LMFDB - Embedded newform 891.2.k.a.404.14

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			404.14
Character	$\chi$	$=$	891.404
Dual form			891.2.k.a.161.14

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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	$-0.566483\pi$
$2$	0.931921	−	0.677080i	0.658967	−	0.478768i	0.866314	+	0.499500i	$0.166483\pi$
$3$		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	$-0.732767\pi$
$5$	0.551104	−	0.758530i	0.246461	−	0.339225i	0.914268	+	0.405110i	$0.132767\pi$
$6$		0			0
$7$	−0.824408	−	0.267866i	−0.311597	−	0.101244i	0.149044	−	0.988831i	$-0.452380\pi$
$7$	−0.824408	−	0.267866i	−0.311597	−	0.101244i	−0.460641	+	0.887587i	$0.652380\pi$
$8$	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	0.894248	−	0.447572i	$-0.147711\pi$
$13$	0.693143	+	0.954029i	0.192243	+	0.264600i	−0.702004	+	0.712173i	$0.747711\pi$
$14$	−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	$-0.176604\pi$
$17$	2.52191	+	1.83228i	0.611653	+	0.444392i	−0.238343	+	0.971181i	$0.576604\pi$
$18$		0			0
$19$	6.59786	−	2.14377i	1.51365	−	0.491816i	0.569688	−	0.821861i	$-0.307064\pi$
$19$	6.59786	−	2.14377i	1.51365	−	0.491816i	0.943965	+	0.330046i	$0.107064\pi$
$20$	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	0.791844	+	0.610724i	$0.209122\pi$
$29$	−1.11875	+	3.44315i	−0.207746	+	0.639376i	−0.999589	+	0.0286522i	$0.990878\pi$
$30$		0			0
$31$	5.13662	−	3.73198i	0.922565	−	0.670283i	−0.0215963	−	0.999767i	$-0.506875\pi$
$31$	5.13662	−	3.73198i	0.922565	−	0.670283i	0.944161	+	0.329484i	$0.106875\pi$
$32$	−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	0.514401	+	0.857550i	$0.328014\pi$
$37$	−2.46847	+	7.59716i	−0.405813	+	1.24897i	−0.920214	+	0.391415i	$0.871986\pi$
$38$	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	$-0.190789\pi$
$41$	−1.11348	−	3.42695i	−0.173897	−	0.535199i	−0.999581	+	0.0289327i	$0.990789\pi$
$42$		0			0
$43$			3.83119i			0.584251i	0.956380	+	0.292126i	$0.0943625\pi$
$43$			3.83119i			0.584251i	−0.956380	+	0.292126i	$0.905637\pi$
$44$	−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	$-0.603718\pi$
$47$	−0.152329	+	0.0494946i	−0.0222194	+	0.00721952i	0.297886	+	0.954601i	$0.403718\pi$
$48$		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	−0.994763	−	0.102205i	$-0.967410\pi$
$53$	−5.71174	−	7.86153i	−0.784567	−	1.07986i	0.210196	−	0.977659i	$-0.432590\pi$
$54$		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	$-0.208466\pi$
$59$	8.27039	+	2.68721i	1.07671	+	0.349845i	0.283614	+	0.958938i	$0.408466\pi$
$60$		0			0
$61$	7.97576	−	10.9777i	1.02119	−	1.40555i	0.109826	−	0.993951i	$-0.464971\pi$
$61$	7.97576	−	10.9777i	1.02119	−	1.40555i	0.911365	−	0.411598i	$-0.135029\pi$
$62$	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	0.219595	+	0.975591i	$0.429526\pi$
$71$	−6.53958	+	9.00097i	−0.776106	+	1.06822i	−0.995701	+	0.0926270i	$0.970474\pi$
$72$		0			0
$73$	3.29787	+	1.07154i	0.385987	+	0.125415i	0.495581	−	0.868562i	$-0.334955\pi$
$73$	3.29787	+	1.07154i	0.385987	+	0.125415i	−0.109594	+	0.993976i	$0.534955\pi$
$74$	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	0.982042	−	0.188664i	$-0.0604158\pi$
$79$	4.43649	+	6.10630i	0.499144	+	0.687012i	−0.482898	+	0.875677i	$0.660416\pi$
$80$	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	$-0.590907\pi$
$83$	−11.6734	−	8.48120i	−1.28132	−	0.930933i	−0.999592	+	0.0285622i	$0.990907\pi$
$84$		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	0.0384957	−	0.999259i	$-0.487743\pi$
$97$	9.85618	−	7.16093i	1.00074	−	0.727082i	0.962247	+	0.272176i	$0.0877434\pi$
$98$	−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	$-0.797457\pi$
$101$	−4.90121	+	3.56094i	−0.487689	+	0.354327i	0.316606	+	0.948557i	$0.397457\pi$
$102$		0			0
$103$	−1.23254	+	3.79337i	−0.121446	+	0.373772i	−0.993237	−	0.116106i	$-0.962959\pi$
$103$	−1.23254	+	3.79337i	−0.121446	+	0.373772i	0.871791	+	0.489878i	$0.162959\pi$
$104$	−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	$-0.00389667\pi$
$107$	1.90097	+	5.85057i	0.183773	+	0.565596i	−0.816152	+	0.577838i	$0.803897\pi$
$108$		0			0
$109$		−	16.9364i		−	1.62221i	−0.584897	−	0.811107i	$-0.698865\pi$
$109$		−	16.9364i		−	1.62221i	0.584897	−	0.811107i	$-0.301135\pi$
$110$	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	$-0.722896\pi$
$113$	−7.61414	+	2.47398i	−0.716278	+	0.232733i	−0.0718692	+	0.997414i	$0.522896\pi$
$114$		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	−0.941911	−	0.335862i	$-0.890972\pi$
$127$	−3.73492	+	5.14068i	−0.331421	+	0.456161i	0.610490	+	0.792024i	$0.290972\pi$
$128$	−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	−0.0849882	−	0.996382i	$-0.527085\pi$
$137$	10.4042	−	14.3201i	0.888890	−	1.22345i	0.973878	−	0.227070i	$-0.0729147\pi$
$138$		0			0
$139$	−5.87651	−	1.90939i	−0.498439	−	0.161953i	0.0489992	−	0.998799i	$-0.484397\pi$
$139$	−5.87651	−	1.90939i	−0.498439	−	0.161953i	−0.547438	+	0.836846i	$0.684397\pi$
$140$	−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	$-0.397777\pi$
$149$	−5.97193	−	4.33886i	−0.489239	−	0.355453i	−0.804892	+	0.593422i	$0.797777\pi$
$150$		0			0
$151$	−12.8241	+	4.16680i	−1.04361	+	0.339090i	−0.780158	−	0.625583i	$-0.784861\pi$
$151$	−12.8241	+	4.16680i	−1.04361	+	0.339090i	−0.263453	+	0.964672i	$0.584861\pi$
$152$	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	0.908366	−	0.418177i	$-0.137331\pi$
$157$	−0.906116	−	2.78874i	−0.0723160	−	0.222566i	−0.980681	+	0.195611i	$0.937331\pi$
$158$	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	0.399985	−	0.916522i	$-0.369015\pi$
$163$	17.8134	−	12.9422i	1.39525	−	1.01371i	0.995266	−	0.0971873i	$-0.0309846\pi$
$164$	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	$-0.692059\pi$
$167$	0.521597	−	0.378963i	0.0403624	−	0.0293250i	0.607784	+	0.794103i	$0.292059\pi$
$168$		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	0.974914	+	0.222582i	$0.0714487\pi$
$173$	4.16978	+	12.8333i	0.317023	+	0.975695i	−0.657891	+	0.753113i	$0.728551\pi$
$174$		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	$-0.586695\pi$
$179$	1.06341	−	0.345524i	0.0794832	−	0.0258256i	0.348489	+	0.937313i	$0.386695\pi$
$180$		0			0
$181$	−18.7897	−	13.6515i	−1.39663	−	1.01471i	−0.995101	−	0.0988656i	$-0.968479\pi$
$181$	−18.7897	−	13.6515i	−1.39663	−	1.01471i	−0.401530	−	0.915846i	$-0.631521\pi$
$182$	−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	$-0.365484\pi$
$191$	2.84491	+	0.924368i	0.205851	+	0.0668849i	−0.204277	+	0.978913i	$0.565484\pi$
$192$		0			0
$193$	5.81321	−	8.00120i	0.418444	−	0.575939i	−0.546808	−	0.837258i	$-0.684157\pi$
$193$	5.81321	−	8.00120i	0.418444	−	0.575939i	0.965253	+	0.261319i	$0.0841573\pi$
$194$	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	0.951024	+	0.309116i	$0.100033\pi$
$211$	13.8159	+	19.0160i	0.951128	+	1.30912i	0.000104069		1.00000i	$0.499967\pi$
$212$	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	−0.895658	−	0.444744i	$-0.853295\pi$
$223$	−6.45815	−	19.8761i	−0.432470	−	1.33100i	0.463188	−	0.886260i	$-0.346705\pi$
$224$	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	−0.752253	−	0.658874i	$-0.771033\pi$
$227$	3.67034	−	11.2961i	0.243609	−	0.749752i	0.995862	−	0.0908773i	$-0.0289671\pi$
$228$		0			0
$229$	−7.92914	+	5.76086i	−0.523972	+	0.380688i	−0.818098	−	0.575078i	$-0.804972\pi$
$229$	−7.92914	+	5.76086i	−0.523972	+	0.380688i	0.294126	+	0.955767i	$0.404972\pi$
$230$	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	$-0.870746\pi$
$233$	−12.6222	+	9.17056i	−0.826907	+	0.600783i	0.0917755	+	0.995780i	$0.470746\pi$
$234$		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	0.532918	+	0.846167i	$0.321096\pi$
$239$	9.26252	+	28.5071i	0.599143	+	1.84397i	0.0662251	+	0.997805i	$0.478904\pi$
$240$		0			0
$241$		−	1.89778i		−	0.122247i	−0.998130	−	0.0611235i	$-0.980532\pi$
$241$		−	1.89778i		−	0.122247i	0.998130	−	0.0611235i	$-0.0194684\pi$
$242$	−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	$-0.172701\pi$
$251$	1.59530	+	2.19574i	0.100694	+	0.138594i	−0.755696	+	0.654922i	$0.772701\pi$
$252$		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	$-0.314367\pi$
$257$	8.10484	+	2.63342i	0.505566	+	0.164268i	−0.0451186	+	0.998982i	$0.514367\pi$
$258$		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	−0.118817	−	0.992916i	$-0.537910\pi$
$269$	14.1414	−	19.4640i	0.862219	−	1.18674i	0.981036	−	0.193826i	$-0.0620898\pi$
$270$		0			0
$271$	12.2868	+	3.99222i	0.746370	+	0.242510i	0.657418	−	0.753526i	$-0.271648\pi$
$271$	12.2868	+	3.99222i	0.746370	+	0.242510i	0.0889514	+	0.996036i	$0.471648\pi$
$272$	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	0.910441	−	0.413640i	$-0.135743\pi$
$277$	3.92290	+	5.39940i	0.235704	+	0.324419i	−0.674737	+	0.738059i	$0.735743\pi$
$278$	−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	$-0.305827\pi$
$281$	−0.496529	−	0.360749i	−0.0296204	−	0.0215205i	−0.602497	+	0.798121i	$0.705827\pi$
$282$		0			0
$283$	17.9806	−	5.84225i	1.06883	−	0.347286i	0.278801	−	0.960349i	$-0.410063\pi$
$283$	17.9806	−	5.84225i	1.06883	−	0.347286i	0.790034	+	0.613063i	$0.210063\pi$
$284$	−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	$-0.880436\pi$
$293$	0.649796	−	1.99987i	0.0379615	−	0.116833i	0.968242	+	0.250017i	$0.0804361\pi$
$294$		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	$0.167607\pi$
$307$			17.6110i			1.00511i	−0.864545	+	0.502556i	$0.832393\pi$
$308$	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	$-0.498997\pi$
$311$	10.4661	−	3.40065i	0.593480	−	0.192833i	0.590330	+	0.807162i	$0.298997\pi$
$312$		0			0
$313$	3.15636	+	2.29323i	0.178408	+	0.129621i	0.673405	−	0.739274i	$-0.264831\pi$
$313$	3.15636	+	2.29323i	0.178408	+	0.129621i	−0.494997	+	0.868895i	$0.664831\pi$
$314$	−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	0.999723	+	0.0235153i	$0.00748586\pi$
$317$	12.6974	+	17.4765i	0.713156	+	0.981576i	−0.286567	+	0.958060i	$0.592514\pi$
$318$		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	0.328101	−	0.944643i	$-0.393591\pi$
$337$	0.702984	+	0.228413i	0.0382940	+	0.0124425i	−0.289807	+	0.957085i	$0.593591\pi$
$338$	−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	$-0.403526\pi$
$347$	−9.63095	−	6.99730i	−0.517017	−	0.375635i	−0.815479	+	0.578787i	$0.803526\pi$
$348$		0			0
$349$	9.68842	−	3.14796i	0.518609	−	0.168506i	−0.0380047	−	0.999278i	$-0.512100\pi$
$349$	9.68842	−	3.14796i	0.518609	−	0.168506i	0.556614	+	0.830771i	$0.312100\pi$
$350$	−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	−0.421279	−	0.906931i	$-0.638419\pi$
$359$	8.57599	−	26.3942i	0.452624	−	1.39303i	0.873903	−	0.486101i	$-0.161581\pi$
$360$		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	0.717520	+	0.696538i	$0.245277\pi$
$367$	−5.21807	+	16.0596i	−0.272381	+	0.838302i	−0.989901	+	0.141764i	$0.954723\pi$
$368$	−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	$0.0497222\pi$
$373$			6.00920i			0.311145i	−0.987824	+	0.155572i	$0.950278\pi$
$374$	−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	0.396799	−	0.917906i	$-0.370121\pi$
$379$	−6.88315	−	5.00090i	−0.353563	−	0.256879i	−0.750362	+	0.661027i	$0.770121\pi$
$380$	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	$-0.283282\pi$
$383$	−5.95093	−	8.19075i	−0.304078	−	0.418528i	−0.933523	+	0.358517i	$0.883282\pi$
$384$		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	$-0.323977\pi$
$389$	8.87507	+	2.88369i	0.449984	+	0.146209i	−0.0752534	+	0.997164i	$0.523977\pi$
$390$		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	$-0.679233\pi$
$401$	8.71867	−	12.0002i	0.435390	−	0.599262i	0.969180	+	0.246355i	$0.0792328\pi$
$402$		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	0.916873	−	0.399179i	$-0.130705\pi$
$409$	5.13485	+	7.06751i	0.253902	+	0.349466i	−0.662971	+	0.748645i	$0.730705\pi$
$410$	−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	0.938324	−	0.345758i	$-0.112378\pi$
$421$	−0.493004	−	1.51731i	−0.0240276	−	0.0739492i	−0.962351	+	0.271809i	$0.912378\pi$
$422$	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	$-0.951523\pi$
$431$	−23.8660	+	17.3397i	−1.14959	+	0.835223i	−0.161160	+	0.986928i	$0.551523\pi$
$432$		0			0
$433$	3.54190	−	10.9008i	0.170213	−	0.523861i	−0.829170	−	0.558997i	$-0.811186\pi$
$433$	3.54190	−	10.9008i	0.170213	−	0.523861i	0.999383	+	0.0351356i	$0.0111863\pi$
$434$	−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	$-0.976904\pi$
$439$		−	3.03783i		−	0.144988i	0.997369	−	0.0724938i	$-0.0230957\pi$
$440$	−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	$-0.471367\pi$
$443$	15.7419	−	5.11484i	0.747918	−	0.243013i	0.658085	+	0.752943i	$0.271367\pi$
$444$		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	$-0.201952\pi$
$449$	−0.152765	−	0.210263i	−0.00720943	−	0.00992293i	−0.812606	+	0.582813i	$0.801952\pi$
$450$		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	−0.877228	−	0.480074i	$-0.840610\pi$
$457$	−3.19749	+	4.40097i	−0.149572	+	0.205869i	0.727656	+	0.685943i	$0.240610\pi$
$458$	−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	−0.802167	−	0.597100i	$-0.796320\pi$
$467$	0.293731	−	0.404285i	0.0135922	−	0.0187081i	0.815759	+	0.578392i	$0.196320\pi$
$468$		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	$-0.378959\pi$
$479$	−8.69444	−	6.31688i	−0.397259	−	0.288625i	−0.768424	+	0.639942i	$0.778959\pi$
$480$		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	0.900653	+	0.434539i	$0.143089\pi$
$487$	9.43244	+	29.0301i	0.427425	+	1.31548i	−0.473228	+	0.880940i	$0.656911\pi$
$488$	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	0.609402	+	0.792862i	$0.291410\pi$
$491$	−7.74766	+	23.8448i	−0.349647	+	1.07610i	−0.959049	+	0.283241i	$0.908590\pi$
$492$		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	−0.910774	−	0.412905i	$-0.864514\pi$
$499$	1.53591	−	4.72705i	0.0687568	−	0.211612i	0.979531	+	0.201293i	$0.0645143\pi$
$500$	−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	0.802079	+	0.597218i	$0.203727\pi$
$503$	11.3085	+	34.8039i	0.504219	+	1.55183i	−0.297860	+	0.954610i	$0.596273\pi$
$504$		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	$-0.499939\pi$
$509$	13.2688	−	4.31130i	0.588131	−	0.191095i	0.587940	+	0.808905i	$0.299939\pi$
$510$		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	$-0.449633\pi$
$521$	−6.74242	−	2.19075i	−0.295391	−	0.0959783i	−0.452963	+	0.891529i	$0.649633\pi$
$522$		0			0
$523$	7.47929	−	10.2944i	0.327047	−	0.450141i	−0.613556	−	0.789651i	$-0.710261\pi$
$523$	7.47929	−	10.2944i	0.327047	−	0.450141i	0.940602	+	0.339510i	$0.110261\pi$
$524$	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	0.855684	−	0.517499i	$-0.173137\pi$
$541$	2.30481	+	3.17230i	0.0990915	+	0.136388i	−0.756592	+	0.653887i	$0.773137\pi$
$542$	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	−0.520294	−	0.853987i	$-0.674177\pi$
$547$	−10.2734	+	3.33803i	−0.439259	+	0.142724i	0.0810349	+	0.996711i	$0.474177\pi$
$548$	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	−0.682595	−	0.730797i	$-0.739149\pi$
$557$	7.06108	−	21.7318i	0.299188	−	0.920805i	0.981783	−	0.190008i	$-0.0608514\pi$
$558$		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	$-0.773386\pi$
$563$	−8.77304	+	6.37399i	−0.369740	+	0.268632i	0.387363	+	0.921927i	$0.373386\pi$
$564$		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	−0.998934	−	0.0461553i	$-0.985303\pi$
$569$	−5.19794	−	15.9976i	−0.217909	−	0.670655i	0.781025	−	0.624499i	$-0.214697\pi$
$570$		0			0
$571$			16.3097i			0.682541i	0.939965	+	0.341271i	$0.110857\pi$
$571$			16.3097i			0.682541i	−0.939965	+	0.341271i	$0.889143\pi$
$572$	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	0.715150	−	0.698971i	$-0.246358\pi$
$577$	6.51886	+	4.73623i	0.271384	+	0.197172i	−0.443767	+	0.896142i	$0.646358\pi$
$578$	−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	$-0.294706\pi$
$587$	14.9678	+	4.86334i	0.617789	+	0.200732i	0.0166304	+	0.999862i	$0.494706\pi$
$588$		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	−0.312981	−	0.949759i	$-0.601328\pi$
$599$	16.8142	−	23.1428i	0.687010	−	0.945588i	0.999991	+	0.00417130i	$0.00132777\pi$
$600$		0			0
$601$	−6.78070	−	2.20318i	−0.276591	−	0.0898697i	0.167437	−	0.985883i	$-0.446451\pi$
$601$	−6.78070	−	2.20318i	−0.276591	−	0.0898697i	−0.444028	+	0.896013i	$0.646451\pi$
$602$	−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	0.751036	−	0.660262i	$-0.229555\pi$
$607$	−2.68531	−	3.69601i	−0.108993	−	0.150017i	−0.860029	+	0.510245i	$0.829555\pi$
$608$	−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	−0.940038	−	0.341069i	$-0.889211\pi$
$613$	−37.1400	+	12.0675i	−1.50007	+	0.487402i	−0.560032	+	0.828471i	$0.689211\pi$
$614$	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	0.924796	+	0.380463i	$0.124235\pi$
$619$	9.95813	+	30.6480i	0.400251	+	1.23185i	−0.524545	+	0.851383i	$0.675765\pi$
$620$	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	−0.961512	−	0.274764i	$-0.911400\pi$
$631$	−0.555911	+	1.71092i	−0.0221305	+	0.0681105i	0.939381	+	0.342874i	$0.111400\pi$
$632$	−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	$-0.648628\pi$
$641$	−7.32843	+	2.38115i	−0.289456	+	0.0940499i	0.160690	+	0.987005i	$0.448628\pi$
$642$		0			0
$643$	−17.1627	−	12.4695i	−0.676832	−	0.491747i	0.195473	−	0.980709i	$-0.437376\pi$
$643$	−17.1627	−	12.4695i	−0.676832	−	0.491747i	−0.872305	+	0.488962i	$0.837376\pi$
$644$	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	−0.719511	−	0.694482i	$-0.755634\pi$
$647$	−29.4465	−	40.5296i	−1.15766	−	1.59338i	−0.438150	−	0.898902i	$-0.644366\pi$
$648$		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	$-0.287981\pi$
$653$	16.7546	+	5.44390i	0.655659	+	0.213036i	0.0377511	+	0.999287i	$0.487981\pi$
$654$		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	−0.999895	−	0.0145116i	$-0.995381\pi$
$673$	−18.2818	−	25.1627i	−0.704712	−	0.969952i	0.295183	−	0.955441i	$-0.404619\pi$
$674$	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	$-0.165386\pi$
$677$	17.2782	+	12.5533i	0.664053	+	0.482463i	−0.203976	+	0.978976i	$0.565386\pi$
$678$		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	−0.861529	−	0.507708i	$-0.830493\pi$
$691$	−16.9524	+	12.3166i	−0.644898	+	0.468546i	0.216631	+	0.976253i	$0.430493\pi$
$692$	−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	0.647364	+	0.762181i	$0.275872\pi$
$701$	15.1348	+	46.5802i	0.571634	+	1.75931i	−0.0757293	+	0.997128i	$0.524128\pi$
$702$		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	−0.263607	−	0.964630i	$-0.584912\pi$
$709$	−33.6162	−	24.4236i	−1.26248	−	0.917248i	−0.998877	+	0.0473823i	$0.984912\pi$
$710$	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	$-0.580736\pi$
$719$	−27.4285	−	8.91207i	−1.02291	−	0.332364i	−0.771984	+	0.635642i	$0.780736\pi$
$720$		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	−0.303106	−	0.952957i	$-0.598024\pi$
$733$	−30.0104	−	9.75096i	−1.10846	−	0.360160i	−0.805352	+	0.592797i	$0.798024\pi$
$734$	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	−0.929422	−	0.369019i	$-0.879694\pi$
$739$	−26.9990	−	37.1609i	−0.993173	−	1.36698i	−0.0637507	−	0.997966i	$-0.520306\pi$
$740$	−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	$-0.169581\pi$
$743$	17.5692	+	12.7648i	0.644551	+	0.468294i	−0.216860	+	0.976203i	$0.569581\pi$
$744$		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	0.999999	+	0.00136956i	$0.000435943\pi$
$751$	5.25583	+	16.1758i	0.191788	+	0.590262i	−0.808211	+	0.588893i	$0.799564\pi$
$752$	−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	−0.875592	−	0.483051i	$-0.839528\pi$
$757$	−18.8951	+	13.7281i	−0.686756	+	0.498957i	0.188836	+	0.982009i	$0.439528\pi$
$758$	−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	$-0.819920\pi$
$761$	−16.4210	+	11.9305i	−0.595259	+	0.432481i	0.248934	+	0.968521i	$0.419920\pi$
$762$		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	$-0.860650\pi$
$769$		−	23.5119i		−	0.847859i	0.905695	−	0.423930i	$-0.139350\pi$
$770$	−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	$-0.521795\pi$
$773$	12.8627	−	4.17933i	0.462638	−	0.150320i	0.531056	+	0.847337i	$0.321795\pi$
$774$		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	−0.0294111	+	0.999567i	$0.509363\pi$
$787$	−27.2391	+	37.4914i	−0.970968	+	1.33642i	−0.941557	+	0.336855i	$0.890637\pi$
$788$	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	0.0990490	−	0.995083i	$-0.468420\pi$
$797$	28.6496	−	39.4328i	1.01482	−	1.39678i	0.915772	−	0.401699i	$-0.131580\pi$
$798$		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	$-0.271519\pi$
$809$	4.11235	+	2.98780i	0.144583	+	0.105045i	−0.513143	+	0.858303i	$0.671519\pi$
$810$		0			0
$811$	5.95516	−	1.93495i	0.209114	−	0.0679453i	−0.202587	−	0.979264i	$-0.564935\pi$
$811$	5.95516	−	1.93495i	0.209114	−	0.0679453i	0.411701	+	0.911319i	$0.364935\pi$
$812$	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	−0.575540	−	0.817774i	$-0.695208\pi$
$821$	10.6233	−	32.6953i	0.370757	−	1.14107i	0.946297	−	0.323299i	$-0.104792\pi$
$822$		0			0
$823$	−8.54662	+	6.20948i	−0.297916	+	0.216449i	−0.726694	−	0.686961i	$-0.758944\pi$
$823$	−8.54662	+	6.20948i	−0.297916	+	0.216449i	0.428778	+	0.903410i	$0.358944\pi$
$824$	−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	$-0.539894\pi$
$827$	22.4299	−	16.2963i	0.779965	−	0.566678i	0.904969	+	0.425479i	$0.139894\pi$
$828$		0			0
$829$	7.49749	−	23.0749i	0.260399	−	0.801425i	−0.732319	−	0.680962i	$-0.761562\pi$
$829$	7.49749	−	23.0749i	0.260399	−	0.801425i	0.992718	−	0.120463i	$-0.0384379\pi$
$830$	−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	$-0.722388\pi$
$839$	−20.6658	+	6.71473i	−0.713463	+	0.231818i	−0.0702762	+	0.997528i	$0.522388\pi$
$840$		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	0.162608	+	0.986691i	$0.448009\pi$
$853$	−24.1254	+	33.2058i	−0.826039	+	1.13695i	−0.988647	+	0.150255i	$0.951991\pi$
$854$	−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	−0.572587	−	0.819844i	$-0.694060\pi$
$863$	11.2828	−	15.5294i	0.384070	−	0.528626i	0.956657	+	0.291217i	$0.0940603\pi$
$864$		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	−0.999972	−	0.00752149i	$-0.997606\pi$
$877$	−53.4401	+	17.3637i	−1.80454	+	0.586332i	−0.804573	+	0.593854i	$0.797606\pi$
$878$	−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	−0.977909	−	0.209031i	$-0.932969\pi$
$883$	−9.20073	−	28.3169i	−0.309629	−	0.952941i	0.668280	−	0.743910i	$-0.267031\pi$
$884$	−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	$-0.893964\pi$
$887$	0.349006	−	1.07413i	0.0117185	−	0.0360657i	0.956745	+	0.290929i	$0.0939642\pi$
$888$		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	0.168880	−	0.985637i	$-0.445985\pi$
$907$	−21.5733	−	15.6739i	−0.716330	−	0.520444i	−0.885209	+	0.465193i	$0.845985\pi$
$908$	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	$-0.220677\pi$
$911$	−2.30320	−	3.17008i	−0.0763084	−	0.105029i	−0.845465	+	0.534031i	$0.820677\pi$
$912$		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	−0.910678	−	0.413117i	$-0.864440\pi$
$919$	−7.16542	+	9.86236i	−0.236365	+	0.325329i	0.674313	+	0.738446i	$0.264440\pi$
$920$	−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	$-0.824673\pi$
$929$	−2.77455	+	3.81885i	−0.0910302	+	0.125292i	0.761073	+	0.648667i	$0.224673\pi$
$930$		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	0.435105	−	0.900380i	$-0.356711\pi$
$937$	−17.0091	−	23.4110i	−0.555662	−	0.764803i	−0.990767	+	0.135577i	$0.956711\pi$
$938$	−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	−0.969372	−	0.245597i	$-0.921016\pi$
$941$	−46.0903	−	33.4866i	−1.50250	−	1.09163i	−0.533129	−	0.846034i	$-0.678984\pi$
$942$		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	$-0.958819\pi$
$953$	−3.50554	+	10.7889i	−0.113556	+	0.349488i	0.878087	+	0.478500i	$0.158819\pi$
$954$		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	$-0.910245\pi$
$967$		−	17.3054i		−	0.556505i	0.960508	−	0.278253i	$-0.0897553\pi$
$968$	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	$-0.730875\pi$
$971$	−23.6890	+	7.69701i	−0.760215	+	0.247009i	−0.0968441	+	0.995300i	$0.530875\pi$
$972$		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	$-0.161774\pi$
$977$	4.40208	+	6.05894i	0.140835	+	0.193843i	−0.732773	+	0.680473i	$0.761774\pi$
$978$		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	$-0.427091\pi$
$983$	−5.06942	−	1.64715i	−0.161689	−	0.0525361i	−0.388743	+	0.921346i	$0.627091\pi$
$984$		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	0.0871692	−	0.996194i	$-0.472218\pi$
$997$	−13.5097	−	4.38958i	−0.427857	−	0.139019i	−0.515026	+	0.857174i	$0.672218\pi$
$998$	−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.404.14		80
3.2	odd	2	inner	891.2.k.a.404.7		80
9.2	odd	6		99.2.p.a.41.8	yes	80
9.4	even	3		99.2.p.a.74.8	yes	80
9.5	odd	6		297.2.t.a.8.3		80
9.7	even	3		297.2.t.a.206.3		80
11.7	odd	10	inner	891.2.k.a.161.7		80
33.29	even	10	inner	891.2.k.a.161.14		80
99.7	odd	30		297.2.t.a.260.3		80
99.29	even	30		99.2.p.a.95.8	yes	80
99.40	odd	30		99.2.p.a.29.8	✓	80
99.95	even	30		297.2.t.a.62.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.8	✓	80	99.40	odd	30
99.2.p.a.41.8	yes	80	9.2	odd	6
99.2.p.a.74.8	yes	80	9.4	even	3
99.2.p.a.95.8	yes	80	99.29	even	30
297.2.t.a.8.3		80	9.5	odd	6
297.2.t.a.62.3		80	99.95	even	30
297.2.t.a.206.3		80	9.7	even	3
297.2.t.a.260.3		80	99.7	odd	30
891.2.k.a.161.7		80	11.7	odd	10	inner
891.2.k.a.161.14		80	33.29	even	10	inner
891.2.k.a.404.7		80	3.2	odd	2	inner
891.2.k.a.404.14		80	1.1	even	1	trivial

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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