LMFDB - Embedded newform 765.2.be.b.406.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			406.3
Character	$\chi$	$=$	765.406
Dual form			765.2.be.b.586.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.680853 - 0.680853i) q^{2} -1.07288i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.85906 + 1.18426i) q^{7} +(-2.09218 + 2.09218i) q^{8} +O(q^{10})$	\(q+(-0.680853 - 0.680853i) q^{2} -1.07288i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.85906 + 1.18426i) q^{7} +(-2.09218 + 2.09218i) q^{8} +(-0.889577 - 0.368475i) q^{10} +(2.34612 - 5.66403i) q^{11} -1.16017i q^{13} +(-1.14029 - 2.75291i) q^{14} +0.703170 q^{16} +(-1.25804 + 3.92649i) q^{17} +(3.83665 + 3.83665i) q^{19} +(-0.410573 - 0.991211i) q^{20} +(-5.45373 + 2.25901i) q^{22} +(1.19300 - 2.88015i) q^{23} +(0.707107 - 0.707107i) q^{25} +(-0.789908 + 0.789908i) q^{26} +(1.27057 - 3.06743i) q^{28} +(4.61660 - 1.91226i) q^{29} +(-1.42666 - 3.44426i) q^{31} +(3.70560 + 3.70560i) q^{32} +(3.52990 - 1.81682i) q^{34} +3.09463 q^{35} +(-0.151817 - 0.366518i) q^{37} -5.22439i q^{38} +(-1.13228 + 2.73356i) q^{40} +(-1.57303 - 0.651568i) q^{41} +(0.0189720 - 0.0189720i) q^{43} +(-6.07683 - 2.51710i) q^{44} +(-2.77321 + 1.14870i) q^{46} -5.43715i q^{47} +(1.82202 + 1.82202i) q^{49} -0.962871 q^{50} -1.24473 q^{52} +(0.244014 + 0.244014i) q^{53} -6.13071i q^{55} +(-8.45936 + 3.50398i) q^{56} +(-4.44519 - 1.84126i) q^{58} +(-2.87128 + 2.87128i) q^{59} +(-11.4953 - 4.76149i) q^{61} +(-1.37369 + 3.31638i) q^{62} -6.45228i q^{64} +(-0.443980 - 1.07186i) q^{65} -5.62508 q^{67} +(4.21265 + 1.34973i) q^{68} +(-2.10699 - 2.10699i) q^{70} +(-4.12510 - 9.95888i) q^{71} +(-1.52840 + 0.633083i) q^{73} +(-0.146180 + 0.352909i) q^{74} +(4.11627 - 4.11627i) q^{76} +(13.4154 - 13.4154i) q^{77} +(2.01785 - 4.87153i) q^{79} +(0.649645 - 0.269092i) q^{80} +(0.627376 + 1.51462i) q^{82} +(8.78638 + 8.78638i) q^{83} +(0.340325 + 4.10904i) q^{85} -0.0258342 q^{86} +(6.94167 + 16.7587i) q^{88} +3.22930i q^{89} +(1.37395 - 3.31701i) q^{91} +(-3.09005 - 1.27994i) q^{92} +(-3.70190 + 3.70190i) q^{94} +(5.01283 + 2.07638i) q^{95} +(11.9502 - 4.94995i) q^{97} -2.48105i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.680853	−	0.680853i	−0.481435	−	0.481435i	0.424154	−	0.905590i	$-0.360571\pi$
$2$	−0.680853	−	0.680853i	−0.481435	−	0.481435i	−0.905590	+	0.424154i	$0.860571\pi$
$3$		0			0
$3$		0			0
$4$		−	1.07288i		−	0.536440i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$6$		0			0
$7$	2.85906	+	1.18426i	1.08062	+	0.447609i	0.850728	−	0.525606i	$-0.176161\pi$
$7$	2.85906	+	1.18426i	1.08062	+	0.447609i	0.229896	+	0.973215i	$0.426161\pi$
$8$	−2.09218	+	2.09218i	−0.739697	+	0.739697i
$9$		0			0
$10$	−0.889577	−	0.368475i	−0.281309	−	0.116522i
$11$	2.34612	−	5.66403i	0.707382	−	1.70777i	0.000939675	−	1.00000i	$-0.499701\pi$
$11$	2.34612	−	5.66403i	0.707382	−	1.70777i	0.706442	−	0.707771i	$-0.250299\pi$
$12$		0			0
$13$		−	1.16017i		−	0.321775i	−0.986973	−	0.160887i	$-0.948564\pi$
$13$		−	1.16017i		−	0.321775i	0.986973	−	0.160887i	$-0.0514356\pi$
$14$	−1.14029	−	2.75291i	−0.304756	−	0.735746i
$15$		0			0
$16$	0.703170			0.175793
$17$	−1.25804	+	3.92649i	−0.305120	+	0.952314i
$17$	−1.25804	+	3.92649i	−0.305120	+	0.952314i
$18$		0			0
$19$	3.83665	+	3.83665i	0.880188	+	0.880188i	0.993553	−	0.113365i	$-0.0361629\pi$
$19$	3.83665	+	3.83665i	0.880188	+	0.880188i	−0.113365	+	0.993553i	$0.536163\pi$
$20$	−0.410573	−	0.991211i	−0.0918070	−	0.221642i
$21$		0			0
$22$	−5.45373	+	2.25901i	−1.16274	+	0.481623i
$23$	1.19300	−	2.88015i	0.248757	−	0.600552i	−0.749342	−	0.662183i	$-0.769630\pi$
$23$	1.19300	−	2.88015i	0.248757	−	0.600552i	0.998099	+	0.0616306i	$0.0196301\pi$
$24$		0			0
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	−0.789908	+	0.789908i	−0.154914	+	0.154914i
$27$		0			0
$28$	1.27057	−	3.06743i	0.240115	−	0.579690i
$29$	4.61660	−	1.91226i	0.857282	−	0.355098i	0.0896380	−	0.995974i	$-0.471429\pi$
$29$	4.61660	−	1.91226i	0.857282	−	0.355098i	0.767644	+	0.640877i	$0.221429\pi$
$30$		0			0
$31$	−1.42666	−	3.44426i	−0.256236	−	0.618608i	0.742448	−	0.669904i	$-0.233665\pi$
$31$	−1.42666	−	3.44426i	−0.256236	−	0.618608i	−0.998683	+	0.0512962i	$0.983665\pi$
$32$	3.70560	+	3.70560i	0.655064	+	0.655064i
$33$		0			0
$34$	3.52990	−	1.81682i	0.605373	−	0.311582i
$35$	3.09463			0.523088
$36$		0			0
$37$	−0.151817	−	0.366518i	−0.0249585	−	0.0602551i	0.910909	−	0.412607i	$-0.135382\pi$
$37$	−0.151817	−	0.366518i	−0.0249585	−	0.0602551i	−0.935867	+	0.352352i	$0.885382\pi$
$38$		−	5.22439i		−	0.847508i
$39$		0			0
$40$	−1.13228	+	2.73356i	−0.179029	+	0.432214i
$41$	−1.57303	−	0.651568i	−0.245665	−	0.101758i	0.256453	−	0.966557i	$-0.417446\pi$
$41$	−1.57303	−	0.651568i	−0.245665	−	0.101758i	−0.502119	+	0.864799i	$0.667446\pi$
$42$		0			0
$43$	0.0189720	−	0.0189720i	0.00289320	−	0.00289320i	−0.705659	−	0.708552i	$-0.749349\pi$
$43$	0.0189720	−	0.0189720i	0.00289320	−	0.00289320i	0.708552	+	0.705659i	$0.249349\pi$
$44$	−6.07683	−	2.51710i	−0.916116	−	0.379468i
$45$		0			0
$46$	−2.77321	+	1.14870i	−0.408888	+	0.169367i
$47$		−	5.43715i		−	0.793090i	−0.918015	−	0.396545i	$-0.870209\pi$
$47$		−	5.43715i		−	0.793090i	0.918015	−	0.396545i	$-0.129791\pi$
$48$		0			0
$49$	1.82202	+	1.82202i	0.260288	+	0.260288i
$50$	−0.962871			−0.136171
$51$		0			0
$52$	−1.24473			−0.172613
$53$	0.244014	+	0.244014i	0.0335179	+	0.0335179i	0.723667	−	0.690149i	$-0.242455\pi$
$53$	0.244014	+	0.244014i	0.0335179	+	0.0335179i	−0.690149	+	0.723667i	$0.742455\pi$
$54$		0			0
$55$		−	6.13071i		−	0.826664i
$56$	−8.45936	+	3.50398i	−1.13043	+	0.468239i
$57$		0			0
$58$	−4.44519	−	1.84126i	−0.583683	−	0.241769i
$59$	−2.87128	+	2.87128i	−0.373808	+	0.373808i	−0.868862	−	0.495054i	$-0.835148\pi$
$59$	−2.87128	+	2.87128i	−0.373808	+	0.373808i	0.495054	+	0.868862i	$0.335148\pi$
$60$		0			0
$61$	−11.4953	−	4.76149i	−1.47182	−	0.609646i	−0.504544	−	0.863386i	$-0.668339\pi$
$61$	−11.4953	−	4.76149i	−1.47182	−	0.609646i	−0.967273	+	0.253740i	$0.918339\pi$
$62$	−1.37369	+	3.31638i	−0.174459	+	0.421181i
$63$		0			0
$64$		−	6.45228i		−	0.806534i
$65$	−0.443980	−	1.07186i	−0.0550689	−	0.132948i
$66$		0			0
$67$	−5.62508			−0.687213			−0.343607	−	0.939114i	$-0.611649\pi$
$67$	−5.62508			−0.687213			−0.343607	+	0.939114i	$0.611649\pi$
$68$	4.21265	+	1.34973i	0.510859	+	0.163678i
$69$		0			0
$70$	−2.10699	−	2.10699i	−0.251833	−	0.251833i
$71$	−4.12510	−	9.95888i	−0.489560	−	1.18190i	−0.954942	−	0.296792i	$-0.904083\pi$
$71$	−4.12510	−	9.95888i	−0.489560	−	1.18190i	0.465383	−	0.885110i	$-0.345917\pi$
$72$		0			0
$73$	−1.52840	+	0.633083i	−0.178886	+	0.0740968i	−0.470329	−	0.882491i	$-0.655865\pi$
$73$	−1.52840	+	0.633083i	−0.178886	+	0.0740968i	0.291443	+	0.956588i	$0.405865\pi$
$74$	−0.146180	+	0.352909i	−0.0169931	+	0.0410249i
$75$		0			0
$76$	4.11627	−	4.11627i	0.472168	−	0.472168i
$77$	13.4154	−	13.4154i	1.52883	−	1.52883i
$78$		0			0
$79$	2.01785	−	4.87153i	0.227026	−	0.548090i	−0.768787	−	0.639505i	$-0.779139\pi$
$79$	2.01785	−	4.87153i	0.227026	−	0.548090i	0.995813	+	0.0914157i	$0.0291392\pi$
$80$	0.649645	−	0.269092i	0.0726325	−	0.0300854i
$81$		0			0
$82$	0.627376	+	1.51462i	0.0692821	+	0.167262i
$83$	8.78638	+	8.78638i	0.964430	+	0.964430i	0.999389	−	0.0349583i	$-0.0111299\pi$
$83$	8.78638	+	8.78638i	0.964430	+	0.964430i	−0.0349583	+	0.999389i	$0.511130\pi$
$84$		0			0
$85$	0.340325	+	4.10904i	0.0369135	+	0.445688i
$86$	−0.0258342			−0.00278577
$87$		0			0
$88$	6.94167	+	16.7587i	0.739984	+	1.78648i
$89$			3.22930i			0.342305i	0.985245	+	0.171152i	$0.0547490\pi$
$89$			3.22930i			0.342305i	−0.985245	+	0.171152i	$0.945251\pi$
$90$		0			0
$91$	1.37395	−	3.31701i	0.144029	−	0.347717i
$92$	−3.09005	−	1.27994i	−0.322160	−	0.133443i
$93$		0			0
$94$	−3.70190	+	3.70190i	−0.381822	+	0.381822i
$95$	5.01283	+	2.07638i	0.514305	+	0.213032i
$96$		0			0
$97$	11.9502	−	4.94995i	1.21336	−	0.502592i	0.318070	−	0.948067i	$-0.396965\pi$
$97$	11.9502	−	4.94995i	1.21336	−	0.502592i	0.895294	+	0.445476i	$0.146965\pi$
$98$		−	2.48105i		−	0.250624i
$99$		0			0
$100$	−0.758640	−	0.758640i	−0.0758640	−	0.0758640i
$101$	−1.46947			−0.146218			−0.0731088	−	0.997324i	$-0.523292\pi$
$101$	−1.46947			−0.146218			−0.0731088	+	0.997324i	$0.523292\pi$
$102$		0			0
$103$	9.80978			0.966586			0.483293	−	0.875459i	$-0.339441\pi$
$103$	9.80978			0.966586			0.483293	+	0.875459i	$0.339441\pi$
$104$	2.42729	+	2.42729i	0.238016	+	0.238016i
$105$		0			0
$106$		−	0.332275i		−	0.0322734i
$107$	2.66763	−	1.10497i	0.257889	−	0.106821i	−0.249993	−	0.968248i	$-0.580428\pi$
$107$	2.66763	−	1.10497i	0.257889	−	0.106821i	0.507882	+	0.861426i	$0.330428\pi$
$108$		0			0
$109$	5.32460	+	2.20552i	0.510004	+	0.211251i	0.622820	−	0.782365i	$-0.285987\pi$
$109$	5.32460	+	2.20552i	0.510004	+	0.211251i	−0.112816	+	0.993616i	$0.535987\pi$
$110$	−4.17411	+	4.17411i	−0.397985	+	0.397985i
$111$		0			0
$112$	2.01041	+	0.832738i	0.189966	+	0.0786864i
$113$	−3.45197	+	8.33379i	−0.324734	+	0.783977i	0.674232	+	0.738519i	$0.264475\pi$
$113$	−3.45197	+	8.33379i	−0.324734	+	0.783977i	−0.998966	+	0.0454578i	$0.985525\pi$
$114$		0			0
$115$		−	3.11745i		−	0.290704i
$116$	−2.05162	−	4.95306i	−0.190489	−	0.459880i
$117$		0			0
$118$	3.90983			0.359929
$119$	−8.24682	+	9.73624i	−0.755984	+	0.892519i
$120$		0			0
$121$	−18.7988	−	18.7988i	−1.70898	−	1.70898i
$122$	4.58470	+	11.0684i	0.415079	+	1.00209i
$123$		0			0
$124$	−3.69528	+	1.53063i	−0.331846	+	0.137455i
$125$	0.382683	−	0.923880i	0.0342282	−	0.0826343i
$126$		0			0
$127$	−9.89892	+	9.89892i	−0.878387	+	0.878387i	−0.993368	−	0.114980i	$-0.963319\pi$
$127$	−9.89892	+	9.89892i	−0.878387	+	0.878387i	0.114980	+	0.993368i	$0.463319\pi$
$128$	3.01815	−	3.01815i	0.266770	−	0.266770i
$129$		0			0
$130$	−0.427495	+	1.03206i	−0.0374938	+	0.0905180i
$131$	−11.7059	+	4.84875i	−1.02275	+	0.423638i	−0.830091	−	0.557628i	$-0.811712\pi$
$131$	−11.7059	+	4.84875i	−1.02275	+	0.423638i	−0.192661	+	0.981265i	$0.561712\pi$
$132$		0			0
$133$	6.42563	+	15.5128i	0.557173	+	1.34513i
$134$	3.82985	+	3.82985i	0.330849	+	0.330849i
$135$		0			0
$136$	−5.58287	−	10.8470i	−0.478728	−	0.930119i
$137$	−2.97888			−0.254503			−0.127251	−	0.991870i	$-0.540616\pi$
$137$	−2.97888			−0.254503			−0.127251	+	0.991870i	$0.540616\pi$
$138$		0			0
$139$	7.51640	+	18.1462i	0.637533	+	1.53914i	0.829956	+	0.557829i	$0.188365\pi$
$139$	7.51640	+	18.1462i	0.637533	+	1.53914i	−0.192423	+	0.981312i	$0.561635\pi$
$140$		−	3.32016i		−	0.280605i
$141$		0			0
$142$	−3.97194	+	9.58911i	−0.333318	+	0.804700i
$143$	−6.57127	−	2.72191i	−0.549517	−	0.227617i
$144$		0			0
$145$	3.53340	−	3.53340i	0.293433	−	0.293433i
$146$	1.47165	+	0.609578i	0.121795	+	0.0504490i
$147$		0			0
$148$	−0.393229	+	0.162881i	−0.0323232	+	0.0133887i
$149$			2.95573i			0.242143i	0.992644	+	0.121072i	$0.0386330\pi$
$149$			2.95573i			0.242143i	−0.992644	+	0.121072i	$0.961367\pi$
$150$		0			0
$151$	15.5848	+	15.5848i	1.26828	+	1.26828i	0.946978	+	0.321298i	$0.104119\pi$
$151$	15.5848	+	15.5848i	1.26828	+	1.26828i	0.321298	+	0.946978i	$0.395881\pi$
$152$	−16.0539			−1.30214
$153$		0			0
$154$	−18.2678			−1.47206
$155$	−2.63612	−	2.63612i	−0.211739	−	0.211739i
$156$		0			0
$157$			12.8666i			1.02686i	0.858130	+	0.513432i	$0.171626\pi$
$157$			12.8666i			1.02686i	−0.858130	+	0.513432i	$0.828374\pi$
$158$	−4.69065	+	1.94293i	−0.373168	+	0.154571i
$159$		0			0
$160$	4.84160	+	2.00546i	0.382762	+	0.158545i
$161$	6.82171	−	6.82171i	0.537626	−	0.537626i
$162$		0			0
$163$	−17.8239	−	7.38291i	−1.39608	−	0.578274i	−0.447347	−	0.894361i	$-0.647631\pi$
$163$	−17.8239	−	7.38291i	−1.39608	−	0.578274i	−0.948730	+	0.316087i	$0.897631\pi$
$164$	−0.699055	+	1.68767i	−0.0545870	+	0.131785i
$165$		0			0
$166$		−	11.9645i		−	0.928622i
$167$	7.21707	+	17.4236i	0.558474	+	1.34828i	0.910974	+	0.412464i	$0.135332\pi$
$167$	7.21707	+	17.4236i	0.558474	+	1.34828i	−0.352500	+	0.935812i	$0.614668\pi$
$168$		0			0
$169$	11.6540			0.896461
$170$	2.56594	−	3.02936i	0.196798	−	0.232341i
$171$		0			0
$172$	−0.0203546	−	0.0203546i	−0.00155203	−	0.00155203i
$173$	8.63985	+	20.8584i	0.656876	+	1.58584i	0.802603	+	0.596513i	$0.203448\pi$
$173$	8.63985	+	20.8584i	0.656876	+	1.58584i	−0.145728	+	0.989325i	$0.546552\pi$
$174$		0			0
$175$	2.85906	−	1.18426i	0.216125	−	0.0895219i
$176$	1.64972	−	3.98278i	0.124352	−	0.300213i
$177$		0			0
$178$	2.19867	−	2.19867i	0.164798	−	0.164798i
$179$	1.38641	−	1.38641i	0.103625	−	0.103625i	−0.653393	−	0.757018i	$-0.726655\pi$
$179$	1.38641	−	1.38641i	0.103625	−	0.103625i	0.757018	+	0.653393i	$0.226655\pi$
$180$		0			0
$181$	0.272363	−	0.657542i	0.0202446	−	0.0488747i	−0.913434	−	0.406987i	$-0.866579\pi$
$181$	0.272363	−	0.657542i	0.0202446	−	0.0488747i	0.933679	+	0.358112i	$0.116579\pi$
$182$	−3.19386	+	1.32294i	−0.236744	+	0.0980627i
$183$		0			0
$184$	3.52982	+	8.52174i	0.260222	+	0.628231i
$185$	−0.280520	−	0.280520i	−0.0206243	−	0.0206243i
$186$		0			0
$187$	19.2883	+	16.3376i	1.41050	+	1.19472i
$188$	−5.83341			−0.425445
$189$		0			0
$190$	−1.99929	−	4.82671i	−0.145044	−	0.350166i
$191$			5.26341i			0.380847i	0.981702	+	0.190423i	$0.0609861\pi$
$191$			5.26341i			0.380847i	−0.981702	+	0.190423i	$0.939014\pi$
$192$		0			0
$193$	5.71352	−	13.7936i	0.411268	−	0.992888i	−0.573530	−	0.819184i	$-0.694426\pi$
$193$	5.71352	−	13.7936i	0.411268	−	0.992888i	0.984798	−	0.173704i	$-0.0555736\pi$
$194$	−11.5065	−	4.76617i	−0.826122	−	0.342191i
$195$		0			0
$196$	1.95481	−	1.95481i	0.139629	−	0.139629i
$197$	−5.84828	−	2.42244i	−0.416673	−	0.172592i	0.164490	−	0.986379i	$-0.447402\pi$
$197$	−5.84828	−	2.42244i	−0.416673	−	0.172592i	−0.581163	+	0.813787i	$0.697402\pi$
$198$		0			0
$199$	−13.7796	+	5.70769i	−0.976809	+	0.404607i	−0.813243	−	0.581925i	$-0.802300\pi$
$199$	−13.7796	+	5.70769i	−0.976809	+	0.404607i	−0.163566	+	0.986532i	$0.552300\pi$
$200$			2.95879i			0.209218i
$201$		0			0
$202$	1.00049	+	1.00049i	0.0703943	+	0.0703943i
$203$	15.4638			1.08534
$204$		0			0
$205$	−1.70263			−0.118917
$206$	−6.67901	−	6.67901i	−0.465349	−	0.465349i
$207$		0			0
$208$		−	0.815800i		−	0.0565656i
$209$	30.7322	−	12.7297i	2.12579	−	0.880531i
$210$		0			0
$211$	12.3788	+	5.12746i	0.852190	+	0.352989i	0.765648	−	0.643260i	$-0.222418\pi$
$211$	12.3788	+	5.12746i	0.852190	+	0.352989i	0.0865417	+	0.996248i	$0.472418\pi$
$212$	0.261797	−	0.261797i	0.0179803	−	0.0179803i
$213$		0			0
$214$	−2.56858	−	1.06394i	−0.175585	−	0.0727295i
$215$	0.0102675	−	0.0247881i	0.000700241	−	0.00169053i
$216$		0			0
$217$		−	11.5369i		−	0.783176i
$218$	−2.12363	−	5.12690i	−0.143830	−	0.347238i
$219$		0			0
$220$	−6.57751			−0.443456
$221$	4.55542	+	1.45955i	0.306430	+	0.0981797i
$222$		0			0
$223$	1.49410	+	1.49410i	0.100053	+	0.100053i	0.755361	−	0.655309i	$-0.227461\pi$
$223$	1.49410	+	1.49410i	0.100053	+	0.100053i	−0.655309	+	0.755361i	$0.727461\pi$
$224$	6.20614	+	14.9830i	0.414665	+	1.00109i
$225$		0			0
$226$	8.02437	−	3.32380i	0.533773	−	0.221096i
$227$	−5.57168	+	13.4512i	−0.369805	+	0.892789i	0.623976	+	0.781443i	$0.285516\pi$
$227$	−5.57168	+	13.4512i	−0.369805	+	0.892789i	−0.993782	+	0.111346i	$0.964484\pi$
$228$		0			0
$229$	−1.87412	+	1.87412i	−0.123845	+	0.123845i	−0.766313	−	0.642468i	$-0.777911\pi$
$229$	−1.87412	+	1.87412i	−0.123845	+	0.123845i	0.642468	+	0.766313i	$0.277911\pi$
$230$	−2.12252	+	2.12252i	−0.139955	+	0.139955i
$231$		0			0
$232$	−5.65797	+	13.6595i	−0.371464	+	0.896793i
$233$	2.90028	−	1.20133i	0.190004	−	0.0787021i	−0.285653	−	0.958333i	$-0.592210\pi$
$233$	2.90028	−	1.20133i	0.190004	−	0.0787021i	0.475657	+	0.879631i	$0.342210\pi$
$234$		0			0
$235$	−2.08071	−	5.02327i	−0.135730	−	0.327682i
$236$	3.08053	+	3.08053i	0.200526	+	0.200526i
$237$		0			0
$238$	12.2438	−	1.01408i	0.793648	−	0.0657328i
$239$	−13.7090			−0.886760			−0.443380	−	0.896334i	$-0.646221\pi$
$239$	−13.7090			−0.886760			−0.443380	+	0.896334i	$0.646221\pi$
$240$		0			0
$241$	−4.77884	−	11.5371i	−0.307832	−	0.743173i	−0.999775	−	0.0212201i	$-0.993245\pi$
$241$	−4.77884	−	11.5371i	−0.307832	−	0.743173i	0.691943	−	0.721952i	$-0.256755\pi$
$242$			25.5985i			1.64553i
$243$		0			0
$244$	−5.10851	+	12.3330i	−0.327039	+	0.789541i
$245$	2.38058	+	0.986069i	0.152090	+	0.0629977i
$246$		0			0
$247$	4.45119	−	4.45119i	0.283222	−	0.283222i
$248$	10.1908	+	4.22118i	0.647119	+	0.268045i
$249$		0			0
$250$	−0.889577	+	0.368475i	−0.0562618	+	0.0233044i
$251$			17.4413i			1.10088i	0.834874	+	0.550441i	$0.185541\pi$
$251$			17.4413i			1.10088i	−0.834874	+	0.550441i	$0.814459\pi$
$252$		0			0
$253$	−13.5143	−	13.5143i	−0.849640	−	0.849640i
$254$	13.4794			0.845774
$255$		0			0
$256$	−17.0144			−1.06340
$257$	4.86561	+	4.86561i	0.303508	+	0.303508i	0.842385	−	0.538876i	$-0.181151\pi$
$257$	4.86561	+	4.86561i	0.303508	+	0.303508i	−0.538876	+	0.842385i	$0.681151\pi$
$258$		0			0
$259$		−	1.22769i		−	0.0762848i
$260$	−1.14998	+	0.476337i	−0.0713186	+	0.0295411i
$261$		0			0
$262$	11.2713	+	4.66872i	0.696343	+	0.288435i
$263$	−4.41100	+	4.41100i	−0.271994	+	0.271994i	−0.829902	−	0.557909i	$-0.811604\pi$
$263$	−4.41100	+	4.41100i	−0.271994	+	0.271994i	0.557909	+	0.829902i	$0.311604\pi$
$264$		0			0
$265$	0.318819	+	0.132059i	0.0195849	+	0.00811233i
$266$	6.18705	−	14.9369i	0.379352	−	0.915838i
$267$		0			0
$268$			6.03504i			0.368648i
$269$	−0.493996	−	1.19261i	−0.0301194	−	0.0727148i	0.908104	−	0.418744i	$-0.137530\pi$
$269$	−0.493996	−	1.19261i	−0.0301194	−	0.0727148i	−0.938224	+	0.346030i	$0.887530\pi$
$270$		0			0
$271$	−10.2849			−0.624764			−0.312382	−	0.949957i	$-0.601127\pi$
$271$	−10.2849			−0.624764			−0.312382	+	0.949957i	$0.601127\pi$
$272$	−0.884617	+	2.76099i	−0.0536378	+	0.167410i
$273$		0			0
$274$	2.02818	+	2.02818i	0.122527	+	0.122527i
$275$	−2.34612	−	5.66403i	−0.141476	−	0.341554i
$276$		0			0
$277$	23.4482	−	9.71258i	1.40887	−	0.583572i	0.456831	−	0.889554i	$-0.348985\pi$
$277$	23.4482	−	9.71258i	1.40887	−	0.583572i	0.952037	+	0.305982i	$0.0989846\pi$
$278$	7.23733	−	17.4724i	0.434066	−	1.04793i
$279$		0			0
$280$	−6.47451	+	6.47451i	−0.386926	+	0.386926i
$281$	4.16880	−	4.16880i	0.248690	−	0.248690i	−0.571743	−	0.820433i	$-0.693733\pi$
$281$	4.16880	−	4.16880i	0.248690	−	0.248690i	0.820433	+	0.571743i	$0.193733\pi$
$282$		0			0
$283$	−7.06675	+	17.0606i	−0.420075	+	1.01415i	0.562250	+	0.826967i	$0.309936\pi$
$283$	−7.06675	+	17.0606i	−0.420075	+	1.01415i	−0.982325	+	0.187183i	$0.940064\pi$
$284$	−10.6847	+	4.42574i	−0.634019	+	0.262619i
$285$		0			0
$286$	2.62085	+	6.32728i	0.154974	+	0.374140i
$287$	−3.72575	−	3.72575i	−0.219924	−	0.219924i
$288$		0			0
$289$	−13.8347	−	9.87937i	−0.813804	−	0.581139i
$290$	−4.81144			−0.282538
$291$		0			0
$292$	0.679222	+	1.63979i	0.0397485	+	0.0959613i
$293$		−	8.31894i		−	0.485998i	−0.970027	−	0.242999i	$-0.921869\pi$
$293$		−	8.31894i		−	0.485998i	0.970027	−	0.242999i	$-0.0781311\pi$
$294$		0			0
$295$	−1.55392	+	3.75150i	−0.0904729	+	0.218421i
$296$	1.08445	+	0.449193i	0.0630322	+	0.0261088i
$297$		0			0
$298$	2.01242	−	2.01242i	0.116576	−	0.116576i
$299$	−3.34148	−	1.38408i	−0.193243	−	0.0800437i
$300$		0			0
$301$	0.0767098	−	0.0317742i	0.00442148	−	0.00183144i
$302$		−	21.2220i		−	1.22119i
$303$		0			0
$304$	2.69782	+	2.69782i	0.154731	+	0.154731i
$305$	−12.4424			−0.712448
$306$		0			0
$307$	−12.2369			−0.698398			−0.349199	−	0.937049i	$-0.613546\pi$
$307$	−12.2369			−0.698398			−0.349199	+	0.937049i	$0.613546\pi$
$308$	−14.3931	−	14.3931i	−0.820124	−	0.820124i
$309$		0			0
$310$			3.58962i			0.203877i
$311$	30.1525	−	12.4896i	1.70979	−	0.708218i	0.709796	−	0.704407i	$-0.248787\pi$
$311$	30.1525	−	12.4896i	1.70979	−	0.708218i	0.999993	−	0.00381046i	$-0.00121291\pi$
$312$		0			0
$313$	−12.4068	−	5.13906i	−0.701273	−	0.290477i	0.00341475	−	0.999994i	$-0.498913\pi$
$313$	−12.4068	−	5.13906i	−0.701273	−	0.290477i	−0.704688	+	0.709517i	$0.748913\pi$
$314$	8.76024	−	8.76024i	0.494369	−	0.494369i
$315$		0			0
$316$	−5.22656	−	2.16491i	−0.294017	−	0.121786i
$317$	3.77845	−	9.12199i	0.212219	−	0.512342i	−0.781545	−	0.623849i	$-0.785568\pi$
$317$	3.77845	−	9.12199i	0.212219	−	0.512342i	0.993764	+	0.111507i	$0.0355678\pi$
$318$		0			0
$319$		−	30.6350i		−	1.71523i
$320$	−2.46918	−	5.96113i	−0.138031	−	0.333237i
$321$		0			0
$322$	−9.28915			−0.517664
$323$	−19.8912	+	10.2379i	−1.10678	+	0.569653i
$324$		0			0
$325$	−0.820367	−	0.820367i	−0.0455058	−	0.0455058i
$326$	7.10879	+	17.1621i	0.393719	+	0.950523i
$327$		0			0
$328$	4.65425	−	1.92785i	0.256988	−	0.106448i
$329$	6.43902	−	15.5452i	0.354995	−	0.857033i
$330$		0			0
$331$	−3.99024	+	3.99024i	−0.219323	+	0.219323i	−0.808213	−	0.588890i	$-0.799565\pi$
$331$	−3.99024	+	3.99024i	−0.219323	+	0.219323i	0.588890	+	0.808213i	$0.299565\pi$
$332$	9.42673	−	9.42673i	0.517359	−	0.517359i
$333$		0			0
$334$	6.94911	−	16.7766i	0.380238	−	0.917977i
$335$	−5.19690	+	2.15263i	−0.283937	+	0.117611i
$336$		0			0
$337$	6.34969	+	15.3295i	0.345890	+	0.835051i	0.997096	+	0.0761510i	$0.0242631\pi$
$337$	6.34969	+	15.3295i	0.345890	+	0.835051i	−0.651207	+	0.758900i	$0.725737\pi$
$338$	−7.93465	−	7.93465i	−0.431588	−	0.431588i
$339$		0			0
$340$	4.40850	−	0.365128i	0.239085	−	0.0198019i
$341$	−22.8555			−1.23770
$342$		0			0
$343$	−5.23832	−	12.6464i	−0.282843	−	0.682843i
$344$			0.0793854i			0.00428017i
$345$		0			0
$346$	8.31906	−	20.0840i	0.447235	−	1.07972i
$347$	−8.54057	−	3.53762i	−0.458482	−	0.189909i	0.141475	−	0.989942i	$-0.454816\pi$
$347$	−8.54057	−	3.53762i	−0.458482	−	0.189909i	−0.599957	+	0.800032i	$0.704816\pi$
$348$		0			0
$349$	−19.0405	+	19.0405i	−1.01921	+	1.01921i	−0.0194030	+	0.999812i	$0.506177\pi$
$349$	−19.0405	+	19.0405i	−1.01921	+	1.01921i	−0.999812	+	0.0194030i	$0.993823\pi$
$350$	−2.75291	−	1.14029i	−0.147149	−	0.0609512i
$351$		0			0
$352$	29.6824	−	12.2949i	1.58208	−	0.655319i
$353$		−	22.9722i		−	1.22269i	−0.791366	−	0.611343i	$-0.790630\pi$
$353$		−	22.9722i		−	1.22269i	0.791366	−	0.611343i	$-0.209370\pi$
$354$		0			0
$355$	−7.62219	−	7.62219i	−0.404544	−	0.404544i
$356$	3.46465			0.183626
$357$		0			0
$358$	−1.88788			−0.0997775
$359$	24.1187	+	24.1187i	1.27293	+	1.27293i	0.944541	+	0.328394i	$0.106507\pi$
$359$	24.1187	+	24.1187i	1.27293	+	1.27293i	0.328394	+	0.944541i	$0.393493\pi$
$360$		0			0
$361$			10.4398i			0.549463i
$362$	−0.633128	+	0.262250i	−0.0332765	+	0.0137836i
$363$		0			0
$364$	−3.55876	−	1.47408i	−0.186529	−	0.0772630i
$365$	−1.16979	+	1.16979i	−0.0612294	+	0.0612294i
$366$		0			0
$367$	8.57000	+	3.54981i	0.447351	+	0.185299i	0.594974	−	0.803745i	$-0.297162\pi$
$367$	8.57000	+	3.54981i	0.447351	+	0.185299i	−0.147623	+	0.989044i	$0.547162\pi$
$368$	0.838880	−	2.02523i	0.0437296	−	0.105573i
$369$		0			0
$370$			0.381986i			0.0198585i
$371$	0.408674	+	0.986627i	0.0212173	+	0.0512231i
$372$		0			0
$373$	3.06857			0.158884			0.0794422	−	0.996839i	$-0.474686\pi$
$373$	3.06857			0.158884			0.0794422	+	0.996839i	$0.474686\pi$
$374$	−2.00897	−	24.2560i	−0.103881	−	1.25425i
$375$		0			0
$376$	11.3755	+	11.3755i	0.586646	+	0.586646i
$377$	−2.21856	−	5.35607i	−0.114261	−	0.275851i
$378$		0			0
$379$	33.7529	−	13.9809i	1.73377	−	0.718151i	0.734556	−	0.678549i	$-0.237391\pi$
$379$	33.7529	−	13.9809i	1.73377	−	0.718151i	0.999215	−	0.0396029i	$-0.0126093\pi$
$380$	2.22771	−	5.37816i	0.114279	−	0.275894i
$381$		0			0
$382$	3.58361	−	3.58361i	0.183353	−	0.183353i
$383$	−6.59130	+	6.59130i	−0.336800	+	0.336800i	−0.855161	−	0.518362i	$-0.826542\pi$
$383$	−6.59130	+	6.59130i	−0.336800	+	0.336800i	0.518362	+	0.855161i	$0.326542\pi$
$384$		0			0
$385$	7.26037	−	17.5281i	0.370023	−	0.893314i
$386$	−13.2815	+	5.50138i	−0.676011	+	0.280013i
$387$		0			0
$388$	−5.31071	−	12.8212i	−0.269610	−	0.650897i
$389$	−23.4493	−	23.4493i	−1.18892	−	1.18892i	−0.977365	−	0.211559i	$-0.932146\pi$
$389$	−23.4493	−	23.4493i	−1.18892	−	1.18892i	−0.211559	−	0.977365i	$-0.567854\pi$
$390$		0			0
$391$	9.80804	+	8.30763i	0.496014	+	0.420135i
$392$	−7.62397			−0.385069
$393$		0			0
$394$	2.33250	+	5.63114i	0.117509	+	0.283693i
$395$		−	5.27290i		−	0.265309i
$396$		0			0
$397$	−3.37734	+	8.15361i	−0.169504	+	0.409218i	−0.985689	−	0.168572i	$-0.946085\pi$
$397$	−3.37734	+	8.15361i	−0.169504	+	0.409218i	0.816186	+	0.577790i	$0.196085\pi$
$398$	13.2680	+	5.49577i	0.665063	+	0.275478i
$399$		0			0
$400$	0.497216	−	0.497216i	0.0248608	−	0.0248608i
$401$	−18.0332	−	7.46960i	−0.900535	−	0.373014i	−0.116109	−	0.993236i	$-0.537042\pi$
$401$	−18.0332	−	7.46960i	−0.900535	−	0.373014i	−0.784426	+	0.620223i	$0.787042\pi$
$402$		0			0
$403$	−3.99595	+	1.65518i	−0.199052	+	0.0824501i
$404$			1.57656i			0.0784369i
$405$		0			0
$406$	−10.5286	−	10.5286i	−0.522523	−	0.522523i
$407$	−2.43215			−0.120557
$408$		0			0
$409$	10.4152			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$409$	10.4152			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$410$	1.15924	+	1.15924i	0.0572508	+	0.0572508i
$411$		0			0
$412$		−	10.5247i		−	0.518515i
$413$	−11.6095	+	4.80881i	−0.571266	+	0.236626i
$414$		0			0
$415$	11.4800	+	4.75515i	0.563529	+	0.233421i
$416$	4.29914	−	4.29914i	0.210783	−	0.210783i
$417$		0			0
$418$	−29.5911	−	12.2570i	−1.44735	−	0.599512i
$419$	−13.5166	+	32.6320i	−0.660329	+	1.59418i	0.136958	+	0.990577i	$0.456267\pi$
$419$	−13.5166	+	32.6320i	−0.660329	+	1.59418i	−0.797288	+	0.603599i	$0.793733\pi$
$420$		0			0
$421$			15.0205i			0.732052i	0.930605	+	0.366026i	$0.119282\pi$
$421$			15.0205i			0.732052i	−0.930605	+	0.366026i	$0.880718\pi$
$422$	−4.93708	−	11.9192i	−0.240333	−	0.580216i
$423$		0			0
$424$	−1.02104			−0.0495861
$425$	1.88688	+	3.66602i	0.0915271	+	0.177828i
$426$		0			0
$427$	−27.2268	−	27.2268i	−1.31760	−	1.31760i
$428$	−1.18550	−	2.86204i	−0.0573031	−	0.138342i
$429$		0			0
$430$	−0.0238677	+	0.00988632i	−0.00115100	+	0.000476761i
$431$	8.93633	−	21.5742i	0.430448	−	1.03919i	−0.548695	−	0.836022i	$-0.684875\pi$
$431$	8.93633	−	21.5742i	0.430448	−	1.03919i	0.979143	−	0.203171i	$-0.0651247\pi$
$432$		0			0
$433$	−12.9455	+	12.9455i	−0.622120	+	0.622120i	−0.946073	−	0.323953i	$-0.894988\pi$
$433$	−12.9455	+	12.9455i	−0.622120	+	0.622120i	0.323953	+	0.946073i	$0.394988\pi$
$434$	−7.85493	+	7.85493i	−0.377049	+	0.377049i
$435$		0			0
$436$	2.36626	−	5.71265i	0.113323	−	0.273586i
$437$	15.6272	−	6.47302i	0.747552	−	0.309646i
$438$		0			0
$439$	7.75689	+	18.7268i	0.370216	+	0.893780i	0.993713	+	0.111955i	$0.0357112\pi$
$439$	7.75689	+	18.7268i	0.370216	+	0.893780i	−0.623497	+	0.781826i	$0.714289\pi$
$440$	12.8265	+	12.8265i	0.611481	+	0.611481i
$441$		0			0
$442$	−2.10783	−	4.09530i	−0.100259	−	0.194794i
$443$	−29.3849			−1.39612			−0.698058	−	0.716041i	$-0.745952\pi$
$443$	−29.3849			−1.39612			−0.698058	+	0.716041i	$0.745952\pi$
$444$		0			0
$445$	1.23580	+	2.98348i	0.0585825	+	0.141431i
$446$		−	2.03453i		−	0.0963376i
$447$		0			0
$448$	7.64119	−	18.4475i	0.361012	−	0.871561i
$449$	30.1572	+	12.4915i	1.42321	+	0.589512i	0.955664	−	0.294459i	$-0.0951394\pi$
$449$	30.1572	+	12.4915i	1.42321	+	0.589512i	0.467543	+	0.883970i	$0.345139\pi$
$450$		0			0
$451$	−7.38101	+	7.38101i	−0.347558	+	0.347558i
$452$	8.94115	+	3.70355i	0.420557	+	0.174200i
$453$		0			0
$454$	12.9518	−	5.36481i	0.607858	−	0.251783i
$455$		−	3.59031i		−	0.168316i
$456$		0			0
$457$	−5.97585	−	5.97585i	−0.279538	−	0.279538i	0.553386	−	0.832925i	$-0.313335\pi$
$457$	−5.97585	−	5.97585i	−0.279538	−	0.279538i	−0.832925	+	0.553386i	$0.813335\pi$
$458$	2.55199			0.119247
$459$		0			0
$460$	−3.34465			−0.155945
$461$	−27.0527	−	27.0527i	−1.25997	−	1.25997i	−0.951106	−	0.308863i	$-0.900051\pi$
$461$	−27.0527	−	27.0527i	−1.25997	−	1.25997i	−0.308863	−	0.951106i	$-0.599949\pi$
$462$		0			0
$463$			27.1761i			1.26298i	0.775383	+	0.631491i	$0.217557\pi$
$463$			27.1761i			1.26298i	−0.775383	+	0.631491i	$0.782443\pi$
$464$	3.24626	−	1.34464i	0.150704	−	0.0624235i
$465$		0			0
$466$	−2.79259	−	1.15673i	−0.129364	−	0.0535845i
$467$	−2.43616	+	2.43616i	−0.112732	+	0.112732i	−0.761223	−	0.648491i	$-0.775401\pi$
$467$	−2.43616	+	2.43616i	−0.112732	+	0.112732i	0.648491	+	0.761223i	$0.275401\pi$
$468$		0			0
$469$	−16.0825	−	6.66158i	−0.742619	−	0.307603i
$470$	−2.00345	+	4.83676i	−0.0924124	+	0.223103i
$471$		0			0
$472$		−	12.0144i		−	0.553009i
$473$	−0.0629473	−	0.151968i	−0.00289432	−	0.00698751i
$474$		0			0
$475$	5.42585			0.248955
$476$	10.4458	+	8.84784i	0.478783	+	0.405540i
$477$		0			0
$478$	9.33380	+	9.33380i	0.426918	+	0.426918i
$479$	−5.87776	−	14.1902i	−0.268562	−	0.648365i	0.730855	−	0.682533i	$-0.239122\pi$
$479$	−5.87776	−	14.1902i	−0.268562	−	0.648365i	−0.999416	+	0.0341684i	$0.989122\pi$
$480$		0			0
$481$	−0.425224	+	0.176134i	−0.0193886	+	0.00803101i
$482$	−4.60141	+	11.1088i	−0.209588	+	0.505991i
$483$		0			0
$484$	−20.1689	+	20.1689i	−0.916767	+	0.916767i
$485$	9.14632	−	9.14632i	0.415313	−	0.415313i
$486$		0			0
$487$	−10.0682	+	24.3068i	−0.456234	+	1.10145i	0.513676	+	0.857984i	$0.328283\pi$
$487$	−10.0682	+	24.3068i	−0.456234	+	1.10145i	−0.969910	+	0.243463i	$0.921717\pi$
$488$	34.0120	−	14.0882i	1.53965	−	0.637744i
$489$		0			0
$490$	−0.949458	−	2.29219i	−0.0428921	−	0.103551i
$491$	20.5320	+	20.5320i	0.926596	+	0.926596i	0.997484	−	0.0708885i	$-0.0225834\pi$
$491$	20.5320	+	20.5320i	0.926596	+	0.926596i	−0.0708885	+	0.997484i	$0.522583\pi$
$492$		0			0
$493$	1.70060	+	20.5328i	0.0765911	+	0.924749i
$494$	−6.06120			−0.272706
$495$		0			0
$496$	−1.00319	−	2.42190i	−0.0450443	−	0.108747i
$497$		−	33.3583i		−	1.49632i
$498$		0			0
$499$	12.4718	−	30.1097i	0.558316	−	1.34789i	−0.352782	−	0.935706i	$-0.614764\pi$
$499$	12.4718	−	30.1097i	0.558316	−	1.34789i	0.911098	−	0.412189i	$-0.135236\pi$
$500$	−0.991211	−	0.410573i	−0.0443283	−	0.0183614i
$501$		0			0
$502$	11.8749	−	11.8749i	0.530004	−	0.530004i
$503$	−21.7473	−	9.00803i	−0.969665	−	0.401648i	−0.159077	−	0.987266i	$-0.550852\pi$
$503$	−21.7473	−	9.00803i	−0.969665	−	0.401648i	−0.810587	+	0.585618i	$0.800852\pi$
$504$		0			0
$505$	−1.35761	+	0.562341i	−0.0604129	+	0.0250239i
$506$			18.4026i			0.818093i
$507$		0			0
$508$	10.6204	+	10.6204i	0.471202	+	0.471202i
$509$	−17.5818			−0.779300			−0.389650	−	0.920963i	$-0.627404\pi$
$509$	−17.5818			−0.779300			−0.389650	+	0.920963i	$0.627404\pi$
$510$		0			0
$511$	−5.11953			−0.226474
$512$	5.54798	+	5.54798i	0.245189	+	0.245189i
$513$		0			0
$514$		−	6.62553i		−	0.292239i
$515$	9.06306	−	3.75404i	0.399366	−	0.165423i
$516$		0			0
$517$	−30.7962	−	12.7562i	−1.35442	−	0.561018i
$518$	−0.835874	+	0.835874i	−0.0367262	+	0.0367262i
$519$		0			0
$520$	3.17141	+	1.31364i	0.139076	+	0.0576070i
$521$	7.84734	−	18.9452i	0.343798	−	0.830002i	−0.653527	−	0.756904i	$-0.726711\pi$
$521$	7.84734	−	18.9452i	0.343798	−	0.830002i	0.997325	−	0.0730986i	$-0.0232888\pi$
$522$		0			0
$523$		−	9.19853i		−	0.402224i	−0.979568	−	0.201112i	$-0.935545\pi$
$523$		−	9.19853i		−	0.402224i	0.979568	−	0.201112i	$-0.0644555\pi$
$524$	5.20213	+	12.5591i	0.227256	+	0.548645i
$525$		0			0
$526$	6.00648			0.261895
$527$	15.3187	−	1.26875i	0.667291	−	0.0552675i
$528$		0			0
$529$	9.39144	+	9.39144i	0.408324	+	0.408324i
$530$	−0.127156	−	0.306982i	−0.00552330	−	0.0133344i
$531$		0			0
$532$	16.6434	−	6.89393i	0.721583	−	0.298890i
$533$	−0.755933	+	1.82498i	−0.0327431	+	0.0790488i
$534$		0			0
$535$	2.04171	−	2.04171i	0.0882710	−	0.0882710i
$536$	11.7687	−	11.7687i	0.508329	−	0.508329i
$537$		0			0
$538$	−0.475654	+	1.14833i	−0.0205069	+	0.0495080i
$539$	14.5946	−	6.04530i	0.628636	−	0.260390i
$540$		0			0
$541$	−5.46780	−	13.2004i	−0.235079	−	0.567531i	0.761682	−	0.647951i	$-0.224374\pi$
$541$	−5.46780	−	13.2004i	−0.235079	−	0.567531i	−0.996761	+	0.0804201i	$0.974374\pi$
$542$	7.00251	+	7.00251i	0.300784	+	0.300784i
$543$		0			0
$544$	−19.2118	+	9.88821i	−0.823699	+	0.423954i
$545$	5.76330			0.246873
$546$		0			0
$547$	9.06998	+	21.8969i	0.387805	+	0.936243i	0.990404	+	0.138199i	$0.0441315\pi$
$547$	9.06998	+	21.8969i	0.387805	+	0.936243i	−0.602600	+	0.798043i	$0.705869\pi$
$548$			3.19598i			0.136525i
$549$		0			0
$550$	−2.25901	+	5.45373i	−0.0963245	+	0.232548i
$551$	25.0490	+	10.3756i	1.06712	+	0.442017i
$552$		0			0
$553$	11.5383	−	11.5383i	0.490660	−	0.490660i
$554$	−22.5776	−	9.35196i	−0.959231	−	0.397327i
$555$		0			0
$556$	19.4687	−	8.06419i	0.825656	−	0.341998i
$557$			0.399812i			0.0169406i	0.999964	+	0.00847028i	$0.00269621\pi$
$557$			0.399812i			0.0169406i	−0.999964	+	0.00847028i	$0.997304\pi$
$558$		0			0
$559$	−0.0220108	−	0.0220108i	−0.000930957	−	0.000930957i
$560$	2.17605			0.0919549
$561$		0			0
$562$	−5.67668			−0.239456
$563$	6.55034	+	6.55034i	0.276064	+	0.276064i	0.831536	−	0.555472i	$-0.187462\pi$
$563$	6.55034	+	6.55034i	0.276064	+	0.276064i	−0.555472	+	0.831536i	$0.687462\pi$
$564$		0			0
$565$			9.02043i			0.379492i
$566$	16.4272	−	6.80437i	0.690487	−	0.286009i
$567$		0			0
$568$	29.4662	+	12.2053i	1.23637	+	0.512123i
$569$	−4.07046	+	4.07046i	−0.170643	+	0.170643i	−0.787262	−	0.616619i	$-0.788502\pi$
$569$	−4.07046	+	4.07046i	−0.170643	+	0.170643i	0.616619	+	0.787262i	$0.288502\pi$
$570$		0			0
$571$	−12.9331	−	5.35705i	−0.541232	−	0.224186i	0.0952826	−	0.995450i	$-0.469625\pi$
$571$	−12.9331	−	5.35705i	−0.541232	−	0.224186i	−0.636515	+	0.771265i	$0.719625\pi$
$572$	−2.92028	+	7.05018i	−0.122103	+	0.294783i
$573$		0			0
$574$			5.07337i			0.211759i
$575$	−1.19300	−	2.88015i	−0.0497514	−	0.120110i
$576$		0			0
$577$	−18.4417			−0.767736			−0.383868	−	0.923388i	$-0.625408\pi$
$577$	−18.4417			−0.767736			−0.383868	+	0.923388i	$0.625408\pi$
$578$	2.69298	+	16.1458i	0.112013	+	0.671575i
$579$		0			0
$580$	−3.79091	−	3.79091i	−0.157409	−	0.157409i
$581$	14.7154	+	35.5262i	0.610499	+	1.47388i
$582$		0			0
$583$	1.95459	−	0.809616i	0.0809507	−	0.0335309i
$584$	1.87316	−	4.52220i	0.0775118	−	0.187130i
$585$		0			0
$586$	−5.66397	+	5.66397i	−0.233977	+	0.233977i
$587$	2.85082	−	2.85082i	0.117666	−	0.117666i	−0.645822	−	0.763488i	$-0.723485\pi$
$587$	2.85082	−	2.85082i	0.117666	−	0.117666i	0.763488	+	0.645822i	$0.223485\pi$
$588$		0			0
$589$	7.74084	−	18.6880i	0.318956	−	0.770027i
$590$	3.61221	−	1.49623i	0.148712	−	0.0615987i
$591$		0			0
$592$	−0.106753	−	0.257724i	−0.00438752	−	0.0105924i
$593$	4.61328	+	4.61328i	0.189445	+	0.189445i	0.795456	−	0.606011i	$-0.207231\pi$
$593$	4.61328	+	4.61328i	0.189445	+	0.189445i	−0.606011	+	0.795456i	$0.707231\pi$
$594$		0			0
$595$	−3.89317	+	12.1510i	−0.159604	+	0.498144i
$596$	3.17114			0.129895
$597$		0			0
$598$	1.33269	+	3.21741i	0.0544979	+	0.131570i
$599$		−	6.81189i		−	0.278326i	−0.990269	−	0.139163i	$-0.955559\pi$
$599$		−	6.81189i		−	0.278326i	0.990269	−	0.139163i	$-0.0444413\pi$
$600$		0			0
$601$	14.6029	−	35.2545i	0.595664	−	1.43806i	−0.282297	−	0.959327i	$-0.591096\pi$
$601$	14.6029	−	35.2545i	0.595664	−	1.43806i	0.877961	−	0.478732i	$-0.158904\pi$
$602$	−0.0738616	−	0.0305945i	−0.00301038	−	0.00124694i
$603$		0			0
$604$	16.7207	−	16.7207i	0.680354	−	0.680354i
$605$	−24.5619	−	10.1739i	−0.998581	−	0.413626i
$606$		0			0
$607$	−25.0895	+	10.3924i	−1.01835	+	0.421816i	−0.828495	−	0.559996i	$-0.810803\pi$
$607$	−25.0895	+	10.3924i	−1.01835	+	0.421816i	−0.189858	+	0.981812i	$0.560803\pi$
$608$			28.4342i			1.15316i
$609$		0			0
$610$	8.47142	+	8.47142i	0.342998	+	0.342998i
$611$	−6.30805			−0.255196
$612$		0			0
$613$	2.48591			0.100405			0.0502025	−	0.998739i	$-0.484013\pi$
$613$	2.48591			0.100405			0.0502025	+	0.998739i	$0.484013\pi$
$614$	8.33154	+	8.33154i	0.336233	+	0.336233i
$615$		0			0
$616$			56.1349i			2.26174i
$617$	−39.9062	+	16.5297i	−1.60656	+	0.665460i	−0.992325	−	0.123661i	$-0.960536\pi$
$617$	−39.9062	+	16.5297i	−1.60656	+	0.665460i	−0.614238	+	0.789121i	$0.710536\pi$
$618$		0			0
$619$	−1.27211	−	0.526923i	−0.0511302	−	0.0211788i	0.356972	−	0.934115i	$-0.383809\pi$
$619$	−1.27211	−	0.526923i	−0.0511302	−	0.0211788i	−0.408102	+	0.912936i	$0.633809\pi$
$620$	−2.82824	+	2.82824i	−0.113585	+	0.113585i
$621$		0			0
$622$	−29.0329	−	12.0258i	−1.16411	−	0.482192i
$623$	−3.82434	+	9.23276i	−0.153219	+	0.369903i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$	4.94825	+	11.9461i	0.197772	+	0.477464i
$627$		0			0
$628$	13.8043			0.550851
$629$	1.63012	−	0.135012i	0.0649971	−	0.00538330i
$630$		0			0
$631$	22.9351	+	22.9351i	0.913032	+	0.913032i	0.996510	−	0.0834781i	$-0.0266029\pi$
$631$	22.9351	+	22.9351i	0.913032	+	0.913032i	−0.0834781	+	0.996510i	$0.526603\pi$
$632$	5.97040	+	14.4138i	0.237490	+	0.573351i
$633$		0			0
$634$	−8.78330	+	3.63816i	−0.348829	+	0.144490i
$635$	−5.35726	+	12.9336i	−0.212596	+	0.513253i
$636$		0			0
$637$	2.11386	−	2.11386i	0.0837542	−	0.0837542i
$638$	−20.8579	+	20.8579i	−0.825773	+	0.825773i
$639$		0			0
$640$	1.63341	−	3.94341i	0.0645663	−	0.155877i
$641$	−20.6017	+	8.53352i	−0.813719	+	0.337054i	−0.750437	−	0.660942i	$-0.770157\pi$
$641$	−20.6017	+	8.53352i	−0.813719	+	0.337054i	−0.0632825	+	0.997996i	$0.520157\pi$
$642$		0			0
$643$	−4.48736	−	10.8335i	−0.176964	−	0.427230i	0.810363	−	0.585929i	$-0.199270\pi$
$643$	−4.48736	−	10.8335i	−0.176964	−	0.427230i	−0.987327	+	0.158699i	$0.949270\pi$
$644$	−7.31887	−	7.31887i	−0.288404	−	0.288404i
$645$		0			0
$646$	20.5135	+	6.57249i	0.807094	+	0.258591i
$647$	37.3217			1.46727			0.733634	−	0.679544i	$-0.237823\pi$
$647$	37.3217			1.46727			0.733634	+	0.679544i	$0.237823\pi$
$648$		0			0
$649$	9.52665	+	22.9994i	0.373954	+	0.902804i
$650$			1.11710i			0.0438162i
$651$		0			0
$652$	−7.92097	+	19.1229i	−0.310209	+	0.748911i
$653$	1.62208	+	0.671889i	0.0634771	+	0.0262931i	0.414196	−	0.910188i	$-0.364063\pi$
$653$	1.62208	+	0.671889i	0.0634771	+	0.0262931i	−0.350719	+	0.936481i	$0.614063\pi$
$654$		0			0
$655$	−8.95933	+	8.95933i	−0.350070	+	0.350070i
$656$	−1.10610	−	0.458164i	−0.0431861	−	0.0178883i
$657$		0			0
$658$	−14.9680	+	6.19994i	−0.583513	+	0.241699i
$659$			6.02834i			0.234831i	0.993083	+	0.117415i	$0.0374609\pi$
$659$			6.02834i			0.234831i	−0.993083	+	0.117415i	$0.962539\pi$
$660$		0			0
$661$	22.6415	+	22.6415i	0.880652	+	0.880652i	0.993601	−	0.112949i	$-0.0360296\pi$
$661$	22.6415	+	22.6415i	0.880652	+	0.880652i	−0.112949	+	0.993601i	$0.536030\pi$
$662$	5.43353			0.211180
$663$		0			0
$664$	−36.7653			−1.42677
$665$	11.8730	+	11.8730i	0.460416	+	0.460416i
$666$		0			0
$667$		−	15.5778i		−	0.603176i
$668$	18.6934	−	7.74305i	0.723269	−	0.299588i
$669$		0			0
$670$	5.00394	+	2.07270i	0.193319	+	0.0800754i
$671$	−53.9385	+	53.9385i	−2.08227	+	2.08227i
$672$		0			0
$673$	−36.5765	−	15.1505i	−1.40992	−	0.584009i	−0.457615	−	0.889150i	$-0.651296\pi$
$673$	−36.5765	−	15.1505i	−1.40992	−	0.584009i	−0.952307	+	0.305142i	$0.901296\pi$
$674$	6.11393	−	14.7603i	0.235500	−	0.568547i
$675$		0			0
$676$		−	12.5033i		−	0.480897i
$677$	−2.67674	−	6.46223i	−0.102876	−	0.248364i	0.864058	−	0.503393i	$-0.167915\pi$
$677$	−2.67674	−	6.46223i	−0.102876	−	0.248364i	−0.966933	+	0.255029i	$0.917915\pi$
$678$		0			0
$679$	40.0286			1.53616
$680$	−9.30886	−	7.88481i	−0.356978	−	0.302369i
$681$		0			0
$682$	15.5613	+	15.5613i	0.595871	+	0.595871i
$683$	−14.2417	−	34.3826i	−0.544945	−	1.31561i	−0.921197	−	0.389097i	$-0.872787\pi$
$683$	−14.2417	−	34.3826i	−0.544945	−	1.31561i	0.376251	−	0.926518i	$-0.377213\pi$
$684$		0			0
$685$	−2.75213	+	1.13997i	−0.105153	+	0.0435559i
$686$	−5.04383	+	12.1769i	−0.192574	+	0.464915i
$687$		0			0
$688$	0.0133405	−	0.0133405i	0.000508602	−	0.000508602i
$689$	0.283098	−	0.283098i	0.0107852	−	0.0107852i
$690$		0			0
$691$	−5.98831	+	14.4571i	−0.227806	+	0.549972i	−0.995910	−	0.0903530i	$-0.971200\pi$
$691$	−5.98831	+	14.4571i	−0.227806	+	0.549972i	0.768104	+	0.640325i	$0.221200\pi$
$692$	22.3786	−	9.26952i	0.850706	−	0.352374i
$693$		0			0
$694$	3.40627	+	8.22347i	0.129300	+	0.312158i
$695$	13.8885	+	13.8885i	0.526821	+	0.526821i
$696$		0			0
$697$	4.53731	−	5.35677i	0.171863	−	0.202902i
$698$	25.9276			0.981372
$699$		0			0
$700$	−1.27057	−	3.06743i	−0.0480231	−	0.115938i
$701$			6.08551i			0.229847i	0.993374	+	0.114923i	$0.0366622\pi$
$701$			6.08551i			0.229847i	−0.993374	+	0.114923i	$0.963338\pi$
$702$		0			0
$703$	0.823733	−	1.98867i	0.0310677	−	0.0750040i
$704$	−36.5459	−	15.1378i	−1.37738	−	0.570528i
$705$		0			0
$706$	−15.6407	+	15.6407i	−0.588644	+	0.588644i
$707$	−4.20130	−	1.74024i	−0.158006	−	0.0654483i
$708$		0			0
$709$	18.2079	−	7.54197i	0.683813	−	0.283245i	−0.0136069	−	0.999907i	$-0.504331\pi$
$709$	18.2079	−	7.54197i	0.683813	−	0.283245i	0.697420	+	0.716663i	$0.254331\pi$
$710$			10.3792i			0.389524i
$711$		0			0
$712$	−6.75626	−	6.75626i	−0.253202	−	0.253202i
$713$	−11.6220			−0.435247
$714$		0			0
$715$	−7.11269			−0.266000
$716$	−1.48745	−	1.48745i	−0.0555886	−	0.0555886i
$717$		0			0
$718$		−	32.8425i		−	1.22567i
$719$	14.7049	−	6.09095i	0.548399	−	0.227154i	−0.0912412	−	0.995829i	$-0.529083\pi$
$719$	14.7049	−	6.09095i	0.548399	−	0.227154i	0.639640	+	0.768675i	$0.279083\pi$
$720$		0			0
$721$	28.0468	+	11.6174i	1.04452	+	0.432653i
$722$	7.10797	−	7.10797i	0.264531	−	0.264531i
$723$		0			0
$724$	−0.705464	−	0.292213i	−0.0262184	−	0.0108600i
$725$	1.91226	−	4.61660i	0.0710196	−	0.171456i
$726$		0			0
$727$		−	22.2643i		−	0.825736i	−0.910791	−	0.412868i	$-0.864527\pi$
$727$		−	22.2643i		−	0.825736i	0.910791	−	0.412868i	$-0.135473\pi$
$728$	4.06523	+	9.81433i	0.150667	+	0.363743i
$729$		0			0
$730$	1.59290			0.0589560
$731$	0.0506257	+	0.0983607i	0.00187246	+	0.00363800i
$732$		0			0
$733$	4.01178	+	4.01178i	0.148178	+	0.148178i	0.777304	−	0.629125i	$-0.216587\pi$
$733$	4.01178	+	4.01178i	0.148178	+	0.148178i	−0.629125	+	0.777304i	$0.716587\pi$
$734$	−3.41801	−	8.25181i	−0.126161	−	0.304580i
$735$		0			0
$736$	15.0934	−	6.25191i	0.556352	−	0.230449i
$737$	−13.1971	+	31.8607i	−0.486122	+	1.17360i
$738$		0			0
$739$	−28.1411	+	28.1411i	−1.03519	+	1.03519i	−0.0358281	+	0.999358i	$0.511407\pi$
$739$	−28.1411	+	28.1411i	−1.03519	+	1.03519i	−0.999358	+	0.0358281i	$0.988593\pi$
$740$	−0.300965	+	0.300965i	−0.0110637	+	0.0110637i
$741$		0			0
$742$	0.393501	−	0.949994i	0.0144459	−	0.0348754i
$743$	9.83928	−	4.07556i	0.360968	−	0.149518i	−0.194826	−	0.980838i	$-0.562414\pi$
$743$	9.83928	−	4.07556i	0.360968	−	0.149518i	0.555794	+	0.831320i	$0.312414\pi$
$744$		0			0
$745$	1.13111	+	2.73074i	0.0414407	+	0.100047i
$746$	−2.08924	−	2.08924i	−0.0764926	−	0.0764926i
$747$		0			0
$748$	17.5283	−	20.6940i	0.640897	−	0.756647i
$749$	8.93549			0.326496
$750$		0			0
$751$	6.93403	+	16.7402i	0.253026	+	0.610860i	0.998446	−	0.0557362i	$-0.0177506\pi$
$751$	6.93403	+	16.7402i	0.253026	+	0.610860i	−0.745419	+	0.666596i	$0.767751\pi$
$752$		−	3.82324i		−	0.139419i
$753$		0			0
$754$	−2.13618	+	5.15720i	−0.0777952	+	0.187814i
$755$	20.3626	+	8.43445i	0.741070	+	0.306961i
$756$		0			0
$757$	12.0753	−	12.0753i	0.438885	−	0.438885i	−0.452752	−	0.891637i	$-0.649558\pi$
$757$	12.0753	−	12.0753i	0.438885	−	0.438885i	0.891637	+	0.452752i	$0.149558\pi$
$758$	−32.4997	−	13.4618i	−1.18044	−	0.488955i
$759$		0			0
$760$	−14.8319	+	6.14357i	−0.538009	+	0.222851i
$761$		−	31.9719i		−	1.15898i	−0.814979	−	0.579491i	$-0.803251\pi$
$761$		−	31.9719i		−	1.15898i	0.814979	−	0.579491i	$-0.196749\pi$
$762$		0			0
$763$	12.6114	+	12.6114i	0.456565	+	0.456565i
$764$	5.64701			0.204301
$765$		0			0
$766$	8.97540			0.324294
$767$	3.33118	+	3.33118i	0.120282	+	0.120282i
$768$		0			0
$769$		−	34.9147i		−	1.25906i	−0.776977	−	0.629529i	$-0.783248\pi$
$769$		−	34.9147i		−	1.25906i	0.776977	−	0.629529i	$-0.216752\pi$
$770$	−16.8773	+	6.99080i	−0.608215	+	0.251931i
$771$		0			0
$772$	−14.7989	−	6.12991i	−0.532625	−	0.220620i
$773$	−3.17604	+	3.17604i	−0.114234	+	0.114234i	−0.761913	−	0.647679i	$-0.775740\pi$
$773$	−3.17604	+	3.17604i	−0.114234	+	0.114234i	0.647679	+	0.761913i	$0.275740\pi$
$774$		0			0
$775$	−3.44426	−	1.42666i	−0.123722	−	0.0512472i
$776$	−14.6459	+	35.3582i	−0.525756	+	1.26929i
$777$		0			0
$778$			31.9310i			1.14478i
$779$	−3.53531	−	8.53499i	−0.126666	−	0.305798i
$780$		0			0
$781$	−66.0854			−2.36472
$782$	−1.02156	−	12.3341i	−0.0365308	−	0.441067i
$783$		0			0
$784$	1.28119	+	1.28119i	0.0457568	+	0.0457568i
$785$	4.92383	+	11.8872i	0.175739	+	0.424271i
$786$		0			0
$787$	−7.99286	+	3.31075i	−0.284915	+	0.118016i	−0.520564	−	0.853823i	$-0.674278\pi$
$787$	−7.99286	+	3.31075i	−0.284915	+	0.118016i	0.235649	+	0.971838i	$0.424278\pi$
$788$	−2.59899	+	6.27451i	−0.0925850	+	0.223520i
$789$		0			0
$790$	−3.59007	+	3.59007i	−0.127729	+	0.127729i
$791$	−19.7388	+	19.7388i	−0.701831	+	0.701831i
$792$		0			0
$793$	−5.52416	+	13.3365i	−0.196169	+	0.473593i
$794$	7.85087	−	3.25194i	0.278617	−	0.115407i
$795$		0			0
$796$	6.12366	+	14.7838i	0.217048	+	0.523999i
$797$	−13.4447	−	13.4447i	−0.476236	−	0.476236i	0.427689	−	0.903926i	$-0.359328\pi$
$797$	−13.4447	−	13.4447i	−0.476236	−	0.476236i	−0.903926	+	0.427689i	$0.859328\pi$
$798$		0			0
$799$	21.3489	+	6.84016i	0.755271	+	0.241987i
$800$	5.24051			0.185280
$801$		0			0
$802$	7.19226	+	17.3636i	0.253967	+	0.613132i
$803$			10.1422i			0.357910i
$804$		0			0
$805$	3.69188	−	8.91299i	0.130122	−	0.314142i
$806$	3.84758	+	1.59372i	0.135525	+	0.0561364i
$807$		0			0
$808$	3.07439	−	3.07439i	0.108157	−	0.108157i
$809$	20.9455	+	8.67589i	0.736403	+	0.305028i	0.719180	−	0.694824i	$-0.244518\pi$
$809$	20.9455	+	8.67589i	0.736403	+	0.305028i	0.0172227	+	0.999852i	$0.494518\pi$
$810$		0			0
$811$	−22.2809	+	9.22904i	−0.782388	+	0.324076i	−0.737879	−	0.674933i	$-0.764172\pi$
$811$	−22.2809	+	9.22904i	−0.782388	+	0.324076i	−0.0445090	+	0.999009i	$0.514172\pi$
$812$		−	16.5908i		−	0.582222i
$813$		0			0
$814$	1.65593	+	1.65593i	0.0580405	+	0.0580405i
$815$	−19.2925			−0.675786
$816$		0			0
$817$	0.145578			0.00509311
$818$	−7.09121	−	7.09121i	−0.247938	−	0.247938i
$819$		0			0
$820$			1.82672i			0.0637917i
$821$	0.105957	−	0.0438888i	0.00369792	−	0.00153173i	−0.380834	−	0.924644i	$-0.624363\pi$
$821$	0.105957	−	0.0438888i	0.00369792	−	0.00153173i	0.384532	+	0.923112i	$0.374363\pi$
$822$		0			0
$823$	−31.2835	−	12.9581i	−1.09047	−	0.451689i	−0.236302	−	0.971680i	$-0.575936\pi$
$823$	−31.2835	−	12.9581i	−1.09047	−	0.451689i	−0.854172	+	0.519990i	$0.825936\pi$
$824$	−20.5238	+	20.5238i	−0.714981	+	0.714981i
$825$		0			0
$826$	11.1785	+	4.63027i	0.388948	+	0.161108i
$827$	7.86974	−	18.9992i	0.273658	−	0.660668i	−0.725976	−	0.687720i	$-0.758612\pi$
$827$	7.86974	−	18.9992i	0.273658	−	0.660668i	0.999634	+	0.0270516i	$0.00861185\pi$
$828$		0			0
$829$		−	26.7935i		−	0.930576i	−0.885159	−	0.465288i	$-0.845951\pi$
$829$		−	26.7935i		−	0.930576i	0.885159	−	0.465288i	$-0.154049\pi$
$830$	−4.57860	−	11.0537i	−0.158926	−	0.383680i
$831$		0			0
$832$	−7.48577			−0.259522
$833$	−9.44631	+	4.86197i	−0.327295	+	0.168457i
$834$		0			0
$835$	13.3354	+	13.3354i	0.461491	+	0.461491i
$836$	−13.6574	−	32.9719i	−0.472352	−	1.14036i
$837$		0			0
$838$	31.4204	−	13.0147i	1.08540	−	0.449587i
$839$	−5.29374	+	12.7802i	−0.182760	+	0.441222i	−0.988533	−	0.151002i	$-0.951750\pi$
$839$	−5.29374	+	12.7802i	−0.182760	+	0.441222i	0.805773	+	0.592224i	$0.201750\pi$
$840$		0			0
$841$	−2.84980	+	2.84980i	−0.0982690	+	0.0982690i
$842$	10.2267	−	10.2267i	0.352436	−	0.352436i
$843$		0			0
$844$	5.50114	−	13.2809i	0.189357	−	0.457149i
$845$	10.7669	−	4.45979i	0.370392	−	0.153421i
$846$		0			0
$847$	−31.4843	−	76.0098i	−1.08181	−	2.61173i
$848$	0.171583	+	0.171583i	0.00589219	+	0.00589219i
$849$		0			0
$850$	1.21133	−	3.78070i	0.0415483	−	0.129677i
$851$	−1.23674			−0.0423950
$852$		0			0
$853$	4.89128	+	11.8086i	0.167474	+	0.404319i	0.985228	−	0.171250i	$-0.0547807\pi$
$853$	4.89128	+	11.8086i	0.167474	+	0.404319i	−0.817753	+	0.575569i	$0.804781\pi$
$854$			37.0749i			1.26868i
$855$		0			0
$856$	−3.26936	+	7.89294i	−0.111744	+	0.269775i
$857$	−5.83483	−	2.41686i	−0.199314	−	0.0825585i	0.280794	−	0.959768i	$-0.409402\pi$
$857$	−5.83483	−	2.41686i	−0.199314	−	0.0825585i	−0.480107	+	0.877210i	$0.659402\pi$
$858$		0			0
$859$	24.8431	−	24.8431i	0.847636	−	0.847636i	−0.142202	−	0.989838i	$-0.545418\pi$
$859$	24.8431	−	24.8431i	0.847636	−	0.847636i	0.989838	+	0.142202i	$0.0454183\pi$
$860$	−0.0265946	−	0.0110158i	−0.000906868	−	0.000375637i
$861$		0			0
$862$	−20.7732	+	8.60453i	−0.707537	+	0.293072i
$863$		−	44.2102i		−	1.50493i	−0.658632	−	0.752466i	$-0.728864\pi$
$863$		−	44.2102i		−	1.50493i	0.658632	−	0.752466i	$-0.271136\pi$
$864$		0			0
$865$	15.9644	+	15.9644i	0.542804	+	0.542804i
$866$	17.6279			0.599022
$867$		0			0
$868$	−12.3777			−0.420127
$869$	−22.8584	−	22.8584i	−0.775417	−	0.775417i
$870$		0			0
$871$			6.52608i			0.221128i
$872$	−15.7543	+	6.52566i	−0.533510	+	0.220987i
$873$		0			0
$874$	−15.0470	−	6.23268i	−0.508973	−	0.210824i
$875$	2.18823	−	2.18823i	0.0739758	−	0.0739758i
$876$		0			0
$877$	21.8103	+	9.03414i	0.736483	+	0.305061i	0.719213	−	0.694790i	$-0.244503\pi$
$877$	21.8103	+	9.03414i	0.736483	+	0.305061i	0.0172700	+	0.999851i	$0.494503\pi$
$878$	7.46888	−	18.0315i	0.252063	−	0.608533i
$879$		0			0
$880$		−	4.31093i		−	0.145321i
$881$	12.6524	+	30.5457i	0.426271	+	1.02911i	0.980460	+	0.196719i	$0.0630286\pi$
$881$	12.6524	+	30.5457i	0.426271	+	1.02911i	−0.554189	+	0.832391i	$0.686971\pi$
$882$		0			0
$883$	−58.1141			−1.95569			−0.977847	−	0.209320i	$-0.932875\pi$
$883$	−58.1141			−1.95569			−0.977847	+	0.209320i	$0.932875\pi$
$884$	1.56592	−	4.88741i	0.0526675	−	0.164381i
$885$		0			0
$886$	20.0068	+	20.0068i	0.672140	+	0.672140i
$887$	10.7189	+	25.8776i	0.359904	+	0.868885i	0.995313	+	0.0967091i	$0.0308316\pi$
$887$	10.7189	+	25.8776i	0.359904	+	0.868885i	−0.635409	+	0.772176i	$0.719168\pi$
$888$		0			0
$889$	−40.0246	+	16.5787i	−1.34238	+	0.556033i
$890$	1.18991	−	2.87271i	0.0398860	−	0.0962933i
$891$		0			0
$892$	1.60299	−	1.60299i	0.0536721	−	0.0536721i
$893$	20.8605	−	20.8605i	0.698069	−	0.698069i
$894$		0			0
$895$	0.750319	−	1.81143i	0.0250804	−	0.0605494i
$896$	12.2034	−	5.05480i	0.407686	−	0.168869i
$897$		0			0
$898$	−12.0277	−	29.0375i	−0.401371	−	0.968994i
$899$	−13.1727	−	13.1727i	−0.439333	−	0.439333i
$900$		0			0
$901$	−1.26510	+	0.651138i	−0.0421465	+	0.0216926i
$902$	10.0508			0.334654
$903$		0			0
$904$	−10.2136	−	24.6579i	−0.339701	−	0.820110i
$905$		−	0.711719i		−	0.0236583i
$906$		0			0
$907$	19.1037	−	46.1204i	0.634328	−	1.53140i	−0.199802	−	0.979836i	$-0.564030\pi$
$907$	19.1037	−	46.1204i	0.634328	−	1.53140i	0.834130	−	0.551568i	$-0.185970\pi$
$908$	14.4315	+	5.97774i	0.478928	+	0.198378i
$909$		0			0
$910$	−2.44447	+	2.44447i	−0.0810334	+	0.0810334i
$911$	20.2142	+	8.37302i	0.669728	+	0.277410i	0.691526	−	0.722352i	$-0.256939\pi$
$911$	20.2142	+	8.37302i	0.669728	+	0.277410i	−0.0217976	+	0.999762i	$0.506939\pi$
$912$		0			0
$913$	70.3802	−	29.1525i	2.32925	−	0.964805i
$914$			8.13734i			0.269159i
$915$		0			0
$916$	2.01070	+	2.01070i	0.0664354	+	0.0664354i
$917$	−39.2102			−1.29483
$918$		0			0
$919$	−11.0529			−0.364600			−0.182300	−	0.983243i	$-0.558354\pi$
$919$	−11.0529			−0.364600			−0.182300	+	0.983243i	$0.558354\pi$
$920$	6.52226	+	6.52226i	0.215033	+	0.215033i
$921$		0			0
$922$			36.8378i			1.21319i
$923$	−11.5540	+	4.78584i	−0.380306	+	0.157528i
$924$		0			0
$925$	−0.366518	−	0.151817i	−0.0120510	−	0.00499170i
$926$	18.5029	−	18.5029i	0.608045	−	0.608045i
$927$		0			0
$928$	24.1934	+	10.0212i	0.794186	+	0.328963i
$929$	−12.6796	+	30.6112i	−0.416003	+	1.00432i	0.567491	+	0.823380i	$0.307914\pi$
$929$	−12.6796	+	30.6112i	−0.416003	+	1.00432i	−0.983494	+	0.180941i	$0.942086\pi$
$930$		0			0
$931$			13.9809i			0.458206i
$932$	−1.28889	−	3.11165i	−0.0422189	−	0.101925i
$933$		0			0
$934$	3.31733			0.108546
$935$	24.0722	+	7.71268i	0.787244	+	0.252231i
$936$		0			0
$937$	41.2820	+	41.2820i	1.34862	+	1.34862i	0.887159	+	0.461465i	$0.152676\pi$
$937$	41.2820	+	41.2820i	1.34862	+	1.34862i	0.461465	+	0.887159i	$0.347324\pi$
$938$	6.41424	+	15.4853i	0.209432	+	0.505614i
$939$		0			0
$940$	−5.38937	+	2.23235i	−0.175782	+	0.0728112i
$941$	2.33416	−	5.63515i	0.0760913	−	0.183701i	−0.881257	−	0.472638i	$-0.843302\pi$
$941$	2.33416	−	5.63515i	0.0760913	−	0.183701i	0.957348	+	0.288937i	$0.0933019\pi$
$942$		0			0
$943$	−3.75323	+	3.75323i	−0.122222	+	0.122222i
$944$	−2.01900	+	2.01900i	−0.0657127	+	0.0657127i
$945$		0			0
$946$	−0.0606101	+	0.146326i	−0.00197061	+	0.00475746i
$947$	−43.5595	+	18.0429i	−1.41549	+	0.586317i	−0.953724	−	0.300683i	$-0.902785\pi$
$947$	−43.5595	+	18.0429i	−1.41549	+	0.586317i	−0.461770	+	0.887000i	$0.652785\pi$
$948$		0			0
$949$	0.734487	+	1.77321i	0.0238425	+	0.0575608i
$950$	−3.69420	−	3.69420i	−0.119856	−	0.119856i
$951$		0			0
$952$	−3.11614	−	37.6237i	−0.100995	−	1.21939i
$953$	−26.8459			−0.869625			−0.434812	−	0.900521i	$-0.643185\pi$
$953$	−26.8459			−0.869625			−0.434812	+	0.900521i	$0.643185\pi$
$954$		0			0
$955$	2.01422	+	4.86276i	0.0651786	+	0.157355i
$956$			14.7081i			0.475694i
$957$		0			0
$958$	−5.65952	+	13.6633i	−0.182851	+	0.441441i
$959$	−8.51680	−	3.52778i	−0.275022	−	0.113918i
$960$		0			0
$961$	12.0927	−	12.0927i	0.390088	−	0.390088i
$962$	0.409436	+	0.169594i	0.0132008	+	0.00546793i
$963$		0			0
$964$	−12.3780	+	5.12712i	−0.398667	+	0.165133i
$965$		−	14.9301i		−	0.480618i
$966$		0			0
$967$	−24.1223	−	24.1223i	−0.775722	−	0.775722i	0.203378	−	0.979100i	$-0.434808\pi$
$967$	−24.1223	−	24.1223i	−0.775722	−	0.775722i	−0.979100	+	0.203378i	$0.934808\pi$
$968$	78.6610			2.52826
$969$		0			0
$970$	−12.4546			−0.399893
$971$	16.2292	+	16.2292i	0.520821	+	0.520821i	0.917819	−	0.396999i	$-0.129948\pi$
$971$	16.2292	+	16.2292i	0.520821	+	0.520821i	−0.396999	+	0.917819i	$0.629948\pi$
$972$		0			0
$973$			60.7825i			1.94860i
$974$	23.4043	−	9.69439i	0.749923	−	0.310628i
$975$		0			0
$976$	−8.08312	−	3.34814i	−0.258734	−	0.107171i
$977$	−14.0530	+	14.0530i	−0.449595	+	0.449595i	−0.895220	−	0.445625i	$-0.852982\pi$
$977$	−14.0530	+	14.0530i	−0.449595	+	0.449595i	0.445625	+	0.895220i	$0.352982\pi$
$978$		0			0
$979$	18.2908	+	7.57632i	0.584578	+	0.242140i
$980$	1.05793	−	2.55408i	0.0337945	−	0.0815870i
$981$		0			0
$982$		−	27.9585i		−	0.892192i
$983$	22.6054	+	54.5743i	0.721001	+	1.74065i	0.670479	+	0.741928i	$0.266089\pi$
$983$	22.6054	+	54.5743i	0.721001	+	1.74065i	0.0505223	+	0.998723i	$0.483911\pi$
$984$		0			0
$985$	−6.33014			−0.201695
$986$	12.8219	−	15.1376i	0.408333	−	0.482081i
$987$		0			0
$988$	−4.77559	−	4.77559i	−0.151932	−	0.151932i
$989$	−0.0320086	−	0.0772755i	−0.00101781	−	0.00245722i
$990$		0			0
$991$	−9.78771	+	4.05420i	−0.310917	+	0.128786i	−0.532685	−	0.846313i	$-0.678817\pi$
$991$	−9.78771	+	4.05420i	−0.310917	+	0.128786i	0.221768	+	0.975099i	$0.428817\pi$
$992$	7.47643	−	18.0497i	0.237377	−	0.573078i
$993$		0			0
$994$	−22.7121	+	22.7121i	−0.720383	+	0.720383i
$995$	−10.5464	+	10.5464i	−0.334345	+	0.334345i
$996$		0			0
$997$	15.6083	−	37.6817i	0.494319	−	1.19339i	−0.458182	−	0.888858i	$-0.651499\pi$
$997$	15.6083	−	37.6817i	0.494319	−	1.19339i	0.952501	−	0.304534i	$-0.0985008\pi$
$998$	−28.9917	+	12.0088i	−0.917718	+	0.380131i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.406.3		24
3.2	odd	2		85.2.l.a.66.4	✓	24
15.2	even	4		425.2.n.c.49.3		24
15.8	even	4		425.2.n.f.49.4		24
15.14	odd	2		425.2.m.b.151.3		24
17.8	even	8	inner	765.2.be.b.586.3		24
51.5	even	16		1445.2.a.p.1.6		12
51.8	odd	8		85.2.l.a.76.4	yes	24
51.14	even	16		1445.2.d.j.866.14		24
51.20	even	16		1445.2.d.j.866.13		24
51.29	even	16		1445.2.a.q.1.6		12
255.8	even	8		425.2.n.c.399.3		24
255.29	even	16		7225.2.a.bq.1.7		12
255.59	odd	8		425.2.m.b.76.3		24
255.209	even	16		7225.2.a.bs.1.7		12
255.212	even	8		425.2.n.f.399.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.4	✓	24	3.2	odd	2
85.2.l.a.76.4	yes	24	51.8	odd	8
425.2.m.b.76.3		24	255.59	odd	8
425.2.m.b.151.3		24	15.14	odd	2
425.2.n.c.49.3		24	15.2	even	4
425.2.n.c.399.3		24	255.8	even	8
425.2.n.f.49.4		24	15.8	even	4
425.2.n.f.399.4		24	255.212	even	8
765.2.be.b.406.3		24	1.1	even	1	trivial
765.2.be.b.586.3		24	17.8	even	8	inner
1445.2.a.p.1.6		12	51.5	even	16
1445.2.a.q.1.6		12	51.29	even	16
1445.2.d.j.866.13		24	51.20	even	16
1445.2.d.j.866.14		24	51.14	even	16
7225.2.a.bq.1.7		12	255.29	even	16
7225.2.a.bs.1.7		12	255.209	even	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.680853 - 0.680853i) q^{2} -1.07288i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.85906 + 1.18426i) q^{7} +(-2.09218 + 2.09218i) q^{8} +O(q^{10})\)	\(q+(-0.680853 - 0.680853i) q^{2} -1.07288i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.85906 + 1.18426i) q^{7} +(-2.09218 + 2.09218i) q^{8} +(-0.889577 - 0.368475i) q^{10} +(2.34612 - 5.66403i) q^{11} -1.16017i q^{13} +(-1.14029 - 2.75291i) q^{14} +0.703170 q^{16} +(-1.25804 + 3.92649i) q^{17} +(3.83665 + 3.83665i) q^{19} +(-0.410573 - 0.991211i) q^{20} +(-5.45373 + 2.25901i) q^{22} +(1.19300 - 2.88015i) q^{23} +(0.707107 - 0.707107i) q^{25} +(-0.789908 + 0.789908i) q^{26} +(1.27057 - 3.06743i) q^{28} +(4.61660 - 1.91226i) q^{29} +(-1.42666 - 3.44426i) q^{31} +(3.70560 + 3.70560i) q^{32} +(3.52990 - 1.81682i) q^{34} +3.09463 q^{35} +(-0.151817 - 0.366518i) q^{37} -5.22439i q^{38} +(-1.13228 + 2.73356i) q^{40} +(-1.57303 - 0.651568i) q^{41} +(0.0189720 - 0.0189720i) q^{43} +(-6.07683 - 2.51710i) q^{44} +(-2.77321 + 1.14870i) q^{46} -5.43715i q^{47} +(1.82202 + 1.82202i) q^{49} -0.962871 q^{50} -1.24473 q^{52} +(0.244014 + 0.244014i) q^{53} -6.13071i q^{55} +(-8.45936 + 3.50398i) q^{56} +(-4.44519 - 1.84126i) q^{58} +(-2.87128 + 2.87128i) q^{59} +(-11.4953 - 4.76149i) q^{61} +(-1.37369 + 3.31638i) q^{62} -6.45228i q^{64} +(-0.443980 - 1.07186i) q^{65} -5.62508 q^{67} +(4.21265 + 1.34973i) q^{68} +(-2.10699 - 2.10699i) q^{70} +(-4.12510 - 9.95888i) q^{71} +(-1.52840 + 0.633083i) q^{73} +(-0.146180 + 0.352909i) q^{74} +(4.11627 - 4.11627i) q^{76} +(13.4154 - 13.4154i) q^{77} +(2.01785 - 4.87153i) q^{79} +(0.649645 - 0.269092i) q^{80} +(0.627376 + 1.51462i) q^{82} +(8.78638 + 8.78638i) q^{83} +(0.340325 + 4.10904i) q^{85} -0.0258342 q^{86} +(6.94167 + 16.7587i) q^{88} +3.22930i q^{89} +(1.37395 - 3.31701i) q^{91} +(-3.09005 - 1.27994i) q^{92} +(-3.70190 + 3.70190i) q^{94} +(5.01283 + 2.07638i) q^{95} +(11.9502 - 4.94995i) q^{97} -2.48105i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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