LMFDB - Embedded newform 891.2.k.a.161.15

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			161.15
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.15

$q$-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	0.917516	−	0.397698i	$-0.130191\pi$
$2$	1.16363	+	0.845427i	0.822811	+	0.597807i	−0.0947056	+	0.995505i	$0.530191\pi$
$3$		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	$0.0939460\pi$
$5$	2.09686	+	2.88608i	0.937743	+	1.29069i	−0.0190182	+	0.999819i	$0.506054\pi$
$6$		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	−0.628950	−	0.777446i	$-0.716515\pi$
$17$	−0.345974	+	0.251365i	−0.0839109	+	0.0609648i	0.545039	+	0.838411i	$0.316515\pi$
$18$		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	$-0.685251\pi$
$23$		−	8.01262i		−	1.67075i	0.549683	−	0.835373i	$-0.314749\pi$
$24$		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	$0.115416\pi$
$29$	2.08433	+	6.41492i	0.387051	+	1.19122i	−0.547930	+	0.836524i	$0.684584\pi$
$30$		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	−0.990005	−	0.141034i	$-0.954957\pi$
$41$	−0.679859	+	2.09239i	−0.106176	+	0.326777i	0.883829	+	0.467811i	$0.154957\pi$
$42$		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	0.0658817	−	0.997827i	$-0.479014\pi$
$47$	−3.20383	−	1.04099i	−0.467327	−	0.151844i	−0.533209	+	0.845984i	$0.679014\pi$
$48$		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	−0.900550	−	0.434753i	$-0.856836\pi$
$53$	−1.52002	+	2.09212i	−0.208790	+	0.287375i	0.691760	+	0.722128i	$0.256836\pi$
$54$		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	−0.579411	−	0.815035i	$-0.696717\pi$
$59$	−4.37133	+	1.42033i	−0.569099	+	0.184912i	0.0103122	+	0.999947i	$0.496717\pi$
$60$		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	0.387572	−	0.921840i	$-0.373314\pi$
$71$	−5.13082	−	7.06197i	−0.608916	−	0.838101i	−0.996488	+	0.0837384i	$0.973314\pi$
$72$		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	0.294398	−	0.955683i	$-0.404881\pi$
$83$	11.7915	−	8.56700i	1.29428	−	0.940350i	0.999882	+	0.0153328i	$0.00488078\pi$
$84$		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	$-0.907497\pi$
$89$		−	5.40631i		−	0.573068i	0.958070	−	0.286534i	$-0.0925031\pi$
$90$		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	0.291445	−	0.956588i	$-0.405864\pi$
$101$	−5.30898	−	3.85720i	−0.528263	−	0.383805i	−0.819708	+	0.572782i	$0.805864\pi$
$102$		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	−0.923588	−	0.383386i	$-0.874758\pi$
$107$	0.506436	−	1.55865i	0.0489590	−	0.150680i	0.972547	+	0.232706i	$0.0747579\pi$
$108$		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	−0.0437190	−	0.999044i	$-0.513921\pi$
$113$	−7.08299	−	2.30140i	−0.666312	−	0.216498i	−0.622593	+	0.782546i	$0.713921\pi$
$114$		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	$-0.451711\pi$
$131$	3.45938			0.302247			0.151124	+	0.988515i	$0.451711\pi$
$132$		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	0.476706	−	0.879063i	$-0.341831\pi$
$137$	−5.93010	−	8.16208i	−0.506643	−	0.697334i	−0.983349	+	0.181729i	$0.941831\pi$
$138$		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	−0.0288711	−	0.999583i	$-0.509191\pi$
$149$	11.1430	−	8.09584i	0.912867	−	0.663237i	0.941738	+	0.336346i	$0.109191\pi$
$150$		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	0.666912	−	0.745137i	$-0.267616\pi$
$167$	2.12363	+	1.54291i	0.164331	+	0.119394i	−0.502580	+	0.864531i	$0.667616\pi$
$168$		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	$0.318581\pi$
$173$	−5.15363	+	15.8612i	−0.391823	+	1.20591i	−0.931408	+	0.363977i	$0.881419\pi$
$174$		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	−0.322110	−	0.946702i	$-0.604392\pi$
$179$	−15.2409	−	4.95208i	−1.13916	−	0.370136i	−0.817050	+	0.576567i	$0.804392\pi$
$180$		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	0.0877752	−	0.996140i	$-0.472024\pi$
$191$	10.2865	−	3.34228i	0.744303	−	0.241839i	0.656528	+	0.754301i	$0.272024\pi$
$192$		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	$-0.208843\pi$
$197$	22.2431			1.58475			0.792377	+	0.610032i	$0.208843\pi$
$198$		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	0.916177	−	0.400774i	$-0.131259\pi$
$227$	−0.912954	−	2.80978i	−0.0605949	−	0.186492i	−0.976772	+	0.214282i	$0.931259\pi$
$228$		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	0.817393	−	0.576080i	$-0.195419\pi$
$233$	7.96945	+	5.79015i	0.522096	+	0.379325i	−0.295297	+	0.955406i	$0.595419\pi$
$234$		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	−0.875190	−	0.483779i	$-0.839264\pi$
$239$	1.81205	−	5.57692i	0.117212	−	0.360741i	0.992402	+	0.123038i	$0.0392637\pi$
$240$		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	$-0.502437\pi$
$251$	14.9833	−	20.6228i	0.945739	−	1.30170i	0.953394	−	0.301727i	$-0.0975630\pi$
$252$		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	−0.417336	−	0.908752i	$-0.637036\pi$
$257$	−3.53996	+	1.15020i	−0.220816	+	0.0717476i	0.196519	+	0.980500i	$0.437036\pi$
$258$		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	$-0.266574\pi$
$263$	21.7100			1.33869			0.669347	+	0.742950i	$0.266574\pi$
$264$		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	$0.110035\pi$
$269$	15.9480	+	21.9505i	0.972365	+	1.33835i	0.0315222	+	0.999503i	$0.489965\pi$
$270$		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	0.162414	−	0.986723i	$-0.448072\pi$
$281$	19.2948	−	14.0185i	1.15103	−	0.836274i	0.988618	+	0.150449i	$0.0480719\pi$
$282$		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	0.903476	−	0.428639i	$-0.141007\pi$
$293$	−1.35909	−	4.18286i	−0.0793990	−	0.244365i	−0.982875	+	0.184274i	$0.941007\pi$
$294$		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	0.503316	−	0.864103i	$-0.332113\pi$
$311$	7.09992	+	2.30691i	0.402600	+	0.130813i	−0.100716	+	0.994915i	$0.532113\pi$
$312$		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	−0.886733	−	0.462282i	$-0.847031\pi$
$317$	−3.08126	+	4.24099i	−0.173061	+	0.238198i	0.713672	+	0.700480i	$0.247031\pi$
$318$		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	−0.966789	−	0.255574i	$-0.917736\pi$
$347$	−19.0467	+	13.8382i	−1.02248	+	0.742874i	−0.0556889	+	0.998448i	$0.517736\pi$
$348$		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	$0.0508092\pi$
$353$			5.97261i			0.317890i	−0.987287	+	0.158945i	$0.949191\pi$
$354$		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	0.987009	−	0.160666i	$-0.0513641\pi$
$359$	1.78228	+	5.48528i	0.0940649	+	0.289502i	−0.892944	+	0.450168i	$0.851364\pi$
$360$		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	−0.770086	−	0.637941i	$-0.779787\pi$
$383$	1.45998	−	2.00949i	0.0746014	−	0.102680i	0.844687	+	0.535260i	$0.179787\pi$
$384$		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	−0.796981	−	0.604004i	$-0.793571\pi$
$389$	−21.4336	+	6.96421i	−1.08673	+	0.353099i	−0.289747	+	0.957103i	$0.593571\pi$
$390$		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	0.436346	−	0.899779i	$-0.356272\pi$
$401$	−11.0985	−	15.2758i	−0.554233	−	0.762836i	−0.990579	+	0.136943i	$0.956272\pi$
$402$		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	$-0.910606\pi$
$419$		−	11.3468i		−	0.554327i	0.960823	−	0.277164i	$-0.0893944\pi$
$420$		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	0.800475	−	0.599366i	$-0.204581\pi$
$431$	9.91948	+	7.20693i	0.477805	+	0.347145i	−0.322670	+	0.946511i	$0.604581\pi$
$432$		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	0.545263	−	0.838265i	$-0.316430\pi$
$443$	10.3906	+	3.37610i	0.493671	+	0.160403i	−0.0515924	+	0.998668i	$0.516430\pi$
$444$		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	$-0.512218\pi$
$449$	19.5758	−	26.9438i	0.923840	−	1.27156i	0.962214	−	0.272293i	$-0.0877819\pi$
$450$		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	$-0.299574\pi$
$461$	25.2871			1.17774			0.588868	+	0.808229i	$0.299574\pi$
$462$		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	0.592120	−	0.805850i	$-0.298291\pi$
$467$	−7.72052	−	10.6264i	−0.357263	−	0.491731i	−0.949384	+	0.314119i	$0.898291\pi$
$468$		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	−0.974486	−	0.224449i	$-0.927942\pi$
$479$	−23.2464	+	16.8895i	−1.06216	+	0.771701i	−0.0876694	+	0.996150i	$0.527942\pi$
$480$		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	0.975210	−	0.221279i	$-0.0710233\pi$
$491$	1.24495	+	3.83157i	0.0561839	+	0.172916i	−0.919027	+	0.394196i	$0.871023\pi$
$492$		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	$0.374577\pi$
$503$	−10.5281	+	32.4020i	−0.469423	+	1.44473i	−0.853334	+	0.521365i	$0.825423\pi$
$504$		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	0.896637	−	0.442766i	$-0.146003\pi$
$509$	30.7232	+	9.98256i	1.36178	+	0.442469i	0.465143	+	0.885236i	$0.346003\pi$
$510$		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	−0.597928	−	0.801550i	$-0.704009\pi$
$521$	−13.9354	+	4.52790i	−0.610523	+	0.198371i	−0.0125949	+	0.999921i	$0.504009\pi$
$522$		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	$0.0496487\pi$
$557$	6.60761	+	20.3361i	0.279974	+	0.861670i	−0.707887	+	0.706326i	$0.750351\pi$
$558$		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	0.502674	−	0.864476i	$-0.332349\pi$
$563$	−3.89503	−	2.82991i	−0.164156	−	0.119266i	−0.666830	+	0.745209i	$0.732349\pi$
$564$		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	$0.207261\pi$
$569$	−4.87428	+	15.0015i	−0.204340	+	0.628895i	−0.999740	+	0.0228093i	$0.992739\pi$
$570$		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	$0.827390\pi$
$587$	−44.8907	+	14.5859i	−1.85284	+	0.602024i	−0.996300	+	0.0859424i	$0.972610\pi$
$588$		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	$-0.251343\pi$
$593$	34.2927			1.40823			0.704117	+	0.710084i	$0.251343\pi$
$594$		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	$-0.929651\pi$
$599$	−21.6027	−	29.7335i	−0.882662	−	1.21488i	0.0930152	−	0.995665i	$-0.470349\pi$
$600$		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	$0.0586272\pi$
$617$			9.09836i			0.366286i	−0.983086	+	0.183143i	$0.941373\pi$
$618$		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	0.117194	−	0.993109i	$-0.462610\pi$
$641$	−9.41144	−	3.05796i	−0.371729	−	0.120782i	−0.488923	+	0.872327i	$0.662610\pi$
$642$		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	−0.999999	−	0.00156921i	$-0.999501\pi$
$647$	−17.5380	+	24.1390i	−0.689490	+	0.949001i	0.310509	+	0.950570i	$0.399501\pi$
$648$		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	0.417350	−	0.908746i	$-0.362959\pi$
$653$	32.9425	−	10.7037i	1.28914	−	0.418867i	0.871791	+	0.489879i	$0.162959\pi$
$654$		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	$-0.480225\pi$
$659$	3.18762			0.124172			0.0620860	+	0.998071i	$0.480225\pi$
$660$		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	$-0.334390\pi$
$677$	38.4032	−	27.9016i	1.47595	−	1.07234i	0.978832	−	0.204663i	$-0.0656100\pi$
$678$		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	$0.124754\pi$
$683$			19.9649i			0.763936i	−0.924175	+	0.381968i	$0.875246\pi$
$684$		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	$-0.667257\pi$
$701$	10.9266	−	33.6287i	0.412694	−	1.27014i	0.914298	−	0.405043i	$-0.132743\pi$
$702$		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	−0.156030	−	0.987752i	$-0.549870\pi$
$719$	7.99933	−	2.59914i	0.298325	−	0.0969316i	0.454355	+	0.890821i	$0.349870\pi$
$720$		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	−0.830693	−	0.556731i	$-0.812056\pi$
$743$	−15.2075	+	11.0489i	−0.557909	+	0.405344i	0.272784	+	0.962075i	$0.412056\pi$
$744$		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	0.607577	−	0.794261i	$-0.292142\pi$
$761$	1.10182	+	0.800522i	0.0399411	+	0.0290189i	−0.567636	+	0.823280i	$0.692142\pi$
$762$		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	0.562158	−	0.827030i	$-0.309971\pi$
$773$	14.7588	+	4.79543i	0.530837	+	0.172479i	−0.0313207	+	0.999509i	$0.509971\pi$
$774$		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	0.506866	−	0.862025i	$-0.330804\pi$
$797$	−13.2573	−	18.2472i	−0.469599	−	0.646348i	−0.976465	+	0.215677i	$0.930804\pi$
$798$		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	−0.845135	−	0.534553i	$-0.820480\pi$
$809$	−17.0062	+	12.3557i	−0.597905	+	0.434404i	0.247229	+	0.968957i	$0.420480\pi$
$810$		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	$0.0713200\pi$
$821$	9.07753	+	27.9378i	0.316808	+	0.975035i	−0.658196	+	0.752847i	$0.728680\pi$
$822$		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	0.944345	−	0.328956i	$-0.106697\pi$
$827$	26.5521	+	19.2912i	0.923308	+	0.670822i	−0.0210374	+	0.999779i	$0.506697\pi$
$828$		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	−0.0853450	−	0.996351i	$-0.527199\pi$
$839$	−21.4354	−	6.96478i	−0.740031	−	0.240451i	−0.654686	+	0.755901i	$0.727199\pi$
$840$		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	$-0.355533\pi$
$857$	25.6700			0.876870			0.438435	+	0.898763i	$0.355533\pi$
$858$		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	0.391927	−	0.919996i	$-0.371808\pi$
$863$	−17.7481	−	24.4282i	−0.604153	−	0.831546i	−0.996081	+	0.0884505i	$0.971808\pi$
$864$		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	$-0.960779\pi$
$881$		−	7.29612i		−	0.245813i	0.992418	−	0.122906i	$-0.0392215\pi$
$882$		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	$0.109334\pi$
$887$	11.2511	+	34.6272i	0.377774	+	1.16267i	−0.563814	+	0.825902i	$0.690666\pi$
$888$		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	−0.431330	−	0.902194i	$-0.641955\pi$
$911$	16.9022	−	23.2639i	0.559996	−	0.770769i	0.991326	+	0.131426i	$0.0419554\pi$
$912$		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	0.326093	−	0.945338i	$-0.394268\pi$
$929$	−20.5354	−	28.2645i	−0.673744	−	0.927330i	−0.999838	+	0.0180080i	$0.994268\pi$
$930$		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	−0.343418	−	0.939183i	$-0.611585\pi$
$941$	13.6101	−	9.88831i	0.443676	−	0.322350i	0.787094	+	0.616833i	$0.211585\pi$
$942$		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	$0.339775\pi$
$947$			53.9128i			1.75193i	−0.482373	+	0.875966i	$0.660225\pi$
$948$		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	0.970433	−	0.241372i	$-0.0775976\pi$
$953$	1.34167	+	4.12923i	0.0434609	+	0.133759i	−0.926972	+	0.375131i	$0.877598\pi$
$954$		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	0.117066	−	0.993124i	$-0.462651\pi$
$971$	−11.5909	−	3.76611i	−0.371970	−	0.120860i	−0.489036	+	0.872264i	$0.662651\pi$
$972$		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	−0.993309	−	0.115484i	$-0.963158\pi$
$977$	−18.0205	+	24.8031i	−0.576528	+	0.793523i	0.416781	+	0.909007i	$0.363158\pi$
$978$		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	−0.108306	−	0.994118i	$-0.534543\pi$
$983$	12.1774	−	3.95668i	0.388399	−	0.126199i	0.496706	+	0.867919i	$0.334543\pi$
$984$		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.161.15		80
3.2	odd	2	inner	891.2.k.a.161.6		80
9.2	odd	6		99.2.p.a.95.4	yes	80
9.4	even	3		99.2.p.a.29.4	✓	80
9.5	odd	6		297.2.t.a.62.7		80
9.7	even	3		297.2.t.a.260.7		80
11.8	odd	10	inner	891.2.k.a.404.6		80
33.8	even	10	inner	891.2.k.a.404.15		80
99.41	even	30		297.2.t.a.8.7		80
99.52	odd	30		297.2.t.a.206.7		80
99.74	even	30		99.2.p.a.41.4	yes	80
99.85	odd	30		99.2.p.a.74.4	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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