LMFDB - Embedded newform 891.2.k.a.161.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

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

lf = mfeigenbasis(mf)

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")

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

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			161.14
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.14

$q$-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	0.866314	−	0.499500i	$-0.166483\pi$
$2$	0.931921	+	0.677080i	0.658967	+	0.478768i	−0.207347	+	0.978268i	$0.566483\pi$
$3$		0			0
$3$		0			0
$4$	−0.207995	−	0.640143i	−0.103998	−	0.320072i
$5$	0.551104	+	0.758530i	0.246461	+	0.339225i	0.914268	−	0.405110i	$-0.132767\pi$
$5$	0.551104	+	0.758530i	0.246461	+	0.339225i	−0.667807	+	0.744335i	$0.732767\pi$
$6$		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	−0.238343	−	0.971181i	$-0.576604\pi$
$17$	2.52191	−	1.83228i	0.611653	−	0.444392i	0.849996	+	0.526789i	$0.176604\pi$
$18$		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	$-0.920644\pi$
$23$		−	2.36655i		−	0.493459i	0.969084	−	0.246730i	$-0.0793559\pi$
$24$		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	$-0.990878\pi$
$29$	−1.11875	−	3.44315i	−0.207746	−	0.639376i	0.791844	−	0.610724i	$-0.209122\pi$
$30$		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	−0.999581	−	0.0289327i	$-0.990789\pi$
$41$	−1.11348	+	3.42695i	−0.173897	+	0.535199i	0.825685	+	0.564132i	$0.190789\pi$
$42$		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	0.297886	−	0.954601i	$-0.403718\pi$
$47$	−0.152329	−	0.0494946i	−0.0222194	−	0.00721952i	−0.320106	+	0.947382i	$0.603718\pi$
$48$		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	$0.432590\pi$
$53$	−5.71174	+	7.86153i	−0.784567	+	1.07986i	−0.994763	+	0.102205i	$0.967410\pi$
$54$		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	0.283614	−	0.958938i	$-0.408466\pi$
$59$	8.27039	−	2.68721i	1.07671	−	0.349845i	0.793099	+	0.609093i	$0.208466\pi$
$60$		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	$-0.970474\pi$
$71$	−6.53958	−	9.00097i	−0.776106	−	1.06822i	0.219595	−	0.975591i	$-0.429526\pi$
$72$		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	−0.999592	−	0.0285622i	$-0.990907\pi$
$83$	−11.6734	+	8.48120i	−1.28132	+	0.930933i	−0.281727	+	0.959495i	$0.590907\pi$
$84$		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	$0.163778\pi$
$89$			9.28531i			0.984241i	−0.870527	+	0.492120i	$0.836222\pi$
$90$		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	0.316606	−	0.948557i	$-0.397457\pi$
$101$	−4.90121	−	3.56094i	−0.487689	−	0.354327i	−0.804295	+	0.594230i	$0.797457\pi$
$102$		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	−0.816152	−	0.577838i	$-0.803897\pi$
$107$	1.90097	−	5.85057i	0.183773	−	0.565596i	0.999925	+	0.0122414i	$0.00389667\pi$
$108$		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	−0.0718692	−	0.997414i	$-0.522896\pi$
$113$	−7.61414	−	2.47398i	−0.716278	−	0.232733i	−0.644409	+	0.764681i	$0.722896\pi$
$114$		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	$-0.774304\pi$
$131$	−17.3740			−1.51797			−0.758985	+	0.651109i	$0.774304\pi$
$132$		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	$0.0729147\pi$
$137$	10.4042	+	14.3201i	0.888890	+	1.22345i	−0.0849882	+	0.996382i	$0.527085\pi$
$138$		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	−0.804892	−	0.593422i	$-0.797777\pi$
$149$	−5.97193	+	4.33886i	−0.489239	+	0.355453i	0.315652	+	0.948875i	$0.397777\pi$
$150$		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	0.607784	−	0.794103i	$-0.292059\pi$
$167$	0.521597	+	0.378963i	0.0403624	+	0.0293250i	−0.567421	+	0.823428i	$0.692059\pi$
$168$		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	$-0.728551\pi$
$173$	4.16978	−	12.8333i	0.317023	−	0.975695i	0.974914	−	0.222582i	$-0.0714487\pi$
$174$		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	0.348489	−	0.937313i	$-0.386695\pi$
$179$	1.06341	+	0.345524i	0.0794832	+	0.0258256i	−0.269005	+	0.963139i	$0.586695\pi$
$180$		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	−0.204277	−	0.978913i	$-0.565484\pi$
$191$	2.84491	−	0.924368i	0.205851	−	0.0668849i	0.410127	+	0.912028i	$0.365484\pi$
$192$		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	$-0.556375\pi$
$197$	−4.94568			−0.352365			−0.176183	+	0.984357i	$0.556375\pi$
$198$		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	$0.0289671\pi$
$227$	3.67034	+	11.2961i	0.243609	+	0.749752i	−0.752253	+	0.658874i	$0.771033\pi$
$228$		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	0.0917755	−	0.995780i	$-0.470746\pi$
$233$	−12.6222	−	9.17056i	−0.826907	−	0.600783i	−0.918683	+	0.394997i	$0.870746\pi$
$234$		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	$-0.478904\pi$
$239$	9.26252	−	28.5071i	0.599143	−	1.84397i	0.532918	−	0.846167i	$-0.321096\pi$
$240$		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	−0.755696	−	0.654922i	$-0.772701\pi$
$251$	1.59530	−	2.19574i	0.100694	−	0.138594i	0.856391	+	0.516328i	$0.172701\pi$
$252$		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	−0.0451186	−	0.998982i	$-0.514367\pi$
$257$	8.10484	−	2.63342i	0.505566	−	0.164268i	0.550685	+	0.834713i	$0.314367\pi$
$258$		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	$-0.236991\pi$
$263$	23.8526			1.47081			0.735407	+	0.677626i	$0.236991\pi$
$264$		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	$0.0620898\pi$
$269$	14.1414	+	19.4640i	0.862219	+	1.18674i	−0.118817	+	0.992916i	$0.537910\pi$
$270$		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	−0.602497	−	0.798121i	$-0.705827\pi$
$281$	−0.496529	+	0.360749i	−0.0296204	+	0.0215205i	0.572877	+	0.819642i	$0.305827\pi$
$282$		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	0.968242	−	0.250017i	$-0.0804361\pi$
$293$	0.649796	+	1.99987i	0.0379615	+	0.116833i	−0.930280	+	0.366850i	$0.880436\pi$
$294$		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	0.590330	−	0.807162i	$-0.298997\pi$
$311$	10.4661	+	3.40065i	0.593480	+	0.192833i	0.00314963	+	0.999995i	$0.498997\pi$
$312$		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	$-0.592514\pi$
$317$	12.6974	−	17.4765i	0.713156	−	0.981576i	0.999723	−	0.0235153i	$-0.00748586\pi$
$318$		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	−0.815479	−	0.578787i	$-0.803526\pi$
$347$	−9.63095	+	6.99730i	−0.517017	+	0.375635i	0.298462	+	0.954421i	$0.403526\pi$
$348$		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	$0.316290\pi$
$353$			31.4901i			1.67605i	−0.545632	+	0.838025i	$0.683710\pi$
$354$		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	$0.161581\pi$
$359$	8.57599	+	26.3942i	0.452624	+	1.39303i	−0.421279	+	0.906931i	$0.638419\pi$
$360$		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	−0.933523	−	0.358517i	$-0.883282\pi$
$383$	−5.95093	+	8.19075i	−0.304078	+	0.418528i	0.629445	+	0.777045i	$0.283282\pi$
$384$		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	−0.0752534	−	0.997164i	$-0.523977\pi$
$389$	8.87507	−	2.88369i	0.449984	−	0.146209i	0.525237	+	0.850956i	$0.323977\pi$
$390$		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	0.969180	−	0.246355i	$-0.0792328\pi$
$401$	8.71867	+	12.0002i	0.435390	+	0.599262i	−0.533790	+	0.845617i	$0.679233\pi$
$402$		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	$0.329000\pi$
$419$			35.1723i			1.71828i	−0.511743	+	0.859139i	$0.671000\pi$
$420$		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	−0.161160	−	0.986928i	$-0.551523\pi$
$431$	−23.8660	−	17.3397i	−1.14959	−	0.835223i	−0.988426	+	0.151706i	$0.951523\pi$
$432$		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	0.658085	−	0.752943i	$-0.271367\pi$
$443$	15.7419	+	5.11484i	0.747918	+	0.243013i	0.0898330	+	0.995957i	$0.471367\pi$
$444$		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	−0.812606	−	0.582813i	$-0.801952\pi$
$449$	−0.152765	+	0.210263i	−0.00720943	+	0.00992293i	0.805397	+	0.592736i	$0.201952\pi$
$450$		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	$-0.739669\pi$
$461$	−29.3632			−1.36758			−0.683789	+	0.729679i	$0.739669\pi$
$462$		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	0.815759	−	0.578392i	$-0.196320\pi$
$467$	0.293731	+	0.404285i	0.0135922	+	0.0187081i	−0.802167	+	0.597100i	$0.796320\pi$
$468$		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	−0.768424	−	0.639942i	$-0.778959\pi$
$479$	−8.69444	+	6.31688i	−0.397259	+	0.288625i	0.371165	+	0.928567i	$0.378959\pi$
$480$		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	$-0.908590\pi$
$491$	−7.74766	−	23.8448i	−0.349647	−	1.07610i	0.609402	−	0.792862i	$-0.291410\pi$
$492$		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	$-0.596273\pi$
$503$	11.3085	−	34.8039i	0.504219	−	1.55183i	0.802079	−	0.597218i	$-0.203727\pi$
$504$		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	0.587940	−	0.808905i	$-0.299939\pi$
$509$	13.2688	+	4.31130i	0.588131	+	0.191095i	0.000190870		1.00000i	$0.499939\pi$
$510$		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	−0.452963	−	0.891529i	$-0.649633\pi$
$521$	−6.74242	+	2.19075i	−0.295391	+	0.0959783i	0.157573	+	0.987507i	$0.449633\pi$
$522$		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	$0.0608514\pi$
$557$	7.06108	+	21.7318i	0.299188	+	0.920805i	−0.682595	+	0.730797i	$0.739149\pi$
$558$		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	0.387363	−	0.921927i	$-0.373386\pi$
$563$	−8.77304	−	6.37399i	−0.369740	−	0.268632i	−0.757103	+	0.653296i	$0.773386\pi$
$564$		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	$0.214697\pi$
$569$	−5.19794	+	15.9976i	−0.217909	+	0.670655i	−0.998934	+	0.0461553i	$0.985303\pi$
$570$		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	0.0166304	−	0.999862i	$-0.494706\pi$
$587$	14.9678	−	4.86334i	0.617789	−	0.200732i	0.601158	+	0.799130i	$0.294706\pi$
$588$		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	$-0.348699\pi$
$593$	22.2880			0.915258			0.457629	+	0.889143i	$0.348699\pi$
$594$		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	0.999991	−	0.00417130i	$-0.00132777\pi$
$599$	16.8142	+	23.1428i	0.687010	+	0.945588i	−0.312981	+	0.949759i	$0.601328\pi$
$600$		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	$-0.783885\pi$
$617$		−	31.1970i		−	1.25594i	0.778236	−	0.627972i	$-0.216115\pi$
$618$		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	0.160690	−	0.987005i	$-0.448628\pi$
$641$	−7.32843	−	2.38115i	−0.289456	−	0.0940499i	−0.450146	+	0.892955i	$0.648628\pi$
$642$		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	$0.644366\pi$
$647$	−29.4465	+	40.5296i	−1.15766	+	1.59338i	−0.719511	+	0.694482i	$0.755634\pi$
$648$		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	0.0377511	−	0.999287i	$-0.487981\pi$
$653$	16.7546	−	5.44390i	0.655659	−	0.213036i	0.617908	+	0.786251i	$0.287981\pi$
$654$		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	$-0.635033\pi$
$659$	−21.1328			−0.823218			−0.411609	+	0.911360i	$0.635033\pi$
$660$		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	−0.203976	−	0.978976i	$-0.565386\pi$
$677$	17.2782	−	12.5533i	0.664053	−	0.482463i	0.868029	+	0.496513i	$0.165386\pi$
$678$		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	$0.107103\pi$
$683$			17.2570i			0.660321i	−0.943925	+	0.330161i	$0.892897\pi$
$684$		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	$-0.524128\pi$
$701$	15.1348	−	46.5802i	0.571634	−	1.75931i	0.647364	−	0.762181i	$-0.275872\pi$
$702$		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	−0.771984	−	0.635642i	$-0.780736\pi$
$719$	−27.4285	+	8.91207i	−1.02291	+	0.332364i	−0.250927	+	0.968006i	$0.580736\pi$
$720$		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	−0.216860	−	0.976203i	$-0.569581\pi$
$743$	17.5692	−	12.7648i	0.644551	−	0.468294i	0.861411	+	0.507909i	$0.169581\pi$
$744$		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	0.248934	−	0.968521i	$-0.419920\pi$
$761$	−16.4210	−	11.9305i	−0.595259	−	0.432481i	−0.844193	+	0.536039i	$0.819920\pi$
$762$		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	0.531056	−	0.847337i	$-0.321795\pi$
$773$	12.8627	+	4.17933i	0.462638	+	0.150320i	−0.0684183	+	0.997657i	$0.521795\pi$
$774$		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	$0.131580\pi$
$797$	28.6496	+	39.4328i	1.01482	+	1.39678i	0.0990490	+	0.995083i	$0.468420\pi$
$798$		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	−0.513143	−	0.858303i	$-0.671519\pi$
$809$	4.11235	−	2.98780i	0.144583	−	0.105045i	0.657725	+	0.753258i	$0.271519\pi$
$810$		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	$0.104792\pi$
$821$	10.6233	+	32.6953i	0.370757	+	1.14107i	−0.575540	+	0.817774i	$0.695208\pi$
$822$		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	0.904969	−	0.425479i	$-0.139894\pi$
$827$	22.4299	+	16.2963i	0.779965	+	0.566678i	−0.125004	+	0.992156i	$0.539894\pi$
$828$		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	−0.0702762	−	0.997528i	$-0.522388\pi$
$839$	−20.6658	−	6.71473i	−0.713463	−	0.231818i	−0.643187	+	0.765709i	$0.722388\pi$
$840$		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	$-0.540850\pi$
$857$	−7.49320			−0.255963			−0.127981	+	0.991777i	$0.540850\pi$
$858$		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	0.956657	−	0.291217i	$-0.0940603\pi$
$863$	11.2828	+	15.5294i	0.384070	+	0.528626i	−0.572587	+	0.819844i	$0.694060\pi$
$864$		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	$-0.911501\pi$
$881$		−	16.2929i		−	0.548922i	0.961598	−	0.274461i	$-0.0884994\pi$
$882$		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	0.956745	−	0.290929i	$-0.0939642\pi$
$887$	0.349006	+	1.07413i	0.0117185	+	0.0360657i	−0.945026	+	0.326994i	$0.893964\pi$
$888$		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	−0.845465	−	0.534031i	$-0.820677\pi$
$911$	−2.30320	+	3.17008i	−0.0763084	+	0.105029i	0.769157	+	0.639060i	$0.220677\pi$
$912$		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	0.761073	−	0.648667i	$-0.224673\pi$
$929$	−2.77455	−	3.81885i	−0.0910302	−	0.125292i	−0.852103	+	0.523374i	$0.824673\pi$
$930$		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	$0.678984\pi$
$941$	−46.0903	+	33.4866i	−1.50250	+	1.09163i	−0.969372	+	0.245597i	$0.921016\pi$
$942$		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	$0.00485516\pi$
$947$			0.938732i			0.0305047i	−0.999884	+	0.0152524i	$0.995145\pi$
$948$		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	0.878087	−	0.478500i	$-0.158819\pi$
$953$	−3.50554	−	10.7889i	−0.113556	−	0.349488i	−0.991643	+	0.129012i	$0.958819\pi$
$954$		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	−0.0968441	−	0.995300i	$-0.530875\pi$
$971$	−23.6890	−	7.69701i	−0.760215	−	0.247009i	−0.663371	+	0.748291i	$0.730875\pi$
$972$		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	−0.732773	−	0.680473i	$-0.761774\pi$
$977$	4.40208	−	6.05894i	0.140835	−	0.193843i	0.873608	+	0.486631i	$0.161774\pi$
$978$		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	−0.388743	−	0.921346i	$-0.627091\pi$
$983$	−5.06942	+	1.64715i	−0.161689	+	0.0525361i	0.227054	+	0.973882i	$0.427091\pi$
$984$		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.161.14		80
3.2	odd	2	inner	891.2.k.a.161.7		80
9.2	odd	6		297.2.t.a.260.3		80
9.4	even	3		297.2.t.a.62.3		80
9.5	odd	6		99.2.p.a.29.8	✓	80
9.7	even	3		99.2.p.a.95.8	yes	80
11.8	odd	10	inner	891.2.k.a.404.7		80
33.8	even	10	inner	891.2.k.a.404.14		80
99.41	even	30		99.2.p.a.74.8	yes	80
99.52	odd	30		99.2.p.a.41.8	yes	80
99.74	even	30		297.2.t.a.206.3		80
99.85	odd	30		297.2.t.a.8.3		80

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