LMFDB - Embedded newform 800.2.bq.b.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

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

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

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.2
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.b.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.802897 - 1.57577i) q^{3} +(1.58800 - 1.57424i) q^{5} +(1.63701 + 1.63701i) q^{7} +(-0.0750643 + 0.103317i) q^{9} +(-1.12357 - 1.54647i) q^{11} +(-0.802739 - 5.06830i) q^{13} +(-3.75566 - 1.23838i) q^{15} +(5.98323 + 3.04861i) q^{17} +(1.06996 + 3.29301i) q^{19} +(1.26521 - 3.89391i) q^{21} +(0.167463 - 1.05732i) q^{23} +(0.0435082 - 4.99981i) q^{25} +(-5.01720 - 0.794647i) q^{27} +(1.58725 + 0.515730i) q^{29} +(-2.42148 + 0.786787i) q^{31} +(-1.53477 + 3.01215i) q^{33} +(5.17664 + 0.0225230i) q^{35} +(2.41558 - 0.382590i) q^{37} +(-7.34197 + 5.33426i) q^{39} +(-3.16381 - 2.29864i) q^{41} +(5.65583 - 5.65583i) q^{43} +(0.0434441 + 0.282238i) q^{45} +(-2.00667 + 1.02245i) q^{47} -1.64038i q^{49} -11.8759i q^{51} +(-10.8796 + 5.54343i) q^{53} +(-4.21876 - 0.687014i) q^{55} +(4.32997 - 4.32997i) q^{57} +(-9.07009 - 6.58981i) q^{59} +(-1.66556 + 1.21010i) q^{61} +(-0.292013 + 0.0462503i) q^{63} +(-9.25349 - 6.78476i) q^{65} +(4.46901 - 8.77093i) q^{67} +(-1.80056 + 0.585036i) q^{69} +(-14.0374 - 4.56101i) q^{71} +(3.53528 + 0.559934i) q^{73} +(-7.91350 + 3.94577i) q^{75} +(0.692281 - 4.37089i) q^{77} +(-1.35379 + 4.16655i) q^{79} +(2.89450 + 8.90837i) q^{81} +(15.5424 + 7.91927i) q^{83} +(14.3006 - 4.57787i) q^{85} +(-0.461727 - 2.91523i) q^{87} +(-0.720489 - 0.991668i) q^{89} +(6.98277 - 9.61096i) q^{91} +(3.18400 + 3.18400i) q^{93} +(6.88311 + 3.54493i) q^{95} +(6.96008 + 13.6599i) q^{97} +0.244117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{5} + 4 q^{7} - 6 q^{13} + 42 q^{15} - 2 q^{17} + 18 q^{19} + 16 q^{21} + 8 q^{23} - 34 q^{25} - 42 q^{27} - 20 q^{31} - 36 q^{33} - 22 q^{35} + 20 q^{37} + 36 q^{39} + 16 q^{41} + 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) $ 56 * q - 2 * q^5 + 4 * q^7 - 6 * q^13 + 42 * q^15 - 2 * q^17 + 18 * q^19 + 16 * q^21 + 8 * q^23 - 34 * q^25 - 42 * q^27 - 20 * q^31 - 36 * q^33 - 22 * q^35 + 20 * q^37 + 36 * q^39 + 16 * q^41 + 32 * q^43 - 4 * q^45 + 8 * q^47 + 48 * q^53 - 8 * q^55 - 8 * q^57 + 4 * q^59 + 36 * q^61 - 2 * q^63 + 2 * q^65 - 6 * q^67 - 60 * q^69 + 10 * q^71 - 2 * q^73 - 26 * q^75 - 72 * q^77 - 16 * q^79 + 54 * q^81 + 28 * q^83 + 62 * q^85 - 24 * q^87 + 30 * q^89 + 30 * q^91 + 20 * q^93 - 8 * q^95 - 46 * q^97 - 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.802897	−	1.57577i	−0.463553	−	0.909774i	−0.997916	−	0.0645189i	$-0.979449\pi$
$3$	−0.802897	−	1.57577i	−0.463553	−	0.909774i	0.534364	−	0.845255i	$-0.320551\pi$
$4$		0			0
$5$	1.58800	−	1.57424i	0.710177	−	0.704024i
$5$	1.58800	−	1.57424i	0.710177	−	0.704024i
$6$		0			0
$7$	1.63701	+	1.63701i	0.618732	+	0.618732i	0.945206	−	0.326474i	$-0.105860\pi$
$7$	1.63701	+	1.63701i	0.618732	+	0.618732i	−0.326474	+	0.945206i	$0.605860\pi$
$8$		0			0
$9$	−0.0750643	+	0.103317i	−0.0250214	+	0.0344391i
$10$		0			0
$11$	−1.12357	−	1.54647i	−0.338770	−	0.466277i	0.605312	−	0.795989i	$-0.293049\pi$
$11$	−1.12357	−	1.54647i	−0.338770	−	0.466277i	−0.944082	+	0.329711i	$0.893049\pi$
$12$		0			0
$13$	−0.802739	−	5.06830i	−0.222640	−	1.40569i	−0.805247	−	0.592939i	$-0.797968\pi$
$13$	−0.802739	−	5.06830i	−0.222640	−	1.40569i	0.582608	−	0.812754i	$-0.302032\pi$
$14$		0			0
$15$	−3.75566	−	1.23838i	−0.969706	−	0.319748i
$16$		0			0
$17$	5.98323	+	3.04861i	1.45115	+	0.739396i	0.989070	−	0.147444i	$-0.0471047\pi$
$17$	5.98323	+	3.04861i	1.45115	+	0.739396i	0.462076	+	0.886840i	$0.347105\pi$
$18$		0			0
$19$	1.06996	+	3.29301i	0.245467	+	0.755469i	0.995559	+	0.0941360i	$0.0300088\pi$
$19$	1.06996	+	3.29301i	0.245467	+	0.755469i	−0.750093	+	0.661333i	$0.769991\pi$
$20$		0			0
$21$	1.26521	−	3.89391i	0.276091	−	0.849722i
$22$		0			0
$23$	0.167463	−	1.05732i	0.0349185	−	0.220467i	−0.964058	−	0.265691i	$-0.914400\pi$
$23$	0.167463	−	1.05732i	0.0349185	−	0.220467i	0.998977	+	0.0452237i	$0.0144001\pi$
$24$		0			0
$25$	0.0435082	−	4.99981i	0.00870164	−	0.999962i
$26$		0			0
$27$	−5.01720	−	0.794647i	−0.965561	−	0.152930i
$28$		0			0
$29$	1.58725	+	0.515730i	0.294746	+	0.0957687i	0.452657	−	0.891685i	$-0.350476\pi$
$29$	1.58725	+	0.515730i	0.294746	+	0.0957687i	−0.157912	+	0.987453i	$0.550476\pi$
$30$		0			0
$31$	−2.42148	+	0.786787i	−0.434911	+	0.141311i	−0.518286	−	0.855207i	$-0.673430\pi$
$31$	−2.42148	+	0.786787i	−0.434911	+	0.141311i	0.0833756	+	0.996518i	$0.473430\pi$
$32$		0			0
$33$	−1.53477	+	3.01215i	−0.267169	+	0.524348i
$34$		0			0
$35$	5.17664	+	0.0225230i	0.875012	+	0.00380709i
$36$		0			0
$37$	2.41558	−	0.382590i	0.397119	−	0.0628975i	0.0453188	−	0.998973i	$-0.485570\pi$
$37$	2.41558	−	0.382590i	0.397119	−	0.0628975i	0.351800	+	0.936075i	$0.385570\pi$
$38$		0			0
$39$	−7.34197	+	5.33426i	−1.17566	+	0.854164i
$40$		0			0
$41$	−3.16381	−	2.29864i	−0.494104	−	0.358988i	0.312656	−	0.949866i	$-0.398781\pi$
$41$	−3.16381	−	2.29864i	−0.494104	−	0.358988i	−0.806760	+	0.590879i	$0.798781\pi$
$42$		0			0
$43$	5.65583	−	5.65583i	0.862506	−	0.862506i	−0.129122	−	0.991629i	$-0.541216\pi$
$43$	5.65583	−	5.65583i	0.862506	−	0.862506i	0.991629	+	0.129122i	$0.0412160\pi$
$44$		0			0
$45$	0.0434441	+	0.282238i	0.00647627	+	0.0420735i
$46$		0			0
$47$	−2.00667	+	1.02245i	−0.292703	+	0.149140i	−0.594176	−	0.804335i	$-0.702522\pi$
$47$	−2.00667	+	1.02245i	−0.292703	+	0.149140i	0.301473	+	0.953475i	$0.402522\pi$
$48$		0			0
$49$		−	1.64038i		−	0.234340i
$50$		0			0
$51$		−	11.8759i		−	1.66296i
$52$		0			0
$53$	−10.8796	+	5.54343i	−1.49443	+	0.761449i	−0.994512	−	0.104624i	$-0.966636\pi$
$53$	−10.8796	+	5.54343i	−1.49443	+	0.761449i	−0.499917	+	0.866074i	$0.666636\pi$
$54$		0			0
$55$	−4.21876	−	0.687014i	−0.568857	−	0.0926370i
$56$		0			0
$57$	4.32997	−	4.32997i	0.573519	−	0.573519i
$58$		0			0
$59$	−9.07009	−	6.58981i	−1.18082	−	0.857920i	−0.188561	−	0.982062i	$-0.560382\pi$
$59$	−9.07009	−	6.58981i	−1.18082	−	0.857920i	−0.992264	+	0.124142i	$0.960382\pi$
$60$		0			0
$61$	−1.66556	+	1.21010i	−0.213253	+	0.154937i	−0.689284	−	0.724491i	$-0.742075\pi$
$61$	−1.66556	+	1.21010i	−0.213253	+	0.154937i	0.476031	+	0.879428i	$0.342075\pi$
$62$		0			0
$63$	−0.292013	+	0.0462503i	−0.0367901	+	0.00582699i
$64$		0			0
$65$	−9.25349	−	6.78476i	−1.14775	−	0.841546i
$66$		0			0
$67$	4.46901	−	8.77093i	0.545977	−	1.07154i	−0.438941	−	0.898516i	$-0.644646\pi$
$67$	4.46901	−	8.77093i	0.545977	−	1.07154i	0.984918	−	0.173024i	$-0.0553538\pi$
$68$		0			0
$69$	−1.80056	+	0.585036i	−0.216761	+	0.0704301i
$70$		0			0
$71$	−14.0374	−	4.56101i	−1.66593	−	0.541293i	−0.683826	−	0.729645i	$-0.739685\pi$
$71$	−14.0374	−	4.56101i	−1.66593	−	0.541293i	−0.982102	+	0.188352i	$0.939685\pi$
$72$		0			0
$73$	3.53528	+	0.559934i	0.413774	+	0.0655353i	0.359851	−	0.933010i	$-0.382828\pi$
$73$	3.53528	+	0.559934i	0.413774	+	0.0655353i	0.0539227	+	0.998545i	$0.482828\pi$
$74$		0			0
$75$	−7.91350	+	3.94577i	−0.913773	+	0.455619i
$76$		0			0
$77$	0.692281	−	4.37089i	0.0788927	−	0.498109i
$78$		0			0
$79$	−1.35379	+	4.16655i	−0.152314	+	0.468773i	−0.997879	−	0.0650989i	$-0.979264\pi$
$79$	−1.35379	+	4.16655i	−0.152314	+	0.468773i	0.845565	+	0.533872i	$0.179264\pi$
$80$		0			0
$81$	2.89450	+	8.90837i	0.321612	+	0.989819i
$82$		0			0
$83$	15.5424	+	7.91927i	1.70601	+	0.869253i	0.984179	+	0.177179i	$0.0566972\pi$
$83$	15.5424	+	7.91927i	1.70601	+	0.869253i	0.721827	+	0.692074i	$0.243303\pi$
$84$		0			0
$85$	14.3006	−	4.57787i	1.55112	−	0.496540i
$86$		0			0
$87$	−0.461727	−	2.91523i	−0.0495024	−	0.312546i
$88$		0			0
$89$	−0.720489	−	0.991668i	−0.0763717	−	0.105117i	0.769122	−	0.639102i	$-0.220694\pi$
$89$	−0.720489	−	0.991668i	−0.0763717	−	0.105117i	−0.845494	+	0.533985i	$0.820694\pi$
$90$		0			0
$91$	6.98277	−	9.61096i	0.731993	−	1.00750i
$92$		0			0
$93$	3.18400	+	3.18400i	0.330165	+	0.330165i
$94$		0			0
$95$	6.88311	+	3.54493i	0.706192	+	0.363702i
$96$		0			0
$97$	6.96008	+	13.6599i	0.706689	+	1.38696i	0.912792	+	0.408425i	$0.133922\pi$
$97$	6.96008	+	13.6599i	0.706689	+	1.38696i	−0.206103	+	0.978530i	$0.566078\pi$
$98$		0			0
$99$	0.244117			0.0245347
$100$		0			0
$101$	11.2777			1.12218			0.561088	−	0.827756i	$-0.310383\pi$
$101$	11.2777			1.12218			0.561088	+	0.827756i	$0.310383\pi$
$102$		0			0
$103$	−0.551746	−	1.08286i	−0.0543651	−	0.106698i	0.862225	−	0.506525i	$-0.169070\pi$
$103$	−0.551746	−	1.08286i	−0.0543651	−	0.106698i	−0.916591	+	0.399827i	$0.869070\pi$
$104$		0			0
$105$	−4.12082	−	8.17530i	−0.402150	−	0.797827i
$106$		0			0
$107$	13.0776	+	13.0776i	1.26426	+	1.26426i	0.949008	+	0.315253i	$0.102089\pi$
$107$	13.0776	+	13.0776i	1.26426	+	1.26426i	0.315253	+	0.949008i	$0.397911\pi$
$108$		0			0
$109$	−8.56546	+	11.7893i	−0.820422	+	1.12921i	0.169208	+	0.985580i	$0.445879\pi$
$109$	−8.56546	+	11.7893i	−0.820422	+	1.12921i	−0.989631	+	0.143634i	$0.954121\pi$
$110$		0			0
$111$	−2.54234	−	3.49923i	−0.241308	−	0.332132i
$112$		0			0
$113$	−0.441788	−	2.78934i	−0.0415599	−	0.262399i	0.958156	−	0.286248i	$-0.0924080\pi$
$113$	−0.441788	−	2.78934i	−0.0415599	−	0.262399i	−0.999716	+	0.0238488i	$0.992408\pi$
$114$		0			0
$115$	−1.39855	−	1.94266i	−0.130416	−	0.181154i
$116$		0			0
$117$	0.583899	+	0.297512i	0.0539815	+	0.0275049i
$118$		0			0
$119$	4.80401	+	14.7852i	0.440383	+	1.35536i
$120$		0			0
$121$	2.27005	−	6.98648i	0.206368	−	0.635135i
$122$		0			0
$123$	−1.08193	+	6.83102i	−0.0975541	+	0.615932i
$124$		0			0
$125$	−7.80183	−	8.00821i	−0.697817	−	0.716276i
$126$		0			0
$127$	15.7328	+	2.49184i	1.39606	+	0.221115i	0.808706	−	0.588213i	$-0.200168\pi$
$127$	15.7328	+	2.49184i	1.39606	+	0.221115i	0.587357	+	0.809328i	$0.300168\pi$
$128$		0			0
$129$	−13.4534	−	4.37126i	−1.18450	−	0.384868i
$130$		0			0
$131$	−4.31577	+	1.40228i	−0.377070	+	0.122518i	−0.491419	−	0.870923i	$-0.663522\pi$
$131$	−4.31577	+	1.40228i	−0.377070	+	0.122518i	0.114349	+	0.993441i	$0.463522\pi$
$132$		0			0
$133$	−3.63916	+	7.14225i	−0.315555	+	0.619311i
$134$		0			0
$135$	−9.21830	+	6.63640i	−0.793385	+	0.571171i
$136$		0			0
$137$	−1.57173	+	0.248938i	−0.134282	+	0.0212682i	−0.223214	−	0.974770i	$-0.571655\pi$
$137$	−1.57173	+	0.248938i	−0.134282	+	0.0212682i	0.0889314	+	0.996038i	$0.471655\pi$
$138$		0			0
$139$	0.720939	−	0.523792i	0.0611492	−	0.0444275i	−0.556791	−	0.830653i	$-0.687967\pi$
$139$	0.720939	−	0.523792i	0.0611492	−	0.0444275i	0.617940	+	0.786225i	$0.287967\pi$
$140$		0			0
$141$	3.22230	+	2.34114i	0.271367	+	0.197159i
$142$		0			0
$143$	−6.93601	+	6.93601i	−0.580019	+	0.580019i
$144$		0			0
$145$	3.33245	−	1.67975i	0.276745	−	0.139495i
$146$		0			0
$147$	−2.58487	+	1.31706i	−0.213197	+	0.108629i
$148$		0			0
$149$			11.5629i			0.947269i	0.880721	+	0.473635i	$0.157058\pi$
$149$			11.5629i			0.947269i	−0.880721	+	0.473635i	$0.842942\pi$
$150$		0			0
$151$			20.3599i			1.65687i	0.560087	+	0.828434i	$0.310768\pi$
$151$			20.3599i			1.65687i	−0.560087	+	0.828434i	$0.689232\pi$
$152$		0			0
$153$	−0.764101	+	0.389329i	−0.0617739	+	0.0314754i
$154$		0			0
$155$	−2.60672	+	5.06142i	−0.209377	+	0.406543i
$156$		0			0
$157$	−1.68701	+	1.68701i	−0.134638	+	0.134638i	−0.771214	−	0.636576i	$-0.780350\pi$
$157$	−1.68701	+	1.68701i	−0.134638	+	0.134638i	0.636576	+	0.771214i	$0.280350\pi$
$158$		0			0
$159$	17.4704	+	12.6930i	1.38549	+	1.00662i
$160$		0			0
$161$	2.00499	−	1.45671i	0.158015	−	0.114805i
$162$		0			0
$163$	18.2675	−	2.89328i	1.43082	−	0.226619i	0.607554	−	0.794278i	$-0.292151\pi$
$163$	18.2675	−	2.89328i	1.43082	−	0.226619i	0.823264	+	0.567659i	$0.192151\pi$
$164$		0			0
$165$	2.30465	+	7.19941i	0.179417	+	0.560473i
$166$		0			0
$167$	10.8718	−	21.3372i	0.841287	−	1.65112i	0.0854655	−	0.996341i	$-0.472762\pi$
$167$	10.8718	−	21.3372i	0.841287	−	1.65112i	0.755822	−	0.654778i	$-0.227238\pi$
$168$		0			0
$169$	−12.6795	+	4.11982i	−0.975347	+	0.316909i
$170$		0			0
$171$	−0.420541	−	0.136642i	−0.0321596	−	0.0104493i
$172$		0			0
$173$	−12.7691	−	2.02243i	−0.970817	−	0.153762i	−0.349170	−	0.937060i	$-0.613536\pi$
$173$	−12.7691	−	2.02243i	−0.970817	−	0.153762i	−0.621647	+	0.783297i	$0.713536\pi$
$174$		0			0
$175$	8.25597	−	8.11353i	0.624093	−	0.613325i
$176$		0			0
$177$	−3.10170	+	19.5833i	−0.233138	+	1.47197i
$178$		0			0
$179$	−2.16773	+	6.67160i	−0.162024	+	0.498659i	−0.998805	−	0.0488796i	$-0.984435\pi$
$179$	−2.16773	+	6.67160i	−0.162024	+	0.498659i	0.836781	+	0.547538i	$0.184435\pi$
$180$		0			0
$181$	1.13046	+	3.47920i	0.0840264	+	0.258607i	0.984239	−	0.176844i	$-0.0565889\pi$
$181$	1.13046	+	3.47920i	0.0840264	+	0.258607i	−0.900212	+	0.435451i	$0.856589\pi$
$182$		0			0
$183$	3.24411	+	1.65296i	0.239812	+	0.122190i
$184$		0			0
$185$	3.23366	−	4.41027i	0.237743	−	0.324249i
$186$		0			0
$187$	−2.00803	−	12.6782i	−0.146842	−	0.927122i
$188$		0			0
$189$	−6.91238	−	9.51407i	−0.502801	−	0.692047i
$190$		0			0
$191$	8.29296	−	11.4143i	0.600058	−	0.825909i	−0.395656	−	0.918399i	$-0.629483\pi$
$191$	8.29296	−	11.4143i	0.600058	−	0.825909i	0.995714	+	0.0924903i	$0.0294827\pi$
$192$		0			0
$193$	14.8817	+	14.8817i	1.07121	+	1.07121i	0.997262	+	0.0739449i	$0.0235589\pi$
$193$	14.8817	+	14.8817i	1.07121	+	1.07121i	0.0739449	+	0.997262i	$0.476441\pi$
$194$		0			0
$195$	−3.26165	+	20.0289i	−0.233572	+	1.43430i
$196$		0			0
$197$	5.73475	+	11.2551i	0.408584	+	0.801891i	0.999990	−	0.00448295i	$-0.00142697\pi$
$197$	5.73475	+	11.2551i	0.408584	+	0.801891i	−0.591406	+	0.806374i	$0.701427\pi$
$198$		0			0
$199$	4.55115			0.322623			0.161311	−	0.986904i	$-0.448428\pi$
$199$	4.55115			0.322623			0.161311	+	0.986904i	$0.448428\pi$
$200$		0			0
$201$	−17.4092			−1.22795
$202$		0			0
$203$	1.75410	+	3.44261i	0.123114	+	0.241624i
$204$		0			0
$205$	−8.64276	+	1.33036i	−0.603637	+	0.0929163i
$206$		0			0
$207$	0.0966690	+	0.0966690i	0.00671896	+	0.00671896i
$208$		0			0
$209$	3.89035	−	5.35461i	0.269101	−	0.370386i
$210$		0			0
$211$	−4.12697	−	5.68028i	−0.284112	−	0.391047i	0.642978	−	0.765884i	$-0.277698\pi$
$211$	−4.12697	−	5.68028i	−0.284112	−	0.391047i	−0.927090	+	0.374838i	$0.877698\pi$
$212$		0			0
$213$	4.08342	+	25.7817i	0.279792	+	1.76653i
$214$		0			0
$215$	0.0778165	−	17.8851i	0.00530704	−	1.21976i
$216$		0			0
$217$	−5.25197	−	2.67601i	−0.356527	−	0.181660i
$218$		0			0
$219$	−1.95614	−	6.02038i	−0.132184	−	0.406819i
$220$		0			0
$221$	10.6483	−	32.7720i	0.716281	−	2.20448i
$222$		0			0
$223$	−2.28864	+	14.4499i	−0.153259	+	0.967639i	0.784444	+	0.620200i	$0.212949\pi$
$223$	−2.28864	+	14.4499i	−0.153259	+	0.967639i	−0.937703	+	0.347439i	$0.887051\pi$
$224$		0			0
$225$	0.513300	+	0.379803i	0.0342200	+	0.0253202i
$226$		0			0
$227$	−17.9295	−	2.83975i	−1.19002	−	0.188481i	−0.470149	−	0.882587i	$-0.655800\pi$
$227$	−17.9295	−	2.83975i	−1.19002	−	0.188481i	−0.719872	+	0.694107i	$0.755800\pi$
$228$		0			0
$229$	−18.5870	−	6.03929i	−1.22826	−	0.399087i	−0.378180	−	0.925732i	$-0.623450\pi$
$229$	−18.5870	−	6.03929i	−1.22826	−	0.399087i	−0.850085	+	0.526645i	$0.823450\pi$
$230$		0			0
$231$	−7.44336	+	2.41850i	−0.489737	+	0.159125i
$232$		0			0
$233$	−5.96169	+	11.7005i	−0.390563	+	0.766523i	−0.999647	−	0.0265828i	$-0.991537\pi$
$233$	−5.96169	+	11.7005i	−0.390563	+	0.766523i	0.609083	+	0.793106i	$0.291537\pi$
$234$		0			0
$235$	−1.57701	+	4.78264i	−0.102873	+	0.311985i
$236$		0			0
$237$	7.65250	−	1.21204i	0.497083	−	0.0787302i
$238$		0			0
$239$	−3.74251	+	2.71909i	−0.242083	+	0.175884i	−0.702211	−	0.711969i	$-0.747804\pi$
$239$	−3.74251	+	2.71909i	−0.242083	+	0.175884i	0.460128	+	0.887853i	$0.347804\pi$
$240$		0			0
$241$	18.1898	+	13.2156i	1.17171	+	0.851294i	0.991212	−	0.132282i	$-0.0422305\pi$
$241$	18.1898	+	13.2156i	1.17171	+	0.851294i	0.180494	+	0.983576i	$0.442230\pi$
$242$		0			0
$243$	0.937823	−	0.937823i	0.0601613	−	0.0601613i
$244$		0			0
$245$	−2.58236	−	2.60493i	−0.164981	−	0.166423i
$246$		0			0
$247$	15.8311	−	8.06633i	1.00731	−	0.513248i
$248$		0			0
$249$		−	30.8497i		−	1.95502i
$250$		0			0
$251$			9.97785i			0.629796i	0.949125	+	0.314898i	$0.101970\pi$
$251$			9.97785i			0.629796i	−0.949125	+	0.314898i	$0.898030\pi$
$252$		0			0
$253$	−1.82327	+	0.929003i	−0.114628	+	0.0584059i
$254$		0			0
$255$	−18.6956	−	18.8590i	−1.17077	−	1.18100i
$256$		0			0
$257$	9.29121	−	9.29121i	0.579570	−	0.579570i	−0.355215	−	0.934785i	$-0.615592\pi$
$257$	9.29121	−	9.29121i	0.579570	−	0.579570i	0.934785	+	0.355215i	$0.115592\pi$
$258$		0			0
$259$	4.58064	+	3.32803i	0.284627	+	0.206794i
$260$		0			0
$261$	−0.172430	+	0.125278i	−0.0106731	+	0.00775450i
$262$		0			0
$263$	4.96316	−	0.786087i	0.306041	−	0.0484722i	−0.00152499	−	0.999999i	$-0.500485\pi$
$263$	4.96316	−	0.786087i	0.306041	−	0.0484722i	0.307566	+	0.951527i	$0.400485\pi$
$264$		0			0
$265$	−8.55012	+	25.9301i	−0.525230	+	1.59288i
$266$		0			0
$267$	−0.984167	+	1.93154i	−0.0602300	+	0.118208i
$268$		0			0
$269$	5.24447	−	1.70403i	0.319761	−	0.103897i	−0.144739	−	0.989470i	$-0.546234\pi$
$269$	5.24447	−	1.70403i	0.319761	−	0.103897i	0.464500	+	0.885573i	$0.346234\pi$
$270$		0			0
$271$	9.52234	+	3.09399i	0.578441	+	0.187947i	0.583602	−	0.812040i	$-0.301643\pi$
$271$	9.52234	+	3.09399i	0.578441	+	0.187947i	−0.00516117	+	0.999987i	$0.501643\pi$
$272$		0			0
$273$	−20.7511	−	3.28666i	−1.25592	−	0.198918i
$274$		0			0
$275$	−7.78093	+	5.55037i	−0.469207	+	0.334700i
$276$		0			0
$277$	−1.87483	+	11.8372i	−0.112648	+	0.711229i	0.865124	+	0.501558i	$0.167239\pi$
$277$	−1.87483	+	11.8372i	−0.112648	+	0.711229i	−0.977772	+	0.209671i	$0.932761\pi$
$278$		0			0
$279$	0.100478	−	0.309240i	0.00601548	−	0.0185137i
$280$		0			0
$281$	3.75565	+	11.5587i	0.224043	+	0.689535i	0.998387	+	0.0567696i	$0.0180800\pi$
$281$	3.75565	+	11.5587i	0.224043	+	0.689535i	−0.774344	+	0.632765i	$0.781920\pi$
$282$		0			0
$283$	13.1948	+	6.72311i	0.784352	+	0.399647i	0.799825	−	0.600233i	$-0.204925\pi$
$283$	13.1948	+	6.72311i	0.784352	+	0.399647i	−0.0154732	+	0.999880i	$0.504925\pi$
$284$		0			0
$285$	0.0595744	−	13.6924i	0.00352889	−	0.811070i
$286$		0			0
$287$	−1.41629	−	8.94210i	−0.0836009	−	0.527835i
$288$		0			0
$289$	16.5127	+	22.7278i	0.971334	+	1.33693i
$290$		0			0
$291$	15.9367	−	21.9350i	0.934227	−	1.28585i
$292$		0			0
$293$	−1.30381	−	1.30381i	−0.0761692	−	0.0761692i	0.667996	−	0.744165i	$-0.267152\pi$
$293$	−1.30381	−	1.30381i	−0.0761692	−	0.0761692i	−0.744165	+	0.667996i	$0.767152\pi$
$294$		0			0
$295$	−24.7773	+	3.81391i	−1.44259	+	0.222054i
$296$		0			0
$297$	4.40830	+	8.65178i	0.255796	+	0.502027i
$298$		0			0
$299$	−5.49325			−0.317683
$300$		0			0
$301$	18.5173			1.06732
$302$		0			0
$303$	−9.05485	−	17.7711i	−0.520187	−	1.02093i
$304$		0			0
$305$	−0.739920	+	4.54363i	−0.0423677	+	0.260168i
$306$		0			0
$307$	−9.07999	−	9.07999i	−0.518222	−	0.518222i	0.398811	−	0.917033i	$-0.369423\pi$
$307$	−9.07999	−	9.07999i	−0.518222	−	0.518222i	−0.917033	+	0.398811i	$0.869423\pi$
$308$		0			0
$309$	−1.26335	+	1.73885i	−0.0718695	+	0.0989199i
$310$		0			0
$311$	−7.93253	−	10.9182i	−0.449813	−	0.619114i	0.522545	−	0.852612i	$-0.324983\pi$
$311$	−7.93253	−	10.9182i	−0.449813	−	0.619114i	−0.972357	+	0.233498i	$0.924983\pi$
$312$		0			0
$313$	−0.856290	−	5.40640i	−0.0484004	−	0.305588i	0.951598	−	0.307345i	$-0.0994406\pi$
$313$	−0.856290	−	5.40640i	−0.0484004	−	0.305588i	−0.999998	+	0.00175729i	$0.999441\pi$
$314$		0			0
$315$	−0.390908	+	0.533145i	−0.0220252	+	0.0300393i
$316$		0			0
$317$	−27.8654	−	14.1981i	−1.56508	−	0.797447i	−0.565451	−	0.824782i	$-0.691298\pi$
$317$	−27.8654	−	14.1981i	−1.56508	−	0.797447i	−0.999626	+	0.0273357i	$0.991298\pi$
$318$		0			0
$319$	−0.985838	−	3.03410i	−0.0551963	−	0.169877i
$320$		0			0
$321$	10.1074	−	31.1073i	0.564139	−	1.73624i
$322$		0			0
$323$	−3.63726	+	22.9647i	−0.202382	+	1.27779i
$324$		0			0
$325$	−25.3754	+	3.79303i	−1.40758	+	0.210400i
$326$		0			0
$327$	25.4545	+	4.03160i	1.40764	+	0.222948i
$328$		0			0
$329$	−4.95871	−	1.61118i	−0.273382	−	0.0888273i
$330$		0			0
$331$	28.7064	−	9.32728i	1.57785	−	0.512673i	0.616346	−	0.787476i	$-0.288612\pi$
$331$	28.7064	−	9.32728i	1.57785	−	0.512673i	0.961501	+	0.274802i	$0.0886124\pi$
$332$		0			0
$333$	−0.141796	+	0.278290i	−0.00777036	+	0.0152502i
$334$		0			0
$335$	−6.71079	−	20.9636i	−0.366649	−	1.14536i
$336$		0			0
$337$	−24.3091	+	3.85019i	−1.32420	+	0.209733i	−0.778182	−	0.628038i	$-0.783858\pi$
$337$	−24.3091	+	3.85019i	−1.32420	+	0.209733i	−0.546021	+	0.837772i	$0.683858\pi$
$338$		0			0
$339$	−4.04066	+	2.93571i	−0.219458	+	0.159446i
$340$		0			0
$341$	3.93745	+	2.86073i	0.213225	+	0.154917i
$342$		0			0
$343$	14.1444	−	14.1444i	0.763726	−	0.763726i
$344$		0			0
$345$	−1.93830	+	3.76355i	−0.104354	+	0.202623i
$346$		0			0
$347$	−29.1884	+	14.8723i	−1.56692	+	0.798384i	−0.999683	−	0.0251719i	$-0.991987\pi$
$347$	−29.1884	+	14.8723i	−1.56692	+	0.798384i	−0.567235	+	0.823556i	$0.691987\pi$
$348$		0			0
$349$		−	14.9232i		−	0.798820i	−0.916773	−	0.399410i	$-0.869215\pi$
$349$		−	14.9232i		−	0.798820i	0.916773	−	0.399410i	$-0.130785\pi$
$350$		0			0
$351$			26.0666i			1.39133i
$352$		0			0
$353$	20.8385	−	10.6177i	1.10912	−	0.565126i	0.199222	−	0.979954i	$-0.436158\pi$
$353$	20.8385	−	10.6177i	1.10912	−	0.565126i	0.909900	+	0.414829i	$0.136158\pi$
$354$		0			0
$355$	−29.4715	+	14.8553i	−1.56419	+	0.788439i
$356$		0			0
$357$	19.4411	−	19.4411i	1.02893	−	1.02893i
$358$		0			0
$359$	14.3121	+	10.3983i	0.755362	+	0.548802i	0.897484	−	0.441047i	$-0.145393\pi$
$359$	14.3121	+	10.3983i	0.755362	+	0.548802i	−0.142122	+	0.989849i	$0.545393\pi$
$360$		0			0
$361$	5.67222	−	4.12111i	0.298538	−	0.216900i
$362$		0			0
$363$	−12.8317	+	2.03235i	−0.673491	+	0.106671i
$364$		0			0
$365$	6.49551	−	4.67622i	0.339991	−	0.244765i
$366$		0			0
$367$	−0.412877	+	0.810317i	−0.0215520	+	0.0422982i	−0.901531	−	0.432714i	$-0.857556\pi$
$367$	−0.412877	+	0.810317i	−0.0215520	+	0.0422982i	0.879979	+	0.475012i	$0.157556\pi$
$368$		0			0
$369$	0.474978	−	0.154330i	0.0247264	−	0.00803409i
$370$		0			0
$371$	−26.8847	−	8.73537i	−1.39578	−	0.453518i
$372$		0			0
$373$	24.7281	+	3.91655i	1.28037	+	0.202791i	0.759312	−	0.650727i	$-0.225536\pi$
$373$	24.7281	+	3.91655i	1.28037	+	0.202791i	0.521063	+	0.853518i	$0.325536\pi$
$374$		0			0
$375$	−6.35506	+	18.7237i	−0.328174	+	0.966887i
$376$		0			0
$377$	1.33972	−	8.45867i	0.0689992	−	0.435644i
$378$		0			0
$379$	−0.569050	+	1.75136i	−0.0292301	+	0.0899611i	−0.964607	−	0.263691i	$-0.915060\pi$
$379$	−0.569050	+	1.75136i	−0.0292301	+	0.0899611i	0.935377	+	0.353652i	$0.115060\pi$
$380$		0			0
$381$	−8.70527	−	26.7921i	−0.445985	−	1.37260i
$382$		0			0
$383$	−13.8405	−	7.05210i	−0.707218	−	0.360345i	0.0630986	−	0.998007i	$-0.479902\pi$
$383$	−13.8405	−	7.05210i	−0.707218	−	0.360345i	−0.770316	+	0.637662i	$0.779902\pi$
$384$		0			0
$385$	−5.78150	−	8.03080i	−0.294653	−	0.409288i
$386$		0			0
$387$	0.159793	+	1.00890i	0.00812275	+	0.0512850i
$388$		0			0
$389$	−12.6454	−	17.4049i	−0.641148	−	0.882464i	0.357529	−	0.933902i	$-0.383619\pi$
$389$	−12.6454	−	17.4049i	−0.641148	−	0.882464i	−0.998676	+	0.0514382i	$0.983619\pi$
$390$		0			0
$391$	4.22533	−	5.81567i	0.213684	−	0.294111i
$392$		0			0
$393$	5.67479	+	5.67479i	0.286255	+	0.286255i
$394$		0			0
$395$	4.40934	+	8.74770i	0.221858	+	0.440144i
$396$		0			0
$397$	15.6893	+	30.7920i	0.787424	+	1.54541i	0.837358	+	0.546655i	$0.184099\pi$
$397$	15.6893	+	30.7920i	0.787424	+	1.54541i	−0.0499334	+	0.998753i	$0.515901\pi$
$398$		0			0
$399$	14.1764			0.709709
$400$		0			0
$401$	12.0007			0.599284			0.299642	−	0.954052i	$-0.403133\pi$
$401$	12.0007			0.599284			0.299642	+	0.954052i	$0.403133\pi$
$402$		0			0
$403$	5.93149	+	11.6412i	0.295468	+	0.579889i
$404$		0			0
$405$	18.6204	+	9.58986i	0.925257	+	0.476524i
$406$		0			0
$407$	−3.30575	−	3.30575i	−0.163860	−	0.163860i
$408$		0			0
$409$	7.13726	−	9.82359i	0.352915	−	0.485745i	−0.595243	−	0.803546i	$-0.702944\pi$
$409$	7.13726	−	9.82359i	0.352915	−	0.485745i	0.948158	+	0.317800i	$0.102944\pi$
$410$		0			0
$411$	1.65421	+	2.27683i	0.0815962	+	0.112308i
$412$		0			0
$413$	−4.06025	−	25.6354i	−0.199792	−	1.26144i
$414$		0			0
$415$	37.1483	−	11.8918i	1.82354	−	0.583745i
$416$		0			0
$417$	−1.40422	−	0.715485i	−0.0687648	−	0.0350374i
$418$		0			0
$419$	0.00780791	+	0.0240303i	0.000381441	+	0.00117396i	0.951247	−	0.308430i	$-0.0998035\pi$
$419$	0.00780791	+	0.0240303i	0.000381441	+	0.00117396i	−0.950866	+	0.309604i	$0.899804\pi$
$420$		0			0
$421$	−5.01573	+	15.4368i	−0.244452	+	0.752345i	0.751274	+	0.659990i	$0.229439\pi$
$421$	−5.01573	+	15.4368i	−0.244452	+	0.752345i	−0.995726	+	0.0923551i	$0.970561\pi$
$422$		0			0
$423$	0.0449928	−	0.284073i	0.00218762	−	0.0138121i
$424$		0			0
$425$	15.5028	−	29.7824i	0.751995	−	1.44466i
$426$		0			0
$427$	−4.70748	−	0.745592i	−0.227811	−	0.0360817i
$428$		0			0
$429$	16.4985	+	5.36069i	0.796555	+	0.258816i
$430$		0			0
$431$	−38.2252	+	12.4201i	−1.84124	+	0.598256i	−0.843073	+	0.537799i	$0.819256\pi$
$431$	−38.2252	+	12.4201i	−1.84124	+	0.598256i	−0.998171	+	0.0604570i	$0.980744\pi$
$432$		0			0
$433$	−5.32284	+	10.4467i	−0.255800	+	0.502035i	−0.982817	−	0.184585i	$-0.940906\pi$
$433$	−5.32284	+	10.4467i	−0.255800	+	0.502035i	0.727017	+	0.686619i	$0.240906\pi$
$434$		0			0
$435$	−5.32251	−	3.90253i	−0.255195	−	0.187112i
$436$		0			0
$437$	3.66095	−	0.579838i	0.175127	−	0.0277374i
$438$		0			0
$439$	19.8543	−	14.4250i	0.947592	−	0.688466i	−0.00264427	−	0.999997i	$-0.500842\pi$
$439$	19.8543	−	14.4250i	0.947592	−	0.688466i	0.950236	+	0.311531i	$0.100842\pi$
$440$		0			0
$441$	0.169480	+	0.123134i	0.00807046	+	0.00586353i
$442$		0			0
$443$	−0.733468	+	0.733468i	−0.0348481	+	0.0348481i	−0.724316	−	0.689468i	$-0.757844\pi$
$443$	−0.733468	+	0.733468i	−0.0348481	+	0.0348481i	0.689468	+	0.724316i	$0.257844\pi$
$444$		0			0
$445$	−2.70527	−	0.440546i	−0.128242	−	0.0208839i
$446$		0			0
$447$	18.2205	−	9.28381i	0.861801	−	0.439109i
$448$		0			0
$449$			36.8453i			1.73884i	0.494075	+	0.869419i	$0.335507\pi$
$449$			36.8453i			1.73884i	−0.494075	+	0.869419i	$0.664493\pi$
$450$		0			0
$451$			7.47542i			0.352004i
$452$		0			0
$453$	32.0826	−	16.3469i	1.50737	−	0.768046i
$454$		0			0
$455$	−4.04134	−	26.2548i	−0.189461	−	1.23084i
$456$		0			0
$457$	20.5195	−	20.5195i	0.959860	−	0.959860i	−0.0393645	−	0.999225i	$-0.512533\pi$
$457$	20.5195	−	20.5195i	0.959860	−	0.959860i	0.999225	+	0.0393645i	$0.0125333\pi$
$458$		0			0
$459$	−27.5965	−	20.0500i	−1.28809	−	0.935856i
$460$		0			0
$461$	−20.1162	+	14.6153i	−0.936903	+	0.680700i	−0.947673	−	0.319242i	$-0.896572\pi$
$461$	−20.1162	+	14.6153i	−0.936903	+	0.680700i	0.0107699	+	0.999942i	$0.496572\pi$
$462$		0			0
$463$	−41.3445	+	6.54832i	−1.92144	+	0.304326i	−0.997026	−	0.0770638i	$-0.975445\pi$
$463$	−41.3445	+	6.54832i	−1.92144	+	0.304326i	−0.924414	+	0.381390i	$0.875445\pi$
$464$		0			0
$465$	10.0686	+	0.0438074i	0.466920	+	0.00203152i
$466$		0			0
$467$	7.38246	−	14.4889i	0.341620	−	0.670466i	−0.654727	−	0.755865i	$-0.727217\pi$
$467$	7.38246	−	14.4889i	0.341620	−	0.670466i	0.996347	+	0.0853991i	$0.0272165\pi$
$468$		0			0
$469$	21.6740	−	7.04229i	1.00081	−	0.325183i
$470$		0			0
$471$	4.01283	+	1.30385i	0.184902	+	0.0600782i
$472$		0			0
$473$	−15.1013	−	2.39181i	−0.694358	−	0.109976i
$474$		0			0
$475$	16.5110	−	5.20635i	0.757576	−	0.238884i
$476$		0			0
$477$	0.243938	−	1.54016i	0.0111692	−	0.0705193i
$478$		0			0
$479$	−2.20447	+	6.78465i	−0.100725	+	0.309998i	−0.988703	−	0.149886i	$-0.952109\pi$
$479$	−2.20447	+	6.78465i	−0.100725	+	0.309998i	0.887979	+	0.459885i	$0.152109\pi$
$480$		0			0
$481$	−3.87816	−	11.9358i	−0.176829	−	0.544224i
$482$		0			0
$483$	−3.90524	−	1.98982i	−0.177695	−	0.0905400i
$484$		0			0
$485$	32.5567	+	10.7351i	1.47832	+	0.487457i
$486$		0			0
$487$	−5.13557	−	32.4247i	−0.232715	−	1.46930i	−0.776520	−	0.630092i	$-0.783017\pi$
$487$	−5.13557	−	32.4247i	−0.232715	−	1.46930i	0.543806	−	0.839211i	$-0.316983\pi$
$488$		0			0
$489$	−19.2260	−	26.4624i	−0.869432	−	1.19667i
$490$		0			0
$491$	−1.51395	+	2.08378i	−0.0683238	+	0.0940396i	−0.841811	−	0.539772i	$-0.818511\pi$
$491$	−1.51395	+	2.08378i	−0.0683238	+	0.0940396i	0.773488	+	0.633811i	$0.218511\pi$
$492$		0			0
$493$	7.92465	+	7.92465i	0.356908	+	0.356908i
$494$		0			0
$495$	0.387658	−	0.384300i	0.0174239	−	0.0172730i
$496$		0			0
$497$	−15.5129	−	30.4458i	−0.695848	−	1.36568i
$498$		0			0
$499$	−29.4600			−1.31881			−0.659406	−	0.751787i	$-0.729192\pi$
$499$	−29.4600			−1.31881			−0.659406	+	0.751787i	$0.729192\pi$
$500$		0			0
$501$	−42.3515			−1.89213
$502$		0			0
$503$	−6.35254	−	12.4676i	−0.283246	−	0.555902i	0.704921	−	0.709286i	$-0.250983\pi$
$503$	−6.35254	−	12.4676i	−0.283246	−	0.555902i	−0.988167	+	0.153385i	$0.950983\pi$
$504$		0			0
$505$	17.9091	−	17.7539i	0.796942	−	0.790038i
$506$		0			0
$507$	16.6722	+	16.6722i	0.740440	+	0.740440i
$508$		0			0
$509$	−7.78677	+	10.7176i	−0.345142	+	0.475048i	−0.945935	−	0.324357i	$-0.894852\pi$
$509$	−7.78677	+	10.7176i	−0.345142	+	0.475048i	0.600792	+	0.799405i	$0.294852\pi$
$510$		0			0
$511$	4.87068	+	6.70392i	0.215466	+	0.296564i
$512$		0			0
$513$	−2.75145	−	17.3720i	−0.121479	−	0.766990i
$514$		0			0
$515$	−2.58086	−	0.851006i	−0.113726	−	0.0374998i
$516$		0			0
$517$	3.83583	+	1.95445i	0.168699	+	0.0859567i
$518$		0			0
$519$	7.06538	+	21.7450i	0.310136	+	0.954500i
$520$		0			0
$521$	7.91273	−	24.3529i	0.346663	−	1.06692i	−0.614025	−	0.789287i	$-0.710450\pi$
$521$	7.91273	−	24.3529i	0.346663	−	1.06692i	0.960688	−	0.277632i	$-0.0895495\pi$
$522$		0			0
$523$	2.94267	−	18.5793i	0.128674	−	0.812416i	−0.835954	−	0.548800i	$-0.815085\pi$
$523$	2.94267	−	18.5793i	0.128674	−	0.812416i	0.964628	−	0.263616i	$-0.0849152\pi$
$524$		0			0
$525$	−19.4138	−	6.49522i	−0.847287	−	0.283475i
$526$		0			0
$527$	−16.8869	−	2.67462i	−0.735604	−	0.116508i
$528$		0			0
$529$	20.7844	+	6.75327i	0.903670	+	0.293620i
$530$		0			0
$531$	1.36168	−	0.442437i	0.0590919	−	0.0192001i
$532$		0			0
$533$	−9.11049	+	17.8803i	−0.394619	+	0.774483i
$534$		0			0
$535$	41.3547	+	0.179930i	1.78792	+	0.00777905i
$536$		0			0
$537$	12.2534	−	1.94075i	0.528773	−	0.0837494i
$538$		0			0
$539$	−2.53680	+	1.84309i	−0.109268	+	0.0793875i
$540$		0			0
$541$	30.8738	+	22.4311i	1.32737	+	0.964390i	0.999809	+	0.0195594i	$0.00622636\pi$
$541$	30.8738	+	22.4311i	1.32737	+	0.964390i	0.327560	+	0.944830i	$0.393774\pi$
$542$		0			0
$543$	4.57479	−	4.57479i	0.196323	−	0.196323i
$544$		0			0
$545$	4.95733	+	32.2057i	0.212349	+	1.37954i
$546$		0			0
$547$	−27.9167	+	14.2243i	−1.19363	+	0.608186i	−0.933914	−	0.357499i	$-0.883630\pi$
$547$	−27.9167	+	14.2243i	−1.19363	+	0.608186i	−0.259718	+	0.965685i	$0.583630\pi$
$548$		0			0
$549$		−	0.262916i		−	0.0112210i
$550$		0			0
$551$			5.77866i			0.246179i
$552$		0			0
$553$	−9.03687	+	4.60451i	−0.384287	+	0.195804i
$554$		0			0
$555$	−9.54588	−	1.55452i	−0.405200	−	0.0659859i
$556$		0			0
$557$	−24.8337	+	24.8337i	−1.05224	+	1.05224i	−0.0536800	+	0.998558i	$0.517095\pi$
$557$	−24.8337	+	24.8337i	−1.05224	+	1.05224i	−0.998558	+	0.0536800i	$0.982905\pi$
$558$		0			0
$559$	−33.2056	−	24.1253i	−1.40445	−	1.02039i
$560$		0			0
$561$	−18.3657	+	13.3435i	−0.775402	+	0.563363i
$562$		0			0
$563$	5.00149	−	0.792158i	0.210788	−	0.0333855i	−0.0501475	−	0.998742i	$-0.515969\pi$
$563$	5.00149	−	0.792158i	0.210788	−	0.0333855i	0.260935	+	0.965356i	$0.415969\pi$
$564$		0			0
$565$	−5.09266	−	3.73399i	−0.214250	−	0.157090i
$566$		0			0
$567$	−9.84477	+	19.3214i	−0.413441	+	0.811424i
$568$		0			0
$569$	−41.8606	+	13.6013i	−1.75489	+	0.570197i	−0.996650	−	0.0817818i	$-0.973939\pi$
$569$	−41.8606	+	13.6013i	−1.75489	+	0.570197i	−0.758237	+	0.651979i	$0.773939\pi$
$570$		0			0
$571$	−23.8146	−	7.73782i	−0.996608	−	0.323818i	−0.235099	−	0.971972i	$-0.575541\pi$
$571$	−23.8146	−	7.73782i	−0.996608	−	0.323818i	−0.761509	+	0.648154i	$0.775541\pi$
$572$		0			0
$573$	−24.6447	−	3.90334i	−1.02955	−	0.163064i
$574$		0			0
$575$	−5.27912	−	0.883287i	−0.220155	−	0.0368356i
$576$		0			0
$577$	−2.44309	+	15.4251i	−0.101707	+	0.642154i	0.883190	+	0.469015i	$0.155391\pi$
$577$	−2.44309	+	15.4251i	−0.101707	+	0.642154i	−0.984897	+	0.173139i	$0.944609\pi$
$578$		0			0
$579$	11.5017	−	35.3986i	0.477995	−	1.47112i
$580$		0			0
$581$	12.4792	+	38.4071i	0.517726	+	1.59340i
$582$		0			0
$583$	20.7968	+	10.5965i	0.861314	+	0.438862i
$584$		0			0
$585$	1.39559	−	0.446751i	0.0577005	−	0.0184709i
$586$		0			0
$587$	3.77597	+	23.8405i	0.155851	+	0.984004i	0.934350	+	0.356358i	$0.115982\pi$
$587$	3.77597	+	23.8405i	0.155851	+	0.984004i	−0.778499	+	0.627646i	$0.784018\pi$
$588$		0			0
$589$	−5.18180	−	7.13213i	−0.213512	−	0.293874i
$590$		0			0
$591$	13.1310	−	18.0733i	0.540139	−	0.743437i
$592$		0			0
$593$	−9.90078	−	9.90078i	−0.406576	−	0.406576i	0.473967	−	0.880543i	$-0.342822\pi$
$593$	−9.90078	−	9.90078i	−0.406576	−	0.406576i	−0.880543	+	0.473967i	$0.842822\pi$
$594$		0			0
$595$	30.9044	+	15.9163i	1.26696	+	0.652505i
$596$		0			0
$597$	−3.65411	−	7.17159i	−0.149553	−	0.293514i
$598$		0			0
$599$	2.63535			0.107678			0.0538388	−	0.998550i	$-0.482854\pi$
$599$	2.63535			0.107678			0.0538388	+	0.998550i	$0.482854\pi$
$600$		0			0
$601$	−27.5274			−1.12287			−0.561433	−	0.827522i	$-0.689750\pi$
$601$	−27.5274			−1.12287			−0.561433	+	0.827522i	$0.689750\pi$
$602$		0			0
$603$	0.570725	+	1.12011i	0.0232417	+	0.0456144i
$604$		0			0
$605$	−7.39359	−	14.6682i	−0.300592	−	0.596346i
$606$		0			0
$607$	12.2589	+	12.2589i	0.497575	+	0.497575i	0.910682	−	0.413107i	$-0.135557\pi$
$607$	12.2589	+	12.2589i	0.497575	+	0.497575i	−0.413107	+	0.910682i	$0.635557\pi$
$608$		0			0
$609$	4.01642	−	5.52812i	0.162753	−	0.224011i
$610$		0			0
$611$	6.79291	+	9.34964i	0.274812	+	0.378246i
$612$		0			0
$613$	−3.40746	−	21.5139i	−0.137626	−	0.868938i	−0.955811	−	0.293982i	$-0.905019\pi$
$613$	−3.40746	−	21.5139i	−0.137626	−	0.868938i	0.818185	−	0.574955i	$-0.194981\pi$
$614$		0			0
$615$	9.03559	+	12.5509i	0.364350	+	0.506101i
$616$		0			0
$617$	−5.88424	−	2.99817i	−0.236891	−	0.120702i	0.331516	−	0.943450i	$-0.392440\pi$
$617$	−5.88424	−	2.99817i	−0.236891	−	0.120702i	−0.568407	+	0.822748i	$0.692440\pi$
$618$		0			0
$619$	−13.7716	−	42.3846i	−0.553528	−	1.70358i	−0.699800	−	0.714338i	$-0.746728\pi$
$619$	−13.7716	−	42.3846i	−0.553528	−	1.70358i	0.146273	−	0.989244i	$-0.453272\pi$
$620$		0			0
$621$	−1.68040	+	5.17172i	−0.0674319	+	0.207534i
$622$		0			0
$623$	0.443924	−	2.80282i	0.0177854	−	0.112293i
$624$		0			0
$625$	−24.9962	−	0.435065i	−0.999849	−	0.0174026i
$626$		0			0
$627$	−11.5612	−	1.83111i	−0.461710	−	0.0731276i
$628$		0			0
$629$	15.6193	+	5.07503i	0.622784	+	0.202355i
$630$		0			0
$631$	−7.02958	+	2.28405i	−0.279843	+	0.0909265i	−0.445576	−	0.895244i	$-0.647001\pi$
$631$	−7.02958	+	2.28405i	−0.279843	+	0.0909265i	0.165733	+	0.986171i	$0.447001\pi$
$632$		0			0
$633$	−5.63731	+	11.0638i	−0.224063	+	0.439748i
$634$		0			0
$635$	28.9065	−	20.8103i	1.14712	−	0.825831i
$636$		0			0
$637$	−8.31394	+	1.31680i	−0.329410	+	0.0521735i
$638$		0			0
$639$	1.52494	−	1.10793i	0.0603255	−	0.0438291i
$640$		0			0
$641$	7.88973	+	5.73223i	0.311626	+	0.226409i	0.732594	−	0.680666i	$-0.238310\pi$
$641$	7.88973	+	5.73223i	0.311626	+	0.226409i	−0.420968	+	0.907075i	$0.638310\pi$
$642$		0			0
$643$	28.0440	−	28.0440i	1.10595	−	1.10595i	0.112270	−	0.993678i	$-0.464188\pi$
$643$	28.0440	−	28.0440i	1.10595	−	1.10595i	0.993678	−	0.112270i	$-0.0358122\pi$
$644$		0			0
$645$	−28.2454	+	14.2373i	−1.11216	+	0.560593i
$646$		0			0
$647$	−14.9306	+	7.60751i	−0.586982	+	0.299082i	−0.722146	−	0.691741i	$-0.756844\pi$
$647$	−14.9306	+	7.60751i	−0.586982	+	0.299082i	0.135164	+	0.990823i	$0.456844\pi$
$648$		0			0
$649$			21.4307i			0.841229i
$650$		0			0
$651$			10.4245i			0.408568i
$652$		0			0
$653$	20.2493	−	10.3175i	0.792417	−	0.403757i	−0.0104270	−	0.999946i	$-0.503319\pi$
$653$	20.2493	−	10.3175i	0.792417	−	0.403757i	0.802844	+	0.596189i	$0.203319\pi$
$654$		0			0
$655$	−4.64592	+	9.02089i	−0.181531	+	0.352475i
$656$		0			0
$657$	−0.323224	+	0.323224i	−0.0126102	+	0.0126102i
$658$		0			0
$659$	27.2858	+	19.8243i	1.06290	+	0.772244i	0.974623	−	0.223852i	$-0.0718632\pi$
$659$	27.2858	+	19.8243i	1.06290	+	0.772244i	0.0882794	+	0.996096i	$0.471863\pi$
$660$		0			0
$661$	−33.0378	+	24.0033i	−1.28502	+	0.933622i	−0.999692	−	0.0248083i	$-0.992102\pi$
$661$	−33.0378	+	24.0033i	−1.28502	+	0.933622i	−0.285328	+	0.958430i	$0.592102\pi$
$662$		0			0
$663$	−60.1908	+	9.53328i	−2.33762	+	0.370242i
$664$		0			0
$665$	5.46465	+	17.0708i	0.211910	+	0.661978i
$666$		0			0
$667$	0.811100	−	1.59187i	0.0314059	−	0.0616376i
$668$		0			0
$669$	24.6074	−	7.99542i	0.951376	−	0.309121i
$670$		0			0
$671$	3.74275	+	1.21609i	0.144487	+	0.0469468i
$672$		0			0
$673$	−6.65972	−	1.05480i	−0.256713	−	0.0406594i	0.0267512	−	0.999642i	$-0.491484\pi$
$673$	−6.65972	−	1.05480i	−0.256713	−	0.0406594i	−0.283465	+	0.958983i	$0.591484\pi$
$674$		0			0
$675$	−4.19137	+	25.0505i	−0.161326	+	0.964194i
$676$		0			0
$677$	6.38634	−	40.3217i	0.245447	−	1.54969i	−0.489766	−	0.871854i	$-0.662918\pi$
$677$	6.38634	−	40.3217i	0.245447	−	1.54969i	0.735213	−	0.677836i	$-0.237082\pi$
$678$		0			0
$679$	−10.9677	+	33.7552i	−0.420903	+	1.29541i
$680$		0			0
$681$	9.92072	+	30.5328i	0.380163	+	1.17002i
$682$		0			0
$683$	23.8558	+	12.1551i	0.912818	+	0.465104i	0.846315	−	0.532683i	$-0.178816\pi$
$683$	23.8558	+	12.1551i	0.912818	+	0.465104i	0.0665024	+	0.997786i	$0.478816\pi$
$684$		0			0
$685$	−2.10403	+	2.86961i	−0.0803908	+	0.109642i
$686$		0			0
$687$	5.40691	+	34.1379i	0.206286	+	1.30244i
$688$		0			0
$689$	36.8293	+	50.6911i	1.40308	+	1.93118i
$690$		0			0
$691$	10.0700	−	13.8601i	0.383079	−	0.527263i	−0.573318	−	0.819333i	$-0.694344\pi$
$691$	10.0700	−	13.8601i	0.383079	−	0.527263i	0.956397	+	0.292070i	$0.0943439\pi$
$692$		0			0
$693$	0.399622	+	0.399622i	0.0151804	+	0.0151804i
$694$		0			0
$695$	0.320275	−	1.96672i	0.0121487	−	0.0746019i
$696$		0			0
$697$	−11.9221	−	23.3985i	−0.451583	−	0.886282i
$698$		0			0
$699$	23.2239			0.878409
$700$		0			0
$701$	−15.5330			−0.586675			−0.293337	−	0.956009i	$-0.594766\pi$
$701$	−15.5330			−0.586675			−0.293337	+	0.956009i	$0.594766\pi$
$702$		0			0
$703$	3.84446	+	7.54518i	0.144997	+	0.284572i
$704$		0			0
$705$	8.80255	−	1.35495i	0.331523	−	0.0510305i
$706$		0			0
$707$	18.4618	+	18.4618i	0.694326	+	0.694326i
$708$		0			0
$709$	13.1370	−	18.0816i	0.493371	−	0.679067i	−0.487634	−	0.873048i	$-0.662140\pi$
$709$	13.1370	−	18.0816i	0.493371	−	0.679067i	0.981005	+	0.193981i	$0.0621400\pi$
$710$		0			0
$711$	−0.328854	−	0.452629i	−0.0123330	−	0.0169749i
$712$		0			0
$713$	0.426378	+	2.69204i	0.0159680	+	0.100818i
$714$		0			0
$715$	−0.0954300	+	21.9334i	−0.00356888	+	0.820263i
$716$		0			0
$717$	7.28953	+	3.71420i	0.272232	+	0.138709i
$718$		0			0
$719$	−5.66246	−	17.4272i	−0.211174	−	0.649927i	−0.999403	−	0.0345449i	$-0.989002\pi$
$719$	−5.66246	−	17.4272i	−0.211174	−	0.649927i	0.788229	−	0.615382i	$-0.210998\pi$
$720$		0			0
$721$	0.869444	−	2.67587i	0.0323798	−	0.0996547i
$722$		0			0
$723$	6.22035	−	39.2738i	0.231337	−	1.46061i
$724$		0			0
$725$	2.64761	−	7.91353i	0.0983298	−	0.293901i
$726$		0			0
$727$	20.0537	+	3.17619i	0.743749	+	0.117798i	0.516797	−	0.856108i	$-0.327124\pi$
$727$	20.0537	+	3.17619i	0.743749	+	0.117798i	0.226951	+	0.973906i	$0.427124\pi$
$728$		0			0
$729$	24.4943	+	7.95869i	0.907197	+	0.294766i
$730$		0			0
$731$	51.0826	−	16.5977i	1.88936	−	0.613889i
$732$		0			0
$733$	14.2639	−	27.9944i	0.526848	−	1.03400i	−0.462252	−	0.886749i	$-0.652958\pi$
$733$	14.2639	−	27.9944i	0.526848	−	1.03400i	0.989100	−	0.147248i	$-0.0470415\pi$
$734$		0			0
$735$	−2.03141	+	6.16071i	−0.0749298	+	0.227241i
$736$		0			0
$737$	−18.5852	+	2.94361i	−0.684595	+	0.108429i
$738$		0			0
$739$	−2.90158	+	2.10812i	−0.106736	+	0.0775486i	−0.639873	−	0.768481i	$-0.721013\pi$
$739$	−2.90158	+	2.10812i	−0.106736	+	0.0775486i	0.533137	+	0.846029i	$0.321013\pi$
$740$		0			0
$741$	−25.4214	−	18.4697i	−0.933879	−	0.678503i
$742$		0			0
$743$	10.7663	−	10.7663i	0.394978	−	0.394978i	−0.481479	−	0.876458i	$-0.659900\pi$
$743$	10.7663	−	10.7663i	0.394978	−	0.394978i	0.876458	+	0.481479i	$0.159900\pi$
$744$		0			0
$745$	18.2028	+	18.3619i	0.666900	+	0.672729i
$746$		0			0
$747$	−1.98488	+	1.01135i	−0.0726230	+	0.0370033i
$748$		0			0
$749$			42.8164i			1.56448i
$750$		0			0
$751$			36.9923i			1.34987i	0.737878	+	0.674934i	$0.235828\pi$
$751$			36.9923i			1.34987i	−0.737878	+	0.674934i	$0.764172\pi$
$752$		0			0
$753$	15.7228	−	8.01118i	0.572972	−	0.291944i
$754$		0			0
$755$	32.0515	+	32.3316i	1.16647	+	1.17667i
$756$		0			0
$757$	−5.41056	+	5.41056i	−0.196650	+	0.196650i	−0.798562	−	0.601912i	$-0.794406\pi$
$757$	−5.41056	+	5.41056i	−0.196650	+	0.196650i	0.601912	+	0.798562i	$0.294406\pi$
$758$		0			0
$759$	2.92780	+	2.12717i	0.106272	+	0.0772113i
$760$		0			0
$761$	−14.0563	+	10.2125i	−0.509539	+	0.370202i	−0.812649	−	0.582754i	$-0.801975\pi$
$761$	−14.0563	+	10.2125i	−0.509539	+	0.370202i	0.303109	+	0.952956i	$0.401975\pi$
$762$		0			0
$763$	−33.3211	+	5.27754i	−1.20630	+	0.191060i
$764$		0			0
$765$	−0.600496	+	1.82114i	−0.0217110	+	0.0658433i
$766$		0			0
$767$	−26.1182	+	51.2598i	−0.943072	+	1.85088i
$768$		0			0
$769$	−13.3053	+	4.32317i	−0.479803	+	0.155897i	−0.538926	−	0.842353i	$-0.681170\pi$
$769$	−13.3053	+	4.32317i	−0.479803	+	0.155897i	0.0591228	+	0.998251i	$0.481170\pi$
$770$		0			0
$771$	−22.1007	−	7.18096i	−0.795938	−	0.258616i
$772$		0			0
$773$	−18.2188	−	2.88557i	−0.655284	−	0.103787i	−0.180066	−	0.983655i	$-0.557631\pi$
$773$	−18.2188	−	2.88557i	−0.655284	−	0.103787i	−0.475219	+	0.879868i	$0.657631\pi$
$774$		0			0
$775$	3.82843	+	12.1412i	0.137521	+	0.436124i
$776$		0			0
$777$	1.56644	−	9.89012i	0.0561958	−	0.354806i
$778$		0			0
$779$	4.18429	−	12.8779i	0.149918	−	0.461400i
$780$		0			0
$781$	8.71855	+	26.8329i	0.311974	+	0.960158i
$782$		0			0
$783$	−7.55375	−	3.84883i	−0.269949	−	0.137546i
$784$		0			0
$785$	−0.0232109	+	5.33473i	−0.000828432	+	0.190405i
$786$		0			0
$787$	4.35561	+	27.5002i	0.155261	+	0.980277i	0.935122	+	0.354325i	$0.115289\pi$
$787$	4.35561	+	27.5002i	0.155261	+	0.980277i	−0.779862	+	0.625952i	$0.784711\pi$
$788$		0			0
$789$	−5.22360	−	7.18967i	−0.185965	−	0.255959i
$790$		0			0
$791$	3.84297	−	5.28939i	0.136640	−	0.188069i
$792$		0			0
$793$	7.47014	+	7.47014i	0.265273	+	0.265273i
$794$		0			0
$795$	47.7249	−	7.34618i	1.69263	−	0.260542i
$796$		0			0
$797$	0.947071	+	1.85873i	0.0335470	+	0.0658397i	0.907172	−	0.420761i	$-0.138237\pi$
$797$	0.947071	+	1.85873i	0.0335470	+	0.0658397i	−0.873625	+	0.486600i	$0.838237\pi$
$798$		0			0
$799$	−15.1234			−0.535028
$800$		0			0
$801$	0.156539			0.00553105
$802$		0			0
$803$	−3.10623	−	6.09633i	−0.109617	−	0.215135i
$804$		0			0
$805$	0.890711	−	5.46960i	0.0313934	−	0.192778i
$806$		0			0
$807$	−6.89593	−	6.89593i	−0.242748	−	0.242748i
$808$		0			0
$809$	6.47075	−	8.90622i	0.227499	−	0.313126i	−0.679973	−	0.733237i	$-0.738009\pi$
$809$	6.47075	−	8.90622i	0.227499	−	0.313126i	0.907473	+	0.420111i	$0.138009\pi$
$810$		0			0
$811$	32.8255	+	45.1804i	1.15266	+	1.58650i	0.735276	+	0.677768i	$0.237053\pi$
$811$	32.8255	+	45.1804i	1.15266	+	1.58650i	0.417383	+	0.908731i	$0.362947\pi$
$812$		0			0
$813$	−2.77002	−	17.4892i	−0.0971488	−	0.613373i
$814$		0			0
$815$	24.4541	−	33.3520i	0.856588	−	1.16827i
$816$		0			0
$817$	24.6763	+	12.5732i	0.863313	+	0.439880i
$818$		0			0
$819$	0.468820	+	1.44288i	0.0163819	+	0.0504183i
$820$		0			0
$821$	12.1155	−	37.2876i	0.422833	−	1.30135i	−0.482221	−	0.876049i	$-0.660170\pi$
$821$	12.1155	−	37.2876i	0.422833	−	1.30135i	0.905054	−	0.425296i	$-0.139830\pi$
$822$		0			0
$823$	−1.70819	+	10.7851i	−0.0595438	+	0.375945i	0.939864	+	0.341548i	$0.110951\pi$
$823$	−1.70819	+	10.7851i	−0.0595438	+	0.375945i	−0.999408	+	0.0343970i	$0.989049\pi$
$824$		0			0
$825$	14.9934	+	7.80460i	0.522004	+	0.271721i
$826$		0			0
$827$	−54.7925	−	8.67827i	−1.90532	−	0.301773i	−0.911369	−	0.411591i	$-0.864973\pi$
$827$	−54.7925	−	8.67827i	−1.90532	−	0.301773i	−0.993952	+	0.109818i	$0.964973\pi$
$828$		0			0
$829$	33.2430	+	10.8013i	1.15458	+	0.375145i	0.822865	−	0.568236i	$-0.192374\pi$
$829$	33.2430	+	10.8013i	1.15458	+	0.375145i	0.331711	+	0.943381i	$0.392374\pi$
$830$		0			0
$831$	20.1581	−	6.54975i	0.699275	−	0.227208i
$832$		0			0
$833$	5.00088	−	9.81478i	0.173270	−	0.340062i
$834$		0			0
$835$	−16.3254	−	50.9984i	−0.564964	−	1.76487i
$836$		0			0
$837$	12.7743	−	2.02325i	0.441544	−	0.0699337i
$838$		0			0
$839$	4.37152	−	3.17609i	0.150922	−	0.109651i	−0.509762	−	0.860315i	$-0.670267\pi$
$839$	4.37152	−	3.17609i	0.150922	−	0.109651i	0.660684	+	0.750665i	$0.270267\pi$
$840$		0			0
$841$	−21.2081	−	15.4086i	−0.731314	−	0.531330i
$842$		0			0
$843$	15.1985	−	15.1985i	0.523464	−	0.523464i
$844$		0			0
$845$	−13.6495	+	26.5029i	−0.469557	+	0.911729i
$846$		0			0
$847$	15.1531	−	7.72087i	0.520665	−	0.265292i
$848$		0			0
$849$		−	26.1901i		−	0.898840i
$850$		0			0
$851$		−	2.61812i		−	0.0897479i
$852$		0			0
$853$	−1.38358	+	0.704971i	−0.0473730	+	0.0241377i	−0.477517	−	0.878623i	$-0.658463\pi$
$853$	−1.38358	+	0.704971i	−0.0473730	+	0.0241377i	0.430144	+	0.902761i	$0.358463\pi$
$854$		0			0
$855$	−0.882928	+	0.445046i	−0.0301955	+	0.0152203i
$856$		0			0
$857$	−9.74010	+	9.74010i	−0.332716	+	0.332716i	−0.853617	−	0.520901i	$-0.825596\pi$
$857$	−9.74010	+	9.74010i	−0.332716	+	0.332716i	0.520901	+	0.853617i	$0.325596\pi$
$858$		0			0
$859$	24.4862	+	17.7903i	0.835458	+	0.606996i	0.921098	−	0.389331i	$-0.127294\pi$
$859$	24.4862	+	17.7903i	0.835458	+	0.606996i	−0.0856403	+	0.996326i	$0.527294\pi$
$860$		0			0
$861$	−12.9536	+	9.41134i	−0.441457	+	0.320737i
$862$		0			0
$863$	31.1887	−	4.93981i	1.06168	−	0.168153i	0.398918	−	0.916987i	$-0.369386\pi$
$863$	31.1887	−	4.93981i	1.06168	−	0.168153i	0.662758	+	0.748834i	$0.269386\pi$
$864$		0			0
$865$	−23.4612	+	16.8901i	−0.797704	+	0.574280i
$866$		0			0
$867$	22.5558	−	44.2683i	0.766036	−	1.50343i
$868$		0			0
$869$	7.96452	−	2.58783i	0.270178	−	0.0877861i
$870$		0			0
$871$	−48.0411	−	15.6095i	−1.62781	−	0.528908i
$872$		0			0
$873$	−1.93376	−	0.306277i	−0.0654478	−	0.0103659i
$874$		0			0
$875$	0.337837	−	25.8812i	0.0114210	−	0.874945i
$876$		0			0
$877$	−1.68458	+	10.6360i	−0.0568843	+	0.359154i	0.942784	+	0.333404i	$0.108197\pi$
$877$	−1.68458	+	10.6360i	−0.0568843	+	0.359154i	−0.999668	+	0.0257497i	$0.991803\pi$
$878$		0			0
$879$	−1.00768	+	3.10133i	−0.0339883	+	0.104605i
$880$		0			0
$881$	−6.51130	−	20.0397i	−0.219371	−	0.675155i	−0.998814	−	0.0486820i	$-0.984498\pi$
$881$	−6.51130	−	20.0397i	−0.219371	−	0.675155i	0.779443	−	0.626473i	$-0.215502\pi$
$882$		0			0
$883$	−22.8713	−	11.6535i	−0.769680	−	0.392171i	0.0246204	−	0.999697i	$-0.492162\pi$
$883$	−22.8713	−	11.6535i	−0.769680	−	0.392171i	−0.794300	+	0.607525i	$0.792162\pi$
$884$		0			0
$885$	25.9035	+	35.9812i	0.870736	+	1.20950i
$886$		0			0
$887$	3.32841	+	21.0148i	0.111757	+	0.705607i	0.978407	+	0.206690i	$0.0662690\pi$
$887$	3.32841	+	21.0148i	0.111757	+	0.705607i	−0.866649	+	0.498918i	$0.833731\pi$
$888$		0			0
$889$	21.6757	+	29.8340i	0.726979	+	1.00060i
$890$		0			0
$891$	10.5243	−	14.4855i	0.352577	−	0.485281i
$892$		0			0
$893$	−5.51401	−	5.51401i	−0.184519	−	0.184519i
$894$		0			0
$895$	7.06036	+	14.0071i	0.236002	+	0.468204i
$896$		0			0
$897$	4.41051	+	8.65612i	0.147263	+	0.289019i
$898$		0			0
$899$	−4.24928			−0.141721
$900$		0			0
$901$	−81.9949			−2.73165
$902$		0			0
$903$	−14.8675	−	29.1791i	−0.494760	−	0.971020i
$904$		0			0
$905$	7.27228	+	3.74536i	0.241739	+	0.124500i
$906$		0			0
$907$	3.71790	+	3.71790i	0.123451	+	0.123451i	0.766133	−	0.642682i	$-0.222178\pi$
$907$	3.71790	+	3.71790i	0.123451	+	0.123451i	−0.642682	+	0.766133i	$0.722178\pi$
$908$		0			0
$909$	−0.846554	+	1.16518i	−0.0280784	+	0.0386467i
$910$		0			0
$911$	34.6026	+	47.6263i	1.14643	+	1.57793i	0.752220	+	0.658913i	$0.228983\pi$
$911$	34.6026	+	47.6263i	1.14643	+	1.57793i	0.394214	+	0.919018i	$0.371017\pi$
$912$		0			0
$913$	−5.21620	−	32.9338i	−0.172631	−	1.08995i
$914$		0			0
$915$	7.75382	−	2.48212i	0.256333	−	0.0820565i
$916$		0			0
$917$	−9.36051	−	4.76942i	−0.309111	−	0.157500i
$918$		0			0
$919$	1.60613	+	4.94315i	0.0529812	+	0.163060i	0.974046	−	0.226350i	$-0.0726792\pi$
$919$	1.60613	+	4.94315i	0.0529812	+	0.163060i	−0.921065	+	0.389409i	$0.872679\pi$
$920$		0			0
$921$	−7.01771	+	21.5983i	−0.231242	+	0.711688i
$922$		0			0
$923$	−11.8482	+	74.8068i	−0.389989	+	2.46230i
$924$		0			0
$925$	−1.80778	−	12.0941i	−0.0594395	−	0.397651i
$926$		0			0
$927$	0.153295	+	0.0242795i	0.00503486	+	0.000797443i
$928$		0			0
$929$	−20.4118	−	6.63220i	−0.669690	−	0.217596i	−0.0456141	−	0.998959i	$-0.514524\pi$
$929$	−20.4118	−	6.63220i	−0.669690	−	0.217596i	−0.624076	+	0.781364i	$0.714524\pi$
$930$		0			0
$931$	5.40180	−	1.75515i	0.177037	−	0.0575227i
$932$		0			0
$933$	−10.8356	+	21.2661i	−0.354742	+	0.696220i
$934$		0			0
$935$	−23.1473	−	16.9719i	−0.756999	−	0.555040i
$936$		0			0
$937$	−8.73364	+	1.38327i	−0.285316	+	0.0451895i	−0.297452	−	0.954737i	$-0.596137\pi$
$937$	−8.73364	+	1.38327i	−0.285316	+	0.0451895i	0.0121363	+	0.999926i	$0.496137\pi$
$938$		0			0
$939$	−7.83176	+	5.69010i	−0.255580	+	0.185690i
$940$		0			0
$941$	23.9277	+	17.3845i	0.780021	+	0.566719i	0.904985	−	0.425443i	$-0.139882\pi$
$941$	23.9277	+	17.3845i	0.780021	+	0.566719i	−0.124964	+	0.992161i	$0.539882\pi$
$942$		0			0
$943$	−2.96023	+	2.96023i	−0.0963982	+	0.0963982i
$944$		0			0
$945$	−25.9543	−	4.22660i	−0.844295	−	0.137491i
$946$		0			0
$947$	−11.3470	+	5.78157i	−0.368727	+	0.187876i	−0.628529	−	0.777786i	$-0.716343\pi$
$947$	−11.3470	+	5.78157i	−0.368727	+	0.187876i	0.259802	+	0.965662i	$0.416343\pi$
$948$		0			0
$949$		−	18.3673i		−	0.596229i
$950$		0			0
$951$			55.3092i			1.79352i
$952$		0			0
$953$	−10.6704	+	5.43682i	−0.345647	+	0.176116i	−0.618192	−	0.786027i	$-0.712135\pi$
$953$	−10.6704	+	5.43682i	−0.345647	+	0.176116i	0.272545	+	0.962143i	$0.412135\pi$
$954$		0			0
$955$	−4.79962	−	31.1811i	−0.155312	−	1.00900i
$956$		0			0
$957$	−3.98952	+	3.98952i	−0.128963	+	0.128963i
$958$		0			0
$959$	−2.98046	−	2.16543i	−0.0962442	−	0.0699255i
$960$		0			0
$961$	−19.8350	+	14.4110i	−0.639838	+	0.464870i
$962$		0			0
$963$	−2.33280	+	0.369480i	−0.0751736	+	0.0119063i
$964$		0			0
$965$	47.0596	+	0.204752i	1.51490	+	0.00659118i
$966$		0			0
$967$	−17.8583	+	35.0489i	−0.574284	+	1.12710i	0.403008	+	0.915197i	$0.367965\pi$
$967$	−17.8583	+	35.0489i	−0.574284	+	1.12710i	−0.977292	+	0.211899i	$0.932035\pi$
$968$		0			0
$969$	39.1076	−	12.7068i	1.25632	−	0.408202i
$970$		0			0
$971$	−30.3771	−	9.87011i	−0.974846	−	0.316747i	−0.222076	−	0.975029i	$-0.571283\pi$
$971$	−30.3771	−	9.87011i	−0.974846	−	0.316747i	−0.752771	+	0.658283i	$0.771283\pi$
$972$		0			0
$973$	2.03764	+	0.322730i	0.0653237	+	0.0103463i
$974$		0			0
$975$	26.3508	+	36.9406i	0.843902	+	1.18304i
$976$		0			0
$977$	1.13690	−	7.17811i	0.0363727	−	0.229648i	−0.962805	−	0.270198i	$-0.912911\pi$
$977$	1.13690	−	7.17811i	0.0363727	−	0.229648i	0.999178	+	0.0405496i	$0.0129109\pi$
$978$		0			0
$979$	−0.724059	+	2.22843i	−0.0231410	+	0.0712208i
$980$		0			0
$981$	−0.575081	−	1.76992i	−0.0183609	−	0.0565092i
$982$		0			0
$983$	2.63672	+	1.34348i	0.0840984	+	0.0428503i	0.495534	−	0.868589i	$-0.334972\pi$
$983$	2.63672	+	1.34348i	0.0840984	+	0.0428503i	−0.411435	+	0.911439i	$0.634972\pi$
$984$		0			0
$985$	26.8250	+	8.84520i	0.854717	+	0.281832i
$986$		0			0
$987$	1.44247	+	9.10741i	0.0459144	+	0.289892i
$988$		0			0
$989$	−5.03289	−	6.92718i	−0.160037	−	0.220271i
$990$		0			0
$991$	−7.22323	+	9.94193i	−0.229454	+	0.315816i	−0.908184	−	0.418572i	$-0.862531\pi$
$991$	−7.22323	+	9.94193i	−0.229454	+	0.315816i	0.678730	+	0.734388i	$0.262531\pi$
$992$		0			0
$993$	−37.7460	−	37.7460i	−1.19783	−	1.19783i
$994$		0			0
$995$	7.22725	−	7.16463i	0.229119	−	0.227134i
$996$		0			0
$997$	−9.37501	−	18.3995i	−0.296910	−	0.582718i	0.693568	−	0.720391i	$-0.256038\pi$
$997$	−9.37501	−	18.3995i	−0.296910	−	0.582718i	−0.990478	+	0.137673i	$0.956038\pi$
$998$		0			0
$999$	−12.4235			−0.393062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.b.223.2	yes	56
4.3	odd	2		800.2.bq.a.223.6	✓	56
25.12	odd	20		800.2.bq.a.287.6	yes	56
100.87	even	20	inner	800.2.bq.b.287.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.a.223.6	✓	56	4.3	odd	2
800.2.bq.a.287.6	yes	56	25.12	odd	20
800.2.bq.b.223.2	yes	56	1.1	even	1	trivial
800.2.bq.b.287.2	yes	56	100.87	even	20	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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.802897 - 1.57577i) q^{3} +(1.58800 - 1.57424i) q^{5} +(1.63701 + 1.63701i) q^{7} +(-0.0750643 + 0.103317i) q^{9} +(-1.12357 - 1.54647i) q^{11} +(-0.802739 - 5.06830i) q^{13} +(-3.75566 - 1.23838i) q^{15} +(5.98323 + 3.04861i) q^{17} +(1.06996 + 3.29301i) q^{19} +(1.26521 - 3.89391i) q^{21} +(0.167463 - 1.05732i) q^{23} +(0.0435082 - 4.99981i) q^{25} +(-5.01720 - 0.794647i) q^{27} +(1.58725 + 0.515730i) q^{29} +(-2.42148 + 0.786787i) q^{31} +(-1.53477 + 3.01215i) q^{33} +(5.17664 + 0.0225230i) q^{35} +(2.41558 - 0.382590i) q^{37} +(-7.34197 + 5.33426i) q^{39} +(-3.16381 - 2.29864i) q^{41} +(5.65583 - 5.65583i) q^{43} +(0.0434441 + 0.282238i) q^{45} +(-2.00667 + 1.02245i) q^{47} -1.64038i q^{49} -11.8759i q^{51} +(-10.8796 + 5.54343i) q^{53} +(-4.21876 - 0.687014i) q^{55} +(4.32997 - 4.32997i) q^{57} +(-9.07009 - 6.58981i) q^{59} +(-1.66556 + 1.21010i) q^{61} +(-0.292013 + 0.0462503i) q^{63} +(-9.25349 - 6.78476i) q^{65} +(4.46901 - 8.77093i) q^{67} +(-1.80056 + 0.585036i) q^{69} +(-14.0374 - 4.56101i) q^{71} +(3.53528 + 0.559934i) q^{73} +(-7.91350 + 3.94577i) q^{75} +(0.692281 - 4.37089i) q^{77} +(-1.35379 + 4.16655i) q^{79} +(2.89450 + 8.90837i) q^{81} +(15.5424 + 7.91927i) q^{83} +(14.3006 - 4.57787i) q^{85} +(-0.461727 - 2.91523i) q^{87} +(-0.720489 - 0.991668i) q^{89} +(6.98277 - 9.61096i) q^{91} +(3.18400 + 3.18400i) q^{93} +(6.88311 + 3.54493i) q^{95} +(6.96008 + 13.6599i) q^{97} +0.244117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{5} + 4 q^{7} - 6 q^{13} + 42 q^{15} - 2 q^{17} + 18 q^{19} + 16 q^{21} + 8 q^{23} - 34 q^{25} - 42 q^{27} - 20 q^{31} - 36 q^{33} - 22 q^{35} + 20 q^{37} + 36 q^{39} + 16 q^{41} + 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) \) 56 * q - 2 * q^5 + 4 * q^7 - 6 * q^13 + 42 * q^15 - 2 * q^17 + 18 * q^19 + 16 * q^21 + 8 * q^23 - 34 * q^25 - 42 * q^27 - 20 * q^31 - 36 * q^33 - 22 * q^35 + 20 * q^37 + 36 * q^39 + 16 * q^41 + 32 * q^43 - 4 * q^45 + 8 * q^47 + 48 * q^53 - 8 * q^55 - 8 * q^57 + 4 * q^59 + 36 * q^61 - 2 * q^63 + 2 * q^65 - 6 * q^67 - 60 * q^69 + 10 * q^71 - 2 * q^73 - 26 * q^75 - 72 * q^77 - 16 * q^79 + 54 * q^81 + 28 * q^83 + 62 * q^85 - 24 * q^87 + 30 * q^89 + 30 * q^91 + 20 * q^93 - 8 * q^95 - 46 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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