LMFDB - Embedded newform 891.2.k.a.161.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.7
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.931921 - 0.677080i) q^{2} +(-0.207995 - 0.640143i) q^{4} +(-0.551104 - 0.758530i) q^{5} +(-0.824408 + 0.267866i) q^{7} +(-0.951517 + 2.92847i) q^{8} +1.08003i q^{10} +(1.59130 + 2.90994i) q^{11} +(0.693143 - 0.954029i) q^{13} +(0.949650 + 0.308560i) q^{14} +(1.78047 - 1.29359i) q^{16} +(-2.52191 + 1.83228i) q^{17} +(6.59786 + 2.14377i) q^{19} +(-0.370941 + 0.510556i) q^{20} +(0.487302 - 3.78927i) q^{22} +2.36655i q^{23} +(1.27343 - 3.91922i) q^{25} +(-1.29191 + 0.419767i) q^{26} +(0.342946 + 0.472024i) q^{28} +(1.11875 + 3.44315i) q^{29} +(5.13662 + 3.73198i) q^{31} +3.62323 q^{32} +3.59082 q^{34} +(0.657520 + 0.477716i) q^{35} +(-2.46847 - 7.59716i) q^{37} +(-4.69717 - 6.46511i) q^{38} +(2.74572 - 0.892138i) q^{40} +(1.11348 - 3.42695i) q^{41} -3.83119i q^{43} +(1.53180 - 1.62391i) q^{44} +(1.60234 - 2.20543i) q^{46} +(0.152329 + 0.0494946i) q^{47} +(-5.05522 + 3.67283i) q^{49} +(-3.84037 + 2.79019i) q^{50} +(-0.754886 - 0.245277i) q^{52} +(5.71174 - 7.86153i) q^{53} +(1.33031 - 2.81073i) q^{55} -2.66913i q^{56} +(1.28870 - 3.96622i) q^{58} +(-8.27039 + 2.68721i) q^{59} +(7.97576 + 10.9777i) q^{61} +(-2.26008 - 6.95581i) q^{62} +(-6.93750 - 5.04039i) q^{64} -1.10565 q^{65} +6.64298 q^{67} +(1.69746 + 1.23328i) q^{68} +(-0.289304 - 0.890387i) q^{70} +(6.53958 + 9.00097i) q^{71} +(3.29787 - 1.07154i) q^{73} +(-2.84347 + 8.75130i) q^{74} -4.66947i q^{76} +(-2.09135 - 1.97273i) q^{77} +(4.43649 - 6.10630i) q^{79} +(-1.96245 - 0.637639i) q^{80} +(-3.35800 + 2.43973i) q^{82} +(11.6734 - 8.48120i) q^{83} +(2.77967 + 0.903171i) q^{85} +(-2.59402 + 3.57037i) q^{86} +(-10.0358 + 1.89120i) q^{88} -9.28531i q^{89} +(-0.315880 + 0.972179i) q^{91} +(1.51493 - 0.492230i) q^{92} +(-0.108446 - 0.149264i) q^{94} +(-2.00999 - 6.18612i) q^{95} +(9.85618 + 7.16093i) q^{97} +7.19787 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.931921	−	0.677080i	−0.658967	−	0.478768i	0.207347	−	0.978268i	$-0.433517\pi$
$2$	−0.931921	−	0.677080i	−0.658967	−	0.478768i	−0.866314	+	0.499500i	$0.833517\pi$
$3$		0			0
$3$		0			0
$4$	−0.207995	−	0.640143i	−0.103998	−	0.320072i
$5$	−0.551104	−	0.758530i	−0.246461	−	0.339225i	0.667807	−	0.744335i	$-0.267233\pi$
$5$	−0.551104	−	0.758530i	−0.246461	−	0.339225i	−0.914268	+	0.405110i	$0.867233\pi$
$6$		0			0
$7$	−0.824408	+	0.267866i	−0.311597	+	0.101244i	−0.460641	−	0.887587i	$-0.652380\pi$
$7$	−0.824408	+	0.267866i	−0.311597	+	0.101244i	0.149044	+	0.988831i	$0.452380\pi$
$8$	−0.951517	+	2.92847i	−0.336412	+	1.03537i
$9$		0			0
$10$			1.08003i			0.341536i
$11$	1.59130	+	2.90994i	0.479794	+	0.877381i
$11$	1.59130	+	2.90994i	0.479794	+	0.877381i
$12$		0			0
$13$	0.693143	−	0.954029i	0.192243	−	0.264600i	−0.702004	−	0.712173i	$-0.747711\pi$
$13$	0.693143	−	0.954029i	0.192243	−	0.264600i	0.894248	+	0.447572i	$0.147711\pi$
$14$	0.949650	+	0.308560i	0.253805	+	0.0824661i
$15$		0			0
$16$	1.78047	−	1.29359i	0.445117	−	0.323397i
$17$	−2.52191	+	1.83228i	−0.611653	+	0.444392i	−0.849996	−	0.526789i	$-0.823396\pi$
$17$	−2.52191	+	1.83228i	−0.611653	+	0.444392i	0.238343	+	0.971181i	$0.423396\pi$
$18$		0			0
$19$	6.59786	+	2.14377i	1.51365	+	0.491816i	0.943965	−	0.330046i	$-0.107064\pi$
$19$	6.59786	+	2.14377i	1.51365	+	0.491816i	0.569688	+	0.821861i	$0.307064\pi$
$20$	−0.370941	+	0.510556i	−0.0829449	+	0.114164i
$21$		0			0
$22$	0.487302	−	3.78927i	0.103893	−	0.807876i
$23$			2.36655i			0.493459i	0.969084	+	0.246730i	$0.0793559\pi$
$23$			2.36655i			0.493459i	−0.969084	+	0.246730i	$0.920644\pi$
$24$		0			0
$25$	1.27343	−	3.91922i	0.254687	−	0.783845i
$26$	−1.29191	+	0.419767i	−0.253364	+	0.0823230i
$27$		0			0
$28$	0.342946	+	0.472024i	0.0648106	+	0.0892042i
$29$	1.11875	+	3.44315i	0.207746	+	0.639376i	0.999589	+	0.0286522i	$0.00912152\pi$
$29$	1.11875	+	3.44315i	0.207746	+	0.639376i	−0.791844	+	0.610724i	$0.790878\pi$
$30$		0			0
$31$	5.13662	+	3.73198i	0.922565	+	0.670283i	0.944161	−	0.329484i	$-0.106875\pi$
$31$	5.13662	+	3.73198i	0.922565	+	0.670283i	−0.0215963	+	0.999767i	$0.506875\pi$
$32$	3.62323			0.640503
$33$		0			0
$34$	3.59082			0.615820
$35$	0.657520	+	0.477716i	0.111141	+	0.0807487i
$36$		0			0
$37$	−2.46847	−	7.59716i	−0.405813	−	1.24897i	−0.920214	−	0.391415i	$-0.871986\pi$
$37$	−2.46847	−	7.59716i	−0.405813	−	1.24897i	0.514401	−	0.857550i	$-0.328014\pi$
$38$	−4.69717	−	6.46511i	−0.761982	−	1.04878i
$39$		0			0
$40$	2.74572	−	0.892138i	0.434136	−	0.141059i
$41$	1.11348	−	3.42695i	0.173897	−	0.535199i	−0.825685	−	0.564132i	$-0.809211\pi$
$41$	1.11348	−	3.42695i	0.173897	−	0.535199i	0.999581	+	0.0289327i	$0.00921085\pi$
$42$		0			0
$43$		−	3.83119i		−	0.584251i	−0.956380	−	0.292126i	$-0.905637\pi$
$43$		−	3.83119i		−	0.584251i	0.956380	−	0.292126i	$-0.0943625\pi$
$44$	1.53180	−	1.62391i	0.230927	−	0.244814i
$45$		0			0
$46$	1.60234	−	2.20543i	0.236252	−	0.325174i
$47$	0.152329	+	0.0494946i	0.0222194	+	0.00721952i	0.320106	−	0.947382i	$-0.396282\pi$
$47$	0.152329	+	0.0494946i	0.0222194	+	0.00721952i	−0.297886	+	0.954601i	$0.596282\pi$
$48$		0			0
$49$	−5.05522	+	3.67283i	−0.722175	+	0.524691i
$50$	−3.84037	+	2.79019i	−0.543110	+	0.394592i
$51$		0			0
$52$	−0.754886	−	0.245277i	−0.104684	−	0.0340138i
$53$	5.71174	−	7.86153i	0.784567	−	1.07986i	−0.210196	−	0.977659i	$-0.567410\pi$
$53$	5.71174	−	7.86153i	0.784567	−	1.07986i	0.994763	−	0.102205i	$-0.0325898\pi$
$54$		0			0
$55$	1.33031	−	2.81073i	0.179379	−	0.378999i
$56$		−	2.66913i		−	0.356678i
$57$		0			0
$58$	1.28870	−	3.96622i	0.169215	−	0.520790i
$59$	−8.27039	+	2.68721i	−1.07671	+	0.349845i	−0.793099	−	0.609093i	$-0.791534\pi$
$59$	−8.27039	+	2.68721i	−1.07671	+	0.349845i	−0.283614	+	0.958938i	$0.591534\pi$
$60$		0			0
$61$	7.97576	+	10.9777i	1.02119	+	1.40555i	0.911365	+	0.411598i	$0.135029\pi$
$61$	7.97576	+	10.9777i	1.02119	+	1.40555i	0.109826	+	0.993951i	$0.464971\pi$
$62$	−2.26008	−	6.95581i	−0.287030	−	0.883389i
$63$		0			0
$64$	−6.93750	−	5.04039i	−0.867188	−	0.630049i
$65$	−1.10565			−0.137140
$66$		0			0
$67$	6.64298			0.811569			0.405785	−	0.913969i	$-0.366998\pi$
$67$	6.64298			0.811569			0.405785	+	0.913969i	$0.366998\pi$
$68$	1.69746	+	1.23328i	0.205848	+	0.149557i
$69$		0			0
$70$	−0.289304	−	0.890387i	−0.0345785	−	0.106422i
$71$	6.53958	+	9.00097i	0.776106	+	1.06822i	0.995701	+	0.0926270i	$0.0295264\pi$
$71$	6.53958	+	9.00097i	0.776106	+	1.06822i	−0.219595	+	0.975591i	$0.570474\pi$
$72$		0			0
$73$	3.29787	−	1.07154i	0.385987	−	0.125415i	−0.109594	−	0.993976i	$-0.534955\pi$
$73$	3.29787	−	1.07154i	0.385987	−	0.125415i	0.495581	+	0.868562i	$0.334955\pi$
$74$	−2.84347	+	8.75130i	−0.330547	+	1.01732i
$75$		0			0
$76$		−	4.66947i		−	0.535625i
$77$	−2.09135	−	1.97273i	−0.238332	−	0.224813i
$78$		0			0
$79$	4.43649	−	6.10630i	0.499144	−	0.687012i	−0.482898	−	0.875677i	$-0.660416\pi$
$79$	4.43649	−	6.10630i	0.499144	−	0.687012i	0.982042	+	0.188664i	$0.0604158\pi$
$80$	−1.96245	−	0.637639i	−0.219409	−	0.0712902i
$81$		0			0
$82$	−3.35800	+	2.43973i	−0.370829	+	0.269423i
$83$	11.6734	−	8.48120i	1.28132	−	0.930933i	0.281727	−	0.959495i	$-0.409093\pi$
$83$	11.6734	−	8.48120i	1.28132	−	0.930933i	0.999592	+	0.0285622i	$0.00909286\pi$
$84$		0			0
$85$	2.77967	+	0.903171i	0.301498	+	0.0979626i
$86$	−2.59402	+	3.57037i	−0.279721	+	0.385003i
$87$		0			0
$88$	−10.0358	+	1.89120i	−1.06982	+	0.201603i
$89$		−	9.28531i		−	0.984241i	−0.870527	−	0.492120i	$-0.836222\pi$
$89$		−	9.28531i		−	0.984241i	0.870527	−	0.492120i	$-0.163778\pi$
$90$		0			0
$91$	−0.315880	+	0.972179i	−0.0331132	+	0.101912i
$92$	1.51493	−	0.492230i	0.157942	−	0.0513186i
$93$		0			0
$94$	−0.108446	−	0.149264i	−0.0111854	−	0.0153954i
$95$	−2.00999	−	6.18612i	−0.206221	−	0.634682i
$96$		0			0
$97$	9.85618	+	7.16093i	1.00074	+	0.727082i	0.962247	−	0.272176i	$-0.0877434\pi$
$97$	9.85618	+	7.16093i	1.00074	+	0.727082i	0.0384957	+	0.999259i	$0.487743\pi$
$98$	7.19787			0.727095
$99$		0			0
$100$	−2.77373			−0.277373
$101$	4.90121	+	3.56094i	0.487689	+	0.354327i	0.804295	−	0.594230i	$-0.202543\pi$
$101$	4.90121	+	3.56094i	0.487689	+	0.354327i	−0.316606	+	0.948557i	$0.602543\pi$
$102$		0			0
$103$	−1.23254	−	3.79337i	−0.121446	−	0.373772i	0.871791	−	0.489878i	$-0.162959\pi$
$103$	−1.23254	−	3.79337i	−0.121446	−	0.373772i	−0.993237	+	0.116106i	$0.962959\pi$
$104$	2.13431	+	2.93762i	0.209286	+	0.288058i
$105$		0			0
$106$	−10.6458	+	3.45902i	−1.03401	+	0.335970i
$107$	−1.90097	+	5.85057i	−0.183773	+	0.565596i	−0.999925	−	0.0122414i	$-0.996103\pi$
$107$	−1.90097	+	5.85057i	−0.183773	+	0.565596i	0.816152	+	0.577838i	$0.196103\pi$
$108$		0			0
$109$			16.9364i			1.62221i	0.584897	+	0.811107i	$0.301135\pi$
$109$			16.9364i			1.62221i	−0.584897	+	0.811107i	$0.698865\pi$
$110$	−3.14283	+	1.71865i	−0.299657	+	0.163867i
$111$		0			0
$112$	−1.12132	+	1.54337i	−0.105955	+	0.145835i
$113$	7.61414	+	2.47398i	0.716278	+	0.232733i	0.644409	−	0.764681i	$-0.277104\pi$
$113$	7.61414	+	2.47398i	0.716278	+	0.232733i	0.0718692	+	0.997414i	$0.477104\pi$
$114$		0			0
$115$	1.79510	−	1.30421i	0.167394	−	0.121619i
$116$	1.97141	−	1.43232i	0.183041	−	0.132987i
$117$		0			0
$118$	9.52681	+	3.09545i	0.877014	+	0.284959i
$119$	1.58828	−	2.18608i	0.145597	−	0.200397i
$120$		0			0
$121$	−5.93555	+	9.26117i	−0.539595	+	0.841925i
$122$		−	15.6306i		−	1.41512i
$123$		0			0
$124$	1.32061	−	4.06441i	0.118594	−	0.364995i
$125$	−8.13317	+	2.64263i	−0.727453	+	0.236364i
$126$		0			0
$127$	−3.73492	−	5.14068i	−0.331421	−	0.456161i	0.610490	−	0.792024i	$-0.290972\pi$
$127$	−3.73492	−	5.14068i	−0.331421	−	0.456161i	−0.941911	+	0.335862i	$0.890972\pi$
$128$	0.813175	+	2.50270i	0.0718752	+	0.221209i
$129$		0			0
$130$	1.03038	+	0.748616i	0.0903705	+	0.0656580i
$131$	17.3740			1.51797			0.758985	−	0.651109i	$-0.225696\pi$
$131$	17.3740			1.51797			0.758985	+	0.651109i	$0.225696\pi$
$132$		0			0
$133$	−6.01357			−0.521443
$134$	−6.19073	−	4.49783i	−0.534798	−	0.388553i
$135$		0			0
$136$	−2.96612	−	9.12878i	−0.254343	−	0.782787i
$137$	−10.4042	−	14.3201i	−0.888890	−	1.22345i	−0.973878	−	0.227070i	$-0.927085\pi$
$137$	−10.4042	−	14.3201i	−0.888890	−	1.22345i	0.0849882	−	0.996382i	$-0.472915\pi$
$138$		0			0
$139$	−5.87651	+	1.90939i	−0.498439	+	0.161953i	−0.547438	−	0.836846i	$-0.684397\pi$
$139$	−5.87651	+	1.90939i	−0.498439	+	0.161953i	0.0489992	+	0.998799i	$0.484397\pi$
$140$	0.169046	−	0.520269i	0.0142870	−	0.0439708i
$141$		0			0
$142$		−	12.8160i		−	1.07550i
$143$	3.87917	+	0.498862i	0.324392	+	0.0417170i
$144$		0			0
$145$	1.99518	−	2.74614i	0.165691	−	0.228054i
$146$	−3.79887	−	1.23433i	−0.314397	−	0.102154i
$147$		0			0
$148$	−4.34984	+	3.16034i	−0.357555	+	0.259779i
$149$	5.97193	−	4.33886i	0.489239	−	0.355453i	−0.315652	−	0.948875i	$-0.602223\pi$
$149$	5.97193	−	4.33886i	0.489239	−	0.355453i	0.804892	+	0.593422i	$0.202223\pi$
$150$		0			0
$151$	−12.8241	−	4.16680i	−1.04361	−	0.339090i	−0.263453	−	0.964672i	$-0.584861\pi$
$151$	−12.8241	−	4.16680i	−1.04361	−	0.339090i	−0.780158	+	0.625583i	$0.784861\pi$
$152$	−12.5560	+	17.2818i	−1.01842	+	1.40174i
$153$		0			0
$154$	0.613283	+	3.25444i	0.0494198	+	0.262250i
$155$		−	5.95299i		−	0.478156i
$156$		0			0
$157$	−0.906116	+	2.78874i	−0.0723160	+	0.222566i	−0.980681	−	0.195611i	$-0.937331\pi$
$157$	−0.906116	+	2.78874i	−0.0723160	+	0.222566i	0.908366	+	0.418177i	$0.137331\pi$
$158$	−8.26891	+	2.68673i	−0.657839	+	0.213745i
$159$		0			0
$160$	−1.99678	−	2.74833i	−0.157859	−	0.217275i
$161$	−0.633918	−	1.95100i	−0.0499598	−	0.153760i
$162$		0			0
$163$	17.8134	+	12.9422i	1.39525	+	1.01371i	0.995266	+	0.0971873i	$0.0309846\pi$
$163$	17.8134	+	12.9422i	1.39525	+	1.01371i	0.399985	+	0.916522i	$0.369015\pi$
$164$	−2.42534			−0.189387
$165$		0			0
$166$	−16.6211			−1.29005
$167$	−0.521597	−	0.378963i	−0.0403624	−	0.0293250i	0.567421	−	0.823428i	$-0.307941\pi$
$167$	−0.521597	−	0.378963i	−0.0403624	−	0.0293250i	−0.607784	+	0.794103i	$0.707941\pi$
$168$		0			0
$169$	3.58750	+	11.0412i	0.275961	+	0.849321i
$170$	−1.97892	−	2.72374i	−0.151776	−	0.208902i
$171$		0			0
$172$	−2.45251	+	0.796869i	−0.187002	+	0.0607607i
$173$	−4.16978	+	12.8333i	−0.317023	+	0.975695i	0.657891	+	0.753113i	$0.271449\pi$
$173$	−4.16978	+	12.8333i	−0.317023	+	0.975695i	−0.974914	+	0.222582i	$0.928551\pi$
$174$		0			0
$175$			3.57215i			0.270029i
$176$	6.59752	+	3.12259i	0.497307	+	0.235374i
$177$		0			0
$178$	−6.28690	+	8.65317i	−0.471223	+	0.648583i
$179$	−1.06341	−	0.345524i	−0.0794832	−	0.0258256i	0.269005	−	0.963139i	$-0.413305\pi$
$179$	−1.06341	−	0.345524i	−0.0794832	−	0.0258256i	−0.348489	+	0.937313i	$0.613305\pi$
$180$		0			0
$181$	−18.7897	+	13.6515i	−1.39663	+	1.01471i	−0.401530	+	0.915846i	$0.631521\pi$
$181$	−18.7897	+	13.6515i	−1.39663	+	1.01471i	−0.995101	+	0.0988656i	$0.968479\pi$
$182$	0.952618	−	0.692118i	0.0706128	−	0.0513032i
$183$		0			0
$184$	−6.93036	−	2.25181i	−0.510913	−	0.166006i
$185$	−4.40229	+	6.05923i	−0.323663	+	0.445484i
$186$		0			0
$187$	−9.34493	−	4.42293i	−0.683369	−	0.323436i
$188$		−	0.107807i		−	0.00786262i
$189$		0			0
$190$	−2.31534	+	7.12590i	−0.167973	+	0.516967i
$191$	−2.84491	+	0.924368i	−0.205851	+	0.0668849i	−0.410127	−	0.912028i	$-0.634516\pi$
$191$	−2.84491	+	0.924368i	−0.205851	+	0.0668849i	0.204277	+	0.978913i	$0.434516\pi$
$192$		0			0
$193$	5.81321	+	8.00120i	0.418444	+	0.575939i	0.965253	−	0.261319i	$-0.0841573\pi$
$193$	5.81321	+	8.00120i	0.418444	+	0.575939i	−0.546808	+	0.837258i	$0.684157\pi$
$194$	−4.33665	−	13.3468i	−0.311353	−	0.958247i
$195$		0			0
$196$	3.40260	+	2.47214i	0.243043	+	0.176581i
$197$	4.94568			0.352365			0.176183	−	0.984357i	$-0.443625\pi$
$197$	4.94568			0.352365			0.176183	+	0.984357i	$0.443625\pi$
$198$		0			0
$199$	−7.64868			−0.542200			−0.271100	−	0.962551i	$-0.587387\pi$
$199$	−7.64868			−0.542200			−0.271100	+	0.962551i	$0.587387\pi$
$200$	10.2656	+	7.45842i	0.725890	+	0.527390i
$201$		0			0
$202$	−2.15650	−	6.63703i	−0.151731	−	0.466980i
$203$	−1.84461	−	2.53888i	−0.129466	−	0.178195i
$204$		0			0
$205$	−3.21309	+	1.04400i	−0.224412	+	0.0729158i
$206$	−1.41978	+	4.36965i	−0.0989211	+	0.304448i
$207$		0			0
$208$		−	2.59526i		−	0.179949i
$209$	4.26089	+	22.6108i	0.294732	+	1.56402i
$210$		0			0
$211$	13.8159	−	19.0160i	0.951128	−	1.30912i	0.000104069	−	1.00000i	$-0.499967\pi$
$211$	13.8159	−	19.0160i	0.951128	−	1.30912i	0.951024	−	0.309116i	$-0.100033\pi$
$212$	−6.22052	−	2.02117i	−0.427227	−	0.138814i
$213$		0			0
$214$	5.73286	−	4.16516i	0.391890	−	0.284725i
$215$	−2.90607	+	2.11139i	−0.198193	+	0.143995i
$216$		0			0
$217$	−5.23434	−	1.70074i	−0.355330	−	0.115454i
$218$	11.4673	−	15.7834i	0.776664	−	1.06899i
$219$		0			0
$220$	−2.07597	−	0.266970i	−0.139962	−	0.0179991i
$221$			3.67601i			0.247275i
$222$		0			0
$223$	−6.45815	+	19.8761i	−0.432470	+	1.33100i	0.463188	+	0.886260i	$0.346705\pi$
$223$	−6.45815	+	19.8761i	−0.432470	+	1.33100i	−0.895658	+	0.444744i	$0.853295\pi$
$224$	−2.98702	+	0.970542i	−0.199579	+	0.0648470i
$225$		0			0
$226$	−5.42069	−	7.46094i	−0.360579	−	0.496294i
$227$	−3.67034	−	11.2961i	−0.243609	−	0.749752i	−0.995862	−	0.0908773i	$-0.971033\pi$
$227$	−3.67034	−	11.2961i	−0.243609	−	0.749752i	0.752253	−	0.658874i	$-0.228967\pi$
$228$		0			0
$229$	−7.92914	−	5.76086i	−0.523972	−	0.380688i	0.294126	−	0.955767i	$-0.404972\pi$
$229$	−7.92914	−	5.76086i	−0.523972	−	0.380688i	−0.818098	+	0.575078i	$0.804972\pi$
$230$	−2.55595			−0.168534
$231$		0			0
$232$	−11.1477			−0.731879
$233$	12.6222	+	9.17056i	0.826907	+	0.600783i	0.918683	−	0.394997i	$-0.129254\pi$
$233$	12.6222	+	9.17056i	0.826907	+	0.600783i	−0.0917755	+	0.995780i	$0.529254\pi$
$234$		0			0
$235$	−0.0464058	−	0.142823i	−0.00302718	−	0.00931671i
$236$	3.44040	+	4.73531i	0.223951	+	0.308242i
$237$		0			0
$238$	−2.96030	+	0.961860i	−0.191888	+	0.0623481i
$239$	−9.26252	+	28.5071i	−0.599143	+	1.84397i	−0.0662251	+	0.997805i	$0.521096\pi$
$239$	−9.26252	+	28.5071i	−0.599143	+	1.84397i	−0.532918	+	0.846167i	$0.678904\pi$
$240$		0			0
$241$			1.89778i			0.122247i	0.998130	+	0.0611235i	$0.0194684\pi$
$241$			1.89778i			0.122247i	−0.998130	+	0.0611235i	$0.980532\pi$
$242$	11.8020	−	4.61184i	0.758662	−	0.296460i
$243$		0			0
$244$	5.36837	−	7.38893i	0.343675	−	0.473028i
$245$	5.57191	+	1.81042i	0.355976	+	0.115664i
$246$		0			0
$247$	6.61848	−	4.80861i	0.421124	−	0.305964i
$248$	−15.8166	+	11.4914i	−1.00435	+	0.729705i
$249$		0			0
$250$	9.36874	+	3.04409i	0.592531	+	0.192525i
$251$	−1.59530	+	2.19574i	−0.100694	+	0.138594i	−0.856391	−	0.516328i	$-0.827299\pi$
$251$	−1.59530	+	2.19574i	−0.100694	+	0.138594i	0.755696	+	0.654922i	$0.227299\pi$
$252$		0			0
$253$	−6.88652	+	3.76588i	−0.432952	+	0.236759i
$254$			7.31955i			0.459269i
$255$		0			0
$256$	−4.36307	+	13.4281i	−0.272692	+	0.839259i
$257$	−8.10484	+	2.63342i	−0.505566	+	0.164268i	−0.550685	−	0.834713i	$-0.685633\pi$
$257$	−8.10484	+	2.63342i	−0.505566	+	0.164268i	0.0451186	+	0.998982i	$0.485633\pi$
$258$		0			0
$259$	4.07005	+	5.60194i	0.252900	+	0.348088i
$260$	0.229971	+	0.707777i	0.0142622	+	0.0438945i
$261$		0			0
$262$	−16.1911	−	11.7636i	−1.00029	−	0.726755i
$263$	−23.8526			−1.47081			−0.735407	−	0.677626i	$-0.763009\pi$
$263$	−23.8526			−1.47081			−0.735407	+	0.677626i	$0.763009\pi$
$264$		0			0
$265$	−9.11097			−0.559682
$266$	5.60417	+	4.07167i	0.343614	+	0.249650i
$267$		0			0
$268$	−1.38171	−	4.25246i	−0.0844012	−	0.259760i
$269$	−14.1414	−	19.4640i	−0.862219	−	1.18674i	−0.981036	−	0.193826i	$-0.937910\pi$
$269$	−14.1414	−	19.4640i	−0.862219	−	1.18674i	0.118817	−	0.992916i	$-0.462090\pi$
$270$		0			0
$271$	12.2868	−	3.99222i	0.746370	−	0.242510i	0.0889514	−	0.996036i	$-0.471648\pi$
$271$	12.2868	−	3.99222i	0.746370	−	0.242510i	0.657418	+	0.753526i	$0.271648\pi$
$272$	−2.11998	+	6.52463i	−0.128543	+	0.395614i
$273$		0			0
$274$			20.3897i			1.23179i
$275$	13.4311	−	2.53103i	0.809928	−	0.152627i
$276$		0			0
$277$	3.92290	−	5.39940i	0.235704	−	0.324419i	−0.674737	−	0.738059i	$-0.735743\pi$
$277$	3.92290	−	5.39940i	0.235704	−	0.324419i	0.910441	+	0.413640i	$0.135743\pi$
$278$	6.76925	+	2.19946i	0.405993	+	0.131915i
$279$		0			0
$280$	−2.02462	+	1.47097i	−0.120994	+	0.0879073i
$281$	0.496529	−	0.360749i	0.0296204	−	0.0215205i	−0.572877	−	0.819642i	$-0.694173\pi$
$281$	0.496529	−	0.360749i	0.0296204	−	0.0215205i	0.602497	+	0.798121i	$0.294173\pi$
$282$		0			0
$283$	17.9806	+	5.84225i	1.06883	+	0.347286i	0.790034	−	0.613063i	$-0.210063\pi$
$283$	17.9806	+	5.84225i	1.06883	+	0.347286i	0.278801	+	0.960349i	$0.410063\pi$
$284$	4.40171	−	6.05843i	0.261193	−	0.359502i
$285$		0			0
$286$	−3.27731	−	3.09141i	−0.193791	−	0.182799i
$287$			3.12347i			0.184372i
$288$		0			0
$289$	−2.25049	+	6.92628i	−0.132381	+	0.407428i
$290$	−3.71871	+	1.20828i	−0.218370	+	0.0709527i
$291$		0			0
$292$	−1.37188	−	1.88823i	−0.0802833	−	0.110501i
$293$	−0.649796	−	1.99987i	−0.0379615	−	0.116833i	0.930280	−	0.366850i	$-0.119564\pi$
$293$	−0.649796	−	1.99987i	−0.0379615	−	0.116833i	−0.968242	+	0.250017i	$0.919564\pi$
$294$		0			0
$295$	6.59618	+	4.79241i	0.384044	+	0.279025i
$296$	24.5968			1.42966
$297$		0			0
$298$	−8.50312			−0.492572
$299$	2.25776	+	1.64036i	0.130569	+	0.0948642i
$300$		0			0
$301$	1.02625	+	3.15846i	0.0591519	+	0.182051i
$302$	9.12979	+	12.5661i	0.525360	+	0.723096i
$303$		0			0
$304$	14.5204	−	4.71798i	0.832805	−	0.270595i
$305$	3.93143	−	12.0997i	0.225113	−	0.692827i
$306$		0			0
$307$		−	17.6110i		−	1.00511i	−0.864545	−	0.502556i	$-0.832393\pi$
$307$		−	17.6110i		−	1.00511i	0.864545	−	0.502556i	$-0.167607\pi$
$308$	−0.827835	+	1.74908i	−0.0471703	+	0.0996633i
$309$		0			0
$310$	−4.03065	+	5.54772i	−0.228926	+	0.315089i
$311$	−10.4661	−	3.40065i	−0.593480	−	0.192833i	−0.00314963	−	0.999995i	$-0.501003\pi$
$311$	−10.4661	−	3.40065i	−0.593480	−	0.192833i	−0.590330	+	0.807162i	$0.701003\pi$
$312$		0			0
$313$	3.15636	−	2.29323i	0.178408	−	0.129621i	−0.494997	−	0.868895i	$-0.664831\pi$
$313$	3.15636	−	2.29323i	0.178408	−	0.129621i	0.673405	+	0.739274i	$0.264831\pi$
$314$	2.73263	−	1.98537i	0.154211	−	0.112041i
$315$		0			0
$316$	−4.83167	−	1.56991i	−0.271803	−	0.0883141i
$317$	−12.6974	+	17.4765i	−0.713156	+	0.981576i	0.286567	+	0.958060i	$0.407486\pi$
$317$	−12.6974	+	17.4765i	−0.713156	+	0.981576i	−0.999723	+	0.0235153i	$0.992514\pi$
$318$		0			0
$319$	−8.23910	+	8.73456i	−0.461301	+	0.489041i
$320$			8.04009i			0.449455i
$321$		0			0
$322$	−0.730222	+	2.24739i	−0.0406937	+	0.125242i
$323$	−20.5672	+	6.68269i	−1.14439	+	0.371835i
$324$		0			0
$325$	−2.85638	−	3.93148i	−0.158444	−	0.218079i
$326$	−7.83776	−	24.1222i	−0.434094	−	1.33600i
$327$		0			0
$328$	8.97621	+	6.52160i	0.495629	+	0.360095i
$329$	−0.138839			−0.00765443
$330$		0			0
$331$	−6.85205			−0.376623			−0.188311	−	0.982109i	$-0.560301\pi$
$331$	−6.85205			−0.376623			−0.188311	+	0.982109i	$0.560301\pi$
$332$	−7.85719	−	5.70858i	−0.431219	−	0.313299i
$333$		0			0
$334$	0.229499	+	0.706326i	0.0125576	+	0.0386485i
$335$	−3.66098	−	5.03890i	−0.200020	−	0.275305i
$336$		0			0
$337$	0.702984	−	0.228413i	0.0382940	−	0.0124425i	−0.289807	−	0.957085i	$-0.593591\pi$
$337$	0.702984	−	0.228413i	0.0382940	−	0.0124425i	0.328101	+	0.944643i	$0.393591\pi$
$338$	4.13250	−	12.7185i	0.224778	−	0.691796i
$339$		0			0
$340$		−	1.96724i		−	0.106689i
$341$	−2.68594	+	20.8860i	−0.145452	+	1.13104i
$342$		0			0
$343$	6.75032	−	9.29102i	0.364483	−	0.501668i
$344$	11.2195	+	3.64544i	0.604916	+	0.196549i
$345$		0			0
$346$	12.5751	−	9.13631i	0.676039	−	0.491171i
$347$	9.63095	−	6.99730i	0.517017	−	0.375635i	−0.298462	−	0.954421i	$-0.596474\pi$
$347$	9.63095	−	6.99730i	0.517017	−	0.375635i	0.815479	+	0.578787i	$0.196474\pi$
$348$		0			0
$349$	9.68842	+	3.14796i	0.518609	+	0.168506i	0.556614	−	0.830771i	$-0.312100\pi$
$349$	9.68842	+	3.14796i	0.518609	+	0.168506i	−0.0380047	+	0.999278i	$0.512100\pi$
$350$	2.41863	−	3.32896i	0.129281	−	0.177940i
$351$		0			0
$352$	5.76564	+	10.5434i	0.307310	+	0.561965i
$353$		−	31.4901i		−	1.67605i	−0.545632	−	0.838025i	$-0.683710\pi$
$353$		−	31.4901i		−	1.67605i	0.545632	−	0.838025i	$-0.316290\pi$
$354$		0			0
$355$	3.22351	−	9.92094i	0.171086	−	0.526549i
$356$	−5.94393	+	1.93130i	−0.315028	+	0.102359i
$357$		0			0
$358$	0.757069	+	1.04202i	0.0400123	+	0.0550722i
$359$	−8.57599	−	26.3942i	−0.452624	−	1.39303i	−0.873903	−	0.486101i	$-0.838419\pi$
$359$	−8.57599	−	26.3942i	−0.452624	−	1.39303i	0.421279	−	0.906931i	$-0.361581\pi$
$360$		0			0
$361$	23.5646	+	17.1207i	1.24024	+	0.901090i
$362$	26.7537			1.40615
$363$		0			0
$364$	0.688035			0.0360629
$365$	−2.63027	−	1.91100i	−0.137675	−	0.100026i
$366$		0			0
$367$	−5.21807	−	16.0596i	−0.272381	−	0.838302i	−0.989901	−	0.141764i	$-0.954723\pi$
$367$	−5.21807	−	16.0596i	−0.272381	−	0.838302i	0.717520	−	0.696538i	$-0.245277\pi$
$368$	3.06133	+	4.21357i	0.159583	+	0.219647i
$369$		0			0
$370$	8.20517	−	2.66602i	0.426567	−	0.138600i
$371$	−2.60296	+	8.01109i	−0.135139	+	0.415915i
$372$		0			0
$373$		−	6.00920i		−	0.311145i	−0.987824	−	0.155572i	$-0.950278\pi$
$373$		−	6.00920i		−	0.311145i	0.987824	−	0.155572i	$-0.0497222\pi$
$374$	5.71406	+	10.4491i	0.295467	+	0.540309i
$375$		0			0
$376$	−0.289887	+	0.398995i	−0.0149498	+	0.0205766i
$377$	4.06031	+	1.31928i	0.209117	+	0.0679462i
$378$		0			0
$379$	−6.88315	+	5.00090i	−0.353563	+	0.256879i	−0.750362	−	0.661027i	$-0.770121\pi$
$379$	−6.88315	+	5.00090i	−0.353563	+	0.256879i	0.396799	+	0.917906i	$0.370121\pi$
$380$	−3.54193	+	2.57336i	−0.181697	+	0.132011i
$381$		0			0
$382$	3.27710	+	1.06480i	0.167671	+	0.0544797i
$383$	5.95093	−	8.19075i	0.304078	−	0.418528i	−0.629445	−	0.777045i	$-0.716718\pi$
$383$	5.95093	−	8.19075i	0.304078	−	0.418528i	0.933523	+	0.358517i	$0.116718\pi$
$384$		0			0
$385$	−0.343817	+	2.67353i	−0.0175226	+	0.136256i
$386$		−	11.3925i		−	0.579863i
$387$		0			0
$388$	2.53398	−	7.79880i	0.128644	−	0.395924i
$389$	−8.87507	+	2.88369i	−0.449984	+	0.146209i	−0.525237	−	0.850956i	$-0.676023\pi$
$389$	−8.87507	+	2.88369i	−0.449984	+	0.146209i	0.0752534	+	0.997164i	$0.476023\pi$
$390$		0			0
$391$	−4.33617	−	5.96822i	−0.219289	−	0.301826i
$392$	−5.94565	−	18.2988i	−0.300301	−	0.924230i
$393$		0			0
$394$	−4.60898	−	3.34862i	−0.232197	−	0.168701i
$395$	−7.07678			−0.356071
$396$		0			0
$397$	10.3328			0.518587			0.259294	−	0.965799i	$-0.416510\pi$
$397$	10.3328			0.518587			0.259294	+	0.965799i	$0.416510\pi$
$398$	7.12796	+	5.17877i	0.357292	+	0.259588i
$399$		0			0
$400$	−2.80255	−	8.62536i	−0.140127	−	0.431268i
$401$	−8.71867	−	12.0002i	−0.435390	−	0.599262i	0.533790	−	0.845617i	$-0.320767\pi$
$401$	−8.71867	−	12.0002i	−0.435390	−	0.599262i	−0.969180	+	0.246355i	$0.920767\pi$
$402$		0			0
$403$	7.12083	−	2.31370i	0.354714	−	0.115253i
$404$	1.26008	−	3.87814i	0.0626915	−	0.192944i
$405$		0			0
$406$			3.61498i			0.179409i
$407$	18.1792	−	19.2724i	0.901111	−	0.955299i
$408$		0			0
$409$	5.13485	−	7.06751i	0.253902	−	0.349466i	−0.662971	−	0.748645i	$-0.730705\pi$
$409$	5.13485	−	7.06751i	0.253902	−	0.349466i	0.916873	+	0.399179i	$0.130705\pi$
$410$	3.70121	+	1.20260i	0.182790	+	0.0593920i
$411$		0			0
$412$	−2.17194	+	1.57800i	−0.107004	+	0.0777427i
$413$	6.09836	−	4.43072i	0.300081	−	0.218021i
$414$		0			0
$415$	−12.8665	−	4.18058i	−0.631591	−	0.205216i
$416$	2.51142	−	3.45667i	0.123132	−	0.169477i
$417$		0			0
$418$	11.3385	−	23.9564i	0.554584	−	1.17175i
$419$		−	35.1723i		−	1.71828i	−0.511743	−	0.859139i	$-0.671000\pi$
$419$		−	35.1723i		−	1.71828i	0.511743	−	0.859139i	$-0.329000\pi$
$420$		0			0
$421$	−0.493004	+	1.51731i	−0.0240276	+	0.0739492i	−0.962351	−	0.271809i	$-0.912378\pi$
$421$	−0.493004	+	1.51731i	−0.0240276	+	0.0739492i	0.938324	+	0.345758i	$0.112378\pi$
$422$	−25.7507	+	8.36692i	−1.25353	+	0.407295i
$423$		0			0
$424$	17.5874	+	24.2070i	0.854121	+	1.17560i
$425$	3.96962	+	12.2172i	0.192555	+	0.592622i
$426$		0			0
$427$	−9.51583	−	6.91366i	−0.460503	−	0.334575i
$428$	4.14060			0.200143
$429$		0			0
$430$	4.13781			0.199543
$431$	23.8660	+	17.3397i	1.14959	+	0.835223i	0.988426	−	0.151706i	$-0.0484766\pi$
$431$	23.8660	+	17.3397i	1.14959	+	0.835223i	0.161160	+	0.986928i	$0.448477\pi$
$432$		0			0
$433$	3.54190	+	10.9008i	0.170213	+	0.523861i	0.999383	−	0.0351356i	$-0.0111863\pi$
$433$	3.54190	+	10.9008i	0.170213	+	0.523861i	−0.829170	+	0.558997i	$0.811186\pi$
$434$	3.72645	+	5.12903i	0.178876	+	0.246201i
$435$		0			0
$436$	10.8417	−	3.52269i	0.519225	−	0.168706i
$437$	−5.07334	+	15.6141i	−0.242691	+	0.746926i
$438$		0			0
$439$			3.03783i			0.144988i	0.997369	+	0.0724938i	$0.0230957\pi$
$439$			3.03783i			0.144988i	−0.997369	+	0.0724938i	$0.976904\pi$
$440$	6.96532	+	6.57023i	0.332059	+	0.313223i
$441$		0			0
$442$	2.48895	−	3.42575i	0.118387	−	0.162946i
$443$	−15.7419	−	5.11484i	−0.747918	−	0.243013i	−0.0898330	−	0.995957i	$-0.528633\pi$
$443$	−15.7419	−	5.11484i	−0.747918	−	0.243013i	−0.658085	+	0.752943i	$0.728633\pi$
$444$		0			0
$445$	−7.04319	+	5.11717i	−0.333879	+	0.242577i
$446$	19.4762	−	14.1503i	0.922225	−	0.670036i
$447$		0			0
$448$	7.06948	+	2.29701i	0.334002	+	0.108524i
$449$	0.152765	−	0.210263i	0.00720943	−	0.00992293i	−0.805397	−	0.592736i	$-0.798048\pi$
$449$	0.152765	−	0.210263i	0.00720943	−	0.00992293i	0.812606	+	0.582813i	$0.198048\pi$
$450$		0			0
$451$	11.7441	−	2.21312i	0.553009	−	0.104212i
$452$		−	5.38872i		−	0.253464i
$453$		0			0
$454$	−4.22793	+	13.0122i	−0.198427	+	0.610694i
$455$	0.911510	−	0.296168i	0.0427323	−	0.0138845i
$456$		0			0
$457$	−3.19749	−	4.40097i	−0.149572	−	0.205869i	0.727656	−	0.685943i	$-0.240610\pi$
$457$	−3.19749	−	4.40097i	−0.149572	−	0.205869i	−0.877228	+	0.480074i	$0.840610\pi$
$458$	3.48877	+	10.7373i	0.163019	+	0.501722i
$459$		0			0
$460$	−1.20826	−	0.877849i	−0.0563352	−	0.0409299i
$461$	29.3632			1.36758			0.683789	−	0.729679i	$-0.260331\pi$
$461$	29.3632			1.36758			0.683789	+	0.729679i	$0.260331\pi$
$462$		0			0
$463$	20.3827			0.947264			0.473632	−	0.880723i	$-0.342943\pi$
$463$	20.3827			0.947264			0.473632	+	0.880723i	$0.342943\pi$
$464$	6.44590	+	4.68322i	0.299244	+	0.217413i
$465$		0			0
$466$	−5.55368	−	17.0925i	−0.257269	−	0.791793i
$467$	−0.293731	−	0.404285i	−0.0135922	−	0.0187081i	0.802167	−	0.597100i	$-0.203680\pi$
$467$	−0.293731	−	0.404285i	−0.0135922	−	0.0187081i	−0.815759	+	0.578392i	$0.803680\pi$
$468$		0			0
$469$	−5.47653	+	1.77943i	−0.252882	+	0.0821665i
$470$	−0.0534557	+	0.164520i	−0.00246573	+	0.00758873i
$471$		0			0
$472$		−	26.7765i		−	1.23249i
$473$	11.1486	−	6.09657i	0.512611	−	0.280320i
$474$		0			0
$475$	16.8039	−	23.1285i	0.771014	−	1.06121i
$476$	−1.72976	−	0.562032i	−0.0792833	−	0.0257607i
$477$		0			0
$478$	27.9335	−	20.2949i	1.27765	−	0.928267i
$479$	8.69444	−	6.31688i	0.397259	−	0.288625i	−0.371165	−	0.928567i	$-0.621041\pi$
$479$	8.69444	−	6.31688i	0.397259	−	0.288625i	0.768424	+	0.639942i	$0.221041\pi$
$480$		0			0
$481$	−8.95891	−	2.91093i	−0.408491	−	0.132727i
$482$	1.28495	−	1.76858i	0.0585279	−	0.0805568i
$483$		0			0
$484$	7.16304	+	1.87332i	0.325593	+	0.0851509i
$485$		−	11.4226i		−	0.518675i
$486$		0			0
$487$	9.43244	−	29.0301i	0.427425	−	1.31548i	−0.473228	−	0.880940i	$-0.656911\pi$
$487$	9.43244	−	29.0301i	0.427425	−	1.31548i	0.900653	−	0.434539i	$-0.143089\pi$
$488$	−39.7369	+	12.9113i	−1.79880	+	0.584467i
$489$		0			0
$490$	−3.96678	−	5.45980i	−0.179201	−	0.246649i
$491$	7.74766	+	23.8448i	0.349647	+	1.07610i	0.959049	+	0.283241i	$0.0914097\pi$
$491$	7.74766	+	23.8448i	0.349647	+	1.07610i	−0.609402	+	0.792862i	$0.708590\pi$
$492$		0			0
$493$	−9.13017	−	6.63346i	−0.411202	−	0.298756i
$494$	−9.42371			−0.423993
$495$		0			0
$496$	13.9732			0.627417
$497$	−7.80234	−	5.66873i	−0.349983	−	0.254277i
$498$		0			0
$499$	1.53591	+	4.72705i	0.0687568	+	0.211612i	0.979531	−	0.201293i	$-0.0645143\pi$
$499$	1.53591	+	4.72705i	0.0687568	+	0.211612i	−0.910774	+	0.412905i	$0.864514\pi$
$500$	3.38332	+	4.65674i	0.151307	+	0.208256i
$501$		0			0
$502$	2.97339	−	0.966111i	0.132709	−	0.0431197i
$503$	−11.3085	+	34.8039i	−0.504219	+	1.55183i	0.297860	+	0.954610i	$0.403727\pi$
$503$	−11.3085	+	34.8039i	−0.504219	+	1.55183i	−0.802079	+	0.597218i	$0.796273\pi$
$504$		0			0
$505$		−	5.68017i		−	0.252764i
$506$	8.96749	+	1.15322i	0.398654	+	0.0512670i
$507$		0			0
$508$	−2.51392	+	3.46012i	−0.111537	+	0.153518i
$509$	−13.2688	−	4.31130i	−0.588131	−	0.191095i	−0.000190870	−	1.00000i	$-0.500061\pi$
$509$	−13.2688	−	4.31130i	−0.588131	−	0.191095i	−0.587940	+	0.808905i	$0.700061\pi$
$510$		0			0
$511$	−2.43176	+	1.76678i	−0.107575	+	0.0781576i
$512$	17.4158	−	12.6533i	0.769677	−	0.559203i
$513$		0			0
$514$	9.33611	+	3.03349i	0.411798	+	0.133801i
$515$	−2.19813	+	3.02546i	−0.0968610	+	0.133318i
$516$		0			0
$517$	0.0983737	+	0.522028i	0.00432647	+	0.0229588i
$518$		−	7.97631i		−	0.350459i
$519$		0			0
$520$	1.05205	−	3.23787i	0.0461354	−	0.141990i
$521$	6.74242	−	2.19075i	0.295391	−	0.0959783i	−0.157573	−	0.987507i	$-0.550367\pi$
$521$	6.74242	−	2.19075i	0.295391	−	0.0959783i	0.452963	+	0.891529i	$0.350367\pi$
$522$		0			0
$523$	7.47929	+	10.2944i	0.327047	+	0.450141i	0.940602	−	0.339510i	$-0.110261\pi$
$523$	7.47929	+	10.2944i	0.327047	+	0.450141i	−0.613556	+	0.789651i	$0.710261\pi$
$524$	−3.61370	−	11.1218i	−0.157865	−	0.485859i
$525$		0			0
$526$	22.2287	+	16.1501i	0.969218	+	0.704178i
$527$	−19.7921			−0.862158
$528$		0			0
$529$	17.3995			0.756498
$530$	8.49070	+	6.16886i	0.368813	+	0.267958i
$531$		0			0
$532$	1.25079	+	3.84955i	0.0542288	+	0.166899i
$533$	−2.49761	−	3.43766i	−0.108183	−	0.148902i
$534$		0			0
$535$	5.48547	−	1.78234i	0.237157	−	0.0770571i
$536$	−6.32091	+	19.4538i	−0.273022	+	0.840275i
$537$		0			0
$538$			27.7138i			1.19483i
$539$	−18.7321	−	8.86584i	−0.806849	−	0.381879i
$540$		0			0
$541$	2.30481	−	3.17230i	0.0990915	−	0.136388i	−0.756592	−	0.653887i	$-0.773137\pi$
$541$	2.30481	−	3.17230i	0.0990915	−	0.136388i	0.855684	+	0.517499i	$0.173137\pi$
$542$	−14.1534	−	4.59871i	−0.607940	−	0.197532i
$543$		0			0
$544$	−9.13747	+	6.63876i	−0.391766	+	0.284634i
$545$	12.8468	−	9.33374i	0.550296	−	0.399813i
$546$		0			0
$547$	−10.2734	−	3.33803i	−0.439259	−	0.142724i	0.0810349	−	0.996711i	$-0.474177\pi$
$547$	−10.2734	−	3.33803i	−0.439259	−	0.142724i	−0.520294	+	0.853987i	$0.674177\pi$
$548$	−7.00292	+	9.63869i	−0.299150	+	0.411745i
$549$		0			0
$550$	−14.2305	−	6.73523i	−0.606789	−	0.287191i
$551$			25.1157i			1.06997i
$552$		0			0
$553$	−2.02180	+	6.22247i	−0.0859758	+	0.264606i
$554$	−7.31166	+	2.37570i	−0.310643	+	0.100934i
$555$		0			0
$556$	2.44457	+	3.36466i	0.103673	+	0.142693i
$557$	−7.06108	−	21.7318i	−0.299188	−	0.920805i	−0.981783	−	0.190008i	$-0.939149\pi$
$557$	−7.06108	−	21.7318i	−0.299188	−	0.920805i	0.682595	−	0.730797i	$-0.260851\pi$
$558$		0			0
$559$	−3.65507	−	2.65556i	−0.154593	−	0.112318i
$560$	1.78866			0.0755847
$561$		0			0
$562$	−0.706982			−0.0298222
$563$	8.77304	+	6.37399i	0.369740	+	0.268632i	0.757103	−	0.653296i	$-0.226614\pi$
$563$	8.77304	+	6.37399i	0.369740	+	0.268632i	−0.387363	+	0.921927i	$0.626614\pi$
$564$		0			0
$565$	−2.31959	−	7.13898i	−0.0975861	−	0.300339i
$566$	−12.8008	−	17.6188i	−0.538058	−	0.740574i
$567$		0			0
$568$	−32.5816	+	10.5864i	−1.36709	+	0.444195i
$569$	5.19794	−	15.9976i	0.217909	−	0.670655i	−0.781025	−	0.624499i	$-0.785303\pi$
$569$	5.19794	−	15.9976i	0.217909	−	0.670655i	0.998934	−	0.0461553i	$-0.0146969\pi$
$570$		0			0
$571$		−	16.3097i		−	0.682541i	−0.939965	−	0.341271i	$-0.889143\pi$
$571$		−	16.3097i		−	0.682541i	0.939965	−	0.341271i	$-0.110857\pi$
$572$	−0.487505	−	2.58698i	−0.0203836	−	0.108167i
$573$		0			0
$574$	2.11484	−	2.91082i	0.0882716	−	0.121495i
$575$	9.27503	+	3.01364i	0.386795	+	0.125677i
$576$		0			0
$577$	6.51886	−	4.73623i	0.271384	−	0.197172i	−0.443767	−	0.896142i	$-0.646358\pi$
$577$	6.51886	−	4.73623i	0.271384	−	0.197172i	0.715150	+	0.698971i	$0.246358\pi$
$578$	6.78692	−	4.93099i	0.282299	−	0.205102i
$579$		0			0
$580$	−2.17291	−	0.706021i	−0.0902251	−	0.0293159i
$581$	−7.35179	+	10.1189i	−0.305004	+	0.419801i
$582$		0			0
$583$	31.9657	+	4.11080i	1.32388	+	0.170252i
$584$			10.6773i			0.441830i
$585$		0			0
$586$	−0.748511	+	2.30368i	−0.0309207	+	0.0951642i
$587$	−14.9678	+	4.86334i	−0.617789	+	0.200732i	−0.601158	−	0.799130i	$-0.705294\pi$
$587$	−14.9678	+	4.86334i	−0.617789	+	0.200732i	−0.0166304	+	0.999862i	$0.505294\pi$
$588$		0			0
$589$	25.8902	+	35.6348i	1.06679	+	1.46831i
$590$	−2.90228	−	8.93228i	−0.119485	−	0.367736i
$591$		0			0
$592$	−14.2226	−	10.3333i	−0.584546	−	0.424697i
$593$	−22.2880			−0.915258			−0.457629	−	0.889143i	$-0.651301\pi$
$593$	−22.2880			−0.915258			−0.457629	+	0.889143i	$0.651301\pi$
$594$		0			0
$595$	−2.53351			−0.103864
$596$	−4.01962	−	2.92043i	−0.164650	−	0.119625i
$597$		0			0
$598$	−0.993397	−	3.05736i	−0.0406230	−	0.125025i
$599$	−16.8142	−	23.1428i	−0.687010	−	0.945588i	0.312981	−	0.949759i	$-0.398672\pi$
$599$	−16.8142	−	23.1428i	−0.687010	−	0.945588i	−0.999991	+	0.00417130i	$0.998672\pi$
$600$		0			0
$601$	−6.78070	+	2.20318i	−0.276591	+	0.0898697i	−0.444028	−	0.896013i	$-0.646451\pi$
$601$	−6.78070	+	2.20318i	−0.276591	+	0.0898697i	0.167437	+	0.985883i	$0.446451\pi$
$602$	1.18215	−	3.63829i	0.0481809	−	0.148286i
$603$		0			0
$604$			9.07594i			0.369295i
$605$	10.2960	−	0.601583i	0.418591	−	0.0244578i
$606$		0			0
$607$	−2.68531	+	3.69601i	−0.108993	+	0.150017i	−0.860029	−	0.510245i	$-0.829555\pi$
$607$	−2.68531	+	3.69601i	−0.108993	+	0.150017i	0.751036	+	0.660262i	$0.229555\pi$
$608$	23.9056	+	7.76739i	0.969499	+	0.315009i
$609$		0			0
$610$	−11.8563	+	8.61407i	−0.480046	+	0.348774i
$611$	0.152805	−	0.111019i	0.00618182	−	0.00449135i
$612$		0			0
$613$	−37.1400	−	12.0675i	−1.50007	−	0.487402i	−0.560032	−	0.828471i	$-0.689211\pi$
$613$	−37.1400	−	12.0675i	−1.50007	−	0.487402i	−0.940038	+	0.341069i	$0.889211\pi$
$614$	−11.9240	+	16.4120i	−0.481215	+	0.662336i
$615$		0			0
$616$	7.76703	−	4.24738i	0.312942	−	0.171132i
$617$			31.1970i			1.25594i	0.778236	+	0.627972i	$0.216115\pi$
$617$			31.1970i			1.25594i	−0.778236	+	0.627972i	$0.783885\pi$
$618$		0			0
$619$	9.95813	−	30.6480i	0.400251	−	1.23185i	−0.524545	−	0.851383i	$-0.675765\pi$
$619$	9.95813	−	30.6480i	0.400251	−	1.23185i	0.924796	−	0.380463i	$-0.124235\pi$
$620$	−3.81077	+	1.23819i	−0.153044	+	0.0497270i
$621$		0			0
$622$	7.45109	+	10.2556i	0.298762	+	0.411210i
$623$	2.48722	+	7.65488i	0.0996484	+	0.306686i
$624$		0			0
$625$	−10.1827	−	7.39818i	−0.407309	−	0.295927i
$626$	−4.49418			−0.179623
$627$		0			0
$628$	1.97366			0.0787576
$629$	20.1453	+	14.6365i	0.803248	+	0.583594i
$630$		0			0
$631$	−0.555911	−	1.71092i	−0.0221305	−	0.0681105i	0.939381	−	0.342874i	$-0.111400\pi$
$631$	−0.555911	−	1.71092i	−0.0221305	−	0.0681105i	−0.961512	+	0.274764i	$0.911400\pi$
$632$	13.6607	+	18.8024i	0.543394	+	0.747918i
$633$		0			0
$634$	23.6659	−	7.68952i	0.939894	−	0.305390i
$635$	−1.84103	+	5.66610i	−0.0730590	+	0.224852i
$636$		0			0
$637$			7.36863i			0.291956i
$638$	13.5922	−	2.56138i	0.538120	−	0.101406i
$639$		0			0
$640$	1.45023	−	1.99606i	0.0573252	−	0.0789014i
$641$	7.32843	+	2.38115i	0.289456	+	0.0940499i	0.450146	−	0.892955i	$-0.351372\pi$
$641$	7.32843	+	2.38115i	0.289456	+	0.0940499i	−0.160690	+	0.987005i	$0.551372\pi$
$642$		0			0
$643$	−17.1627	+	12.4695i	−0.676832	+	0.491747i	−0.872305	−	0.488962i	$-0.837376\pi$
$643$	−17.1627	+	12.4695i	−0.676832	+	0.491747i	0.195473	+	0.980709i	$0.437376\pi$
$644$	−1.11707	+	0.811597i	−0.0440186	+	0.0319814i
$645$		0			0
$646$	23.6917	+	7.69791i	0.932138	+	0.302870i
$647$	29.4465	−	40.5296i	1.15766	−	1.59338i	0.438150	−	0.898902i	$-0.355634\pi$
$647$	29.4465	−	40.5296i	1.15766	−	1.59338i	0.719511	−	0.694482i	$-0.244366\pi$
$648$		0			0
$649$	−20.9803	−	19.7902i	−0.823548	−	0.776834i
$650$			5.59782i			0.219565i
$651$		0			0
$652$	4.57975	−	14.0950i	0.179357	−	0.552004i
$653$	−16.7546	+	5.44390i	−0.655659	+	0.213036i	−0.617908	−	0.786251i	$-0.712019\pi$
$653$	−16.7546	+	5.44390i	−0.655659	+	0.213036i	−0.0377511	+	0.999287i	$0.512019\pi$
$654$		0			0
$655$	−9.57486	−	13.1787i	−0.374121	−	0.514933i
$656$	−2.45053	−	7.54197i	−0.0956772	−	0.294464i
$657$		0			0
$658$	0.129387	+	0.0940050i	0.00504402	+	0.00366470i
$659$	21.1328			0.823218			0.411609	−	0.911360i	$-0.364967\pi$
$659$	21.1328			0.823218			0.411609	+	0.911360i	$0.364967\pi$
$660$		0			0
$661$	−11.0329			−0.429131			−0.214566	−	0.976710i	$-0.568834\pi$
$661$	−11.0329			−0.429131			−0.214566	+	0.976710i	$0.568834\pi$
$662$	6.38557	+	4.63939i	0.248182	+	0.180315i
$663$		0			0
$664$	13.7295	+	42.2551i	0.532809	+	1.63982i
$665$	3.31411	+	4.56147i	0.128515	+	0.176886i
$666$		0			0
$667$	−8.14837	+	2.64757i	−0.315506	+	0.102514i
$668$	−0.134101	+	0.412719i	−0.00518851	+	0.0159686i
$669$		0			0
$670$			7.17463i			0.277180i
$671$	−19.2527	+	40.6778i	−0.743240	+	1.57035i
$672$		0			0
$673$	−18.2818	+	25.1627i	−0.704712	+	0.969952i	0.295183	+	0.955441i	$0.404619\pi$
$673$	−18.2818	+	25.1627i	−0.704712	+	0.969952i	−0.999895	+	0.0145116i	$0.995381\pi$
$674$	−0.809780	−	0.263113i	−0.0311915	−	0.0101347i
$675$		0			0
$676$	6.32175	−	4.59302i	0.243144	−	0.176655i
$677$	−17.2782	+	12.5533i	−0.664053	+	0.482463i	−0.868029	−	0.496513i	$-0.834614\pi$
$677$	−17.2782	+	12.5533i	−0.664053	+	0.482463i	0.203976	+	0.978976i	$0.434614\pi$
$678$		0			0
$679$	−10.0437	−	3.26339i	−0.385441	−	0.125237i
$680$	−5.28981	+	7.28081i	−0.202855	+	0.279206i
$681$		0			0
$682$	16.6446	−	17.6455i	0.637353	−	0.675680i
$683$		−	17.2570i		−	0.660321i	−0.943925	−	0.330161i	$-0.892897\pi$
$683$		−	17.2570i		−	0.660321i	0.943925	−	0.330161i	$-0.107103\pi$
$684$		0			0
$685$	−5.12846	+	15.7838i	−0.195949	+	0.603068i
$686$	−12.5815	+	4.08799i	−0.480365	+	0.156080i
$687$		0			0
$688$	−4.95598	−	6.82132i	−0.188945	−	0.260060i
$689$	−3.54108	−	10.8983i	−0.134904	−	0.415193i
$690$		0			0
$691$	−16.9524	−	12.3166i	−0.644898	−	0.468546i	0.216631	−	0.976253i	$-0.430493\pi$
$691$	−16.9524	−	12.3166i	−0.644898	−	0.468546i	−0.861529	+	0.507708i	$0.830493\pi$
$692$	9.08243			0.345262
$693$		0			0
$694$	−13.7130			−0.520539
$695$	4.68690	+	3.40523i	0.177784	+	0.129168i
$696$		0			0
$697$	3.47101	+	10.6827i	0.131474	+	0.404635i
$698$	−6.89742	−	9.49349i	−0.261071	−	0.359334i
$699$		0			0
$700$	2.28669	−	0.742990i	0.0864286	−	0.0280824i
$701$	−15.1348	+	46.5802i	−0.571634	+	1.75931i	0.0757293	+	0.997128i	$0.475872\pi$
$701$	−15.1348	+	46.5802i	−0.571634	+	1.75931i	−0.647364	+	0.762181i	$0.724128\pi$
$702$		0			0
$703$		−	55.4168i		−	2.09008i
$704$	3.62762	−	28.2085i	0.136721	−	1.06315i
$705$		0			0
$706$	−21.3213	+	29.3463i	−0.802439	+	1.10446i
$707$	−4.99445	−	1.62280i	−0.187836	−	0.0610315i
$708$		0			0
$709$	−33.6162	+	24.4236i	−1.26248	+	0.917248i	−0.998877	−	0.0473823i	$-0.984912\pi$
$709$	−33.6162	+	24.4236i	−1.26248	+	0.917248i	−0.263607	+	0.964630i	$0.584912\pi$
$710$	−9.72133	+	7.06296i	−0.364835	+	0.265068i
$711$		0			0
$712$	27.1917	+	8.83513i	1.01905	+	0.331111i
$713$	−8.83189	+	12.1561i	−0.330757	+	0.455248i
$714$		0			0
$715$	−1.75942	−	3.21739i	−0.0657988	−	0.120324i
$716$			0.752603i			0.0281261i
$717$		0			0
$718$	−9.87884	+	30.4039i	−0.368675	+	1.13466i
$719$	27.4285	−	8.91207i	1.02291	−	0.332364i	0.250927	−	0.968006i	$-0.419264\pi$
$719$	27.4285	−	8.91207i	1.02291	−	0.332364i	0.771984	+	0.635642i	$0.219264\pi$
$720$		0			0
$721$	2.03223	+	2.79713i	0.0756843	+	0.104170i
$722$	−10.3683	−	31.9103i	−0.385868	−	1.18758i
$723$		0			0
$724$	12.6471	+	9.18867i	0.470027	+	0.341494i
$725$	14.9191			0.554082
$726$		0			0
$727$	18.3843			0.681838			0.340919	−	0.940093i	$-0.389262\pi$
$727$	18.3843			0.681838			0.340919	+	0.940093i	$0.389262\pi$
$728$	−2.54643	−	1.85009i	−0.0943770	−	0.0685689i
$729$		0			0
$730$	1.15730	+	3.56181i	0.0428336	+	0.131828i
$731$	7.01980	+	9.66193i	0.259637	+	0.357359i
$732$		0			0
$733$	−30.0104	+	9.75096i	−1.10846	+	0.360160i	−0.805352	−	0.592797i	$-0.798024\pi$
$733$	−30.0104	+	9.75096i	−1.10846	+	0.360160i	−0.303106	+	0.952957i	$0.598024\pi$
$734$	−6.01078	+	18.4993i	−0.221862	+	0.682821i
$735$		0			0
$736$			8.57455i			0.316062i
$737$	10.5710	+	19.3307i	0.389386	+	0.712055i
$738$		0			0
$739$	−26.9990	+	37.1609i	−0.993173	+	1.36698i	−0.0637507	+	0.997966i	$0.520306\pi$
$739$	−26.9990	+	37.1609i	−0.993173	+	1.36698i	−0.929422	+	0.369019i	$0.879694\pi$
$740$	4.79443	+	1.55781i	0.176247	+	0.0572661i
$741$		0			0
$742$	7.84990	−	5.70329i	0.288179	−	0.209374i
$743$	−17.5692	+	12.7648i	−0.644551	+	0.468294i	−0.861411	−	0.507909i	$-0.830419\pi$
$743$	−17.5692	+	12.7648i	−0.644551	+	0.468294i	0.216860	+	0.976203i	$0.430419\pi$
$744$		0			0
$745$	−6.58231	−	2.13872i	−0.241157	−	0.0783567i
$746$	−4.06871	+	5.60010i	−0.148966	+	0.205034i
$747$		0			0
$748$	−0.887605	+	6.90204i	−0.0324541	+	0.252364i
$749$		−	5.33246i		−	0.194844i
$750$		0			0
$751$	5.25583	−	16.1758i	0.191788	−	0.590262i	−0.808211	−	0.588893i	$-0.799564\pi$
$751$	5.25583	−	16.1758i	0.191788	−	0.590262i	0.999999	−	0.00136956i	$-0.000435943\pi$
$752$	0.335242	−	0.108927i	0.0122250	−	0.00397215i
$753$		0			0
$754$	−2.89064	−	3.97862i	−0.105271	−	0.144893i
$755$	3.90677	+	12.0238i	0.142182	+	0.437591i
$756$		0			0
$757$	−18.8951	−	13.7281i	−0.686756	−	0.498957i	0.188836	−	0.982009i	$-0.439528\pi$
$757$	−18.8951	−	13.7281i	−0.686756	−	0.498957i	−0.875592	+	0.483051i	$0.839528\pi$
$758$	9.80055			0.355972
$759$		0			0
$760$	20.0284			0.726506
$761$	16.4210	+	11.9305i	0.595259	+	0.432481i	0.844193	−	0.536039i	$-0.180080\pi$
$761$	16.4210	+	11.9305i	0.595259	+	0.432481i	−0.248934	+	0.968521i	$0.580080\pi$
$762$		0			0
$763$	−4.53670	−	13.9625i	−0.164239	−	0.505477i
$764$	1.18346	+	1.62889i	0.0428159	+	0.0589310i
$765$		0			0
$766$	−11.0916	+	3.60388i	−0.400755	+	0.130213i
$767$	−3.16888	+	9.75282i	−0.114422	+	0.352154i
$768$		0			0
$769$			23.5119i			0.847859i	0.905695	+	0.423930i	$0.139350\pi$
$769$			23.5119i			0.847859i	−0.905695	+	0.423930i	$0.860650\pi$
$770$	2.13061	−	2.25873i	0.0767817	−	0.0813989i
$771$		0			0
$772$	3.91280	−	5.38550i	0.140825	−	0.193828i
$773$	−12.8627	−	4.17933i	−0.462638	−	0.150320i	0.0684183	−	0.997657i	$-0.478205\pi$
$773$	−12.8627	−	4.17933i	−0.462638	−	0.150320i	−0.531056	+	0.847337i	$0.678205\pi$
$774$		0			0
$775$	21.1676	−	15.3792i	0.760362	−	0.552436i
$776$	−30.3489	+	22.0498i	−1.08946	+	0.791540i
$777$		0			0
$778$	10.2233	+	3.32177i	0.366525	+	0.119091i
$779$	14.6932	−	20.2235i	0.526439	−	0.724581i
$780$		0			0
$781$	−15.7859	+	33.3530i	−0.564863	+	1.19347i
$782$			8.49784i			0.303882i
$783$		0			0
$784$	−4.24954	+	13.0787i	−0.151769	+	0.467098i
$785$	2.61471	−	0.849570i	0.0933229	−	0.0303225i
$786$		0			0
$787$	−27.2391	−	37.4914i	−0.970968	−	1.33642i	−0.941557	−	0.336855i	$-0.890637\pi$
$787$	−27.2391	−	37.4914i	−0.970968	−	1.33642i	−0.0294111	−	0.999567i	$-0.509363\pi$
$788$	−1.02868	−	3.16595i	−0.0366451	−	0.112782i
$789$		0			0
$790$	6.59500	+	4.79155i	0.234639	+	0.170476i
$791$	−6.93985			−0.246753
$792$		0			0
$793$	16.0014			0.568226
$794$	−9.62933	−	6.99612i	−0.341732	−	0.248283i
$795$		0			0
$796$	1.59089	+	4.89625i	0.0563875	+	0.173543i
$797$	−28.6496	−	39.4328i	−1.01482	−	1.39678i	−0.915772	−	0.401699i	$-0.868420\pi$
$797$	−28.6496	−	39.4328i	−1.01482	−	1.39678i	−0.0990490	−	0.995083i	$-0.531580\pi$
$798$		0			0
$799$	−0.474847	+	0.154287i	−0.0167989	+	0.00545829i
$800$	4.61394	−	14.2003i	0.163127	−	0.502055i
$801$		0			0
$802$			17.0865i			0.603345i
$803$	8.36602	+	7.89147i	0.295231	+	0.278484i
$804$		0			0
$805$	−1.13054	+	1.55605i	−0.0398462	+	0.0548436i
$806$	−8.20261	−	2.66519i	−0.288924	−	0.0938773i
$807$		0			0
$808$	−15.0917	+	10.9648i	−0.530924	+	0.385739i
$809$	−4.11235	+	2.98780i	−0.144583	+	0.105045i	−0.657725	−	0.753258i	$-0.728481\pi$
$809$	−4.11235	+	2.98780i	−0.144583	+	0.105045i	0.513143	+	0.858303i	$0.328481\pi$
$810$		0			0
$811$	5.95516	+	1.93495i	0.209114	+	0.0679453i	0.411701	−	0.911319i	$-0.364935\pi$
$811$	5.95516	+	1.93495i	0.209114	+	0.0679453i	−0.202587	+	0.979264i	$0.564935\pi$
$812$	−1.24158	+	1.70889i	−0.0435709	+	0.0599702i
$813$		0			0
$814$	−29.9906	+	5.65158i	−1.05117	+	0.198088i
$815$		−	20.6445i		−	0.723144i
$816$		0			0
$817$	8.21321	−	25.2777i	0.287344	−	0.884353i
$818$	−9.57054	+	3.10966i	−0.334626	+	0.108727i
$819$		0			0
$820$	1.33661	+	1.83969i	0.0466766	+	0.0642448i
$821$	−10.6233	−	32.6953i	−0.370757	−	1.14107i	−0.946297	−	0.323299i	$-0.895208\pi$
$821$	−10.6233	−	32.6953i	−0.370757	−	1.14107i	0.575540	−	0.817774i	$-0.304792\pi$
$822$		0			0
$823$	−8.54662	−	6.20948i	−0.297916	−	0.216449i	0.428778	−	0.903410i	$-0.358944\pi$
$823$	−8.54662	−	6.20948i	−0.297916	−	0.216449i	−0.726694	+	0.686961i	$0.758944\pi$
$824$	12.2815			0.427848
$825$		0			0
$826$	−8.68314			−0.302125
$827$	−22.4299	−	16.2963i	−0.779965	−	0.566678i	0.125004	−	0.992156i	$-0.460106\pi$
$827$	−22.4299	−	16.2963i	−0.779965	−	0.566678i	−0.904969	+	0.425479i	$0.860106\pi$
$828$		0			0
$829$	7.49749	+	23.0749i	0.260399	+	0.801425i	0.992718	+	0.120463i	$0.0384379\pi$
$829$	7.49749	+	23.0749i	0.260399	+	0.801425i	−0.732319	+	0.680962i	$0.761562\pi$
$830$	9.15996	+	12.6076i	0.317947	+	0.437616i
$831$		0			0
$832$	−9.61736	+	3.12487i	−0.333422	+	0.108335i
$833$	6.01918	−	18.5251i	0.208552	−	0.641858i
$834$		0			0
$835$			0.604495i			0.0209194i
$836$	13.5879	−	7.43051i	0.469947	−	0.256990i
$837$		0			0
$838$	−23.8144	+	32.7778i	−0.822656	+	1.13229i
$839$	20.6658	+	6.71473i	0.713463	+	0.231818i	0.643187	−	0.765709i	$-0.277612\pi$
$839$	20.6658	+	6.71473i	0.713463	+	0.231818i	0.0702762	+	0.997528i	$0.477612\pi$
$840$		0			0
$841$	12.8578	−	9.34176i	0.443373	−	0.322130i
$842$	1.48678	−	1.08021i	0.0512379	−	0.0372265i
$843$		0			0
$844$	−15.0466	−	4.88894i	−0.517926	−	0.168284i
$845$	6.39798	−	8.80607i	0.220097	−	0.302938i
$846$		0			0
$847$	2.41255	−	9.22492i	0.0828963	−	0.316972i
$848$		−	21.3858i		−	0.734393i
$849$		0			0
$850$	4.57267	−	14.0732i	0.156841	−	0.482708i
$851$	17.9790	−	5.84174i	0.616313	−	0.200252i
$852$		0			0
$853$	−24.1254	−	33.2058i	−0.826039	−	1.13695i	−0.988647	−	0.150255i	$-0.951991\pi$
$853$	−24.1254	−	33.2058i	−0.826039	−	1.13695i	0.162608	−	0.986691i	$-0.448009\pi$
$854$	4.18690	+	12.8860i	0.143273	+	0.440948i
$855$		0			0
$856$	−15.3244	−	11.1338i	−0.523778	−	0.380547i
$857$	7.49320			0.255963			0.127981	−	0.991777i	$-0.459150\pi$
$857$	7.49320			0.255963			0.127981	+	0.991777i	$0.459150\pi$
$858$		0			0
$859$	1.63002			0.0556156			0.0278078	−	0.999613i	$-0.491147\pi$
$859$	1.63002			0.0556156			0.0278078	+	0.999613i	$0.491147\pi$
$860$	1.95604	+	1.42115i	0.0667004	+	0.0484607i
$861$		0			0
$862$	−10.5009	−	32.3184i	−0.357662	−	1.10077i
$863$	−11.2828	−	15.5294i	−0.384070	−	0.528626i	0.572587	−	0.819844i	$-0.305940\pi$
$863$	−11.2828	−	15.5294i	−0.384070	−	0.528626i	−0.956657	+	0.291217i	$0.905940\pi$
$864$		0			0
$865$	12.0324	−	3.90957i	0.409114	−	0.132929i
$866$	4.07998	−	12.5569i	0.138643	−	0.426700i
$867$		0			0
$868$			3.70448i			0.125738i
$869$	24.8288	+	3.19299i	0.842258	+	0.108315i
$870$		0			0
$871$	4.60454	−	6.33760i	0.156019	−	0.214741i
$872$	−49.5978	−	16.1153i	−1.67959	−	0.545733i
$873$		0			0
$874$	15.3000	−	11.1161i	0.517529	−	0.376007i
$875$	5.99718	−	4.35721i	0.202742	−	0.147300i
$876$		0			0
$877$	−53.4401	−	17.3637i	−1.80454	−	0.586332i	−0.804573	−	0.593854i	$-0.797606\pi$
$877$	−53.4401	−	17.3637i	−1.80454	−	0.586332i	−0.999972	+	0.00752149i	$0.997606\pi$
$878$	2.05685	−	2.83101i	0.0694154	−	0.0955421i
$879$		0			0
$880$	−1.26735	−	6.72529i	−0.0427223	−	0.226709i
$881$			16.2929i			0.548922i	0.961598	+	0.274461i	$0.0884994\pi$
$881$			16.2929i			0.548922i	−0.961598	+	0.274461i	$0.911501\pi$
$882$		0			0
$883$	−9.20073	+	28.3169i	−0.309629	+	0.952941i	0.668280	+	0.743910i	$0.267031\pi$
$883$	−9.20073	+	28.3169i	−0.309629	+	0.952941i	−0.977909	+	0.209031i	$0.932969\pi$
$884$	2.35317	−	0.764592i	0.0791457	−	0.0257160i
$885$		0			0
$886$	11.2070	+	15.4251i	0.376507	+	0.518217i
$887$	−0.349006	−	1.07413i	−0.0117185	−	0.0360657i	0.945026	−	0.326994i	$-0.106036\pi$
$887$	−0.349006	−	1.07413i	−0.0117185	−	0.0360657i	−0.956745	+	0.290929i	$0.906036\pi$
$888$		0			0
$889$	4.45611	+	3.23756i	0.149453	+	0.108584i
$890$	10.0284			0.336154
$891$		0			0
$892$	14.0668			0.470992
$893$	0.898937	+	0.653116i	0.0300818	+	0.0218557i
$894$		0			0
$895$	0.323961	+	0.997050i	0.0108288	+	0.0333277i
$896$	−1.34078	−	1.84542i	−0.0447922	−	0.0616511i
$897$		0			0
$898$	−0.284730	+	0.0925143i	−0.00950156	+	0.00308724i
$899$	−7.10316	+	21.8613i	−0.236904	+	0.729114i
$900$		0			0
$901$			30.2916i			1.00916i
$902$	−12.4430	−	5.88925i	−0.414308	−	0.196091i
$903$		0			0
$904$	−14.4900	+	19.9437i	−0.481929	+	0.663319i
$905$	20.7102	+	6.72916i	0.688431	+	0.223685i
$906$		0			0
$907$	−21.5733	+	15.6739i	−0.716330	+	0.520444i	−0.885209	−	0.465193i	$-0.845985\pi$
$907$	−21.5733	+	15.6739i	−0.716330	+	0.520444i	0.168880	+	0.985637i	$0.445985\pi$
$908$	−6.46774	+	4.69909i	−0.214639	+	0.155945i
$909$		0			0
$910$	−1.04998	−	0.341161i	−0.0348066	−	0.0113094i
$911$	2.30320	−	3.17008i	0.0763084	−	0.105029i	−0.769157	−	0.639060i	$-0.779323\pi$
$911$	2.30320	−	3.17008i	0.0763084	−	0.105029i	0.845465	+	0.534031i	$0.179323\pi$
$912$		0			0
$913$	43.2556	+	20.4727i	1.43155	+	0.677549i
$914$			6.26632i			0.207271i
$915$		0			0
$916$	−2.03855	+	6.27402i	−0.0673556	+	0.207299i
$917$	−14.3232	+	4.65390i	−0.472994	+	0.153685i
$918$		0			0
$919$	−7.16542	−	9.86236i	−0.236365	−	0.325329i	0.674313	−	0.738446i	$-0.264440\pi$
$919$	−7.16542	−	9.86236i	−0.236365	−	0.325329i	−0.910678	+	0.413117i	$0.864440\pi$
$920$	2.11129	+	6.49787i	0.0696070	+	0.214228i
$921$		0			0
$922$	−27.3641	−	19.8812i	−0.901190	−	0.654753i
$923$	13.1201			0.431852
$924$		0			0
$925$	−32.9184			−1.08235
$926$	−18.9950	−	13.8007i	−0.624216	−	0.453519i
$927$		0			0
$928$	4.05348	+	12.4753i	0.133062	+	0.409522i
$929$	2.77455	+	3.81885i	0.0910302	+	0.125292i	0.852103	−	0.523374i	$-0.175327\pi$
$929$	2.77455	+	3.81885i	0.0910302	+	0.125292i	−0.761073	+	0.648667i	$0.775327\pi$
$930$		0			0
$931$	−41.2274	+	13.3956i	−1.35117	+	0.439023i
$932$	3.24512	−	9.98744i	0.106297	−	0.327149i
$933$		0			0
$934$			0.575641i			0.0188356i
$935$	1.79511	+	9.52591i	0.0587064	+	0.311530i
$936$		0			0
$937$	−17.0091	+	23.4110i	−0.555662	+	0.764803i	−0.990767	−	0.135577i	$-0.956711\pi$
$937$	−17.0091	+	23.4110i	−0.555662	+	0.764803i	0.435105	+	0.900380i	$0.356711\pi$
$938$	6.30850	+	2.04976i	0.205980	+	0.0669270i
$939$		0			0
$940$	−0.0817747	+	0.0594128i	−0.00266720	+	0.00193783i
$941$	46.0903	−	33.4866i	1.50250	−	1.09163i	0.533129	−	0.846034i	$-0.321016\pi$
$941$	46.0903	−	33.4866i	1.50250	−	1.09163i	0.969372	−	0.245597i	$-0.0789841\pi$
$942$		0			0
$943$	8.11003	+	2.63511i	0.264099	+	0.0858110i
$944$	−11.2490	+	15.4830i	−0.366125	+	0.503928i
$945$		0			0
$946$	−14.5174	−	1.86695i	−0.472002	−	0.0606997i
$947$		−	0.938732i		−	0.0305047i	−0.999884	−	0.0152524i	$-0.995145\pi$
$947$		−	0.938732i		−	0.0305047i	0.999884	−	0.0152524i	$-0.00485516\pi$
$948$		0			0
$949$	1.26361	−	3.88900i	0.0410186	−	0.126242i
$950$	−31.3197	+	10.1764i	−1.01615	+	0.330166i
$951$		0			0
$952$	4.89059	+	6.73132i	0.158505	+	0.218163i
$953$	3.50554	+	10.7889i	0.113556	+	0.349488i	0.991643	−	0.129012i	$-0.0411806\pi$
$953$	3.50554	+	10.7889i	0.113556	+	0.349488i	−0.878087	+	0.478500i	$0.841181\pi$
$954$		0			0
$955$	2.26900	+	1.64853i	0.0734232	+	0.0533451i
$956$	20.1752			0.652512
$957$		0			0
$958$	−12.3796			−0.399965
$959$	12.4132	+	9.01870i	0.400843	+	0.291229i
$960$		0			0
$961$	2.87773	+	8.85675i	0.0928301	+	0.285702i
$962$	6.37807	+	8.77866i	0.205637	+	0.283035i
$963$		0			0
$964$	1.21485	−	0.394730i	0.0391278	−	0.0127134i
$965$	2.86547	−	8.81900i	0.0922426	−	0.283894i
$966$		0			0
$967$			17.3054i			0.556505i	0.960508	+	0.278253i	$0.0897553\pi$
$967$			17.3054i			0.556505i	−0.960508	+	0.278253i	$0.910245\pi$
$968$	−21.4733	−	26.1942i	−0.690177	−	0.841914i
$969$		0			0
$970$	−7.73403	+	10.6450i	−0.248325	+	0.341790i
$971$	23.6890	+	7.69701i	0.760215	+	0.247009i	0.663371	−	0.748291i	$-0.269125\pi$
$971$	23.6890	+	7.69701i	0.760215	+	0.247009i	0.0968441	+	0.995300i	$0.469125\pi$
$972$		0			0
$973$	4.33318	−	3.14824i	0.138915	−	0.100928i
$974$	−28.4460	+	20.6672i	−0.911468	+	0.662220i
$975$		0			0
$976$	28.4012	+	9.22811i	0.909100	+	0.295384i
$977$	−4.40208	+	6.05894i	−0.140835	+	0.193843i	−0.873608	−	0.486631i	$-0.838226\pi$
$977$	−4.40208	+	6.05894i	−0.140835	+	0.193843i	0.732773	+	0.680473i	$0.238226\pi$
$978$		0			0
$979$	27.0197	−	14.7757i	0.863554	−	0.472233i
$980$		−	3.94338i		−	0.125967i
$981$		0			0
$982$	8.92466	−	27.4673i	0.284797	−	0.876516i
$983$	5.06942	−	1.64715i	0.161689	−	0.0525361i	−0.227054	−	0.973882i	$-0.572909\pi$
$983$	5.06942	−	1.64715i	0.161689	−	0.0525361i	0.388743	+	0.921346i	$0.372909\pi$
$984$		0			0
$985$	−2.72559	−	3.75145i	−0.0868445	−	0.119531i
$986$	4.01722	+	12.3637i	0.127934	+	0.393741i
$987$		0			0
$988$	−4.45481	−	3.23661i	−0.141726	−	0.102970i
$989$	9.06669			0.288304
$990$		0			0
$991$	−23.5423			−0.747846			−0.373923	−	0.927460i	$-0.621988\pi$
$991$	−23.5423			−0.747846			−0.373923	+	0.927460i	$0.621988\pi$
$992$	18.6112	+	13.5218i	0.590905	+	0.429318i
$993$		0			0
$994$	3.43298	+	10.5656i	0.108887	+	0.335121i
$995$	4.21522	+	5.80175i	0.133631	+	0.183928i
$996$		0			0
$997$	−13.5097	+	4.38958i	−0.427857	+	0.139019i	−0.515026	−	0.857174i	$-0.672218\pi$
$997$	−13.5097	+	4.38958i	−0.427857	+	0.139019i	0.0871692	+	0.996194i	$0.472218\pi$
$998$	1.76924	−	5.44517i	0.0560044	−	0.172364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.7		80
3.2	odd	2	inner	891.2.k.a.161.14		80
9.2	odd	6		99.2.p.a.95.8	yes	80
9.4	even	3		99.2.p.a.29.8	✓	80
9.5	odd	6		297.2.t.a.62.3		80
9.7	even	3		297.2.t.a.260.3		80
11.8	odd	10	inner	891.2.k.a.404.14		80
33.8	even	10	inner	891.2.k.a.404.7		80
99.41	even	30		297.2.t.a.8.3		80
99.52	odd	30		297.2.t.a.206.3		80
99.74	even	30		99.2.p.a.41.8	yes	80
99.85	odd	30		99.2.p.a.74.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.8	✓	80	9.4	even	3
99.2.p.a.41.8	yes	80	99.74	even	30
99.2.p.a.74.8	yes	80	99.85	odd	30
99.2.p.a.95.8	yes	80	9.2	odd	6
297.2.t.a.8.3		80	99.41	even	30
297.2.t.a.62.3		80	9.5	odd	6
297.2.t.a.206.3		80	99.52	odd	30
297.2.t.a.260.3		80	9.7	even	3
891.2.k.a.161.7		80	1.1	even	1	trivial
891.2.k.a.161.14		80	3.2	odd	2	inner
891.2.k.a.404.7		80	33.8	even	10	inner
891.2.k.a.404.14		80	11.8	odd	10	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.931921 - 0.677080i) q^{2} +(-0.207995 - 0.640143i) q^{4} +(-0.551104 - 0.758530i) q^{5} +(-0.824408 + 0.267866i) q^{7} +(-0.951517 + 2.92847i) q^{8} +1.08003i q^{10} +(1.59130 + 2.90994i) q^{11} +(0.693143 - 0.954029i) q^{13} +(0.949650 + 0.308560i) q^{14} +(1.78047 - 1.29359i) q^{16} +(-2.52191 + 1.83228i) q^{17} +(6.59786 + 2.14377i) q^{19} +(-0.370941 + 0.510556i) q^{20} +(0.487302 - 3.78927i) q^{22} +2.36655i q^{23} +(1.27343 - 3.91922i) q^{25} +(-1.29191 + 0.419767i) q^{26} +(0.342946 + 0.472024i) q^{28} +(1.11875 + 3.44315i) q^{29} +(5.13662 + 3.73198i) q^{31} +3.62323 q^{32} +3.59082 q^{34} +(0.657520 + 0.477716i) q^{35} +(-2.46847 - 7.59716i) q^{37} +(-4.69717 - 6.46511i) q^{38} +(2.74572 - 0.892138i) q^{40} +(1.11348 - 3.42695i) q^{41} -3.83119i q^{43} +(1.53180 - 1.62391i) q^{44} +(1.60234 - 2.20543i) q^{46} +(0.152329 + 0.0494946i) q^{47} +(-5.05522 + 3.67283i) q^{49} +(-3.84037 + 2.79019i) q^{50} +(-0.754886 - 0.245277i) q^{52} +(5.71174 - 7.86153i) q^{53} +(1.33031 - 2.81073i) q^{55} -2.66913i q^{56} +(1.28870 - 3.96622i) q^{58} +(-8.27039 + 2.68721i) q^{59} +(7.97576 + 10.9777i) q^{61} +(-2.26008 - 6.95581i) q^{62} +(-6.93750 - 5.04039i) q^{64} -1.10565 q^{65} +6.64298 q^{67} +(1.69746 + 1.23328i) q^{68} +(-0.289304 - 0.890387i) q^{70} +(6.53958 + 9.00097i) q^{71} +(3.29787 - 1.07154i) q^{73} +(-2.84347 + 8.75130i) q^{74} -4.66947i q^{76} +(-2.09135 - 1.97273i) q^{77} +(4.43649 - 6.10630i) q^{79} +(-1.96245 - 0.637639i) q^{80} +(-3.35800 + 2.43973i) q^{82} +(11.6734 - 8.48120i) q^{83} +(2.77967 + 0.903171i) q^{85} +(-2.59402 + 3.57037i) q^{86} +(-10.0358 + 1.89120i) q^{88} -9.28531i q^{89} +(-0.315880 + 0.972179i) q^{91} +(1.51493 - 0.492230i) q^{92} +(-0.108446 - 0.149264i) q^{94} +(-2.00999 - 6.18612i) q^{95} +(9.85618 + 7.16093i) q^{97} +7.19787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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