LMFDB - Embedded newform 387.2.v.a.242.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(8,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 13]))

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

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

chi := DirichletCharacter("387.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.v (of order $14$, degree $6$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			242.11
Character	$\chi$	$=$	387.242
Dual form			387.2.v.a.8.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236651 + 1.03684i) q^{2} +(0.782911 - 0.377030i) q^{4} +(2.02001 + 2.53301i) q^{5} +1.06119i q^{7} +(1.90236 + 2.38548i) q^{8} +O(q^{10})$	\(q+(0.236651 + 1.03684i) q^{2} +(0.782911 - 0.377030i) q^{4} +(2.02001 + 2.53301i) q^{5} +1.06119i q^{7} +(1.90236 + 2.38548i) q^{8} +(-2.14828 + 2.69386i) q^{10} +(0.719103 - 1.49323i) q^{11} +(-4.06847 - 5.10170i) q^{13} +(-1.10028 + 0.251132i) q^{14} +(-0.939580 + 1.17820i) q^{16} +(-1.29154 - 1.02997i) q^{17} +(1.13937 + 2.36592i) q^{19} +(2.53650 + 1.22152i) q^{20} +(1.71842 + 0.392217i) q^{22} +(-0.374849 + 0.778382i) q^{23} +(-1.22310 + 5.35874i) q^{25} +(4.32683 - 5.42567i) q^{26} +(0.400100 + 0.830817i) q^{28} +(1.22530 + 5.36840i) q^{29} +(0.0455817 + 0.199706i) q^{31} +(4.05403 + 1.95232i) q^{32} +(0.762267 - 1.58286i) q^{34} +(-2.68800 + 2.14361i) q^{35} -7.02048i q^{37} +(-2.18345 + 1.74124i) q^{38} +(-2.19967 + 9.63738i) q^{40} +(-4.30116 + 0.981711i) q^{41} +(-5.66107 - 3.30942i) q^{43} -1.44019i q^{44} +(-0.895764 - 0.204452i) q^{46} +(-5.34040 - 11.0894i) q^{47} +5.87388 q^{49} -5.84558 q^{50} +(-5.10875 - 2.46024i) q^{52} +(8.56238 + 6.82827i) q^{53} +(5.23496 - 1.19485i) q^{55} +(-2.53145 + 2.01876i) q^{56} +(-5.27618 + 2.54088i) q^{58} +(-2.92782 - 2.33486i) q^{59} +(1.79863 + 0.410525i) q^{61} +(-0.196276 + 0.0945216i) q^{62} +(-1.73551 + 7.60376i) q^{64} +(4.70431 - 20.6109i) q^{65} +(7.53881 - 3.63050i) q^{67} +(-1.39949 - 0.319425i) q^{68} +(-2.85869 - 2.27973i) q^{70} +(-7.08370 + 3.41133i) q^{71} +(11.9991 - 9.56898i) q^{73} +(7.27909 - 1.66141i) q^{74} +(1.78405 + 1.42273i) q^{76} +(1.58460 + 0.763105i) q^{77} -12.4186 q^{79} -4.88233 q^{80} +(-2.03575 - 4.22728i) q^{82} +(-14.9305 - 3.40780i) q^{83} -5.35203i q^{85} +(2.09163 - 6.65279i) q^{86} +(4.93008 - 1.12526i) q^{88} +(-0.961212 + 4.21135i) q^{89} +(5.41387 - 4.31742i) q^{91} +0.750733i q^{92} +(10.2341 - 8.16145i) q^{94} +(-3.69137 + 7.66521i) q^{95} +(2.13114 + 1.02630i) q^{97} +(1.39006 + 6.09025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 20 q^{4}+O(q^{10}) $ 96 * q - 20 * q^4	$ 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) $ 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.236651	+	1.03684i	0.167338	+	0.733154i	0.987054	+	0.160385i	$0.0512737\pi$
$2$	0.236651	+	1.03684i	0.167338	+	0.733154i	−0.819717	+	0.572769i	$0.805869\pi$
$3$		0			0
$3$		0			0
$4$	0.782911	−	0.377030i	0.391455	−	0.188515i
$5$	2.02001	+	2.53301i	0.903374	+	1.13280i	0.990625	+	0.136609i	$0.0436203\pi$
$5$	2.02001	+	2.53301i	0.903374	+	1.13280i	−0.0872511	+	0.996186i	$0.527808\pi$
$6$		0			0
$7$			1.06119i			0.401092i	0.979684	+	0.200546i	$0.0642716\pi$
$7$			1.06119i			0.401092i	−0.979684	+	0.200546i	$0.935728\pi$
$8$	1.90236	+	2.38548i	0.672586	+	0.843396i
$9$		0			0
$10$	−2.14828	+	2.69386i	−0.679345	+	0.851872i
$11$	0.719103	−	1.49323i	0.216818	−	0.450227i	−0.763984	−	0.645236i	$-0.776759\pi$
$11$	0.719103	−	1.49323i	0.216818	−	0.450227i	0.980802	+	0.195009i	$0.0624735\pi$
$12$		0			0
$13$	−4.06847	−	5.10170i	−1.12839	−	1.41496i	−0.896963	−	0.442107i	$-0.854231\pi$
$13$	−4.06847	−	5.10170i	−1.12839	−	1.41496i	−0.231429	−	0.972852i	$-0.574340\pi$
$14$	−1.10028	+	0.251132i	−0.294062	+	0.0671178i
$15$		0			0
$16$	−0.939580	+	1.17820i	−0.234895	+	0.294549i
$17$	−1.29154	−	1.02997i	−0.313245	−	0.249805i	0.454228	−	0.890885i	$-0.349915\pi$
$17$	−1.29154	−	1.02997i	−0.313245	−	0.249805i	−0.767474	+	0.641081i	$0.778486\pi$
$18$		0			0
$19$	1.13937	+	2.36592i	0.261389	+	0.542780i	0.989818	−	0.142342i	$-0.0454632\pi$
$19$	1.13937	+	2.36592i	0.261389	+	0.542780i	−0.728428	+	0.685122i	$0.759749\pi$
$20$	2.53650	+	1.22152i	0.567179	+	0.273139i
$21$		0			0
$22$	1.71842	+	0.392217i	0.366368	+	0.0836210i
$23$	−0.374849	+	0.778382i	−0.0781614	+	0.162304i	−0.936387	−	0.350968i	$-0.885853\pi$
$23$	−0.374849	+	0.778382i	−0.0781614	+	0.162304i	0.858226	+	0.513272i	$0.171567\pi$
$24$		0			0
$25$	−1.22310	+	5.35874i	−0.244619	+	1.07175i
$26$	4.32683	−	5.42567i	0.848561	−	1.06406i
$27$		0			0
$28$	0.400100	+	0.830817i	0.0756118	+	0.157010i
$29$	1.22530	+	5.36840i	0.227533	+	0.996887i	0.951644	+	0.307203i	$0.0993931\pi$
$29$	1.22530	+	5.36840i	0.227533	+	0.996887i	−0.724111	+	0.689683i	$0.757750\pi$
$30$		0			0
$31$	0.0455817	+	0.199706i	0.00818671	+	0.0358683i	0.978856	−	0.204549i	$-0.0655728\pi$
$31$	0.0455817	+	0.199706i	0.00818671	+	0.0358683i	−0.970670	+	0.240417i	$0.922716\pi$
$32$	4.05403	+	1.95232i	0.716658	+	0.345124i
$33$		0			0
$34$	0.762267	−	1.58286i	0.130728	−	0.271459i
$35$	−2.68800	+	2.14361i	−0.454355	+	0.362336i
$36$		0			0
$37$		−	7.02048i		−	1.15416i	−0.816688	−	0.577080i	$-0.804192\pi$
$37$		−	7.02048i		−	1.15416i	0.816688	−	0.577080i	$-0.195808\pi$
$38$	−2.18345	+	1.74124i	−0.354202	+	0.282466i
$39$		0			0
$40$	−2.19967	+	9.63738i	−0.347798	+	1.52380i
$41$	−4.30116	+	0.981711i	−0.671728	+	0.153318i	−0.544763	−	0.838590i	$-0.683381\pi$
$41$	−4.30116	+	0.981711i	−0.671728	+	0.153318i	−0.126964	+	0.991907i	$0.540523\pi$
$42$		0			0
$43$	−5.66107	−	3.30942i	−0.863306	−	0.504681i
$43$	−5.66107	−	3.30942i	−0.863306	−	0.504681i
$44$		−	1.44019i		−	0.217117i
$45$		0			0
$46$	−0.895764	−	0.204452i	−0.132073	−	0.0301448i
$47$	−5.34040	−	11.0894i	−0.778977	−	1.61756i	−0.786500	−	0.617590i	$-0.788109\pi$
$47$	−5.34040	−	11.0894i	−0.778977	−	1.61756i	0.00752335	−	0.999972i	$-0.497605\pi$
$48$		0			0
$49$	5.87388			0.839125
$50$	−5.84558			−0.826691
$51$		0			0
$52$	−5.10875	−	2.46024i	−0.708456	−	0.341174i
$53$	8.56238	+	6.82827i	1.17613	+	0.937936i	0.998930	−	0.0462386i	$-0.0147235\pi$
$53$	8.56238	+	6.82827i	1.17613	+	0.937936i	0.177204	+	0.984174i	$0.443295\pi$
$54$		0			0
$55$	5.23496	−	1.19485i	0.705882	−	0.161113i
$56$	−2.53145	+	2.01876i	−0.338279	+	0.269769i
$57$		0			0
$58$	−5.27618	+	2.54088i	−0.692797	+	0.333633i
$59$	−2.92782	−	2.33486i	−0.381170	−	0.303973i	0.414097	−	0.910233i	$-0.364098\pi$
$59$	−2.92782	−	2.33486i	−0.381170	−	0.303973i	−0.795266	+	0.606260i	$0.792669\pi$
$60$		0			0
$61$	1.79863	+	0.410525i	0.230290	+	0.0525623i	0.336109	−	0.941823i	$-0.390889\pi$
$61$	1.79863	+	0.410525i	0.230290	+	0.0525623i	−0.105818	+	0.994385i	$0.533746\pi$
$62$	−0.196276	+	0.0945216i	−0.0249271	+	0.0120042i
$63$		0			0
$64$	−1.73551	+	7.60376i	−0.216939	+	0.950470i
$65$	4.70431	−	20.6109i	0.583498	−	2.55647i
$66$		0			0
$67$	7.53881	−	3.63050i	0.921012	−	0.443536i	0.0875798	−	0.996158i	$-0.472087\pi$
$67$	7.53881	−	3.63050i	0.921012	−	0.443536i	0.833432	+	0.552621i	$0.186372\pi$
$68$	−1.39949	−	0.319425i	−0.169713	−	0.0387360i
$69$		0			0
$70$	−2.85869	−	2.27973i	−0.341679	−	0.272480i
$71$	−7.08370	+	3.41133i	−0.840681	+	0.404851i	−0.804110	−	0.594480i	$-0.797358\pi$
$71$	−7.08370	+	3.41133i	−0.840681	+	0.404851i	−0.0365710	+	0.999331i	$0.511643\pi$
$72$		0			0
$73$	11.9991	−	9.56898i	1.40439	−	1.11996i	0.428043	−	0.903758i	$-0.359203\pi$
$73$	11.9991	−	9.56898i	1.40439	−	1.11996i	0.976348	−	0.216206i	$-0.0693684\pi$
$74$	7.27909	−	1.66141i	0.846177	−	0.193134i
$75$		0			0
$76$	1.78405	+	1.42273i	0.204644	+	0.163199i
$77$	1.58460	+	0.763105i	0.180582	+	0.0869639i
$78$		0			0
$79$	−12.4186			−1.39721			−0.698604	−	0.715509i	$-0.746195\pi$
$79$	−12.4186			−1.39721			−0.698604	+	0.715509i	$0.746195\pi$
$80$	−4.88233			−0.545862
$81$		0			0
$82$	−2.03575	−	4.22728i	−0.224811	−	0.466824i
$83$	−14.9305	−	3.40780i	−1.63884	−	0.374055i	−0.698854	−	0.715265i	$-0.746306\pi$
$83$	−14.9305	−	3.40780i	−1.63884	−	0.374055i	−0.939987	+	0.341210i	$0.889163\pi$
$84$		0			0
$85$		−	5.35203i		−	0.580510i
$86$	2.09163	−	6.65279i	0.225546	−	0.717389i
$87$		0			0
$88$	4.93008	−	1.12526i	0.525548	−	0.119953i
$89$	−0.961212	+	4.21135i	−0.101888	+	0.446402i	0.898090	+	0.439812i	$0.144955\pi$
$89$	−0.961212	+	4.21135i	−0.101888	+	0.446402i	−0.999978	+	0.00659004i	$0.997902\pi$
$90$		0			0
$91$	5.41387	−	4.31742i	0.567528	−	0.452589i
$92$			0.750733i			0.0782693i
$93$		0			0
$94$	10.2341	−	8.16145i	1.05557	−	0.841789i
$95$	−3.69137	+	7.66521i	−0.378727	+	0.786434i
$96$		0			0
$97$	2.13114	+	1.02630i	0.216384	+	0.104205i	0.538936	−	0.842347i	$-0.318826\pi$
$97$	2.13114	+	1.02630i	0.216384	+	0.104205i	−0.322552	+	0.946552i	$0.604541\pi$
$98$	1.39006	+	6.09025i	0.140417	+	0.615208i
$99$		0			0
$100$	1.06283	+	4.65656i	0.106283	+	0.465656i
$101$	−1.04369	−	2.16725i	−0.103851	−	0.215649i	0.842568	−	0.538590i	$-0.181043\pi$
$101$	−1.04369	−	2.16725i	−0.103851	−	0.215649i	−0.946419	+	0.322941i	$0.895329\pi$
$102$		0			0
$103$	6.84237	−	8.58006i	0.674199	−	0.845418i	−0.320607	−	0.947212i	$-0.603887\pi$
$103$	6.84237	−	8.58006i	0.674199	−	0.845418i	0.994805	+	0.101794i	$0.0324583\pi$
$104$	4.43033	−	19.4106i	0.434430	−	1.90336i
$105$		0			0
$106$	−5.05351	+	10.4937i	−0.490840	+	1.01924i
$107$	−6.37782	−	1.45569i	−0.616567	−	0.140727i	−0.0971803	−	0.995267i	$-0.530982\pi$
$107$	−6.37782	−	1.45569i	−0.616567	−	0.140727i	−0.519386	+	0.854539i	$0.673839\pi$
$108$		0			0
$109$	9.21959	+	4.43992i	0.883077	+	0.425267i	0.819747	−	0.572725i	$-0.194114\pi$
$109$	9.21959	+	4.43992i	0.883077	+	0.425267i	0.0633296	+	0.997993i	$0.479828\pi$
$110$	2.47772	+	5.14504i	0.236241	+	0.490561i
$111$		0			0
$112$	−1.25029	−	0.997072i	−0.118141	−	0.0942144i
$113$	2.63959	−	3.30994i	0.248312	−	0.311373i	−0.642018	−	0.766690i	$-0.721903\pi$
$113$	2.63959	−	3.30994i	0.248312	−	0.311373i	0.890330	+	0.455317i	$0.150474\pi$
$114$		0			0
$115$	−2.72885	+	0.622841i	−0.254466	+	0.0580802i
$116$	2.98335	+	3.74100i	0.276997	+	0.347343i
$117$		0			0
$118$	1.72800	−	3.58822i	0.159075	−	0.330322i
$119$	1.09299	−	1.37057i	0.100195	−	0.125640i
$120$		0			0
$121$	5.14575	+	6.45257i	0.467796	+	0.586597i
$122$			1.96203i			0.177634i
$123$		0			0
$124$	0.110982	+	0.139167i	0.00996645	+	0.0124975i
$125$	−1.44942	+	0.698003i	−0.129640	+	0.0624313i
$126$		0			0
$127$	−3.43005	−	15.0280i	−0.304368	−	1.33352i	−0.863460	−	0.504418i	$-0.831707\pi$
$127$	−3.43005	−	15.0280i	−0.304368	−	1.33352i	0.559092	−	0.829106i	$-0.311150\pi$
$128$	0.704699			0.0622872
$129$		0			0
$130$	22.4835			1.97193
$131$	2.59764	+	11.3810i	0.226957	+	0.994362i	0.952105	+	0.305770i	$0.0989139\pi$
$131$	2.59764	+	11.3810i	0.226957	+	0.994362i	−0.725149	+	0.688592i	$0.758229\pi$
$132$		0			0
$133$	−2.51069	+	1.20909i	−0.217705	+	0.104841i
$134$	5.54831	+	6.95735i	0.479301	+	0.601024i
$135$		0			0
$136$		−	5.04033i		−	0.432205i
$137$	2.20354	+	2.76315i	0.188261	+	0.236072i	0.867000	−	0.498307i	$-0.166045\pi$
$137$	2.20354	+	2.76315i	0.188261	+	0.236072i	−0.678740	+	0.734379i	$0.737473\pi$
$138$		0			0
$139$	−3.97416	+	4.98344i	−0.337084	+	0.422690i	−0.921266	−	0.388932i	$-0.872844\pi$
$139$	−3.97416	+	4.98344i	−0.337084	+	0.422690i	0.584182	+	0.811623i	$0.301415\pi$
$140$	−1.29626	+	2.69171i	−0.109554	+	0.227491i
$141$		0			0
$142$	−5.21336	−	6.53735i	−0.437496	−	0.548602i
$143$	−10.5437	+	2.40653i	−0.881708	+	0.201244i
$144$		0			0
$145$	−11.1231	+	13.9479i	−0.923721	+	1.15831i
$146$	12.7611	+	10.1766i	1.05611	+	0.842223i
$147$		0			0
$148$	−2.64693	−	5.49641i	−0.217576	−	0.451802i
$149$	−9.35036	−	4.50290i	−0.766012	−	0.368892i	0.00972160	−	0.999953i	$-0.496905\pi$
$149$	−9.35036	−	4.50290i	−0.766012	−	0.368892i	−0.775733	+	0.631061i	$0.782620\pi$
$150$		0			0
$151$	−17.9597	−	4.09920i	−1.46154	−	0.333588i	−0.583478	−	0.812129i	$-0.698309\pi$
$151$	−17.9597	−	4.09920i	−1.46154	−	0.333588i	−0.878065	+	0.478541i	$0.841166\pi$
$152$	−3.47638	+	7.21879i	−0.281972	+	0.585521i
$153$		0			0
$154$	−0.416217	+	1.82357i	−0.0335397	+	0.146947i
$155$	−0.413782	+	0.518867i	−0.0332358	+	0.0416764i
$156$		0			0
$157$	−1.31580	−	2.73230i	−0.105013	−	0.218061i	0.841841	−	0.539725i	$-0.181472\pi$
$157$	−1.31580	−	2.73230i	−0.105013	−	0.218061i	−0.946854	+	0.321665i	$0.895758\pi$
$158$	−2.93889	−	12.8761i	−0.233805	−	1.02437i
$159$		0			0
$160$	3.24393	+	14.2126i	0.256455	+	1.12360i
$161$	−0.826011	−	0.397786i	−0.0650988	−	0.0313499i
$162$		0			0
$163$	−9.58584	+	19.9052i	−0.750821	+	1.55910i	0.0763086	+	0.997084i	$0.475687\pi$
$163$	−9.58584	+	19.9052i	−0.750821	+	1.55910i	−0.827130	+	0.562011i	$0.810028\pi$
$164$	−2.99729	+	2.39026i	−0.234049	+	0.186648i
$165$		0			0
$166$		−	16.2870i		−	1.26412i
$167$	14.2265	−	11.3453i	1.10088	−	0.877925i	0.107665	−	0.994187i	$-0.465663\pi$
$167$	14.2265	−	11.3453i	1.10088	−	0.877925i	0.993219	+	0.116262i	$0.0370913\pi$
$168$		0			0
$169$	−6.58214	+	28.8382i	−0.506318	+	2.21833i
$170$	5.54919	−	1.26657i	0.425603	−	0.0971411i
$171$		0			0
$172$	−5.67986	−	0.456584i	−0.433086	−	0.0348142i
$173$		−	10.7197i		−	0.815005i	−0.913204	−	0.407502i	$-0.866400\pi$
$173$		−	10.7197i		−	0.815005i	0.913204	−	0.407502i	$-0.133600\pi$
$174$		0			0
$175$	−5.68664	−	1.29794i	−0.429869	−	0.0981148i
$176$	1.08367	+	2.25026i	0.0816844	+	0.169619i
$177$		0			0
$178$	−4.59395			−0.344331
$179$	12.4914			0.933653			0.466827	−	0.884349i	$-0.345397\pi$
$179$	12.4914			0.933653			0.466827	+	0.884349i	$0.345397\pi$
$180$		0			0
$181$	−15.5958	−	7.51054i	−1.15923	−	0.558254i	−0.247434	−	0.968905i	$-0.579587\pi$
$181$	−15.5958	−	7.51054i	−1.15923	−	0.558254i	−0.911793	+	0.410651i	$0.865302\pi$
$182$	5.75766	+	4.59158i	0.426786	+	0.340351i
$183$		0			0
$184$	−2.56992	+	0.586567i	−0.189457	+	0.0432423i
$185$	17.7829	−	14.1814i	1.30743	−	1.04264i
$186$		0			0
$187$	−2.46674	+	1.18792i	−0.180386	+	0.0868693i
$188$	−8.36211	−	6.66856i	−0.609869	−	0.486354i
$189$		0			0
$190$	−8.82114	−	2.01337i	−0.639953	−	0.146065i
$191$	−16.4224	+	7.90860i	−1.18828	+	0.572246i	−0.920314	−	0.391181i	$-0.872067\pi$
$191$	−16.4224	+	7.90860i	−1.18828	+	0.572246i	−0.267968	+	0.963428i	$0.586352\pi$
$192$		0			0
$193$	−4.87277	+	21.3490i	−0.350749	+	1.53673i	0.424706	+	0.905331i	$0.360377\pi$
$193$	−4.87277	+	21.3490i	−0.350749	+	1.53673i	−0.775456	+	0.631402i	$0.782480\pi$
$194$	−0.559771	+	2.45252i	−0.0401892	+	0.176080i
$195$		0			0
$196$	4.59872	−	2.21463i	0.328480	−	0.158188i
$197$	11.7811	+	2.68896i	0.839369	+	0.191580i	0.620532	−	0.784181i	$-0.286917\pi$
$197$	11.7811	+	2.68896i	0.839369	+	0.191580i	0.218837	+	0.975761i	$0.429774\pi$
$198$		0			0
$199$	19.0689	+	15.2069i	1.35176	+	1.07799i	0.989285	+	0.145998i	$0.0466393\pi$
$199$	19.0689	+	15.2069i	1.35176	+	1.07799i	0.362474	+	0.931994i	$0.381932\pi$
$200$	−15.1100	+	7.27657i	−1.06843	+	0.514531i
$201$		0			0
$202$	2.00009	−	1.59502i	0.140726	−	0.112225i
$203$	−5.69689	+	1.30028i	−0.399843	+	0.0912616i
$204$		0			0
$205$	−11.1750	−	8.91180i	−0.780499	−	0.622427i
$206$	10.5154	+	5.06394i	0.732641	+	0.352821i
$207$		0			0
$208$	9.83346			0.681828
$209$	4.35220			0.301048
$210$		0			0
$211$	−1.68387	−	3.49660i	−0.115923	−	0.240716i	0.834932	−	0.550353i	$-0.185507\pi$
$211$	−1.68387	−	3.49660i	−0.115923	−	0.240716i	−0.950855	+	0.309637i	$0.899792\pi$
$212$	9.27805	+	2.11765i	0.637219	+	0.145441i
$213$		0			0
$214$		−	6.95725i		−	0.475588i
$215$	−3.05262	−	21.0246i	−0.208187	−	1.43386i
$216$		0			0
$217$	−0.211926	+	0.0483708i	−0.0143865	+	0.00328362i
$218$	−2.42165	+	10.6099i	−0.164015	+	0.718595i
$219$		0			0
$220$	3.64802	−	2.90920i	0.245949	−	0.196138i
$221$			10.7795i			0.725106i
$222$		0			0
$223$	0.286645	−	0.228592i	0.0191952	−	0.0153077i	−0.613845	−	0.789426i	$-0.710378\pi$
$223$	0.286645	−	0.228592i	0.0191952	−	0.0153077i	0.633040	+	0.774119i	$0.281807\pi$
$224$	−2.07178	+	4.30209i	−0.138427	+	0.287446i
$225$		0			0
$226$	4.05653	+	1.95352i	0.269836	+	0.129946i
$227$	2.76603	+	12.1188i	0.183588	+	0.804351i	0.979904	+	0.199470i	$0.0639221\pi$
$227$	2.76603	+	12.1188i	0.183588	+	0.804351i	−0.796316	+	0.604881i	$0.793221\pi$
$228$		0			0
$229$	2.33976	+	10.2511i	0.154615	+	0.677414i	0.991508	+	0.130047i	$0.0415128\pi$
$229$	2.33976	+	10.2511i	0.154615	+	0.677414i	−0.836892	+	0.547367i	$0.815630\pi$
$230$	−1.29157	−	2.68197i	−0.0851636	−	0.176844i
$231$		0			0
$232$	−10.4753	+	13.1356i	−0.687735	+	0.862392i
$233$	−5.97366	+	26.1723i	−0.391347	+	1.71460i	0.268565	+	0.963262i	$0.413451\pi$
$233$	−5.97366	+	26.1723i	−0.391347	+	1.71460i	−0.659912	+	0.751343i	$0.729406\pi$
$234$		0			0
$235$	17.3020	−	35.9280i	1.12866	−	2.34368i
$236$	−3.17253	−	0.724110i	−0.206514	−	0.0471356i
$237$		0			0
$238$	1.67972	+	0.808909i	0.108880	+	0.0524338i
$239$	6.80166	+	14.1238i	0.439963	+	0.913592i	0.996565	+	0.0828128i	$0.0263903\pi$
$239$	6.80166	+	14.1238i	0.439963	+	0.913592i	−0.556603	+	0.830779i	$0.687895\pi$
$240$		0			0
$241$	−0.794428	−	0.633535i	−0.0511736	−	0.0408096i	0.597569	−	0.801817i	$-0.296133\pi$
$241$	−0.794428	−	0.633535i	−0.0511736	−	0.0408096i	−0.648743	+	0.761008i	$0.724705\pi$
$242$	−5.47251	+	6.86231i	−0.351786	+	0.441126i
$243$		0			0
$244$	1.56294	−	0.356732i	0.100057	−	0.0228374i
$245$	11.8653	+	14.8786i	0.758044	+	0.950557i
$246$		0			0
$247$	7.43476	−	15.4384i	0.473062	−	0.982324i
$248$	−0.389684	+	0.488648i	−0.0247449	+	0.0310292i
$249$		0			0
$250$	−1.06672	−	1.33763i	−0.0674654	−	0.0845990i
$251$		−	4.96044i		−	0.313100i	−0.987670	−	0.156550i	$-0.949963\pi$
$251$		−	4.96044i		−	0.313100i	0.987670	−	0.156550i	$-0.0500372\pi$
$252$		0			0
$253$	0.892751	+	1.11947i	0.0561268	+	0.0703808i
$254$	14.7699	−	7.11281i	0.926746	−	0.446298i
$255$		0			0
$256$	3.63778	+	15.9382i	0.227361	+	0.996136i
$257$	−1.55279			−0.0968601			−0.0484300	−	0.998827i	$-0.515422\pi$
$257$	−1.55279			−0.0968601			−0.0484300	+	0.998827i	$0.515422\pi$
$258$		0			0
$259$	7.45006			0.462924
$260$	−4.08789	−	17.9102i	−0.253520	−	1.11074i
$261$		0			0
$262$	−11.1855	+	5.38666i	−0.691043	+	0.332789i
$263$	8.44204	+	10.5860i	0.520558	+	0.652759i	0.970727	−	0.240184i	$-0.0772077\pi$
$263$	8.44204	+	10.5860i	0.520558	+	0.652759i	−0.450169	+	0.892943i	$0.648636\pi$
$264$		0			0
$265$			35.4817i			2.17963i
$266$	−1.84778	−	2.31705i	−0.113295	−	0.142067i
$267$		0			0
$268$	4.53341	−	5.68471i	0.276922	−	0.347249i
$269$	8.39296	−	17.4282i	0.511728	−	1.06261i	−0.471775	−	0.881719i	$-0.656386\pi$
$269$	8.39296	−	17.4282i	0.511728	−	1.06261i	0.983503	−	0.180894i	$-0.0578992\pi$
$270$		0			0
$271$	14.4043	+	18.0625i	0.875001	+	1.09722i	0.994537	+	0.104387i	$0.0332881\pi$
$271$	14.4043	+	18.0625i	0.875001	+	1.09722i	−0.119535	+	0.992830i	$0.538140\pi$
$272$	2.42701	−	0.553950i	0.147159	−	0.0335882i
$273$		0			0
$274$	−2.34346	+	2.93861i	−0.141574	+	0.177528i
$275$	7.12231	+	5.67986i	0.429492	+	0.342508i
$276$		0			0
$277$	−0.0114759	−	0.0238300i	−0.000689521	−	0.00143181i	0.900624	−	0.434600i	$-0.143110\pi$
$277$	−0.0114759	−	0.0238300i	−0.000689521	−	0.00143181i	−0.901313	+	0.433168i	$0.857396\pi$
$278$	−6.10751	−	2.94122i	−0.366304	−	0.176403i
$279$		0			0
$280$	−10.2271	−	2.33427i	−0.611185	−	0.139499i
$281$	4.23277	−	8.78944i	0.252506	−	0.524334i	−0.735729	−	0.677276i	$-0.763160\pi$
$281$	4.23277	−	8.78944i	0.252506	−	0.524334i	0.988235	+	0.152942i	$0.0488747\pi$
$282$		0			0
$283$	3.63942	−	15.9454i	0.216341	−	0.947853i	−0.743814	−	0.668386i	$-0.766985\pi$
$283$	3.63942	−	15.9454i	0.216341	−	0.947853i	0.960155	−	0.279466i	$-0.0901576\pi$
$284$	−4.25973	+	5.34154i	−0.252769	+	0.316962i
$285$		0			0
$286$	−4.99036	−	10.3626i	−0.295086	−	0.612752i
$287$	−1.04178	−	4.56434i	−0.0614944	−	0.269425i
$288$		0			0
$289$	−3.17561	−	13.9133i	−0.186801	−	0.818428i
$290$	−17.0940	−	8.23203i	−1.00379	−	0.483401i
$291$		0			0
$292$	5.78645	−	12.0157i	0.338626	−	0.703165i
$293$	−15.4255	+	12.3014i	−0.901169	+	0.718658i	−0.960116	−	0.279603i	$-0.909797\pi$
$293$	−15.4255	+	12.3014i	−0.901169	+	0.718658i	0.0589470	+	0.998261i	$0.481226\pi$
$294$		0			0
$295$		−	12.1326i		−	0.706388i
$296$	16.7472	−	13.3555i	0.973413	−	0.776271i
$297$		0			0
$298$	2.45600	−	10.7604i	0.142272	−	0.623334i
$299$	5.49614	−	1.25446i	0.317850	−	0.0725472i
$300$		0			0
$301$	3.51192	−	6.00747i	0.202424	−	0.346265i
$302$		−	19.5914i		−	1.12736i
$303$		0			0
$304$	−3.85805	−	0.880575i	−0.221274	−	0.0505044i
$305$	2.59337	+	5.38519i	0.148496	+	0.308355i
$306$		0			0
$307$	−22.8306			−1.30301			−0.651504	−	0.758645i	$-0.725862\pi$
$307$	−22.8306			−1.30301			−0.651504	+	0.758645i	$0.725862\pi$
$308$	1.52832			0.0870839
$309$		0			0
$310$	−0.635902	−	0.306234i	−0.0361168	−	0.0173929i
$311$	−7.17437	−	5.72137i	−0.406821	−	0.324429i	0.398608	−	0.917122i	$-0.369494\pi$
$311$	−7.17437	−	5.72137i	−0.406821	−	0.324429i	−0.805429	+	0.592692i	$0.798065\pi$
$312$		0			0
$313$	−28.8754	+	6.59061i	−1.63213	+	0.372524i	−0.937812	−	0.347143i	$-0.887152\pi$
$313$	−28.8754	+	6.59061i	−1.63213	+	0.372524i	−0.694320	+	0.719666i	$0.744295\pi$
$314$	2.52156	−	2.01088i	0.142300	−	0.113480i
$315$		0			0
$316$	−9.72269	+	4.68220i	−0.546944	+	0.263394i
$317$	−6.45543	−	5.14804i	−0.362573	−	0.289143i	0.425210	−	0.905095i	$-0.360200\pi$
$317$	−6.45543	−	5.14804i	−0.362573	−	0.289143i	−0.787784	+	0.615952i	$0.788772\pi$
$318$		0			0
$319$	8.89739	+	2.03077i	0.498158	+	0.113701i
$320$	−22.7661	+	10.9636i	−1.27266	+	0.612883i
$321$		0			0
$322$	0.216963	−	0.950575i	0.0120909	−	0.0529735i
$323$	0.965290	−	4.22921i	0.0537102	−	0.235320i
$324$		0			0
$325$	32.3148	−	15.5620i	1.79250	−	0.863225i
$326$	−22.9069	−	5.22836i	−1.26870	−	0.289572i
$327$		0			0
$328$	−10.5242	−	8.39277i	−0.581102	−	0.463413i
$329$	11.7680	−	5.66717i	0.648791	−	0.312441i
$330$		0			0
$331$	3.64017	−	2.90294i	0.200082	−	0.159560i	−0.518324	−	0.855185i	$-0.673444\pi$
$331$	3.64017	−	2.90294i	0.200082	−	0.159560i	0.718405	+	0.695625i	$0.244872\pi$
$332$	−12.9741	+	2.96126i	−0.712048	+	0.162520i
$333$		0			0
$334$	15.1299	+	12.0657i	0.827874	+	0.660207i
$335$	24.4245	+	11.7622i	1.33445	+	0.642639i
$336$		0			0
$337$	22.7693			1.24032			0.620161	−	0.784475i	$-0.287067\pi$
$337$	22.7693			1.24032			0.620161	+	0.784475i	$0.287067\pi$
$338$	−31.4582			−1.71110
$339$		0			0
$340$	−2.01788	−	4.19016i	−0.109435	−	0.227244i
$341$	0.330986	+	0.0755455i	0.0179239	+	0.00409102i
$342$		0			0
$343$			13.6616i			0.737658i
$344$	−2.87484	−	19.8001i	−0.155001	−	1.06755i
$345$		0			0
$346$	11.1146	−	2.53683i	0.597524	−	0.136381i
$347$	−7.74386	+	33.9281i	−0.415712	+	1.82135i	0.140211	+	0.990122i	$0.455222\pi$
$347$	−7.74386	+	33.9281i	−0.415712	+	1.82135i	−0.555924	+	0.831233i	$0.687635\pi$
$348$		0			0
$349$	0.590652	−	0.471029i	0.0316169	−	0.0252136i	−0.607554	−	0.794278i	$-0.707849\pi$
$349$	0.590652	−	0.471029i	0.0316169	−	0.0252136i	0.639171	+	0.769065i	$0.279278\pi$
$350$		−	6.20327i		−	0.331579i
$351$		0			0
$352$	5.83053	−	4.64969i	0.310768	−	0.247830i
$353$	−1.77620	+	3.68832i	−0.0945377	+	0.196310i	−0.942875	−	0.333146i	$-0.891890\pi$
$353$	−1.77620	+	3.68832i	−0.0945377	+	0.196310i	0.848337	+	0.529456i	$0.177604\pi$
$354$		0			0
$355$	−22.9501	−	11.0522i	−1.21806	−	0.586588i
$356$	0.835260	+	3.65951i	0.0442687	+	0.193954i
$357$		0			0
$358$	2.95611	+	12.9516i	0.156235	+	0.684512i
$359$	−7.73395	−	16.0597i	−0.408182	−	0.847599i	−0.999163	−	0.0409132i	$-0.986973\pi$
$359$	−7.73395	−	16.0597i	−0.408182	−	0.847599i	0.590981	−	0.806686i	$-0.298741\pi$
$360$		0			0
$361$	7.54687	−	9.46347i	0.397204	−	0.498078i
$362$	4.09644	−	17.9477i	0.215304	−	0.943309i
$363$		0			0
$364$	2.61078	−	5.42135i	0.136842	−	0.284156i
$365$	48.4766	+	11.0645i	2.53738	+	0.579141i
$366$		0			0
$367$	21.9461	+	10.5687i	1.14558	+	0.551681i	0.907702	−	0.419615i	$-0.137835\pi$
$367$	21.9461	+	10.5687i	1.14558	+	0.551681i	0.237875	+	0.971296i	$0.423549\pi$
$368$	−0.564886	−	1.17300i	−0.0294467	−	0.0611467i
$369$		0			0
$370$	18.9122	+	15.0819i	0.983196	+	0.784073i
$371$	−7.24609	+	9.08631i	−0.376198	+	0.471738i
$372$		0			0
$373$	4.01917	−	0.917348i	0.208105	−	0.0474985i	−0.117198	−	0.993109i	$-0.537391\pi$
$373$	4.01917	−	0.917348i	0.208105	−	0.0474985i	0.325302	+	0.945610i	$0.394534\pi$
$374$	−1.81544	−	2.27648i	−0.0938739	−	0.117714i
$375$		0			0
$376$	16.2943	−	33.8355i	0.840316	−	1.74493i
$377$	22.4029	−	28.0923i	1.15381	−	1.44683i
$378$		0			0
$379$	7.78243	+	9.75886i	0.399756	+	0.501279i	0.940446	−	0.339944i	$-0.110408\pi$
$379$	7.78243	+	9.75886i	0.399756	+	0.501279i	−0.540689	+	0.841222i	$0.681837\pi$
$380$			7.39293i			0.379250i
$381$		0			0
$382$	−12.0863	−	15.1558i	−0.618389	−	0.775436i
$383$	−29.4808	+	14.1972i	−1.50640	+	0.725443i	−0.991292	−	0.131684i	$-0.957962\pi$
$383$	−29.4808	+	14.1972i	−1.50640	+	0.725443i	−0.515106	+	0.857127i	$0.672247\pi$
$384$		0			0
$385$	1.26796	+	5.55529i	0.0646211	+	0.283124i
$386$	−23.2886			−1.18536
$387$		0			0
$388$	2.05544			0.104349
$389$	−6.96820	−	30.5297i	−0.353302	−	1.54792i	−0.769502	−	0.638644i	$-0.779496\pi$
$389$	−6.96820	−	30.5297i	−0.353302	−	1.54792i	0.416200	−	0.909273i	$-0.363362\pi$
$390$		0			0
$391$	1.28584	−	0.619230i	0.0650280	−	0.0313158i
$392$	11.1742	+	14.0120i	0.564384	+	0.707715i
$393$		0			0
$394$			12.8514i			0.647446i
$395$	−25.0857	−	31.4565i	−1.26220	−	1.58275i
$396$		0			0
$397$	−13.8349	+	17.3485i	−0.694356	+	0.870695i	−0.996588	−	0.0825397i	$-0.973697\pi$
$397$	−13.8349	+	17.3485i	−0.694356	+	0.870695i	0.302232	+	0.953234i	$0.402268\pi$
$398$	−11.2544	+	23.3701i	−0.564134	+	1.17144i
$399$		0			0
$400$	−5.16444	−	6.47601i	−0.258222	−	0.323800i
$401$	−6.27770	+	1.43284i	−0.313493	+	0.0715528i	−0.376373	−	0.926468i	$-0.622829\pi$
$401$	−6.27770	+	1.43284i	−0.313493	+	0.0715528i	0.0628794	+	0.998021i	$0.479972\pi$
$402$		0			0
$403$	0.833395	−	1.04504i	0.0415144	−	0.0520574i
$404$	−1.63424	−	1.30326i	−0.0813063	−	0.0648396i
$405$		0			0
$406$	−2.69635	−	5.59903i	−0.133818	−	0.277875i
$407$	−10.4832	−	5.04845i	−0.519634	−	0.250242i
$408$		0			0
$409$	11.9469	+	2.72680i	0.590736	+	0.134832i	0.507431	−	0.861693i	$-0.330595\pi$
$409$	11.9469	+	2.72680i	0.590736	+	0.134832i	0.0833049	+	0.996524i	$0.473452\pi$
$410$	6.59549	−	13.6957i	0.325728	−	0.676382i
$411$		0			0
$412$	2.12202	−	9.29720i	0.104545	−	0.458040i
$413$	2.47773	−	3.10697i	0.121921	−	0.152884i
$414$		0			0
$415$	−21.5278	−	44.7030i	−1.05676	−	2.19438i
$416$	−6.53356	−	28.6254i	−0.320334	−	1.40348i
$417$		0			0
$418$	1.02995	+	4.51252i	0.0503767	+	0.220715i
$419$	−9.90671	−	4.77082i	−0.483975	−	0.233070i	0.175954	−	0.984398i	$-0.443699\pi$
$419$	−9.90671	−	4.77082i	−0.483975	−	0.233070i	−0.659928	+	0.751329i	$0.729413\pi$
$420$		0			0
$421$	−5.37980	+	11.1713i	−0.262196	+	0.544455i	−0.989956	−	0.141377i	$-0.954847\pi$
$421$	−5.37980	+	11.1713i	−0.262196	+	0.544455i	0.727760	+	0.685832i	$0.240561\pi$
$422$	3.22691	−	2.57338i	0.157084	−	0.125270i
$423$		0			0
$424$			33.4153i			1.62279i
$425$	7.09903	−	5.66128i	0.344353	−	0.274613i
$426$		0			0
$427$	−0.435644	+	1.90868i	−0.0210823	+	0.0923676i
$428$	−5.54210	+	1.26495i	−0.267888	+	0.0611436i
$429$		0			0
$430$	21.0767	−	8.14057i	1.01641	−	0.392573i
$431$		−	2.68007i		−	0.129095i	−0.997915	−	0.0645473i	$-0.979440\pi$
$431$		−	2.68007i		−	0.129095i	0.997915	−	0.0645473i	$-0.0205603\pi$
$432$		0			0
$433$	−12.4983	−	2.85266i	−0.600631	−	0.137090i	−0.0886149	−	0.996066i	$-0.528244\pi$
$433$	−12.4983	−	2.85266i	−0.600631	−	0.137090i	−0.512016	+	0.858976i	$0.671101\pi$
$434$	−0.100305	−	0.208286i	−0.00481481	−	0.00999805i
$435$		0			0
$436$	8.89210			0.425854
$437$	−2.26869			−0.108526
$438$		0			0
$439$	−11.6091	−	5.59063i	−0.554070	−	0.266826i	0.135828	−	0.990732i	$-0.456630\pi$
$439$	−11.6091	−	5.59063i	−0.554070	−	0.266826i	−0.689898	+	0.723906i	$0.742345\pi$
$440$	12.8091	+	10.2149i	0.610648	+	0.486976i
$441$		0			0
$442$	−11.1766	+	2.55098i	−0.531615	+	0.121338i
$443$	13.5398	−	10.7976i	0.643294	−	0.513010i	−0.246635	−	0.969108i	$-0.579325\pi$
$443$	13.5398	−	10.7976i	0.643294	−	0.513010i	0.889929	+	0.456098i	$0.150753\pi$
$444$		0			0
$445$	−12.6090	+	6.07219i	−0.597725	+	0.287849i
$446$	0.304848	+	0.243108i	0.0144350	+	0.0115115i
$447$		0			0
$448$	−8.06903	−	1.84170i	−0.381226	−	0.0870123i
$449$	6.37006	−	3.06766i	0.300622	−	0.144772i	−0.277492	−	0.960728i	$-0.589503\pi$
$449$	6.37006	−	3.06766i	0.300622	−	0.144772i	0.578114	+	0.815956i	$0.303789\pi$
$450$		0			0
$451$	−1.62705	+	7.12858i	−0.0766149	+	0.335672i
$452$	0.818616	−	3.58659i	0.0385044	−	0.168699i
$453$		0			0
$454$	−11.9106	+	5.73584i	−0.558992	+	0.269196i
$455$	21.8721	+	4.99217i	1.02538	+	0.234036i
$456$		0			0
$457$	16.8231	+	13.4160i	0.786950	+	0.627572i	0.932250	−	0.361816i	$-0.117843\pi$
$457$	16.8231	+	13.4160i	0.786950	+	0.627572i	−0.145299	+	0.989388i	$0.546415\pi$
$458$	−10.0751	+	4.85189i	−0.470776	+	0.226714i
$459$		0			0
$460$	−1.90161	+	1.51649i	−0.0886631	+	0.0707065i
$461$	−34.3321	+	7.83609i	−1.59901	+	0.364963i	−0.926846	−	0.375442i	$-0.877491\pi$
$461$	−34.3321	+	7.83609i	−1.59901	+	0.364963i	−0.672161	+	0.740405i	$0.734634\pi$
$462$		0			0
$463$	−15.0342	−	11.9894i	−0.698698	−	0.557193i	0.208436	−	0.978036i	$-0.433163\pi$
$463$	−15.0342	−	11.9894i	−0.698698	−	0.557193i	−0.907133	+	0.420843i	$0.861734\pi$
$464$	−7.47629	−	3.60039i	−0.347078	−	0.167144i
$465$		0			0
$466$	−28.5501			−1.32256
$467$	3.93392			0.182040			0.0910201	−	0.995849i	$-0.470987\pi$
$467$	3.93392			0.182040			0.0910201	+	0.995849i	$0.470987\pi$
$468$		0			0
$469$	3.85265	+	8.00011i	0.177899	+	0.369411i
$470$	41.3460	+	9.43696i	1.90715	+	0.435295i
$471$		0			0
$472$		−	11.4260i		−	0.525925i
$473$	−9.01263	+	6.07349i	−0.414401	+	0.279259i
$474$		0			0
$475$	−14.0719	+	3.21183i	−0.645664	+	0.147369i
$476$	0.338970	−	1.48513i	0.0155367	−	0.0680707i
$477$		0			0
$478$	−13.0344	+	10.3946i	−0.596181	+	0.475439i
$479$			37.3125i			1.70485i	0.522849	+	0.852425i	$0.324869\pi$
$479$			37.3125i			1.70485i	−0.522849	+	0.852425i	$0.675131\pi$
$480$		0			0
$481$	−35.8164	+	28.5626i	−1.63309	+	1.30234i
$482$	0.468870	−	0.973619i	0.0213564	−	0.0443471i
$483$		0			0
$484$	6.46147	+	3.11168i	0.293703	+	0.141440i
$485$	1.70528	+	7.47132i	0.0774327	+	0.339255i
$486$		0			0
$487$	−3.38265	−	14.8204i	−0.153283	−	0.671575i	−0.991918	−	0.126881i	$-0.959503\pi$
$487$	−3.38265	−	14.8204i	−0.153283	−	0.671575i	0.838635	−	0.544693i	$-0.183354\pi$
$488$	2.44233	+	5.07156i	0.110559	+	0.229579i
$489$		0			0
$490$	−12.6187	+	15.8234i	−0.570056	+	0.714827i
$491$	0.698873	−	3.06196i	0.0315397	−	0.138184i	−0.956707	−	0.291054i	$-0.905994\pi$
$491$	0.698873	−	3.06196i	0.0315397	−	0.138184i	0.988246	+	0.152869i	$0.0488513\pi$
$492$		0			0
$493$	3.94676	−	8.19554i	0.177753	−	0.369109i
$494$	17.7666	+	4.05511i	0.799356	+	0.182448i
$495$		0			0
$496$	−0.278121	−	0.133936i	−0.0124880	−	0.00601390i
$497$	−3.62007	−	7.51715i	−0.162382	−	0.337190i
$498$		0			0
$499$	25.3909	+	20.2486i	1.13665	+	0.906452i	0.996493	−	0.0836771i	$-0.0266664\pi$
$499$	25.3909	+	20.2486i	1.13665	+	0.906452i	0.140161	+	0.990129i	$0.455238\pi$
$500$	−0.871597	+	1.09295i	−0.0389790	+	0.0488781i
$501$		0			0
$502$	5.14316	−	1.17389i	0.229551	−	0.0523934i
$503$	−18.9751	−	23.7940i	−0.846058	−	1.06092i	−0.997373	−	0.0724372i	$-0.976922\pi$
$503$	−18.9751	−	23.7940i	−0.846058	−	1.06092i	0.151315	−	0.988486i	$-0.451649\pi$
$504$		0			0
$505$	3.38139	−	7.02154i	0.150470	−	0.312454i
$506$	−0.949442	+	1.19056i	−0.0422078	+	0.0529270i
$507$		0			0
$508$	−8.35145	−	10.4724i	−0.370536	−	0.464637i
$509$		−	13.3892i		−	0.593465i	−0.954961	−	0.296733i	$-0.904103\pi$
$509$		−	13.3892i		−	0.593465i	0.954961	−	0.296733i	$-0.0958970\pi$
$510$		0			0
$511$	10.1545	+	12.7333i	0.449209	+	0.563290i
$512$	−14.3946	+	6.93206i	−0.636156	+	0.306357i
$513$		0			0
$514$	−0.367469	−	1.60999i	−0.0162083	−	0.0710134i
$515$	35.5550			1.56674
$516$		0			0
$517$	−20.3994			−0.897166
$518$	1.76307	+	7.72450i	0.0774647	+	0.339395i
$519$		0			0
$520$	58.1164	−	27.9874i	2.54857	−	1.22733i
$521$	10.9132	+	13.6847i	0.478115	+	0.599538i	0.961137	−	0.276071i	$-0.0890324\pi$
$521$	10.9132	+	13.6847i	0.478115	+	0.599538i	−0.483022	+	0.875608i	$0.660461\pi$
$522$		0			0
$523$		−	30.4372i		−	1.33093i	−0.746430	−	0.665464i	$-0.768234\pi$
$523$		−	30.4372i		−	1.33093i	0.746430	−	0.665464i	$-0.231766\pi$
$524$	6.32470	+	7.93092i	0.276296	+	0.346464i
$525$		0			0
$526$	−8.97812	+	11.2582i	−0.391464	+	0.490881i
$527$	0.146821	−	0.304877i	0.00639563	−	0.0132807i
$528$		0			0
$529$	13.8749	+	17.3986i	0.603256	+	0.756460i
$530$	−36.7888	+	8.39680i	−1.59800	+	0.364734i
$531$		0			0
$532$	−1.50979	+	1.89321i	−0.0654576	+	0.0820812i
$533$	22.5075	+	17.9492i	0.974910	+	0.777465i
$534$		0			0
$535$	−9.19594	−	19.0956i	−0.397575	−	0.825573i
$536$	23.0020	+	11.0772i	0.993536	+	0.478462i
$537$		0			0
$538$	20.0564	+	4.57773i	0.864691	+	0.197360i
$539$	4.22392	−	8.77107i	0.181937	−	0.377797i
$540$		0			0
$541$	9.26974	−	40.6134i	0.398537	−	1.74611i	−0.234624	−	0.972086i	$-0.575386\pi$
$541$	9.26974	−	40.6134i	0.398537	−	1.74611i	0.633161	−	0.774020i	$-0.281757\pi$
$542$	−15.3190	+	19.2095i	−0.658009	+	0.825117i
$543$		0			0
$544$	−3.22512	−	6.69703i	−0.138276	−	0.287133i
$545$	7.37728	+	32.3220i	0.316008	+	1.38452i
$546$		0			0
$547$	7.86379	+	34.4535i	0.336231	+	1.47313i	0.806833	+	0.590779i	$0.201180\pi$
$547$	7.86379	+	34.4535i	0.336231	+	1.47313i	−0.470602	+	0.882346i	$0.655963\pi$
$548$	2.76696	+	1.33250i	0.118199	+	0.0569215i
$549$		0			0
$550$	−4.20358	+	8.72882i	−0.179241	+	0.372198i
$551$	−11.3052	+	9.01556i	−0.481616	+	0.384076i
$552$		0			0
$553$		−	13.1785i		−	0.560408i
$554$	0.0219920	−	0.0175381i	0.000934352	−	0.000745121i
$555$		0			0
$556$	−1.23251	+	5.39997i	−0.0522700	+	0.229010i
$557$	6.91743	−	1.57886i	0.293101	−	0.0668983i	−0.0734422	−	0.997299i	$-0.523398\pi$
$557$	6.91743	−	1.57886i	0.293101	−	0.0668983i	0.366543	+	0.930401i	$0.380541\pi$
$558$		0			0
$559$	6.14826	+	42.3454i	0.260044	+	1.79102i
$560$		−	5.18108i		−	0.218941i
$561$		0			0
$562$	10.1149	+	2.30866i	0.426671	+	0.0973850i
$563$	−18.1277	−	37.6425i	−0.763990	−	1.58644i	−0.809248	−	0.587467i	$-0.800125\pi$
$563$	−18.1277	−	37.6425i	−0.763990	−	1.58644i	0.0452578	−	0.998975i	$-0.485589\pi$
$564$		0			0
$565$	13.7161			0.577040
$566$	17.3940			0.731125
$567$		0			0
$568$	−21.6134	−	10.4085i	−0.906879	−	0.436730i
$569$	27.4478	+	21.8889i	1.15067	+	0.917629i	0.997507	−	0.0705723i	$-0.0224825\pi$
$569$	27.4478	+	21.8889i	1.15067	+	0.917629i	0.153163	+	0.988201i	$0.451054\pi$
$570$		0			0
$571$	−17.4112	+	3.97400i	−0.728638	+	0.166307i	−0.570719	−	0.821145i	$-0.693335\pi$
$571$	−17.4112	+	3.97400i	−0.728638	+	0.166307i	−0.157919	+	0.987452i	$0.550478\pi$
$572$	−7.34743	+	5.85938i	−0.307212	+	0.244993i
$573$		0			0
$574$	4.48594	−	2.16031i	0.187240	−	0.0901698i
$575$	−3.71267	−	2.96076i	−0.154829	−	0.123472i
$576$		0			0
$577$	33.9796	+	7.75562i	1.41459	+	0.322871i	0.860442	−	0.509548i	$-0.170187\pi$
$577$	33.9796	+	7.75562i	1.41459	+	0.322871i	0.554147	+	0.832419i	$0.313044\pi$
$578$	13.6743	−	6.58519i	0.568775	−	0.273908i
$579$		0			0
$580$	−3.44960	+	15.1137i	−0.143237	+	0.627562i
$581$	3.61632	−	15.8441i	0.150030	−	0.657326i
$582$		0			0
$583$	16.3534	−	7.87541i	0.677291	−	0.326166i
$584$	45.6533	+	10.4201i	1.88915	+	0.431185i
$585$		0			0
$586$	−16.4051	−	13.0826i	−0.677687	−	0.540437i
$587$	−3.08978	+	1.48796i	−0.127529	+	0.0614147i	−0.496560	−	0.868002i	$-0.665404\pi$
$587$	−3.08978	+	1.48796i	−0.127529	+	0.0614147i	0.369031	+	0.929417i	$0.379690\pi$
$588$		0			0
$589$	−0.420556	+	0.335382i	−0.0173287	+	0.0138192i
$590$	12.5795	−	2.87120i	0.517892	−	0.118205i
$591$		0			0
$592$	8.27150	+	6.59630i	0.339956	+	0.271106i
$593$	29.9729	+	14.4342i	1.23084	+	0.592741i	0.932310	−	0.361660i	$-0.117790\pi$
$593$	29.9729	+	14.4342i	1.23084	+	0.592741i	0.298529	+	0.954401i	$0.403504\pi$
$594$		0			0
$595$	5.67952			0.232838
$596$	−9.01823			−0.369401
$597$		0			0
$598$	2.60134	+	5.40173i	0.106377	+	0.220893i
$599$	25.5340	+	5.82797i	1.04329	+	0.238125i	0.709635	−	0.704570i	$-0.248860\pi$
$599$	25.5340	+	5.82797i	1.04329	+	0.238125i	0.333657	+	0.942694i	$0.391717\pi$
$600$		0			0
$601$		−	8.15642i		−	0.332707i	−0.986066	−	0.166354i	$-0.946801\pi$
$601$		−	8.15642i		−	0.332707i	0.986066	−	0.166354i	$-0.0531993\pi$
$602$	7.05987	+	2.21961i	0.287739	+	0.0904646i
$603$		0			0
$604$	−15.6064	+	3.56206i	−0.635015	+	0.144938i
$605$	−5.94995	+	26.0684i	−0.241900	+	1.05983i
$606$		0			0
$607$	−36.2201	+	28.8845i	−1.47013	+	1.17239i	−0.522657	+	0.852543i	$0.675059\pi$
$607$	−36.2201	+	28.8845i	−1.47013	+	1.17239i	−0.947470	+	0.319844i	$0.896369\pi$
$608$			11.8159i			0.479200i
$609$		0			0
$610$	−4.96984	+	3.96332i	−0.201223	+	0.160470i
$611$	−34.8478	+	72.3622i	−1.40979	+	2.92746i
$612$		0			0
$613$	−11.7538	−	5.66031i	−0.474730	−	0.228618i	0.181190	−	0.983448i	$-0.442005\pi$
$613$	−11.7538	−	5.66031i	−0.474730	−	0.228618i	−0.655920	+	0.754830i	$0.727719\pi$
$614$	−5.40288	−	23.6716i	−0.218043	−	0.955307i
$615$		0			0
$616$	1.19411	+	5.23175i	0.0481121	+	0.210793i
$617$	5.07505	+	10.5384i	0.204314	+	0.424262i	0.977797	−	0.209555i	$-0.0672016\pi$
$617$	5.07505	+	10.5384i	0.204314	+	0.424262i	−0.773483	+	0.633817i	$0.781487\pi$
$618$		0			0
$619$	14.0697	−	17.6428i	0.565508	−	0.709125i	−0.414057	−	0.910251i	$-0.635889\pi$
$619$	14.0697	−	17.6428i	0.565508	−	0.709125i	0.979565	+	0.201126i	$0.0644600\pi$
$620$	−0.128326	+	0.562235i	−0.00515371	+	0.0225799i
$621$		0			0
$622$	4.23430	−	8.79262i	0.169780	−	0.352552i
$623$	−4.46904	−	1.02003i	−0.179048	−	0.0408666i
$624$		0			0
$625$	20.0652	+	9.66290i	0.802608	+	0.386516i
$626$	−13.6668	−	28.3794i	−0.546235	−	1.13427i
$627$		0			0
$628$	−2.06031	−	1.64305i	−0.0822155	−	0.0655647i
$629$	−7.23089	+	9.06725i	−0.288314	+	0.361535i
$630$		0			0
$631$	1.58367	−	0.361463i	0.0630451	−	0.0143896i	−0.190882	−	0.981613i	$-0.561135\pi$
$631$	1.58367	−	0.361463i	0.0630451	−	0.0143896i	0.253927	+	0.967223i	$0.418278\pi$
$632$	−23.6247	−	29.6245i	−0.939741	−	1.17840i
$633$		0			0
$634$	3.80999	−	7.91152i	0.151314	−	0.314207i
$635$	31.1374	−	39.0451i	1.23565	−	1.54946i
$636$		0			0
$637$	−23.8977	−	29.9668i	−0.946862	−	1.18733i
$638$			9.70573i			0.384253i
$639$		0			0
$640$	1.42350	+	1.78501i	0.0562686	+	0.0705586i
$641$	−9.51046	+	4.57999i	−0.375640	+	0.180899i	−0.612171	−	0.790725i	$-0.709704\pi$
$641$	−9.51046	+	4.57999i	−0.375640	+	0.180899i	0.236531	+	0.971624i	$0.423990\pi$
$642$		0			0
$643$	0.231601	+	1.01471i	0.00913346	+	0.0400163i	0.979289	−	0.202466i	$-0.0648955\pi$
$643$	0.231601	+	1.01471i	0.00913346	+	0.0400163i	−0.970156	+	0.242482i	$0.922038\pi$
$644$	−0.796670			−0.0313932
$645$		0			0
$646$	4.61344			0.181513
$647$	1.13406	+	4.96866i	0.0445846	+	0.195338i	0.992316	−	0.123732i	$-0.0394865\pi$
$647$	1.13406	+	4.96866i	0.0445846	+	0.195338i	−0.947731	+	0.319071i	$0.896629\pi$
$648$		0			0
$649$	−5.59190	+	2.69291i	−0.219501	+	0.105706i
$650$	23.7826	+	29.8224i	0.932831	+	1.16973i
$651$		0			0
$652$			19.1981i			0.751857i
$653$	5.73110	+	7.18658i	0.224275	+	0.281232i	0.881220	−	0.472706i	$-0.156723\pi$
$653$	5.73110	+	7.18658i	0.224275	+	0.281232i	−0.656945	+	0.753939i	$0.728151\pi$
$654$		0			0
$655$	−23.5809	+	29.5695i	−0.921382	+	1.15538i
$656$	2.88463	−	5.99000i	0.112626	−	0.233870i
$657$		0			0
$658$	8.66084	+	10.8604i	0.337635	+	0.423381i
$659$	−38.0081	+	8.67509i	−1.48058	+	0.337934i	−0.885088	−	0.465425i	$-0.845902\pi$
$659$	−38.0081	+	8.67509i	−1.48058	+	0.337934i	−0.595496	+	0.803358i	$0.703045\pi$
$660$		0			0
$661$	14.3224	−	17.9598i	0.557078	−	0.698553i	−0.420937	−	0.907090i	$-0.638299\pi$
$661$	14.3224	−	17.9598i	0.557078	−	0.698553i	0.978015	+	0.208537i	$0.0668700\pi$
$662$	3.87132	+	3.08728i	0.150463	+	0.119990i
$663$		0			0
$664$	−20.2740	−	42.0994i	−0.786785	−	1.63378i
$665$	−8.13424	−	3.91724i	−0.315432	−	0.151904i
$666$		0			0
$667$	−4.63797	−	1.05859i	−0.179583	−	0.0409886i
$668$	6.86060	−	14.2462i	0.265445	−	0.551201i
$669$		0			0
$670$	−6.41542	+	28.1078i	−0.247849	+	1.08590i
$671$	1.90641	−	2.39056i	0.0735960	−	0.0922865i
$672$		0			0
$673$	−10.5892	−	21.9888i	−0.408185	−	0.847606i	−0.999163	−	0.0409174i	$-0.986972\pi$
$673$	−10.5892	−	21.9888i	−0.408185	−	0.847606i	0.590977	−	0.806688i	$-0.298742\pi$
$674$	5.38838	+	23.6080i	0.207553	+	0.909347i
$675$		0			0
$676$	5.71965	+	25.0594i	0.219987	+	0.963824i
$677$	−15.9582	−	7.68507i	−0.613324	−	0.295361i	0.101315	−	0.994854i	$-0.467695\pi$
$677$	−15.9582	−	7.68507i	−0.613324	−	0.295361i	−0.714639	+	0.699493i	$0.753409\pi$
$678$		0			0
$679$	−1.08910	+	2.26154i	−0.0417958	+	0.0867899i
$680$	12.7672	−	10.1815i	0.489599	−	0.390442i
$681$		0			0
$682$			0.361057i			0.0138256i
$683$	−4.18394	+	3.33658i	−0.160094	+	0.127671i	−0.700260	−	0.713888i	$-0.746933\pi$
$683$	−4.18394	+	3.33658i	−0.160094	+	0.127671i	0.540166	+	0.841558i	$0.318361\pi$
$684$		0			0
$685$	−2.54792	+	11.1631i	−0.0973509	+	0.426522i
$686$	−14.1649	+	3.23304i	−0.540817	+	0.123438i
$687$		0			0
$688$	9.21817	−	3.56039i	0.351439	−	0.135739i
$689$		−	71.4634i		−	2.72254i
$690$		0			0
$691$	20.0132	+	4.56789i	0.761340	+	0.173771i	0.585527	−	0.810653i	$-0.300888\pi$
$691$	20.0132	+	4.56789i	0.761340	+	0.173771i	0.175813	+	0.984424i	$0.443745\pi$
$692$	−4.04165	−	8.39258i	−0.153641	−	0.319038i
$693$		0			0
$694$	−37.0105			−1.40490
$695$	−20.6509			−0.783334
$696$		0			0
$697$	6.56626	+	3.16214i	0.248715	+	0.119775i
$698$	0.628159	+	0.500940i	0.0237762	+	0.0189609i
$699$		0			0
$700$	−4.94149	+	1.12786i	−0.186771	+	0.0426292i
$701$	−26.3851	+	21.0414i	−0.996550	+	0.794722i	−0.978737	−	0.205119i	$-0.934242\pi$
$701$	−26.3851	+	21.0414i	−0.996550	+	0.794722i	−0.0178128	+	0.999841i	$0.505670\pi$
$702$		0			0
$703$	16.6099	−	7.99892i	0.626455	−	0.301685i
$704$	10.1062	+	8.05941i	0.380891	+	0.303750i
$705$		0			0
$706$	−4.24453	−	0.968786i	−0.159745	−	0.0364607i
$707$	2.29986	−	1.10756i	0.0864952	−	0.0416539i
$708$		0			0
$709$	5.47816	−	24.0014i	0.205736	−	0.901390i	−0.761631	−	0.648011i	$-0.775601\pi$
$709$	5.47816	−	24.0014i	0.205736	−	0.901390i	0.967367	−	0.253379i	$-0.0815420\pi$
$710$	6.02813	−	26.4110i	0.226232	−	0.991186i
$711$		0			0
$712$	−11.8747	+	5.71854i	−0.445022	+	0.214311i
$713$	−0.172534	−	0.0393798i	−0.00646146	−	0.00147479i
$714$		0			0
$715$	−27.3941	−	21.8460i	−1.02448	−	0.816996i
$716$	9.77967	−	4.70964i	0.365484	−	0.176008i
$717$		0			0
$718$	14.8211	−	11.8194i	0.553117	−	0.441096i
$719$	40.7152	−	9.29297i	1.51842	−	0.346569i	0.619610	−	0.784910i	$-0.287291\pi$
$719$	40.7152	−	9.29297i	1.51842	−	0.346569i	0.898809	+	0.438340i	$0.144434\pi$
$720$		0			0
$721$	9.10507	+	7.26105i	0.339090	+	0.270416i
$722$	11.5981	+	5.58533i	0.431635	+	0.207864i
$723$		0			0
$724$	−15.0418			−0.559025
$725$	−30.2665			−1.12407
$726$		0			0
$727$	1.43168	+	2.97291i	0.0530979	+	0.110259i	0.925830	−	0.377941i	$-0.123368\pi$
$727$	1.43168	+	2.97291i	0.0530979	+	0.110259i	−0.872732	+	0.488200i	$0.837654\pi$
$728$	20.5983	+	4.70142i	0.763423	+	0.174246i
$729$		0			0
$730$			52.8807i			1.95720i
$731$	3.90291	+	10.1050i	0.144354	+	0.373747i
$732$		0			0
$733$	−19.2756	+	4.39953i	−0.711960	+	0.162500i	−0.563137	−	0.826364i	$-0.690406\pi$
$733$	−19.2756	+	4.39953i	−0.711960	+	0.162500i	−0.148823	+	0.988864i	$0.547549\pi$
$734$	−5.76443	+	25.2556i	−0.212769	+	0.932202i
$735$		0			0
$736$	−3.03930	+	2.42376i	−0.112030	+	0.0893410i
$737$		−	13.8679i		−	0.510831i
$738$		0			0
$739$	−13.5340	+	10.7930i	−0.497855	+	0.397026i	−0.839971	−	0.542632i	$-0.817428\pi$
$739$	−13.5340	+	10.7930i	−0.497855	+	0.397026i	0.342116	+	0.939658i	$0.388856\pi$
$740$	8.57563	−	17.8075i	0.315246	−	0.654616i
$741$		0			0
$742$	−11.1358	−	5.36273i	−0.408809	−	0.196872i
$743$	−5.81989	−	25.4986i	−0.213511	−	0.935453i	−0.962160	−	0.272486i	$-0.912154\pi$
$743$	−5.81989	−	25.4986i	−0.213511	−	0.935453i	0.748649	−	0.662967i	$-0.230703\pi$
$744$		0			0
$745$	−7.48192	−	32.7804i	−0.274116	−	1.20098i
$746$	1.90228	+	3.95013i	0.0696475	+	0.144624i
$747$		0			0
$748$	−1.48336	+	1.86007i	−0.0542369	+	0.0680109i
$749$	1.54477	−	6.76807i	0.0564446	−	0.247300i
$750$		0			0
$751$	−1.16706	+	2.42343i	−0.0425868	+	0.0884324i	−0.921177	−	0.389145i	$-0.872771\pi$
$751$	−1.16706	+	2.42343i	−0.0425868	+	0.0884324i	0.878590	+	0.477577i	$0.158485\pi$
$752$	18.0833	+	4.12739i	0.659429	+	0.150510i
$753$		0			0
$754$	34.4288	+	16.5800i	1.25382	+	0.603810i
$755$	−25.8955	−	53.7726i	−0.942434	−	1.95698i
$756$		0			0
$757$	22.8263	+	18.2034i	0.829636	+	0.661613i	0.943313	−	0.331905i	$-0.107691\pi$
$757$	22.8263	+	18.2034i	0.829636	+	0.661613i	−0.113677	+	0.993518i	$0.536263\pi$
$758$	−8.27662	+	10.3786i	−0.300620	+	0.376966i
$759$		0			0
$760$	−25.3076	+	5.77628i	−0.918001	+	0.209528i
$761$	−12.4479	−	15.6092i	−0.451238	−	0.565834i	0.503229	−	0.864153i	$-0.332145\pi$
$761$	−12.4479	−	15.6092i	−0.451238	−	0.565834i	−0.954466	+	0.298319i	$0.903574\pi$
$762$		0			0
$763$	−4.71160	+	9.78374i	−0.170571	+	0.354195i
$764$	−9.87548	+	12.3835i	−0.357282	+	0.448018i
$765$		0			0
$766$	−21.6968	−	27.2070i	−0.783939	−	0.983028i
$767$			24.4362i			0.882340i
$768$		0			0
$769$	−12.6099	−	15.8123i	−0.454723	−	0.570205i	0.500634	−	0.865659i	$-0.333100\pi$
$769$	−12.6099	−	15.8123i	−0.454723	−	0.570205i	−0.955357	+	0.295455i	$0.904529\pi$
$770$	−5.45986	+	2.62933i	−0.196760	+	0.0947545i
$771$		0			0
$772$	4.23426	+	18.5515i	0.152394	+	0.667684i
$773$	−50.2888			−1.80876			−0.904381	−	0.426726i	$-0.859667\pi$
$773$	−50.2888			−1.80876			−0.904381	+	0.426726i	$0.859667\pi$
$774$		0			0
$775$	−1.12593			−0.0404444
$776$	1.60596	+	7.03618i	0.0576507	+	0.252584i
$777$		0			0
$778$	30.0053	−	14.4498i	1.07574	−	0.518050i
$779$	−7.22326	−	9.05768i	−0.258800	−	0.324525i
$780$		0			0
$781$			13.0307i			0.466276i
$782$	0.946337	+	1.18667i	0.0338410	+	0.0424352i
$783$		0			0
$784$	−5.51898	+	6.92058i	−0.197106	+	0.247163i
$785$	4.26299	−	8.85220i	0.152153	−	0.315948i
$786$		0			0
$787$	−3.43211	−	4.30373i	−0.122342	−	0.153411i	0.716889	−	0.697188i	$-0.245566\pi$
$787$	−3.43211	−	4.30373i	−0.122342	−	0.153411i	−0.839230	+	0.543776i	$0.816994\pi$
$788$	10.2374	−	2.33661i	0.364691	−	0.0832384i
$789$		0			0
$790$	26.6787	−	33.4540i	0.949186	−	1.19024i
$791$	3.51247	+	2.80110i	0.124889	+	0.0995957i
$792$		0			0
$793$	−5.22329	−	10.8463i	−0.185484	−	0.385162i
$794$	−21.2616	−	10.2390i	−0.754546	−	0.363370i
$795$		0			0
$796$	20.6627	+	4.71613i	0.732371	+	0.167159i
$797$	−6.80106	+	14.1226i	−0.240906	+	0.500246i	−0.986007	−	0.166706i	$-0.946687\pi$
$797$	−6.80106	+	14.1226i	−0.240906	+	0.500246i	0.745101	+	0.666952i	$0.232401\pi$
$798$		0			0
$799$	−4.52446	+	19.8229i	−0.160064	+	0.701285i
$800$	−15.4204	+	19.3366i	−0.545194	+	0.683652i
$801$		0			0
$802$	−2.97125	−	6.16987i	−0.104919	−	0.217866i
$803$	−5.66011	−	24.7986i	−0.199741	−	0.875123i
$804$		0			0
$805$	−0.660952	−	2.89582i	−0.0232955	−	0.102064i
$806$	1.28076	+	0.616784i	0.0451130	+	0.0217253i
$807$		0			0
$808$	3.18446	−	6.61260i	0.112029	−	0.232630i
$809$	32.2905	−	25.7508i	1.13527	−	0.905349i	0.138888	−	0.990308i	$-0.455647\pi$
$809$	32.2905	−	25.7508i	1.13527	−	0.905349i	0.996384	+	0.0849588i	$0.0270759\pi$
$810$		0			0
$811$			9.24297i			0.324565i	0.986744	+	0.162282i	$0.0518855\pi$
$811$			9.24297i			0.324565i	−0.986744	+	0.162282i	$0.948114\pi$
$812$	−3.96991	+	3.16590i	−0.139317	+	0.111101i
$813$		0			0
$814$	2.75355	−	12.0641i	0.0965120	−	0.422847i
$815$	−69.7835	+	15.9276i	−2.44441	+	0.557920i
$816$		0			0
$817$	1.37978	−	17.1643i	0.0482724	−	0.600504i
$818$			13.0323i			0.455663i
$819$		0			0
$820$	−12.1091	−	2.76382i	−0.422867	−	0.0965167i
$821$	−5.58786	−	11.6033i	−0.195018	−	0.404958i	0.780413	−	0.625264i	$-0.215009\pi$
$821$	−5.58786	−	11.6033i	−0.195018	−	0.404958i	−0.975431	+	0.220306i	$0.929294\pi$
$822$		0			0
$823$	43.7807			1.52610			0.763050	−	0.646339i	$-0.223701\pi$
$823$	43.7807			1.52610			0.763050	+	0.646339i	$0.223701\pi$
$824$	33.4842			1.16648
$825$		0			0
$826$	3.80778	+	1.83373i	0.132490	+	0.0638036i
$827$	9.80060	+	7.81571i	0.340800	+	0.271779i	0.778901	−	0.627147i	$-0.215777\pi$
$827$	9.80060	+	7.81571i	0.340800	+	0.271779i	−0.438101	+	0.898926i	$0.644349\pi$
$828$		0			0
$829$	16.3252	−	3.72612i	0.566997	−	0.129413i	0.0705932	−	0.997505i	$-0.477511\pi$
$829$	16.3252	−	3.72612i	0.566997	−	0.129413i	0.496404	+	0.868092i	$0.334654\pi$
$830$	41.2551	−	32.8998i	1.43199	−	1.14197i
$831$		0			0
$832$	45.8530	−	22.0816i	1.58967	−	0.765543i
$833$	−7.58636	−	6.04992i	−0.262852	−	0.209617i
$834$		0			0
$835$	57.4754	+	13.1184i	1.98902	+	0.453980i
$836$	3.40739	−	1.64091i	0.117847	−	0.0567521i
$837$		0			0
$838$	2.60213	−	11.4007i	0.0898890	−	0.393829i
$839$	10.7664	−	47.1705i	0.371696	−	1.62851i	−0.350319	−	0.936631i	$-0.613927\pi$
$839$	10.7664	−	47.1705i	0.371696	−	1.62851i	0.722015	−	0.691878i	$-0.243216\pi$
$840$		0			0
$841$	−1.19024	+	0.573188i	−0.0410427	+	0.0197651i
$842$	−12.8559	−	2.93428i	−0.443045	−	0.101122i
$843$		0			0
$844$	−2.63665	−	2.10265i	−0.0907571	−	0.0723764i
$845$	−86.3434	+	41.5808i	−2.97030	+	1.43042i
$846$		0			0
$847$	−6.84740	+	5.46062i	−0.235279	+	0.187629i
$848$	−16.0901	+	3.67246i	−0.552536	+	0.126113i
$849$		0			0
$850$	7.54982	+	6.02078i	0.258957	+	0.206511i
$851$	5.46462	+	2.63162i	0.187325	+	0.0902108i
$852$		0			0
$853$	2.20208			0.0753977			0.0376989	−	0.999289i	$-0.487997\pi$
$853$	2.20208			0.0753977			0.0376989	+	0.999289i	$0.487997\pi$
$854$	−2.08209			−0.0712476
$855$		0			0
$856$	−8.66036	−	17.9834i	−0.296005	−	0.614661i
$857$	−19.4518	−	4.43974i	−0.664460	−	0.151659i	−0.123028	−	0.992403i	$-0.539261\pi$
$857$	−19.4518	−	4.43974i	−0.664460	−	0.151659i	−0.541432	+	0.840744i	$0.682118\pi$
$858$		0			0
$859$		−	34.3577i		−	1.17227i	−0.810214	−	0.586134i	$-0.800649\pi$
$859$		−	34.3577i		−	1.17227i	0.810214	−	0.586134i	$-0.199351\pi$
$860$	−10.3168	−	15.3094i	−0.351801	−	0.522048i
$861$		0			0
$862$	2.77880	−	0.634242i	0.0946462	−	0.0216024i
$863$	−0.468603	+	2.05308i	−0.0159514	+	0.0698878i	−0.982277	−	0.187434i	$-0.939983\pi$
$863$	−0.468603	+	2.05308i	−0.0159514	+	0.0698878i	0.966326	+	0.257322i	$0.0828401\pi$
$864$		0			0
$865$	27.1531	−	21.6539i	0.923233	−	0.736254i
$866$		−	13.6338i		−	0.463296i
$867$		0			0
$868$	−0.147682	+	0.117773i	−0.00501266	+	0.00399746i
$869$	−8.93029	+	18.5439i	−0.302939	+	0.629060i
$870$		0			0
$871$	−49.1932	−	23.6902i	−1.66685	−	0.802712i
$872$	6.94762	+	30.4395i	0.235276	+	1.03081i
$873$		0			0
$874$	−0.536887	−	2.35226i	−0.0181605	−	0.0795663i
$875$	−0.740714	−	1.53811i	−0.0250407	−	0.0519975i
$876$		0			0
$877$	−14.0307	+	17.5940i	−0.473785	+	0.594107i	−0.960093	−	0.279680i	$-0.909772\pi$
$877$	−14.0307	+	17.5940i	−0.473785	+	0.594107i	0.486309	+	0.873787i	$0.338343\pi$
$878$	3.04927	−	13.3597i	0.102908	−	0.450869i
$879$		0			0
$880$	−3.51090	+	7.29046i	−0.118353	+	0.245762i
$881$	55.7457	+	12.7236i	1.87812	+	0.428669i	0.998863	−	0.0476797i	$-0.0151827\pi$
$881$	55.7457	+	12.7236i	1.87812	+	0.428669i	0.879257	+	0.476348i	$0.158040\pi$
$882$		0			0
$883$	−12.8213	−	6.17440i	−0.431470	−	0.207785i	0.205527	−	0.978652i	$-0.434109\pi$
$883$	−12.8213	−	6.17440i	−0.431470	−	0.207785i	−0.636997	+	0.770866i	$0.719824\pi$
$884$	4.06419	+	8.43937i	0.136693	+	0.283847i
$885$		0			0
$886$	14.3996	+	11.4833i	0.483763	+	0.385788i
$887$	13.6222	−	17.0817i	0.457388	−	0.573546i	−0.498645	−	0.866806i	$-0.666169\pi$
$887$	13.6222	−	17.0817i	0.457388	−	0.573546i	0.956033	+	0.293260i	$0.0947402\pi$
$888$		0			0
$889$	15.9476	−	3.63994i	0.534865	−	0.122080i
$890$	−9.27981	−	11.6365i	−0.311060	−	0.390057i
$891$		0			0
$892$	0.138232	−	0.287041i	0.00462834	−	0.00961084i
$893$	20.1521	−	25.2699i	0.674365	−	0.845627i
$894$		0			0
$895$	25.2328	+	31.6409i	0.843438	+	1.05764i
$896$			0.747819i			0.0249829i
$897$		0			0
$898$	4.68814	+	5.87875i	0.156445	+	0.196176i
$899$	−1.01625	+	0.489401i	−0.0338939	+	0.0163224i
$900$		0			0
$901$	−4.02576	−	17.6380i	−0.134118	−	0.587607i
$902$	−7.77622			−0.258920
$903$		0			0
$904$	12.9172			0.429621
$905$	−12.4794	−	54.6756i	−0.414828	−	1.81748i
$906$		0			0
$907$	2.28388	−	1.09986i	0.0758349	−	0.0365202i	−0.395582	−	0.918431i	$-0.629457\pi$
$907$	2.28388	−	1.09986i	0.0758349	−	0.0365202i	0.471417	+	0.881911i	$0.343743\pi$
$908$	6.73469	+	8.44503i	0.223499	+	0.280258i
$909$		0			0
$910$			23.8592i			0.790925i
$911$	−0.210717	−	0.264230i	−0.00698136	−	0.00875435i	0.778329	−	0.627857i	$-0.216068\pi$
$911$	−0.210717	−	0.264230i	−0.00698136	−	0.00875435i	−0.785310	+	0.619103i	$0.787496\pi$
$912$		0			0
$913$	−15.8252	+	19.8442i	−0.523739	+	0.656748i
$914$	−9.92895	+	20.6177i	−0.328421	+	0.681972i
$915$		0			0
$916$	5.69680	+	7.14357i	0.188228	+	0.236030i
$917$	−12.0774	+	2.75659i	−0.398831	+	0.0910305i
$918$		0			0
$919$	19.6795	−	24.6773i	0.649166	−	0.814029i	−0.342950	−	0.939354i	$-0.611426\pi$
$919$	19.6795	−	24.6773i	0.649166	−	0.814029i	0.992116	+	0.125325i	$0.0399974\pi$
$920$	−6.67702	−	5.32475i	−0.220135	−	0.175552i
$921$		0			0
$922$	−16.2495	−	33.7424i	−0.535148	−	1.11125i
$923$	46.2235	+	22.2601i	1.52146	+	0.732699i
$924$		0			0
$925$	37.6209	+	8.58673i	1.23697	+	0.282330i
$926$	8.87315	−	18.4253i	0.291590	−	0.605493i
$927$		0			0
$928$	−5.51341	+	24.1558i	−0.180986	+	0.792954i
$929$	21.1799	−	26.5587i	0.694890	−	0.871364i	−0.301740	−	0.953390i	$-0.597568\pi$
$929$	21.1799	−	26.5587i	0.694890	−	0.871364i	0.996630	+	0.0820259i	$0.0261390\pi$
$930$		0			0
$931$	6.69252	+	13.8972i	0.219338	+	0.455461i
$932$	5.19090	+	22.7428i	0.170034	+	0.744966i
$933$		0			0
$934$	0.930968	+	4.07884i	0.0304622	+	0.133464i
$935$	−7.99184	−	3.84867i	−0.261361	−	0.125865i
$936$		0			0
$937$	−1.04741	+	2.17497i	−0.0342175	+	0.0710533i	−0.917377	−	0.398020i	$-0.869698\pi$
$937$	−1.04741	+	2.17497i	−0.0342175	+	0.0710533i	0.883159	+	0.469073i	$0.155412\pi$
$938$	−7.38307	+	5.88780i	−0.241066	+	0.192244i
$939$		0			0
$940$		−	34.6518i		−	1.13022i
$941$	−25.4623	+	20.3055i	−0.830046	+	0.661940i	−0.943415	−	0.331613i	$-0.892407\pi$
$941$	−25.4623	+	20.3055i	−0.830046	+	0.661940i	0.113369	+	0.993553i	$0.463836\pi$
$942$		0			0
$943$	0.848139	−	3.71594i	0.0276192	−	0.121008i
$944$	5.50184	−	1.25576i	0.179070	−	0.0408715i
$945$		0			0
$946$	−8.43007	−	7.90733i	−0.274085	−	0.257089i
$947$		−	50.4407i		−	1.63910i	−0.573006	−	0.819551i	$-0.694223\pi$
$947$		−	50.4407i		−	1.63910i	0.573006	−	0.819551i	$-0.305777\pi$
$948$		0			0
$949$	−97.6362	−	22.2848i	−3.16941	−	0.723396i
$950$	−6.66028	−	13.8302i	−0.216088	−	0.448711i
$951$		0			0
$952$	5.34874			0.173354
$953$	42.1962			1.36687			0.683434	−	0.730012i	$-0.260486\pi$
$953$	42.1962			1.36687			0.683434	+	0.730012i	$0.260486\pi$
$954$		0			0
$955$	−53.2059	−	25.6226i	−1.72170	−	0.829127i
$956$	10.6502	+	8.49323i	0.344451	+	0.274691i
$957$		0			0
$958$	−38.6870	+	8.83005i	−1.24992	+	0.285286i
$959$	−2.93222	+	2.33837i	−0.0946864	+	0.0755099i
$960$		0			0
$961$	27.8922	−	13.4322i	0.899749	−	0.433296i
$962$	−38.0908	−	30.3764i	−1.22810	−	0.979374i
$963$		0			0
$964$	−0.860828	−	0.196478i	−0.0277254	−	0.00632814i
$965$	−63.9201	+	30.7823i	−2.05766	+	0.990918i
$966$		0			0
$967$	−3.34549	+	14.6575i	−0.107584	+	0.471355i	0.892221	+	0.451599i	$0.149146\pi$
$967$	−3.34549	+	14.6575i	−0.107584	+	0.471355i	−0.999805	+	0.0197561i	$0.993711\pi$
$968$	−5.60342	+	24.5502i	−0.180101	+	0.789074i
$969$		0			0
$970$	−7.34298	+	3.53619i	−0.235769	+	0.113540i
$971$	−17.7561	−	4.05271i	−0.569819	−	0.130058i	−0.0721026	−	0.997397i	$-0.522971\pi$
$971$	−17.7561	−	4.05271i	−0.569819	−	0.130058i	−0.497717	+	0.867340i	$0.665828\pi$
$972$		0			0
$973$	−5.28838	−	4.21734i	−0.169538	−	0.135202i
$974$	14.5658	−	7.01452i	0.466718	−	0.224760i
$975$		0			0
$976$	−2.17363	+	1.73341i	−0.0695762	+	0.0554852i
$977$	−23.2738	+	5.31210i	−0.744595	+	0.169949i	−0.577955	−	0.816069i	$-0.696149\pi$
$977$	−23.2738	+	5.31210i	−0.744595	+	0.169949i	−0.166640	+	0.986018i	$0.553292\pi$
$978$		0			0
$979$	5.59731	+	4.46371i	0.178891	+	0.142661i
$980$	14.8991	+	7.17503i	0.475935	+	0.229198i
$981$		0			0
$982$	3.34015			0.106588
$983$	17.9051			0.571085			0.285542	−	0.958366i	$-0.407826\pi$
$983$	17.9051			0.571085			0.285542	+	0.958366i	$0.407826\pi$
$984$		0			0
$985$	16.9867	+	35.2733i	0.541243	+	1.12390i
$986$	9.43145	+	2.15267i	0.300358	+	0.0685549i
$987$		0			0
$988$		−	14.8900i		−	0.473715i
$989$	4.69804	−	3.16595i	0.149389	−	0.100671i
$990$		0			0
$991$	−6.86480	+	1.56685i	−0.218068	+	0.0497725i	−0.330159	−	0.943925i	$-0.607102\pi$
$991$	−6.86480	+	1.56685i	−0.218068	+	0.0497725i	0.112091	+	0.993698i	$0.464245\pi$
$992$	−0.205101	+	0.898606i	−0.00651196	+	0.0285308i
$993$		0			0
$994$	6.93737	−	5.53237i	0.220040	−	0.175476i
$995$			79.0198i			2.50510i
$996$		0			0
$997$	−4.49342	+	3.58338i	−0.142308	+	0.113487i	−0.692056	−	0.721844i	$-0.743295\pi$
$997$	−4.49342	+	3.58338i	−0.142308	+	0.113487i	0.549748	+	0.835330i	$0.314724\pi$
$998$	−14.9857	+	31.1181i	−0.474364	+	0.985027i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.v.a.242.11	yes	96
3.2	odd	2	inner	387.2.v.a.242.6	yes	96
43.8	odd	14	inner	387.2.v.a.8.6	✓	96
129.8	even	14	inner	387.2.v.a.8.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.v.a.8.6	✓	96	43.8	odd	14	inner
387.2.v.a.8.11	yes	96	129.8	even	14	inner
387.2.v.a.242.6	yes	96	3.2	odd	2	inner
387.2.v.a.242.11	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.236651 + 1.03684i) q^{2} +(0.782911 - 0.377030i) q^{4} +(2.02001 + 2.53301i) q^{5} +1.06119i q^{7} +(1.90236 + 2.38548i) q^{8} +O(q^{10})\)	\(q+(0.236651 + 1.03684i) q^{2} +(0.782911 - 0.377030i) q^{4} +(2.02001 + 2.53301i) q^{5} +1.06119i q^{7} +(1.90236 + 2.38548i) q^{8} +(-2.14828 + 2.69386i) q^{10} +(0.719103 - 1.49323i) q^{11} +(-4.06847 - 5.10170i) q^{13} +(-1.10028 + 0.251132i) q^{14} +(-0.939580 + 1.17820i) q^{16} +(-1.29154 - 1.02997i) q^{17} +(1.13937 + 2.36592i) q^{19} +(2.53650 + 1.22152i) q^{20} +(1.71842 + 0.392217i) q^{22} +(-0.374849 + 0.778382i) q^{23} +(-1.22310 + 5.35874i) q^{25} +(4.32683 - 5.42567i) q^{26} +(0.400100 + 0.830817i) q^{28} +(1.22530 + 5.36840i) q^{29} +(0.0455817 + 0.199706i) q^{31} +(4.05403 + 1.95232i) q^{32} +(0.762267 - 1.58286i) q^{34} +(-2.68800 + 2.14361i) q^{35} -7.02048i q^{37} +(-2.18345 + 1.74124i) q^{38} +(-2.19967 + 9.63738i) q^{40} +(-4.30116 + 0.981711i) q^{41} +(-5.66107 - 3.30942i) q^{43} -1.44019i q^{44} +(-0.895764 - 0.204452i) q^{46} +(-5.34040 - 11.0894i) q^{47} +5.87388 q^{49} -5.84558 q^{50} +(-5.10875 - 2.46024i) q^{52} +(8.56238 + 6.82827i) q^{53} +(5.23496 - 1.19485i) q^{55} +(-2.53145 + 2.01876i) q^{56} +(-5.27618 + 2.54088i) q^{58} +(-2.92782 - 2.33486i) q^{59} +(1.79863 + 0.410525i) q^{61} +(-0.196276 + 0.0945216i) q^{62} +(-1.73551 + 7.60376i) q^{64} +(4.70431 - 20.6109i) q^{65} +(7.53881 - 3.63050i) q^{67} +(-1.39949 - 0.319425i) q^{68} +(-2.85869 - 2.27973i) q^{70} +(-7.08370 + 3.41133i) q^{71} +(11.9991 - 9.56898i) q^{73} +(7.27909 - 1.66141i) q^{74} +(1.78405 + 1.42273i) q^{76} +(1.58460 + 0.763105i) q^{77} -12.4186 q^{79} -4.88233 q^{80} +(-2.03575 - 4.22728i) q^{82} +(-14.9305 - 3.40780i) q^{83} -5.35203i q^{85} +(2.09163 - 6.65279i) q^{86} +(4.93008 - 1.12526i) q^{88} +(-0.961212 + 4.21135i) q^{89} +(5.41387 - 4.31742i) q^{91} +0.750733i q^{92} +(10.2341 - 8.16145i) q^{94} +(-3.69137 + 7.66521i) q^{95} +(2.13114 + 1.02630i) q^{97} +(1.39006 + 6.09025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 20 q^{4}+O(q^{10}) \) 96 * q - 20 * q^4	\( 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) \) 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

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