LMFDB - Embedded newform 1386.2.ba.a.989.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			989.7
Character	$\chi$	$=$	1386.989
Dual form			1386.2.ba.a.1187.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.03699 - 0.598709i) q^{5} +(-2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.03699 - 0.598709i) q^{5} +(-2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +(1.03699 - 0.598709i) q^{10} +(-0.396361 - 3.29286i) q^{11} +3.26196i q^{13} +(0.586237 - 2.57999i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.21006 + 3.82794i) q^{17} +(-6.73468 - 3.88827i) q^{19} +1.19742i q^{20} +(3.04988 + 1.30317i) q^{22} +(5.94749 + 3.43378i) q^{23} +(-1.78309 - 3.08841i) q^{25} +(-2.82494 - 1.63098i) q^{26} +(1.94121 + 1.79769i) q^{28} +7.85827 q^{29} +(-0.103382 - 0.179063i) q^{31} +(-0.500000 - 0.866025i) q^{32} -4.42012 q^{34} +(3.08932 + 0.701970i) q^{35} +(3.83230 - 6.63773i) q^{37} +(6.73468 - 3.88827i) q^{38} +(-1.03699 - 0.598709i) q^{40} +3.15304 q^{41} +8.00258i q^{43} +(-2.65352 + 1.98969i) q^{44} +(-5.94749 + 3.43378i) q^{46} +(-0.355926 - 0.205494i) q^{47} +(5.77602 - 3.95444i) q^{49} +3.56619 q^{50} +(2.82494 - 1.63098i) q^{52} +(5.02547 - 2.90146i) q^{53} +(-1.56044 + 3.65198i) q^{55} +(-2.52745 + 0.782297i) q^{56} +(-3.92914 + 6.80547i) q^{58} +(3.66888 - 2.11823i) q^{59} +(9.94695 + 5.74287i) q^{61} +0.206764 q^{62} +1.00000 q^{64} +(1.95297 - 3.38264i) q^{65} +(5.61793 + 9.73055i) q^{67} +(2.21006 - 3.82794i) q^{68} +(-2.15258 + 2.32445i) q^{70} -3.80688i q^{71} +(-0.195764 + 0.113024i) q^{73} +(3.83230 + 6.63773i) q^{74} +7.77654i q^{76} +(3.57778 + 8.01246i) q^{77} +(-2.00851 - 1.15961i) q^{79} +(1.03699 - 0.598709i) q^{80} +(-1.57652 + 2.73061i) q^{82} +10.8698 q^{83} -5.29274i q^{85} +(-6.93044 - 4.00129i) q^{86} +(-0.396361 - 3.29286i) q^{88} +(-11.4053 - 6.58488i) q^{89} +(-2.55183 - 8.24446i) q^{91} -6.86757i q^{92} +(0.355926 - 0.205494i) q^{94} +(4.65588 + 8.06422i) q^{95} +13.1097 q^{97} +(0.536631 + 6.97940i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.03699	−	0.598709i	−0.463758	−	0.267751i	0.249865	−	0.968281i	$-0.419614\pi$
$5$	−1.03699	−	0.598709i	−0.463758	−	0.267751i	−0.713623	+	0.700530i	$0.752947\pi$
$6$		0			0
$7$	−2.52745	+	0.782297i	−0.955287	+	0.295681i
$7$	−2.52745	+	0.782297i	−0.955287	+	0.295681i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.03699	−	0.598709i	0.327926	−	0.189328i
$11$	−0.396361	−	3.29286i	−0.119507	−	0.992833i
$11$	−0.396361	−	3.29286i	−0.119507	−	0.992833i
$12$		0			0
$13$			3.26196i			0.904706i	0.891839	+	0.452353i	$0.149415\pi$
$13$			3.26196i			0.904706i	−0.891839	+	0.452353i	$0.850585\pi$
$14$	0.586237	−	2.57999i	0.156678	−	0.689530i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.21006	+	3.82794i	0.536019	+	0.928412i	0.999113	+	0.0421028i	$0.0134057\pi$
$17$	2.21006	+	3.82794i	0.536019	+	0.928412i	−0.463095	+	0.886309i	$0.653261\pi$
$18$		0			0
$19$	−6.73468	−	3.88827i	−1.54504	−	0.892030i	−0.998509	−	0.0545917i	$-0.982614\pi$
$19$	−6.73468	−	3.88827i	−1.54504	−	0.892030i	−0.546532	−	0.837438i	$-0.684052\pi$
$20$			1.19742i			0.267751i
$21$		0			0
$22$	3.04988	+	1.30317i	0.650236	+	0.277836i
$23$	5.94749	+	3.43378i	1.24014	+	0.715993i	0.969122	−	0.246582i	$-0.0793073\pi$
$23$	5.94749	+	3.43378i	1.24014	+	0.715993i	0.271015	+	0.962575i	$0.412641\pi$
$24$		0			0
$25$	−1.78309	−	3.08841i	−0.356619	−	0.617682i
$26$	−2.82494	−	1.63098i	−0.554017	−	0.319862i
$27$		0			0
$28$	1.94121	+	1.79769i	0.366855	+	0.339731i
$29$	7.85827			1.45924			0.729622	−	0.683850i	$-0.239696\pi$
$29$	7.85827			1.45924			0.729622	+	0.683850i	$0.239696\pi$
$30$		0			0
$31$	−0.103382	−	0.179063i	−0.0185680	−	0.0321607i	0.856592	−	0.515994i	$-0.172577\pi$
$31$	−0.103382	−	0.179063i	−0.0185680	−	0.0321607i	−0.875160	+	0.483833i	$0.839244\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−4.42012			−0.758045
$35$	3.08932	+	0.701970i	0.522191	+	0.118655i
$36$		0			0
$37$	3.83230	−	6.63773i	0.630026	−	1.09124i	−0.357520	−	0.933905i	$-0.616378\pi$
$37$	3.83230	−	6.63773i	0.630026	−	1.09124i	0.987546	−	0.157331i	$-0.0502891\pi$
$38$	6.73468	−	3.88827i	1.09251	−	0.630760i
$39$		0			0
$40$	−1.03699	−	0.598709i	−0.163963	−	0.0946642i
$41$	3.15304			0.492422			0.246211	−	0.969216i	$-0.420814\pi$
$41$	3.15304			0.492422			0.246211	+	0.969216i	$0.420814\pi$
$42$		0			0
$43$			8.00258i			1.22038i	0.792254	+	0.610191i	$0.208907\pi$
$43$			8.00258i			1.22038i	−0.792254	+	0.610191i	$0.791093\pi$
$44$	−2.65352	+	1.98969i	−0.400033	+	0.299957i
$45$		0			0
$46$	−5.94749	+	3.43378i	−0.876909	+	0.506284i
$47$	−0.355926	−	0.205494i	−0.0519172	−	0.0299744i	0.473817	−	0.880623i	$-0.342876\pi$
$47$	−0.355926	−	0.205494i	−0.0519172	−	0.0299744i	−0.525734	+	0.850649i	$0.676209\pi$
$48$		0			0
$49$	5.77602	−	3.95444i	0.825146	−	0.564919i
$50$	3.56619			0.504335
$51$		0			0
$52$	2.82494	−	1.63098i	0.391749	−	0.226177i
$53$	5.02547	−	2.90146i	0.690302	−	0.398546i	−0.113423	−	0.993547i	$-0.536182\pi$
$53$	5.02547	−	2.90146i	0.690302	−	0.398546i	0.803725	+	0.595001i	$0.202848\pi$
$54$		0			0
$55$	−1.56044	+	3.65198i	−0.210409	+	0.492433i
$56$	−2.52745	+	0.782297i	−0.337745	+	0.104539i
$57$		0			0
$58$	−3.92914	+	6.80547i	−0.515921	+	0.893601i
$59$	3.66888	−	2.11823i	0.477647	−	0.275770i	−0.241788	−	0.970329i	$-0.577734\pi$
$59$	3.66888	−	2.11823i	0.477647	−	0.275770i	0.719436	+	0.694559i	$0.244401\pi$
$60$		0			0
$61$	9.94695	+	5.74287i	1.27358	+	0.735300i	0.975659	−	0.219292i	$-0.0703747\pi$
$61$	9.94695	+	5.74287i	1.27358	+	0.735300i	0.297917	+	0.954592i	$0.403708\pi$
$62$	0.206764			0.0262591
$63$		0			0
$64$	1.00000			0.125000
$65$	1.95297	−	3.38264i	0.242236	−	0.419565i
$66$		0			0
$67$	5.61793	+	9.73055i	0.686340	+	1.18878i	0.973014	+	0.230747i	$0.0741170\pi$
$67$	5.61793	+	9.73055i	0.686340	+	1.18878i	−0.286674	+	0.958028i	$0.592550\pi$
$68$	2.21006	−	3.82794i	0.268009	−	0.464206i
$69$		0			0
$70$	−2.15258	+	2.32445i	−0.257283	+	0.277824i
$71$		−	3.80688i		−	0.451793i	−0.974151	−	0.225897i	$-0.927469\pi$
$71$		−	3.80688i		−	0.451793i	0.974151	−	0.225897i	$-0.0725312\pi$
$72$		0			0
$73$	−0.195764	+	0.113024i	−0.0229124	+	0.0132285i	−0.511412	−	0.859335i	$-0.670878\pi$
$73$	−0.195764	+	0.113024i	−0.0229124	+	0.0132285i	0.488500	+	0.872564i	$0.337544\pi$
$74$	3.83230	+	6.63773i	0.445496	+	0.771621i
$75$		0			0
$76$			7.77654i			0.892030i
$77$	3.57778	+	8.01246i	0.407725	+	0.913105i
$78$		0			0
$79$	−2.00851	−	1.15961i	−0.225975	−	0.130466i	0.382739	−	0.923856i	$-0.374981\pi$
$79$	−2.00851	−	1.15961i	−0.225975	−	0.130466i	−0.608714	+	0.793390i	$0.708314\pi$
$80$	1.03699	−	0.598709i	0.115940	−	0.0669377i
$81$		0			0
$82$	−1.57652	+	2.73061i	−0.174098	+	0.301546i
$83$	10.8698			1.19311			0.596557	−	0.802571i	$-0.296535\pi$
$83$	10.8698			1.19311			0.596557	+	0.802571i	$0.296535\pi$
$84$		0			0
$85$		−	5.29274i		−	0.574078i
$86$	−6.93044	−	4.00129i	−0.747329	−	0.431470i
$87$		0			0
$88$	−0.396361	−	3.29286i	−0.0422523	−	0.351020i
$89$	−11.4053	−	6.58488i	−1.20896	−	0.697996i	−0.246431	−	0.969160i	$-0.579258\pi$
$89$	−11.4053	−	6.58488i	−1.20896	−	0.697996i	−0.962533	+	0.271165i	$0.912591\pi$
$90$		0			0
$91$	−2.55183	−	8.24446i	−0.267504	−	0.864254i
$92$		−	6.86757i		−	0.715993i
$93$		0			0
$94$	0.355926	−	0.205494i	0.0367110	−	0.0211951i
$95$	4.65588	+	8.06422i	0.477683	+	0.827372i
$96$		0			0
$97$	13.1097			1.33109			0.665545	−	0.746357i	$-0.268199\pi$
$97$	13.1097			1.33109			0.665545	+	0.746357i	$0.268199\pi$
$98$	0.536631	+	6.97940i	0.0542079	+	0.705026i
$99$		0			0
$100$	−1.78309	+	3.08841i	−0.178309	+	0.308841i
$101$	4.82575	+	8.35845i	0.480181	+	0.831697i	0.999741	−	0.0227363i	$-0.00723780\pi$
$101$	4.82575	+	8.35845i	0.480181	+	0.831697i	−0.519561	+	0.854433i	$0.673904\pi$
$102$		0			0
$103$	4.95521	−	8.58267i	0.488251	−	0.845676i	−0.511658	−	0.859189i	$-0.670968\pi$
$103$	4.95521	−	8.58267i	0.488251	−	0.845676i	0.999909	+	0.0135137i	$0.00430167\pi$
$104$			3.26196i			0.319862i
$105$		0			0
$106$			5.80291i			0.563629i
$107$	4.82669	−	8.36007i	0.466614	−	0.808199i	−0.532659	−	0.846330i	$-0.678807\pi$
$107$	4.82669	−	8.36007i	0.466614	−	0.808199i	0.999273	+	0.0381312i	$0.0121405\pi$
$108$		0			0
$109$	−6.34796	+	3.66500i	−0.608024	+	0.351043i	−0.772192	−	0.635390i	$-0.780840\pi$
$109$	−6.34796	+	3.66500i	−0.608024	+	0.351043i	0.164168	+	0.986432i	$0.447506\pi$
$110$	−2.38249	−	3.17737i	−0.227161	−	0.302950i
$111$		0			0
$112$	0.586237	−	2.57999i	0.0553941	−	0.243786i
$113$			12.0213i			1.13087i	0.824792	+	0.565436i	$0.191292\pi$
$113$			12.0213i			1.13087i	−0.824792	+	0.565436i	$0.808708\pi$
$114$		0			0
$115$	−4.11168	−	7.12163i	−0.383416	−	0.664095i
$116$	−3.92914	−	6.80547i	−0.364811	−	0.631872i
$117$		0			0
$118$			4.23646i			0.389997i
$119$	−8.58041	−	7.94601i	−0.786565	−	0.728409i
$120$		0			0
$121$	−10.6858	+	2.61032i	−0.971436	+	0.237302i
$122$	−9.94695	+	5.74287i	−0.900555	+	0.519935i
$123$		0			0
$124$	−0.103382	+	0.179063i	−0.00928400	+	0.0160804i
$125$			10.2573i			0.917442i
$126$		0			0
$127$		−	18.1862i		−	1.61376i	−0.590715	−	0.806880i	$-0.701154\pi$
$127$		−	18.1862i		−	1.61376i	0.590715	−	0.806880i	$-0.298846\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.95297	+	3.38264i	0.171287	+	0.296677i
$131$	−0.397483	+	0.688460i	−0.0347282	+	0.0601511i	−0.882867	−	0.469623i	$-0.844390\pi$
$131$	−0.397483	+	0.688460i	−0.0347282	+	0.0601511i	0.848139	+	0.529774i	$0.177723\pi$
$132$		0			0
$133$	20.0634	+	4.55889i	1.73971	+	0.395306i
$134$	−11.2359			−0.970631
$135$		0			0
$136$	2.21006	+	3.82794i	0.189511	+	0.328243i
$137$	5.20922	−	3.00754i	0.445053	−	0.256952i	−0.260685	−	0.965424i	$-0.583949\pi$
$137$	5.20922	−	3.00754i	0.445053	−	0.256952i	0.705739	+	0.708472i	$0.250615\pi$
$138$		0			0
$139$			11.8585i			1.00583i	0.864337	+	0.502913i	$0.167738\pi$
$139$			11.8585i			1.00583i	−0.864337	+	0.502913i	$0.832262\pi$
$140$	−0.936737	−	3.02642i	−0.0791687	−	0.255779i
$141$		0			0
$142$	3.29685	+	1.90344i	0.276666	+	0.159733i
$143$	10.7412	−	1.29292i	0.898222	−	0.108119i
$144$		0			0
$145$	−8.14899	−	4.70482i	−0.676737	−	0.390714i
$146$		−	0.226048i		−	0.0187079i
$147$		0			0
$148$	−7.66460			−0.630026
$149$	9.00137	−	15.5908i	0.737421	−	1.27725i	−0.216232	−	0.976342i	$-0.569377\pi$
$149$	9.00137	−	15.5908i	0.737421	−	1.27725i	0.953653	−	0.300908i	$-0.0972898\pi$
$150$		0			0
$151$	4.49066	−	2.59269i	0.365445	−	0.210990i	−0.306022	−	0.952025i	$-0.598998\pi$
$151$	4.49066	−	2.59269i	0.365445	−	0.210990i	0.671467	+	0.741035i	$0.265665\pi$
$152$	−6.73468	−	3.88827i	−0.546254	−	0.315380i
$153$		0			0
$154$	−8.72788	−	0.907785i	−0.703313	−	0.0731514i
$155$			0.247583i			0.0198864i
$156$		0			0
$157$	9.83949	+	17.0425i	0.785277	+	1.36014i	0.928834	+	0.370497i	$0.120813\pi$
$157$	9.83949	+	17.0425i	0.785277	+	1.36014i	−0.143557	+	0.989642i	$0.545854\pi$
$158$	2.00851	−	1.15961i	0.159788	−	0.0922537i
$159$		0			0
$160$			1.19742i			0.0946642i
$161$	−17.7182	−	4.02602i	−1.39639	−	0.317295i
$162$		0			0
$163$	−12.0169	+	20.8138i	−0.941234	+	1.63026i	−0.178111	+	0.984010i	$0.556999\pi$
$163$	−12.0169	+	20.8138i	−0.941234	+	1.63026i	−0.763122	+	0.646254i	$0.776335\pi$
$164$	−1.57652	−	2.73061i	−0.123106	−	0.213225i
$165$		0			0
$166$	−5.43489	+	9.41350i	−0.421829	+	0.730630i
$167$	−13.3713			−1.03471			−0.517353	−	0.855772i	$-0.673082\pi$
$167$	−13.3713			−1.03471			−0.517353	+	0.855772i	$0.673082\pi$
$168$		0			0
$169$	2.35959			0.181507
$170$	4.58364	+	2.64637i	0.351549	+	0.202967i
$171$		0			0
$172$	6.93044	−	4.00129i	0.528441	−	0.305096i
$173$	−11.9348	+	20.6717i	−0.907385	+	1.57164i	−0.0897011	+	0.995969i	$0.528591\pi$
$173$	−11.9348	+	20.6717i	−0.907385	+	1.57164i	−0.817684	+	0.575668i	$0.804742\pi$
$174$		0			0
$175$	6.92274	+	6.41090i	0.523310	+	0.484618i
$176$	3.04988	+	1.30317i	0.229893	+	0.0982300i
$177$		0			0
$178$	11.4053	−	6.58488i	0.854867	−	0.493558i
$179$	17.6015	−	10.1622i	1.31560	−	0.759560i	0.332580	−	0.943075i	$-0.392081\pi$
$179$	17.6015	−	10.1622i	1.31560	−	0.759560i	0.983017	+	0.183515i	$0.0587476\pi$
$180$		0			0
$181$	−19.4560			−1.44616			−0.723078	−	0.690766i	$-0.757273\pi$
$181$	−19.4560			−1.44616			−0.723078	+	0.690766i	$0.757273\pi$
$182$	8.41582	+	1.91228i	0.623822	+	0.141748i
$183$		0			0
$184$	5.94749	+	3.43378i	0.438455	+	0.253142i
$185$	−7.94814	+	4.58886i	−0.584359	+	0.337380i
$186$		0			0
$187$	11.7289	−	8.79466i	0.857700	−	0.643129i
$188$			0.410988i			0.0299744i
$189$		0			0
$190$	−9.31176			−0.675546
$191$	8.14743	+	4.70392i	0.589527	+	0.340364i	0.764911	−	0.644136i	$-0.222783\pi$
$191$	8.14743	+	4.70392i	0.589527	+	0.340364i	−0.175383	+	0.984500i	$0.556116\pi$
$192$		0			0
$193$	−2.92081	+	1.68633i	−0.210245	+	0.121385i	−0.601425	−	0.798929i	$-0.705400\pi$
$193$	−2.92081	+	1.68633i	−0.210245	+	0.121385i	0.391180	+	0.920314i	$0.372067\pi$
$194$	−6.55486	+	11.3534i	−0.470612	+	0.815123i
$195$		0			0
$196$	−6.31265	−	3.02496i	−0.450904	−	0.216069i
$197$	6.33128			0.451085			0.225543	−	0.974233i	$-0.427585\pi$
$197$	6.33128			0.451085			0.225543	+	0.974233i	$0.427585\pi$
$198$		0			0
$199$	0.331375	+	0.573958i	0.0234905	+	0.0406868i	0.877532	−	0.479519i	$-0.159189\pi$
$199$	0.331375	+	0.573958i	0.0234905	+	0.0406868i	−0.854041	+	0.520205i	$0.825855\pi$
$200$	−1.78309	−	3.08841i	−0.126084	−	0.218384i
$201$		0			0
$202$	−9.65151			−0.679078
$203$	−19.8614	+	6.14751i	−1.39400	+	0.431470i
$204$		0			0
$205$	−3.26969	−	1.88775i	−0.228365	−	0.131846i
$206$	4.95521	+	8.58267i	0.345246	+	0.597983i
$207$		0			0
$208$	−2.82494	−	1.63098i	−0.195875	−	0.113088i
$209$	−10.1341	+	23.7175i	−0.700993	+	1.64057i
$210$		0			0
$211$		−	14.9427i		−	1.02870i	−0.857580	−	0.514350i	$-0.828033\pi$
$211$		−	14.9427i		−	1.02870i	0.857580	−	0.514350i	$-0.171967\pi$
$212$	−5.02547	−	2.90146i	−0.345151	−	0.199273i
$213$		0			0
$214$	4.82669	+	8.36007i	0.329946	+	0.571483i
$215$	4.79122	−	8.29864i	0.326758	−	0.565962i
$216$		0			0
$217$	0.401374	+	0.371698i	0.0272471	+	0.0252325i
$218$		−	7.32999i		−	0.496450i
$219$		0			0
$220$	3.94292	−	0.474610i	0.265832	−	0.0319982i
$221$	−12.4866	+	7.20914i	−0.839940	+	0.484939i
$222$		0			0
$223$	−17.0313			−1.14050			−0.570250	−	0.821471i	$-0.693154\pi$
$223$	−17.0313			−1.14050			−0.570250	+	0.821471i	$0.693154\pi$
$224$	1.94121	+	1.79769i	0.129703	+	0.120113i
$225$		0			0
$226$	−10.4108	−	6.01066i	−0.692514	−	0.399823i
$227$	−9.58521	−	16.6021i	−0.636193	−	1.10192i	−0.986261	−	0.165194i	$-0.947175\pi$
$227$	−9.58521	−	16.6021i	−0.636193	−	1.10192i	0.350068	−	0.936724i	$-0.386158\pi$
$228$		0			0
$229$	6.51023	−	11.2760i	0.430208	−	0.745142i	−0.566683	−	0.823936i	$-0.691774\pi$
$229$	6.51023	−	11.2760i	0.430208	−	0.745142i	0.996891	+	0.0787938i	$0.0251069\pi$
$230$	8.22335			0.542232
$231$		0			0
$232$	7.85827			0.515921
$233$	2.04857	−	3.54823i	0.134206	−	0.232452i	−0.791088	−	0.611703i	$-0.790485\pi$
$233$	2.04857	−	3.54823i	0.134206	−	0.232452i	0.925294	+	0.379251i	$0.123818\pi$
$234$		0			0
$235$	0.246063	+	0.426193i	0.0160513	+	0.0278018i
$236$	−3.66888	−	2.11823i	−0.238824	−	0.137885i
$237$		0			0
$238$	11.1716	−	3.45785i	0.724150	−	0.224139i
$239$	−4.68979			−0.303357			−0.151679	−	0.988430i	$-0.548468\pi$
$239$	−4.68979			−0.303357			−0.151679	+	0.988430i	$0.548468\pi$
$240$		0			0
$241$	11.0323	−	6.36950i	0.710652	−	0.410295i	−0.100650	−	0.994922i	$-0.532092\pi$
$241$	11.0323	−	6.36950i	0.710652	−	0.410295i	0.811303	+	0.584627i	$0.198759\pi$
$242$	3.08229	−	10.5593i	0.198137	−	0.678780i
$243$		0			0
$244$		−	11.4857i		−	0.735300i
$245$	−8.35726	+	0.642572i	−0.533926	+	0.0410524i
$246$		0			0
$247$	12.6834	−	21.9683i	0.807025	−	1.39781i
$248$	−0.103382	−	0.179063i	−0.00656478	−	0.0113705i
$249$		0			0
$250$	−8.88309	−	5.12866i	−0.561816	−	0.324365i
$251$			25.6272i			1.61758i	0.588100	+	0.808788i	$0.299876\pi$
$251$			25.6272i			1.61758i	−0.588100	+	0.808788i	$0.700124\pi$
$252$		0			0
$253$	8.94960	−	20.9452i	0.562657	−	1.31682i
$254$	15.7497	+	9.09308i	0.988222	+	0.570550i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.92122	+	2.84127i	0.306978	+	0.177234i	0.645573	−	0.763698i	$-0.276619\pi$
$257$	4.92122	+	2.84127i	0.306978	+	0.177234i	−0.338596	+	0.940932i	$0.609952\pi$
$258$		0			0
$259$	−4.49327	+	19.7745i	−0.279198	+	1.22873i
$260$	−3.90594			−0.242236
$261$		0			0
$262$	−0.397483	−	0.688460i	−0.0245566	−	0.0425332i
$263$	−14.4242	−	24.9835i	−0.889436	−	1.54055i	−0.840544	−	0.541744i	$-0.817764\pi$
$263$	−14.4242	−	24.9835i	−0.889436	−	1.54055i	−0.0488920	−	0.998804i	$-0.515569\pi$
$264$		0			0
$265$	−6.94852			−0.426844
$266$	−13.9798	+	15.0959i	−0.857156	+	0.925591i
$267$		0			0
$268$	5.61793	−	9.73055i	0.343170	−	0.594388i
$269$	15.8208	−	9.13413i	0.964610	−	0.556918i	0.0670210	−	0.997752i	$-0.478651\pi$
$269$	15.8208	−	9.13413i	0.964610	−	0.556918i	0.897589	+	0.440834i	$0.145317\pi$
$270$		0			0
$271$	−5.05904	−	2.92084i	−0.307315	−	0.177428i	0.338410	−	0.940999i	$-0.390111\pi$
$271$	−5.05904	−	2.92084i	−0.307315	−	0.177428i	−0.645724	+	0.763571i	$0.723444\pi$
$272$	−4.42012			−0.268009
$273$		0			0
$274$			6.01509i			0.363385i
$275$	−9.46294	+	7.09560i	−0.570637	+	0.427881i
$276$		0			0
$277$	13.0938	−	7.55973i	0.786732	−	0.454220i	−0.0520786	−	0.998643i	$-0.516585\pi$
$277$	13.0938	−	7.55973i	0.786732	−	0.454220i	0.838811	+	0.544423i	$0.183251\pi$
$278$	−10.2698	−	5.92926i	−0.615940	−	0.355613i
$279$		0			0
$280$	3.08932	+	0.701970i	0.184622	+	0.0419507i
$281$	−7.22799			−0.431186			−0.215593	−	0.976483i	$-0.569168\pi$
$281$	−7.22799			−0.431186			−0.215593	+	0.976483i	$0.569168\pi$
$282$		0			0
$283$	−0.0575633	+	0.0332342i	−0.00342179	+	0.00197557i	−0.501710	−	0.865036i	$-0.667296\pi$
$283$	−0.0575633	+	0.0332342i	−0.00342179	+	0.00197557i	0.498288	+	0.867011i	$0.333962\pi$
$284$	−3.29685	+	1.90344i	−0.195632	+	0.112948i
$285$		0			0
$286$	−4.25089	+	9.94859i	−0.251360	+	0.588272i
$287$	−7.96916	+	2.46662i	−0.470405	+	0.145600i
$288$		0			0
$289$	−1.26875	+	2.19753i	−0.0746322	+	0.129267i
$290$	8.14899	−	4.70482i	0.478525	−	0.276277i
$291$		0			0
$292$	0.195764	+	0.113024i	0.0114562	+	0.00661424i
$293$	22.1095			1.29165			0.645824	−	0.763486i	$-0.276514\pi$
$293$	22.1095			1.29165			0.645824	+	0.763486i	$0.276514\pi$
$294$		0			0
$295$	−5.07281			−0.295350
$296$	3.83230	−	6.63773i	0.222748	−	0.385810i
$297$		0			0
$298$	9.00137	+	15.5908i	0.521435	+	0.903152i
$299$	−11.2009	+	19.4005i	−0.647764	+	1.12196i
$300$		0			0
$301$	−6.26040	−	20.2261i	−0.360843	−	1.16582i
$302$			5.18537i			0.298385i
$303$		0			0
$304$	6.73468	−	3.88827i	0.386260	−	0.223007i
$305$	−6.87662	−	11.9107i	−0.393754	−	0.682002i
$306$		0			0
$307$		−	20.0987i		−	1.14710i	−0.819172	−	0.573548i	$-0.805567\pi$
$307$		−	20.0987i		−	1.14710i	0.819172	−	0.573548i	$-0.194433\pi$
$308$	5.15011	−	7.10468i	0.293455	−	0.404826i
$309$		0			0
$310$	−0.214414	−	0.123792i	−0.0121779	−	0.00703090i
$311$	13.7708	−	7.95055i	0.780868	−	0.450834i	−0.0558698	−	0.998438i	$-0.517793\pi$
$311$	13.7708	−	7.95055i	0.780868	−	0.450834i	0.836738	+	0.547604i	$0.184460\pi$
$312$		0			0
$313$	8.27538	−	14.3334i	0.467752	−	0.810170i	−0.531569	−	0.847015i	$-0.678397\pi$
$313$	8.27538	−	14.3334i	0.467752	−	0.810170i	0.999321	+	0.0368447i	$0.0117307\pi$
$314$	−19.6790			−1.11055
$315$		0			0
$316$			2.31922i			0.130466i
$317$	−8.65990	−	4.99980i	−0.486389	−	0.280817i	0.236686	−	0.971586i	$-0.423939\pi$
$317$	−8.65990	−	4.99980i	−0.486389	−	0.280817i	−0.723075	+	0.690770i	$0.757272\pi$
$318$		0			0
$319$	−3.11472	−	25.8762i	−0.174391	−	1.44879i
$320$	−1.03699	−	0.598709i	−0.0579698	−	0.0334689i
$321$		0			0
$322$	12.3457	−	13.3314i	0.688002	−	0.742931i
$323$		−	34.3733i		−	1.91258i
$324$		0			0
$325$	10.0743	−	5.81639i	0.558821	−	0.322635i
$326$	−12.0169	−	20.8138i	−0.665553	−	1.15277i
$327$		0			0
$328$	3.15304			0.174098
$329$	1.06034	+	0.240936i	0.0584587	+	0.0132833i
$330$		0			0
$331$	−16.5068	+	28.5906i	−0.907294	+	1.57148i	−0.0894857	+	0.995988i	$0.528522\pi$
$331$	−16.5068	+	28.5906i	−0.907294	+	1.57148i	−0.817808	+	0.575491i	$0.804811\pi$
$332$	−5.43489	−	9.41350i	−0.298278	−	0.516633i
$333$		0			0
$334$	6.68567	−	11.5799i	0.365824	−	0.633625i
$335$		−	13.4540i		−	0.735072i
$336$		0			0
$337$			0.870822i			0.0474367i	0.999719	+	0.0237184i	$0.00755050\pi$
$337$			0.870822i			0.0474367i	−0.999719	+	0.0237184i	$0.992450\pi$
$338$	−1.17979	+	2.04346i	−0.0641724	+	0.111150i
$339$		0			0
$340$	−4.58364	+	2.64637i	−0.248583	+	0.143519i
$341$	−0.548653	+	0.411397i	−0.0297112	+	0.0222784i
$342$		0			0
$343$	−11.5051	+	14.5132i	−0.621215	+	0.783640i
$344$			8.00258i			0.431470i
$345$		0			0
$346$	−11.9348	−	20.6717i	−0.641618	−	1.11131i
$347$	−3.92630	−	6.80054i	−0.210775	−	0.365072i	0.741183	−	0.671304i	$-0.234265\pi$
$347$	−3.92630	−	6.80054i	−0.210775	−	0.365072i	−0.951957	+	0.306231i	$0.900932\pi$
$348$		0			0
$349$		−	20.6953i		−	1.10779i	−0.832586	−	0.553896i	$-0.813140\pi$
$349$		−	20.6953i		−	1.10779i	0.832586	−	0.553896i	$-0.186860\pi$
$350$	−9.01337	+	2.78982i	−0.481785	+	0.149122i
$351$		0			0
$352$	−2.65352	+	1.98969i	−0.141433	+	0.106051i
$353$	−23.0277	+	13.2951i	−1.22564	+	0.707625i	−0.966115	−	0.258111i	$-0.916900\pi$
$353$	−23.0277	+	13.2951i	−1.22564	+	0.707625i	−0.259527	+	0.965736i	$0.583567\pi$
$354$		0			0
$355$	−2.27921	+	3.94771i	−0.120968	+	0.209523i
$356$			13.1698i			0.697996i
$357$		0			0
$358$			20.3244i			1.07418i
$359$	0.0346521	−	0.0600191i	0.00182887	−	0.00316769i	−0.865110	−	0.501583i	$-0.832751\pi$
$359$	0.0346521	−	0.0600191i	0.00182887	−	0.00316769i	0.866938	+	0.498415i	$0.166085\pi$
$360$		0			0
$361$	20.7373	+	35.9180i	1.09143	+	1.89042i
$362$	9.72802	−	16.8494i	0.511293	−	0.885586i
$363$		0			0
$364$	−5.86400	+	6.33217i	−0.307357	+	0.331896i
$365$	0.270674			0.0141677
$366$		0			0
$367$	−18.5149	−	32.0687i	−0.966469	−	1.67397i	−0.705615	−	0.708595i	$-0.749329\pi$
$367$	−18.5149	−	32.0687i	−0.966469	−	1.67397i	−0.260854	−	0.965378i	$-0.584004\pi$
$368$	−5.94749	+	3.43378i	−0.310034	+	0.178998i
$369$		0			0
$370$		−	9.17773i		−	0.477127i
$371$	−10.4318	+	11.2647i	−0.541594	+	0.584834i
$372$		0			0
$373$	−10.9206	−	6.30501i	−0.565447	−	0.326461i	0.189882	−	0.981807i	$-0.439190\pi$
$373$	−10.9206	−	6.30501i	−0.565447	−	0.326461i	−0.755329	+	0.655346i	$0.772523\pi$
$374$	1.75197	+	14.5548i	0.0905920	+	0.752612i
$375$		0			0
$376$	−0.355926	−	0.205494i	−0.0183555	−	0.0105976i
$377$			25.6334i			1.32019i
$378$		0			0
$379$	−4.45725			−0.228954			−0.114477	−	0.993426i	$-0.536519\pi$
$379$	−4.45725			−0.228954			−0.114477	+	0.993426i	$0.536519\pi$
$380$	4.65588	−	8.06422i	0.238842	−	0.413686i
$381$		0			0
$382$	−8.14743	+	4.70392i	−0.416859	+	0.240674i
$383$	11.0167	+	6.36051i	0.562928	+	0.325007i	0.754320	−	0.656507i	$-0.227967\pi$
$383$	11.0167	+	6.36051i	0.562928	+	0.325007i	−0.191392	+	0.981514i	$0.561300\pi$
$384$		0			0
$385$	1.08700	−	10.4509i	0.0553986	−	0.532628i
$386$		−	3.37267i		−	0.171664i
$387$		0			0
$388$	−6.55486	−	11.3534i	−0.332773	−	0.576379i
$389$	18.7691	−	10.8364i	0.951633	−	0.549426i	0.0580454	−	0.998314i	$-0.481513\pi$
$389$	18.7691	−	10.8364i	0.951633	−	0.549426i	0.893588	+	0.448888i	$0.148180\pi$
$390$		0			0
$391$			30.3555i			1.53514i
$392$	5.77602	−	3.95444i	0.291733	−	0.199729i
$393$		0			0
$394$	−3.16564	+	5.48305i	−0.159483	+	0.276232i
$395$	1.38854	+	2.40502i	0.0698650	+	0.121010i
$396$		0			0
$397$	−6.77259	+	11.7305i	−0.339907	+	0.588736i	−0.984415	−	0.175862i	$-0.943729\pi$
$397$	−6.77259	+	11.7305i	−0.339907	+	0.588736i	0.644508	+	0.764597i	$0.277062\pi$
$398$	−0.662749			−0.0332206
$399$		0			0
$400$	3.56619			0.178309
$401$	23.0277	+	13.2951i	1.14995	+	0.663924i	0.948875	−	0.315652i	$-0.102223\pi$
$401$	23.0277	+	13.2951i	1.14995	+	0.663924i	0.201075	+	0.979576i	$0.435557\pi$
$402$		0			0
$403$	0.584098	−	0.337229i	0.0290960	−	0.0167986i
$404$	4.82575	−	8.35845i	0.240090	−	0.415849i
$405$		0			0
$406$	4.60681	−	20.2742i	0.228632	−	1.00619i
$407$	−23.3761	−	9.98826i	−1.15871	−	0.495100i
$408$		0			0
$409$	−5.51290	+	3.18288i	−0.272596	+	0.157383i	−0.630067	−	0.776541i	$-0.716972\pi$
$409$	−5.51290	+	3.18288i	−0.272596	+	0.157383i	0.357471	+	0.933924i	$0.383639\pi$
$410$	3.26969	−	1.88775i	0.161478	−	0.0932296i
$411$		0			0
$412$	−9.91042			−0.488251
$413$	−7.61583	+	8.22387i	−0.374751	+	0.404670i
$414$		0			0
$415$	−11.2719	−	6.50783i	−0.553316	−	0.319457i
$416$	2.82494	−	1.63098i	0.138504	−	0.0799655i
$417$		0			0
$418$	−15.4729	−	20.6352i	−0.756803	−	1.00930i
$419$			21.1161i			1.03159i	0.856713	+	0.515794i	$0.172503\pi$
$419$			21.1161i			1.03159i	−0.856713	+	0.515794i	$0.827497\pi$
$420$		0			0
$421$	−8.94131			−0.435773			−0.217886	−	0.975974i	$-0.569916\pi$
$421$	−8.94131			−0.435773			−0.217886	+	0.975974i	$0.569916\pi$
$422$	12.9408	+	7.47137i	0.629948	+	0.363701i
$423$		0			0
$424$	5.02547	−	2.90146i	0.244058	−	0.140907i
$425$	7.88150	−	13.6512i	0.382309	−	0.662178i
$426$		0			0
$427$	−29.6331	−	6.73337i	−1.43404	−	0.325850i
$428$	−9.65338			−0.466614
$429$		0			0
$430$	4.79122	+	8.29864i	0.231053	+	0.400196i
$431$	4.16534	+	7.21459i	0.200638	+	0.347514i	0.948734	−	0.316076i	$-0.102365\pi$
$431$	4.16534	+	7.21459i	0.200638	+	0.347514i	−0.748096	+	0.663590i	$0.769032\pi$
$432$		0			0
$433$	0.288704			0.0138742			0.00693711	−	0.999976i	$-0.497792\pi$
$433$	0.288704			0.0138742			0.00693711	+	0.999976i	$0.497792\pi$
$434$	−0.522587	+	0.161751i	−0.0250850	+	0.00776431i
$435$		0			0
$436$	6.34796	+	3.66500i	0.304012	+	0.175521i
$437$	−26.7029	−	46.2509i	−1.27738	−	2.21248i
$438$		0			0
$439$	10.0491	+	5.80186i	0.479618	+	0.276908i	0.720257	−	0.693707i	$-0.244024\pi$
$439$	10.0491	+	5.80186i	0.479618	+	0.276908i	−0.240639	+	0.970615i	$0.577357\pi$
$440$	−1.56044	+	3.65198i	−0.0743910	+	0.174101i
$441$		0			0
$442$		−	14.4183i		−	0.685808i
$443$	−4.34544	−	2.50884i	−0.206458	−	0.119199i	0.393206	−	0.919450i	$-0.371366\pi$
$443$	−4.34544	−	2.50884i	−0.206458	−	0.119199i	−0.599664	+	0.800252i	$0.704699\pi$
$444$		0			0
$445$	7.88485	+	13.6570i	0.373778	+	0.647402i
$446$	8.51565	−	14.7495i	0.403228	−	0.698411i
$447$		0			0
$448$	−2.52745	+	0.782297i	−0.119411	+	0.0369601i
$449$		−	14.7868i		−	0.697835i	−0.937154	−	0.348917i	$-0.886549\pi$
$449$		−	14.7868i		−	0.697835i	0.937154	−	0.348917i	$-0.113451\pi$
$450$		0			0
$451$	−1.24974	−	10.3825i	−0.0588482	−	0.488893i
$452$	10.4108	−	6.01066i	0.489682	−	0.282718i
$453$		0			0
$454$	19.1704			0.899712
$455$	−2.28980	+	10.0773i	−0.107348	+	0.472429i
$456$		0			0
$457$	29.4805	+	17.0205i	1.37904	+	0.796188i	0.992044	−	0.125895i	$-0.0401801\pi$
$457$	29.4805	+	17.0205i	1.37904	+	0.796188i	0.386994	+	0.922082i	$0.373513\pi$
$458$	6.51023	+	11.2760i	0.304203	+	0.526895i
$459$		0			0
$460$	−4.11168	+	7.12163i	−0.191708	+	0.332048i
$461$	31.2127			1.45372			0.726861	−	0.686785i	$-0.240979\pi$
$461$	31.2127			1.45372			0.726861	+	0.686785i	$0.240979\pi$
$462$		0			0
$463$	6.66544			0.309769			0.154885	−	0.987933i	$-0.450499\pi$
$463$	6.66544			0.309769			0.154885	+	0.987933i	$0.450499\pi$
$464$	−3.92914	+	6.80547i	−0.182406	+	0.315936i
$465$		0			0
$466$	2.04857	+	3.54823i	0.0948983	+	0.164369i
$467$	6.58720	+	3.80312i	0.304819	+	0.175987i	0.644606	−	0.764515i	$-0.277022\pi$
$467$	6.58720	+	3.80312i	0.304819	+	0.175987i	−0.339787	+	0.940503i	$0.610355\pi$
$468$		0			0
$469$	−21.8112	−	20.1986i	−1.00715	−	0.932684i
$470$	−0.492125			−0.0227000
$471$		0			0
$472$	3.66888	−	2.11823i	0.168874	−	0.0974994i
$473$	26.3514	−	3.17192i	1.21164	−	0.145845i
$474$		0			0
$475$			27.7326i			1.27246i
$476$	−2.59124	+	11.4039i	−0.118769	+	0.522695i
$477$		0			0
$478$	2.34489	−	4.06147i	0.107253	−	0.185767i
$479$	7.64294	+	13.2380i	0.349215	+	0.604858i	0.986110	−	0.166092i	$-0.0531150\pi$
$479$	7.64294	+	13.2380i	0.349215	+	0.604858i	−0.636895	+	0.770950i	$0.719782\pi$
$480$		0			0
$481$	21.6521	+	12.5008i	0.987249	+	0.569988i
$482$			12.7390i			0.580245i
$483$		0			0
$484$	7.60350	+	7.94901i	0.345614	+	0.361319i
$485$	−13.5947	−	7.84891i	−0.617304	−	0.356401i
$486$		0			0
$487$	0.790493	+	1.36917i	0.0358206	+	0.0620432i	0.883380	−	0.468658i	$-0.155262\pi$
$487$	0.790493	+	1.36917i	0.0358206	+	0.0620432i	−0.847559	+	0.530701i	$0.821929\pi$
$488$	9.94695	+	5.74287i	0.450277	+	0.259968i
$489$		0			0
$490$	3.62215	−	7.55889i	0.163632	−	0.341476i
$491$	6.90788			0.311748			0.155874	−	0.987777i	$-0.450181\pi$
$491$	6.90788			0.311748			0.155874	+	0.987777i	$0.450181\pi$
$492$		0			0
$493$	17.3673	+	30.0810i	0.782183	+	1.35478i
$494$	12.6834	+	21.9683i	0.570653	+	0.988400i
$495$		0			0
$496$	0.206764			0.00928400
$497$	2.97811	+	9.62170i	0.133587	+	0.431592i
$498$		0			0
$499$	−0.474107	+	0.821178i	−0.0212240	+	0.0367610i	−0.876442	−	0.481507i	$-0.840090\pi$
$499$	−0.474107	+	0.821178i	−0.0212240	+	0.0367610i	0.855218	+	0.518268i	$0.173423\pi$
$500$	8.88309	−	5.12866i	0.397264	−	0.229360i
$501$		0			0
$502$	−22.1938	−	12.8136i	−0.990559	−	0.571900i
$503$	−30.8752			−1.37666			−0.688328	−	0.725400i	$-0.741655\pi$
$503$	−30.8752			−1.37666			−0.688328	+	0.725400i	$0.741655\pi$
$504$		0			0
$505$		−	11.5569i		−	0.514275i
$506$	13.6643	+	18.2232i	0.607453	+	0.810120i
$507$		0			0
$508$	−15.7497	+	9.09308i	−0.698779	+	0.403440i
$509$	−31.6394	−	18.2670i	−1.40239	−	0.809670i	−0.407752	−	0.913093i	$-0.633687\pi$
$509$	−31.6394	−	18.2670i	−1.40239	−	0.809670i	−0.994638	+	0.103422i	$0.967021\pi$
$510$		0			0
$511$	0.406364	−	0.438808i	0.0179765	−	0.0194117i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−4.92122	+	2.84127i	−0.217066	+	0.125323i
$515$	−10.2770	+	5.93346i	−0.452861	+	0.261459i
$516$		0			0
$517$	−0.535587	+	1.25346i	−0.0235551	+	0.0551273i
$518$	−14.8786	−	13.7786i	−0.653729	−	0.605395i
$519$		0			0
$520$	1.95297	−	3.38264i	0.0856433	−	0.148339i
$521$	−0.780812	+	0.450802i	−0.0342080	+	0.0197500i	−0.517006	−	0.855981i	$-0.672954\pi$
$521$	−0.780812	+	0.450802i	−0.0342080	+	0.0197500i	0.482798	+	0.875731i	$0.339620\pi$
$522$		0			0
$523$	−8.65582	−	4.99744i	−0.378492	−	0.218523i	0.298670	−	0.954357i	$-0.403457\pi$
$523$	−8.65582	−	4.99744i	−0.378492	−	0.218523i	−0.677162	+	0.735834i	$0.736790\pi$
$524$	0.794965			0.0347282
$525$		0			0
$526$	28.8484			1.25785
$527$	0.456962	−	0.791482i	0.0199056	−	0.0344775i
$528$		0			0
$529$	12.0817	+	20.9262i	0.525293	+	0.909835i
$530$	3.47426	−	6.01759i	0.150912	−	0.261387i
$531$		0			0
$532$	−6.08356	−	19.6548i	−0.263756	−	0.852144i
$533$			10.2851i			0.445498i
$534$		0			0
$535$	−10.0105	+	5.77957i	−0.432792	+	0.249872i
$536$	5.61793	+	9.73055i	0.242658	+	0.420296i
$537$		0			0
$538$			18.2683i			0.787601i
$539$	−15.3108	−	17.4522i	−0.659482	−	0.751720i
$540$		0			0
$541$	−30.8485	−	17.8104i	−1.32628	−	0.765727i	−0.341557	−	0.939861i	$-0.610954\pi$
$541$	−30.8485	−	17.8104i	−1.32628	−	0.765727i	−0.984722	+	0.174134i	$0.944287\pi$
$542$	5.05904	−	2.92084i	0.217304	−	0.125461i
$543$		0			0
$544$	2.21006	−	3.82794i	0.0947556	−	0.164122i
$545$	8.77706			0.375968
$546$		0			0
$547$			7.11968i			0.304416i	0.988349	+	0.152208i	$0.0486383\pi$
$547$			7.11968i			0.304416i	−0.988349	+	0.152208i	$0.951362\pi$
$548$	−5.20922	−	3.00754i	−0.222527	−	0.128476i
$549$		0			0
$550$	−1.41350	−	11.7429i	−0.0602719	−	0.500721i
$551$	−52.9229	−	30.5551i	−2.25459	−	1.30169i
$552$		0			0
$553$	5.98356	+	1.35961i	0.254447	+	0.0578166i
$554$			15.1195i			0.642364i
$555$		0			0
$556$	10.2698	−	5.92926i	0.435535	−	0.251457i
$557$	9.08485	+	15.7354i	0.384938	+	0.666731i	0.991761	−	0.128106i	$-0.0408896\pi$
$557$	9.08485	+	15.7354i	0.384938	+	0.666731i	−0.606823	+	0.794837i	$0.707556\pi$
$558$		0			0
$559$	−26.1041			−1.10409
$560$	−2.15258	+	2.32445i	−0.0909633	+	0.0982258i
$561$		0			0
$562$	3.61399	−	6.25962i	0.152447	−	0.264046i
$563$	6.69275	+	11.5922i	0.282066	+	0.488552i	0.971893	−	0.235422i	$-0.0756471\pi$
$563$	6.69275	+	11.5922i	0.282066	+	0.488552i	−0.689828	+	0.723974i	$0.742314\pi$
$564$		0			0
$565$	7.19728	−	12.4660i	0.302792	−	0.524451i
$566$		−	0.0664684i		−	0.00279388i
$567$		0			0
$568$		−	3.80688i		−	0.159733i
$569$	−0.774915	+	1.34219i	−0.0324861	+	0.0562676i	−0.881811	−	0.471602i	$-0.843676\pi$
$569$	−0.774915	+	1.34219i	−0.0324861	+	0.0562676i	0.849325	+	0.527870i	$0.177009\pi$
$570$		0			0
$571$	36.9067	−	21.3081i	1.54450	−	0.891715i	0.545949	−	0.837819i	$-0.316169\pi$
$571$	36.9067	−	21.3081i	1.54450	−	0.891715i	0.998547	−	0.0538962i	$-0.0171640\pi$
$572$	−6.49029	−	8.65567i	−0.271373	−	0.361912i
$573$		0			0
$574$	1.84843	−	8.13480i	0.0771519	−	0.339540i
$575$		−	24.4911i		−	1.02135i
$576$		0			0
$577$	0.303156	+	0.525081i	0.0126205	+	0.0218594i	0.872267	−	0.489030i	$-0.162649\pi$
$577$	0.303156	+	0.525081i	0.0126205	+	0.0218594i	−0.859646	+	0.510890i	$0.829316\pi$
$578$	−1.26875	−	2.19753i	−0.0527729	−	0.0914054i
$579$		0			0
$580$			9.40964i			0.390714i
$581$	−27.4728	+	8.50340i	−1.13977	+	0.352780i
$582$		0			0
$583$	−11.5460	−	15.3981i	−0.478186	−	0.637725i
$584$	−0.195764	+	0.113024i	−0.00810075	+	0.00467697i
$585$		0			0
$586$	−11.0547	+	19.1474i	−0.456667	+	0.790970i
$587$			2.21478i			0.0914137i	0.998955	+	0.0457069i	$0.0145540\pi$
$587$			2.21478i			0.0914137i	−0.998955	+	0.0457069i	$0.985446\pi$
$588$		0			0
$589$			1.60791i			0.0662528i
$590$	2.53641	−	4.39318i	0.104422	−	0.180864i
$591$		0			0
$592$	3.83230	+	6.63773i	0.157506	+	0.272809i
$593$	−16.2190	+	28.0922i	−0.666036	+	1.15361i	0.312967	+	0.949764i	$0.398677\pi$
$593$	−16.2190	+	28.0922i	−0.666036	+	1.15361i	−0.979003	+	0.203844i	$0.934656\pi$
$594$		0			0
$595$	4.14049	+	13.3771i	0.169744	+	0.548409i
$596$	−18.0027			−0.737421
$597$		0			0
$598$	−11.2009	−	19.4005i	−0.458038	−	0.793345i
$599$	39.3780	−	22.7349i	1.60894	−	0.928922i	0.619333	−	0.785128i	$-0.287403\pi$
$599$	39.3780	−	22.7349i	1.60894	−	0.928922i	0.989608	−	0.143794i	$-0.0459302\pi$
$600$		0			0
$601$			23.7080i			0.967069i	0.875325	+	0.483535i	$0.160647\pi$
$601$			23.7080i			0.967069i	−0.875325	+	0.483535i	$0.839353\pi$
$602$	20.6466	+	4.69141i	0.841491	+	0.191207i
$603$		0			0
$604$	−4.49066	−	2.59269i	−0.182723	−	0.105495i
$605$	12.6439	+	3.69079i	0.514049	+	0.150052i
$606$		0			0
$607$	16.5637	+	9.56306i	0.672300	+	0.388153i	0.796948	−	0.604049i	$-0.206447\pi$
$607$	16.5637	+	9.56306i	0.672300	+	0.388153i	−0.124648	+	0.992201i	$0.539780\pi$
$608$			7.77654i			0.315380i
$609$		0			0
$610$	13.7532			0.556853
$611$	0.670315	−	1.16102i	0.0271180	−	0.0469698i
$612$		0			0
$613$	3.26599	−	1.88562i	0.131912	−	0.0761595i	−0.432592	−	0.901590i	$-0.642401\pi$
$613$	3.26599	−	1.88562i	0.131912	−	0.0761595i	0.564504	+	0.825430i	$0.309068\pi$
$614$	17.4060	+	10.0494i	0.702450	+	0.405560i
$615$		0			0
$616$	3.57778	+	8.01246i	0.144153	+	0.322831i
$617$		−	13.0431i		−	0.525096i	−0.964919	−	0.262548i	$-0.915437\pi$
$617$		−	13.0431i		−	0.525096i	0.964919	−	0.262548i	$-0.0845628\pi$
$618$		0			0
$619$	20.6271	+	35.7272i	0.829074	+	1.43600i	0.898766	+	0.438429i	$0.144465\pi$
$619$	20.6271	+	35.7272i	0.829074	+	1.43600i	−0.0696922	+	0.997569i	$0.522202\pi$
$620$	0.214414	−	0.123792i	0.00861106	−	0.00497160i
$621$		0			0
$622$			15.9011i			0.637576i
$623$	33.9778	+	7.72059i	1.36129	+	0.309319i
$624$		0			0
$625$	−2.77433	+	4.80528i	−0.110973	+	0.192211i
$626$	8.27538	+	14.3334i	0.330751	+	0.572877i
$627$		0			0
$628$	9.83949	−	17.0425i	0.392638	−	0.680070i
$629$	33.8785			1.35082
$630$		0			0
$631$	−35.4512			−1.41129			−0.705645	−	0.708566i	$-0.749343\pi$
$631$	−35.4512			−1.41129			−0.705645	+	0.708566i	$0.749343\pi$
$632$	−2.00851	−	1.15961i	−0.0798941	−	0.0461269i
$633$		0			0
$634$	8.65990	−	4.99980i	0.343929	−	0.198567i
$635$	−10.8882	+	18.8589i	−0.432086	+	0.748394i
$636$		0			0
$637$	12.8992	+	18.8412i	0.511086	+	0.746515i
$638$	23.9668	+	10.2407i	0.948854	+	0.405431i
$639$		0			0
$640$	1.03699	−	0.598709i	0.0409908	−	0.0236661i
$641$	−14.8938	+	8.59891i	−0.588268	+	0.339637i	−0.764412	−	0.644728i	$-0.776971\pi$
$641$	−14.8938	+	8.59891i	−0.588268	+	0.339637i	0.176144	+	0.984364i	$0.443637\pi$
$642$		0			0
$643$	−14.9068			−0.587869			−0.293934	−	0.955826i	$-0.594965\pi$
$643$	−14.9068			−0.587869			−0.293934	+	0.955826i	$0.594965\pi$
$644$	5.37248	+	17.3574i	0.211705	+	0.683979i
$645$		0			0
$646$	29.7681	+	17.1866i	1.17121	+	0.676199i
$647$	−8.06855	+	4.65838i	−0.317208	+	0.183140i	−0.650147	−	0.759808i	$-0.725293\pi$
$647$	−8.06855	+	4.65838i	−0.317208	+	0.183140i	0.332940	+	0.942948i	$0.391959\pi$
$648$		0			0
$649$	−8.42922	−	11.2415i	−0.330876	−	0.441268i
$650$			11.6328i			0.456275i
$651$		0			0
$652$	24.0337			0.941234
$653$	16.4127	+	9.47591i	0.642281	+	0.370821i	0.785492	−	0.618871i	$-0.212410\pi$
$653$	16.4127	+	9.47591i	0.642281	+	0.370821i	−0.143212	+	0.989692i	$0.545743\pi$
$654$		0			0
$655$	0.824375	−	0.475953i	0.0322110	−	0.0185970i
$656$	−1.57652	+	2.73061i	−0.0615528	+	0.106613i
$657$		0			0
$658$	−0.738829	+	0.797817i	−0.0288026	+	0.0311021i
$659$	22.1801			0.864016			0.432008	−	0.901870i	$-0.357805\pi$
$659$	22.1801			0.864016			0.432008	+	0.901870i	$0.357805\pi$
$660$		0			0
$661$	17.8342	+	30.8897i	0.693670	+	1.20147i	0.970627	+	0.240589i	$0.0773406\pi$
$661$	17.8342	+	30.8897i	0.693670	+	1.20147i	−0.276957	+	0.960882i	$0.589326\pi$
$662$	−16.5068	−	28.5906i	−0.641554	−	1.11120i
$663$		0			0
$664$	10.8698			0.421829
$665$	−18.0761	−	16.7397i	−0.700963	−	0.649136i
$666$		0			0
$667$	46.7370	+	26.9836i	1.80966	+	1.04481i
$668$	6.68567	+	11.5799i	0.258676	+	0.448041i
$669$		0			0
$670$	11.6515	+	6.72702i	0.450138	+	0.259887i
$671$	14.9679	−	35.0301i	0.577828	−	1.35232i
$672$		0			0
$673$			18.5749i			0.716010i	0.933720	+	0.358005i	$0.116543\pi$
$673$			18.5749i			0.716010i	−0.933720	+	0.358005i	$0.883457\pi$
$674$	−0.754154	−	0.435411i	−0.0290489	−	0.0167714i
$675$		0			0
$676$	−1.17979	−	2.04346i	−0.0453767	−	0.0785948i
$677$	0.0528202	−	0.0914873i	0.00203005	−	0.00351614i	−0.865009	−	0.501757i	$-0.832687\pi$
$677$	0.0528202	−	0.0914873i	0.00203005	−	0.00351614i	0.867039	+	0.498241i	$0.166020\pi$
$678$		0			0
$679$	−33.1342	+	10.2557i	−1.27157	+	0.393578i
$680$		−	5.29274i		−	0.202967i
$681$		0			0
$682$	−0.0819535	−	0.680845i	−0.00313816	−	0.0260709i
$683$	6.42302	−	3.70833i	0.245770	−	0.141895i	−0.372056	−	0.928210i	$-0.621347\pi$
$683$	6.42302	−	3.70833i	0.245770	−	0.141895i	0.617826	+	0.786315i	$0.288014\pi$
$684$		0			0
$685$	−7.20257			−0.275196
$686$	−6.81627	−	17.2203i	−0.260247	−	0.657474i
$687$		0			0
$688$	−6.93044	−	4.00129i	−0.264221	−	0.152548i
$689$	9.46445	+	16.3929i	0.360567	+	0.624520i
$690$		0			0
$691$	−10.5227	+	18.2258i	−0.400302	+	0.693343i	−0.993762	−	0.111520i	$-0.964428\pi$
$691$	−10.5227	+	18.2258i	−0.400302	+	0.693343i	0.593460	+	0.804863i	$0.297761\pi$
$692$	23.8696			0.907385
$693$		0			0
$694$	7.85259			0.298080
$695$	7.09980	−	12.2972i	0.269311	−	0.466460i
$696$		0			0
$697$	6.96842	+	12.0697i	0.263948	+	0.457171i
$698$	17.9226	+	10.3476i	0.678382	+	0.391664i
$699$		0			0
$700$	2.09063	−	9.20072i	0.0790184	−	0.347755i
$701$	−2.71470			−0.102533			−0.0512663	−	0.998685i	$-0.516326\pi$
$701$	−2.71470			−0.102533			−0.0512663	+	0.998685i	$0.516326\pi$
$702$		0			0
$703$	−51.6186	+	29.8020i	−1.94683	+	1.12400i
$704$	−0.396361	−	3.29286i	−0.0149384	−	0.124104i
$705$		0			0
$706$		−	26.5901i		−	1.00073i
$707$	−18.7357	−	17.3504i	−0.704627	−	0.652529i
$708$		0			0
$709$	−11.7895	+	20.4200i	−0.442763	+	0.766888i	−0.997893	−	0.0648754i	$-0.979335\pi$
$709$	−11.7895	+	20.4200i	−0.442763	+	0.766888i	0.555130	+	0.831763i	$0.312668\pi$
$710$	−2.27921	−	3.94771i	−0.0855373	−	0.148155i
$711$		0			0
$712$	−11.4053	−	6.58488i	−0.427433	−	0.246779i
$713$		−	1.41997i		−	0.0531783i
$714$		0			0
$715$	−11.9126	−	5.09009i	−0.445507	−	0.190359i
$716$	−17.6015	−	10.1622i	−0.657798	−	0.379780i
$717$		0			0
$718$	0.0346521	+	0.0600191i	0.00129320	+	0.00223989i
$719$	39.6365	+	22.8842i	1.47819	+	0.853435i	0.999696	−	0.0246536i	$-0.00784827\pi$
$719$	39.6365	+	22.8842i	1.47819	+	0.853435i	0.478497	+	0.878089i	$0.341182\pi$
$720$		0			0
$721$	−5.80985	+	25.5687i	−0.216370	+	0.952229i
$722$	−41.4745			−1.54352
$723$		0			0
$724$	9.72802	+	16.8494i	0.361539	+	0.626204i
$725$	−14.0120	−	24.2696i	−0.520394	−	0.901350i
$726$		0			0
$727$	−6.07152			−0.225180			−0.112590	−	0.993642i	$-0.535915\pi$
$727$	−6.07152			−0.225180			−0.112590	+	0.993642i	$0.535915\pi$
$728$	−2.55183	−	8.24446i	−0.0945769	−	0.305560i
$729$		0			0
$730$	−0.135337	+	0.234411i	−0.00500905	+	0.00867593i
$731$	−30.6334	+	17.6862i	−1.13302	+	0.654148i
$732$		0			0
$733$	36.1021	+	20.8436i	1.33346	+	0.769875i	0.985829	−	0.167755i	$-0.0536518\pi$
$733$	36.1021	+	20.8436i	1.33346	+	0.769875i	0.347634	+	0.937630i	$0.386985\pi$
$734$	37.0298			1.36679
$735$		0			0
$736$		−	6.86757i		−	0.253142i
$737$	29.8146	−	22.3559i	1.09823	−	0.823489i
$738$		0			0
$739$	−7.62892	+	4.40456i	−0.280635	+	0.162024i	−0.633711	−	0.773570i	$-0.718469\pi$
$739$	−7.62892	+	4.40456i	−0.280635	+	0.162024i	0.353076	+	0.935595i	$0.385136\pi$
$740$	7.94814	+	4.58886i	0.292180	+	0.168690i
$741$		0			0
$742$	−4.53960	−	14.6666i	−0.166654	−	0.538427i
$743$	45.0818			1.65389			0.826945	−	0.562283i	$-0.190077\pi$
$743$	45.0818			1.65389			0.826945	+	0.562283i	$0.190077\pi$
$744$		0			0
$745$	−18.6687	+	10.7784i	−0.683970	+	0.394890i
$746$	10.9206	−	6.30501i	0.399831	−	0.230843i
$747$		0			0
$748$	−13.4808	−	5.76017i	−0.492908	−	0.210613i
$749$	−5.65916	+	24.9056i	−0.206781	+	0.910030i
$750$		0			0
$751$	0.739343	−	1.28058i	0.0269790	−	0.0467290i	−0.852221	−	0.523183i	$-0.824745\pi$
$751$	0.739343	−	1.28058i	0.0269790	−	0.0467290i	0.879200	+	0.476453i	$0.158078\pi$
$752$	0.355926	−	0.205494i	0.0129793	−	0.00749360i
$753$		0			0
$754$	−22.1992	−	12.8167i	−0.808447	−	0.466757i
$755$	−6.20906			−0.225971
$756$		0			0
$757$	19.5239			0.709608			0.354804	−	0.934941i	$-0.384548\pi$
$757$	19.5239			0.709608			0.354804	+	0.934941i	$0.384548\pi$
$758$	2.22863	−	3.86010i	0.0809474	−	0.140205i
$759$		0			0
$760$	4.65588	+	8.06422i	0.168887	+	0.292520i
$761$	−14.9359	+	25.8697i	−0.541426	+	0.937777i	0.457396	+	0.889263i	$0.348782\pi$
$761$	−14.9359	+	25.8697i	−0.541426	+	0.937777i	−0.998822	+	0.0485145i	$0.984551\pi$
$762$		0			0
$763$	13.1770	−	14.2291i	0.477041	−	0.515128i
$764$		−	9.40784i		−	0.340364i
$765$		0			0
$766$	−11.0167	+	6.36051i	−0.398050	+	0.229815i
$767$	6.90959	+	11.9678i	0.249491	+	0.432131i
$768$		0			0
$769$			2.72669i			0.0983268i	0.998791	+	0.0491634i	$0.0156555\pi$
$769$			2.72669i			0.0983268i	−0.998791	+	0.0491634i	$0.984344\pi$
$770$	8.50727	+	6.16683i	0.306581	+	0.222237i
$771$		0			0
$772$	2.92081	+	1.68633i	0.105122	+	0.0606925i
$773$	−9.27880	+	5.35712i	−0.333735	+	0.192682i	−0.657498	−	0.753456i	$-0.728385\pi$
$773$	−9.27880	+	5.35712i	−0.333735	+	0.192682i	0.323763	+	0.946138i	$0.395052\pi$
$774$		0			0
$775$	−0.368681	+	0.638574i	−0.0132434	+	0.0229382i
$776$	13.1097			0.470612
$777$		0			0
$778$			21.6727i			0.777005i
$779$	−21.2347	−	12.2599i	−0.760813	−	0.439255i
$780$		0			0
$781$	−12.5355	+	1.50890i	−0.448555	+	0.0539927i
$782$	−26.2886	−	15.1778i	−0.940080	−	0.542755i
$783$		0			0
$784$	0.536631	+	6.97940i	0.0191654	+	0.249264i
$785$		−	23.5640i		−	0.841034i
$786$		0			0
$787$	13.6208	−	7.86396i	0.485529	−	0.280320i	−0.237189	−	0.971464i	$-0.576226\pi$
$787$	13.6208	−	7.86396i	0.485529	−	0.280320i	0.722718	+	0.691143i	$0.242893\pi$
$788$	−3.16564	−	5.48305i	−0.112771	−	0.195326i
$789$		0			0
$790$	−2.77708			−0.0988040
$791$	−9.40425	−	30.3833i	−0.334377	−	1.08031i
$792$		0			0
$793$	−18.7331	+	32.4466i	−0.665230	+	1.15221i
$794$	−6.77259	−	11.7305i	−0.240350	−	0.416299i
$795$		0			0
$796$	0.331375	−	0.573958i	0.0117453	−	0.0203434i
$797$			22.1018i			0.782884i	0.920203	+	0.391442i	$0.128024\pi$
$797$			22.1018i			0.782884i	−0.920203	+	0.391442i	$0.871976\pi$
$798$		0			0
$799$		−	1.81662i		−	0.0642674i
$800$	−1.78309	+	3.08841i	−0.0630419	+	0.109192i
$801$		0			0
$802$	−23.0277	+	13.2951i	−0.813137	+	0.469465i
$803$	0.449765	+	0.599823i	0.0158719	+	0.0211673i
$804$		0			0
$805$	15.9633	+	14.7830i	0.562632	+	0.521033i
$806$			0.674458i			0.0237568i
$807$		0			0
$808$	4.82575	+	8.35845i	0.169769	+	0.294049i
$809$	22.1026	+	38.2828i	0.777086	+	1.34595i	0.933614	+	0.358280i	$0.116637\pi$
$809$	22.1026	+	38.2828i	0.777086	+	1.34595i	−0.156528	+	0.987674i	$0.550030\pi$
$810$		0			0
$811$		−	19.1956i		−	0.674048i	−0.941496	−	0.337024i	$-0.890580\pi$
$811$		−	19.1956i		−	0.674048i	0.941496	−	0.337024i	$-0.109420\pi$
$812$	15.2546	+	14.1267i	0.535332	+	0.495751i
$813$		0			0
$814$	20.3381	−	15.2501i	0.712851	−	0.534517i
$815$	24.9228	−	14.3892i	0.873009	−	0.504032i
$816$		0			0
$817$	31.1162	−	53.8948i	1.08862	−	1.88554i
$818$		−	6.36575i		−	0.222573i
$819$		0			0
$820$			3.77551i			0.131846i
$821$	−23.2612	+	40.2895i	−0.811821	+	1.40611i	0.0997680	+	0.995011i	$0.468190\pi$
$821$	−23.2612	+	40.2895i	−0.811821	+	1.40611i	−0.911589	+	0.411104i	$0.865143\pi$
$822$		0			0
$823$	12.0487	+	20.8689i	0.419990	+	0.727444i	0.995938	−	0.0900423i	$-0.0287002\pi$
$823$	12.0487	+	20.8689i	0.419990	+	0.727444i	−0.575948	+	0.817486i	$0.695367\pi$
$824$	4.95521	−	8.58267i	0.172623	−	0.298992i
$825$		0			0
$826$	−3.31417	−	10.7074i	−0.115315	−	0.372559i
$827$	39.8140			1.38447			0.692235	−	0.721673i	$-0.256626\pi$
$827$	39.8140			1.38447			0.692235	+	0.721673i	$0.256626\pi$
$828$		0			0
$829$	−15.4410	−	26.7447i	−0.536289	−	0.928880i	−0.999100	−	0.0424231i	$-0.986492\pi$
$829$	−15.4410	−	26.7447i	−0.536289	−	0.928880i	0.462810	−	0.886457i	$-0.346841\pi$
$830$	11.2719	−	6.50783i	0.391253	−	0.225890i
$831$		0			0
$832$			3.26196i			0.113088i
$833$	27.9027	+	13.3707i	0.966772	+	0.463268i
$834$		0			0
$835$	13.8660	+	8.00554i	0.479853	+	0.277043i
$836$	25.6070	−	3.08232i	0.885637	−	0.106604i
$837$		0			0
$838$	−18.2871	−	10.5580i	−0.631716	−	0.364721i
$839$			11.6938i			0.403716i	0.979415	+	0.201858i	$0.0646980\pi$
$839$			11.6938i			0.403716i	−0.979415	+	0.201858i	$0.935302\pi$
$840$		0			0
$841$	32.7525			1.12940
$842$	4.47066	−	7.74340i	0.154069	−	0.266855i
$843$		0			0
$844$	−12.9408	+	7.47137i	−0.445440	+	0.257175i
$845$	−2.44688	−	1.41271i	−0.0841753	−	0.0485986i
$846$		0			0
$847$	24.9658	−	14.9569i	0.857834	−	0.513926i
$848$			5.80291i			0.199273i
$849$		0			0
$850$	7.88150	+	13.6512i	0.270333	+	0.468231i
$851$	45.5851	−	26.3186i	1.56264	−	0.902189i
$852$		0			0
$853$		−	28.8586i		−	0.988098i	−0.869434	−	0.494049i	$-0.835516\pi$
$853$		−	28.8586i		−	0.988098i	0.869434	−	0.494049i	$-0.164484\pi$
$854$	20.6478	−	22.2963i	0.706553	−	0.762964i
$855$		0			0
$856$	4.82669	−	8.36007i	0.164973	−	0.285741i
$857$	−5.00247	−	8.66454i	−0.170881	−	0.295975i	0.767847	−	0.640633i	$-0.221328\pi$
$857$	−5.00247	−	8.66454i	−0.170881	−	0.295975i	−0.938728	+	0.344658i	$0.887995\pi$
$858$		0			0
$859$	−18.4504	+	31.9570i	−0.629519	+	1.09036i	0.358129	+	0.933672i	$0.383415\pi$
$859$	−18.4504	+	31.9570i	−0.629519	+	1.09036i	−0.987648	+	0.156687i	$0.949919\pi$
$860$	−9.58244			−0.326758
$861$		0			0
$862$	−8.33069			−0.283744
$863$	8.29145	+	4.78707i	0.282244	+	0.162954i	0.634439	−	0.772973i	$-0.281231\pi$
$863$	8.29145	+	4.78707i	0.282244	+	0.162954i	−0.352195	+	0.935927i	$0.614565\pi$
$864$		0			0
$865$	24.7526	−	14.2909i	0.841614	−	0.485906i
$866$	−0.144352	+	0.250025i	−0.00490528	+	0.00849619i
$867$		0			0
$868$	0.121213	−	0.533449i	0.00411423	−	0.0181065i
$869$	−3.02234	+	7.07334i	−0.102526	+	0.239947i
$870$		0			0
$871$	−31.7407	+	18.3255i	−1.07549	+	0.620936i
$872$	−6.34796	+	3.66500i	−0.214969	+	0.124112i
$873$		0			0
$874$	53.4059			1.80648
$875$	−8.02427	−	25.9249i	−0.271270	−	0.876420i
$876$		0			0
$877$	23.9020	+	13.7998i	0.807114	+	0.465987i	0.845952	−	0.533258i	$-0.179033\pi$
$877$	23.9020	+	13.7998i	0.807114	+	0.465987i	−0.0388390	+	0.999245i	$0.512366\pi$
$878$	−10.0491	+	5.80186i	−0.339141	+	0.195803i
$879$		0			0
$880$	−2.38249	−	3.17737i	−0.0803136	−	0.107109i
$881$		−	12.0483i		−	0.405916i	−0.979187	−	0.202958i	$-0.934944\pi$
$881$		−	12.0483i		−	0.405916i	0.979187	−	0.202958i	$-0.0650555\pi$
$882$		0			0
$883$	11.1451			0.375061			0.187531	−	0.982259i	$-0.439952\pi$
$883$	11.1451			0.375061			0.187531	+	0.982259i	$0.439952\pi$
$884$	12.4866	+	7.20914i	0.419970	+	0.242470i
$885$		0			0
$886$	4.34544	−	2.50884i	0.145988	−	0.0842862i
$887$	9.43091	−	16.3348i	0.316659	−	0.548469i	−0.663130	−	0.748504i	$-0.730772\pi$
$887$	9.43091	−	16.3348i	0.316659	−	0.548469i	0.979789	+	0.200035i	$0.0641056\pi$
$888$		0			0
$889$	14.2270	+	45.9646i	0.477158	+	1.54160i
$890$	−15.7697			−0.528602
$891$		0			0
$892$	8.51565	+	14.7495i	0.285125	+	0.493851i
$893$	1.59803	+	2.76787i	0.0534761	+	0.0926234i
$894$		0			0
$895$	−24.3369			−0.813491
$896$	0.586237	−	2.57999i	0.0195848	−	0.0861913i
$897$		0			0
$898$	12.8058	+	7.39342i	0.427335	+	0.246722i
$899$	−0.812406	−	1.40713i	−0.0270953	−	0.0469304i
$900$		0			0
$901$	22.2132	+	12.8248i	0.740029	+	0.427256i
$902$	9.61639	+	4.10895i	0.320191	+	0.136813i
$903$		0			0
$904$			12.0213i			0.399823i
$905$	20.1758	+	11.6485i	0.670666	+	0.387209i
$906$		0			0
$907$	−26.2003	−	45.3802i	−0.869965	−	1.50682i	−0.862031	−	0.506855i	$-0.830808\pi$
$907$	−26.2003	−	45.3802i	−0.869965	−	1.50682i	−0.00793394	−	0.999969i	$-0.502525\pi$
$908$	−9.58521	+	16.6021i	−0.318096	+	0.550959i
$909$		0			0
$910$	−7.58226	−	7.02165i	−0.251349	−	0.232766i
$911$		−	36.2035i		−	1.19948i	−0.800197	−	0.599738i	$-0.795272\pi$
$911$		−	36.2035i		−	1.19948i	0.800197	−	0.599738i	$-0.204728\pi$
$912$		0			0
$913$	−4.30836	−	35.7926i	−0.142586	−	1.18456i
$914$	−29.4805	+	17.0205i	−0.975127	+	0.562990i
$915$		0			0
$916$	−13.0205			−0.430208
$917$	0.466038	−	2.05100i	0.0153899	−	0.0677300i
$918$		0			0
$919$	−29.5266	−	17.0472i	−0.973991	−	0.562334i	−0.0735407	−	0.997292i	$-0.523430\pi$
$919$	−29.5266	−	17.0472i	−0.973991	−	0.562334i	−0.900451	+	0.434958i	$0.856763\pi$
$920$	−4.11168	−	7.12163i	−0.135558	−	0.234793i
$921$		0			0
$922$	−15.6064	+	27.0310i	−0.513968	+	0.890219i
$923$	12.4179			0.408740
$924$		0			0
$925$	−27.3334			−0.898717
$926$	−3.33272	+	5.77244i	−0.109520	+	0.189694i
$927$		0			0
$928$	−3.92914	−	6.80547i	−0.128980	−	0.223400i
$929$	−5.38330	−	3.10805i	−0.176620	−	0.101972i	0.409083	−	0.912497i	$-0.365848\pi$
$929$	−5.38330	−	3.10805i	−0.176620	−	0.101972i	−0.585704	+	0.810525i	$0.699182\pi$
$930$		0			0
$931$	−54.2756	+	4.17313i	−1.77881	+	0.136769i
$932$	−4.09714			−0.134206
$933$		0			0
$934$	−6.58720	+	3.80312i	−0.215540	+	0.124442i
$935$	−17.4282	+	2.09784i	−0.569964	+	0.0686066i
$936$		0			0
$937$		−	36.8415i		−	1.20356i	−0.798662	−	0.601780i	$-0.794458\pi$
$937$		−	36.8415i		−	1.20356i	0.798662	−	0.601780i	$-0.205542\pi$
$938$	28.3981	−	8.78979i	0.927231	−	0.286997i
$939$		0			0
$940$	0.246063	−	0.426193i	0.00802567	−	0.0139009i
$941$	−18.3238	−	31.7377i	−0.597337	−	1.03462i	−0.993212	−	0.116314i	$-0.962892\pi$
$941$	−18.3238	−	31.7377i	−0.597337	−	1.03462i	0.395875	−	0.918304i	$-0.370441\pi$
$942$		0			0
$943$	18.7527	+	10.8269i	0.610671	+	0.352571i
$944$			4.23646i			0.137885i
$945$		0			0
$946$	−10.4287	+	24.4069i	−0.339067	+	0.793537i
$947$	−25.5002	−	14.7226i	−0.828646	−	0.478419i	0.0247427	−	0.999694i	$-0.492123\pi$
$947$	−25.5002	−	14.7226i	−0.828646	−	0.478419i	−0.853389	+	0.521275i	$0.825457\pi$
$948$		0			0
$949$	−0.368681	−	0.638574i	−0.0119679	−	0.0207290i
$950$	−24.0171	−	13.8663i	−0.779219	−	0.449882i
$951$		0			0
$952$	−8.58041	−	7.94601i	−0.278093	−	0.257532i
$953$	10.3535			0.335384			0.167692	−	0.985839i	$-0.446369\pi$
$953$	10.3535			0.335384			0.167692	+	0.985839i	$0.446369\pi$
$954$		0			0
$955$	−5.63256	−	9.75588i	−0.182265	−	0.315693i
$956$	2.34489	+	4.06147i	0.0758393	+	0.131357i
$957$		0			0
$958$	−15.2859			−0.493864
$959$	−10.8133	+	11.6766i	−0.349178	+	0.377056i
$960$		0			0
$961$	15.4786	−	26.8098i	0.499310	−	0.864831i
$962$	−21.6521	+	12.5008i	−0.698090	+	0.403043i
$963$		0			0
$964$	−11.0323	−	6.36950i	−0.355326	−	0.205148i
$965$	4.03849			0.130004
$966$		0			0
$967$		−	0.804904i		−	0.0258840i	−0.999916	−	0.0129420i	$-0.995880\pi$
$967$		−	0.804904i		−	0.0258840i	0.999916	−	0.0129420i	$-0.00411968\pi$
$968$	−10.6858	+	2.61032i	−0.343454	+	0.0838989i
$969$		0			0
$970$	13.5947	−	7.84891i	0.436500	−	0.252013i
$971$	−34.1340	−	19.7073i	−1.09541	−	0.632436i	−0.160399	−	0.987052i	$-0.551278\pi$
$971$	−34.1340	−	19.7073i	−1.09541	−	0.632436i	−0.935012	+	0.354616i	$0.884612\pi$
$972$		0			0
$973$	−9.27688	−	29.9718i	−0.297403	−	0.960852i
$974$	−1.58099			−0.0506580
$975$		0			0
$976$	−9.94695	+	5.74287i	−0.318394	+	0.183825i
$977$	−21.2420	+	12.2641i	−0.679592	+	0.392363i	−0.799701	−	0.600398i	$-0.795009\pi$
$977$	−21.2420	+	12.2641i	−0.679592	+	0.392363i	0.120109	+	0.992761i	$0.461676\pi$
$978$		0			0
$979$	−17.1624	+	40.1661i	−0.548513	+	1.28372i
$980$	4.73511	+	6.91631i	0.151258	+	0.220934i
$981$		0			0
$982$	−3.45394	+	5.98240i	−0.110220	+	0.190906i
$983$	−3.94538	+	2.27787i	−0.125838	+	0.0726526i	−0.561598	−	0.827410i	$-0.689813\pi$
$983$	−3.94538	+	2.27787i	−0.125838	+	0.0726526i	0.435760	+	0.900063i	$0.356480\pi$
$984$		0			0
$985$	−6.56550	−	3.79060i	−0.209194	−	0.120778i
$986$	−34.7345			−1.10617
$987$		0			0
$988$	−25.3668			−0.807025
$989$	−27.4791	+	47.5953i	−0.873786	+	1.51344i
$990$		0			0
$991$	−7.66468	−	13.2756i	−0.243477	−	0.421714i	0.718226	−	0.695810i	$-0.244955\pi$
$991$	−7.66468	−	13.2756i	−0.243477	−	0.421714i	−0.961702	+	0.274096i	$0.911621\pi$
$992$	−0.103382	+	0.179063i	−0.00328239	+	0.00568526i
$993$		0			0
$994$	−9.82169	−	2.23173i	−0.311525	−	0.0707862i
$995$		−	0.793588i		−	0.0251584i
$996$		0			0
$997$	−49.8972	+	28.8082i	−1.58026	+	0.912364i	−0.585441	+	0.810715i	$0.699079\pi$
$997$	−49.8972	+	28.8082i	−1.58026	+	0.912364i	−0.994820	+	0.101649i	$0.967588\pi$
$998$	−0.474107	−	0.821178i	−0.0150076	−	0.0259939i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.a.989.7	✓	32
3.2	odd	2		1386.2.ba.b.989.10	yes	32
7.4	even	3	inner	1386.2.ba.a.1187.10	yes	32
11.10	odd	2		1386.2.ba.b.989.7	yes	32
21.11	odd	6		1386.2.ba.b.1187.7	yes	32
33.32	even	2	inner	1386.2.ba.a.989.10	yes	32
77.32	odd	6		1386.2.ba.b.1187.10	yes	32
231.32	even	6	inner	1386.2.ba.a.1187.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.7	✓	32	1.1	even	1	trivial
1386.2.ba.a.989.10	yes	32	33.32	even	2	inner
1386.2.ba.a.1187.7	yes	32	231.32	even	6	inner
1386.2.ba.a.1187.10	yes	32	7.4	even	3	inner
1386.2.ba.b.989.7	yes	32	11.10	odd	2
1386.2.ba.b.989.10	yes	32	3.2	odd	2
1386.2.ba.b.1187.7	yes	32	21.11	odd	6
1386.2.ba.b.1187.10	yes	32	77.32	odd	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.03699 - 0.598709i) q^{5} +(-2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.03699 - 0.598709i) q^{5} +(-2.52745 + 0.782297i) q^{7} +1.00000 q^{8} +(1.03699 - 0.598709i) q^{10} +(-0.396361 - 3.29286i) q^{11} +3.26196i q^{13} +(0.586237 - 2.57999i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.21006 + 3.82794i) q^{17} +(-6.73468 - 3.88827i) q^{19} +1.19742i q^{20} +(3.04988 + 1.30317i) q^{22} +(5.94749 + 3.43378i) q^{23} +(-1.78309 - 3.08841i) q^{25} +(-2.82494 - 1.63098i) q^{26} +(1.94121 + 1.79769i) q^{28} +7.85827 q^{29} +(-0.103382 - 0.179063i) q^{31} +(-0.500000 - 0.866025i) q^{32} -4.42012 q^{34} +(3.08932 + 0.701970i) q^{35} +(3.83230 - 6.63773i) q^{37} +(6.73468 - 3.88827i) q^{38} +(-1.03699 - 0.598709i) q^{40} +3.15304 q^{41} +8.00258i q^{43} +(-2.65352 + 1.98969i) q^{44} +(-5.94749 + 3.43378i) q^{46} +(-0.355926 - 0.205494i) q^{47} +(5.77602 - 3.95444i) q^{49} +3.56619 q^{50} +(2.82494 - 1.63098i) q^{52} +(5.02547 - 2.90146i) q^{53} +(-1.56044 + 3.65198i) q^{55} +(-2.52745 + 0.782297i) q^{56} +(-3.92914 + 6.80547i) q^{58} +(3.66888 - 2.11823i) q^{59} +(9.94695 + 5.74287i) q^{61} +0.206764 q^{62} +1.00000 q^{64} +(1.95297 - 3.38264i) q^{65} +(5.61793 + 9.73055i) q^{67} +(2.21006 - 3.82794i) q^{68} +(-2.15258 + 2.32445i) q^{70} -3.80688i q^{71} +(-0.195764 + 0.113024i) q^{73} +(3.83230 + 6.63773i) q^{74} +7.77654i q^{76} +(3.57778 + 8.01246i) q^{77} +(-2.00851 - 1.15961i) q^{79} +(1.03699 - 0.598709i) q^{80} +(-1.57652 + 2.73061i) q^{82} +10.8698 q^{83} -5.29274i q^{85} +(-6.93044 - 4.00129i) q^{86} +(-0.396361 - 3.29286i) q^{88} +(-11.4053 - 6.58488i) q^{89} +(-2.55183 - 8.24446i) q^{91} -6.86757i q^{92} +(0.355926 - 0.205494i) q^{94} +(4.65588 + 8.06422i) q^{95} +13.1097 q^{97} +(0.536631 + 6.97940i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

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