LMFDB - Embedded newform 800.2.bq.a.223.6

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			223.6
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.a.287.6

$q$-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	$0.0205513\pi$
$3$	0.802897	+	1.57577i	0.463553	+	0.909774i	−0.534364	+	0.845255i	$0.679449\pi$
$4$		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	0.326474	−	0.945206i	$-0.394140\pi$
$7$	−1.63701	−	1.63701i	−0.618732	−	0.618732i	−0.945206	+	0.326474i	$0.894140\pi$
$8$		0			0
$9$	−0.0750643	+	0.103317i	−0.0250214	+	0.0344391i
$10$		0			0
$11$	1.12357	+	1.54647i	0.338770	+	0.466277i	0.944082	−	0.329711i	$-0.106951\pi$
$11$	1.12357	+	1.54647i	0.338770	+	0.466277i	−0.605312	+	0.795989i	$0.706951\pi$
$12$		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	$-0.969991\pi$
$19$	−1.06996	−	3.29301i	−0.245467	−	0.755469i	0.750093	−	0.661333i	$-0.230009\pi$
$20$		0			0
$21$	1.26521	−	3.89391i	0.276091	−	0.849722i
$22$		0			0
$23$	−0.167463	+	1.05732i	−0.0349185	+	0.220467i	−0.998977	−	0.0452237i	$-0.985600\pi$
$23$	−0.167463	+	1.05732i	−0.0349185	+	0.220467i	0.964058	+	0.265691i	$0.0855999\pi$
$24$		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	−0.0833756	−	0.996518i	$-0.526570\pi$
$31$	2.42148	−	0.786787i	0.434911	−	0.141311i	0.518286	+	0.855207i	$0.326570\pi$
$32$		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	−0.991629	−	0.129122i	$-0.958784\pi$
$43$	−5.65583	+	5.65583i	−0.862506	+	0.862506i	0.129122	+	0.991629i	$0.458784\pi$
$44$		0			0
$45$	0.0434441	+	0.282238i	0.00647627	+	0.0420735i
$46$		0			0
$47$	2.00667	−	1.02245i	0.292703	−	0.149140i	−0.301473	−	0.953475i	$-0.597478\pi$
$47$	2.00667	−	1.02245i	0.292703	−	0.149140i	0.594176	+	0.804335i	$0.297478\pi$
$48$		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	0.992264	−	0.124142i	$-0.0396178\pi$
$59$	9.07009	+	6.58981i	1.18082	+	0.857920i	0.188561	+	0.982062i	$0.439618\pi$
$60$		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	$0.355354\pi$
$67$	−4.46901	+	8.77093i	−0.545977	+	1.07154i	−0.984918	+	0.173024i	$0.944646\pi$
$68$		0			0
$69$	−1.80056	+	0.585036i	−0.216761	+	0.0704301i
$70$		0			0
$71$	14.0374	+	4.56101i	1.66593	+	0.541293i	0.982102	−	0.188352i	$-0.0603147\pi$
$71$	14.0374	+	4.56101i	1.66593	+	0.541293i	0.683826	+	0.729645i	$0.260315\pi$
$72$		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	−0.845565	−	0.533872i	$-0.820736\pi$
$79$	1.35379	−	4.16655i	0.152314	−	0.468773i	0.997879	+	0.0650989i	$0.0207363\pi$
$80$		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	$-0.943303\pi$
$83$	−15.5424	−	7.91927i	−1.70601	−	0.869253i	−0.721827	−	0.692074i	$-0.756697\pi$
$84$		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	0.916591	−	0.399827i	$-0.130930\pi$
$103$	0.551746	+	1.08286i	0.0543651	+	0.106698i	−0.862225	+	0.506525i	$0.830930\pi$
$104$		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	$-0.897911\pi$
$107$	−13.0776	−	13.0776i	−1.26426	−	1.26426i	−0.315253	−	0.949008i	$-0.602089\pi$
$108$		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	−0.587357	−	0.809328i	$-0.699832\pi$
$127$	−15.7328	−	2.49184i	−1.39606	−	0.221115i	−0.808706	+	0.588213i	$0.799832\pi$
$128$		0			0
$129$	−13.4534	−	4.37126i	−1.18450	−	0.384868i
$130$		0			0
$131$	4.31577	−	1.40228i	0.377070	−	0.122518i	−0.114349	−	0.993441i	$-0.536478\pi$
$131$	4.31577	−	1.40228i	0.377070	−	0.122518i	0.491419	+	0.870923i	$0.336478\pi$
$132$		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	−0.617940	−	0.786225i	$-0.712033\pi$
$139$	−0.720939	+	0.523792i	−0.0611492	+	0.0444275i	0.556791	+	0.830653i	$0.312033\pi$
$140$		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	$-0.689232\pi$
$151$		−	20.3599i		−	1.65687i	0.560087	−	0.828434i	$-0.310768\pi$
$152$		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	−0.823264	−	0.567659i	$-0.807849\pi$
$163$	−18.2675	+	2.89328i	−1.43082	+	0.226619i	−0.607554	+	0.794278i	$0.707849\pi$
$164$		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	$0.527238\pi$
$167$	−10.8718	+	21.3372i	−0.841287	+	1.65112i	−0.755822	+	0.654778i	$0.772762\pi$
$168$		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	−0.836781	−	0.547538i	$-0.815565\pi$
$179$	2.16773	−	6.67160i	0.162024	−	0.498659i	0.998805	+	0.0488796i	$0.0155651\pi$
$180$		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	−0.995714	−	0.0924903i	$-0.970517\pi$
$191$	−8.29296	+	11.4143i	−0.600058	+	0.825909i	0.395656	+	0.918399i	$0.370517\pi$
$192$		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	$-0.551572\pi$
$199$	−4.55115			−0.322623			−0.161311	+	0.986904i	$0.551572\pi$
$200$		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	0.927090	−	0.374838i	$-0.122302\pi$
$211$	4.12697	+	5.68028i	0.284112	+	0.391047i	−0.642978	+	0.765884i	$0.722302\pi$
$212$		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	$-0.787051\pi$
$223$	2.28864	−	14.4499i	0.153259	−	0.967639i	0.937703	−	0.347439i	$-0.112949\pi$
$224$		0			0
$225$	0.513300	+	0.379803i	0.0342200	+	0.0253202i
$226$		0			0
$227$	17.9295	+	2.83975i	1.19002	+	0.188481i	0.719872	−	0.694107i	$-0.244200\pi$
$227$	17.9295	+	2.83975i	1.19002	+	0.188481i	0.470149	+	0.882587i	$0.344200\pi$
$228$		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	−0.460128	−	0.887853i	$-0.652196\pi$
$239$	3.74251	−	2.71909i	0.242083	−	0.175884i	0.702211	+	0.711969i	$0.252196\pi$
$240$		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	$-0.898030\pi$
$251$		−	9.97785i		−	0.629796i	0.949125	−	0.314898i	$-0.101970\pi$
$252$		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	−0.307566	−	0.951527i	$-0.599515\pi$
$263$	−4.96316	+	0.786087i	−0.306041	+	0.0484722i	0.00152499	+	0.999999i	$0.499515\pi$
$264$		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	0.00516117	−	0.999987i	$-0.498357\pi$
$271$	−9.52234	−	3.09399i	−0.578441	−	0.187947i	−0.583602	+	0.812040i	$0.698357\pi$
$272$		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	0.0154732	−	0.999880i	$-0.495075\pi$
$283$	−13.1948	−	6.72311i	−0.784352	−	0.399647i	−0.799825	+	0.600233i	$0.795075\pi$
$284$		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	0.917033	−	0.398811i	$-0.130577\pi$
$307$	9.07999	+	9.07999i	0.518222	+	0.518222i	−0.398811	+	0.917033i	$0.630577\pi$
$308$		0			0
$309$	−1.26335	+	1.73885i	−0.0718695	+	0.0989199i
$310$		0			0
$311$	7.93253	+	10.9182i	0.449813	+	0.619114i	0.972357	−	0.233498i	$-0.0750172\pi$
$311$	7.93253	+	10.9182i	0.449813	+	0.619114i	−0.522545	+	0.852612i	$0.675017\pi$
$312$		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	−0.961501	−	0.274802i	$-0.911388\pi$
$331$	−28.7064	+	9.32728i	−1.57785	+	0.512673i	−0.616346	+	0.787476i	$0.711388\pi$
$332$		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	0.567235	−	0.823556i	$-0.308013\pi$
$347$	29.1884	−	14.8723i	1.56692	−	0.798384i	0.999683	+	0.0251719i	$0.00801330\pi$
$348$		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	0.142122	−	0.989849i	$-0.454607\pi$
$359$	−14.3121	−	10.3983i	−0.755362	−	0.548802i	−0.897484	+	0.441047i	$0.854607\pi$
$360$		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	−0.879979	−	0.475012i	$-0.842444\pi$
$367$	0.412877	−	0.810317i	0.0215520	−	0.0422982i	0.901531	+	0.432714i	$0.142444\pi$
$368$		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	−0.935377	−	0.353652i	$-0.884940\pi$
$379$	0.569050	−	1.75136i	0.0292301	−	0.0899611i	0.964607	+	0.263691i	$0.0849398\pi$
$380$		0			0
$381$	−8.70527	−	26.7921i	−0.445985	−	1.37260i
$382$		0			0
$383$	13.8405	+	7.05210i	0.707218	+	0.360345i	0.770316	−	0.637662i	$-0.220098\pi$
$383$	13.8405	+	7.05210i	0.707218	+	0.360345i	−0.0630986	+	0.998007i	$0.520098\pi$
$384$		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	0.950866	−	0.309604i	$-0.100196\pi$
$419$	−0.00780791	−	0.0240303i	−0.000381441	−	0.00117396i	−0.951247	+	0.308430i	$0.900196\pi$
$420$		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	$-0.180744\pi$
$431$	38.2252	−	12.4201i	1.84124	−	0.598256i	0.998171	−	0.0604570i	$-0.0192558\pi$
$432$		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	−0.950236	−	0.311531i	$-0.899158\pi$
$439$	−19.8543	+	14.4250i	−0.947592	+	0.688466i	0.00264427	+	0.999997i	$0.499158\pi$
$440$		0			0
$441$	0.169480	+	0.123134i	0.00807046	+	0.00586353i
$442$		0			0
$443$	0.733468	−	0.733468i	0.0348481	−	0.0348481i	−0.689468	−	0.724316i	$-0.742156\pi$
$443$	0.733468	−	0.733468i	0.0348481	−	0.0348481i	0.724316	+	0.689468i	$0.242156\pi$
$444$		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	0.924414	−	0.381390i	$-0.124555\pi$
$463$	41.3445	−	6.54832i	1.92144	−	0.304326i	0.997026	+	0.0770638i	$0.0245545\pi$
$464$		0			0
$465$	10.0686	+	0.0438074i	0.466920	+	0.00203152i
$466$		0			0
$467$	−7.38246	+	14.4889i	−0.341620	+	0.670466i	−0.996347	−	0.0853991i	$-0.972783\pi$
$467$	−7.38246	+	14.4889i	−0.341620	+	0.670466i	0.654727	+	0.755865i	$0.272783\pi$
$468$		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	−0.887979	−	0.459885i	$-0.847891\pi$
$479$	2.20447	−	6.78465i	0.100725	−	0.309998i	0.988703	+	0.149886i	$0.0478907\pi$
$480$		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	$0.216983\pi$
$487$	5.13557	+	32.4247i	0.232715	+	1.46930i	−0.543806	+	0.839211i	$0.683017\pi$
$488$		0			0
$489$	−19.2260	−	26.4624i	−0.869432	−	1.19667i
$490$		0			0
$491$	1.51395	−	2.08378i	0.0683238	−	0.0940396i	−0.773488	−	0.633811i	$-0.781489\pi$
$491$	1.51395	−	2.08378i	0.0683238	−	0.0940396i	0.841811	+	0.539772i	$0.181489\pi$
$492$		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	$-0.270808\pi$
$499$	29.4600			1.31881			0.659406	+	0.751787i	$0.270808\pi$
$500$		0			0
$501$	−42.3515			−1.89213
$502$		0			0
$503$	6.35254	+	12.4676i	0.283246	+	0.555902i	0.988167	−	0.153385i	$-0.0490174\pi$
$503$	6.35254	+	12.4676i	0.283246	+	0.555902i	−0.704921	+	0.709286i	$0.749017\pi$
$504$		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	$0.184915\pi$
$523$	−2.94267	+	18.5793i	−0.128674	+	0.812416i	−0.964628	+	0.263616i	$0.915085\pi$
$524$		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	0.259718	−	0.965685i	$-0.416370\pi$
$547$	27.9167	−	14.2243i	1.19363	−	0.608186i	0.933914	+	0.357499i	$0.116370\pi$
$548$		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	−0.260935	−	0.965356i	$-0.584031\pi$
$563$	−5.00149	+	0.792158i	−0.210788	+	0.0333855i	0.0501475	+	0.998742i	$0.484031\pi$
$564$		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	0.761509	−	0.648154i	$-0.224459\pi$
$571$	23.8146	+	7.73782i	0.996608	+	0.323818i	0.235099	+	0.971972i	$0.424459\pi$
$572$		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	$-0.884018\pi$
$587$	−3.77597	−	23.8405i	−0.155851	−	0.984004i	0.778499	−	0.627646i	$-0.215982\pi$
$588$		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	$-0.517146\pi$
$599$	−2.63535			−0.107678			−0.0538388	+	0.998550i	$0.517146\pi$
$600$		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	0.413107	−	0.910682i	$-0.364443\pi$
$607$	−12.2589	−	12.2589i	−0.497575	−	0.497575i	−0.910682	+	0.413107i	$0.864443\pi$
$608$		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	$0.253272\pi$
$619$	13.7716	+	42.3846i	0.553528	+	1.70358i	−0.146273	+	0.989244i	$0.546728\pi$
$620$		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	−0.165733	−	0.986171i	$-0.552999\pi$
$631$	7.02958	−	2.28405i	0.279843	−	0.0909265i	0.445576	+	0.895244i	$0.352999\pi$
$632$		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	$0.535812\pi$
$643$	−28.0440	+	28.0440i	−1.10595	+	1.10595i	−0.993678	+	0.112270i	$0.964188\pi$
$644$		0			0
$645$	−28.2454	+	14.2373i	−1.11216	+	0.560593i
$646$		0			0
$647$	14.9306	−	7.60751i	0.586982	−	0.299082i	−0.135164	−	0.990823i	$-0.543156\pi$
$647$	14.9306	−	7.60751i	0.586982	−	0.299082i	0.722146	+	0.691741i	$0.243156\pi$
$648$		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	−0.0882794	−	0.996096i	$-0.528137\pi$
$659$	−27.2858	−	19.8243i	−1.06290	−	0.772244i	−0.974623	+	0.223852i	$0.928137\pi$
$660$		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	−0.0665024	−	0.997786i	$-0.521184\pi$
$683$	−23.8558	−	12.1551i	−0.912818	−	0.465104i	−0.846315	+	0.532683i	$0.821184\pi$
$684$		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	−0.956397	−	0.292070i	$-0.905656\pi$
$691$	−10.0700	+	13.8601i	−0.383079	+	0.527263i	0.573318	+	0.819333i	$0.305656\pi$
$692$		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	$0.0109982\pi$
$719$	5.66246	+	17.4272i	0.211174	+	0.649927i	−0.788229	+	0.615382i	$0.789002\pi$
$720$		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	−0.226951	−	0.973906i	$-0.572876\pi$
$727$	−20.0537	−	3.17619i	−0.743749	−	0.117798i	−0.516797	+	0.856108i	$0.672876\pi$
$728$		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	−0.533137	−	0.846029i	$-0.678987\pi$
$739$	2.90158	−	2.10812i	0.106736	−	0.0775486i	0.639873	+	0.768481i	$0.278987\pi$
$740$		0			0
$741$	−25.4214	−	18.4697i	−0.933879	−	0.678503i
$742$		0			0
$743$	−10.7663	+	10.7663i	−0.394978	+	0.394978i	−0.876458	−	0.481479i	$-0.840100\pi$
$743$	−10.7663	+	10.7663i	−0.394978	+	0.394978i	0.481479	+	0.876458i	$0.340100\pi$
$744$		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	$-0.764172\pi$
$751$		−	36.9923i		−	1.34987i	0.737878	−	0.674934i	$-0.235828\pi$
$752$		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	$-0.884711\pi$
$787$	−4.35561	−	27.5002i	−0.155261	−	0.980277i	0.779862	−	0.625952i	$-0.215289\pi$
$788$		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	$-0.762947\pi$
$811$	−32.8255	−	45.1804i	−1.15266	−	1.58650i	−0.417383	−	0.908731i	$-0.637053\pi$
$812$		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	$-0.889049\pi$
$823$	1.70819	−	10.7851i	0.0595438	−	0.375945i	0.999408	−	0.0343970i	$-0.0109511\pi$
$824$		0			0
$825$	14.9934	+	7.80460i	0.522004	+	0.271721i
$826$		0			0
$827$	54.7925	+	8.67827i	1.90532	+	0.301773i	0.993952	−	0.109818i	$-0.0350269\pi$
$827$	54.7925	+	8.67827i	1.90532	+	0.301773i	0.911369	+	0.411591i	$0.135027\pi$
$828$		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	−0.660684	−	0.750665i	$-0.729733\pi$
$839$	−4.37152	+	3.17609i	−0.150922	+	0.109651i	0.509762	+	0.860315i	$0.329733\pi$
$840$		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	0.0856403	−	0.996326i	$-0.472706\pi$
$859$	−24.4862	−	17.7903i	−0.835458	−	0.606996i	−0.921098	+	0.389331i	$0.872706\pi$
$860$		0			0
$861$	−12.9536	+	9.41134i	−0.441457	+	0.320737i
$862$		0			0
$863$	−31.1887	+	4.93981i	−1.06168	+	0.168153i	−0.662758	−	0.748834i	$-0.730614\pi$
$863$	−31.1887	+	4.93981i	−1.06168	+	0.168153i	−0.398918	+	0.916987i	$0.630614\pi$
$864$		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	0.794300	−	0.607525i	$-0.207838\pi$
$883$	22.8713	+	11.6535i	0.769680	+	0.392171i	−0.0246204	+	0.999697i	$0.507838\pi$
$884$		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	$-0.933731\pi$
$887$	−3.32841	−	21.0148i	−0.111757	−	0.705607i	0.866649	−	0.498918i	$-0.166269\pi$
$888$		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	0.642682	−	0.766133i	$-0.277822\pi$
$907$	−3.71790	−	3.71790i	−0.123451	−	0.123451i	−0.766133	+	0.642682i	$0.777822\pi$
$908$		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	$-0.771017\pi$
$911$	−34.6026	−	47.6263i	−1.14643	−	1.57793i	−0.394214	−	0.919018i	$-0.628983\pi$
$912$		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	0.921065	−	0.389409i	$-0.127321\pi$
$919$	−1.60613	−	4.94315i	−0.0529812	−	0.163060i	−0.974046	+	0.226350i	$0.927321\pi$
$920$		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	−0.259802	−	0.965662i	$-0.583657\pi$
$947$	11.3470	−	5.78157i	0.368727	−	0.187876i	0.628529	+	0.777786i	$0.283657\pi$
$948$		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	$-0.632035\pi$
$967$	17.8583	−	35.0489i	0.574284	−	1.12710i	0.977292	−	0.211899i	$-0.0679647\pi$
$968$		0			0
$969$	39.1076	−	12.7068i	1.25632	−	0.408202i
$970$		0			0
$971$	30.3771	+	9.87011i	0.974846	+	0.316747i	0.752771	−	0.658283i	$-0.228717\pi$
$971$	30.3771	+	9.87011i	0.974846	+	0.316747i	0.222076	+	0.975029i	$0.428717\pi$
$972$		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	0.411435	−	0.911439i	$-0.365028\pi$
$983$	−2.63672	−	1.34348i	−0.0840984	−	0.0428503i	−0.495534	+	0.868589i	$0.665028\pi$
$984$		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	−0.678730	−	0.734388i	$-0.737469\pi$
$991$	7.22323	−	9.94193i	0.229454	−	0.315816i	0.908184	+	0.418572i	$0.137469\pi$
$992$		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.a.223.6	✓	56
4.3	odd	2		800.2.bq.b.223.2	yes	56
25.12	odd	20		800.2.bq.b.287.2	yes	56
100.87	even	20	inner	800.2.bq.a.287.6	yes	56

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

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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