LMFDB - Embedded newform 1386.2.ba.a.1187.7

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			1187.7
Character	$\chi$	$=$	1386.1187
Dual form			1386.2.ba.a.989.7

$q$-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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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	−0.713623	−	0.700530i	$-0.752947\pi$
$5$	−1.03699	+	0.598709i	−0.463758	+	0.267751i	0.249865	+	0.968281i	$0.419614\pi$
$6$		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	$-0.850585\pi$
$13$		−	3.26196i		−	0.904706i	0.891839	−	0.452353i	$-0.149415\pi$
$14$	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	−0.463095	−	0.886309i	$-0.653261\pi$
$17$	2.21006	−	3.82794i	0.536019	−	0.928412i	0.999113	−	0.0421028i	$-0.0134057\pi$
$18$		0			0
$19$	−6.73468	+	3.88827i	−1.54504	+	0.892030i	−0.546532	+	0.837438i	$0.684052\pi$
$19$	−6.73468	+	3.88827i	−1.54504	+	0.892030i	−0.998509	+	0.0545917i	$0.982614\pi$
$20$		−	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	0.271015	−	0.962575i	$-0.412641\pi$
$23$	5.94749	−	3.43378i	1.24014	−	0.715993i	0.969122	+	0.246582i	$0.0793073\pi$
$24$		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	−0.875160	−	0.483833i	$-0.839244\pi$
$31$	−0.103382	+	0.179063i	−0.0185680	+	0.0321607i	0.856592	+	0.515994i	$0.172577\pi$
$32$	−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	0.987546	+	0.157331i	$0.0502891\pi$
$37$	3.83230	+	6.63773i	0.630026	+	1.09124i	−0.357520	+	0.933905i	$0.616378\pi$
$38$	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	$-0.791093\pi$
$43$		−	8.00258i		−	1.22038i	0.792254	−	0.610191i	$-0.208907\pi$
$44$	−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	−0.525734	−	0.850649i	$-0.676209\pi$
$47$	−0.355926	+	0.205494i	−0.0519172	+	0.0299744i	0.473817	+	0.880623i	$0.342876\pi$
$48$		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	0.803725	−	0.595001i	$-0.202848\pi$
$53$	5.02547	+	2.90146i	0.690302	+	0.398546i	−0.113423	+	0.993547i	$0.536182\pi$
$54$		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	0.719436	−	0.694559i	$-0.244401\pi$
$59$	3.66888	+	2.11823i	0.477647	+	0.275770i	−0.241788	+	0.970329i	$0.577734\pi$
$60$		0			0
$61$	9.94695	−	5.74287i	1.27358	−	0.735300i	0.297917	−	0.954592i	$-0.403708\pi$
$61$	9.94695	−	5.74287i	1.27358	−	0.735300i	0.975659	+	0.219292i	$0.0703747\pi$
$62$	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	−0.286674	−	0.958028i	$-0.592550\pi$
$67$	5.61793	−	9.73055i	0.686340	−	1.18878i	0.973014	−	0.230747i	$-0.0741170\pi$
$68$	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	$0.0725312\pi$
$71$			3.80688i			0.451793i	−0.974151	+	0.225897i	$0.927469\pi$
$72$		0			0
$73$	−0.195764	−	0.113024i	−0.0229124	−	0.0132285i	0.488500	−	0.872564i	$-0.337544\pi$
$73$	−0.195764	−	0.113024i	−0.0229124	−	0.0132285i	−0.511412	+	0.859335i	$0.670878\pi$
$74$	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	−0.608714	−	0.793390i	$-0.708314\pi$
$79$	−2.00851	+	1.15961i	−0.225975	+	0.130466i	0.382739	+	0.923856i	$0.374981\pi$
$80$	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	−0.962533	−	0.271165i	$-0.912591\pi$
$89$	−11.4053	+	6.58488i	−1.20896	+	0.697996i	−0.246431	+	0.969160i	$0.579258\pi$
$90$		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	−0.519561	−	0.854433i	$-0.673904\pi$
$101$	4.82575	−	8.35845i	0.480181	−	0.831697i	0.999741	+	0.0227363i	$0.00723780\pi$
$102$		0			0
$103$	4.95521	+	8.58267i	0.488251	+	0.845676i	0.999909	−	0.0135137i	$-0.00430167\pi$
$103$	4.95521	+	8.58267i	0.488251	+	0.845676i	−0.511658	+	0.859189i	$0.670968\pi$
$104$		−	3.26196i		−	0.319862i
$105$		0			0
$106$		−	5.80291i		−	0.563629i
$107$	4.82669	+	8.36007i	0.466614	+	0.808199i	0.999273	−	0.0381312i	$-0.0121405\pi$
$107$	4.82669	+	8.36007i	0.466614	+	0.808199i	−0.532659	+	0.846330i	$0.678807\pi$
$108$		0			0
$109$	−6.34796	−	3.66500i	−0.608024	−	0.351043i	0.164168	−	0.986432i	$-0.447506\pi$
$109$	−6.34796	−	3.66500i	−0.608024	−	0.351043i	−0.772192	+	0.635390i	$0.780840\pi$
$110$	−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	$-0.808708\pi$
$113$		−	12.0213i		−	1.13087i	0.824792	−	0.565436i	$-0.191292\pi$
$114$		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	$0.298846\pi$
$127$			18.1862i			1.61376i	−0.590715	+	0.806880i	$0.701154\pi$
$128$	−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	0.848139	−	0.529774i	$-0.177723\pi$
$131$	−0.397483	−	0.688460i	−0.0347282	−	0.0601511i	−0.882867	+	0.469623i	$0.844390\pi$
$132$		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	0.705739	−	0.708472i	$-0.250615\pi$
$137$	5.20922	+	3.00754i	0.445053	+	0.256952i	−0.260685	+	0.965424i	$0.583949\pi$
$138$		0			0
$139$		−	11.8585i		−	1.00583i	−0.864337	−	0.502913i	$-0.832262\pi$
$139$		−	11.8585i		−	1.00583i	0.864337	−	0.502913i	$-0.167738\pi$
$140$	−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	0.953653	+	0.300908i	$0.0972898\pi$
$149$	9.00137	+	15.5908i	0.737421	+	1.27725i	−0.216232	+	0.976342i	$0.569377\pi$
$150$		0			0
$151$	4.49066	+	2.59269i	0.365445	+	0.210990i	0.671467	−	0.741035i	$-0.265665\pi$
$151$	4.49066	+	2.59269i	0.365445	+	0.210990i	−0.306022	+	0.952025i	$0.598998\pi$
$152$	−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	−0.143557	−	0.989642i	$-0.545854\pi$
$157$	9.83949	−	17.0425i	0.785277	−	1.36014i	0.928834	−	0.370497i	$-0.120813\pi$
$158$	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	−0.763122	−	0.646254i	$-0.776335\pi$
$163$	−12.0169	−	20.8138i	−0.941234	−	1.63026i	−0.178111	−	0.984010i	$-0.556999\pi$
$164$	−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	−0.817684	−	0.575668i	$-0.804742\pi$
$173$	−11.9348	−	20.6717i	−0.907385	−	1.57164i	−0.0897011	−	0.995969i	$-0.528591\pi$
$174$		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	0.983017	−	0.183515i	$-0.0587476\pi$
$179$	17.6015	+	10.1622i	1.31560	+	0.759560i	0.332580	+	0.943075i	$0.392081\pi$
$180$		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	−0.175383	−	0.984500i	$-0.556116\pi$
$191$	8.14743	−	4.70392i	0.589527	−	0.340364i	0.764911	+	0.644136i	$0.222783\pi$
$192$		0			0
$193$	−2.92081	−	1.68633i	−0.210245	−	0.121385i	0.391180	−	0.920314i	$-0.372067\pi$
$193$	−2.92081	−	1.68633i	−0.210245	−	0.121385i	−0.601425	+	0.798929i	$0.705400\pi$
$194$	−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	−0.854041	−	0.520205i	$-0.825855\pi$
$199$	0.331375	−	0.573958i	0.0234905	−	0.0406868i	0.877532	+	0.479519i	$0.159189\pi$
$200$	−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	$0.171967\pi$
$211$			14.9427i			1.02870i	−0.857580	+	0.514350i	$0.828033\pi$
$212$	−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	0.350068	+	0.936724i	$0.386158\pi$
$227$	−9.58521	+	16.6021i	−0.636193	+	1.10192i	−0.986261	+	0.165194i	$0.947175\pi$
$228$		0			0
$229$	6.51023	+	11.2760i	0.430208	+	0.745142i	0.996891	−	0.0787938i	$-0.0251069\pi$
$229$	6.51023	+	11.2760i	0.430208	+	0.745142i	−0.566683	+	0.823936i	$0.691774\pi$
$230$	8.22335			0.542232
$231$		0			0
$232$	7.85827			0.515921
$233$	2.04857	+	3.54823i	0.134206	+	0.232452i	0.925294	−	0.379251i	$-0.123818\pi$
$233$	2.04857	+	3.54823i	0.134206	+	0.232452i	−0.791088	+	0.611703i	$0.790485\pi$
$234$		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	0.811303	−	0.584627i	$-0.198759\pi$
$241$	11.0323	+	6.36950i	0.710652	+	0.410295i	−0.100650	+	0.994922i	$0.532092\pi$
$242$	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	$-0.700124\pi$
$251$		−	25.6272i		−	1.61758i	0.588100	−	0.808788i	$-0.299876\pi$
$252$		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	−0.338596	−	0.940932i	$-0.609952\pi$
$257$	4.92122	−	2.84127i	0.306978	−	0.177234i	0.645573	+	0.763698i	$0.276619\pi$
$258$		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	−0.0488920	+	0.998804i	$0.515569\pi$
$263$	−14.4242	+	24.9835i	−0.889436	+	1.54055i	−0.840544	+	0.541744i	$0.817764\pi$
$264$		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	0.897589	−	0.440834i	$-0.145317\pi$
$269$	15.8208	+	9.13413i	0.964610	+	0.556918i	0.0670210	+	0.997752i	$0.478651\pi$
$270$		0			0
$271$	−5.05904	+	2.92084i	−0.307315	+	0.177428i	−0.645724	−	0.763571i	$-0.723444\pi$
$271$	−5.05904	+	2.92084i	−0.307315	+	0.177428i	0.338410	+	0.940999i	$0.390111\pi$
$272$	−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	0.838811	−	0.544423i	$-0.183251\pi$
$277$	13.0938	+	7.55973i	0.786732	+	0.454220i	−0.0520786	+	0.998643i	$0.516585\pi$
$278$	−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	0.498288	−	0.867011i	$-0.333962\pi$
$283$	−0.0575633	−	0.0332342i	−0.00342179	−	0.00197557i	−0.501710	+	0.865036i	$0.667296\pi$
$284$	−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	$0.194433\pi$
$307$			20.0987i			1.14710i	−0.819172	+	0.573548i	$0.805567\pi$
$308$	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	0.836738	−	0.547604i	$-0.184460\pi$
$311$	13.7708	+	7.95055i	0.780868	+	0.450834i	−0.0558698	+	0.998438i	$0.517793\pi$
$312$		0			0
$313$	8.27538	+	14.3334i	0.467752	+	0.810170i	0.999321	−	0.0368447i	$-0.0117307\pi$
$313$	8.27538	+	14.3334i	0.467752	+	0.810170i	−0.531569	+	0.847015i	$0.678397\pi$
$314$	−19.6790			−1.11055
$315$		0			0
$316$		−	2.31922i		−	0.130466i
$317$	−8.65990	+	4.99980i	−0.486389	+	0.280817i	−0.723075	−	0.690770i	$-0.757272\pi$
$317$	−8.65990	+	4.99980i	−0.486389	+	0.280817i	0.236686	+	0.971586i	$0.423939\pi$
$318$		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	−0.817808	−	0.575491i	$-0.804811\pi$
$331$	−16.5068	−	28.5906i	−0.907294	−	1.57148i	−0.0894857	−	0.995988i	$-0.528522\pi$
$332$	−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	$-0.992450\pi$
$337$		−	0.870822i		−	0.0474367i	0.999719	−	0.0237184i	$-0.00755050\pi$
$338$	−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	−0.951957	−	0.306231i	$-0.900932\pi$
$347$	−3.92630	+	6.80054i	−0.210775	+	0.365072i	0.741183	+	0.671304i	$0.234265\pi$
$348$		0			0
$349$			20.6953i			1.10779i	0.832586	+	0.553896i	$0.186860\pi$
$349$			20.6953i			1.10779i	−0.832586	+	0.553896i	$0.813140\pi$
$350$	−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	−0.259527	−	0.965736i	$-0.583567\pi$
$353$	−23.0277	−	13.2951i	−1.22564	−	0.707625i	−0.966115	+	0.258111i	$0.916900\pi$
$354$		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	0.866938	−	0.498415i	$-0.166085\pi$
$359$	0.0346521	+	0.0600191i	0.00182887	+	0.00316769i	−0.865110	+	0.501583i	$0.832751\pi$
$360$		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	−0.260854	+	0.965378i	$0.584004\pi$
$367$	−18.5149	+	32.0687i	−0.966469	+	1.67397i	−0.705615	+	0.708595i	$0.749329\pi$
$368$	−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	−0.755329	−	0.655346i	$-0.772523\pi$
$373$	−10.9206	+	6.30501i	−0.565447	+	0.326461i	0.189882	+	0.981807i	$0.439190\pi$
$374$	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	−0.191392	−	0.981514i	$-0.561300\pi$
$383$	11.0167	−	6.36051i	0.562928	−	0.325007i	0.754320	+	0.656507i	$0.227967\pi$
$384$		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	0.893588	−	0.448888i	$-0.148180\pi$
$389$	18.7691	+	10.8364i	0.951633	+	0.549426i	0.0580454	+	0.998314i	$0.481513\pi$
$390$		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	0.644508	−	0.764597i	$-0.277062\pi$
$397$	−6.77259	−	11.7305i	−0.339907	−	0.588736i	−0.984415	+	0.175862i	$0.943729\pi$
$398$	−0.662749			−0.0332206
$399$		0			0
$400$	3.56619			0.178309
$401$	23.0277	−	13.2951i	1.14995	−	0.663924i	0.201075	−	0.979576i	$-0.435557\pi$
$401$	23.0277	−	13.2951i	1.14995	−	0.663924i	0.948875	+	0.315652i	$0.102223\pi$
$402$		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	0.357471	−	0.933924i	$-0.383639\pi$
$409$	−5.51290	−	3.18288i	−0.272596	−	0.157383i	−0.630067	+	0.776541i	$0.716972\pi$
$410$	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	$-0.827497\pi$
$419$		−	21.1161i		−	1.03159i	0.856713	−	0.515794i	$-0.172503\pi$
$420$		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	−0.748096	−	0.663590i	$-0.769032\pi$
$431$	4.16534	−	7.21459i	0.200638	−	0.347514i	0.948734	+	0.316076i	$0.102365\pi$
$432$		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	−0.240639	−	0.970615i	$-0.577357\pi$
$439$	10.0491	−	5.80186i	0.479618	−	0.276908i	0.720257	+	0.693707i	$0.244024\pi$
$440$	−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	−0.599664	−	0.800252i	$-0.704699\pi$
$443$	−4.34544	+	2.50884i	−0.206458	+	0.119199i	0.393206	+	0.919450i	$0.371366\pi$
$444$		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	$0.113451\pi$
$449$			14.7868i			0.697835i	−0.937154	+	0.348917i	$0.886549\pi$
$450$		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	0.386994	−	0.922082i	$-0.373513\pi$
$457$	29.4805	−	17.0205i	1.37904	−	0.796188i	0.992044	+	0.125895i	$0.0401801\pi$
$458$	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	−0.339787	−	0.940503i	$-0.610355\pi$
$467$	6.58720	−	3.80312i	0.304819	−	0.175987i	0.644606	+	0.764515i	$0.277022\pi$
$468$		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	−0.636895	−	0.770950i	$-0.719782\pi$
$479$	7.64294	−	13.2380i	0.349215	−	0.604858i	0.986110	+	0.166092i	$0.0531150\pi$
$480$		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	−0.847559	−	0.530701i	$-0.821929\pi$
$487$	0.790493	−	1.36917i	0.0358206	−	0.0620432i	0.883380	+	0.468658i	$0.155262\pi$
$488$	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	0.855218	−	0.518268i	$-0.173423\pi$
$499$	−0.474107	−	0.821178i	−0.0212240	−	0.0367610i	−0.876442	+	0.481507i	$0.840090\pi$
$500$	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	−0.994638	−	0.103422i	$-0.967021\pi$
$509$	−31.6394	+	18.2670i	−1.40239	+	0.809670i	−0.407752	+	0.913093i	$0.633687\pi$
$510$		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	0.482798	−	0.875731i	$-0.339620\pi$
$521$	−0.780812	−	0.450802i	−0.0342080	−	0.0197500i	−0.517006	+	0.855981i	$0.672954\pi$
$522$		0			0
$523$	−8.65582	+	4.99744i	−0.378492	+	0.218523i	−0.677162	−	0.735834i	$-0.736790\pi$
$523$	−8.65582	+	4.99744i	−0.378492	+	0.218523i	0.298670	+	0.954357i	$0.403457\pi$
$524$	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	−0.984722	−	0.174134i	$-0.944287\pi$
$541$	−30.8485	+	17.8104i	−1.32628	+	0.765727i	−0.341557	+	0.939861i	$0.610954\pi$
$542$	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	$-0.951362\pi$
$547$		−	7.11968i		−	0.304416i	0.988349	−	0.152208i	$-0.0486383\pi$
$548$	−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	−0.606823	−	0.794837i	$-0.707556\pi$
$557$	9.08485	−	15.7354i	0.384938	−	0.666731i	0.991761	+	0.128106i	$0.0408896\pi$
$558$		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	−0.689828	−	0.723974i	$-0.742314\pi$
$563$	6.69275	−	11.5922i	0.282066	−	0.488552i	0.971893	+	0.235422i	$0.0756471\pi$
$564$		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	0.849325	−	0.527870i	$-0.177009\pi$
$569$	−0.774915	−	1.34219i	−0.0324861	−	0.0562676i	−0.881811	+	0.471602i	$0.843676\pi$
$570$		0			0
$571$	36.9067	+	21.3081i	1.54450	+	0.891715i	0.998547	+	0.0538962i	$0.0171640\pi$
$571$	36.9067	+	21.3081i	1.54450	+	0.891715i	0.545949	+	0.837819i	$0.316169\pi$
$572$	−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	−0.859646	−	0.510890i	$-0.829316\pi$
$577$	0.303156	−	0.525081i	0.0126205	−	0.0218594i	0.872267	+	0.489030i	$0.162649\pi$
$578$	−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	$-0.985446\pi$
$587$		−	2.21478i		−	0.0914137i	0.998955	−	0.0457069i	$-0.0145540\pi$
$588$		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	−0.979003	−	0.203844i	$-0.934656\pi$
$593$	−16.2190	−	28.0922i	−0.666036	−	1.15361i	0.312967	−	0.949764i	$-0.398677\pi$
$594$		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	0.989608	+	0.143794i	$0.0459302\pi$
$599$	39.3780	+	22.7349i	1.60894	+	0.928922i	0.619333	+	0.785128i	$0.287403\pi$
$600$		0			0
$601$		−	23.7080i		−	0.967069i	−0.875325	−	0.483535i	$-0.839353\pi$
$601$		−	23.7080i		−	0.967069i	0.875325	−	0.483535i	$-0.160647\pi$
$602$	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	−0.124648	−	0.992201i	$-0.539780\pi$
$607$	16.5637	−	9.56306i	0.672300	−	0.388153i	0.796948	+	0.604049i	$0.206447\pi$
$608$		−	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	0.564504	−	0.825430i	$-0.309068\pi$
$613$	3.26599	+	1.88562i	0.131912	+	0.0761595i	−0.432592	+	0.901590i	$0.642401\pi$
$614$	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	$0.0845628\pi$
$617$			13.0431i			0.525096i	−0.964919	+	0.262548i	$0.915437\pi$
$618$		0			0
$619$	20.6271	−	35.7272i	0.829074	−	1.43600i	−0.0696922	−	0.997569i	$-0.522202\pi$
$619$	20.6271	−	35.7272i	0.829074	−	1.43600i	0.898766	−	0.438429i	$-0.144465\pi$
$620$	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	0.176144	−	0.984364i	$-0.443637\pi$
$641$	−14.8938	−	8.59891i	−0.588268	−	0.339637i	−0.764412	+	0.644728i	$0.776971\pi$
$642$		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	0.332940	−	0.942948i	$-0.391959\pi$
$647$	−8.06855	−	4.65838i	−0.317208	−	0.183140i	−0.650147	+	0.759808i	$0.725293\pi$
$648$		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	−0.143212	−	0.989692i	$-0.545743\pi$
$653$	16.4127	−	9.47591i	0.642281	−	0.370821i	0.785492	+	0.618871i	$0.212410\pi$
$654$		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	−0.276957	−	0.960882i	$-0.589326\pi$
$661$	17.8342	−	30.8897i	0.693670	−	1.20147i	0.970627	−	0.240589i	$-0.0773406\pi$
$662$	−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	$-0.883457\pi$
$673$		−	18.5749i		−	0.716010i	0.933720	−	0.358005i	$-0.116543\pi$
$674$	−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	0.867039	−	0.498241i	$-0.166020\pi$
$677$	0.0528202	+	0.0914873i	0.00203005	+	0.00351614i	−0.865009	+	0.501757i	$0.832687\pi$
$678$		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	0.617826	−	0.786315i	$-0.288014\pi$
$683$	6.42302	+	3.70833i	0.245770	+	0.141895i	−0.372056	+	0.928210i	$0.621347\pi$
$684$		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	0.593460	−	0.804863i	$-0.297761\pi$
$691$	−10.5227	−	18.2258i	−0.400302	−	0.693343i	−0.993762	+	0.111520i	$0.964428\pi$
$692$	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	0.555130	−	0.831763i	$-0.312668\pi$
$709$	−11.7895	−	20.4200i	−0.442763	−	0.766888i	−0.997893	+	0.0648754i	$0.979335\pi$
$710$	−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	0.478497	−	0.878089i	$-0.341182\pi$
$719$	39.6365	−	22.8842i	1.47819	−	0.853435i	0.999696	+	0.0246536i	$0.00784827\pi$
$720$		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	0.347634	−	0.937630i	$-0.386985\pi$
$733$	36.1021	−	20.8436i	1.33346	−	0.769875i	0.985829	+	0.167755i	$0.0536518\pi$
$734$	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	0.353076	−	0.935595i	$-0.385136\pi$
$739$	−7.62892	−	4.40456i	−0.280635	−	0.162024i	−0.633711	+	0.773570i	$0.718469\pi$
$740$	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	0.879200	−	0.476453i	$-0.158078\pi$
$751$	0.739343	+	1.28058i	0.0269790	+	0.0467290i	−0.852221	+	0.523183i	$0.824745\pi$
$752$	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	−0.998822	−	0.0485145i	$-0.984551\pi$
$761$	−14.9359	−	25.8697i	−0.541426	−	0.937777i	0.457396	−	0.889263i	$-0.348782\pi$
$762$		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	$-0.984344\pi$
$769$		−	2.72669i		−	0.0983268i	0.998791	−	0.0491634i	$-0.0156555\pi$
$770$	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	0.323763	−	0.946138i	$-0.395052\pi$
$773$	−9.27880	−	5.35712i	−0.333735	−	0.192682i	−0.657498	+	0.753456i	$0.728385\pi$
$774$		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	0.722718	−	0.691143i	$-0.242893\pi$
$787$	13.6208	+	7.86396i	0.485529	+	0.280320i	−0.237189	+	0.971464i	$0.576226\pi$
$788$	−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	$-0.871976\pi$
$797$		−	22.1018i		−	0.782884i	0.920203	−	0.391442i	$-0.128024\pi$
$798$		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	−0.156528	−	0.987674i	$-0.550030\pi$
$809$	22.1026	−	38.2828i	0.777086	−	1.34595i	0.933614	−	0.358280i	$-0.116637\pi$
$810$		0			0
$811$			19.1956i			0.674048i	0.941496	+	0.337024i	$0.109420\pi$
$811$			19.1956i			0.674048i	−0.941496	+	0.337024i	$0.890580\pi$
$812$	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	−0.911589	−	0.411104i	$-0.865143\pi$
$821$	−23.2612	−	40.2895i	−0.811821	−	1.40611i	0.0997680	−	0.995011i	$-0.468190\pi$
$822$		0			0
$823$	12.0487	−	20.8689i	0.419990	−	0.727444i	−0.575948	−	0.817486i	$-0.695367\pi$
$823$	12.0487	−	20.8689i	0.419990	−	0.727444i	0.995938	+	0.0900423i	$0.0287002\pi$
$824$	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	0.462810	+	0.886457i	$0.346841\pi$
$829$	−15.4410	+	26.7447i	−0.536289	+	0.928880i	−0.999100	+	0.0424231i	$0.986492\pi$
$830$	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	$-0.935302\pi$
$839$		−	11.6938i		−	0.403716i	0.979415	−	0.201858i	$-0.0646980\pi$
$840$		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	$0.164484\pi$
$853$			28.8586i			0.988098i	−0.869434	+	0.494049i	$0.835516\pi$
$854$	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	−0.938728	−	0.344658i	$-0.887995\pi$
$857$	−5.00247	+	8.66454i	−0.170881	+	0.295975i	0.767847	+	0.640633i	$0.221328\pi$
$858$		0			0
$859$	−18.4504	−	31.9570i	−0.629519	−	1.09036i	−0.987648	−	0.156687i	$-0.949919\pi$
$859$	−18.4504	−	31.9570i	−0.629519	−	1.09036i	0.358129	−	0.933672i	$-0.383415\pi$
$860$	−9.58244			−0.326758
$861$		0			0
$862$	−8.33069			−0.283744
$863$	8.29145	−	4.78707i	0.282244	−	0.162954i	−0.352195	−	0.935927i	$-0.614565\pi$
$863$	8.29145	−	4.78707i	0.282244	−	0.162954i	0.634439	+	0.772973i	$0.281231\pi$
$864$		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	−0.0388390	−	0.999245i	$-0.512366\pi$
$877$	23.9020	−	13.7998i	0.807114	−	0.465987i	0.845952	+	0.533258i	$0.179033\pi$
$878$	−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	$0.0650555\pi$
$881$			12.0483i			0.405916i	−0.979187	+	0.202958i	$0.934944\pi$
$882$		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	0.979789	−	0.200035i	$-0.0641056\pi$
$887$	9.43091	+	16.3348i	0.316659	+	0.548469i	−0.663130	+	0.748504i	$0.730772\pi$
$888$		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	−0.00793394	+	0.999969i	$0.502525\pi$
$907$	−26.2003	+	45.3802i	−0.869965	+	1.50682i	−0.862031	+	0.506855i	$0.830808\pi$
$908$	−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	$0.204728\pi$
$911$			36.2035i			1.19948i	−0.800197	+	0.599738i	$0.795272\pi$
$912$		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	−0.900451	−	0.434958i	$-0.856763\pi$
$919$	−29.5266	+	17.0472i	−0.973991	+	0.562334i	−0.0735407	+	0.997292i	$0.523430\pi$
$920$	−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	−0.585704	−	0.810525i	$-0.699182\pi$
$929$	−5.38330	+	3.10805i	−0.176620	+	0.101972i	0.409083	+	0.912497i	$0.365848\pi$
$930$		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	$0.205542\pi$
$937$			36.8415i			1.20356i	−0.798662	+	0.601780i	$0.794458\pi$
$938$	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	0.395875	+	0.918304i	$0.370441\pi$
$941$	−18.3238	+	31.7377i	−0.597337	+	1.03462i	−0.993212	+	0.116314i	$0.962892\pi$
$942$		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	−0.853389	−	0.521275i	$-0.825457\pi$
$947$	−25.5002	+	14.7226i	−0.828646	+	0.478419i	0.0247427	+	0.999694i	$0.492123\pi$
$948$		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	$0.00411968\pi$
$967$			0.804904i			0.0258840i	−0.999916	+	0.0129420i	$0.995880\pi$
$968$	−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	−0.935012	−	0.354616i	$-0.884612\pi$
$971$	−34.1340	+	19.7073i	−1.09541	+	0.632436i	−0.160399	+	0.987052i	$0.551278\pi$
$972$		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	0.120109	−	0.992761i	$-0.461676\pi$
$977$	−21.2420	−	12.2641i	−0.679592	−	0.392363i	−0.799701	+	0.600398i	$0.795009\pi$
$978$		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	0.435760	−	0.900063i	$-0.356480\pi$
$983$	−3.94538	−	2.27787i	−0.125838	−	0.0726526i	−0.561598	+	0.827410i	$0.689813\pi$
$984$		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	−0.961702	−	0.274096i	$-0.911621\pi$
$991$	−7.66468	+	13.2756i	−0.243477	+	0.421714i	0.718226	+	0.695810i	$0.244955\pi$
$992$	−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	−0.994820	−	0.101649i	$-0.967588\pi$
$997$	−49.8972	−	28.8082i	−1.58026	−	0.912364i	−0.585441	−	0.810715i	$-0.699079\pi$
$998$	−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.1187.7	yes	32
3.2	odd	2		1386.2.ba.b.1187.10	yes	32
7.2	even	3	inner	1386.2.ba.a.989.10	yes	32
11.10	odd	2		1386.2.ba.b.1187.7	yes	32
21.2	odd	6		1386.2.ba.b.989.7	yes	32
33.32	even	2	inner	1386.2.ba.a.1187.10	yes	32
77.65	odd	6		1386.2.ba.b.989.10	yes	32
231.65	even	6	inner	1386.2.ba.a.989.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.7	✓	32	231.65	even	6	inner
1386.2.ba.a.989.10	yes	32	7.2	even	3	inner
1386.2.ba.a.1187.7	yes	32	1.1	even	1	trivial
1386.2.ba.a.1187.10	yes	32	33.32	even	2	inner
1386.2.ba.b.989.7	yes	32	21.2	odd	6
1386.2.ba.b.989.10	yes	32	77.65	odd	6
1386.2.ba.b.1187.7	yes	32	11.10	odd	2
1386.2.ba.b.1187.10	yes	32	3.2	odd	2

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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