LMFDB - Embedded newform 891.2.k.a.161.6

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			161.6
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16363 - 0.845427i) q^{2} +(0.0212543 + 0.0654141i) q^{4} +(-2.09686 - 2.88608i) q^{5} +(2.05824 - 0.668764i) q^{7} +(-0.858363 + 2.64177i) q^{8} +5.13106i q^{10} +(-3.14809 + 1.04380i) q^{11} +(-1.65695 + 2.28059i) q^{13} +(-2.96042 - 0.961900i) q^{14} +(3.34353 - 2.42922i) q^{16} +(0.345974 - 0.251365i) q^{17} +(-3.47799 - 1.13007i) q^{19} +(0.144223 - 0.198506i) q^{20} +(4.54567 + 1.44689i) q^{22} +8.01262i q^{23} +(-2.38754 + 7.34810i) q^{25} +(3.85615 - 1.25294i) q^{26} +(0.0874932 + 0.120424i) q^{28} +(-2.08433 - 6.41492i) q^{29} +(0.102264 + 0.0742991i) q^{31} -0.388910 q^{32} -0.615095 q^{34} +(-6.24595 - 4.53795i) q^{35} +(1.89382 + 5.82859i) q^{37} +(3.09171 + 4.25537i) q^{38} +(9.42422 - 3.06211i) q^{40} +(0.679859 - 2.09239i) q^{41} -2.87217i q^{43} +(-0.135190 - 0.183744i) q^{44} +(6.77408 - 9.32372i) q^{46} +(3.20383 + 1.04099i) q^{47} +(-1.87400 + 1.36154i) q^{49} +(8.99050 - 6.53198i) q^{50} +(-0.184400 - 0.0599153i) q^{52} +(1.52002 - 2.09212i) q^{53} +(9.61358 + 6.89694i) q^{55} +6.01145i q^{56} +(-2.99795 + 9.22674i) q^{58} +(4.37133 - 1.42033i) q^{59} +(4.71412 + 6.48843i) q^{61} +(-0.0561830 - 0.172913i) q^{62} +(-6.23451 - 4.52964i) q^{64} +10.0564 q^{65} -5.51612 q^{67} +(0.0237962 + 0.0172890i) q^{68} +(3.43147 + 10.5610i) q^{70} +(5.13082 + 7.06197i) q^{71} +(4.81457 - 1.56435i) q^{73} +(2.72393 - 8.38341i) q^{74} -0.251529i q^{76} +(-5.78149 + 4.25372i) q^{77} +(-8.07272 + 11.1111i) q^{79} +(-14.0218 - 4.55596i) q^{80} +(-2.56007 + 1.86000i) q^{82} +(-11.7915 + 8.56700i) q^{83} +(-1.45091 - 0.471431i) q^{85} +(-2.42821 + 3.34215i) q^{86} +(-0.0552663 - 9.21250i) q^{88} +5.40631i q^{89} +(-1.88523 + 5.80213i) q^{91} +(-0.524138 + 0.170303i) q^{92} +(-2.84800 - 3.91993i) q^{94} +(4.03139 + 12.4073i) q^{95} +(-5.75596 - 4.18195i) q^{97} +3.33172 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.16363	−	0.845427i	−0.822811	−	0.597807i	0.0947056	−	0.995505i	$-0.469809\pi$
$2$	−1.16363	−	0.845427i	−0.822811	−	0.597807i	−0.917516	+	0.397698i	$0.869809\pi$
$3$		0			0
$3$		0			0
$4$	0.0212543	+	0.0654141i	0.0106272	+	0.0327071i
$5$	−2.09686	−	2.88608i	−0.937743	−	1.29069i	−0.956761	−	0.290874i	$-0.906054\pi$
$5$	−2.09686	−	2.88608i	−0.937743	−	1.29069i	0.0190182	−	0.999819i	$-0.493946\pi$
$6$		0			0
$7$	2.05824	−	0.668764i	0.777943	−	0.252769i	0.106981	−	0.994261i	$-0.465881\pi$
$7$	2.05824	−	0.668764i	0.777943	−	0.252769i	0.670962	+	0.741492i	$0.265881\pi$
$8$	−0.858363	+	2.64177i	−0.303477	+	0.934007i
$9$		0			0
$10$			5.13106i			1.62259i
$11$	−3.14809	+	1.04380i	−0.949186	+	0.314717i
$11$	−3.14809	+	1.04380i	−0.949186	+	0.314717i
$12$		0			0
$13$	−1.65695	+	2.28059i	−0.459555	+	0.632523i	−0.974416	−	0.224750i	$-0.927843\pi$
$13$	−1.65695	+	2.28059i	−0.459555	+	0.632523i	0.514861	+	0.857273i	$0.327843\pi$
$14$	−2.96042	−	0.961900i	−0.791207	−	0.257079i
$15$		0			0
$16$	3.34353	−	2.42922i	0.835882	−	0.607304i
$17$	0.345974	−	0.251365i	0.0839109	−	0.0609648i	−0.545039	−	0.838411i	$-0.683485\pi$
$17$	0.345974	−	0.251365i	0.0839109	−	0.0609648i	0.628950	+	0.777446i	$0.283485\pi$
$18$		0			0
$19$	−3.47799	−	1.13007i	−0.797906	−	0.259255i	−0.118439	−	0.992961i	$-0.537789\pi$
$19$	−3.47799	−	1.13007i	−0.797906	−	0.259255i	−0.679467	+	0.733706i	$0.737789\pi$
$20$	0.144223	−	0.198506i	0.0322492	−	0.0443872i
$21$		0			0
$22$	4.54567	+	1.44689i	0.969140	+	0.308477i
$23$			8.01262i			1.67075i	0.549683	+	0.835373i	$0.314749\pi$
$23$			8.01262i			1.67075i	−0.549683	+	0.835373i	$0.685251\pi$
$24$		0			0
$25$	−2.38754	+	7.34810i	−0.477509	+	1.46962i
$26$	3.85615	−	1.25294i	0.756253	−	0.245722i
$27$		0			0
$28$	0.0874932	+	0.120424i	0.0165347	+	0.0227580i
$29$	−2.08433	−	6.41492i	−0.387051	−	1.19122i	−0.934981	−	0.354697i	$-0.884584\pi$
$29$	−2.08433	−	6.41492i	−0.387051	−	1.19122i	0.547930	−	0.836524i	$-0.315416\pi$
$30$		0			0
$31$	0.102264	+	0.0742991i	0.0183672	+	0.0133445i	0.596931	−	0.802293i	$-0.296387\pi$
$31$	0.102264	+	0.0742991i	0.0183672	+	0.0133445i	−0.578564	+	0.815637i	$0.696387\pi$
$32$	−0.388910			−0.0687503
$33$		0			0
$34$	−0.615095			−0.105488
$35$	−6.24595	−	4.53795i	−1.05576	−	0.767053i
$36$		0			0
$37$	1.89382	+	5.82859i	0.311343	+	0.958214i	0.977234	+	0.212165i	$0.0680515\pi$
$37$	1.89382	+	5.82859i	0.311343	+	0.958214i	−0.665891	+	0.746049i	$0.731949\pi$
$38$	3.09171	+	4.25537i	0.501541	+	0.690312i
$39$		0			0
$40$	9.42422	−	3.06211i	1.49010	−	0.484163i
$41$	0.679859	−	2.09239i	0.106176	−	0.326777i	−0.883829	−	0.467811i	$-0.845043\pi$
$41$	0.679859	−	2.09239i	0.106176	−	0.326777i	0.990005	+	0.141034i	$0.0450428\pi$
$42$		0			0
$43$		−	2.87217i		−	0.438002i	−0.975725	−	0.219001i	$-0.929720\pi$
$43$		−	2.87217i		−	0.438002i	0.975725	−	0.219001i	$-0.0702799\pi$
$44$	−0.135190	−	0.183744i	−0.0203806	−	0.0277005i
$45$		0			0
$46$	6.77408	−	9.32372i	0.998784	−	1.37471i
$47$	3.20383	+	1.04099i	0.467327	+	0.151844i	0.533209	−	0.845984i	$-0.320986\pi$
$47$	3.20383	+	1.04099i	0.467327	+	0.151844i	−0.0658817	+	0.997827i	$0.520986\pi$
$48$		0			0
$49$	−1.87400	+	1.36154i	−0.267714	+	0.194505i
$50$	8.99050	−	6.53198i	1.27145	−	0.923761i
$51$		0			0
$52$	−0.184400	−	0.0599153i	−0.0255717	−	0.00830876i
$53$	1.52002	−	2.09212i	0.208790	−	0.287375i	−0.691760	−	0.722128i	$-0.743164\pi$
$53$	1.52002	−	2.09212i	0.208790	−	0.287375i	0.900550	+	0.434753i	$0.143164\pi$
$54$		0			0
$55$	9.61358	+	6.89694i	1.29630	+	0.929984i
$56$			6.01145i			0.803314i
$57$		0			0
$58$	−2.99795	+	9.22674i	−0.393650	+	1.21153i
$59$	4.37133	−	1.42033i	0.569099	−	0.184912i	−0.0103122	−	0.999947i	$-0.503283\pi$
$59$	4.37133	−	1.42033i	0.569099	−	0.184912i	0.579411	+	0.815035i	$0.303283\pi$
$60$		0			0
$61$	4.71412	+	6.48843i	0.603581	+	0.830759i	0.996030	−	0.0890153i	$-0.0283720\pi$
$61$	4.71412	+	6.48843i	0.603581	+	0.830759i	−0.392449	+	0.919774i	$0.628372\pi$
$62$	−0.0561830	−	0.172913i	−0.00713524	−	0.0219600i
$63$		0			0
$64$	−6.23451	−	4.52964i	−0.779314	−	0.566205i
$65$	10.0564			1.24734
$66$		0			0
$67$	−5.51612			−0.673901			−0.336951	−	0.941522i	$-0.609396\pi$
$67$	−5.51612			−0.673901			−0.336951	+	0.941522i	$0.609396\pi$
$68$	0.0237962	+	0.0172890i	0.00288572	+	0.00209659i
$69$		0			0
$70$	3.43147	+	10.5610i	0.410139	+	1.26228i
$71$	5.13082	+	7.06197i	0.608916	+	0.838101i	0.996488	−	0.0837384i	$-0.0266860\pi$
$71$	5.13082	+	7.06197i	0.608916	+	0.838101i	−0.387572	+	0.921840i	$0.626686\pi$
$72$		0			0
$73$	4.81457	−	1.56435i	0.563503	−	0.183093i	−0.0133940	−	0.999910i	$-0.504264\pi$
$73$	4.81457	−	1.56435i	0.563503	−	0.183093i	0.576897	+	0.816817i	$0.304264\pi$
$74$	2.72393	−	8.38341i	0.316651	−	0.974551i
$75$		0			0
$76$		−	0.251529i		−	0.0288523i
$77$	−5.78149	+	4.25372i	−0.658862	+	0.484756i
$78$		0			0
$79$	−8.07272	+	11.1111i	−0.908252	+	1.25010i	0.0595080	+	0.998228i	$0.481047\pi$
$79$	−8.07272	+	11.1111i	−0.908252	+	1.25010i	−0.967760	+	0.251874i	$0.918953\pi$
$80$	−14.0218	−	4.55596i	−1.56769	−	0.509372i
$81$		0			0
$82$	−2.56007	+	1.86000i	−0.282712	+	0.205402i
$83$	−11.7915	+	8.56700i	−1.29428	+	0.940350i	−0.999882	−	0.0153328i	$-0.995119\pi$
$83$	−11.7915	+	8.56700i	−1.29428	+	0.940350i	−0.294398	+	0.955683i	$0.595119\pi$
$84$		0			0
$85$	−1.45091	−	0.471431i	−0.157374	−	0.0511338i
$86$	−2.42821	+	3.34215i	−0.261841	+	0.360393i
$87$		0			0
$88$	−0.0552663	−	9.21250i	−0.00589141	−	0.982056i
$89$			5.40631i			0.573068i	0.958070	+	0.286534i	$0.0925031\pi$
$89$			5.40631i			0.573068i	−0.958070	+	0.286534i	$0.907497\pi$
$90$		0			0
$91$	−1.88523	+	5.80213i	−0.197625	+	0.608228i
$92$	−0.524138	+	0.170303i	−0.0546452	+	0.0177553i
$93$		0			0
$94$	−2.84800	−	3.91993i	−0.293748	−	0.404310i
$95$	4.03139	+	12.4073i	0.413612	+	1.27297i
$96$		0			0
$97$	−5.75596	−	4.18195i	−0.584429	−	0.424613i	0.255889	−	0.966706i	$-0.417632\pi$
$97$	−5.75596	−	4.18195i	−0.584429	−	0.424613i	−0.840318	+	0.542094i	$0.817632\pi$
$98$	3.33172			0.336554
$99$		0			0
$100$	−0.531415			−0.0531415
$101$	5.30898	+	3.85720i	0.528263	+	0.383805i	0.819708	−	0.572782i	$-0.194136\pi$
$101$	5.30898	+	3.85720i	0.528263	+	0.383805i	−0.291445	+	0.956588i	$0.594136\pi$
$102$		0			0
$103$	2.81887	+	8.67559i	0.277752	+	0.854831i	0.988478	+	0.151363i	$0.0483663\pi$
$103$	2.81887	+	8.67559i	0.277752	+	0.854831i	−0.710727	+	0.703468i	$0.751634\pi$
$104$	−4.60254	−	6.33486i	−0.451317	−	0.621184i
$105$		0			0
$106$	−3.53747	+	1.14939i	−0.343589	+	0.111639i
$107$	−0.506436	+	1.55865i	−0.0489590	+	0.150680i	−0.972547	−	0.232706i	$-0.925242\pi$
$107$	−0.506436	+	1.55865i	−0.0489590	+	0.150680i	0.923588	+	0.383386i	$0.125242\pi$
$108$		0			0
$109$		−	13.4796i		−	1.29111i	−0.763714	−	0.645555i	$-0.776626\pi$
$109$		−	13.4796i		−	1.29111i	0.763714	−	0.645555i	$-0.223374\pi$
$110$	−5.35579	−	16.1531i	−0.510655	−	1.54013i
$111$		0			0
$112$	5.25723	−	7.23595i	0.496761	−	0.683733i
$113$	7.08299	+	2.30140i	0.666312	+	0.216498i	0.622593	−	0.782546i	$-0.286079\pi$
$113$	7.08299	+	2.30140i	0.666312	+	0.216498i	0.0437190	+	0.999044i	$0.486079\pi$
$114$		0			0
$115$	23.1250	−	16.8013i	2.15642	−	1.56673i
$116$	0.375325	−	0.272690i	0.0348481	−	0.0253186i
$117$		0			0
$118$	−6.28740	−	2.04290i	−0.578802	−	0.188064i
$119$	0.543994	−	0.748744i	0.0498679	−	0.0686373i
$120$		0			0
$121$	8.82097	−	6.57194i	0.801907	−	0.597449i
$122$		−	11.5356i		−	1.04438i
$123$		0			0
$124$	−0.00268666	+	0.00826869i	−0.000241269	+	0.000742550i
$125$	9.24960	−	3.00538i	0.827309	−	0.268809i
$126$		0			0
$127$	−1.80470	−	2.48395i	−0.160141	−	0.220415i	0.721405	−	0.692514i	$-0.243497\pi$
$127$	−1.80470	−	2.48395i	−0.160141	−	0.220415i	−0.881546	+	0.472098i	$0.843497\pi$
$128$	3.66555	+	11.2814i	0.323992	+	0.997144i
$129$		0			0
$130$	−11.7019	−	8.50191i	−1.02632	−	0.745667i
$131$	−3.45938			−0.302247			−0.151124	−	0.988515i	$-0.548289\pi$
$131$	−3.45938			−0.302247			−0.151124	+	0.988515i	$0.548289\pi$
$132$		0			0
$133$	−7.91431			−0.686257
$134$	6.41872	+	4.66347i	0.554493	+	0.402863i
$135$		0			0
$136$	0.367076	+	1.12975i	0.0314765	+	0.0968748i
$137$	5.93010	+	8.16208i	0.506643	+	0.697334i	0.983349	−	0.181729i	$-0.0581694\pi$
$137$	5.93010	+	8.16208i	0.506643	+	0.697334i	−0.476706	+	0.879063i	$0.658169\pi$
$138$		0			0
$139$	−6.32229	+	2.05424i	−0.536250	+	0.174238i	−0.564607	−	0.825360i	$-0.690972\pi$
$139$	−6.32229	+	2.05424i	−0.536250	+	0.174238i	0.0283573	+	0.999598i	$0.490972\pi$
$140$	0.164092	−	0.505024i	0.0138683	−	0.0426823i
$141$		0			0
$142$		−	12.5552i		−	1.05361i
$143$	2.83575	−	8.90904i	0.237137	−	0.745011i
$144$		0			0
$145$	−14.1434	+	19.4667i	−1.17455	+	1.61662i
$146$	−6.92492	−	2.25004i	−0.573110	−	0.186215i
$147$		0			0
$148$	−0.341020	+	0.247765i	−0.0280317	+	0.0203662i
$149$	−11.1430	+	8.09584i	−0.912867	+	0.663237i	−0.941738	−	0.336346i	$-0.890809\pi$
$149$	−11.1430	+	8.09584i	−0.912867	+	0.663237i	0.0288711	+	0.999583i	$0.490809\pi$
$150$		0			0
$151$	−19.5502	−	6.35224i	−1.59097	−	0.516938i	−0.626118	−	0.779728i	$-0.715357\pi$
$151$	−19.5502	−	6.35224i	−1.59097	−	0.516938i	−0.964853	+	0.262791i	$0.915357\pi$
$152$	5.97076	−	8.21805i	0.484293	−	0.666572i
$153$		0			0
$154$	10.3237	−	0.0619326i	0.831909	−	0.00499067i
$155$		−	0.450936i		−	0.0362201i
$156$		0			0
$157$	2.36366	−	7.27460i	0.188641	−	0.580576i	−0.811351	−	0.584559i	$-0.801268\pi$
$157$	2.36366	−	7.27460i	0.188641	−	0.580576i	0.999992	+	0.00398241i	$0.00126764\pi$
$158$	18.7873	−	6.10437i	1.49464	−	0.485638i
$159$		0			0
$160$	0.815490	+	1.12243i	0.0644701	+	0.0887355i
$161$	5.35855	+	16.4919i	0.422313	+	1.29975i
$162$		0			0
$163$	−7.23192	−	5.25430i	−0.566448	−	0.411548i	0.267365	−	0.963595i	$-0.413847\pi$
$163$	−7.23192	−	5.25430i	−0.566448	−	0.411548i	−0.833813	+	0.552047i	$0.813847\pi$
$164$	0.151322			0.0118163
$165$		0			0
$166$	20.9637			1.62710
$167$	−2.12363	−	1.54291i	−0.164331	−	0.119394i	0.502580	−	0.864531i	$-0.332384\pi$
$167$	−2.12363	−	1.54291i	−0.164331	−	0.119394i	−0.666912	+	0.745137i	$0.732384\pi$
$168$		0			0
$169$	1.56159	+	4.80608i	0.120122	+	0.369698i
$170$	1.28977	+	1.77521i	0.0989206	+	0.136153i
$171$		0			0
$172$	0.187881	−	0.0610461i	0.0143258	−	0.00465472i
$173$	5.15363	−	15.8612i	0.391823	−	1.20591i	−0.539585	−	0.841931i	$-0.681419\pi$
$173$	5.15363	−	15.8612i	0.391823	−	1.20591i	0.931408	−	0.363977i	$-0.118581\pi$
$174$		0			0
$175$			16.7209i			1.26398i
$176$	−7.99013	+	11.1374i	−0.602279	+	0.839511i
$177$		0			0
$178$	4.57064	−	6.29094i	0.342584	−	0.471526i
$179$	15.2409	+	4.95208i	1.13916	+	0.370136i	0.817050	−	0.576567i	$-0.195608\pi$
$179$	15.2409	+	4.95208i	1.13916	+	0.370136i	0.322110	+	0.946702i	$0.395608\pi$
$180$		0			0
$181$	−10.6647	+	7.74833i	−0.792698	+	0.575929i	−0.908763	−	0.417313i	$-0.862972\pi$
$181$	−10.6647	+	7.74833i	−0.792698	+	0.575929i	0.116065	+	0.993242i	$0.462972\pi$
$182$	7.09898	−	5.15771i	0.526211	−	0.382315i
$183$		0			0
$184$	−21.1675	−	6.87774i	−1.56049	−	0.507034i
$185$	12.8507	−	17.6874i	0.944801	−	1.30041i
$186$		0			0
$187$	−0.826783	+	1.15245i	−0.0604604	+	0.0842751i
$188$			0.231701i			0.0168986i
$189$		0			0
$190$	5.79845	−	17.8458i	0.420664	−	1.29467i
$191$	−10.2865	+	3.34228i	−0.744303	+	0.241839i	−0.656528	−	0.754301i	$-0.727976\pi$
$191$	−10.2865	+	3.34228i	−0.744303	+	0.241839i	−0.0877752	+	0.996140i	$0.527976\pi$
$192$		0			0
$193$	−5.43455	−	7.48001i	−0.391187	−	0.538423i	0.567318	−	0.823499i	$-0.307981\pi$
$193$	−5.43455	−	7.48001i	−0.391187	−	0.538423i	−0.958505	+	0.285076i	$0.907981\pi$
$194$	3.16227	+	9.73248i	0.227038	+	0.698751i
$195$		0			0
$196$	−0.128894	−	0.0936472i	−0.00920674	−	0.00668909i
$197$	−22.2431			−1.58475			−0.792377	−	0.610032i	$-0.791157\pi$
$197$	−22.2431			−1.58475			−0.792377	+	0.610032i	$0.791157\pi$
$198$		0			0
$199$	−2.40521			−0.170500			−0.0852502	−	0.996360i	$-0.527169\pi$
$199$	−2.40521			−0.170500			−0.0852502	+	0.996360i	$0.527169\pi$
$200$	−17.3626	−	12.6147i	−1.22772	−	0.891993i
$201$		0			0
$202$	−2.91671	−	8.97670i	−0.205219	−	0.631598i
$203$	−8.58014	−	11.8095i	−0.602207	−	0.828867i
$204$		0			0
$205$	−7.46437	+	2.42532i	−0.521334	+	0.169392i
$206$	4.05445	−	12.4783i	0.282487	−	0.869406i
$207$		0			0
$208$			11.6503i			0.807805i
$209$	12.1286	−	0.0727602i	0.838953	−	0.00503293i
$210$		0			0
$211$	−10.3971	+	14.3103i	−0.715763	+	0.985163i	0.283891	+	0.958857i	$0.408375\pi$
$211$	−10.3971	+	14.3103i	−0.715763	+	0.985163i	−0.999654	+	0.0263064i	$0.991625\pi$
$212$	0.169161	+	0.0549638i	0.0116180	+	0.00377493i
$213$		0			0
$214$	1.90703	−	1.38554i	0.130362	−	0.0947134i
$215$	−8.28931	+	6.02254i	−0.565327	+	0.410734i
$216$		0			0
$217$	0.260173	+	0.0845353i	0.0176617	+	0.00573863i
$218$	−11.3960	+	15.6852i	−0.771834	+	1.06234i
$219$		0			0
$220$	−0.246827	+	0.775454i	−0.0166411	+	0.0522811i
$221$			1.20552i			0.0810923i
$222$		0			0
$223$	1.94588	−	5.98880i	0.130306	−	0.401040i	−0.864525	−	0.502590i	$-0.832380\pi$
$223$	1.94588	−	5.98880i	0.130306	−	0.401040i	0.994830	+	0.101551i	$0.0323804\pi$
$224$	−0.800472	+	0.260089i	−0.0534838	+	0.0173779i
$225$		0			0
$226$	−6.29631	−	8.66613i	−0.418824	−	0.576462i
$227$	0.912954	+	2.80978i	0.0605949	+	0.186492i	0.976772	−	0.214282i	$-0.0687412\pi$
$227$	0.912954	+	2.80978i	0.0605949	+	0.186492i	−0.916177	+	0.400774i	$0.868741\pi$
$228$		0			0
$229$	−15.4862	−	11.2514i	−1.02336	−	0.743512i	−0.0563886	−	0.998409i	$-0.517959\pi$
$229$	−15.4862	−	11.2514i	−1.02336	−	0.743512i	−0.966968	+	0.254897i	$0.917959\pi$
$230$	−41.1133			−2.71093
$231$		0			0
$232$	18.7359			1.23007
$233$	−7.96945	−	5.79015i	−0.522096	−	0.379325i	0.295297	−	0.955406i	$-0.404581\pi$
$233$	−7.96945	−	5.79015i	−0.522096	−	0.379325i	−0.817393	+	0.576080i	$0.804581\pi$
$234$		0			0
$235$	−3.71361	−	11.4293i	−0.242249	−	0.745566i
$236$	0.185820	+	0.255759i	0.0120958	+	0.0166485i
$237$		0			0
$238$	−1.26602	+	0.411354i	−0.0820636	+	0.0266641i
$239$	−1.81205	+	5.57692i	−0.117212	+	0.360741i	−0.992402	−	0.123038i	$-0.960736\pi$
$239$	−1.81205	+	5.57692i	−0.117212	+	0.360741i	0.875190	+	0.483779i	$0.160736\pi$
$240$		0			0
$241$		−	6.53045i		−	0.420663i	−0.977630	−	0.210332i	$-0.932546\pi$
$241$		−	6.53045i		−	0.420663i	0.977630	−	0.210332i	$-0.0674543\pi$
$242$	−15.8204	+	0.189822i	−1.01698	+	0.0122022i
$243$		0			0
$244$	−0.324239	+	0.446277i	−0.0207573	+	0.0285700i
$245$	7.85901	+	2.55355i	0.502094	+	0.163140i
$246$		0			0
$247$	8.34008	−	6.05943i	0.530667	−	0.385552i
$248$	−0.284061	+	0.206382i	−0.0180379	+	0.0131053i
$249$		0			0
$250$	−13.3039	−	4.32271i	−0.841414	−	0.273392i
$251$	−14.9833	+	20.6228i	−0.945739	+	1.30170i	0.00765590	+	0.999971i	$0.497563\pi$
$251$	−14.9833	+	20.6228i	−0.945739	+	1.30170i	−0.953394	+	0.301727i	$0.902437\pi$
$252$		0			0
$253$	−8.36355	−	25.2245i	−0.525812	−	1.58585i
$254$			4.41614i			0.277093i
$255$		0			0
$256$	0.509508	−	1.56810i	0.0318442	−	0.0980064i
$257$	3.53996	−	1.15020i	0.220816	−	0.0717476i	−0.196519	−	0.980500i	$-0.562964\pi$
$257$	3.53996	−	1.15020i	0.220816	−	0.0717476i	0.417336	+	0.908752i	$0.362964\pi$
$258$		0			0
$259$	7.79590	+	10.7301i	0.484414	+	0.666738i
$260$	0.213741	+	0.657828i	0.0132557	+	0.0407967i
$261$		0			0
$262$	4.02543	+	2.92465i	0.248692	+	0.180685i
$263$	−21.7100			−1.33869			−0.669347	−	0.742950i	$-0.733426\pi$
$263$	−21.7100			−1.33869			−0.669347	+	0.742950i	$0.733426\pi$
$264$		0			0
$265$	−9.22528			−0.566704
$266$	9.20932	+	6.69097i	0.564660	+	0.410249i
$267$		0			0
$268$	−0.117241	−	0.360832i	−0.00716166	−	0.0220413i
$269$	−15.9480	−	21.9505i	−0.972365	−	1.33835i	−0.940843	−	0.338843i	$-0.889965\pi$
$269$	−15.9480	−	21.9505i	−0.972365	−	1.33835i	−0.0315222	−	0.999503i	$-0.510035\pi$
$270$		0			0
$271$	19.9213	−	6.47282i	1.21013	−	0.393196i	0.366654	−	0.930358i	$-0.380503\pi$
$271$	19.9213	−	6.47282i	1.21013	−	0.393196i	0.843479	+	0.537162i	$0.180503\pi$
$272$	0.546154	−	1.68089i	0.0331155	−	0.101919i
$273$		0			0
$274$		−	14.5111i		−	0.876648i
$275$	−0.153724	−	25.6246i	−0.00926988	−	1.54522i
$276$		0			0
$277$	−12.5150	+	17.2254i	−0.751955	+	1.03498i	0.245886	+	0.969299i	$0.420921\pi$
$277$	−12.5150	+	17.2254i	−0.751955	+	1.03498i	−0.997841	+	0.0656780i	$0.979079\pi$
$278$	9.09352	+	2.95466i	0.545393	+	0.177209i
$279$		0			0
$280$	17.3495	−	12.6052i	1.03683	−	0.753302i
$281$	−19.2948	+	14.0185i	−1.15103	+	0.836274i	−0.988618	−	0.150449i	$-0.951928\pi$
$281$	−19.2948	+	14.0185i	−1.15103	+	0.836274i	−0.162414	+	0.986723i	$0.551928\pi$
$282$		0			0
$283$	31.1914	+	10.1347i	1.85414	+	0.602445i	0.996035	+	0.0889651i	$0.0283560\pi$
$283$	31.1914	+	10.1347i	1.85414	+	0.602445i	0.858101	+	0.513480i	$0.171644\pi$
$284$	−0.352900	+	0.485725i	−0.0209408	+	0.0288225i
$285$		0			0
$286$	−10.8317	+	7.96941i	−0.640492	+	0.471241i
$287$		−	4.76132i		−	0.281052i
$288$		0			0
$289$	−5.19678	+	15.9940i	−0.305693	+	0.940825i
$290$	32.9154	−	10.6949i	1.93286	−	0.628023i
$291$		0			0
$292$	0.204661	+	0.281691i	0.0119769	+	0.0164847i
$293$	1.35909	+	4.18286i	0.0793990	+	0.244365i	0.982875	−	0.184274i	$-0.0589933\pi$
$293$	1.35909	+	4.18286i	0.0793990	+	0.244365i	−0.903476	+	0.428639i	$0.858993\pi$
$294$		0			0
$295$	−13.2653	−	9.63777i	−0.772333	−	0.561133i
$296$	−17.0234			−0.989464
$297$		0			0
$298$	19.8107			1.14760
$299$	−18.2735	−	13.2765i	−1.05679	−	0.767800i
$300$		0			0
$301$	−1.92081	−	5.91163i	−0.110713	−	0.340741i
$302$	17.3788	+	23.9199i	1.00004	+	1.37643i
$303$		0			0
$304$	−14.3740	+	4.67038i	−0.824403	+	0.267865i
$305$	8.84127	−	27.2106i	0.506250	−	1.55808i
$306$		0			0
$307$			10.1101i			0.577013i	0.957478	+	0.288507i	$0.0931587\pi$
$307$			10.1101i			0.577013i	−0.957478	+	0.288507i	$0.906841\pi$
$308$	−0.401135	−	0.287781i	−0.0228568	−	0.0163978i
$309$		0			0
$310$	−0.381234	+	0.524723i	−0.0216526	+	0.0298023i
$311$	−7.09992	−	2.30691i	−0.402600	−	0.130813i	0.100716	−	0.994915i	$-0.467887\pi$
$311$	−7.09992	−	2.30691i	−0.402600	−	0.130813i	−0.503316	+	0.864103i	$0.667887\pi$
$312$		0			0
$313$	−24.0261	+	17.4560i	−1.35803	+	0.986670i	−0.359467	+	0.933158i	$0.617042\pi$
$313$	−24.0261	+	17.4560i	−1.35803	+	0.986670i	−0.998567	+	0.0535123i	$0.982958\pi$
$314$	−8.90057	+	6.46664i	−0.502288	+	0.364934i
$315$		0			0
$316$	−0.898406	−	0.291910i	−0.0505393	−	0.0164212i
$317$	3.08126	−	4.24099i	0.173061	−	0.238198i	−0.713672	−	0.700480i	$-0.752969\pi$
$317$	3.08126	−	4.24099i	0.173061	−	0.238198i	0.886733	+	0.462282i	$0.152969\pi$
$318$		0			0
$319$	13.2576	+	18.0191i	0.742281	+	1.00888i
$320$			27.4913i			1.53681i
$321$		0			0
$322$	7.70734	−	23.7208i	0.429513	−	1.32191i
$323$	−1.48735	+	0.483270i	−0.0827585	+	0.0268899i
$324$		0			0
$325$	−12.8020	−	17.6204i	−0.710128	−	0.977407i
$326$	3.97315	+	12.2281i	0.220053	+	0.677252i
$327$		0			0
$328$	4.94405	+	3.59207i	0.272990	+	0.198339i
$329$	7.29045			0.401935
$330$		0			0
$331$	15.2622			0.838885			0.419442	−	0.907782i	$-0.362226\pi$
$331$	15.2622			0.838885			0.419442	+	0.907782i	$0.362226\pi$
$332$	−0.811022	−	0.589242i	−0.0445106	−	0.0323389i
$333$		0			0
$334$	1.16670	+	3.59074i	0.0638392	+	0.196477i
$335$	11.5665	+	15.9199i	0.631946	+	0.869799i
$336$		0			0
$337$	−6.35159	+	2.06376i	−0.345993	+	0.112420i	−0.476858	−	0.878980i	$-0.658225\pi$
$337$	−6.35159	+	2.06376i	−0.345993	+	0.112420i	0.130865	+	0.991400i	$0.458225\pi$
$338$	2.24607	−	6.91270i	0.122170	−	0.376002i
$339$		0			0
$340$		−	0.104930i		−	0.00569064i
$341$	−0.399490	−	0.127158i	−0.0216336	−	0.00688597i
$342$		0			0
$343$	−11.8510	+	16.3116i	−0.639896	+	0.880742i
$344$	7.58763	+	2.46537i	0.409097	+	0.132924i
$345$		0			0
$346$	−19.4064	+	14.0996i	−1.04330	+	0.757999i
$347$	19.0467	−	13.8382i	1.02248	−	0.742874i	0.0556889	−	0.998448i	$-0.482264\pi$
$347$	19.0467	−	13.8382i	1.02248	−	0.742874i	0.966789	+	0.255574i	$0.0822645\pi$
$348$		0			0
$349$	32.4487	+	10.5432i	1.73694	+	0.564367i	0.994424	−	0.105460i	$-0.0336314\pi$
$349$	32.4487	+	10.5432i	1.73694	+	0.564367i	0.742518	+	0.669826i	$0.233631\pi$
$350$	14.1363	−	19.4569i	0.755616	−	1.04002i
$351$		0			0
$352$	1.22433	−	0.405944i	0.0652568	−	0.0216369i
$353$		−	5.97261i		−	0.317890i	−0.987287	−	0.158945i	$-0.949191\pi$
$353$		−	5.97261i		−	0.317890i	0.987287	−	0.158945i	$-0.0508092\pi$
$354$		0			0
$355$	9.62278	−	29.6159i	0.510724	−	1.57185i
$356$	−0.353649	+	0.114908i	−0.0187434	+	0.00609009i
$357$		0			0
$358$	−13.5482	−	18.6475i	−0.716043	−	0.985549i
$359$	−1.78228	−	5.48528i	−0.0940649	−	0.289502i	0.892944	−	0.450168i	$-0.148636\pi$
$359$	−1.78228	−	5.48528i	−0.0940649	−	0.289502i	−0.987009	+	0.160666i	$0.948636\pi$
$360$		0			0
$361$	−4.55194	−	3.30718i	−0.239576	−	0.174062i
$362$	18.9604			0.996534
$363$		0			0
$364$	−0.419610			−0.0219935
$365$	−14.6103	−	10.6150i	−0.764738	−	0.555614i
$366$		0			0
$367$	5.74255	+	17.6738i	0.299759	+	0.922563i	0.981581	+	0.191045i	$0.0611877\pi$
$367$	5.74255	+	17.6738i	0.299759	+	0.922563i	−0.681822	+	0.731518i	$0.738812\pi$
$368$	19.4644	+	26.7904i	1.01465	+	1.39655i
$369$		0			0
$370$	−29.9069	+	9.71733i	−1.55478	+	0.505180i
$371$	1.72943	−	5.32263i	0.0897874	−	0.276337i
$372$		0			0
$373$			0.609885i			0.0315786i	0.999875	+	0.0157893i	$0.00502610\pi$
$373$			0.609885i			0.0315786i	−0.999875	+	0.0157893i	$0.994974\pi$
$374$	1.93638	−	0.642035i	0.100128	−	0.0331988i
$375$		0			0
$376$	−5.50011	+	7.57025i	−0.283646	+	0.390406i
$377$	18.0835	+	5.87567i	0.931346	+	0.302613i
$378$		0			0
$379$	−3.40205	+	2.47174i	−0.174752	+	0.126965i	−0.671723	−	0.740802i	$-0.734445\pi$
$379$	−3.40205	+	2.47174i	−0.174752	+	0.126965i	0.496971	+	0.867767i	$0.334445\pi$
$380$	−0.725931	+	0.527420i	−0.0372395	+	0.0270561i
$381$		0			0
$382$	14.7953	+	4.80729i	0.756994	+	0.245962i
$383$	−1.45998	+	2.00949i	−0.0746014	+	0.102680i	−0.844687	−	0.535260i	$-0.820213\pi$
$383$	−1.45998	+	2.00949i	−0.0746014	+	0.102680i	0.770086	+	0.637941i	$0.220213\pi$
$384$		0			0
$385$	24.3995	+	7.76637i	1.24351	+	0.395811i
$386$			13.2985i			0.676875i
$387$		0			0
$388$	0.151219	−	0.465405i	0.00767700	−	0.0236274i
$389$	21.4336	−	6.96421i	1.08673	−	0.353099i	0.289747	−	0.957103i	$-0.406429\pi$
$389$	21.4336	−	6.96421i	1.08673	−	0.353099i	0.796981	+	0.604004i	$0.206429\pi$
$390$		0			0
$391$	2.01409	+	2.77215i	0.101857	+	0.140194i
$392$	−1.98830	−	6.11936i	−0.100424	−	0.309075i
$393$		0			0
$394$	25.8827	+	18.8049i	1.30395	+	0.947377i
$395$	48.9950			2.46520
$396$		0			0
$397$	5.07245			0.254579			0.127289	−	0.991866i	$-0.459372\pi$
$397$	5.07245			0.254579			0.127289	+	0.991866i	$0.459372\pi$
$398$	2.79877	+	2.03342i	0.140290	+	0.101926i
$399$		0			0
$400$	9.86731	+	30.3685i	0.493366	+	1.51842i
$401$	11.0985	+	15.2758i	0.554233	+	0.762836i	0.990579	−	0.136943i	$-0.0437276\pi$
$401$	11.0985	+	15.2758i	0.554233	+	0.762836i	−0.436346	+	0.899779i	$0.643728\pi$
$402$		0			0
$403$	−0.338892	+	0.110113i	−0.0168814	+	0.00548511i
$404$	−0.139476	+	0.429264i	−0.00693921	+	0.0213567i
$405$		0			0
$406$			20.9958i			1.04200i
$407$	−12.0458	−	16.3722i	−0.597088	−	0.811538i
$408$		0			0
$409$	−14.6101	+	20.1091i	−0.722425	+	0.994333i	0.277015	+	0.960866i	$0.410655\pi$
$409$	−14.6101	+	20.1091i	−0.722425	+	0.994333i	−0.999440	+	0.0334670i	$0.989345\pi$
$410$	10.7362	+	3.48840i	0.530223	+	0.172280i
$411$		0			0
$412$	−0.507593	+	0.368788i	−0.0250073	+	0.0181689i
$413$	8.04740	−	5.84678i	0.395987	−	0.287701i
$414$		0			0
$415$	49.4500	+	16.0673i	2.42741	+	0.788712i
$416$	0.644405	−	0.886947i	0.0315945	−	0.0434861i
$417$		0			0
$418$	−14.1747	−	10.1692i	−0.693308	−	0.497391i
$419$			11.3468i			0.554327i	0.960823	+	0.277164i	$0.0893944\pi$
$419$			11.3468i			0.554327i	−0.960823	+	0.277164i	$0.910606\pi$
$420$		0			0
$421$	9.93555	−	30.5785i	0.484229	−	1.49030i	−0.348866	−	0.937173i	$-0.613433\pi$
$421$	9.93555	−	30.5785i	0.484229	−	1.49030i	0.833095	−	0.553131i	$-0.186567\pi$
$422$	24.1966	−	7.86197i	1.17787	−	0.382715i
$423$		0			0
$424$	4.22218	+	5.81133i	0.205047	+	0.282223i
$425$	1.02103	+	3.14239i	0.0495270	+	0.152428i
$426$		0			0
$427$	14.0420	+	10.2021i	0.679542	+	0.493716i
$428$	−0.112722			−0.00544861
$429$		0			0
$430$	14.7373			0.710696
$431$	−9.91948	−	7.20693i	−0.477805	−	0.347145i	0.322670	−	0.946511i	$-0.395419\pi$
$431$	−9.91948	−	7.20693i	−0.477805	−	0.347145i	−0.800475	+	0.599366i	$0.795419\pi$
$432$		0			0
$433$	6.07293	+	18.6905i	0.291846	+	0.898210i	0.984263	+	0.176712i	$0.0565462\pi$
$433$	6.07293	+	18.6905i	0.291846	+	0.898210i	−0.692416	+	0.721498i	$0.743454\pi$
$434$	−0.231276	−	0.318325i	−0.0111016	−	0.0152801i
$435$		0			0
$436$	0.881755	−	0.286499i	0.0422284	−	0.0137208i
$437$	9.05481	−	27.8678i	0.433150	−	1.33310i
$438$		0			0
$439$			16.5342i			0.789137i	0.918867	+	0.394568i	$0.129106\pi$
$439$			16.5342i			0.789137i	−0.918867	+	0.394568i	$0.870894\pi$
$440$	−26.4721	+	19.4768i	−1.26201	+	0.928520i
$441$		0			0
$442$	1.01918	−	1.40278i	0.0484775	−	0.0667236i
$443$	−10.3906	−	3.37610i	−0.493671	−	0.160403i	0.0515924	−	0.998668i	$-0.483570\pi$
$443$	−10.3906	−	3.37610i	−0.493671	−	0.160403i	−0.545263	+	0.838265i	$0.683570\pi$
$444$		0			0
$445$	15.6030	−	11.3363i	0.739654	−	0.537390i
$446$	−7.32737	+	5.32365i	−0.346961	+	0.252082i
$447$		0			0
$448$	−15.8614	−	5.15368i	−0.749381	−	0.243489i
$449$	−19.5758	+	26.9438i	−0.923840	+	1.27156i	0.0383749	+	0.999263i	$0.487782\pi$
$449$	−19.5758	+	26.9438i	−0.923840	+	1.27156i	−0.962214	+	0.272293i	$0.912218\pi$
$450$		0			0
$451$	0.0437732	+	7.29668i	0.00206120	+	0.343587i
$452$			0.512242i			0.0240938i
$453$		0			0
$454$	1.31313	−	4.04138i	0.0616280	−	0.189672i
$455$	20.6984	−	6.72533i	0.970358	−	0.315288i
$456$		0			0
$457$	−18.5963	−	25.5956i	−0.869897	−	1.19731i	−0.979118	−	0.203293i	$-0.934836\pi$
$457$	−18.5963	−	25.5956i	−0.869897	−	1.19731i	0.109221	−	0.994017i	$-0.465164\pi$
$458$	8.50799	+	26.1849i	0.397552	+	1.22354i
$459$		0			0
$460$	1.59055	+	1.15560i	0.0741598	+	0.0538803i
$461$	−25.2871			−1.17774			−0.588868	−	0.808229i	$-0.700426\pi$
$461$	−25.2871			−1.17774			−0.588868	+	0.808229i	$0.700426\pi$
$462$		0			0
$463$	0.935012			0.0434537			0.0217269	−	0.999764i	$-0.493084\pi$
$463$	0.935012			0.0434537			0.0217269	+	0.999764i	$0.493084\pi$
$464$	−22.5523	−	16.3852i	−1.04696	−	0.760663i
$465$		0			0
$466$	4.37835	+	13.4752i	0.202823	+	0.624225i
$467$	7.72052	+	10.6264i	0.357263	+	0.491731i	0.949384	−	0.314119i	$-0.101709\pi$
$467$	7.72052	+	10.6264i	0.357263	+	0.491731i	−0.592120	+	0.805850i	$0.701709\pi$
$468$		0			0
$469$	−11.3535	+	3.68898i	−0.524257	+	0.170341i
$470$	−5.34138	+	16.4391i	−0.246380	+	0.758278i
$471$		0			0
$472$			12.7672i			0.587659i
$473$	2.99797	+	9.04187i	0.137847	+	0.415746i
$474$		0			0
$475$	16.6077	−	22.8586i	0.762014	−	1.04882i
$476$	0.0605407	+	0.0196709i	0.00277488	+	0.000901612i
$477$		0			0
$478$	6.82344	−	4.95752i	0.312097	−	0.226752i
$479$	23.2464	−	16.8895i	1.06216	−	0.771701i	0.0876694	−	0.996150i	$-0.472058\pi$
$479$	23.2464	−	16.8895i	1.06216	−	0.771701i	0.974486	+	0.224449i	$0.0720581\pi$
$480$		0			0
$481$	−16.4306	−	5.33863i	−0.749172	−	0.243421i
$482$	−5.52101	+	7.59902i	−0.251475	+	0.346126i
$483$		0			0
$484$	0.617382	+	0.437334i	0.0280628	+	0.0198788i
$485$			25.3811i			1.15250i
$486$		0			0
$487$	2.91324	−	8.96603i	0.132011	−	0.406289i	−0.863102	−	0.505030i	$-0.831481\pi$
$487$	2.91324	−	8.96603i	0.132011	−	0.406289i	0.995113	+	0.0987406i	$0.0314814\pi$
$488$	−21.1874	+	6.88420i	−0.959108	+	0.311633i
$489$		0			0
$490$	−6.98614	−	9.61560i	−0.315602	−	0.434388i
$491$	−1.24495	−	3.83157i	−0.0561839	−	0.172916i	0.919027	−	0.394196i	$-0.128977\pi$
$491$	−1.24495	−	3.83157i	−0.0561839	−	0.172916i	−0.975210	+	0.221279i	$0.928977\pi$
$492$		0			0
$493$	−2.33361	−	1.69547i	−0.105100	−	0.0763599i
$494$	−14.8276			−0.667124
$495$		0			0
$496$	0.522411			0.0234570
$497$	15.2833	+	11.1039i	0.685548	+	0.498080i
$498$		0			0
$499$	−7.16604	−	22.0548i	−0.320796	−	0.987308i	−0.973303	−	0.229525i	$-0.926283\pi$
$499$	−7.16604	−	22.0548i	−0.320796	−	0.987308i	0.652507	−	0.757783i	$-0.273717\pi$
$500$	0.393188	+	0.541177i	0.0175839	+	0.0242022i
$501$		0			0
$502$	34.8701	−	11.3300i	1.55633	−	0.505681i
$503$	10.5281	−	32.4020i	0.469423	−	1.44473i	−0.383911	−	0.923370i	$-0.625423\pi$
$503$	10.5281	−	32.4020i	0.469423	−	1.44473i	0.853334	−	0.521365i	$-0.174577\pi$
$504$		0			0
$505$		−	23.4101i		−	1.04174i
$506$	−11.5934	+	36.4227i	−0.515388	+	1.61919i
$507$		0			0
$508$	0.124128	−	0.170847i	0.00550729	−	0.00758013i
$509$	−30.7232	−	9.98256i	−1.36178	−	0.442469i	−0.465143	−	0.885236i	$-0.653997\pi$
$509$	−30.7232	−	9.98256i	−1.36178	−	0.442469i	−0.896637	+	0.442766i	$0.853997\pi$
$510$		0			0
$511$	8.86338	−	6.43962i	0.392093	−	0.284872i
$512$	17.2745	−	12.5506i	0.763431	−	0.554665i
$513$		0			0
$514$	−5.09161	−	1.65436i	−0.224581	−	0.0729709i
$515$	19.1277	−	26.3270i	0.842865	−	1.16010i
$516$		0			0
$517$	−11.1725	+	0.0670248i	−0.491368	+	0.00294775i
$518$		−	19.0768i		−	0.838185i
$519$		0			0
$520$	−8.63201	+	26.5666i	−0.378539	+	1.16502i
$521$	13.9354	−	4.52790i	0.610523	−	0.198371i	0.0125949	−	0.999921i	$-0.495991\pi$
$521$	13.9354	−	4.52790i	0.610523	−	0.198371i	0.597928	+	0.801550i	$0.295991\pi$
$522$		0			0
$523$	8.72743	+	12.0123i	0.381624	+	0.525260i	0.956014	−	0.293322i	$-0.0947607\pi$
$523$	8.72743	+	12.0123i	0.381624	+	0.525260i	−0.574390	+	0.818582i	$0.694761\pi$
$524$	−0.0735267	−	0.226292i	−0.00321203	−	0.00988561i
$525$		0			0
$526$	25.2624	+	18.3542i	1.10149	+	0.800280i
$527$	0.0540568			0.00235475
$528$		0			0
$529$	−41.2021			−1.79139
$530$	10.7348	+	7.79930i	0.466290	+	0.338780i
$531$		0			0
$532$	−0.168213	−	0.517707i	−0.00729297	−	0.0224455i
$533$	3.64540	+	5.01747i	0.157900	+	0.217331i
$534$		0			0
$535$	5.56031	−	1.80665i	0.240393	−	0.0781085i
$536$	4.73483	−	14.5723i	0.204514	−	0.629428i
$537$		0			0
$538$			39.0251i			1.68249i
$539$	4.47834	−	6.24232i	0.192896	−	0.268876i
$540$		0			0
$541$	−9.38031	+	12.9109i	−0.403291	+	0.555082i	−0.961566	−	0.274574i	$-0.911463\pi$
$541$	−9.38031	+	12.9109i	−0.403291	+	0.555082i	0.558275	+	0.829656i	$0.311463\pi$
$542$	−28.6533	−	9.31003i	−1.23077	−	0.399900i
$543$		0			0
$544$	−0.134553	+	0.0977583i	−0.00576890	+	0.00419135i
$545$	−38.9031	+	28.2648i	−1.66643	+	1.21073i
$546$		0			0
$547$	13.3357	+	4.33304i	0.570194	+	0.185267i	0.579903	−	0.814686i	$-0.303091\pi$
$547$	13.3357	+	4.33304i	0.570194	+	0.185267i	−0.00970898	+	0.999953i	$0.503091\pi$
$548$	−0.407875	+	0.561392i	−0.0174236	+	0.0239815i
$549$		0			0
$550$	−21.4849	+	29.9475i	−0.916117	+	1.27697i
$551$			24.6665i			1.05083i
$552$		0			0
$553$	−9.18489	+	28.2682i	−0.390581	+	1.20209i
$554$	29.1257	−	9.46351i	1.23743	−	0.402066i
$555$		0			0
$556$	−0.268752	−	0.369906i	−0.0113976	−	0.0156875i
$557$	−6.60761	−	20.3361i	−0.279974	−	0.861670i	−0.987860	−	0.155344i	$-0.950351\pi$
$557$	−6.60761	−	20.3361i	−0.279974	−	0.861670i	0.707887	−	0.706326i	$-0.249649\pi$
$558$		0			0
$559$	6.55026	+	4.75904i	0.277047	+	0.201286i
$560$	−31.9072			−1.34832
$561$		0			0
$562$	34.3036			1.44701
$563$	3.89503	+	2.82991i	0.164156	+	0.119266i	0.666830	−	0.745209i	$-0.267651\pi$
$563$	3.89503	+	2.82991i	0.164156	+	0.119266i	−0.502674	+	0.864476i	$0.667651\pi$
$564$		0			0
$565$	−8.21000	−	25.2678i	−0.345397	−	1.06302i
$566$	−27.7271	−	38.1631i	−1.16546	−	1.60411i
$567$		0			0
$568$	−23.0602	+	7.49271i	−0.967585	+	0.314387i
$569$	4.87428	−	15.0015i	0.204340	−	0.628895i	−0.795400	−	0.606085i	$-0.792739\pi$
$569$	4.87428	−	15.0015i	0.204340	−	0.628895i	0.999740	−	0.0228093i	$-0.00726105\pi$
$570$		0			0
$571$			9.88179i			0.413540i	0.978390	+	0.206770i	$0.0662952\pi$
$571$			9.88179i			0.413540i	−0.978390	+	0.206770i	$0.933705\pi$
$572$	0.643049	−	0.00385769i	0.0268872	−	0.000161298i
$573$		0			0
$574$	−4.02534	+	5.54041i	−0.168015	+	0.231252i
$575$	−58.8776	−	19.1305i	−2.45536	−	0.797796i
$576$		0			0
$577$	29.2977	−	21.2860i	1.21968	−	0.886147i	0.223604	−	0.974680i	$-0.428218\pi$
$577$	29.2977	−	21.2860i	1.21968	−	0.886147i	0.996073	+	0.0885327i	$0.0282178\pi$
$578$	19.5689	−	14.2176i	0.813959	−	0.591376i
$579$		0			0
$580$	−1.57401	−	0.511426i	−0.0653571	−	0.0212358i
$581$	−18.5404	+	25.5187i	−0.769185	+	1.05869i
$582$		0			0
$583$	−2.60140	+	8.17278i	−0.107739	+	0.338482i
$584$			14.0618i			0.581880i
$585$		0			0
$586$	1.95482	−	6.01631i	0.0807527	−	0.248531i
$587$	44.8907	−	14.5859i	1.85284	−	0.602024i	0.856539	−	0.516082i	$-0.172610\pi$
$587$	44.8907	−	14.5859i	1.85284	−	0.602024i	0.996300	−	0.0859424i	$-0.0273901\pi$
$588$		0			0
$589$	−0.271710	−	0.373977i	−0.0111956	−	0.0154095i
$590$	7.28782	+	22.4296i	0.300035	+	0.923412i
$591$		0			0
$592$	20.4910	+	14.8876i	0.842173	+	0.611875i
$593$	−34.2927			−1.40823			−0.704117	−	0.710084i	$-0.748657\pi$
$593$	−34.2927			−1.40823			−0.704117	+	0.710084i	$0.748657\pi$
$594$		0			0
$595$	−3.30161			−0.135353
$596$	−0.766418	−	0.556835i	−0.0313937	−	0.0228089i
$597$		0			0
$598$	10.0393	+	30.8979i	0.410539	+	1.26351i
$599$	21.6027	+	29.7335i	0.882662	+	1.21488i	0.975677	+	0.219215i	$0.0703495\pi$
$599$	21.6027	+	29.7335i	0.882662	+	1.21488i	−0.0930152	+	0.995665i	$0.529651\pi$
$600$		0			0
$601$	−2.59005	+	0.841557i	−0.105650	+	0.0343278i	−0.361365	−	0.932424i	$-0.617689\pi$
$601$	−2.59005	+	0.841557i	−0.105650	+	0.0343278i	0.255715	+	0.966752i	$0.417689\pi$
$602$	−2.76274	+	8.50285i	−0.112601	+	0.346550i
$603$		0			0
$604$		−	1.41387i		−	0.0575295i
$605$	−37.4635	−	11.6776i	−1.52311	−	0.474761i
$606$		0			0
$607$	6.93963	−	9.55158i	0.281671	−	0.387687i	−0.644616	−	0.764507i	$-0.722983\pi$
$607$	6.93963	−	9.55158i	0.281671	−	0.387687i	0.926286	+	0.376820i	$0.122983\pi$
$608$	1.35263	+	0.439495i	0.0548563	+	0.0178239i
$609$		0			0
$610$	−33.2926	+	24.1885i	−1.34798	+	0.979362i
$611$	−7.68266	+	5.58178i	−0.310807	+	0.225815i
$612$		0			0
$613$	−8.06638	−	2.62093i	−0.325798	−	0.105858i	0.141551	−	0.989931i	$-0.454791\pi$
$613$	−8.06638	−	2.62093i	−0.325798	−	0.105858i	−0.467349	+	0.884073i	$0.654791\pi$
$614$	8.54733	−	11.7644i	0.344942	−	0.474772i
$615$		0			0
$616$	−6.27474	−	18.9246i	−0.252816	−	0.762494i
$617$		−	9.09836i		−	0.366286i	−0.983086	−	0.183143i	$-0.941373\pi$
$617$		−	9.09836i		−	0.366286i	0.983086	−	0.183143i	$-0.0586272\pi$
$618$		0			0
$619$	−6.70184	+	20.6261i	−0.269370	+	0.829035i	0.721285	+	0.692639i	$0.243552\pi$
$619$	−6.70184	+	20.6261i	−0.269370	+	0.829035i	−0.990654	+	0.136396i	$0.956448\pi$
$620$	0.0294976	−	0.00958435i	0.00118465	−	0.000384917i
$621$		0			0
$622$	6.31136	+	8.68685i	0.253063	+	0.348311i
$623$	3.61555	+	11.1275i	0.144854	+	0.445814i
$624$		0			0
$625$	3.18452	+	2.31369i	0.127381	+	0.0925475i
$626$	42.7152			1.70724
$627$		0			0
$628$	0.526100			0.0209937
$629$	2.12031	+	1.54050i	0.0845424	+	0.0614237i
$630$		0			0
$631$	−6.35103	−	19.5465i	−0.252831	−	0.778133i	−0.994249	−	0.107090i	$-0.965847\pi$
$631$	−6.35103	−	19.5465i	−0.252831	−	0.778133i	0.741419	−	0.671043i	$-0.234153\pi$
$632$	−22.4238	−	30.8637i	−0.891970	−	1.22769i
$633$		0			0
$634$	−7.17090	+	2.32997i	−0.284793	+	0.0925348i
$635$	−3.38469	+	10.4170i	−0.134317	+	0.413386i
$636$		0			0
$637$		−	6.52982i		−	0.258721i
$638$	−0.193025	−	32.1759i	−0.00764194	−	1.27386i
$639$		0			0
$640$	24.8728	−	34.2345i	0.983186	−	1.35324i
$641$	9.41144	+	3.05796i	0.371729	+	0.120782i	0.488923	−	0.872327i	$-0.337390\pi$
$641$	9.41144	+	3.05796i	0.371729	+	0.120782i	−0.117194	+	0.993109i	$0.537390\pi$
$642$		0			0
$643$	32.7841	−	23.8190i	1.29288	−	0.939330i	0.293018	−	0.956107i	$-0.405340\pi$
$643$	32.7841	−	23.8190i	1.29288	−	0.939330i	0.999859	+	0.0167766i	$0.00534040\pi$
$644$	−0.964912	+	0.701050i	−0.0380229	+	0.0276252i
$645$		0			0
$646$	2.13930	+	0.695100i	0.0841695	+	0.0273483i
$647$	17.5380	−	24.1390i	0.689490	−	0.949001i	−0.310509	−	0.950570i	$-0.600499\pi$
$647$	17.5380	−	24.1390i	0.689490	−	0.949001i	0.999999	+	0.00156921i	$0.000499494\pi$
$648$		0			0
$649$	−12.2788	+	9.03412i	−0.481986	+	0.354620i
$650$			31.3268i			1.22874i
$651$		0			0
$652$	0.189995	−	0.584746i	0.00744080	−	0.0229004i
$653$	−32.9425	+	10.7037i	−1.28914	+	0.418867i	−0.871791	−	0.489879i	$-0.837041\pi$
$653$	−32.9425	+	10.7037i	−1.28914	+	0.418867i	−0.417350	+	0.908746i	$0.637041\pi$
$654$		0			0
$655$	7.25382	+	9.98403i	0.283430	+	0.390108i
$656$	−2.80974	−	8.64750i	−0.109702	−	0.337628i
$657$		0			0
$658$	−8.48338	−	6.16354i	−0.330717	−	0.240280i
$659$	−3.18762			−0.124172			−0.0620860	−	0.998071i	$-0.519775\pi$
$659$	−3.18762			−0.124172			−0.0620860	+	0.998071i	$0.519775\pi$
$660$		0			0
$661$	−9.68991			−0.376894			−0.188447	−	0.982083i	$-0.560345\pi$
$661$	−9.68991			−0.376894			−0.188447	+	0.982083i	$0.560345\pi$
$662$	−17.7595	−	12.9030i	−0.690243	−	0.501491i
$663$		0			0
$664$	−12.5107	−	38.5039i	−0.485509	−	1.49424i
$665$	16.5952	+	22.8413i	0.643533	+	0.885748i
$666$		0			0
$667$	51.4003	−	16.7010i	1.99023	−	0.646664i
$668$	0.0557915	−	0.171709i	0.00215864	−	0.00664361i
$669$		0			0
$670$		−	28.3036i		−	1.09346i
$671$	−21.6131	−	15.5056i	−0.834364	−	0.598587i
$672$		0			0
$673$	2.68084	−	3.68987i	0.103339	−	0.142234i	−0.754216	−	0.656627i	$-0.771983\pi$
$673$	2.68084	−	3.68987i	0.103339	−	0.142234i	0.857555	+	0.514393i	$0.171983\pi$
$674$	9.13566	+	2.96836i	0.351892	+	0.114337i
$675$		0			0
$676$	−0.281195	+	0.204300i	−0.0108152	+	0.00785769i
$677$	−38.4032	+	27.9016i	−1.47595	+	1.07234i	−0.497122	+	0.867680i	$0.665610\pi$
$677$	−38.4032	+	27.9016i	−1.47595	+	1.07234i	−0.978832	+	0.204663i	$0.934390\pi$
$678$		0			0
$679$	−14.6439	−	4.75809i	−0.561981	−	0.182599i
$680$	2.49082	−	3.42833i	0.0955187	−	0.131470i
$681$		0			0
$682$	0.357356	+	0.485704i	0.0136839	+	0.0185986i
$683$		−	19.9649i		−	0.763936i	−0.924175	−	0.381968i	$-0.875246\pi$
$683$		−	19.9649i		−	0.763936i	0.924175	−	0.381968i	$-0.124754\pi$
$684$		0			0
$685$	11.1218	−	34.2294i	0.424943	−	1.30784i
$686$	27.5805	−	8.96144i	1.05303	−	0.342149i
$687$		0			0
$688$	−6.97713	−	9.60320i	−0.266001	−	0.366118i
$689$	2.25269	+	6.93308i	0.0858208	+	0.264129i
$690$		0			0
$691$	−4.23810	−	3.07916i	−0.161225	−	0.117137i	0.504248	−	0.863559i	$-0.331770\pi$
$691$	−4.23810	−	3.07916i	−0.161225	−	0.117137i	−0.665472	+	0.746422i	$0.731770\pi$
$692$	1.14709			0.0436057
$693$		0			0
$694$	−33.8625			−1.28540
$695$	19.1856	+	13.9392i	0.727753	+	0.528743i
$696$		0			0
$697$	−0.290740	−	0.894805i	−0.0110126	−	0.0338931i
$698$	−28.8448	−	39.7015i	−1.09179	−	1.50272i
$699$		0			0
$700$	−1.09378	+	0.355391i	−0.0413411	+	0.0134325i
$701$	−10.9266	+	33.6287i	−0.412694	+	1.27014i	0.501604	+	0.865097i	$0.332743\pi$
$701$	−10.9266	+	33.6287i	−0.412694	+	1.27014i	−0.914298	+	0.405043i	$0.867257\pi$
$702$		0			0
$703$		−	22.4119i		−	0.845282i
$704$	24.3548	+	7.75215i	0.917908	+	0.292170i
$705$		0			0
$706$	−5.04940	+	6.94990i	−0.190037	+	0.261563i
$707$	13.5067	+	4.38860i	0.507973	+	0.165050i
$708$		0			0
$709$	−4.55413	+	3.30877i	−0.171034	+	0.124263i	−0.670009	−	0.742353i	$-0.733710\pi$
$709$	−4.55413	+	3.30877i	−0.171034	+	0.124263i	0.498975	+	0.866616i	$0.333710\pi$
$710$	−36.2354	+	26.3266i	−1.35989	+	0.988018i
$711$		0			0
$712$	−14.2822	−	4.64058i	−0.535249	−	0.173913i
$713$	−0.595331	+	0.819403i	−0.0222953	+	0.0306869i
$714$		0			0
$715$	−31.6583	+	10.4968i	−1.18395	+	0.392558i
$716$			1.10222i			0.0411921i
$717$		0			0
$718$	−2.56349	+	7.88962i	−0.0956687	+	0.294438i
$719$	−7.99933	+	2.59914i	−0.298325	+	0.0969316i	−0.454355	−	0.890821i	$-0.650130\pi$
$719$	−7.99933	+	2.59914i	−0.298325	+	0.0969316i	0.156030	+	0.987752i	$0.450130\pi$
$720$		0			0
$721$	11.6038	+	15.9713i	0.432150	+	0.594803i
$722$	2.50080	+	7.69666i	0.0930701	+	0.286440i
$723$		0			0
$724$	−0.733520	−	0.532933i	−0.0272611	−	0.0198063i
$725$	52.1139			1.93546
$726$		0			0
$727$	24.5536			0.910641			0.455321	−	0.890328i	$-0.349525\pi$
$727$	24.5536			0.910641			0.455321	+	0.890328i	$0.349525\pi$
$728$	−13.7097	−	9.96067i	−0.508115	−	0.369167i
$729$		0			0
$730$	8.02677	+	24.7039i	0.297084	+	0.914331i
$731$	−0.721962	−	0.993696i	−0.0267027	−	0.0367532i
$732$		0			0
$733$	−15.3133	+	4.97559i	−0.565610	+	0.183778i	−0.577844	−	0.816147i	$-0.696106\pi$
$733$	−15.3133	+	4.97559i	−0.565610	+	0.183778i	0.0122341	+	0.999925i	$0.496106\pi$
$734$	8.25966	−	25.4206i	0.304870	−	0.938293i
$735$		0			0
$736$		−	3.11619i		−	0.114864i
$737$	17.3652	−	5.75771i	0.639657	−	0.212088i
$738$		0			0
$739$	−6.18559	+	8.51373i	−0.227540	+	0.313183i	−0.907488	−	0.420078i	$-0.862003\pi$
$739$	−6.18559	+	8.51373i	−0.227540	+	0.313183i	0.679947	+	0.733261i	$0.262003\pi$
$740$	1.43014	+	0.464681i	0.0525730	+	0.0170820i
$741$		0			0
$742$	−6.51230	+	4.73147i	−0.239074	+	0.173698i
$743$	15.2075	−	11.0489i	0.557909	−	0.405344i	−0.272784	−	0.962075i	$-0.587944\pi$
$743$	15.2075	−	11.0489i	0.557909	−	0.405344i	0.830693	+	0.556731i	$0.187944\pi$
$744$		0			0
$745$	46.7304	+	15.1836i	1.71207	+	0.556285i
$746$	0.515613	−	0.709680i	0.0188779	−	0.0259832i
$747$		0			0
$748$	−0.0929589	−	0.0295888i	−0.00339891	−	0.00108187i
$749$			3.54677i			0.129596i
$750$		0			0
$751$	−4.17651	+	12.8540i	−0.152403	+	0.469048i	−0.997889	−	0.0649502i	$-0.979311\pi$
$751$	−4.17651	+	12.8540i	−0.152403	+	0.469048i	0.845486	+	0.533998i	$0.179311\pi$
$752$	13.2409	−	4.30223i	0.482846	−	0.156886i
$753$		0			0
$754$	−16.0750	−	22.1254i	−0.585417	−	0.805758i
$755$	22.6609	+	69.7430i	0.824714	+	2.53821i
$756$		0			0
$757$	24.2204	+	17.5972i	0.880307	+	0.639581i	0.933333	−	0.359013i	$-0.116887\pi$
$757$	24.2204	+	17.5972i	0.880307	+	0.639581i	−0.0530256	+	0.998593i	$0.516887\pi$
$758$	6.04840			0.219688
$759$		0			0
$760$	−36.2378			−1.31448
$761$	−1.10182	−	0.800522i	−0.0399411	−	0.0290189i	0.567636	−	0.823280i	$-0.307858\pi$
$761$	−1.10182	−	0.800522i	−0.0399411	−	0.0290189i	−0.607577	+	0.794261i	$0.707858\pi$
$762$		0			0
$763$	−9.01466	−	27.7443i	−0.326353	−	1.00441i
$764$	−0.437264	−	0.601843i	−0.0158197	−	0.0217739i
$765$		0			0
$766$	3.39775	−	1.10400i	0.122766	−	0.0398890i
$767$	−4.00387	+	12.3227i	−0.144572	+	0.444945i
$768$		0			0
$769$		−	30.1716i		−	1.08802i	−0.839080	−	0.544008i	$-0.816906\pi$
$769$		−	30.1716i		−	1.08802i	0.839080	−	0.544008i	$-0.183094\pi$
$770$	−21.8261	−	29.6652i	−0.786559	−	1.06906i
$771$		0			0
$772$	0.373791	−	0.514479i	0.0134530	−	0.0185165i
$773$	−14.7588	−	4.79543i	−0.530837	−	0.172479i	0.0313207	−	0.999509i	$-0.490029\pi$
$773$	−14.7588	−	4.79543i	−0.530837	−	0.172479i	−0.562158	+	0.827030i	$0.690029\pi$
$774$		0			0
$775$	−0.790117	+	0.574054i	−0.0283819	+	0.0206206i
$776$	15.9885	−	11.6163i	0.573952	−	0.417001i
$777$		0			0
$778$	−30.8285	−	10.0168i	−1.10526	−	0.359120i
$779$	−4.72909	+	6.50904i	−0.169437	+	0.233210i
$780$		0			0
$781$	−23.5236	−	16.8762i	−0.841739	−	0.603877i
$782$		−	4.92853i		−	0.176244i
$783$		0			0
$784$	−2.95829	+	9.10469i	−0.105653	+	0.325167i
$785$	−25.9513	+	8.43209i	−0.926242	+	0.300954i
$786$		0			0
$787$	13.4366	+	18.4938i	0.478962	+	0.659234i	0.978305	−	0.207170i	$-0.0664253\pi$
$787$	13.4366	+	18.4938i	0.478962	+	0.659234i	−0.499343	+	0.866404i	$0.666425\pi$
$788$	−0.472762	−	1.45501i	−0.0168414	−	0.0518326i
$789$		0			0
$790$	−57.0120	−	41.4217i	−2.02840	−	1.47372i
$791$	16.1176			0.573076
$792$		0			0
$793$	−22.6085			−0.802853
$794$	−5.90245	−	4.28838i	−0.209470	−	0.152189i
$795$		0			0
$796$	−0.0511210	−	0.157334i	−0.00181194	−	0.00557657i
$797$	13.2573	+	18.2472i	0.469599	+	0.646348i	0.976465	−	0.215677i	$-0.0691960\pi$
$797$	13.2573	+	18.2472i	0.469599	+	0.646348i	−0.506866	+	0.862025i	$0.669196\pi$
$798$		0			0
$799$	1.37011	−	0.445176i	0.0484710	−	0.0157492i
$800$	0.928540	−	2.85775i	0.0328289	−	0.101037i
$801$		0			0
$802$		−	27.1583i		−	0.958994i
$803$	−13.5238	+	9.95015i	−0.477246	+	0.351133i
$804$		0			0
$805$	36.3608	−	50.0464i	1.28155	−	1.76390i
$806$	0.487438	+	0.158378i	0.0171693	+	0.00557863i
$807$		0			0
$808$	−14.7469	+	10.7142i	−0.518793	+	0.376925i
$809$	17.0062	−	12.3557i	0.597905	−	0.434404i	−0.247229	−	0.968957i	$-0.579520\pi$
$809$	17.0062	−	12.3557i	0.597905	−	0.434404i	0.845135	+	0.534553i	$0.179520\pi$
$810$		0			0
$811$	−52.0358	−	16.9075i	−1.82722	−	0.593701i	−0.999468	−	0.0326137i	$-0.989617\pi$
$811$	−52.0358	−	16.9075i	−1.82722	−	0.593701i	−0.827756	−	0.561088i	$-0.810383\pi$
$812$	0.590146	−	0.812266i	0.0207101	−	0.0285049i
$813$		0			0
$814$	0.175382	+	29.2350i	0.00614715	+	1.02469i
$815$			31.8894i			1.11704i
$816$		0			0
$817$	−3.24575	+	9.98940i	−0.113555	+	0.349485i
$818$	34.0016	−	11.0478i	1.18884	−	0.386277i
$819$		0			0
$820$	−0.317300	−	0.436727i	−0.0110806	−	0.0152512i
$821$	−9.07753	−	27.9378i	−0.316808	−	0.975035i	−0.975004	−	0.222188i	$-0.928680\pi$
$821$	−9.07753	−	27.9378i	−0.316808	−	0.975035i	0.658196	−	0.752847i	$-0.271320\pi$
$822$		0			0
$823$	−19.3666	−	14.0706i	−0.675076	−	0.490471i	0.196645	−	0.980475i	$-0.436995\pi$
$823$	−19.3666	−	14.0706i	−0.675076	−	0.490471i	−0.871720	+	0.490004i	$0.836995\pi$
$824$	−25.3385			−0.882710
$825$		0			0
$826$	−14.3072			−0.497812
$827$	−26.5521	−	19.2912i	−0.923308	−	0.670822i	0.0210374	−	0.999779i	$-0.493303\pi$
$827$	−26.5521	−	19.2912i	−0.923308	−	0.670822i	−0.944345	+	0.328956i	$0.893303\pi$
$828$		0			0
$829$	1.05596	+	3.24990i	0.0366749	+	0.112874i	0.967718	−	0.252036i	$-0.0811000\pi$
$829$	1.05596	+	3.24990i	0.0366749	+	0.112874i	−0.931043	+	0.364909i	$0.881100\pi$
$830$	−43.9578	−	60.5027i	−1.52580	−	2.10008i
$831$		0			0
$832$	20.6605	−	6.71301i	0.716275	−	0.232732i
$833$	−0.306111	+	0.942112i	−0.0106061	+	0.0326423i
$834$		0			0
$835$			9.36421i			0.324062i
$836$	0.262545	+	0.791835i	0.00908031	+	0.0273862i
$837$		0			0
$838$	9.59288	−	13.2035i	0.331381	−	0.456106i
$839$	21.4354	+	6.96478i	0.740031	+	0.240451i	0.654686	−	0.755901i	$-0.272801\pi$
$839$	21.4354	+	6.96478i	0.740031	+	0.240451i	0.0853450	+	0.996351i	$0.472801\pi$
$840$		0			0
$841$	−13.3453	+	9.69590i	−0.460182	+	0.334341i
$842$	−37.4131	+	27.1822i	−1.28934	+	0.936762i
$843$		0			0
$844$	−1.15708	−	0.375958i	−0.0398283	−	0.0129410i
$845$	10.5963	−	14.5845i	0.364523	−	0.501723i
$846$		0			0
$847$	13.7606	−	19.4258i	0.472821	−	0.667479i
$848$		−	10.6875i		−	0.367011i
$849$		0			0
$850$	1.46857	−	4.51978i	0.0503714	−	0.155027i
$851$	−46.7023	+	15.1745i	−1.60093	+	0.520175i
$852$		0			0
$853$	−12.0798	−	16.6264i	−0.413605	−	0.569278i	0.550488	−	0.834843i	$-0.314442\pi$
$853$	−12.0798	−	16.6264i	−0.413605	−	0.569278i	−0.964093	+	0.265565i	$0.914442\pi$
$854$	−7.71458	−	23.7430i	−0.263987	−	0.812470i
$855$		0			0
$856$	−3.68289	−	2.67578i	−0.125879	−	0.0914562i
$857$	−25.6700			−0.876870			−0.438435	−	0.898763i	$-0.644467\pi$
$857$	−25.6700			−0.876870			−0.438435	+	0.898763i	$0.644467\pi$
$858$		0			0
$859$	2.87353			0.0980435			0.0490218	−	0.998798i	$-0.484390\pi$
$859$	2.87353			0.0980435			0.0490218	+	0.998798i	$0.484390\pi$
$860$	−0.570143	−	0.414233i	−0.0194417	−	0.0141252i
$861$		0			0
$862$	5.44968	+	16.7724i	0.185617	+	0.571270i
$863$	17.7481	+	24.4282i	0.604153	+	0.831546i	0.996081	−	0.0884505i	$-0.0281915\pi$
$863$	17.7481	+	24.4282i	0.604153	+	0.831546i	−0.391927	+	0.919996i	$0.628192\pi$
$864$		0			0
$865$	−56.5832	+	18.3850i	−1.92389	+	0.625108i
$866$	8.73485	−	26.8831i	0.296822	−	0.913525i
$867$		0			0
$868$			0.0188157i			0.000638647i
$869$	13.8159	−	43.4052i	0.468672	−	1.47242i
$870$		0			0
$871$	9.13993	−	12.5800i	0.309695	−	0.426258i
$872$	35.6100	+	11.5704i	1.20591	+	0.391823i
$873$		0			0
$874$	−34.0967	+	24.7727i	−1.15334	+	0.837948i
$875$	17.0280	−	12.3716i	0.575653	−	0.418236i
$876$		0			0
$877$	14.0967	+	4.58030i	0.476012	+	0.154666i	0.537190	−	0.843461i	$-0.319486\pi$
$877$	14.0967	+	4.58030i	0.476012	+	0.154666i	−0.0611780	+	0.998127i	$0.519486\pi$
$878$	13.9785	−	19.2397i	0.471751	−	0.649310i
$879$		0			0
$880$	48.8975	−	0.293339i	1.64833	−	0.00988845i
$881$			7.29612i			0.245813i	0.992418	+	0.122906i	$0.0392215\pi$
$881$			7.29612i			0.245813i	−0.992418	+	0.122906i	$0.960779\pi$
$882$		0			0
$883$	−13.3053	+	40.9496i	−0.447760	+	1.37806i	0.431668	+	0.902032i	$0.357925\pi$
$883$	−13.3053	+	40.9496i	−0.447760	+	1.37806i	−0.879428	+	0.476031i	$0.842075\pi$
$884$	−0.0788582	+	0.0256226i	−0.00265229	+	0.000861781i
$885$		0			0
$886$	9.23653	+	12.7130i	0.310307	+	0.427102i
$887$	−11.2511	−	34.6272i	−0.377774	−	1.16267i	−0.941588	−	0.336767i	$-0.890666\pi$
$887$	−11.2511	−	34.6272i	−0.377774	−	1.16267i	0.563814	−	0.825902i	$-0.309334\pi$
$888$		0			0
$889$	−5.37569	−	3.90566i	−0.180295	−	0.130992i
$890$	−27.7401			−0.929851
$891$		0			0
$892$	0.433110			0.0145016
$893$	−9.96652	−	7.24110i	−0.333517	−	0.242314i
$894$		0			0
$895$	−17.6660	−	54.3703i	−0.590508	−	1.81740i
$896$	15.0892	+	20.7685i	0.504094	+	0.693826i
$897$		0			0
$898$	45.5580	−	14.8027i	1.52029	−	0.493972i
$899$	0.263471	−	0.810880i	0.00878724	−	0.0270443i
$900$		0			0
$901$		−	1.10590i		−	0.0368428i
$902$	6.11787	−	8.52764i	0.203703	−	0.283939i
$903$		0			0
$904$	−12.1596	+	16.7362i	−0.404421	+	0.556638i
$905$	44.7245	+	14.5319i	1.48669	+	0.483056i
$906$		0			0
$907$	36.9890	−	26.8741i	1.22820	−	0.892340i	0.231446	−	0.972848i	$-0.425654\pi$
$907$	36.9890	−	26.8741i	1.22820	−	0.892340i	0.996754	+	0.0805082i	$0.0256543\pi$
$908$	−0.164395	+	0.119440i	−0.00545565	+	0.00396376i
$909$		0			0
$910$	−29.7711	−	9.67321i	−0.986902	−	0.320664i
$911$	−16.9022	+	23.2639i	−0.559996	+	0.770769i	−0.991326	−	0.131426i	$-0.958045\pi$
$911$	−16.9022	+	23.2639i	−0.559996	+	0.770769i	0.431330	+	0.902194i	$0.358045\pi$
$912$		0			0
$913$	28.1784	−	39.2776i	0.932569	−	1.29990i
$914$			45.5056i			1.50519i
$915$		0			0
$916$	0.406850	−	1.25216i	0.0134427	−	0.0413724i
$917$	−7.12024	+	2.31351i	−0.235131	+	0.0763987i
$918$		0			0
$919$	−4.49558	−	6.18764i	−0.148296	−	0.204111i	0.728406	−	0.685145i	$-0.240261\pi$
$919$	−4.49558	−	6.18764i	−0.148296	−	0.204111i	−0.876702	+	0.481034i	$0.840261\pi$
$920$	24.5356	+	75.5127i	0.808914	+	2.48958i
$921$		0			0
$922$	29.4248	+	21.3784i	0.969053	+	0.704058i
$923$	−24.6070			−0.809949
$924$		0			0
$925$	−47.3507			−1.55688
$926$	−1.08801	−	0.790484i	−0.0357542	−	0.0259769i
$927$		0			0
$928$	0.810619	+	2.49483i	0.0266099	+	0.0818968i
$929$	20.5354	+	28.2645i	0.673744	+	0.927330i	0.999838	−	0.0180080i	$-0.00573243\pi$
$929$	20.5354	+	28.2645i	0.673744	+	0.927330i	−0.326093	+	0.945338i	$0.605732\pi$
$930$		0			0
$931$	8.05638	−	2.61768i	0.264037	−	0.0857909i
$932$	0.209372	−	0.644380i	0.00685820	−	0.0211074i
$933$		0			0
$934$		−	18.8923i		−	0.618176i
$935$	5.05969	−	0.0303534i	0.165470	−	0.000992662i
$936$		0			0
$937$	33.5209	−	46.1375i	1.09508	−	1.50725i	0.253328	−	0.967381i	$-0.418475\pi$
$937$	33.5209	−	46.1375i	1.09508	−	1.50725i	0.841751	−	0.539866i	$-0.181525\pi$
$938$	16.3301	+	5.30596i	0.533195	+	0.173246i
$939$		0			0
$940$	0.668708	−	0.485845i	0.0218109	−	0.0158465i
$941$	−13.6101	+	9.88831i	−0.443676	+	0.322350i	−0.787094	−	0.616833i	$-0.788415\pi$
$941$	−13.6101	+	9.88831i	−0.443676	+	0.322350i	0.343418	+	0.939183i	$0.388415\pi$
$942$		0			0
$943$	16.7655	+	5.44745i	0.545961	+	0.177394i
$944$	11.1654	−	15.3678i	0.363402	−	0.500181i
$945$		0			0
$946$	4.15571	−	13.0559i	0.135114	−	0.424486i
$947$		−	53.9128i		−	1.75193i	−0.482373	−	0.875966i	$-0.660225\pi$
$947$		−	53.9128i		−	1.75193i	0.482373	−	0.875966i	$-0.339775\pi$
$948$		0			0
$949$	−4.40985	+	13.5721i	−0.143150	+	0.440570i
$950$	−38.6505	+	12.5583i	−1.25399	+	0.407445i
$951$		0			0
$952$	1.51107	+	2.07980i	0.0489739	+	0.0674068i
$953$	−1.34167	−	4.12923i	−0.0434609	−	0.133759i	0.926972	−	0.375131i	$-0.122402\pi$
$953$	−1.34167	−	4.12923i	−0.0434609	−	0.133759i	−0.970433	+	0.241372i	$0.922402\pi$
$954$		0			0
$955$	31.2154	+	22.6793i	1.01011	+	0.733884i
$956$	−0.403323			−0.0130444
$957$		0			0
$958$	−41.3290			−1.33528
$959$	17.6641	+	12.8337i	0.570403	+	0.414422i
$960$		0			0
$961$	−9.57459	−	29.4676i	−0.308858	−	0.950566i
$962$	14.6057	+	20.1031i	0.470908	+	0.648149i
$963$		0			0
$964$	0.427183	−	0.138800i	0.0137586	−	0.00447046i
$965$	−10.1924	+	31.3690i	−0.328106	+	1.00981i
$966$		0			0
$967$		−	18.4429i		−	0.593085i	−0.955020	−	0.296542i	$-0.904166\pi$
$967$		−	18.4429i		−	0.593085i	0.955020	−	0.296542i	$-0.0958336\pi$
$968$	9.78996	+	28.9441i	0.314661	+	0.930299i
$969$		0			0
$970$	21.4578	−	29.5342i	0.688970	−	0.948286i
$971$	11.5909	+	3.76611i	0.371970	+	0.120860i	0.489036	−	0.872264i	$-0.337349\pi$
$971$	11.5909	+	3.76611i	0.371970	+	0.120860i	−0.117066	+	0.993124i	$0.537349\pi$
$972$		0			0
$973$	−11.6390	+	8.45625i	−0.373130	+	0.271095i
$974$	−10.9700	+	7.97021i	−0.351503	+	0.255382i
$975$		0			0
$976$	31.5236	+	10.2426i	1.00905	+	0.327859i
$977$	18.0205	−	24.8031i	0.576528	−	0.793523i	−0.416781	−	0.909007i	$-0.636842\pi$
$977$	18.0205	−	24.8031i	0.576528	−	0.793523i	0.993309	+	0.115484i	$0.0368419\pi$
$978$		0			0
$979$	−5.64309	−	17.0196i	−0.180354	−	0.543948i
$980$			0.568364i			0.0181557i
$981$		0			0
$982$	−1.79065	+	5.51104i	−0.0571418	+	0.175864i
$983$	−12.1774	+	3.95668i	−0.388399	+	0.126199i	−0.496706	−	0.867919i	$-0.665457\pi$
$983$	−12.1774	+	3.95668i	−0.388399	+	0.126199i	0.108306	+	0.994118i	$0.465457\pi$
$984$		0			0
$985$	46.6406	+	64.1953i	1.48609	+	2.04543i
$986$	1.28206	+	3.94579i	0.0408292	+	0.125659i
$987$		0			0
$988$	0.573635	+	0.416770i	0.0182498	+	0.0132592i
$989$	23.0136			0.731791
$990$		0			0
$991$	13.7769			0.437638			0.218819	−	0.975765i	$-0.429780\pi$
$991$	13.7769			0.437638			0.218819	+	0.975765i	$0.429780\pi$
$992$	−0.0397715	−	0.0288957i	−0.00126275	−	0.000917440i
$993$		0			0
$994$	−8.39650	−	25.8418i	−0.266321	−	0.819651i
$995$	5.04337	+	6.94161i	0.159886	+	0.220064i
$996$		0			0
$997$	−6.24178	+	2.02808i	−0.197679	+	0.0642298i	−0.406183	−	0.913792i	$-0.633141\pi$
$997$	−6.24178	+	2.02808i	−0.197679	+	0.0642298i	0.208504	+	0.978021i	$0.433141\pi$
$998$	−10.3071	+	31.7220i	−0.326265	+	1.00414i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.6		80
3.2	odd	2	inner	891.2.k.a.161.15		80
9.2	odd	6		297.2.t.a.260.7		80
9.4	even	3		297.2.t.a.62.7		80
9.5	odd	6		99.2.p.a.29.4	✓	80
9.7	even	3		99.2.p.a.95.4	yes	80
11.8	odd	10	inner	891.2.k.a.404.15		80
33.8	even	10	inner	891.2.k.a.404.6		80
99.41	even	30		99.2.p.a.74.4	yes	80
99.52	odd	30		99.2.p.a.41.4	yes	80
99.74	even	30		297.2.t.a.206.7		80
99.85	odd	30		297.2.t.a.8.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.4	✓	80	9.5	odd	6
99.2.p.a.41.4	yes	80	99.52	odd	30
99.2.p.a.74.4	yes	80	99.41	even	30
99.2.p.a.95.4	yes	80	9.7	even	3
297.2.t.a.8.7		80	99.85	odd	30
297.2.t.a.62.7		80	9.4	even	3
297.2.t.a.206.7		80	99.74	even	30
297.2.t.a.260.7		80	9.2	odd	6
891.2.k.a.161.6		80	1.1	even	1	trivial
891.2.k.a.161.15		80	3.2	odd	2	inner
891.2.k.a.404.6		80	33.8	even	10	inner
891.2.k.a.404.15		80	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.16363 - 0.845427i) q^{2} +(0.0212543 + 0.0654141i) q^{4} +(-2.09686 - 2.88608i) q^{5} +(2.05824 - 0.668764i) q^{7} +(-0.858363 + 2.64177i) q^{8} +5.13106i q^{10} +(-3.14809 + 1.04380i) q^{11} +(-1.65695 + 2.28059i) q^{13} +(-2.96042 - 0.961900i) q^{14} +(3.34353 - 2.42922i) q^{16} +(0.345974 - 0.251365i) q^{17} +(-3.47799 - 1.13007i) q^{19} +(0.144223 - 0.198506i) q^{20} +(4.54567 + 1.44689i) q^{22} +8.01262i q^{23} +(-2.38754 + 7.34810i) q^{25} +(3.85615 - 1.25294i) q^{26} +(0.0874932 + 0.120424i) q^{28} +(-2.08433 - 6.41492i) q^{29} +(0.102264 + 0.0742991i) q^{31} -0.388910 q^{32} -0.615095 q^{34} +(-6.24595 - 4.53795i) q^{35} +(1.89382 + 5.82859i) q^{37} +(3.09171 + 4.25537i) q^{38} +(9.42422 - 3.06211i) q^{40} +(0.679859 - 2.09239i) q^{41} -2.87217i q^{43} +(-0.135190 - 0.183744i) q^{44} +(6.77408 - 9.32372i) q^{46} +(3.20383 + 1.04099i) q^{47} +(-1.87400 + 1.36154i) q^{49} +(8.99050 - 6.53198i) q^{50} +(-0.184400 - 0.0599153i) q^{52} +(1.52002 - 2.09212i) q^{53} +(9.61358 + 6.89694i) q^{55} +6.01145i q^{56} +(-2.99795 + 9.22674i) q^{58} +(4.37133 - 1.42033i) q^{59} +(4.71412 + 6.48843i) q^{61} +(-0.0561830 - 0.172913i) q^{62} +(-6.23451 - 4.52964i) q^{64} +10.0564 q^{65} -5.51612 q^{67} +(0.0237962 + 0.0172890i) q^{68} +(3.43147 + 10.5610i) q^{70} +(5.13082 + 7.06197i) q^{71} +(4.81457 - 1.56435i) q^{73} +(2.72393 - 8.38341i) q^{74} -0.251529i q^{76} +(-5.78149 + 4.25372i) q^{77} +(-8.07272 + 11.1111i) q^{79} +(-14.0218 - 4.55596i) q^{80} +(-2.56007 + 1.86000i) q^{82} +(-11.7915 + 8.56700i) q^{83} +(-1.45091 - 0.471431i) q^{85} +(-2.42821 + 3.34215i) q^{86} +(-0.0552663 - 9.21250i) q^{88} +5.40631i q^{89} +(-1.88523 + 5.80213i) q^{91} +(-0.524138 + 0.170303i) q^{92} +(-2.84800 - 3.91993i) q^{94} +(4.03139 + 12.4073i) q^{95} +(-5.75596 - 4.18195i) q^{97} +3.33172 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 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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