LMFDB - Embedded newform 297.2.f.b.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 51x^{12} - 249x^{10} + 1476x^{8} - 2875x^{6} + 2335x^{4} + 125x^{2} + 25 $ x^16 - 9x^14 + 51x^12 - 249x^10 + 1476x^8 - 2875x^6 + 2335x^4 + 125*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.2
Root			$-2.33991 + 0.760284i$ of defining polynomial
Character	$\chi$	$=$	297.163
Dual form			297.2.f.b.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.386556 + 1.18970i) q^{2} +(0.352078 + 0.255800i) q^{4} +(0.507211 + 1.56103i) q^{5} +(2.37869 + 1.72822i) q^{7} +(-2.46446 + 1.79053i) q^{8} -2.05323 q^{10} +(-0.315878 - 3.30155i) q^{11} +(1.11803 - 3.44095i) q^{13} +(-2.97556 + 2.16187i) q^{14} +(-0.908579 - 2.79632i) q^{16} +(1.98276 + 6.10230i) q^{17} +(-5.02334 + 3.64967i) q^{19} +(-0.220734 + 0.679350i) q^{20} +(4.04995 + 0.900435i) q^{22} +0.390446 q^{23} +(1.86552 - 1.35538i) q^{25} +(3.66151 + 2.66025i) q^{26} +(0.395406 + 1.21694i) q^{28} +(-4.28698 - 3.11467i) q^{29} +(-1.05137 + 3.23578i) q^{31} -2.41448 q^{32} -8.02635 q^{34} +(-1.49131 + 4.58979i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(-2.40020 - 7.38706i) q^{38} +(-4.04508 - 2.93893i) q^{40} +(6.33138 - 4.60002i) q^{41} +0.650930 q^{43} +(0.733321 - 1.24320i) q^{44} +(-0.150930 + 0.464513i) q^{46} +(10.8534 - 7.88544i) q^{47} +(0.508307 + 1.56441i) q^{49} +(0.891363 + 2.74333i) q^{50} +(1.27383 - 0.925491i) q^{52} +(1.48983 - 4.58522i) q^{53} +(4.99362 - 2.16768i) q^{55} -8.95662 q^{56} +(5.36268 - 3.89621i) q^{58} +(1.58991 + 1.15514i) q^{59} +(3.53164 + 10.8693i) q^{61} +(-3.44318 - 2.50162i) q^{62} +(2.75049 - 8.46514i) q^{64} +5.93853 q^{65} +0.854102 q^{67} +(-0.862881 + 2.65567i) q^{68} +(-4.88399 - 3.54843i) q^{70} +(0.340470 + 1.04786i) q^{71} +(2.52131 + 1.83184i) q^{73} +(3.27496 - 2.37940i) q^{74} -2.70219 q^{76} +(4.95443 - 8.39927i) q^{77} +(0.511416 - 1.57398i) q^{79} +(3.90431 - 2.83665i) q^{80} +(3.02520 + 9.31060i) q^{82} +(-3.99797 - 12.3045i) q^{83} +(-8.52023 + 6.19031i) q^{85} +(-0.251621 + 0.774410i) q^{86} +(6.69000 + 7.57094i) q^{88} +5.92297 q^{89} +(8.60618 - 6.25276i) q^{91} +(0.137467 + 0.0998760i) q^{92} +(5.18585 + 15.9604i) q^{94} +(-8.24515 - 5.99045i) q^{95} +(5.76066 - 17.7295i) q^{97} -2.05766 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.386556	+	1.18970i	−0.273337	+	0.841244i	0.716318	+	0.697774i	$0.245826\pi$
$2$	−0.386556	+	1.18970i	−0.273337	+	0.841244i	−0.989655	+	0.143470i	$0.954174\pi$
$3$		0			0
$3$		0			0
$4$	0.352078	+	0.255800i	0.176039	+	0.127900i
$5$	0.507211	+	1.56103i	0.226832	+	0.698116i	0.998101	+	0.0616065i	$0.0196224\pi$
$5$	0.507211	+	1.56103i	0.226832	+	0.698116i	−0.771269	+	0.636509i	$0.780378\pi$
$6$		0			0
$7$	2.37869	+	1.72822i	0.899061	+	0.653206i	0.938225	−	0.346027i	$-0.112469\pi$
$7$	2.37869	+	1.72822i	0.899061	+	0.653206i	−0.0391639	+	0.999233i	$0.512469\pi$
$8$	−2.46446	+	1.79053i	−0.871317	+	0.633049i
$9$		0			0
$10$	−2.05323			−0.649287
$11$	−0.315878	−	3.30155i	−0.0952407	−	0.995454i
$11$	−0.315878	−	3.30155i	−0.0952407	−	0.995454i
$12$		0			0
$13$	1.11803	−	3.44095i	0.310087	−	0.954349i	−0.667643	−	0.744482i	$-0.732697\pi$
$13$	1.11803	−	3.44095i	0.310087	−	0.954349i	0.977730	−	0.209868i	$-0.0673033\pi$
$14$	−2.97556	+	2.16187i	−0.795252	+	0.577784i
$15$		0			0
$16$	−0.908579	−	2.79632i	−0.227145	−	0.699080i
$17$	1.98276	+	6.10230i	0.480889	+	1.48003i	0.837847	+	0.545905i	$0.183814\pi$
$17$	1.98276	+	6.10230i	0.480889	+	1.48003i	−0.356958	+	0.934121i	$0.616186\pi$
$18$		0			0
$19$	−5.02334	+	3.64967i	−1.15243	+	0.837291i	−0.988802	−	0.149230i	$-0.952320\pi$
$19$	−5.02334	+	3.64967i	−1.15243	+	0.837291i	−0.163630	+	0.986522i	$0.552320\pi$
$20$	−0.220734	+	0.679350i	−0.0493577	+	0.151907i
$21$		0			0
$22$	4.04995	+	0.900435i	0.863452	+	0.191973i
$23$	0.390446			0.0814137			0.0407068	−	0.999171i	$-0.487039\pi$
$23$	0.390446			0.0814137			0.0407068	+	0.999171i	$0.487039\pi$
$24$		0			0
$25$	1.86552	−	1.35538i	0.373104	−	0.271076i
$26$	3.66151	+	2.66025i	0.718082	+	0.521717i
$27$		0			0
$28$	0.395406	+	1.21694i	0.0747248	+	0.229979i
$29$	−4.28698	−	3.11467i	−0.796072	−	0.578380i	0.113688	−	0.993517i	$-0.463734\pi$
$29$	−4.28698	−	3.11467i	−0.796072	−	0.578380i	−0.909759	+	0.415137i	$0.863734\pi$
$30$		0			0
$31$	−1.05137	+	3.23578i	−0.188831	+	0.581163i	−0.999993	−	0.00365875i	$-0.998835\pi$
$31$	−1.05137	+	3.23578i	−0.188831	+	0.581163i	0.811162	+	0.584821i	$0.198835\pi$
$32$	−2.41448			−0.426824
$33$		0			0
$34$	−8.02635			−1.37651
$35$	−1.49131	+	4.58979i	−0.252078	+	0.775816i
$36$		0			0
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	0.351408	−	0.936223i	$-0.385703\pi$
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	−0.781810	+	0.623517i	$0.785703\pi$
$38$	−2.40020	−	7.38706i	−0.389364	−	1.19834i
$39$		0			0
$40$	−4.04508	−	2.93893i	−0.639584	−	0.464685i
$41$	6.33138	−	4.60002i	0.988795	−	0.718402i	0.0291384	−	0.999575i	$-0.490724\pi$
$41$	6.33138	−	4.60002i	0.988795	−	0.718402i	0.959657	+	0.281173i	$0.0907236\pi$
$42$		0			0
$43$	0.650930			0.0992658			0.0496329	−	0.998768i	$-0.484195\pi$
$43$	0.650930			0.0992658			0.0496329	+	0.998768i	$0.484195\pi$
$44$	0.733321	−	1.24320i	0.110552	−	0.187420i
$45$		0			0
$46$	−0.150930	+	0.464513i	−0.0222533	+	0.0684888i
$47$	10.8534	−	7.88544i	1.58313	−	1.15021i	0.670129	−	0.742245i	$-0.266239\pi$
$47$	10.8534	−	7.88544i	1.58313	−	1.15021i	0.912998	−	0.407964i	$-0.133761\pi$
$48$		0			0
$49$	0.508307	+	1.56441i	0.0726152	+	0.223487i
$50$	0.891363	+	2.74333i	0.126058	+	0.387966i
$51$		0			0
$52$	1.27383	−	0.925491i	0.176648	−	0.128343i
$53$	1.48983	−	4.58522i	0.204644	−	0.629828i	−0.795084	−	0.606499i	$-0.792573\pi$
$53$	1.48983	−	4.58522i	0.204644	−	0.629828i	0.999728	−	0.0233292i	$-0.00742659\pi$
$54$		0			0
$55$	4.99362	−	2.16768i	0.673339	−	0.292290i
$56$	−8.95662			−1.19688
$57$		0			0
$58$	5.36268	−	3.89621i	0.704154	−	0.511598i
$59$	1.58991	+	1.15514i	0.206988	+	0.150386i	0.686450	−	0.727177i	$-0.259168\pi$
$59$	1.58991	+	1.15514i	0.206988	+	0.150386i	−0.479462	+	0.877563i	$0.659168\pi$
$60$		0			0
$61$	3.53164	+	10.8693i	0.452181	+	1.39167i	0.874413	+	0.485182i	$0.161247\pi$
$61$	3.53164	+	10.8693i	0.452181	+	1.39167i	−0.422233	+	0.906488i	$0.638753\pi$
$62$	−3.44318	−	2.50162i	−0.437285	−	0.317706i
$63$		0			0
$64$	2.75049	−	8.46514i	0.343811	−	1.05814i
$65$	5.93853			0.736584
$66$		0			0
$67$	0.854102			0.104345			0.0521726	−	0.998638i	$-0.483385\pi$
$67$	0.854102			0.104345			0.0521726	+	0.998638i	$0.483385\pi$
$68$	−0.862881	+	2.65567i	−0.104640	+	0.322048i
$69$		0			0
$70$	−4.88399	−	3.54843i	−0.583748	−	0.424118i
$71$	0.340470	+	1.04786i	0.0404064	+	0.124358i	0.969225	−	0.246177i	$-0.0791744\pi$
$71$	0.340470	+	1.04786i	0.0404064	+	0.124358i	−0.928819	+	0.370535i	$0.879174\pi$
$72$		0			0
$73$	2.52131	+	1.83184i	0.295097	+	0.214401i	0.725476	−	0.688248i	$-0.241620\pi$
$73$	2.52131	+	1.83184i	0.295097	+	0.214401i	−0.430378	+	0.902649i	$0.641620\pi$
$74$	3.27496	−	2.37940i	0.380706	−	0.276599i
$75$		0			0
$76$	−2.70219			−0.309962
$77$	4.95443	−	8.39927i	0.564609	−	0.957186i
$78$		0			0
$79$	0.511416	−	1.57398i	0.0575388	−	0.177086i	−0.918156	−	0.396218i	$-0.870322\pi$
$79$	0.511416	−	1.57398i	0.0575388	−	0.177086i	0.975695	+	0.219132i	$0.0703224\pi$
$80$	3.90431	−	2.83665i	0.436515	−	0.317147i
$81$		0			0
$82$	3.02520	+	9.31060i	0.334077	+	1.02818i
$83$	−3.99797	−	12.3045i	−0.438834	−	1.35059i	−0.889106	−	0.457701i	$-0.848673\pi$
$83$	−3.99797	−	12.3045i	−0.438834	−	1.35059i	0.450272	−	0.892891i	$-0.351327\pi$
$84$		0			0
$85$	−8.52023	+	6.19031i	−0.924149	+	0.671433i
$86$	−0.251621	+	0.774410i	−0.0271330	+	0.0835068i
$87$		0			0
$88$	6.69000	+	7.57094i	0.713156	+	0.807065i
$89$	5.92297			0.627834			0.313917	−	0.949451i	$-0.398359\pi$
$89$	5.92297			0.627834			0.313917	+	0.949451i	$0.398359\pi$
$90$		0			0
$91$	8.60618	−	6.25276i	0.902173	−	0.655467i
$92$	0.137467	+	0.0998760i	0.0143320	+	0.0104128i
$93$		0			0
$94$	5.18585	+	15.9604i	0.534880	+	1.64619i
$95$	−8.24515	−	5.99045i	−0.845935	−	0.614608i
$96$		0			0
$97$	5.76066	−	17.7295i	0.584906	−	1.80016i	−0.0147411	−	0.999891i	$-0.504692\pi$
$97$	5.76066	−	17.7295i	0.584906	−	1.80016i	0.599647	−	0.800264i	$-0.295308\pi$
$98$	−2.05766			−0.207855
$99$		0			0
$100$	1.00351			0.100351
$101$	−0.559719	+	1.72264i	−0.0556941	+	0.171409i	−0.975034	−	0.222055i	$-0.928723\pi$
$101$	−0.559719	+	1.72264i	−0.0556941	+	0.171409i	0.919340	+	0.393464i	$0.128723\pi$
$102$		0			0
$103$	−13.0948	−	9.51391i	−1.29027	−	0.937433i	−0.290455	−	0.956889i	$-0.593807\pi$
$103$	−13.0948	−	9.51391i	−1.29027	−	0.937433i	−0.999811	+	0.0194556i	$0.993807\pi$
$104$	3.40580	+	10.4820i	0.333966	+	1.02784i
$105$		0			0
$106$	4.87912	+	3.54489i	0.473902	+	0.344310i
$107$	−8.63171	+	6.27130i	−0.834459	+	0.606270i	−0.920817	−	0.389994i	$-0.872477\pi$
$107$	−8.63171	+	6.27130i	−0.834459	+	0.606270i	0.0863585	+	0.996264i	$0.472477\pi$
$108$		0			0
$109$	3.37595			0.323357			0.161679	−	0.986843i	$-0.448309\pi$
$109$	3.37595			0.323357			0.161679	+	0.986843i	$0.448309\pi$
$110$	0.648568	+	6.77883i	0.0618386	+	0.646336i
$111$		0			0
$112$	2.67143	−	8.22180i	0.252426	−	0.776887i
$113$	11.1692	−	8.11493i	1.05071	−	0.763389i	0.0783663	−	0.996925i	$-0.475030\pi$
$113$	11.1692	−	8.11493i	1.05071	−	0.763389i	0.972348	+	0.233536i	$0.0750296\pi$
$114$		0			0
$115$	0.198039	+	0.609500i	0.0184672	+	0.0568362i
$116$	−0.712618	−	2.19321i	−0.0661649	−	0.203635i
$117$		0			0
$118$	−1.98885	+	1.44499i	−0.183089	+	0.133022i
$119$	−5.82975	+	17.9421i	−0.534412	+	1.64475i
$120$		0			0
$121$	−10.8004	+	2.08577i	−0.981858	+	0.189616i
$122$	−14.2963			−1.29433
$123$		0			0
$124$	−1.19787	+	0.870306i	−0.107572	+	0.0781558i
$125$	9.70148	+	7.04854i	0.867727	+	0.630440i
$126$		0			0
$127$	0.297703	+	0.916236i	0.0264169	+	0.0813028i	0.963396	−	0.268083i	$-0.0863902\pi$
$127$	0.297703	+	0.916236i	0.0264169	+	0.0813028i	−0.936979	+	0.349386i	$0.886390\pi$
$128$	5.10103	+	3.70612i	0.450872	+	0.327578i
$129$		0			0
$130$	−2.29558	+	7.06506i	−0.201335	+	0.619647i
$131$	−10.2867			−0.898754			−0.449377	−	0.893342i	$-0.648354\pi$
$131$	−10.2867			−0.898754			−0.449377	+	0.893342i	$0.648354\pi$
$132$		0			0
$133$	−18.2564			−1.58303
$134$	−0.330159	+	1.01612i	−0.0285214	+	0.0877797i
$135$		0			0
$136$	−15.8128	−	11.4887i	−1.35594	−	0.985145i
$137$	5.95281	+	18.3209i	0.508583	+	1.56526i	0.794663	+	0.607051i	$0.207648\pi$
$137$	5.95281	+	18.3209i	0.508583	+	1.56526i	−0.286080	+	0.958206i	$0.592352\pi$
$138$		0			0
$139$	−4.57957	−	3.32725i	−0.388434	−	0.282214i	0.376379	−	0.926466i	$-0.377169\pi$
$139$	−4.57957	−	3.32725i	−0.388434	−	0.282214i	−0.764814	+	0.644252i	$0.777169\pi$
$140$	−1.69912	+	1.23449i	−0.143602	+	0.104333i
$141$		0			0
$142$	−1.37825			−0.115660
$143$	−11.7136	−	2.60432i	−0.979544	−	0.217784i
$144$		0			0
$145$	2.68771	−	8.27191i	0.223202	−	0.686945i
$146$	−3.15397	+	2.29149i	−0.261024	+	0.189645i
$147$		0			0
$148$	−0.435192	−	1.33938i	−0.0357726	−	0.110097i
$149$	2.44777	+	7.53347i	0.200529	+	0.617166i	0.999867	+	0.0162843i	$0.00518369\pi$
$149$	2.44777	+	7.53347i	0.200529	+	0.617166i	−0.799338	+	0.600882i	$0.794816\pi$
$150$		0			0
$151$	−13.5468	+	9.84236i	−1.10243	+	0.800960i	−0.981454	−	0.191696i	$-0.938601\pi$
$151$	−13.5468	+	9.84236i	−1.10243	+	0.800960i	−0.120972	+	0.992656i	$0.538601\pi$
$152$	5.84495	−	17.9889i	0.474088	−	1.45909i
$153$		0			0
$154$	8.07743	+	9.14106i	0.650898	+	0.736608i
$155$	−5.58442			−0.448552
$156$		0			0
$157$	10.7161	−	7.78569i	0.855236	−	0.621365i	−0.0713487	−	0.997451i	$-0.522730\pi$
$157$	10.7161	−	7.78569i	0.855236	−	0.621365i	0.926585	+	0.376086i	$0.122730\pi$
$158$	1.67487	+	1.21686i	0.133245	+	0.0968084i
$159$		0			0
$160$	−1.22465	−	3.76909i	−0.0968172	−	0.297973i
$161$	0.928751	+	0.674777i	0.0731958	+	0.0531799i
$162$		0			0
$163$	−4.12803	+	12.7048i	−0.323333	+	0.995115i	0.648855	+	0.760912i	$0.275248\pi$
$163$	−4.12803	+	12.7048i	−0.323333	+	0.995115i	−0.972188	+	0.234203i	$0.924752\pi$
$164$	3.40582			0.265950
$165$		0			0
$166$	16.1841			1.25613
$167$	−1.66688	+	5.13013i	−0.128987	+	0.396981i	−0.994606	−	0.103721i	$-0.966925\pi$
$167$	−1.66688	+	5.13013i	−0.128987	+	0.396981i	0.865619	+	0.500703i	$0.166925\pi$
$168$		0			0
$169$	−0.0729490	−	0.0530006i	−0.00561146	−	0.00407697i
$170$	−4.07105	−	12.5294i	−0.312235	−	0.960961i
$171$		0			0
$172$	0.229178	+	0.166507i	0.0174746	+	0.0126961i
$173$	−5.19482	+	3.77426i	−0.394955	+	0.286951i	−0.767483	−	0.641070i	$-0.778491\pi$
$173$	−5.19482	+	3.77426i	−0.394955	+	0.286951i	0.372528	+	0.928021i	$0.378491\pi$
$174$		0			0
$175$	6.77988			0.512511
$176$	−8.94518	+	3.88301i	−0.674268	+	0.292693i
$177$		0			0
$178$	−2.28956	+	7.04655i	−0.171610	+	0.528161i
$179$	−16.0419	+	11.6551i	−1.19903	+	0.871144i	−0.994189	−	0.107651i	$-0.965667\pi$
$179$	−16.0419	+	11.6551i	−1.19903	+	0.871144i	−0.204839	+	0.978796i	$0.565667\pi$
$180$		0			0
$181$	−2.22263	−	6.84054i	−0.165207	−	0.508454i	0.833845	−	0.551999i	$-0.186135\pi$
$181$	−2.22263	−	6.84054i	−0.165207	−	0.508454i	−0.999051	+	0.0435452i	$0.986135\pi$
$182$	4.11212	+	12.6558i	0.304811	+	0.938111i
$183$		0			0
$184$	−0.962238	+	0.699107i	−0.0709372	+	0.0515389i
$185$	1.64137	−	5.05161i	0.120676	−	0.371402i
$186$		0			0
$187$	19.5207	−	8.47375i	1.42750	−	0.619662i
$188$	5.83832			0.425803
$189$		0			0
$190$	10.3140	−	7.49359i	0.748260	−	0.543643i
$191$	−2.10511	−	1.52945i	−0.152320	−	0.110667i	0.509015	−	0.860758i	$-0.330010\pi$
$191$	−2.10511	−	1.52945i	−0.152320	−	0.110667i	−0.661335	+	0.750091i	$0.730010\pi$
$192$		0			0
$193$	7.79105	+	23.9784i	0.560812	+	1.72600i	0.680078	+	0.733140i	$0.261946\pi$
$193$	7.79105	+	23.9784i	0.560812	+	1.72600i	−0.119266	+	0.992862i	$0.538054\pi$
$194$	18.8659	+	13.7069i	1.35449	+	0.984097i
$195$		0			0
$196$	−0.221211	+	0.680818i	−0.0158008	+	0.0486298i
$197$	−21.2052			−1.51081			−0.755403	−	0.655260i	$-0.772559\pi$
$197$	−21.2052			−1.51081			−0.755403	+	0.655260i	$0.772559\pi$
$198$		0			0
$199$	−23.5761			−1.67126			−0.835632	−	0.549289i	$-0.814898\pi$
$199$	−23.5761			−1.67126			−0.835632	+	0.549289i	$0.814898\pi$
$200$	−2.17064	+	6.68055i	−0.153487	+	0.472386i
$201$		0			0
$202$	−1.83306	−	1.33179i	−0.128973	−	0.0937046i
$203$	−4.81456	−	14.8177i	−0.337916	−	1.04000i
$204$		0			0
$205$	10.3921	+	7.55033i	0.725818	+	0.527338i
$206$	16.3805	−	11.9012i	1.14129	−	0.829193i
$207$		0			0
$208$	−10.6378			−0.737601
$209$	13.6363	+	15.4319i	0.943244	+	1.06745i
$210$		0			0
$211$	8.38892	−	25.8184i	0.577517	−	1.77741i	−0.0499269	−	0.998753i	$-0.515899\pi$
$211$	8.38892	−	25.8184i	0.577517	−	1.77741i	0.627444	−	0.778662i	$-0.284101\pi$
$212$	1.69743	−	1.23326i	0.116580	−	0.0847004i
$213$		0			0
$214$	−4.12432	−	12.6933i	−0.281932	−	0.867699i
$215$	0.330159	+	1.01612i	0.0225166	+	0.0692991i
$216$		0			0
$217$	−8.09301	+	5.87992i	−0.549389	+	0.399155i
$218$	−1.30500	+	4.01636i	−0.0883855	+	0.272022i
$219$		0			0
$220$	2.31263	+	0.514173i	0.155918	+	0.0346655i
$221$	23.2145			1.56158
$222$		0			0
$223$	5.37869	−	3.90785i	0.360184	−	0.261689i	−0.392945	−	0.919562i	$-0.628544\pi$
$223$	5.37869	−	3.90785i	0.360184	−	0.261689i	0.753129	+	0.657873i	$0.228544\pi$
$224$	−5.74331	−	4.17276i	−0.383741	−	0.278804i
$225$		0			0
$226$	5.33678	+	16.4249i	0.354997	+	1.09257i
$227$	−8.59821	−	6.24697i	−0.570683	−	0.414626i	0.264670	−	0.964339i	$-0.414737\pi$
$227$	−8.59821	−	6.24697i	−0.570683	−	0.414626i	−0.835353	+	0.549713i	$0.814737\pi$
$228$		0			0
$229$	1.31094	−	4.03465i	0.0866293	−	0.266618i	−0.898353	−	0.439275i	$-0.855235\pi$
$229$	1.31094	−	4.03465i	0.0866293	−	0.266618i	0.984982	+	0.172657i	$0.0552354\pi$
$230$	−0.801675			−0.0528609
$231$		0			0
$232$	16.1420			1.05977
$233$	5.26466	−	16.2029i	0.344899	−	1.06149i	−0.616739	−	0.787168i	$-0.711546\pi$
$233$	5.26466	−	16.2029i	0.344899	−	1.06149i	0.961638	−	0.274322i	$-0.0884535\pi$
$234$		0			0
$235$	17.8144	+	12.9429i	1.16208	+	0.844302i
$236$	0.264288	+	0.813395i	0.0172037	+	0.0529475i
$237$		0			0
$238$	−19.0922	−	13.8713i	−1.23756	−	0.899142i
$239$	−13.2997	+	9.66277i	−0.860283	+	0.625032i	−0.927962	−	0.372675i	$-0.878441\pi$
$239$	−13.2997	+	9.66277i	−0.860283	+	0.625032i	0.0676787	+	0.997707i	$0.478441\pi$
$240$		0			0
$241$	−3.12273			−0.201153			−0.100577	−	0.994929i	$-0.532069\pi$
$241$	−3.12273			−0.201153			−0.100577	+	0.994929i	$0.532069\pi$
$242$	1.69354	−	13.6555i	0.108865	−	0.877811i
$243$		0			0
$244$	−1.53694	+	4.73023i	−0.0983927	+	0.302822i
$245$	−2.18428	+	1.58697i	−0.139548	+	0.101388i
$246$		0			0
$247$	6.94208	+	21.3655i	0.441714	+	1.35946i
$248$	−3.20271	−	9.85694i	−0.203373	−	0.625916i
$249$		0			0
$250$	−12.1358	+	8.81718i	−0.767536	+	0.557647i
$251$	3.20271	−	9.85694i	0.202154	−	0.622165i	−0.797665	−	0.603101i	$-0.793932\pi$
$251$	3.20271	−	9.85694i	0.202154	−	0.622165i	0.999818	−	0.0190635i	$-0.00606848\pi$
$252$		0			0
$253$	−0.123333	−	1.28908i	−0.00775390	−	0.0810436i
$254$	−1.20512			−0.0756161
$255$		0			0
$256$	8.02076	−	5.82743i	0.501298	−	0.364214i
$257$	−13.7688	−	10.0036i	−0.858872	−	0.624007i	0.0687057	−	0.997637i	$-0.478113\pi$
$257$	−13.7688	−	10.0036i	−0.858872	−	0.624007i	−0.927578	+	0.373630i	$0.878113\pi$
$258$		0			0
$259$	−2.94022	−	9.04908i	−0.182697	−	0.562282i
$260$	2.09082	+	1.51907i	0.129667	+	0.0942089i
$261$		0			0
$262$	3.97639	−	12.2381i	0.245662	−	0.756071i
$263$	13.1664			0.811876			0.405938	−	0.913901i	$-0.366945\pi$
$263$	13.1664			0.811876			0.405938	+	0.913901i	$0.366945\pi$
$264$		0			0
$265$	7.91334			0.486113
$266$	7.05713	−	21.7196i	0.432700	−	1.33171i
$267$		0			0
$268$	0.300710	+	0.218479i	0.0183688	+	0.0133457i
$269$	2.84018	+	8.74119i	0.173169	+	0.532960i	0.999545	−	0.0301591i	$-0.00960140\pi$
$269$	2.84018	+	8.74119i	0.173169	+	0.532960i	−0.826376	+	0.563119i	$0.809601\pi$
$270$		0			0
$271$	6.17656	+	4.48753i	0.375199	+	0.272598i	0.759364	−	0.650667i	$-0.225510\pi$
$271$	6.17656	+	4.48753i	0.375199	+	0.272598i	−0.384164	+	0.923265i	$0.625510\pi$
$272$	15.2625	−	11.0888i	0.925424	−	0.672360i
$273$		0			0
$274$	−24.0974			−1.45578
$275$	−5.06412	−	5.73096i	−0.305378	−	0.345590i
$276$		0			0
$277$	0.229785	−	0.707207i	0.0138065	−	0.0424920i	−0.943916	−	0.330186i	$-0.892889\pi$
$277$	0.229785	−	0.707207i	0.0138065	−	0.0424920i	0.957722	+	0.287694i	$0.0928886\pi$
$278$	5.72869	−	4.16214i	0.343584	−	0.249628i
$279$		0			0
$280$	−4.54290	−	13.9816i	−0.271490	−	0.835560i
$281$	−7.67220	−	23.6126i	−0.457685	−	1.40861i	−0.867954	−	0.496645i	$-0.834565\pi$
$281$	−7.67220	−	23.6126i	−0.457685	−	1.40861i	0.410269	−	0.911965i	$-0.365435\pi$
$282$		0			0
$283$	13.1976	−	9.58862i	0.784516	−	0.569984i	−0.121815	−	0.992553i	$-0.538871\pi$
$283$	13.1976	−	9.58862i	0.784516	−	0.569984i	0.906331	+	0.422568i	$0.138871\pi$
$284$	−0.148170	+	0.456021i	−0.00879228	+	0.0270598i
$285$		0			0
$286$	7.62634	−	12.9290i	0.450955	−	0.764507i
$287$	23.0102			1.35825
$288$		0			0
$289$	−19.5535	+	14.2064i	−1.15020	+	0.835672i
$290$	8.80213	+	6.39512i	0.516879	+	0.375535i
$291$		0			0
$292$	0.419114	+	1.28990i	0.0245268	+	0.0754858i
$293$	4.62082	+	3.35722i	0.269951	+	0.196131i	0.714522	−	0.699612i	$-0.246644\pi$
$293$	4.62082	+	3.35722i	0.269951	+	0.196131i	−0.444571	+	0.895743i	$0.646644\pi$
$294$		0			0
$295$	−0.996788	+	3.06780i	−0.0580352	+	0.178614i
$296$	9.85783			0.572975
$297$		0			0
$298$	−9.90876			−0.573999
$299$	0.436532	−	1.34351i	0.0252453	−	0.0776971i
$300$		0			0
$301$	1.54836	+	1.12495i	0.0892460	+	0.0648410i
$302$	−6.47282	−	19.9213i	−0.372469	−	1.14634i
$303$		0			0
$304$	14.7697	+	10.7308i	0.847102	+	0.615456i
$305$	−15.1760	+	11.0260i	−0.868978	+	0.631349i
$306$		0			0
$307$	−1.48842			−0.0849485			−0.0424743	−	0.999098i	$-0.513524\pi$
$307$	−1.48842			−0.0849485			−0.0424743	+	0.999098i	$0.513524\pi$
$308$	3.89287	−	1.68986i	0.221817	−	0.0962885i
$309$		0			0
$310$	2.15870	−	6.64378i	0.122606	−	0.377341i
$311$	−23.9989	+	17.4362i	−1.36085	+	0.988716i	−0.362461	+	0.931999i	$0.618063\pi$
$311$	−23.9989	+	17.4362i	−1.36085	+	0.988716i	−0.998390	+	0.0567176i	$0.981937\pi$
$312$		0			0
$313$	5.75235	+	17.7039i	0.325142	+	1.00068i	0.971376	+	0.237545i	$0.0763428\pi$
$313$	5.75235	+	17.7039i	0.325142	+	1.00068i	−0.646234	+	0.763139i	$0.723657\pi$
$314$	5.12025	+	15.7585i	0.288952	+	0.889304i
$315$		0			0
$316$	0.582681	−	0.423343i	0.0327784	−	0.0238149i
$317$	−1.44317	+	4.44163i	−0.0810567	+	0.249467i	−0.983370	−	0.181614i	$-0.941868\pi$
$317$	−1.44317	+	4.44163i	−0.0810567	+	0.249467i	0.902313	+	0.431081i	$0.141868\pi$
$318$		0			0
$319$	−8.92908	+	15.1375i	−0.499932	+	0.847538i
$320$	14.6095			0.816694
$321$		0			0
$322$	−1.16180	+	0.844094i	−0.0647444	+	0.0470395i
$323$	−32.2314	−	23.4175i	−1.79341	−	1.30299i
$324$		0			0
$325$	−2.57808	−	7.93452i	−0.143006	−	0.440128i
$326$	−13.5191	−	9.82223i	−0.748756	−	0.544003i
$327$		0			0
$328$	−7.36693	+	22.6731i	−0.406771	+	1.25191i
$329$	39.4446			2.17465
$330$		0			0
$331$	−25.4751			−1.40024			−0.700119	−	0.714026i	$-0.746870\pi$
$331$	−25.4751			−1.40024			−0.700119	+	0.714026i	$0.746870\pi$
$332$	1.73988	−	5.35481i	0.0954885	−	0.293883i
$333$		0			0
$334$	−5.45896	−	3.96617i	−0.298701	−	0.217019i
$335$	0.433210	+	1.33328i	0.0236688	+	0.0728450i
$336$		0			0
$337$	−21.2718	−	15.4548i	−1.15875	−	0.841879i	−0.169128	−	0.985594i	$-0.554095\pi$
$337$	−21.2718	−	15.4548i	−1.15875	−	0.841879i	−0.989619	+	0.143715i	$0.954095\pi$
$338$	0.0912536	−	0.0662996i	0.00496354	−	0.00360622i
$339$		0			0
$340$	−4.58326			−0.248562
$341$	11.0152	+	2.44903i	0.596505	+	0.132622i
$342$		0			0
$343$	4.86552	−	14.9745i	0.262713	−	0.808548i
$344$	−1.60419	+	1.16551i	−0.0864920	+	0.0628401i
$345$		0			0
$346$	−2.48214	−	7.63923i	−0.133440	−	0.410687i
$347$	−3.45245	−	10.6255i	−0.185337	−	0.570409i	0.814617	−	0.580000i	$-0.196947\pi$
$347$	−3.45245	−	10.6255i	−0.185337	−	0.570409i	−0.999954	+	0.00959020i	$0.996947\pi$
$348$		0			0
$349$	−5.91087	+	4.29450i	−0.316402	+	0.229879i	−0.734639	−	0.678459i	$-0.762648\pi$
$349$	−5.91087	+	4.29450i	−0.316402	+	0.229879i	0.418237	+	0.908338i	$0.362648\pi$
$350$	−2.62081	+	8.06602i	−0.140088	+	0.431147i
$351$		0			0
$352$	0.762681	+	7.97153i	0.0406510	+	0.424884i
$353$	−20.0572			−1.06754			−0.533768	−	0.845631i	$-0.679224\pi$
$353$	−20.0572			−1.06754			−0.533768	+	0.845631i	$0.679224\pi$
$354$		0			0
$355$	−1.46306	+	1.06297i	−0.0776510	+	0.0564167i
$356$	2.08535	+	1.51509i	0.110523	+	0.0802998i
$357$		0			0
$358$	−7.66498	−	23.5904i	−0.405107	−	1.24679i
$359$	22.4760	+	16.3297i	1.18624	+	0.861851i	0.992861	−	0.119274i	$-0.0380567\pi$
$359$	22.4760	+	16.3297i	1.18624	+	0.861851i	0.193375	+	0.981125i	$0.438057\pi$
$360$		0			0
$361$	6.04252	−	18.5970i	0.318027	−	0.978788i
$362$	8.99735			0.472890
$363$		0			0
$364$	4.62950			0.242652
$365$	−1.58073	+	4.86499i	−0.0827392	+	0.254645i
$366$		0			0
$367$	−22.7476	−	16.5271i	−1.18741	−	0.862706i	−0.194424	−	0.980918i	$-0.562284\pi$
$367$	−22.7476	−	16.5271i	−1.18741	−	0.862706i	−0.992988	+	0.118212i	$0.962284\pi$
$368$	−0.354751	−	1.09181i	−0.0184927	−	0.0569147i
$369$		0			0
$370$	5.37542	+	3.90547i	0.279455	+	0.203036i
$371$	11.4681	−	8.33207i	0.595394	−	0.432579i
$372$		0			0
$373$	26.3287			1.36325			0.681625	−	0.731701i	$-0.261273\pi$
$373$	26.3287			1.36325			0.681625	+	0.731701i	$0.261273\pi$
$374$	2.53534	+	26.4994i	0.131099	+	1.37025i
$375$		0			0
$376$	−12.6285	+	38.8666i	−0.651267	+	2.00439i
$377$	−15.5104	+	11.2690i	−0.798828	+	0.580382i
$378$		0			0
$379$	1.83772	+	5.65591i	0.0943972	+	0.290525i	0.987096	−	0.160129i	$-0.0511910\pi$
$379$	1.83772	+	5.65591i	0.0943972	+	0.290525i	−0.892699	+	0.450654i	$0.851191\pi$
$380$	−1.37058	−	4.21821i	−0.0703093	−	0.216390i
$381$		0			0
$382$	2.63332	−	1.91322i	0.134733	−	0.0978890i
$383$	−4.13615	+	12.7297i	−0.211347	+	0.650460i	0.788046	+	0.615617i	$0.211093\pi$
$383$	−4.13615	+	12.7297i	−0.211347	+	0.650460i	−0.999393	+	0.0348429i	$0.988907\pi$
$384$		0			0
$385$	15.6245	+	3.47383i	0.796298	+	0.177043i
$386$	−31.5387			−1.60528
$387$		0			0
$388$	6.56339	−	4.76858i	0.333206	−	0.242088i
$389$	−15.7386	−	11.4348i	−0.797979	−	0.579766i	0.112342	−	0.993670i	$-0.464165\pi$
$389$	−15.7386	−	11.4348i	−0.797979	−	0.579766i	−0.910321	+	0.413904i	$0.864165\pi$
$390$		0			0
$391$	0.774161	+	2.38262i	0.0391510	+	0.120494i
$392$	−4.05382	−	2.94527i	−0.204749	−	0.148759i
$393$		0			0
$394$	8.19700	−	25.2278i	0.412959	−	1.27096i
$395$	2.71643			0.136678
$396$		0			0
$397$	22.4919			1.12884			0.564419	−	0.825489i	$-0.309100\pi$
$397$	22.4919			1.12884			0.564419	+	0.825489i	$0.309100\pi$
$398$	9.11349	−	28.0484i	0.456818	−	1.40594i
$399$		0			0
$400$	−5.48504	−	3.98512i	−0.274252	−	0.199256i
$401$	1.62801	+	5.01049i	0.0812988	+	0.250212i	0.983442	−	0.181226i	$-0.0580065\pi$
$401$	1.62801	+	5.01049i	0.0812988	+	0.250212i	−0.902143	+	0.431438i	$0.858006\pi$
$402$		0			0
$403$	9.95870	+	7.23542i	0.496078	+	0.360422i
$404$	−0.637714	+	0.463327i	−0.0317275	+	0.0230514i
$405$		0			0
$406$	19.4897			0.967256
$407$	−5.45294	+	9.24440i	−0.270292	+	0.458228i
$408$		0			0
$409$	3.52168	−	10.8386i	0.174136	−	0.535936i	−0.825457	−	0.564465i	$-0.809082\pi$
$409$	3.52168	−	10.8386i	0.174136	−	0.535936i	0.999593	+	0.0285295i	$0.00908245\pi$
$410$	−12.9998	+	9.44487i	−0.642012	+	0.466449i
$411$		0			0
$412$	−2.17672	−	6.69927i	−0.107240	−	0.330049i
$413$	1.78557	+	5.49542i	0.0878622	+	0.270412i
$414$		0			0
$415$	17.1799	−	12.4819i	0.843328	−	0.612714i
$416$	−2.69947	+	8.30812i	−0.132353	+	0.407339i
$417$		0			0
$418$	−23.6306	+	10.2578i	−1.15581	+	0.501725i
$419$	−15.6598			−0.765032			−0.382516	−	0.923949i	$-0.624942\pi$
$419$	−15.6598			−0.765032			−0.382516	+	0.923949i	$0.624942\pi$
$420$		0			0
$421$	−20.8919	+	15.1789i	−1.01821	+	0.739773i	−0.965915	−	0.258858i	$-0.916654\pi$
$421$	−20.8919	+	15.1789i	−1.01821	+	0.739773i	−0.0522953	+	0.998632i	$0.516654\pi$
$422$	27.4734	+	19.9606i	1.33738	+	0.971665i
$423$		0			0
$424$	4.53837	+	13.9677i	0.220403	+	0.678330i
$425$	11.9698	+	8.69657i	0.580620	+	0.421845i
$426$		0			0
$427$	−10.3838	+	31.9581i	−0.502508	+	1.54656i
$428$	−4.64323			−0.224439
$429$		0			0
$430$	−1.33651			−0.0644520
$431$	−2.82734	+	8.70166i	−0.136188	+	0.419144i	−0.995773	−	0.0918491i	$-0.970722\pi$
$431$	−2.82734	+	8.70166i	−0.136188	+	0.419144i	0.859585	+	0.510993i	$0.170722\pi$
$432$		0			0
$433$	10.9105	+	7.92694i	0.524325	+	0.380945i	0.818231	−	0.574890i	$-0.194955\pi$
$433$	10.9105	+	7.92694i	0.524325	+	0.380945i	−0.293906	+	0.955834i	$0.594955\pi$
$434$	−3.86692	−	11.9012i	−0.185618	−	0.571274i
$435$		0			0
$436$	1.18860	+	0.863567i	0.0569235	+	0.0413573i
$437$	−1.96134	+	1.42500i	−0.0938238	+	0.0681670i
$438$		0			0
$439$	30.1667			1.43978			0.719889	−	0.694089i	$-0.244193\pi$
$439$	30.1667			1.43978			0.719889	+	0.694089i	$0.244193\pi$
$440$	−8.42525	+	14.2834i	−0.401658	+	0.680934i
$441$		0			0
$442$	−8.97373	+	27.6183i	−0.426837	+	1.31367i
$443$	0.0419890	−	0.0305068i	0.00199496	−	0.00144942i	−0.586787	−	0.809741i	$-0.699608\pi$
$443$	0.0419890	−	0.0305068i	0.00199496	−	0.00144942i	0.588782	+	0.808292i	$0.299608\pi$
$444$		0			0
$445$	3.00420	+	9.24596i	0.142413	+	0.438301i
$446$	2.56999	+	7.90962i	0.121693	+	0.374531i
$447$		0			0
$448$	21.1722	−	15.3825i	1.00029	−	0.726755i
$449$	−9.77373	+	30.0804i	−0.461251	+	1.41958i	0.402387	+	0.915470i	$0.368181\pi$
$449$	−9.77373	+	30.0804i	−0.461251	+	1.41958i	−0.863637	+	0.504114i	$0.831819\pi$
$450$		0			0
$451$	−17.1871	−	19.4503i	−0.809310	−	0.915879i
$452$	6.00824			0.282604
$453$		0			0
$454$	10.7557	−	7.81447i	0.504790	−	0.366751i
$455$	14.1259	+	10.2631i	0.662234	+	0.481141i
$456$		0			0
$457$	−4.59230	−	14.1337i	−0.214819	−	0.661144i	−0.999166	−	0.0408228i	$-0.987002\pi$
$457$	−4.59230	−	14.1337i	−0.214819	−	0.661144i	0.784348	−	0.620322i	$-0.212998\pi$
$458$	4.29327	+	3.11924i	0.200611	+	0.145753i
$459$		0			0
$460$	−0.0861849	+	0.265250i	−0.00401839	+	0.0123673i
$461$	−6.40815			−0.298457			−0.149229	−	0.988803i	$-0.547679\pi$
$461$	−6.40815			−0.298457			−0.149229	+	0.988803i	$0.547679\pi$
$462$		0			0
$463$	13.1457			0.610932			0.305466	−	0.952203i	$-0.401188\pi$
$463$	13.1457			0.610932			0.305466	+	0.952203i	$0.401188\pi$
$464$	−4.81456	+	14.8177i	−0.223510	+	0.687893i
$465$		0			0
$466$	17.2415	+	12.5267i	0.798699	+	0.580288i
$467$	3.71967	+	11.4480i	0.172126	+	0.529749i	0.999491	−	0.0319163i	$-0.0101610\pi$
$467$	3.71967	+	11.4480i	0.172126	+	0.529749i	−0.827365	+	0.561665i	$0.810161\pi$
$468$		0			0
$469$	2.03164	+	1.47608i	0.0938126	+	0.0681589i
$470$	−22.2844	+	16.1906i	−1.02790	+	0.746816i
$471$		0			0
$472$	−5.98657			−0.275554
$473$	−0.205614	−	2.14908i	−0.00945415	−	0.0988146i
$474$		0			0
$475$	−4.42445	+	13.6170i	−0.203008	+	0.624793i
$476$	−6.64211	+	4.82578i	−0.304441	+	0.221189i
$477$		0			0
$478$	−6.35471	−	19.5578i	−0.290658	−	0.894552i
$479$	−3.21707	−	9.90114i	−0.146992	−	0.452395i	0.850270	−	0.526347i	$-0.176439\pi$
$479$	−3.21707	−	9.90114i	−0.146992	−	0.452395i	−0.997262	+	0.0739524i	$0.976439\pi$
$480$		0			0
$481$	−9.47214	+	6.88191i	−0.431892	+	0.313788i
$482$	1.20711	−	3.71511i	0.0549825	−	0.169219i
$483$		0			0
$484$	−4.33614	−	2.02839i	−0.197097	−	0.0921997i
$485$	30.5982			1.38939
$486$		0			0
$487$	−13.3271	+	9.68267i	−0.603907	+	0.438764i	−0.847263	−	0.531173i	$-0.821751\pi$
$487$	−13.3271	+	9.68267i	−0.603907	+	0.438764i	0.243357	+	0.969937i	$0.421751\pi$
$488$	−28.1654	−	20.4634i	−1.27499	−	0.926333i
$489$		0			0
$490$	−1.04367	−	3.21208i	−0.0471481	−	0.145107i
$491$	−13.3154	−	9.67422i	−0.600917	−	0.436592i	0.245287	−	0.969450i	$-0.421118\pi$
$491$	−13.3154	−	9.67422i	−0.600917	−	0.436592i	−0.846204	+	0.532859i	$0.821118\pi$
$492$		0			0
$493$	10.5066	−	32.3361i	0.473194	−	1.45634i
$494$	−28.1020			−1.26437
$495$		0			0
$496$	10.0035			0.449171
$497$	−1.00106	+	3.08094i	−0.0449036	+	0.138199i
$498$		0			0
$499$	16.3521	+	11.8805i	0.732023	+	0.531846i	0.890203	−	0.455565i	$-0.150563\pi$
$499$	16.3521	+	11.8805i	0.732023	+	0.531846i	−0.158180	+	0.987410i	$0.550563\pi$
$500$	1.61266	+	4.96327i	0.0721205	+	0.221964i
$501$		0			0
$502$	10.4888	+	7.62053i	0.468136	+	0.340121i
$503$	19.6309	−	14.2627i	0.875299	−	0.635942i	−0.0567046	−	0.998391i	$-0.518059\pi$
$503$	19.6309	−	14.2627i	0.875299	−	0.635942i	0.932004	+	0.362449i	$0.118059\pi$
$504$		0			0
$505$	−2.97299			−0.132296
$506$	1.58129	+	0.351572i	0.0702968	+	0.0156293i
$507$		0			0
$508$	−0.129558	+	0.398739i	−0.00574821	+	0.0176912i
$509$	20.7067	−	15.0443i	0.917810	−	0.666828i	−0.0251682	−	0.999683i	$-0.508012\pi$
$509$	20.7067	−	15.0443i	0.917810	−	0.666828i	0.942978	+	0.332856i	$0.108012\pi$
$510$		0			0
$511$	2.83160	+	8.71477i	0.125263	+	0.385519i
$512$	7.72924	+	23.7882i	0.341587	+	1.05130i
$513$		0			0
$514$	17.2237	−	12.5137i	0.759703	−	0.551957i
$515$	8.20973	−	25.2669i	0.361764	−	1.11339i
$516$		0			0
$517$	−29.4625	−	33.3421i	−1.29576	−	1.46638i
$518$	11.9022			0.522954
$519$		0			0
$520$	−14.6353	+	10.6331i	−0.641798	+	0.466294i
$521$	−19.4725	−	14.1476i	−0.853105	−	0.619817i	0.0728952	−	0.997340i	$-0.476776\pi$
$521$	−19.4725	−	14.1476i	−0.853105	−	0.619817i	−0.926000	+	0.377522i	$0.876776\pi$
$522$		0			0
$523$	−4.79382	−	14.7539i	−0.209619	−	0.645141i	−0.999492	−	0.0318707i	$-0.989854\pi$
$523$	−4.79382	−	14.7539i	−0.209619	−	0.645141i	0.789873	−	0.613271i	$-0.210146\pi$
$524$	−3.62172	−	2.63134i	−0.158216	−	0.114950i
$525$		0			0
$526$	−5.08956	+	15.6641i	−0.221915	+	0.682986i
$527$	−21.8303			−0.950942
$528$		0			0
$529$	−22.8476			−0.993372
$530$	−3.05895	+	9.41449i	−0.132872	+	0.408939i
$531$		0			0
$532$	−6.42767	−	4.66998i	−0.278675	−	0.202469i
$533$	−8.74975	−	26.9290i	−0.378994	−	1.16642i
$534$		0			0
$535$	−14.1678	−	10.2935i	−0.612528	−	0.445028i
$536$	−2.10490	+	1.52930i	−0.0909178	+	0.0660556i
$537$		0			0
$538$	−11.4973			−0.495682
$539$	5.00440	−	2.17236i	0.215555	−	0.0935702i
$540$		0			0
$541$	−3.39223	+	10.4402i	−0.145844	+	0.448860i	−0.997119	−	0.0758596i	$-0.975830\pi$
$541$	−3.39223	+	10.4402i	−0.145844	+	0.448860i	0.851275	+	0.524720i	$0.175830\pi$
$542$	−7.72640	+	5.61356i	−0.331877	+	0.241123i
$543$		0			0
$544$	−4.78733	−	14.7339i	−0.205255	−	0.631711i
$545$	1.71232	+	5.26998i	0.0733477	+	0.225741i
$546$		0			0
$547$	−6.81617	+	4.95224i	−0.291439	+	0.211743i	−0.723891	−	0.689914i	$-0.757648\pi$
$547$	−6.81617	+	4.95224i	−0.291439	+	0.211743i	0.432453	+	0.901657i	$0.357648\pi$
$548$	−2.59062	+	7.97310i	−0.110666	+	0.340594i
$549$		0			0
$550$	8.77569	−	3.80944i	0.374197	−	0.162435i
$551$	32.9024			1.40169
$552$		0			0
$553$	3.93668	−	2.86017i	0.167405	−	0.121627i
$554$	0.752538	+	0.546751i	0.0319723	+	0.0232292i
$555$		0			0
$556$	−0.761256	−	2.34290i	−0.0322844	−	0.0993613i
$557$	19.9867	+	14.5212i	0.846864	+	0.615283i	0.924280	−	0.381716i	$-0.124667\pi$
$557$	19.9867	+	14.5212i	0.846864	+	0.615283i	−0.0774156	+	0.996999i	$0.524667\pi$
$558$		0			0
$559$	0.727761	−	2.23982i	0.0307810	−	0.0947343i
$560$	14.1895			0.599616
$561$		0			0
$562$	31.0576			1.31009
$563$	−1.32894	+	4.09006i	−0.0560082	+	0.172376i	−0.975147	−	0.221558i	$-0.928886\pi$
$563$	−1.32894	+	4.09006i	−0.0560082	+	0.172376i	0.919139	+	0.393933i	$0.128886\pi$
$564$		0			0
$565$	18.3329	+	13.3196i	0.771269	+	0.560360i
$566$	6.30595	+	19.4077i	0.265059	+	0.815767i
$567$		0			0
$568$	−2.71530	−	1.97278i	−0.113932	−	0.0827762i
$569$	−6.37655	+	4.63283i	−0.267319	+	0.194218i	−0.713367	−	0.700790i	$-0.752831\pi$
$569$	−6.37655	+	4.63283i	−0.267319	+	0.194218i	0.446049	+	0.895009i	$0.352831\pi$
$570$		0			0
$571$	−23.0070			−0.962814			−0.481407	−	0.876497i	$-0.659874\pi$
$571$	−23.0070			−0.962814			−0.481407	+	0.876497i	$0.659874\pi$
$572$	−3.45793	−	3.91327i	−0.144583	−	0.163622i
$573$		0			0
$574$	−8.89475	+	27.3752i	−0.371260	+	1.14262i
$575$	0.728385	−	0.529202i	0.0303757	−	0.0220693i
$576$		0			0
$577$	7.80507	+	24.0215i	0.324929	+	1.00003i	0.971472	+	0.237152i	$0.0762140\pi$
$577$	7.80507	+	24.0215i	0.324929	+	1.00003i	−0.646543	+	0.762877i	$0.723786\pi$
$578$	−9.34284	−	28.7543i	−0.388611	−	1.19602i
$579$		0			0
$580$	3.06223	−	2.22484i	0.127152	−	0.0923816i
$581$	11.7549	−	36.1779i	0.487676	−	1.50091i
$582$		0			0
$583$	−15.6089	−	3.47037i	−0.646456	−	0.143728i
$584$	−9.49365			−0.392850
$585$		0			0
$586$	−5.78029	+	4.19962i	−0.238781	+	0.173485i
$587$	18.8302	+	13.6810i	0.777206	+	0.564673i	0.904139	−	0.427238i	$-0.140513\pi$
$587$	18.8302	+	13.6810i	0.777206	+	0.564673i	−0.126933	+	0.991911i	$0.540513\pi$
$588$		0			0
$589$	−6.52814	−	20.0915i	−0.268987	−	0.827858i
$590$	−3.26444	−	2.37175i	−0.134395	−	0.0976436i
$591$		0			0
$592$	−2.94022	+	9.04908i	−0.120842	+	0.371915i
$593$	17.1253			0.703251			0.351626	−	0.936141i	$-0.385629\pi$
$593$	17.1253			0.703251			0.351626	+	0.936141i	$0.385629\pi$
$594$		0			0
$595$	−30.9652			−1.26945
$596$	−1.06525	+	3.27851i	−0.0436344	+	0.134293i
$597$		0			0
$598$	1.42963	+	1.03868i	0.0584617	+	0.0424749i
$599$	13.2055	+	40.6423i	0.539561	+	1.66060i	0.733582	+	0.679601i	$0.237847\pi$
$599$	13.2055	+	40.6423i	0.539561	+	1.66060i	−0.194021	+	0.980997i	$0.562153\pi$
$600$		0			0
$601$	−10.3607	−	7.52751i	−0.422623	−	0.307053i	0.356069	−	0.934459i	$-0.384117\pi$
$601$	−10.3607	−	7.52751i	−0.422623	−	0.307053i	−0.778692	+	0.627406i	$0.784117\pi$
$602$	−1.93688	+	1.40722i	−0.0789413	+	0.0573542i
$603$		0			0
$604$	−7.28721			−0.296512
$605$	−8.73406	−	15.8019i	−0.355090	−	0.642440i
$606$		0			0
$607$	3.53526	−	10.8804i	0.143492	−	0.441622i	−0.853322	−	0.521384i	$-0.825416\pi$
$607$	3.53526	−	10.8804i	0.143492	−	0.441622i	0.996814	+	0.0797617i	$0.0254159\pi$
$608$	12.1288	−	8.81206i	0.491886	−	0.357376i
$609$		0			0
$610$	−7.25126	−	22.3171i	−0.293595	−	0.903593i
$611$	−14.9990	−	46.1621i	−0.606794	−	1.86752i
$612$		0			0
$613$	−15.2464	+	11.0772i	−0.615796	+	0.447402i	−0.851451	−	0.524435i	$-0.824277\pi$
$613$	−15.2464	+	11.0772i	−0.615796	+	0.447402i	0.235654	+	0.971837i	$0.424277\pi$
$614$	0.575358	−	1.77077i	0.0232195	−	0.0714624i
$615$		0			0
$616$	2.82920	+	29.5707i	0.113992	+	1.19144i
$617$	−15.3198			−0.616754			−0.308377	−	0.951264i	$-0.599786\pi$
$617$	−15.3198			−0.616754			−0.308377	+	0.951264i	$0.599786\pi$
$618$		0			0
$619$	1.79498	−	1.30413i	0.0721462	−	0.0524173i	−0.551128	−	0.834421i	$-0.685802\pi$
$619$	1.79498	−	1.30413i	0.0721462	−	0.0524173i	0.623274	+	0.782004i	$0.285802\pi$
$620$	−1.96615	−	1.42849i	−0.0789626	−	0.0573697i
$621$		0			0
$622$	−11.4669	−	35.2915i	−0.459781	−	1.41506i
$623$	14.0889	+	10.2362i	0.564460	+	0.410104i
$624$		0			0
$625$	−2.51949	+	7.75421i	−0.100780	+	0.310168i
$626$	−23.2859			−0.930693
$627$		0			0
$628$	5.76447			0.230027
$629$	6.41634	−	19.7475i	0.255836	−	0.787383i
$630$		0			0
$631$	10.0626	+	7.31089i	0.400585	+	0.291042i	0.769779	−	0.638310i	$-0.220366\pi$
$631$	10.0626	+	7.31089i	0.400585	+	0.291042i	−0.369194	+	0.929352i	$0.620366\pi$
$632$	1.55790	+	4.79471i	0.0619698	+	0.190723i
$633$		0			0
$634$	−4.72634	−	3.43388i	−0.187707	−	0.136377i
$635$	−1.27928	+	0.929450i	−0.0507666	+	0.0368841i
$636$		0			0
$637$	5.95136			0.235801
$638$	−14.5575	−	16.4744i	−0.576336	−	0.652228i
$639$		0			0
$640$	−3.19808	+	9.84267i	−0.126415	+	0.389066i
$641$	19.9564	−	14.4992i	0.788230	−	0.572683i	−0.119208	−	0.992869i	$-0.538035\pi$
$641$	19.9564	−	14.4992i	0.788230	−	0.572683i	0.907438	+	0.420187i	$0.138035\pi$
$642$		0			0
$643$	5.28099	+	16.2532i	0.208262	+	0.640964i	0.999564	+	0.0295382i	$0.00940368\pi$
$643$	5.28099	+	16.2532i	0.208262	+	0.640964i	−0.791302	+	0.611426i	$0.790596\pi$
$644$	0.154385	+	0.475148i	0.00608362	+	0.0187235i
$645$		0			0
$646$	40.3190	−	29.2935i	1.58633	−	1.15254i
$647$	12.2195	−	37.6077i	0.480398	−	1.47851i	−0.358139	−	0.933668i	$-0.616589\pi$
$647$	12.2195	−	37.6077i	0.480398	−	1.47851i	0.838537	−	0.544844i	$-0.183411\pi$
$648$		0			0
$649$	3.31152	−	5.61404i	0.129988	−	0.220370i
$650$	10.4363			0.409344
$651$		0			0
$652$	−4.70327	+	3.41712i	−0.184194	+	0.133825i
$653$	23.3943	+	16.9970i	0.915491	+	0.665143i	0.942398	−	0.334495i	$-0.108566\pi$
$653$	23.3943	+	16.9970i	0.915491	+	0.665143i	−0.0269068	+	0.999638i	$0.508566\pi$
$654$		0			0
$655$	−5.21753	−	16.0579i	−0.203866	−	0.627435i
$656$	−18.6157	−	13.5251i	−0.726820	−	0.528066i
$657$		0			0
$658$	−15.2476	+	46.9272i	−0.594412	+	1.82941i
$659$	−24.4688			−0.953171			−0.476585	−	0.879128i	$-0.658126\pi$
$659$	−24.4688			−0.953171			−0.476585	+	0.879128i	$0.658126\pi$
$660$		0			0
$661$	29.8732			1.16193			0.580967	−	0.813927i	$-0.302674\pi$
$661$	29.8732			1.16193			0.580967	+	0.813927i	$0.302674\pi$
$662$	9.84757	−	30.3077i	0.382737	−	1.17794i
$663$		0			0
$664$	31.8844	+	23.1654i	1.23735	+	0.898991i
$665$	−9.25985	−	28.4989i	−0.359081	−	1.10514i
$666$		0			0
$667$	−1.67383	−	1.21611i	−0.0648111	−	0.0470880i
$668$	−1.89916	+	1.37982i	−0.0734806	+	0.0533868i
$669$		0			0
$670$	−1.75366			−0.0677500
$671$	34.7699	−	15.0933i	1.34228	−	0.582669i
$672$		0			0
$673$	8.12448	−	25.0046i	0.313176	−	0.963856i	−0.663323	−	0.748333i	$-0.730854\pi$
$673$	8.12448	−	25.0046i	0.313176	−	0.963856i	0.976499	−	0.215523i	$-0.0691455\pi$
$674$	26.6093	−	19.3328i	1.02495	−	0.744672i
$675$		0			0
$676$	−0.0121262	−	0.0373206i	−0.000466393	−	0.00143541i
$677$	13.5153	+	41.5959i	0.519436	+	1.59866i	0.775064	+	0.631883i	$0.217718\pi$
$677$	13.5153	+	41.5959i	0.519436	+	1.59866i	−0.255628	+	0.966775i	$0.582282\pi$
$678$		0			0
$679$	44.3433	−	32.2173i	1.70174	−	1.23639i
$680$	9.91379	−	30.5115i	0.380176	−	1.17006i
$681$		0			0
$682$	−7.17159	+	12.1580i	−0.274615	+	0.465556i
$683$	−14.0939			−0.539288			−0.269644	−	0.962960i	$-0.586906\pi$
$683$	−14.0939			−0.539288			−0.269644	+	0.962960i	$0.586906\pi$
$684$		0			0
$685$	−25.5802	+	18.5851i	−0.977368	+	0.710100i
$686$	15.9344	+	11.5770i	0.608377	+	0.442012i
$687$		0			0
$688$	−0.591421	−	1.82021i	−0.0225477	−	0.0693947i
$689$	−14.1119	−	10.2529i	−0.537619	−	0.390603i
$690$		0			0
$691$	−1.81507	+	5.58621i	−0.0690485	+	0.212510i	−0.979627	−	0.200828i	$-0.935637\pi$
$691$	−1.81507	+	5.58621i	−0.0690485	+	0.212510i	0.910578	+	0.413337i	$0.135637\pi$
$692$	−2.79443			−0.106228
$693$		0			0
$694$	13.9758			0.530513
$695$	2.87115	−	8.83649i	0.108909	−	0.335187i
$696$		0			0
$697$	40.6243	+	29.5153i	1.53875	+	1.11797i
$698$	−2.82427	−	8.69222i	−0.106900	−	0.329005i
$699$		0			0
$700$	2.38705	+	1.73429i	0.0902219	+	0.0655500i
$701$	0.165822	−	0.120477i	0.00626302	−	0.00455035i	−0.584649	−	0.811286i	$-0.698768\pi$
$701$	0.165822	−	0.120477i	0.00626302	−	0.00455035i	0.590912	+	0.806736i	$0.298768\pi$
$702$		0			0
$703$	20.0934			0.757835
$704$	−28.8169	−	6.40693i	−1.08608	−	0.241470i
$705$		0			0
$706$	7.75323	−	23.8620i	0.291797	−	0.898058i
$707$	−4.30849	+	3.13030i	−0.162038	+	0.117727i
$708$		0			0
$709$	−11.8427	−	36.4480i	−0.444761	−	1.36883i	−0.882745	−	0.469852i	$-0.844307\pi$
$709$	−11.8427	−	36.4480i	−0.444761	−	1.36883i	0.437984	−	0.898983i	$-0.355693\pi$
$710$	−0.699063	−	2.15149i	−0.0262354	−	0.0807441i
$711$		0			0
$712$	−14.5969	+	10.6053i	−0.547042	+	0.397449i
$713$	−0.410503	+	1.26340i	−0.0153734	+	0.0473146i
$714$		0			0
$715$	−1.87585	−	19.6063i	−0.0701528	−	0.733236i
$716$	−8.62937			−0.322495
$717$		0			0
$718$	−28.1157	+	20.4272i	−1.04927	+	0.762338i
$719$	32.0818	+	23.3088i	1.19645	+	0.869270i	0.993931	−	0.110009i	$-0.0350878\pi$
$719$	32.0818	+	23.3088i	1.19645	+	0.869270i	0.202517	+	0.979279i	$0.435088\pi$
$720$		0			0
$721$	−14.7063	−	45.2613i	−0.547691	−	1.68562i
$722$	19.7890	+	14.3776i	0.736470	+	0.535077i
$723$		0			0
$724$	0.967270	−	2.97695i	0.0359483	−	0.110638i
$725$	−12.2190			−0.453802
$726$		0			0
$727$	−12.1950			−0.452287			−0.226144	−	0.974094i	$-0.572612\pi$
$727$	−12.1950			−0.452287			−0.226144	+	0.974094i	$0.572612\pi$
$728$	−10.0138	+	30.8193i	−0.371136	+	1.14224i
$729$		0			0
$730$	−5.17683	−	3.76119i	−0.191603	−	0.139208i
$731$	1.29064	+	3.97217i	0.0477359	+	0.146916i
$732$		0			0
$733$	−12.2163	−	8.87569i	−0.451221	−	0.327831i	0.338857	−	0.940838i	$-0.389960\pi$
$733$	−12.2163	−	8.87569i	−0.451221	−	0.327831i	−0.790078	+	0.613007i	$0.789960\pi$
$734$	28.4554	−	20.6741i	1.05031	−	0.763094i
$735$		0			0
$736$	−0.942726			−0.0347493
$737$	−0.269792	−	2.81986i	−0.00993791	−	0.103871i
$738$		0			0
$739$	−5.34127	+	16.4387i	−0.196482	+	0.604709i	0.803474	+	0.595339i	$0.202982\pi$
$739$	−5.34127	+	16.4387i	−0.196482	+	0.604709i	−0.999956	+	0.00936931i	$0.997018\pi$
$740$	1.87009	−	1.35870i	0.0687459	−	0.0499468i
$741$		0			0
$742$	5.47958	+	16.8644i	0.201162	+	0.619112i
$743$	6.03380	+	18.5701i	0.221359	+	0.681272i	0.998641	+	0.0521198i	$0.0165978\pi$
$743$	6.03380	+	18.5701i	0.221359	+	0.681272i	−0.777282	+	0.629152i	$0.783402\pi$
$744$		0			0
$745$	−10.5185	+	7.64212i	−0.385367	+	0.279986i
$746$	−10.1775	+	31.3233i	−0.372626	+	1.14683i
$747$		0			0
$748$	9.04040	+	2.00997i	0.330550	+	0.0734919i
$749$	−31.3704			−1.14625
$750$		0			0
$751$	−29.2755	+	21.2699i	−1.06828	+	0.776149i	−0.975602	−	0.219547i	$-0.929542\pi$
$751$	−29.2755	+	21.2699i	−1.06828	+	0.776149i	−0.0926760	+	0.995696i	$0.529542\pi$
$752$	−31.9113	−	23.1849i	−1.16369	−	0.845468i
$753$		0			0
$754$	−7.41104	−	22.8088i	−0.269894	−	0.830648i
$755$	−22.2354	−	16.1549i	−0.809228	−	0.587938i
$756$		0			0
$757$	−8.14836	+	25.0781i	−0.296157	+	0.911479i	0.686673	+	0.726967i	$0.259070\pi$
$757$	−8.14836	+	25.0781i	−0.296157	+	0.911479i	−0.982830	+	0.184512i	$0.940930\pi$
$758$	−7.43921			−0.270204
$759$		0			0
$760$	31.0459			1.12615
$761$	−2.61323	+	8.04271i	−0.0947297	+	0.291548i	−0.987183	−	0.159591i	$-0.948982\pi$
$761$	−2.61323	+	8.04271i	−0.0947297	+	0.291548i	0.892453	+	0.451139i	$0.148982\pi$
$762$		0			0
$763$	8.03034	+	5.83439i	0.290718	+	0.211219i
$764$	−0.349929	−	1.07697i	−0.0126600	−	0.0389634i
$765$		0			0
$766$	−13.5457	−	9.84153i	−0.489426	−	0.355589i
$767$	5.75234	−	4.17932i	0.207705	−	0.150906i
$768$		0			0
$769$	5.06099			0.182504			0.0912520	−	0.995828i	$-0.470913\pi$
$769$	5.06099			0.182504			0.0912520	+	0.995828i	$0.470913\pi$
$770$	−10.1726	+	17.2456i	−0.366594	+	0.621488i
$771$		0			0
$772$	−3.39060	+	10.4352i	−0.122030	+	0.375571i
$773$	21.8296	−	15.8601i	0.785156	−	0.570449i	−0.121366	−	0.992608i	$-0.538727\pi$
$773$	21.8296	−	15.8601i	0.785156	−	0.570449i	0.906522	+	0.422159i	$0.138727\pi$
$774$		0			0
$775$	2.42436	+	7.46140i	0.0870854	+	0.268021i
$776$	17.5483	+	54.0082i	0.629948	+	1.93878i
$777$		0			0
$778$	19.6878	−	14.3040i	0.705841	−	0.512824i
$779$	−15.0161	+	46.2149i	−0.538008	+	1.65582i
$780$		0			0
$781$	3.35201	−	1.45508i	0.119945	−	0.0520667i
$782$	−3.13386			−0.112066
$783$		0			0
$784$	3.91274	−	2.84277i	0.139741	−	0.101528i
$785$	17.5890	+	12.7792i	0.627780	+	0.456109i
$786$		0			0
$787$	4.70862	+	14.4916i	0.167844	+	0.516571i	0.999235	−	0.0391175i	$-0.0124547\pi$
$787$	4.70862	+	14.4916i	0.167844	+	0.516571i	−0.831390	+	0.555689i	$0.812455\pi$
$788$	−7.46587	−	5.42427i	−0.265961	−	0.193232i
$789$		0			0
$790$	−1.05005	+	3.23173i	−0.0373592	+	0.114980i
$791$	40.5926			1.44331
$792$		0			0
$793$	41.3492			1.46835
$794$	−8.69440	+	26.7586i	−0.308553	+	0.949628i
$795$		0			0
$796$	−8.30062	−	6.03075i	−0.294208	−	0.213754i
$797$	−3.07043	−	9.44981i	−0.108760	−	0.334730i	0.881834	−	0.471559i	$-0.156309\pi$
$797$	−3.07043	−	9.44981i	−0.108760	−	0.334730i	−0.990595	+	0.136830i	$0.956309\pi$
$798$		0			0
$799$	69.6389	+	50.5956i	2.46365	+	1.78994i
$800$	−4.50426	+	3.27254i	−0.159250	+	0.115702i
$801$		0			0
$802$	−6.59029			−0.232711
$803$	5.25149	−	8.90288i	0.185321	−	0.314176i
$804$		0			0
$805$	−0.582278	+	1.79207i	−0.0205226	+	0.0631621i
$806$	−12.4576	+	9.05095i	−0.438799	+	0.318806i
$807$		0			0
$808$	−1.70504	−	5.24756i	−0.0599830	−	0.184609i
$809$	−11.4547	−	35.2540i	−0.402727	−	1.23947i	−0.922778	−	0.385331i	$-0.874087\pi$
$809$	−11.4547	−	35.2540i	−0.402727	−	1.23947i	0.520052	−	0.854135i	$-0.325913\pi$
$810$		0			0
$811$	34.3539	−	24.9596i	1.20633	−	0.876449i	0.211436	−	0.977392i	$-0.432186\pi$
$811$	34.3539	−	24.9596i	1.20633	−	0.876449i	0.994892	+	0.100943i	$0.0321860\pi$
$812$	2.09526	−	6.44854i	0.0735291	−	0.226299i
$813$		0			0
$814$	−8.89018	−	10.0608i	−0.311601	−	0.352632i
$815$	−21.9264			−0.768048
$816$		0			0
$817$	−3.26984	+	2.37568i	−0.114397	+	0.0831144i
$818$	11.5334	+	8.37948i	0.403255	+	0.292982i
$819$		0			0
$820$	1.72747	+	5.31660i	0.0603258	+	0.185664i
$821$	−6.19916	−	4.50395i	−0.216352	−	0.157189i	0.474331	−	0.880347i	$-0.342690\pi$
$821$	−6.19916	−	4.50395i	−0.216352	−	0.157189i	−0.690683	+	0.723158i	$0.742690\pi$
$822$		0			0
$823$	1.14657	−	3.52878i	0.0399669	−	0.123005i	−0.929082	−	0.369873i	$-0.879401\pi$
$823$	1.14657	−	3.52878i	0.0399669	−	0.123005i	0.969049	+	0.246867i	$0.0794012\pi$
$824$	49.3065			1.71767
$825$		0			0
$826$	−7.22812			−0.251498
$827$	1.30500	−	4.01636i	0.0453791	−	0.139663i	−0.925800	−	0.378014i	$-0.876607\pi$
$827$	1.30500	−	4.01636i	0.0453791	−	0.139663i	0.971179	+	0.238352i	$0.0766070\pi$
$828$		0			0
$829$	21.2154	+	15.4139i	0.736840	+	0.535346i	0.891720	−	0.452588i	$-0.149499\pi$
$829$	21.2154	+	15.4139i	0.736840	+	0.535346i	−0.154880	+	0.987933i	$0.549499\pi$
$830$	8.20873	+	25.2639i	0.284929	+	0.876922i
$831$		0			0
$832$	−26.0530	−	18.9286i	−0.903226	−	0.656232i
$833$	−8.53863	+	6.20368i	−0.295846	+	0.214945i
$834$		0			0
$835$	−8.85377			−0.306397
$836$	0.853561	+	8.92141i	0.0295210	+	0.308553i
$837$		0			0
$838$	6.05340	−	18.6305i	0.209111	−	0.643578i
$839$	13.2460	−	9.62378i	0.457303	−	0.332250i	−0.335170	−	0.942158i	$-0.608794\pi$
$839$	13.2460	−	9.62378i	0.457303	−	0.332250i	0.792472	+	0.609908i	$0.208794\pi$
$840$		0			0
$841$	−0.284500	−	0.875601i	−0.00981035	−	0.0301932i
$842$	−9.98238	−	30.7226i	−0.344015	−	1.05877i
$843$		0			0
$844$	9.55790	−	6.94422i	0.328996	−	0.239030i
$845$	0.0457352	−	0.140758i	0.00157334	−	0.00484224i
$846$		0			0
$847$	−29.2956	−	13.7041i	−1.00661	−	0.470880i
$848$	−14.1754			−0.486784
$849$		0			0
$850$	−14.9733	+	10.8787i	−0.513580	+	0.373138i
$851$	−1.02220	−	0.742673i	−0.0350406	−	0.0254585i
$852$		0			0
$853$	12.8957	+	39.6889i	0.441541	+	1.35892i	0.886233	+	0.463239i	$0.153313\pi$
$853$	12.8957	+	39.6889i	0.441541	+	1.35892i	−0.444693	+	0.895683i	$0.646687\pi$
$854$	−34.0066	−	24.7072i	−1.16368	−	0.845464i
$855$		0			0
$856$	10.0435	−	30.9107i	0.343280	−	1.05651i
$857$	−44.2534			−1.51167			−0.755834	−	0.654763i	$-0.772768\pi$
$857$	−44.2534			−1.51167			−0.755834	+	0.654763i	$0.772768\pi$
$858$		0			0
$859$	−22.5724			−0.770159			−0.385080	−	0.922883i	$-0.625826\pi$
$859$	−22.5724			−0.770159			−0.385080	+	0.922883i	$0.625826\pi$
$860$	−0.143682	+	0.442209i	−0.00489953	+	0.0150792i
$861$		0			0
$862$	−9.25942	−	6.72736i	−0.315377	−	0.229135i
$863$	−0.793169	−	2.44112i	−0.0269998	−	0.0830968i	0.936649	−	0.350270i	$-0.113910\pi$
$863$	−0.793169	−	2.44112i	−0.0269998	−	0.0830968i	−0.963648	+	0.267174i	$0.913910\pi$
$864$		0			0
$865$	−8.52661	−	6.19495i	−0.289914	−	0.210635i
$866$	−13.6482	+	9.91599i	−0.463785	+	0.336959i
$867$		0			0
$868$	−4.35345			−0.147766
$869$	−5.35811	−	1.19128i	−0.181761	−	0.0404114i
$870$		0			0
$871$	0.954915	−	2.93893i	0.0323561	−	0.0995817i
$872$	−8.31989	+	6.04475i	−0.281747	+	0.204701i
$873$		0			0
$874$	−0.937150	−	2.88425i	−0.0316996	−	0.0975612i
$875$	10.8954	+	33.5326i	0.368332	+	1.13361i
$876$		0			0
$877$	−43.5174	+	31.6172i	−1.46948	+	1.06764i	−0.488712	+	0.872445i	$0.662533\pi$
$877$	−43.5174	+	31.6172i	−1.46948	+	1.06764i	−0.980765	+	0.195192i	$0.937467\pi$
$878$	−11.6611	+	35.8893i	−0.393544	+	1.21120i
$879$		0			0
$880$	−10.5986	−	11.9942i	−0.357279	−	0.404326i
$881$	−42.7815			−1.44134			−0.720672	−	0.693276i	$-0.756167\pi$
$881$	−42.7815			−1.44134			−0.720672	+	0.693276i	$0.756167\pi$
$882$		0			0
$883$	−2.00195	+	1.45450i	−0.0673711	+	0.0489479i	−0.620961	−	0.783841i	$-0.713257\pi$
$883$	−2.00195	+	1.45450i	−0.0673711	+	0.0489479i	0.553590	+	0.832789i	$0.313257\pi$
$884$	8.17332	+	5.93827i	0.274899	+	0.199726i
$885$		0			0
$886$	0.0200628	+	0.0617468i	0.000674021	+	0.00207442i
$887$	1.70335	+	1.23756i	0.0571929	+	0.0415531i	0.616014	−	0.787735i	$-0.288746\pi$
$887$	1.70335	+	1.23756i	0.0571929	+	0.0415531i	−0.558821	+	0.829288i	$0.688746\pi$
$888$		0			0
$889$	−0.875313	+	2.69394i	−0.0293571	+	0.0903518i
$890$	−12.1612			−0.407644
$891$		0			0
$892$	2.89334			0.0968763
$893$	−25.7409	+	79.2224i	−0.861387	+	2.65108i
$894$		0			0
$895$	−26.3307	−	19.1304i	−0.880137	−	0.639457i
$896$	5.72879	+	17.6314i	0.191386	+	0.589024i
$897$		0			0
$898$	−32.0085	−	23.2556i	−1.06814	−	0.776048i
$899$	14.5856	−	10.5970i	0.486456	−	0.353431i
$900$		0			0
$901$	30.9344			1.03057
$902$	29.7838	−	12.9288i	0.991692	−	0.430483i
$903$		0			0
$904$	−12.9961	+	39.9978i	−0.432243	+	1.33031i
$905$	9.55099	−	6.93920i	0.317486	−	0.230667i
$906$		0			0
$907$	−4.21739	−	12.9798i	−0.140036	−	0.430987i	0.856303	−	0.516474i	$-0.172756\pi$
$907$	−4.21739	−	12.9798i	−0.140036	−	0.430987i	−0.996339	+	0.0854865i	$0.972756\pi$
$908$	−1.42927	−	4.39884i	−0.0474319	−	0.145980i
$909$		0			0
$910$	−17.6704	+	12.8383i	−0.585769	+	0.425586i
$911$	−2.34075	+	7.20410i	−0.0775526	+	0.238682i	−0.982315	−	0.187233i	$-0.940048\pi$
$911$	−2.34075	+	7.20410i	−0.0775526	+	0.238682i	0.904763	+	0.425916i	$0.140048\pi$
$912$		0			0
$913$	−39.3610	+	17.0862i	−1.30266	+	0.565470i
$914$	18.5900			0.614901
$915$		0			0
$916$	1.49362	−	1.08517i	0.0493504	−	0.0358552i
$917$	−24.4689	−	17.7777i	−0.808034	−	0.587071i
$918$		0			0
$919$	−5.16917	−	15.9091i	−0.170515	−	0.524792i	0.828885	−	0.559419i	$-0.188976\pi$
$919$	−5.16917	−	15.9091i	−0.170515	−	0.524792i	−0.999400	+	0.0346269i	$0.988976\pi$
$920$	−1.57939	−	1.14749i	−0.0520709	−	0.0378317i
$921$		0			0
$922$	2.47711	−	7.62376i	0.0815793	−	0.251075i
$923$	3.98630			0.131211
$924$		0			0
$925$	−7.46207			−0.245351
$926$	−5.08155	+	15.6394i	−0.166990	+	0.513943i
$927$		0			0
$928$	10.3508	+	7.52032i	0.339783	+	0.246866i
$929$	6.37449	+	19.6187i	0.209140	+	0.643668i	0.999518	+	0.0310478i	$0.00988441\pi$
$929$	6.37449	+	19.6187i	0.209140	+	0.643668i	−0.790378	+	0.612620i	$0.790116\pi$
$930$		0			0
$931$	−8.26296	−	6.00339i	−0.270808	−	0.196753i
$932$	5.99828	−	4.35800i	0.196480	−	0.142751i
$933$		0			0
$934$	−15.0575			−0.492696
$935$	23.1290	+	26.1746i	0.756398	+	0.856000i
$936$		0			0
$937$	−9.60247	+	29.5534i	−0.313699	+	0.965466i	0.662588	+	0.748984i	$0.269458\pi$
$937$	−9.60247	+	29.5534i	−0.313699	+	0.965466i	−0.976287	+	0.216482i	$0.930542\pi$
$938$	−2.54143	+	1.84646i	−0.0829806	+	0.0602890i
$939$		0			0
$940$	2.96126	+	9.11382i	0.0965857	+	0.297260i
$941$	4.88055	+	15.0208i	0.159101	+	0.489664i	0.998553	−	0.0537700i	$-0.0171238\pi$
$941$	4.88055	+	15.0208i	0.159101	+	0.489664i	−0.839452	+	0.543434i	$0.817124\pi$
$942$		0			0
$943$	2.47206	−	1.79606i	0.0805015	−	0.0584877i
$944$	1.78557	−	5.49542i	0.0581154	−	0.178861i
$945$		0			0
$946$	2.63623	+	0.586120i	0.0857113	+	0.0190564i
$947$	52.7074			1.71276			0.856381	−	0.516345i	$-0.172708\pi$
$947$	52.7074			1.71276			0.856381	+	0.516345i	$0.172708\pi$
$948$		0			0
$949$	9.12220	−	6.62767i	0.296119	−	0.215143i
$950$	−14.4899	−	10.5275i	−0.470114	−	0.341558i
$951$		0			0
$952$	−17.7588	−	54.6560i	−0.575566	−	1.77141i
$953$	−38.4078	−	27.9049i	−1.24415	−	0.903928i	−0.246282	−	0.969198i	$-0.579209\pi$
$953$	−38.4078	−	27.9049i	−1.24415	−	0.903928i	−0.997868	+	0.0652707i	$0.979209\pi$
$954$		0			0
$955$	1.31979	−	4.06190i	0.0427074	−	0.131440i
$956$	−7.15425			−0.231385
$957$		0			0
$958$	13.0229			0.420752
$959$	−17.5026	+	53.8674i	−0.565188	+	1.73947i
$960$		0			0
$961$	15.7147	+	11.4174i	0.506924	+	0.368302i
$962$	−4.52588	−	13.9292i	−0.145920	−	0.449096i
$963$		0			0
$964$	−1.09945	−	0.798794i	−0.0354108	−	0.0257274i
$965$	−33.4794	+	24.3242i	−1.07774	+	0.783024i
$966$		0			0
$967$	13.1340			0.422361			0.211180	−	0.977447i	$-0.432269\pi$
$967$	13.1340			0.422361			0.211180	+	0.977447i	$0.432269\pi$
$968$	22.8826	−	24.4788i	0.735474	−	0.786780i
$969$		0			0
$970$	−11.8279	+	36.4026i	−0.379772	+	1.16882i
$971$	26.8860	−	19.5338i	0.862814	−	0.626871i	−0.0658353	−	0.997831i	$-0.520971\pi$
$971$	26.8860	−	19.5338i	0.862814	−	0.626871i	0.928649	+	0.370960i	$0.120971\pi$
$972$		0			0
$973$	−5.14316	−	15.8290i	−0.164882	−	0.507455i
$974$	−6.36780	−	19.5981i	−0.204037	−	0.627963i
$975$		0			0
$976$	27.1852	−	19.7512i	0.870177	−	0.632221i
$977$	−4.75476	+	14.6336i	−0.152118	+	0.468171i	−0.997858	−	0.0654248i	$-0.979160\pi$
$977$	−4.75476	+	14.6336i	−0.152118	+	0.468171i	0.845739	+	0.533596i	$0.179160\pi$
$978$		0			0
$979$	−1.87093	−	19.5550i	−0.0597953	−	0.624980i
$980$	−1.17498			−0.0375334
$981$		0			0
$982$	16.6566	−	12.1017i	0.531532	−	0.386181i
$983$	31.1885	+	22.6598i	0.994760	+	0.722735i	0.960958	−	0.276693i	$-0.0892386\pi$
$983$	31.1885	+	22.6598i	0.994760	+	0.722735i	0.0338015	+	0.999429i	$0.489239\pi$
$984$		0			0
$985$	−10.7555	−	33.1020i	−0.342699	−	1.05472i
$986$	34.4088	+	24.9994i	1.09580	+	0.796144i
$987$		0			0
$988$	−3.02114	+	9.29811i	−0.0961152	+	0.295812i
$989$	0.254153			0.00808160
$990$		0			0
$991$	10.3606			0.329114			0.164557	−	0.986368i	$-0.447381\pi$
$991$	10.3606			0.329114			0.164557	+	0.986368i	$0.447381\pi$
$992$	2.53851	−	7.81272i	0.0805977	−	0.248054i
$993$		0			0
$994$	−3.27843	−	2.38192i	−0.103985	−	0.0755498i
$995$	−11.9580	−	36.8031i	−0.379096	−	1.16674i
$996$		0			0
$997$	3.69329	+	2.68333i	0.116968	+	0.0849820i	0.644731	−	0.764409i	$-0.276969\pi$
$997$	3.69329	+	2.68333i	0.116968	+	0.0849820i	−0.527764	+	0.849391i	$0.676969\pi$
$998$	−20.4553	+	14.8616i	−0.647500	+	0.470437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.b.163.2	yes	16
3.2	odd	2	inner	297.2.f.b.163.3	yes	16
9.2	odd	6		891.2.n.h.757.2		32
9.4	even	3		891.2.n.h.460.2		32
9.5	odd	6		891.2.n.h.460.3		32
9.7	even	3		891.2.n.h.757.3		32
11.4	even	5		3267.2.a.bj.1.3		8
11.5	even	5	inner	297.2.f.b.82.2	✓	16
11.7	odd	10		3267.2.a.bi.1.6		8
33.5	odd	10	inner	297.2.f.b.82.3	yes	16
33.26	odd	10		3267.2.a.bj.1.6		8
33.29	even	10		3267.2.a.bi.1.3		8
99.5	odd	30		891.2.n.h.379.2		32
99.16	even	15		891.2.n.h.676.2		32
99.38	odd	30		891.2.n.h.676.3		32
99.49	even	15		891.2.n.h.379.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.2	✓	16	11.5	even	5	inner
297.2.f.b.82.3	yes	16	33.5	odd	10	inner
297.2.f.b.163.2	yes	16	1.1	even	1	trivial
297.2.f.b.163.3	yes	16	3.2	odd	2	inner
891.2.n.h.379.2		32	99.5	odd	30
891.2.n.h.379.3		32	99.49	even	15
891.2.n.h.460.2		32	9.4	even	3
891.2.n.h.460.3		32	9.5	odd	6
891.2.n.h.676.2		32	99.16	even	15
891.2.n.h.676.3		32	99.38	odd	30
891.2.n.h.757.2		32	9.2	odd	6
891.2.n.h.757.3		32	9.7	even	3
3267.2.a.bi.1.3		8	33.29	even	10
3267.2.a.bi.1.6		8	11.7	odd	10
3267.2.a.bj.1.3		8	11.4	even	5
3267.2.a.bj.1.6		8	33.26	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.386556 + 1.18970i) q^{2} +(0.352078 + 0.255800i) q^{4} +(0.507211 + 1.56103i) q^{5} +(2.37869 + 1.72822i) q^{7} +(-2.46446 + 1.79053i) q^{8} -2.05323 q^{10} +(-0.315878 - 3.30155i) q^{11} +(1.11803 - 3.44095i) q^{13} +(-2.97556 + 2.16187i) q^{14} +(-0.908579 - 2.79632i) q^{16} +(1.98276 + 6.10230i) q^{17} +(-5.02334 + 3.64967i) q^{19} +(-0.220734 + 0.679350i) q^{20} +(4.04995 + 0.900435i) q^{22} +0.390446 q^{23} +(1.86552 - 1.35538i) q^{25} +(3.66151 + 2.66025i) q^{26} +(0.395406 + 1.21694i) q^{28} +(-4.28698 - 3.11467i) q^{29} +(-1.05137 + 3.23578i) q^{31} -2.41448 q^{32} -8.02635 q^{34} +(-1.49131 + 4.58979i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(-2.40020 - 7.38706i) q^{38} +(-4.04508 - 2.93893i) q^{40} +(6.33138 - 4.60002i) q^{41} +0.650930 q^{43} +(0.733321 - 1.24320i) q^{44} +(-0.150930 + 0.464513i) q^{46} +(10.8534 - 7.88544i) q^{47} +(0.508307 + 1.56441i) q^{49} +(0.891363 + 2.74333i) q^{50} +(1.27383 - 0.925491i) q^{52} +(1.48983 - 4.58522i) q^{53} +(4.99362 - 2.16768i) q^{55} -8.95662 q^{56} +(5.36268 - 3.89621i) q^{58} +(1.58991 + 1.15514i) q^{59} +(3.53164 + 10.8693i) q^{61} +(-3.44318 - 2.50162i) q^{62} +(2.75049 - 8.46514i) q^{64} +5.93853 q^{65} +0.854102 q^{67} +(-0.862881 + 2.65567i) q^{68} +(-4.88399 - 3.54843i) q^{70} +(0.340470 + 1.04786i) q^{71} +(2.52131 + 1.83184i) q^{73} +(3.27496 - 2.37940i) q^{74} -2.70219 q^{76} +(4.95443 - 8.39927i) q^{77} +(0.511416 - 1.57398i) q^{79} +(3.90431 - 2.83665i) q^{80} +(3.02520 + 9.31060i) q^{82} +(-3.99797 - 12.3045i) q^{83} +(-8.52023 + 6.19031i) q^{85} +(-0.251621 + 0.774410i) q^{86} +(6.69000 + 7.57094i) q^{88} +5.92297 q^{89} +(8.60618 - 6.25276i) q^{91} +(0.137467 + 0.0998760i) q^{92} +(5.18585 + 15.9604i) q^{94} +(-8.24515 - 5.99045i) q^{95} +(5.76066 - 17.7295i) q^{97} -2.05766 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

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