008\pi$
$354$		0			0
$355$	−10.3607	−	14.9145i	−0.549886	−	0.791581i
$356$		0			0
$357$	−1.59476	−	1.59476i	−0.0844036	−	0.0844036i
$358$		0			0
$359$	0.640564			0.0338077			0.0169038	−	0.999857i	$-0.494619\pi$
$359$	0.640564			0.0338077			0.0169038	+	0.999857i	$0.494619\pi$
$360$		0			0
$361$	8.35897			0.439946
$362$		0			0
$363$	1.89543	+	1.89543i	0.0994841	+	0.0994841i
$364$		0			0
$365$	−0.845502	+	4.69275i	−0.0442556	+	0.245630i
$366$		0			0
$367$	−23.8146	+	23.8146i	−1.24311	+	1.24311i	−0.284409	+	0.958703i	$0.591797\pi$
$367$	−23.8146	+	23.8146i	−1.24311	+	1.24311i	−0.958703	+	0.284409i	$0.908203\pi$
$368$		0			0
$369$		−	35.3462i		−	1.84005i
$370$		0			0
$371$			20.4070i			1.05948i
$372$		0			0
$373$	−3.51904	+	3.51904i	−0.182209	+	0.182209i	−0.792318	−	0.610109i	$-0.791126\pi$
$373$	−3.51904	+	3.51904i	−0.182209	+	0.182209i	0.610109	+	0.792318i	$0.291126\pi$
$374$		0			0
$375$	1.98532	−	3.35158i	0.102522	−	0.173075i
$376$		0			0
$377$	1.30182	+	1.30182i	0.0670473	+	0.0670473i
$378$		0			0
$379$	21.2507			1.09158			0.545788	−	0.837924i	$-0.316231\pi$
$379$	21.2507			1.09158			0.545788	+	0.837924i	$0.316231\pi$
$380$		0			0
$381$	2.02651			0.103821
$382$		0			0
$383$	−16.1452	−	16.1452i	−0.824982	−	0.824982i	0.161836	−	0.986818i	$-0.448259\pi$
$383$	−16.1452	−	16.1452i	−0.824982	−	0.824982i	−0.986818	+	0.161836i	$0.948259\pi$
$384$		0			0
$385$	−15.6557	−	2.82071i	−0.797888	−	0.143757i
$386$		0			0
$387$	−4.48755	+	4.48755i	−0.228115	+	0.228115i
$388$		0			0
$389$			1.83207i			0.0928895i	0.998921	+	0.0464447i	$0.0147891\pi$
$389$			1.83207i			0.0928895i	−0.998921	+	0.0464447i	$0.985211\pi$
$390$		0			0
$391$			11.4972i			0.581438i
$392$		0			0
$393$	−1.59005	+	1.59005i	−0.0802072	+	0.0802072i
$394$		0			0
$395$	3.53827	−	2.45793i	0.178030	−	0.123672i
$396$		0			0
$397$	11.5929	+	11.5929i	0.581831	+	0.581831i	0.935406	−	0.353575i	$-0.115034\pi$
$397$	11.5929	+	11.5929i	0.581831	+	0.581831i	−0.353575	+	0.935406i	$0.615034\pi$
$398$		0			0
$399$	2.99870			0.150123
$400$		0			0
$401$	−5.97724			−0.298489			−0.149245	−	0.988800i	$-0.547684\pi$
$401$	−5.97724			−0.298489			−0.149245	+	0.988800i	$0.547684\pi$
$402$		0			0
$403$	−6.12165	−	6.12165i	−0.304941	−	0.304941i
$404$		0			0
$405$	14.5486	−	10.1065i	0.722927	−	0.502195i
$406$		0			0
$407$	−13.5385	+	13.5385i	−0.671078	+	0.671078i
$408$		0			0
$409$			5.68842i			0.281274i	0.990061	+	0.140637i	$0.0449151\pi$
$409$			5.68842i			0.281274i	−0.990061	+	0.140637i	$0.955085\pi$
$410$		0			0
$411$			4.90084i			0.241741i
$412$		0			0
$413$	10.1331	−	10.1331i	0.498618	−	0.498618i
$414$		0			0
$415$	−27.2818	−	4.91542i	−1.33921	−	0.241288i
$416$		0			0
$417$	−4.43046	−	4.43046i	−0.216961	−	0.216961i
$418$		0			0
$419$	−4.31787			−0.210942			−0.105471	−	0.994422i	$-0.533635\pi$
$419$	−4.31787			−0.210942			−0.105471	+	0.994422i	$0.533635\pi$
$420$		0			0
$421$	−6.27822			−0.305982			−0.152991	−	0.988228i	$-0.548890\pi$
$421$	−6.27822			−0.305982			−0.152991	+	0.988228i	$0.548890\pi$
$422$		0			0
$423$	23.6323	+	23.6323i	1.14904	+	1.14904i
$424$		0			0
$425$	17.8882	−	8.17966i	0.867705	−	0.396772i
$426$		0			0
$427$	3.39903	−	3.39903i	0.164491	−	0.164491i
$428$		0			0
$429$			1.50643i			0.0727310i
$430$		0			0
$431$			22.3369i			1.07593i	0.842967	+	0.537966i	$0.180807\pi$
$431$			22.3369i			1.07593i	−0.842967	+	0.537966i	$0.819193\pi$
$432$		0			0
$433$	3.99322	−	3.99322i	0.191902	−	0.191902i	−0.604616	−	0.796517i	$-0.706673\pi$
$433$	3.99322	−	3.99322i	0.191902	−	0.191902i	0.796517	+	0.604616i	$0.206673\pi$
$434$		0			0
$435$	0.254335	−	1.41162i	0.0121944	−	0.0676822i
$436$		0			0
$437$	−10.8094	−	10.8094i	−0.517083	−	0.517083i
$438$		0			0
$439$	−30.7390			−1.46709			−0.733546	−	0.679640i	$-0.762136\pi$
$439$	−30.7390			−1.46709			−0.733546	+	0.679640i	$0.762136\pi$
$440$		0			0
$441$	12.3566			0.588407
$442$		0			0
$443$	16.0102	+	16.0102i	0.760670	+	0.760670i	0.976443	−	0.215774i	$-0.0692273\pi$
$443$	16.0102	+	16.0102i	0.760670	+	0.760670i	−0.215774	+	0.976443i	$0.569227\pi$
$444$		0			0
$445$	10.5532	+	15.1917i	0.500270	+	0.720157i
$446$		0			0
$447$	−3.10258	+	3.10258i	−0.146747	+	0.146747i
$448$		0			0
$449$			10.1010i			0.476696i	0.971180	+	0.238348i	$0.0766058\pi$
$449$			10.1010i			0.476696i	−0.971180	+	0.238348i	$0.923394\pi$
$450$		0			0
$451$			53.0891i			2.49987i
$452$		0			0
$453$	−3.02524	+	3.02524i	−0.142138	+	0.142138i
$454$		0			0
$455$	−2.09911	−	3.02175i	−0.0984079	−	0.141662i
$456$		0			0
$457$	24.7257	+	24.7257i	1.15662	+	1.15662i	0.985197	+	0.171424i	$0.0548368\pi$
$457$	24.7257	+	24.7257i	1.15662	+	1.15662i	0.171424	+	0.985197i	$0.445163\pi$
$458$		0			0
$459$	−8.05757			−0.376095
$460$		0			0
$461$	−1.86674			−0.0869428			−0.0434714	−	0.999055i	$-0.513842\pi$
$461$	−1.86674			−0.0869428			−0.0434714	+	0.999055i	$0.513842\pi$
$462$		0			0
$463$	−0.712601	−	0.712601i	−0.0331174	−	0.0331174i	0.690354	−	0.723472i	$-0.257455\pi$
$463$	−0.712601	−	0.712601i	−0.0331174	−	0.0331174i	−0.723472	+	0.690354i	$0.757455\pi$
$464$		0			0
$465$	−1.19598	+	6.63797i	−0.0554621	+	0.307829i
$466$		0			0
$467$	7.79059	−	7.79059i	0.360506	−	0.360506i	−0.503493	−	0.863999i	$-0.667952\pi$
$467$	7.79059	−	7.79059i	0.360506	−	0.360506i	0.863999	+	0.503493i	$0.167952\pi$
$468$		0			0
$469$			23.7219i			1.09538i
$470$		0			0
$471$		−	3.11611i		−	0.143583i
$472$		0			0
$473$	6.74018	−	6.74018i	0.309914	−	0.309914i
$474$		0			0
$475$	−9.12773	+	24.5083i	−0.418809	+	1.12452i
$476$		0			0
$477$	25.2445	+	25.2445i	1.15587	+	1.15587i
$478$		0			0
$479$	29.4402			1.34516			0.672578	−	0.740026i	$-0.265187\pi$
$479$	29.4402			1.34516			0.672578	+	0.740026i	$0.265187\pi$
$480$		0			0
$481$	−4.42834			−0.201915
$482$		0			0
$483$	−1.18477	−	1.18477i	−0.0539090	−	0.0539090i
$484$		0			0
$485$	16.7310	+	3.01446i	0.759717	+	0.136880i
$486$		0			0
$487$	8.88941	−	8.88941i	0.402818	−	0.402818i	−0.476407	−	0.879225i	$-0.658061\pi$
$487$	8.88941	−	8.88941i	0.402818	−	0.402818i	0.879225	+	0.476407i	$0.158061\pi$
$488$		0			0
$489$			7.40662i			0.334939i
$490$		0			0
$491$		−	14.3436i		−	0.647319i	−0.946174	−	0.323659i	$-0.895087\pi$
$491$		−	14.3436i		−	0.647319i	0.946174	−	0.323659i	$-0.104913\pi$
$492$		0			0
$493$	5.12128	−	5.12128i	0.230651	−	0.230651i
$494$		0			0
$495$	−22.8562	+	15.8775i	−1.02731	+	0.713640i
$496$		0			0
$497$	9.44923	+	9.44923i	0.423856	+	0.423856i
$498$		0			0
$499$	−14.1398			−0.632986			−0.316493	−	0.948595i	$-0.602505\pi$
$499$	−14.1398			−0.632986			−0.316493	+	0.948595i	$0.602505\pi$
$500$		0			0
$501$	1.03382			0.0461876
$502$		0			0
$503$	30.6600	+	30.6600i	1.36706	+	1.36706i	0.864595	+	0.502469i	$0.167575\pi$
$503$	30.6600	+	30.6600i	1.36706	+	1.36706i	0.502469	+	0.864595i	$0.332425\pi$
$504$		0			0
$505$	−4.18437	+	2.90675i	−0.186202	+	0.129349i
$506$		0			0
$507$	−0.246371	+	0.246371i	−0.0109417	+	0.0109417i
$508$		0			0
$509$		−	17.4719i		−	0.774429i	−0.921990	−	0.387215i	$-0.873437\pi$
$509$		−	17.4719i		−	0.774429i	0.921990	−	0.387215i	$-0.126563\pi$
$510$		0			0
$511$		−	3.50881i		−	0.155221i
$512$		0			0
$513$	7.57553	−	7.57553i	0.334468	−	0.334468i
$514$		0			0
$515$	5.79088	+	1.04335i	0.255177	+	0.0459757i
$516$		0			0
$517$	−35.4951	−	35.4951i	−1.56107	−	1.56107i
$518$		0			0
$519$	−2.13875			−0.0938806
$520$		0			0
$521$	15.5798			0.682565			0.341282	−	0.939961i	$-0.389139\pi$
$521$	15.5798			0.682565			0.341282	+	0.939961i	$0.389139\pi$
$522$		0			0
$523$	−26.9403	−	26.9403i	−1.17802	−	1.17802i	−0.980249	−	0.197766i	$-0.936631\pi$
$523$	−26.9403	−	26.9403i	−1.17802	−	1.17802i	−0.197766	−	0.980249i	$-0.563369\pi$
$524$		0			0
$525$	−1.00045	+	2.68626i	−0.0436634	+	0.117238i
$526$		0			0
$527$	−24.0821	+	24.0821i	−1.04903	+	1.04903i
$528$		0			0
$529$		−	14.4586i		−	0.628633i
$530$		0			0
$531$		−	25.0703i		−	1.08796i
$532$		0			0
$533$	−8.68253	+	8.68253i	−0.376082	+	0.376082i
$534$		0			0
$535$	−3.08117	+	17.1013i	−0.133211	+	0.739354i
$536$		0			0
$537$	−0.899510	−	0.899510i	−0.0388167	−	0.0388167i
$538$		0			0
$539$	−18.5592			−0.799402
$540$		0			0
$541$	−2.30676			−0.0991754			−0.0495877	−	0.998770i	$-0.515791\pi$
$541$	−2.30676			−0.0991754			−0.0495877	+	0.998770i	$0.515791\pi$
$542$		0			0
$543$	2.57847	+	2.57847i	0.110653	+	0.110653i
$544$		0			0
$545$	−6.11467	−	8.80229i	−0.261924	−	0.377049i
$546$		0			0
$547$	−22.0332	+	22.0332i	−0.942073	+	0.942073i	−0.998412	−	0.0563390i	$-0.982057\pi$
$547$	−22.0332	+	22.0332i	−0.942073	+	0.942073i	0.0563390	+	0.998412i	$0.482057\pi$
$548$		0			0
$549$		−	8.40953i		−	0.358910i
$550$		0			0
$551$			9.62979i			0.410243i
$552$		0			0
$553$	−2.24170	+	2.24170i	−0.0953270	+	0.0953270i
$554$		0			0
$555$	1.96834	+	2.83350i	0.0835515	+	0.120275i
$556$		0			0
$557$	−12.3558	−	12.3558i	−0.523533	−	0.523533i	0.395104	−	0.918636i	$-0.370709\pi$
$557$	−12.3558	−	12.3558i	−0.523533	−	0.523533i	−0.918636	+	0.395104i	$0.870709\pi$
$558$		0			0
$559$	2.20466			0.0932474
$560$		0			0
$561$	5.92617			0.250203
$562$		0			0
$563$	10.4884	+	10.4884i	0.442033	+	0.442033i	0.892695	−	0.450662i	$-0.148812\pi$
$563$	10.4884	+	10.4884i	0.442033	+	0.442033i	−0.450662	+	0.892695i	$0.648812\pi$
$564$		0			0
$565$	−5.24155	+	29.0919i	−0.220514	+	1.22391i
$566$		0			0
$567$	−9.21741	+	9.21741i	−0.387095	+	0.387095i
$568$		0			0
$569$			37.7121i			1.58097i	0.612480	+	0.790486i	$0.290172\pi$
$569$			37.7121i			1.58097i	−0.612480	+	0.790486i	$0.709828\pi$
$570$		0			0
$571$		−	26.4970i		−	1.10887i	−0.832228	−	0.554433i	$-0.812935\pi$
$571$		−	26.4970i		−	1.10887i	0.832228	−	0.554433i	$-0.187065\pi$
$572$		0			0
$573$	5.44715	−	5.44715i	0.227558	−	0.227558i
$574$		0			0
$575$	13.2894	−	6.07679i	0.554207	−	0.253420i
$576$		0			0
$577$	4.94574	+	4.94574i	0.205894	+	0.205894i	0.802520	−	0.596626i	$-0.203492\pi$
$577$	4.94574	+	4.94574i	0.205894	+	0.205894i	−0.596626	+	0.802520i	$0.703492\pi$
$578$		0			0
$579$	8.53821			0.354836
$580$		0			0
$581$	20.3988			0.846287
$582$		0			0
$583$	−37.9165	−	37.9165i	−1.57034	−	1.57034i
$584$		0			0
$585$	−6.33475	−	1.14134i	−0.261910	−	0.0471888i
$586$		0			0
$587$	−25.4176	+	25.4176i	−1.04910	+	1.04910i	−0.0503663	+	0.998731i	$0.516039\pi$
$587$	−25.4176	+	25.4176i	−1.04910	+	1.04910i	−0.998731	+	0.0503663i	$0.983961\pi$
$588$		0			0
$589$		−	45.2828i		−	1.86585i
$590$		0			0
$591$			3.82170i			0.157204i
$592$		0			0
$593$	−14.9104	+	14.9104i	−0.612298	+	0.612298i	−0.943544	−	0.331246i	$-0.892531\pi$
$593$	−14.9104	+	14.9104i	−0.612298	+	0.612298i	0.331246	+	0.943544i	$0.392531\pi$
$594$		0			0
$595$	−11.8873	+	8.25776i	−0.487333	+	0.338535i
$596$		0			0
$597$	0.519747	+	0.519747i	0.0212718	+	0.0212718i
$598$		0			0
$599$	2.65582			0.108514			0.0542569	−	0.998527i	$-0.482721\pi$
$599$	2.65582			0.108514			0.0542569	+	0.998527i	$0.482721\pi$
$600$		0			0
$601$	28.2609			1.15279			0.576394	−	0.817172i	$-0.304459\pi$
$601$	28.2609			1.15279			0.576394	+	0.817172i	$0.304459\pi$
$602$		0			0
$603$	29.3451	+	29.3451i	1.19503	+	1.19503i
$604$		0			0
$605$	14.1285	−	9.81463i	0.574406	−	0.399021i
$606$		0			0
$607$	6.81993	−	6.81993i	0.276813	−	0.276813i	−0.555023	−	0.831835i	$-0.687290\pi$
$607$	6.81993	−	6.81993i	0.276813	−	0.276813i	0.831835	+	0.555023i	$0.187290\pi$
$608$		0			0
$609$			1.05548i			0.0427703i
$610$		0			0
$611$		−	11.6102i		−	0.469697i
$612$		0			0
$613$	32.8434	−	32.8434i	1.32653	−	1.32653i	0.418160	−	0.908373i	$-0.362675\pi$
$613$	32.8434	−	32.8434i	1.32653	−	1.32653i	0.908373	−	0.418160i	$-0.137325\pi$
$614$		0			0
$615$	9.41484	+	1.69629i	0.379643	+	0.0684010i
$616$		0			0
$617$	−3.80269	−	3.80269i	−0.153090	−	0.153090i	0.626406	−	0.779497i	$-0.284525\pi$
$617$	−3.80269	−	3.80269i	−0.153090	−	0.153090i	−0.779497	+	0.626406i	$0.784525\pi$
$618$		0			0
$619$	−0.734037			−0.0295034			−0.0147517	−	0.999891i	$-0.504696\pi$
$619$	−0.734037			−0.0295034			−0.0147517	+	0.999891i	$0.504696\pi$
$620$		0			0
$621$	−5.98610			−0.240214
$622$		0			0
$623$	−9.62485	−	9.62485i	−0.385611	−	0.385611i
$624$		0			0
$625$	−18.9095	−	16.3534i	−0.756378	−	0.654134i
$626$		0			0
$627$	−5.57164	+	5.57164i	−0.222510	+	0.222510i
$628$		0			0
$629$			17.4208i			0.694612i
$630$		0			0
$631$			16.7470i			0.666688i	0.942805	+	0.333344i	$0.108177\pi$
$631$			16.7470i			0.666688i	−0.942805	+	0.333344i	$0.891823\pi$
$632$		0			0
$633$	−6.28933	+	6.28933i	−0.249979	+	0.249979i
$634$		0			0
$635$	2.30611	−	12.7995i	0.0915151	−	0.507932i
$636$		0			0
$637$	−3.03529	−	3.03529i	−0.120263	−	0.120263i
$638$		0			0
$639$	23.3783			0.924832
$640$		0			0
$641$	−0.737562			−0.0291319			−0.0145660	−	0.999894i	$-0.504637\pi$
$641$	−0.737562			−0.0291319			−0.0145660	+	0.999894i	$0.504637\pi$
$642$		0			0
$643$	29.4334	+	29.4334i	1.16074	+	1.16074i	0.984314	+	0.176424i	$0.0564531\pi$
$643$	29.4334	+	29.4334i	1.16074	+	1.16074i	0.176424	+	0.984314i	$0.443547\pi$
$644$		0			0
$645$	−0.979946	−	1.41067i	−0.0385853	−	0.0555450i
$646$		0			0
$647$	31.5530	−	31.5530i	1.24048	−	1.24048i	0.280672	−	0.959804i	$-0.409443\pi$
$647$	31.5530	−	31.5530i	1.24048	−	1.24048i	0.959804	−	0.280672i	$-0.0905573\pi$
$648$		0			0
$649$			37.6550i			1.47809i
$650$		0			0
$651$		−	4.96327i		−	0.194526i
$652$		0			0
$653$	2.53459	−	2.53459i	0.0991863	−	0.0991863i	−0.655772	−	0.754959i	$-0.727657\pi$
$653$	2.53459	−	2.53459i	0.0991863	−	0.0991863i	0.754959	+	0.655772i	$0.227657\pi$
$654$		0			0
$655$	8.23335	+	11.8522i	0.321704	+	0.463104i
$656$		0			0
$657$	−4.34057	−	4.34057i	−0.169342	−	0.169342i
$658$		0			0
$659$	15.0824			0.587525			0.293762	−	0.955878i	$-0.405093\pi$
$659$	15.0824			0.587525			0.293762	+	0.955878i	$0.405093\pi$
$660$		0			0
$661$	−34.5297			−1.34305			−0.671525	−	0.740982i	$-0.734361\pi$
$661$	−34.5297			−1.34305			−0.671525	+	0.740982i	$0.734361\pi$
$662$		0			0
$663$	0.969204	+	0.969204i	0.0376408	+	0.0376408i
$664$		0			0
$665$	3.41244	−	18.9399i	0.132329	−	0.734458i
$666$		0			0
$667$	3.80468	−	3.80468i	0.147318	−	0.147318i
$668$		0			0
$669$		−	4.58336i		−	0.177203i
$670$		0			0
$671$			12.6309i			0.487610i
$672$		0			0
$673$	−23.1456	+	23.1456i	−0.892196	+	0.892196i	−0.994730	−	0.102534i	$-0.967305\pi$
$673$	−23.1456	+	23.1456i	−0.892196	+	0.892196i	0.102534	+	0.994730i	$0.467305\pi$
$674$		0			0
$675$	4.25879	+	9.31362i	0.163921	+	0.358481i
$676$		0			0
$677$	21.2732	+	21.2732i	0.817594	+	0.817594i	0.985759	−	0.168165i	$-0.0537841\pi$
$677$	21.2732	+	21.2732i	0.817594	+	0.817594i	−0.168165	+	0.985759i	$0.553784\pi$
$678$		0			0
$679$	−12.5099			−0.480087
$680$		0			0
$681$	−3.26294			−0.125036
$682$		0			0
$683$	10.8905	+	10.8905i	0.416715	+	0.416715i	0.884070	−	0.467355i	$-0.154793\pi$
$683$	10.8905	+	10.8905i	0.416715	+	0.416715i	−0.467355	+	0.884070i	$0.654793\pi$
$684$		0			0
$685$	30.9539	+	5.57702i	1.18269	+	0.213087i
$686$		0			0
$687$	−1.41527	+	1.41527i	−0.0539961	+	0.0539961i
$688$		0			0
$689$		−	12.4022i		−	0.472487i
$690$		0			0
$691$		−	14.8406i		−	0.564562i	−0.959332	−	0.282281i	$-0.908909\pi$
$691$		−	14.8406i		−	0.564562i	0.959332	−	0.282281i	$-0.0910910\pi$
$692$		0			0
$693$	14.4807	−	14.4807i	0.550078	−	0.550078i
$694$		0			0
$695$	−33.0247	+	22.9412i	−1.25270	+	0.870209i
$696$		0			0
$697$	34.1564	+	34.1564i	1.29377	+	1.29377i
$698$		0			0
$699$	8.65473			0.327352
$700$		0			0
$701$	28.5818			1.07952			0.539760	−	0.841819i	$-0.318515\pi$
$701$	28.5818			1.07952			0.539760	+	0.841819i	$0.318515\pi$
$702$		0			0
$703$	−16.3786	−	16.3786i	−0.617729	−	0.617729i
$704$		0			0
$705$	−7.42884	+	5.16058i	−0.279786	+	0.194359i
$706$		0			0
$707$	2.65104	−	2.65104i	0.0997027	−	0.0997027i
$708$		0			0
$709$		−	32.4717i		−	1.21950i	−0.792593	−	0.609751i	$-0.791269\pi$
$709$		−	32.4717i		−	1.21950i	0.792593	−	0.609751i	$-0.208731\pi$
$710$		0			0
$711$			5.54619i			0.207999i
$712$		0			0
$713$	−17.8910	+	17.8910i	−0.670023	+	0.670023i
$714$		0			0
$715$	9.51463	+	1.71427i	0.355827	+	0.0641101i
$716$		0			0
$717$	−1.46380	−	1.46380i	−0.0546666	−	0.0546666i
$718$		0			0
$719$	−13.3806			−0.499012			−0.249506	−	0.968373i	$-0.580268\pi$
$719$	−13.3806			−0.499012			−0.249506	+	0.968373i	$0.580268\pi$
$720$		0			0
$721$	−4.32989			−0.161254
$722$		0			0
$723$	−7.12151	−	7.12151i	−0.264852	−	0.264852i
$724$		0			0
$725$	−8.62643	−	3.21277i	−0.320378	−	0.119319i
$726$		0			0
$727$	17.7614	−	17.7614i	0.658734	−	0.658734i	−0.296346	−	0.955081i	$-0.595768\pi$
$727$	17.7614	−	17.7614i	0.658734	−	0.658734i	0.955081	+	0.296346i	$0.0957682\pi$
$728$		0			0
$729$			20.6638i			0.765327i
$730$		0			0
$731$		−	8.67299i		−	0.320782i
$732$		0			0
$733$	0.0966147	−	0.0966147i	0.00356855	−	0.00356855i	−0.705320	−	0.708889i	$-0.749197\pi$
$733$	0.0966147	−	0.0966147i	0.00356855	−	0.00356855i	0.708889	+	0.705320i	$0.249197\pi$
$734$		0			0
$735$	−0.593000	+	3.29130i	−0.0218731	+	0.121401i
$736$		0			0
$737$	−44.0756	−	44.0756i	−1.62355	−	1.62355i
$738$		0			0
$739$	−35.1261			−1.29214			−0.646068	−	0.763280i	$-0.723588\pi$
$739$	−35.1261			−1.29214			−0.646068	+	0.763280i	$0.723588\pi$
$740$		0			0
$741$	−1.82244			−0.0669491
$742$		0			0
$743$	−2.76695	−	2.76695i	−0.101510	−	0.101510i	0.654528	−	0.756038i	$-0.272867\pi$
$743$	−2.76695	−	2.76695i	−0.101510	−	0.101510i	−0.756038	+	0.654528i	$0.772867\pi$
$744$		0			0
$745$	16.0654	+	23.1267i	0.588589	+	0.847295i
$746$		0			0
$747$	25.2344	−	25.2344i	0.923277	−	0.923277i
$748$		0			0
$749$		−	12.7868i		−	0.467219i
$750$		0			0
$751$		−	28.1711i		−	1.02798i	−0.857797	−	0.513989i	$-0.828167\pi$
$751$		−	28.1711i		−	1.02798i	0.857797	−	0.513989i	$-0.171833\pi$
$752$		0			0
$753$	2.37304	−	2.37304i	0.0864785	−	0.0864785i
$754$		0			0
$755$	15.6649	+	22.5502i	0.570104	+	0.820685i
$756$		0			0
$757$	2.05357	+	2.05357i	0.0746383	+	0.0746383i	0.743440	−	0.668802i	$-0.233193\pi$
$757$	2.05357	+	2.05357i	0.0746383	+	0.0746383i	−0.668802	+	0.743440i	$0.733193\pi$
$758$		0			0
$759$	4.40265			0.159806
$760$		0			0
$761$	25.0768			0.909035			0.454518	−	0.890738i	$-0.349812\pi$
$761$	25.0768			0.909035			0.454518	+	0.890738i	$0.349812\pi$
$762$		0			0
$763$	5.57677	+	5.57677i	0.201893	+	0.201893i
$764$		0			0
$765$	−4.48997	+	24.9205i	−0.162335	+	0.901001i
$766$		0			0
$767$	−6.15834	+	6.15834i	−0.222365	+	0.222365i
$768$		0			0
$769$			19.7961i			0.713865i	0.934130	+	0.356933i	$0.116177\pi$
$769$			19.7961i			0.713865i	−0.934130	+	0.356933i	$0.883823\pi$
$770$		0			0
$771$			0.830847i			0.0299222i
$772$		0			0
$773$	26.8647	−	26.8647i	0.966256	−	0.966256i	−0.0331930	−	0.999449i	$-0.510568\pi$
$773$	26.8647	−	26.8647i	0.966256	−	0.966256i	0.999449	+	0.0331930i	$0.0105676\pi$
$774$		0			0
$775$	40.5647	+	15.1076i	1.45713	+	0.542683i
$776$		0			0
$777$	−1.79519	−	1.79519i	−0.0644020	−	0.0644020i
$778$		0			0
$779$	−64.2260			−2.30114
$780$		0			0
$781$	−35.1136			−1.25646
$782$		0			0
$783$	2.66643	+	2.66643i	0.0952904	+	0.0952904i
$784$		0			0
$785$	−19.6815	−	3.54604i	−0.702461	−	0.126564i
$786$		0			0
$787$	11.2158	−	11.2158i	0.399801	−	0.399801i	−0.478362	−	0.878163i	$-0.658769\pi$
$787$	11.2158	−	11.2158i	0.399801	−	0.399801i	0.878163	+	0.478362i	$0.158769\pi$
$788$		0			0
$789$			8.94141i			0.318323i
$790$		0			0
$791$		−	21.7523i		−	0.773421i
$792$		0			0
$793$	−2.06574	+	2.06574i	−0.0733565	+	0.0733565i
$794$		0			0
$795$	−7.93563	+	5.51263i	−0.281448	+	0.195513i
$796$		0			0
$797$	0.0427440	+	0.0427440i	0.00151407	+	0.00151407i	0.707863	−	0.706349i	$-0.249659\pi$
$797$	0.0427440	+	0.0427440i	0.00151407	+	0.00151407i	−0.706349	+	0.707863i	$0.749659\pi$
$798$		0			0
$799$	−45.6736			−1.61582
$800$		0			0
$801$	−23.8128			−0.841384
$802$		0			0
$803$	6.51942	+	6.51942i	0.230065	+	0.230065i
$804$		0			0
$805$	−8.83129	+	6.13482i	−0.311262	+	0.216224i
$806$		0			0
$807$	−3.70417	+	3.70417i	−0.130393	+	0.130393i
$808$		0			0
$809$			25.4690i			0.895443i	0.894173	+	0.447721i	$0.147764\pi$
$809$			25.4690i			0.895443i	−0.894173	+	0.447721i	$0.852236\pi$
$810$		0			0
$811$			7.67222i			0.269408i	0.990886	+	0.134704i	$0.0430084\pi$
$811$			7.67222i			0.269408i	−0.990886	+	0.134704i	$0.956992\pi$
$812$		0			0
$813$	−6.43978	+	6.43978i	−0.225853	+	0.225853i
$814$		0			0
$815$	46.7805	+	8.42852i	1.63865	+	0.295238i
$816$		0			0
$817$	8.15413	+	8.15413i	0.285277	+	0.285277i
$818$		0			0
$819$	4.73655			0.165508
$820$		0			0
$821$	4.39287			0.153312			0.0766561	−	0.997058i	$-0.475576\pi$
$821$	4.39287			0.153312			0.0766561	+	0.997058i	$0.475576\pi$
$822$		0			0
$823$	−1.13588	−	1.13588i	−0.0395944	−	0.0395944i	0.687032	−	0.726627i	$-0.258913\pi$
$823$	−1.13588	−	1.13588i	−0.0395944	−	0.0395944i	−0.726627	+	0.687032i	$0.758913\pi$
$824$		0			0
$825$	−3.13225	−	6.84996i	−0.109051	−	0.238485i
$826$		0			0
$827$	−11.9176	+	11.9176i	−0.414415	+	0.414415i	−0.883273	−	0.468858i	$-0.844665\pi$
$827$	−11.9176	+	11.9176i	−0.414415	+	0.414415i	0.468858	+	0.883273i	$0.344665\pi$
$828$		0			0
$829$		−	37.4933i		−	1.30220i	−0.758993	−	0.651098i	$-0.774309\pi$
$829$		−	37.4933i		−	1.30220i	0.758993	−	0.651098i	$-0.225691\pi$
$830$		0			0
$831$		−	2.92650i		−	0.101519i
$832$		0			0
$833$	−11.9406	+	11.9406i	−0.413718	+	0.413718i
$834$		0			0
$835$	1.17645	−	6.52962i	0.0407129	−	0.225967i
$836$		0			0
$837$	−12.5385	−	12.5385i	−0.433395	−	0.433395i
$838$		0			0
$839$	−17.7228			−0.611859			−0.305930	−	0.952054i	$-0.598967\pi$
$839$	−17.7228			−0.611859			−0.305930	+	0.952054i	$0.598967\pi$
$840$		0			0
$841$	25.6105			0.883121
$842$		0			0
$843$	−4.71388	−	4.71388i	−0.162355	−	0.162355i
$844$		0			0
$845$	1.27572	+	1.83645i	0.0438861	+	0.0631757i
$846$		0			0
$847$	−8.95124	+	8.95124i	−0.307568	+	0.307568i
$848$		0			0
$849$			6.82773i			0.234327i
$850$		0			0
$851$			12.9422i			0.443652i
$852$		0			0
$853$	−1.04281	+	1.04281i	−0.0357052	+	0.0357052i	−0.724734	−	0.689029i	$-0.758037\pi$
$853$	−1.04281	+	1.04281i	−0.0357052	+	0.0357052i	0.689029	+	0.724734i	$0.258037\pi$
$854$		0			0
$855$	−19.2082	−	27.6509i	−0.656908	−	0.945642i
$856$		0			0
$857$	−26.3137	−	26.3137i	−0.898857	−	0.898857i	0.0964779	−	0.995335i	$-0.469242\pi$
$857$	−26.3137	−	26.3137i	−0.898857	−	0.898857i	−0.995335	+	0.0964779i	$0.969242\pi$
$858$		0			0
$859$	−13.2757			−0.452961			−0.226480	−	0.974016i	$-0.572722\pi$
$859$	−13.2757			−0.452961			−0.226480	+	0.974016i	$0.572722\pi$
$860$		0			0
$861$	−7.03955			−0.239907
$862$		0			0
$863$	−3.34086	−	3.34086i	−0.113724	−	0.113724i	0.647955	−	0.761679i	$-0.275625\pi$
$863$	−3.34086	−	3.34086i	−0.113724	−	0.113724i	−0.761679	+	0.647955i	$0.775625\pi$
$864$		0			0
$865$	−2.43383	+	13.5084i	−0.0827528	+	0.459299i
$866$		0			0
$867$	−0.375522	+	0.375522i	−0.0127534	+	0.0127534i
$868$		0			0
$869$		−	8.33024i		−	0.282584i
$870$		0			0
$871$		−	14.4168i		−	0.488495i
$872$		0			0
$873$	−15.4754	+	15.4754i	−0.523763	+	0.523763i
$874$		0			0
$875$	15.8280	+	9.37578i	0.535084	+	0.316959i
$876$		0			0
$877$	−1.82995	−	1.82995i	−0.0617929	−	0.0617929i	0.675535	−	0.737328i	$-0.263913\pi$
$877$	−1.82995	−	1.82995i	−0.0617929	−	0.0617929i	−0.737328	+	0.675535i	$0.763913\pi$
$878$		0			0
$879$	0.315371			0.0106372
$880$		0			0
$881$	−0.983071			−0.0331205			−0.0165603	−	0.999863i	$-0.505272\pi$
$881$	−0.983071			−0.0331205			−0.0165603	+	0.999863i	$0.505272\pi$
$882$		0			0
$883$	−5.42128	−	5.42128i	−0.182441	−	0.182441i	0.609978	−	0.792418i	$-0.291178\pi$
$883$	−5.42128	−	5.42128i	−0.182441	−	0.182441i	−0.792418	+	0.609978i	$0.791178\pi$
$884$		0			0
$885$	6.67775	+	1.20314i	0.224470	+	0.0404432i
$886$		0			0
$887$	37.3247	−	37.3247i	1.25324	−	1.25324i	0.298982	−	0.954259i	$-0.403353\pi$
$887$	37.3247	−	37.3247i	1.25324	−	1.25324i	0.954259	−	0.298982i	$-0.0966472\pi$
$888$		0			0
$889$			9.57028i			0.320977i
$890$		0			0
$891$		−	34.2522i		−	1.14749i
$892$		0			0
$893$	42.9412	−	42.9412i	1.43697	−	1.43697i
$894$		0			0
$895$	−6.70495	+	4.65771i	−0.224122	+	0.155690i
$896$		0			0
$897$	0.720037	+	0.720037i	0.0240413	+	0.0240413i
$898$		0			0
$899$	15.9386			0.531583
$900$		0			0
$901$	−48.7894			−1.62541
$902$		0			0
$903$	0.893740	+	0.893740i	0.0297418	+	0.0297418i
$904$		0			0
$905$	19.2199	−	13.3515i	0.638892	−	0.443818i
$906$		0			0
$907$	34.9197	−	34.9197i	1.15949	−	1.15949i	0.174903	−	0.984586i	$-0.444039\pi$
$907$	34.9197	−	34.9197i	1.15949	−	1.15949i	0.984586	−	0.174903i	$-0.0559611\pi$
$908$		0			0
$909$		−	6.55894i		−	0.217546i
$910$		0			0
$911$			19.2932i			0.639211i	0.947551	+	0.319606i	$0.103550\pi$
$911$			19.2932i			0.639211i	−0.947551	+	0.319606i	$0.896450\pi$
$912$		0			0
$913$	−37.9013	+	37.9013i	−1.25435	+	1.25435i
$914$		0			0
$915$	2.23997	+	0.403579i	0.0740511	+	0.0133419i
$916$		0			0
$917$	−7.50906	−	7.50906i	−0.247971	−	0.247971i
$918$		0			0
$919$	−23.2893			−0.768243			−0.384122	−	0.923283i	$-0.625496\pi$
$919$	−23.2893			−0.768243			−0.384122	+	0.923283i	$0.625496\pi$
$920$		0			0
$921$	−0.224338			−0.00739218
$922$		0			0
$923$	−5.74270	−	5.74270i	−0.189023	−	0.189023i
$924$		0			0
$925$	20.1364	−	9.20767i	0.662080	−	0.302746i
$926$		0			0
$927$	−5.35629	+	5.35629i	−0.175923	+	0.175923i
$928$		0			0
$929$			51.0425i			1.67465i	0.546705	+	0.837326i	$0.315882\pi$
$929$			51.0425i			1.67465i	−0.546705	+	0.837326i	$0.684118\pi$
$930$		0			0
$931$		−	22.4525i		−	0.735852i
$932$		0			0
$933$	0.456068	−	0.456068i	0.0149310	−	0.0149310i
$934$		0			0
$935$	6.74381	−	37.4299i	0.220546	−	1.22409i
$936$		0			0
$937$	−21.9246	−	21.9246i	−0.716245	−	0.716245i	0.251589	−	0.967834i	$-0.419047\pi$
$937$	−21.9246	−	21.9246i	−0.716245	−	0.716245i	−0.967834	+	0.251589i	$0.919047\pi$
$938$		0			0
$939$	−3.84152			−0.125363
$940$		0			0
$941$	58.1843			1.89675			0.948376	−	0.317147i	$-0.102725\pi$
$941$	58.1843			1.89675			0.948376	+	0.317147i	$0.102725\pi$
$942$		0			0
$943$	25.3754	+	25.3754i	0.826335	+	0.826335i
$944$		0			0
$945$	−4.29946	−	6.18922i	−0.139861	−	0.201335i
$946$		0			0
$947$	20.5621	−	20.5621i	0.668178	−	0.668178i	−0.289116	−	0.957294i	$-0.593361\pi$
$947$	20.5621	−	20.5621i	0.668178	−	0.668178i	0.957294	+	0.289116i	$0.0933613\pi$
$948$		0			0
$949$			2.13245i			0.0692224i
$950$		0			0
$951$		−	11.3888i		−	0.369307i
$952$		0			0
$953$	−10.8259	+	10.8259i	−0.350684	+	0.350684i	−0.860364	−	0.509680i	$-0.829764\pi$
$953$	−10.8259	+	10.8259i	−0.350684	+	0.350684i	0.509680	+	0.860364i	$0.329764\pi$
$954$		0			0
$955$	−28.2056	−	40.6030i	−0.912713	−	1.31388i
$956$		0			0
$957$	−1.96110	−	1.96110i	−0.0633934	−	0.0633934i
$958$		0			0
$959$	−23.1445			−0.747374
$960$		0			0
$961$	−43.9493			−1.41772
$962$		0			0
$963$	−15.8179	−	15.8179i	−0.509724	−	0.509724i
$964$		0			0
$965$	9.71623	−	53.9276i	0.312777	−	1.73599i
$966$		0			0
$967$	6.31772	−	6.31772i	0.203164	−	0.203164i	−0.598190	−	0.801354i	$-0.704113\pi$
$967$	6.31772	−	6.31772i	0.203164	−	0.203164i	0.801354	+	0.598190i	$0.204113\pi$
$968$		0			0
$969$			7.16935i			0.230313i
$970$		0			0
$971$			31.2104i			1.00159i	0.865566	+	0.500795i	$0.166959\pi$
$971$			31.2104i			1.00159i	−0.865566	+	0.500795i	$0.833041\pi$
$972$		0			0
$973$	20.9231	−	20.9231i	0.670763	−	0.670763i
$974$		0			0
$975$	0.608019	−	1.63255i	0.0194722	−	0.0522836i
$976$		0			0
$977$	13.2434	+	13.2434i	0.423692	+	0.423692i	0.886473	−	0.462781i	$-0.153148\pi$
$977$	13.2434	+	13.2434i	0.423692	+	0.423692i	−0.462781	+	0.886473i	$0.653148\pi$
$978$		0			0
$979$	35.7662			1.14309
$980$		0			0
$981$	13.7975			0.440519
$982$		0			0
$983$	−31.1731	−	31.1731i	−0.994267	−	0.994267i	0.00571644	−	0.999984i	$-0.498180\pi$
$983$	−31.1731	−	31.1731i	−0.994267	−	0.994267i	−0.999984	+	0.00571644i	$0.998180\pi$
$984$		0			0
$985$	24.1380	+	4.34898i	0.769099	+	0.138570i
$986$		0			0
$987$	4.70660	−	4.70660i	0.149813	−	0.149813i
$988$		0			0
$989$		−	6.44330i		−	0.204885i
$990$		0			0
$991$		−	32.1409i		−	1.02099i	−0.859881	−	0.510494i	$-0.829462\pi$
$991$		−	32.1409i		−	1.02099i	0.859881	−	0.510494i	$-0.170538\pi$
$992$		0			0
$993$	3.87011	−	3.87011i	0.122814	−	0.122814i
$994$		0			0
$995$	3.87420	−	2.69128i	0.122820	−	0.0853194i
$996$		0			0
$997$	−28.6825	−	28.6825i	−0.908385	−	0.908385i	0.0877572	−	0.996142i	$-0.472030\pi$
$997$	−28.6825	−	28.6825i	−0.908385	−	0.908385i	−0.996142	+	0.0877572i	$0.972030\pi$
$998$		0			0
$999$	−9.07024			−0.286970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bp.b.287.12	✓	48
4.3	odd	2	inner	1040.2.bp.b.287.13	yes	48
5.3	odd	4	inner	1040.2.bp.b.703.13	yes	48
20.3	even	4	inner	1040.2.bp.b.703.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1040.2.bp.b.287.12	✓	48	1.1	even	1	trivial
1040.2.bp.b.287.13	yes	48	4.3	odd	2	inner
1040.2.bp.b.703.12	yes	48	20.3	even	4	inner
1040.2.bp.b.703.13	yes	48	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bp (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.246371 - 0.246371i) q^{3} +(-1.83645 + 1.27572i) q^{5} +(1.16350 - 1.16350i) q^{7} -2.87860i q^{9} +O(q^{10})\)	\(q+(-0.246371 - 0.246371i) q^{3} +(-1.83645 + 1.27572i) q^{5} +(1.16350 - 1.16350i) q^{7} -2.87860i q^{9} +4.32359i q^{11} +(-0.707107 + 0.707107i) q^{13} +(0.766746 + 0.138146i) q^{15} +(2.78171 + 2.78171i) q^{17} -5.23058 q^{19} -0.573302 q^{21} +(2.06657 + 2.06657i) q^{23} +(1.74507 - 4.68559i) q^{25} +(-1.44831 + 1.44831i) q^{27} -1.84106i q^{29} +8.65733i q^{31} +(1.06520 - 1.06520i) q^{33} +(-0.652402 + 3.62100i) q^{35} +(3.13131 + 3.13131i) q^{37} +0.348421 q^{39} +12.2790 q^{41} +(-1.55893 - 1.55893i) q^{43} +(3.67230 + 5.28640i) q^{45} +(-8.20963 + 8.20963i) q^{47} +4.29255i q^{49} -1.37066i q^{51} +(-8.76970 + 8.76970i) q^{53} +(-5.51569 - 7.94003i) q^{55} +(1.28866 + 1.28866i) q^{57} +8.70920 q^{59} +2.92139 q^{61} +(-3.34924 - 3.34924i) q^{63} +(0.396493 - 2.20063i) q^{65} +(-10.1942 + 10.1942i) q^{67} -1.01829i q^{69} +8.12141i q^{71} +(1.50787 - 1.50787i) q^{73} +(-1.58432 + 0.724457i) q^{75} +(5.03048 + 5.03048i) q^{77} -1.92670 q^{79} -7.92217 q^{81} +(8.76618 + 8.76618i) q^{83} +(-8.65714 - 1.55977i) q^{85} +(-0.453582 + 0.453582i) q^{87} -8.27235i q^{89} +1.64543i q^{91} +(2.13291 - 2.13291i) q^{93} +(9.60568 - 6.67276i) q^{95} +(-5.37601 - 5.37601i) q^{97} +12.4459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5}+O(q^{10}) \) 48 * q + 8 * q^5	\( 48 q + 8 q^{5} - 16 q^{17} + 32 q^{21} + 16 q^{25} - 24 q^{33} + 24 q^{37} - 16 q^{41} - 48 q^{45} + 40 q^{53} - 8 q^{57} - 16 q^{61} + 40 q^{73} - 72 q^{77} - 160 q^{81} - 64 q^{85} - 8 q^{93} + 16 q^{97}+O(q^{100}) \) 48 * q + 8 * q^5 - 16 * q^17 + 32 * q^21 + 16 * q^25 - 24 * q^33 + 24 * q^37 - 16 * q^41 - 48 * q^45 + 40 * q^53 - 8 * q^57 - 16 * q^61 + 40 * q^73 - 72 * q^77 - 160 * q^81 - 64 * q^85 - 8 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

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