LMFDB - Embedded newform 891.2.n.a.784.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not 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:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			784.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	891.784
Dual form			891.2.n.a.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.169131 + 1.60917i) q^{2} +(-0.604528 + 0.128496i) q^{4} +(-0.0399263 + 0.379874i) q^{5} +(2.00739 + 2.22943i) q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})$	\(q+(0.169131 + 1.60917i) q^{2} +(-0.604528 + 0.128496i) q^{4} +(-0.0399263 + 0.379874i) q^{5} +(2.00739 + 2.22943i) q^{7} +(0.690983 + 2.12663i) q^{8} -0.618034 q^{10} +(-0.122602 - 3.31436i) q^{11} +(5.69693 + 2.53644i) q^{13} +(-3.24803 + 3.60730i) q^{14} +(-4.43444 + 1.97434i) q^{16} +(-0.500000 - 0.363271i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(-0.0246758 - 0.234775i) q^{20} +(5.31263 - 0.757847i) q^{22} +(-2.73607 - 4.73901i) q^{23} +(4.74803 + 1.00922i) q^{25} +(-3.11803 + 9.59632i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(2.99244 + 3.32344i) q^{29} +(-3.52090 - 1.56760i) q^{31} +(-1.69098 - 2.92887i) q^{32} +(0.500000 - 0.866025i) q^{34} +(-0.927051 + 0.673542i) q^{35} +(-1.30902 + 4.02874i) q^{37} +(1.26249 - 0.562096i) q^{38} +(-0.835438 + 0.177578i) q^{40} +(-3.97749 + 4.41745i) q^{41} +(-0.881966 + 1.52761i) q^{43} +(0.500000 + 1.98787i) q^{44} +(7.16312 - 5.20431i) q^{46} +(-0.604528 - 0.128496i) q^{47} +(-0.209057 + 1.98904i) q^{49} +(-0.820977 + 7.81108i) q^{50} +(-3.76988 - 0.801313i) q^{52} +(-5.97214 + 4.33901i) q^{53} +(1.26393 + 0.0857567i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(-4.84187 + 5.37745i) q^{58} +(-5.20985 + 1.10739i) q^{59} +(1.04683 - 0.466079i) q^{61} +(1.92705 - 5.93085i) q^{62} +(-3.42705 + 2.48990i) q^{64} +(-1.19098 + 2.06284i) q^{65} +(-5.28115 - 9.14723i) q^{67} +(0.348943 + 0.155360i) q^{68} +(-1.24064 - 1.37787i) q^{70} +(11.7812 + 8.55951i) q^{71} +(0.381966 - 1.17557i) q^{73} +(-6.70432 - 1.42505i) q^{74} +(0.263932 + 0.457144i) q^{76} +(7.14303 - 6.92655i) q^{77} +(-0.0551768 - 0.524972i) q^{79} +(-0.572949 - 1.76336i) q^{80} +(-7.78115 - 5.65334i) q^{82} +(11.6095 - 5.16889i) q^{83} +(0.157960 - 0.175433i) q^{85} +(-2.60735 - 1.16087i) q^{86} +(6.96369 - 2.55089i) q^{88} -9.47214 q^{89} +(5.78115 + 17.7926i) q^{91} +(2.26298 + 2.51329i) q^{92} +(0.104528 - 0.994522i) q^{94} +(0.319109 - 0.0678287i) q^{95} +(-1.57153 - 14.9521i) q^{97} -3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8}+O(q^{10}) $ 8 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 + 10 * q^8	$ 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8} + 4 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} - 9 q^{16} - 4 q^{17} - 20 q^{19} + 3 q^{20} + 8 q^{22} - 4 q^{23} + 6 q^{25} - 16 q^{26} - 12 q^{28} - 10 q^{29} - 8 q^{31} - 18 q^{32} + 4 q^{34} + 6 q^{35} - 6 q^{37} - 10 q^{40} + 23 q^{41} - 16 q^{43} + 4 q^{44} + 26 q^{46} - 3 q^{47} + 2 q^{49} + 12 q^{50} - 7 q^{52} - 12 q^{53} + 28 q^{55} - 20 q^{59} - 3 q^{61} + 2 q^{62} - 14 q^{64} - 14 q^{65} - 2 q^{67} - q^{68} + 9 q^{70} + 54 q^{71} + 12 q^{73} - 4 q^{74} + 20 q^{76} - 3 q^{77} - 5 q^{79} - 18 q^{80} - 22 q^{82} + 21 q^{83} - 7 q^{85} - 7 q^{86} + 25 q^{88} - 40 q^{89} + 6 q^{91} + 7 q^{92} - q^{94} + 25 q^{95} + 33 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 + 10 * q^8 + 4 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 - 9 * q^16 - 4 * q^17 - 20 * q^19 + 3 * q^20 + 8 * q^22 - 4 * q^23 + 6 * q^25 - 16 * q^26 - 12 * q^28 - 10 * q^29 - 8 * q^31 - 18 * q^32 + 4 * q^34 + 6 * q^35 - 6 * q^37 - 10 * q^40 + 23 * q^41 - 16 * q^43 + 4 * q^44 + 26 * q^46 - 3 * q^47 + 2 * q^49 + 12 * q^50 - 7 * q^52 - 12 * q^53 + 28 * q^55 - 20 * q^59 - 3 * q^61 + 2 * q^62 - 14 * q^64 - 14 * q^65 - 2 * q^67 - q^68 + 9 * q^70 + 54 * q^71 + 12 * q^73 - 4 * q^74 + 20 * q^76 - 3 * q^77 - 5 * q^79 - 18 * q^80 - 22 * q^82 + 21 * q^83 - 7 * q^85 - 7 * q^86 + 25 * q^88 - 40 * q^89 + 6 * q^91 + 7 * q^92 - q^94 + 25 * q^95 + 33 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.169131	+	1.60917i	0.119593	+	1.13786i	0.875514	+	0.483192i	$0.160523\pi$
$2$	0.169131	+	1.60917i	0.119593	+	1.13786i	−0.755921	+	0.654663i	$0.772811\pi$
$3$		0			0
$3$		0			0
$4$	−0.604528	+	0.128496i	−0.302264	+	0.0642482i
$5$	−0.0399263	+	0.379874i	−0.0178556	+	0.169885i	−0.999816	−	0.0192042i	$-0.993887\pi$
$5$	−0.0399263	+	0.379874i	−0.0178556	+	0.169885i	0.981960	+	0.189089i	$0.0605534\pi$
$6$		0			0
$7$	2.00739	+	2.22943i	0.758723	+	0.842647i	0.991530	−	0.129876i	$-0.0414579\pi$
$7$	2.00739	+	2.22943i	0.758723	+	0.842647i	−0.232807	+	0.972523i	$0.574791\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	−0.122602	−	3.31436i	−0.0369660	−	0.999317i
$11$	−0.122602	−	3.31436i	−0.0369660	−	0.999317i
$12$		0			0
$13$	5.69693	+	2.53644i	1.58004	+	0.703481i	0.994261	−	0.106986i	$-0.0341200\pi$
$13$	5.69693	+	2.53644i	1.58004	+	0.703481i	0.585784	+	0.810467i	$0.300787\pi$
$14$	−3.24803	+	3.60730i	−0.868072	+	0.964092i
$15$		0			0
$16$	−4.43444	+	1.97434i	−1.10861	+	0.493585i
$17$	−0.500000	−	0.363271i	−0.121268	−	0.0881062i	0.525498	−	0.850795i	$-0.323879\pi$
$17$	−0.500000	−	0.363271i	−0.121268	−	0.0881062i	−0.646766	+	0.762688i	$0.723879\pi$
$18$		0			0
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$	−0.0246758	−	0.234775i	−0.00551768	−	0.0524972i
$21$		0			0
$22$	5.31263	−	0.757847i	1.13266	−	0.161574i
$23$	−2.73607	−	4.73901i	−0.570510	−	0.988152i	−0.996514	−	0.0834304i	$-0.973412\pi$
$23$	−2.73607	−	4.73901i	−0.570510	−	0.988152i	0.426004	−	0.904721i	$-0.359921\pi$
$24$		0			0
$25$	4.74803	+	1.00922i	0.949606	+	0.201845i
$26$	−3.11803	+	9.59632i	−0.611497	+	1.88199i
$27$		0			0
$28$	−1.50000	−	1.08981i	−0.283473	−	0.205955i
$29$	2.99244	+	3.32344i	0.555683	+	0.617148i	0.953893	−	0.300146i	$-0.0970353\pi$
$29$	2.99244	+	3.32344i	0.555683	+	0.617148i	−0.398211	+	0.917294i	$0.630369\pi$
$30$		0			0
$31$	−3.52090	−	1.56760i	−0.632372	−	0.281550i	0.0654122	−	0.997858i	$-0.479164\pi$
$31$	−3.52090	−	1.56760i	−0.632372	−	0.281550i	−0.697784	+	0.716308i	$0.745830\pi$
$32$	−1.69098	−	2.92887i	−0.298926	−	0.517756i
$33$		0			0
$34$	0.500000	−	0.866025i	0.0857493	−	0.148522i
$35$	−0.927051	+	0.673542i	−0.156700	+	0.113849i
$36$		0			0
$37$	−1.30902	+	4.02874i	−0.215201	+	0.662321i	0.783938	+	0.620839i	$0.213208\pi$
$37$	−1.30902	+	4.02874i	−0.215201	+	0.662321i	−0.999139	+	0.0414819i	$0.986792\pi$
$38$	1.26249	−	0.562096i	0.204803	−	0.0911840i
$39$		0			0
$40$	−0.835438	+	0.177578i	−0.132094	+	0.0280775i
$41$	−3.97749	+	4.41745i	−0.621180	+	0.689891i	−0.968828	−	0.247735i	$-0.920314\pi$
$41$	−3.97749	+	4.41745i	−0.621180	+	0.689891i	0.347648	+	0.937625i	$0.386981\pi$
$42$		0			0
$43$	−0.881966	+	1.52761i	−0.134499	+	0.232958i	−0.925406	−	0.378978i	$-0.876276\pi$
$43$	−0.881966	+	1.52761i	−0.134499	+	0.232958i	0.790907	+	0.611936i	$0.209609\pi$
$44$	0.500000	+	1.98787i	0.0753778	+	0.299683i
$45$		0			0
$46$	7.16312	−	5.20431i	1.05614	−	0.767334i
$47$	−0.604528	−	0.128496i	−0.0881795	−	0.0187431i	0.163611	−	0.986525i	$-0.447686\pi$
$47$	−0.604528	−	0.128496i	−0.0881795	−	0.0187431i	−0.251790	+	0.967782i	$0.581019\pi$
$48$		0			0
$49$	−0.209057	+	1.98904i	−0.0298653	+	0.284149i
$50$	−0.820977	+	7.81108i	−0.116104	+	1.10465i
$51$		0			0
$52$	−3.76988	−	0.801313i	−0.522788	−	0.111122i
$53$	−5.97214	+	4.33901i	−0.820336	+	0.596009i	−0.916809	−	0.399327i	$-0.869244\pi$
$53$	−5.97214	+	4.33901i	−0.820336	+	0.596009i	0.0964728	+	0.995336i	$0.469244\pi$
$54$		0			0
$55$	1.26393	+	0.0857567i	0.170429	+	0.0115634i
$56$	−3.35410	+	5.80948i	−0.448211	+	0.776324i
$57$		0			0
$58$	−4.84187	+	5.37745i	−0.635769	+	0.706093i
$59$	−5.20985	+	1.10739i	−0.678264	+	0.144170i	−0.534148	−	0.845391i	$-0.679367\pi$
$59$	−5.20985	+	1.10739i	−0.678264	+	0.144170i	−0.144117	+	0.989561i	$0.546034\pi$
$60$		0			0
$61$	1.04683	−	0.466079i	0.134033	−	0.0596753i	−0.338624	−	0.940922i	$-0.609962\pi$
$61$	1.04683	−	0.466079i	0.134033	−	0.0596753i	0.472657	+	0.881246i	$0.343295\pi$
$62$	1.92705	−	5.93085i	0.244736	−	0.753219i
$63$		0			0
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$	−1.19098	+	2.06284i	−0.147723	+	0.255864i
$66$		0			0
$67$	−5.28115	−	9.14723i	−0.645196	−	1.11751i	−0.984256	−	0.176747i	$-0.943443\pi$
$67$	−5.28115	−	9.14723i	−0.645196	−	1.11751i	0.339061	−	0.940764i	$-0.389891\pi$
$68$	0.348943	+	0.155360i	0.0423156	+	0.0188401i
$69$		0			0
$70$	−1.24064	−	1.37787i	−0.148284	−	0.164687i
$71$	11.7812	+	8.55951i	1.39817	+	1.01583i	0.994913	+	0.100738i	$0.0321204\pi$
$71$	11.7812	+	8.55951i	1.39817	+	1.01583i	0.403253	+	0.915089i	$0.367880\pi$
$72$		0			0
$73$	0.381966	−	1.17557i	0.0447057	−	0.137590i	−0.926212	−	0.377003i	$-0.876955\pi$
$73$	0.381966	−	1.17557i	0.0447057	−	0.137590i	0.970918	+	0.239412i	$0.0769548\pi$
$74$	−6.70432	−	1.42505i	−0.779362	−	0.165658i
$75$		0			0
$76$	0.263932	+	0.457144i	0.0302751	+	0.0524380i
$77$	7.14303	−	6.92655i	0.814024	−	0.789354i
$78$		0			0
$79$	−0.0551768	−	0.524972i	−0.00620788	−	0.0590640i	0.990979	−	0.134014i	$-0.0427868\pi$
$79$	−0.0551768	−	0.524972i	−0.00620788	−	0.0590640i	−0.997187	+	0.0749504i	$0.976120\pi$
$80$	−0.572949	−	1.76336i	−0.0640576	−	0.197149i
$81$		0			0
$82$	−7.78115	−	5.65334i	−0.859285	−	0.624307i
$83$	11.6095	−	5.16889i	1.27431	−	0.567360i	0.345676	−	0.938354i	$-0.387650\pi$
$83$	11.6095	−	5.16889i	1.27431	−	0.567360i	0.928635	+	0.370994i	$0.120983\pi$
$84$		0			0
$85$	0.157960	−	0.175433i	0.0171332	−	0.0190283i
$86$	−2.60735	−	1.16087i	−0.281158	−	0.125180i
$87$		0			0
$88$	6.96369	−	2.55089i	0.742332	−	0.271926i
$89$	−9.47214			−1.00404			−0.502022	−	0.864855i	$-0.667410\pi$
$89$	−9.47214			−1.00404			−0.502022	+	0.864855i	$0.667410\pi$
$90$		0			0
$91$	5.78115	+	17.7926i	0.606029	+	1.86517i
$92$	2.26298	+	2.51329i	0.235932	+	0.262029i
$93$		0			0
$94$	0.104528	−	0.994522i	0.0107813	−	0.102577i
$95$	0.319109	−	0.0678287i	0.0327399	−	0.00695908i
$96$		0			0
$97$	−1.57153	−	14.9521i	−0.159564	−	1.51815i	−0.722336	−	0.691542i	$-0.756932\pi$
$97$	−1.57153	−	14.9521i	−0.159564	−	1.51815i	0.562772	−	0.826612i	$-0.309735\pi$
$98$	−3.23607			−0.326892
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−0.313585	−	2.98357i	−0.0312029	−	0.296876i	−0.998983	−	0.0450803i	$-0.985646\pi$
$101$	−0.313585	−	2.98357i	−0.0312029	−	0.296876i	0.967780	−	0.251796i	$-0.0810210\pi$
$102$		0			0
$103$	5.86889	−	1.24747i	0.578278	−	0.122917i	0.0905187	−	0.995895i	$-0.471148\pi$
$103$	5.86889	−	1.24747i	0.578278	−	0.122917i	0.487760	+	0.872978i	$0.337814\pi$
$104$	−1.45757	+	13.8679i	−0.142927	+	1.35986i
$105$		0			0
$106$	−7.99228	−	8.87632i	−0.776279	−	0.862145i
$107$	−0.0729490	−	0.224514i	−0.00705225	−	0.0217046i	0.947468	−	0.319849i	$-0.103632\pi$
$107$	−0.0729490	−	0.224514i	−0.00705225	−	0.0217046i	−0.954521	+	0.298145i	$0.903632\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	0.0757724	+	2.04839i	0.00722462	+	0.195306i
$111$		0			0
$112$	−13.3033	−	5.92302i	−1.25705	−	0.559673i
$113$	8.50345	−	9.44404i	0.799937	−	0.888420i	−0.195801	−	0.980644i	$-0.562731\pi$
$113$	8.50345	−	9.44404i	0.799937	−	0.888420i	0.995738	+	0.0922234i	$0.0293974\pi$
$114$		0			0
$115$	1.90947	−	0.850149i	0.178059	−	0.0792768i
$116$	−2.23607	−	1.62460i	−0.207614	−	0.150840i
$117$		0			0
$118$	−2.66312	−	8.19624i	−0.245160	−	0.754525i
$119$	−0.193806	−	1.84395i	−0.0177662	−	0.169034i
$120$		0			0
$121$	−10.9699	+	0.812696i	−0.997267	+	0.0738815i
$122$	0.927051	+	1.60570i	0.0839313	+	0.145373i
$123$		0			0
$124$	2.32991	+	0.495239i	0.209232	+	0.0444737i
$125$	−1.16312	+	3.57971i	−0.104033	+	0.320179i
$126$		0			0
$127$	−7.85410	−	5.70634i	−0.696939	−	0.506356i	0.181995	−	0.983299i	$-0.441745\pi$
$127$	−7.85410	−	5.70634i	−0.696939	−	0.506356i	−0.878934	+	0.476944i	$0.841745\pi$
$128$	−9.11224	−	10.1202i	−0.805416	−	0.894505i
$129$		0			0
$130$	−3.52090	−	1.56760i	−0.308803	−	0.137488i
$131$	−6.92705	−	11.9980i	−0.605219	−	1.04827i	−0.992017	−	0.126106i	$-0.959752\pi$
$131$	−6.92705	−	11.9980i	−0.605219	−	1.04827i	0.386798	−	0.922165i	$-0.373581\pi$
$132$		0			0
$133$	1.28115	−	2.21902i	0.111090	−	0.192414i
$134$	13.8262	−	10.0453i	1.19441	−	0.867786i
$135$		0			0
$136$	0.427051	−	1.31433i	0.0366193	−	0.112703i
$137$	1.34486	−	0.598772i	0.114899	−	0.0511565i	−0.348482	−	0.937316i	$-0.613303\pi$
$137$	1.34486	−	0.598772i	0.114899	−	0.0511565i	0.463381	+	0.886159i	$0.346636\pi$
$138$		0			0
$139$	−5.72618	+	1.21714i	−0.485688	+	0.103236i	−0.444246	−	0.895905i	$-0.646528\pi$
$139$	−5.72618	+	1.21714i	−0.485688	+	0.103236i	−0.0414417	+	0.999141i	$0.513195\pi$
$140$	0.473881	−	0.526298i	0.0400502	−	0.0444803i
$141$		0			0
$142$	−11.7812	+	20.4056i	−0.988652	+	1.71240i
$143$	7.70820	−	19.1926i	0.644592	−	1.60497i
$144$		0			0
$145$	−1.38197	+	1.00406i	−0.114766	+	0.0833824i
$146$	1.95630	+	0.415823i	0.161904	+	0.0344138i
$147$		0			0
$148$	0.273659	−	2.60369i	0.0224946	−	0.214022i
$149$	1.56793	−	14.9178i	0.128450	−	1.22212i	−0.720429	−	0.693529i	$-0.756055\pi$
$149$	1.56793	−	14.9178i	0.128450	−	1.22212i	0.848879	−	0.528588i	$-0.177278\pi$
$150$		0			0
$151$	−1.95630	−	0.415823i	−0.159201	−	0.0338392i	0.127622	−	0.991823i	$-0.459266\pi$
$151$	−1.95630	−	0.415823i	−0.159201	−	0.0338392i	−0.286823	+	0.957984i	$0.592599\pi$
$152$	1.54508	−	1.12257i	0.125323	−	0.0910524i
$153$		0			0
$154$	12.3541	+	10.3229i	0.995522	+	0.831840i
$155$	0.736068	−	1.27491i	0.0591224	−	0.102403i
$156$		0			0
$157$	6.49606	−	7.21460i	0.518442	−	0.575788i	−0.425893	−	0.904773i	$-0.640040\pi$
$157$	6.49606	−	7.21460i	0.518442	−	0.575788i	0.944335	+	0.328986i	$0.106707\pi$
$158$	0.835438	−	0.177578i	0.0664639	−	0.0141273i
$159$		0			0
$160$	1.18011	−	0.525421i	0.0932962	−	0.0415382i
$161$	5.07295	−	15.6129i	0.399804	−	1.23047i
$162$		0			0
$163$	12.3541	−	8.97578i	0.967648	−	0.703037i	0.0127336	−	0.999919i	$-0.495947\pi$
$163$	12.3541	−	8.97578i	0.967648	−	0.703037i	0.954914	+	0.296882i	$0.0959467\pi$
$164$	1.83688	−	3.18157i	0.143436	−	0.248439i
$165$		0			0
$166$	10.2812	+	17.8075i	0.797972	+	1.38213i
$167$	17.3888	+	7.74200i	1.34559	+	0.599094i	0.947942	−	0.318444i	$-0.103160\pi$
$167$	17.3888	+	7.74200i	1.34559	+	0.599094i	0.397646	+	0.917539i	$0.369827\pi$
$168$		0			0
$169$	17.3228	+	19.2389i	1.33252	+	1.47992i
$170$	0.309017	+	0.224514i	0.0237005	+	0.0172194i
$171$		0			0
$172$	0.336881	−	1.03681i	0.0256869	−	0.0790563i
$173$	17.2330	+	3.66300i	1.31020	+	0.278492i	0.809497	−	0.587124i	$-0.199740\pi$
$173$	17.2330	+	3.66300i	1.31020	+	0.278492i	0.500707	+	0.865617i	$0.333073\pi$
$174$		0			0
$175$	7.28115	+	12.6113i	0.550403	+	0.953327i
$176$	7.08735	+	14.4553i	0.534229	+	1.08961i
$177$		0			0
$178$	−1.60203	−	15.2423i	−0.120077	−	1.14246i
$179$	−0.690983	−	2.12663i	−0.0516465	−	0.158952i	0.921907	−	0.387412i	$-0.126631\pi$
$179$	−0.690983	−	2.12663i	−0.0516465	−	0.158952i	−0.973553	+	0.228460i	$0.926631\pi$
$180$		0			0
$181$	6.89919	+	5.01255i	0.512813	+	0.372580i	0.813889	−	0.581020i	$-0.197346\pi$
$181$	6.89919	+	5.01255i	0.512813	+	0.372580i	−0.301077	+	0.953600i	$0.597346\pi$
$182$	−27.6535	+	12.3121i	−2.04981	+	0.912635i
$183$		0			0
$184$	8.18753	−	9.09317i	0.603593	−	0.670357i
$185$	−1.47815	−	0.658114i	−0.108676	−	0.0483855i
$186$		0			0
$187$	−1.14271	+	1.70172i	−0.0835632	+	0.124442i
$188$	0.381966			0.0278577
$189$		0			0
$190$	0.163119	+	0.502029i	0.0118339	+	0.0364210i
$191$	−0.985051	−	1.09401i	−0.0712758	−	0.0791598i	0.706452	−	0.707761i	$-0.250295\pi$
$191$	−0.985051	−	1.09401i	−0.0712758	−	0.0791598i	−0.777728	+	0.628601i	$0.783628\pi$
$192$		0			0
$193$	−0.163305	+	1.55375i	−0.0117550	+	0.111841i	−0.998826	−	0.0484425i	$-0.984574\pi$
$193$	−0.163305	+	1.55375i	−0.0117550	+	0.111841i	0.987071	+	0.160284i	$0.0512409\pi$
$194$	23.7947	−	5.05771i	1.70836	−	0.363122i
$195$		0			0
$196$	−0.129204	−	1.22930i	−0.00922888	−	0.0878069i
$197$	−26.6180			−1.89646			−0.948228	−	0.317590i	$-0.897127\pi$
$197$	−26.6180			−1.89646			−0.948228	+	0.317590i	$0.897127\pi$
$198$		0			0
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$	1.13456	+	10.7946i	0.0802257	+	0.763296i
$201$		0			0
$202$	4.74803	−	1.00922i	0.334070	−	0.0710088i
$203$	−1.40240	+	13.3429i	−0.0984289	+	0.936489i
$204$		0			0
$205$	−1.51927	−	1.68732i	−0.106110	−	0.117847i
$206$	3.00000	+	9.23305i	0.209020	+	0.643297i
$207$		0			0
$208$	−30.2705			−2.09888
$209$	−2.65989	+	0.974355i	−0.183989	+	0.0673975i
$210$		0			0
$211$	10.2961	+	4.58413i	0.708814	+	0.315584i	0.729289	−	0.684206i	$-0.239851\pi$
$211$	10.2961	+	4.58413i	0.708814	+	0.315584i	−0.0204746	+	0.999790i	$0.506518\pi$
$212$	3.05278	−	3.39045i	0.209666	−	0.232857i
$213$		0			0
$214$	0.348943	−	0.155360i	0.0238533	−	0.0106202i
$215$	−0.545085	−	0.396027i	−0.0371745	−	0.0270088i
$216$		0			0
$217$	−3.57295	−	10.9964i	−0.242548	−	0.746485i
$218$		0			0
$219$		0			0
$220$	−0.775102	+	0.110568i	−0.0522574	+	0.00745452i
$221$	−1.92705	−	3.33775i	−0.129627	−	0.224521i
$222$		0			0
$223$	12.4305	+	2.64218i	0.832408	+	0.176934i	0.604355	−	0.796715i	$-0.293431\pi$
$223$	12.4305	+	2.64218i	0.832408	+	0.176934i	0.228053	+	0.973649i	$0.426764\pi$
$224$	3.13525	−	9.64932i	0.209483	−	0.644722i
$225$		0			0
$226$	16.6353	+	12.0862i	1.10656	+	0.803963i
$227$	−7.28586	−	8.09176i	−0.483579	−	0.537069i	0.451141	−	0.892453i	$-0.351017\pi$
$227$	−7.28586	−	8.09176i	−0.483579	−	0.537069i	−0.934721	+	0.355383i	$0.884350\pi$
$228$		0			0
$229$	9.13545	+	4.06737i	0.603688	+	0.268779i	0.685737	−	0.727849i	$-0.259480\pi$
$229$	9.13545	+	4.06737i	0.603688	+	0.268779i	−0.0820495	+	0.996628i	$0.526147\pi$
$230$	1.69098	+	2.92887i	0.111500	+	0.193124i
$231$		0			0
$232$	−5.00000	+	8.66025i	−0.328266	+	0.568574i
$233$	7.01722	−	5.09831i	0.459713	−	0.334001i	−0.333705	−	0.942677i	$-0.608299\pi$
$233$	7.01722	−	5.09831i	0.459713	−	0.334001i	0.793419	+	0.608676i	$0.208299\pi$
$234$		0			0
$235$	0.0729490	−	0.224514i	0.00475867	−	0.0146457i
$236$	3.00721	−	1.33889i	0.195752	−	0.0871546i
$237$		0			0
$238$	2.93444	−	0.623735i	0.190212	−	0.0404307i
$239$	11.7515	−	13.0513i	0.760140	−	0.844221i	−0.231557	−	0.972821i	$-0.574382\pi$
$239$	11.7515	−	13.0513i	0.760140	−	0.844221i	0.991696	+	0.128601i	$0.0410485\pi$
$240$		0			0
$241$	−8.56231	+	14.8303i	−0.551547	+	0.955307i	0.446617	+	0.894725i	$0.352629\pi$
$241$	−8.56231	+	14.8303i	−0.551547	+	0.955307i	−0.998163	+	0.0605813i	$0.980705\pi$
$242$	−3.16312	−	17.5150i	−0.203333	−	1.12591i
$243$		0			0
$244$	−0.572949	+	0.416272i	−0.0366793	+	0.0266491i
$245$	−0.747238	−	0.158830i	−0.0477393	−	0.0101473i
$246$		0			0
$247$	0.556743	−	5.29706i	0.0354247	−	0.337044i
$248$	0.900830	−	8.57082i	0.0572028	−	0.544248i
$249$		0			0
$250$	−5.95709	−	1.26622i	−0.376759	−	0.0800826i
$251$	13.5902	−	9.87384i	0.857804	−	0.623231i	−0.0694827	−	0.997583i	$-0.522135\pi$
$251$	13.5902	−	9.87384i	0.857804	−	0.623231i	0.927287	+	0.374352i	$0.122135\pi$
$252$		0			0
$253$	−15.3713	+	9.64932i	−0.966387	+	0.606648i
$254$	7.85410	−	13.6037i	0.492810	−	0.853572i
$255$		0			0
$256$	9.07495	−	10.0788i	0.567185	−	0.629922i
$257$	−26.7291	+	5.68144i	−1.66732	+	0.354399i	−0.942413	−	0.334453i	$-0.891449\pi$
$257$	−26.7291	+	5.68144i	−1.66732	+	0.354399i	−0.724903	+	0.688851i	$0.758115\pi$
$258$		0			0
$259$	−11.6095	+	5.16889i	−0.721381	+	0.321179i
$260$	0.454915	−	1.40008i	0.0282126	−	0.0868296i
$261$		0			0
$262$	18.1353	−	13.1760i	1.12040	−	0.814018i
$263$	−0.336881	+	0.583495i	−0.0207730	+	0.0359798i	−0.876225	−	0.481902i	$-0.839946\pi$
$263$	−0.336881	+	0.583495i	−0.0207730	+	0.0359798i	0.855452	+	0.517882i	$0.173279\pi$
$264$		0			0
$265$	−1.40983	−	2.44190i	−0.0866052	−	0.150005i
$266$	3.78747	+	1.68629i	0.232224	+	0.103393i
$267$		0			0
$268$	4.36799	+	4.85115i	0.266818	+	0.296331i
$269$	19.7984	+	14.3844i	1.20713	+	0.877030i	0.994967	−	0.100205i	$-0.0319498\pi$
$269$	19.7984	+	14.3844i	1.20713	+	0.877030i	0.212161	+	0.977235i	$0.431950\pi$
$270$		0			0
$271$	1.93769	−	5.96361i	0.117707	−	0.362263i	−0.874795	−	0.484493i	$-0.839004\pi$
$271$	1.93769	−	5.96361i	0.117707	−	0.362263i	0.992502	+	0.122229i	$0.0390043\pi$
$272$	2.93444	+	0.623735i	0.177927	+	0.0378195i
$273$		0			0
$274$	1.19098	+	2.06284i	0.0719499	+	0.124621i
$275$	2.76281	−	15.8604i	0.166604	−	0.956418i
$276$		0			0
$277$	−1.09104	−	10.3805i	−0.0655540	−	0.623705i	−0.977140	−	0.212596i	$-0.931808\pi$
$277$	−1.09104	−	10.3805i	−0.0655540	−	0.623705i	0.911586	−	0.411109i	$-0.134858\pi$
$278$	−2.92705	−	9.00854i	−0.175553	−	0.540296i
$279$		0			0
$280$	−2.07295	−	1.50609i	−0.123882	−	0.0900058i
$281$	4.78339	−	2.12970i	0.285353	−	0.127047i	−0.259069	−	0.965859i	$-0.583416\pi$
$281$	4.78339	−	2.12970i	0.285353	−	0.127047i	0.544422	+	0.838812i	$0.316749\pi$
$282$		0			0
$283$	−14.8415	+	16.4832i	−0.882238	+	0.979825i	−0.999913	−	0.0132274i	$-0.995789\pi$
$283$	−14.8415	+	16.4832i	−0.882238	+	0.979825i	0.117674	+	0.993052i	$0.462456\pi$
$284$	−8.22191	−	3.66063i	−0.487881	−	0.217218i
$285$		0			0
$286$	32.1879	+	9.15775i	1.90331	+	0.541509i
$287$	−17.8328			−1.05264
$288$		0			0
$289$	−5.13525	−	15.8047i	−0.302074	−	0.929688i
$290$	−1.84943	−	2.05400i	−0.108602	−	0.120615i
$291$		0			0
$292$	−0.0798526	+	0.759747i	−0.00467302	+	0.0444608i
$293$	17.5521	−	3.73082i	1.02541	−	0.217957i	0.335642	−	0.941990i	$-0.391047\pi$
$293$	17.5521	−	3.73082i	1.02541	−	0.217957i	0.689766	+	0.724033i	$0.257714\pi$
$294$		0			0
$295$	−0.212657	−	2.02330i	−0.0123814	−	0.117801i
$296$	−9.47214			−0.550557
$297$		0			0
$298$	24.2705			1.40595
$299$	−3.56699	−	33.9377i	−0.206285	−	1.96267i
$300$		0			0
$301$	−5.17616	+	1.10023i	−0.298349	+	0.0634160i
$302$	0.338261	−	3.21834i	0.0194647	−	0.185195i
$303$		0			0
$304$	2.77415	+	3.08100i	0.159108	+	0.176708i
$305$	0.135255	+	0.416272i	0.00774467	+	0.0238357i
$306$		0			0
$307$	−19.5623			−1.11648			−0.558240	−	0.829680i	$-0.688523\pi$
$307$	−19.5623			−1.11648			−0.558240	+	0.829680i	$0.688523\pi$
$308$	−3.42813	+	5.10515i	−0.195336	+	0.290893i
$309$		0			0
$310$	2.17603	+	0.968833i	0.123590	+	0.0550260i
$311$	−7.67636	+	8.52546i	−0.435286	+	0.483434i	−0.920379	−	0.391029i	$-0.872119\pi$
$311$	−7.67636	+	8.52546i	−0.435286	+	0.483434i	0.485092	+	0.874463i	$0.338786\pi$
$312$		0			0
$313$	−25.4265	+	11.3206i	−1.43719	+	0.639880i	−0.969740	−	0.244138i	$-0.921495\pi$
$313$	−25.4265	+	11.3206i	−1.43719	+	0.639880i	−0.467453	+	0.884018i	$0.654828\pi$
$314$	12.7082	+	9.23305i	0.717165	+	0.521051i
$315$		0			0
$316$	0.100813	+	0.310271i	0.00567118	+	0.0174541i
$317$	2.65091	+	25.2218i	0.148890	+	1.41659i	0.772577	+	0.634921i	$0.218967\pi$
$317$	2.65091	+	25.2218i	0.148890	+	1.41659i	−0.623687	+	0.781674i	$0.714366\pi$
$318$		0			0
$319$	10.6482	−	10.3255i	0.596185	−	0.578116i
$320$	−0.809017	−	1.40126i	−0.0452254	−	0.0783327i
$321$		0			0
$322$	25.9819	+	5.52261i	1.44791	+	0.307763i
$323$	−0.163119	+	0.502029i	−0.00907618	+	0.0279336i
$324$		0			0
$325$	24.4894	+	17.7926i	1.35843	+	0.986954i
$326$	16.5330	+	18.3618i	0.915679	+	1.01696i
$327$		0			0
$328$	−12.1427	−	5.40626i	−0.670466	−	0.298511i
$329$	−0.927051	−	1.60570i	−0.0511100	−	0.0885251i
$330$		0			0
$331$	11.2984	−	19.5694i	0.621015	−	1.07563i	−0.368282	−	0.929714i	$-0.620054\pi$
$331$	11.2984	−	19.5694i	0.621015	−	1.07563i	0.989297	−	0.145915i	$-0.0466127\pi$
$332$	−6.35410	+	4.61653i	−0.348727	+	0.253365i
$333$		0			0
$334$	−9.51722	+	29.2910i	−0.520759	+	1.60273i
$335$	3.68565	−	1.64096i	0.201368	−	0.0896550i
$336$		0			0
$337$	13.4086	−	2.85010i	0.730416	−	0.155255i	0.172331	−	0.985039i	$-0.444870\pi$
$337$	13.4086	−	2.85010i	0.730416	−	0.155255i	0.558084	+	0.829784i	$0.311537\pi$
$338$	−28.0289	+	31.1293i	−1.52457	+	1.69321i
$339$		0			0
$340$	−0.0729490	+	0.126351i	−0.00395622	+	0.00685237i
$341$	−4.76393	+	11.8617i	−0.257981	+	0.642347i
$342$		0			0
$343$	12.1353	−	8.81678i	0.655242	−	0.476061i
$344$	−3.85808	−	0.820060i	−0.208014	−	0.0442147i
$345$		0			0
$346$	−2.97975	+	28.3504i	−0.160192	+	1.52413i
$347$	−0.319411	+	3.03899i	−0.0171469	+	0.163141i	−0.999744	−	0.0226055i	$-0.992804\pi$
$347$	−0.319411	+	3.03899i	−0.0171469	+	0.163141i	0.982598	+	0.185747i	$0.0594705\pi$
$348$		0			0
$349$	−29.4663	−	6.26326i	−1.57730	−	0.335265i	−0.665657	−	0.746258i	$-0.731849\pi$
$349$	−29.4663	−	6.26326i	−1.57730	−	0.335265i	−0.911638	+	0.410993i	$0.865182\pi$
$350$	−19.0623	+	13.8496i	−1.01892	+	0.740291i
$351$		0			0
$352$	−9.50000	+	5.96361i	−0.506352	+	0.317861i
$353$	−0.763932	+	1.32317i	−0.0406600	+	0.0704252i	−0.885639	−	0.464374i	$-0.846279\pi$
$353$	−0.763932	+	1.32317i	−0.0406600	+	0.0704252i	0.844979	+	0.534799i	$0.179613\pi$
$354$		0			0
$355$	−3.72191	+	4.13360i	−0.197538	+	0.219389i
$356$	5.72618	−	1.21714i	0.303487	−	0.0645081i
$357$		0			0
$358$	3.30524	−	1.47159i	0.174687	−	0.0777758i
$359$	5.32624	−	16.3925i	0.281108	−	0.865162i	−0.706430	−	0.707783i	$-0.749696\pi$
$359$	5.32624	−	16.3925i	0.281108	−	0.865162i	0.987538	−	0.157379i	$-0.0503044\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	−6.89919	+	11.9497i	−0.362613	+	0.628065i
$363$		0			0
$364$	−5.78115	−	10.0133i	−0.303015	−	0.524837i
$365$	0.431318	+	0.192035i	0.0225762	+	0.0100516i
$366$		0			0
$367$	−9.74408	−	10.8219i	−0.508637	−	0.564899i	0.433058	−	0.901366i	$-0.357435\pi$
$367$	−9.74408	−	10.8219i	−0.508637	−	0.564899i	−0.941695	+	0.336467i	$0.890768\pi$
$368$	21.4894	+	15.6129i	1.12021	+	0.813880i
$369$		0			0
$370$	0.809017	−	2.48990i	0.0420588	−	0.129444i
$371$	−21.6620	−	4.60439i	−1.12463	−	0.239048i
$372$		0			0
$373$	−11.2082	−	19.4132i	−0.580339	−	1.00518i	−0.995439	−	0.0954006i	$-0.969587\pi$
$373$	−11.2082	−	19.4132i	−0.580339	−	1.00518i	0.415100	−	0.909776i	$-0.363747\pi$
$374$	−2.93162	−	1.55100i	−0.151590	−	0.0802004i
$375$		0			0
$376$	−0.144455	−	1.37440i	−0.00744969	−	0.0708790i
$377$	8.61803	+	26.5236i	0.443851	+	1.36603i
$378$		0			0
$379$	−22.9894	−	16.7027i	−1.18088	−	0.857962i	−0.188613	−	0.982052i	$-0.560399\pi$
$379$	−22.9894	−	16.7027i	−1.18088	−	0.857962i	−0.992271	+	0.124089i	$0.960399\pi$
$380$	−0.184195	+	0.0820087i	−0.00944899	+	0.00420696i
$381$		0			0
$382$	1.59385	−	1.77015i	0.0815483	−	0.0905685i
$383$	8.12009	+	3.61530i	0.414917	+	0.184733i	0.603569	−	0.797311i	$-0.293745\pi$
$383$	8.12009	+	3.61530i	0.414917	+	0.184733i	−0.188651	+	0.982044i	$0.560412\pi$
$384$		0			0
$385$	2.34602	+	2.99000i	0.119564	+	0.152385i
$386$	−2.52786			−0.128665
$387$		0			0
$388$	2.87132	+	8.83702i	0.145769	+	0.448632i
$389$	6.20318	+	6.88933i	0.314514	+	0.349303i	0.879587	−	0.475738i	$-0.157819\pi$
$389$	6.20318	+	6.88933i	0.314514	+	0.349303i	−0.565073	+	0.825041i	$0.691152\pi$
$390$		0			0
$391$	−0.353512	+	3.36344i	−0.0178779	+	0.170096i
$392$	−4.37441	+	0.929809i	−0.220941	+	0.0469625i
$393$		0			0
$394$	−4.50192	−	42.8329i	−0.226804	−	2.15789i
$395$	0.201626			0.0101449
$396$		0			0
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$	−0.556743	−	5.29706i	−0.0279070	−	0.265518i
$399$		0			0
$400$	−23.0474	+	4.89888i	−1.15237	+	0.244944i
$401$	−1.55850	+	14.8282i	−0.0778279	+	0.740483i	0.884122	+	0.467256i	$0.154757\pi$
$401$	−1.55850	+	14.8282i	−0.0778279	+	0.740483i	−0.961950	+	0.273226i	$0.911909\pi$
$402$		0			0
$403$	−16.0822	−	17.8611i	−0.801110	−	0.889723i
$404$	0.572949	+	1.76336i	0.0285053	+	0.0877302i
$405$		0			0
$406$	−21.7082			−1.07736
$407$	13.5132	+	3.84462i	0.669823	+	0.190571i
$408$		0			0
$409$	−26.4419	−	11.7727i	−1.30747	−	0.582122i	−0.369625	−	0.929181i	$-0.620514\pi$
$409$	−26.4419	−	11.7727i	−1.30747	−	0.582122i	−0.937843	+	0.347059i	$0.887180\pi$
$410$	2.45823	−	2.73014i	0.121403	−	0.134832i
$411$		0			0
$412$	−3.38761	+	1.50826i	−0.166896	+	0.0743068i
$413$	−12.9271	−	9.39205i	−0.636099	−	0.462153i
$414$		0			0
$415$	1.50000	+	4.61653i	0.0736321	+	0.226616i
$416$	−2.20452	−	20.9746i	−0.108086	−	1.02837i
$417$		0			0
$418$	−2.01777	−	4.11543i	−0.0986925	−	0.201292i
$419$	−10.7533	−	18.6252i	−0.525333	−	0.909903i	−0.999565	−	0.0295028i	$-0.990608\pi$
$419$	−10.7533	−	18.6252i	−0.525333	−	0.909903i	0.474232	−	0.880400i	$-0.342726\pi$
$420$		0			0
$421$	3.64799	+	0.775405i	0.177792	+	0.0377909i	0.295947	−	0.955204i	$-0.404365\pi$
$421$	3.64799	+	0.775405i	0.177792	+	0.0377909i	−0.118155	+	0.992995i	$0.537698\pi$
$422$	−5.63525	+	17.3435i	−0.274320	+	0.844270i
$423$		0			0
$424$	−13.3541	−	9.70232i	−0.648533	−	0.471186i
$425$	−2.00739	−	2.22943i	−0.0973728	−	0.108143i
$426$		0			0
$427$	3.14049	+	1.39824i	0.151979	+	0.0676654i
$428$	0.0729490	+	0.126351i	0.00352612	+	0.00610743i
$429$		0			0
$430$	0.545085	−	0.944115i	0.0262863	−	0.0455293i
$431$	−1.20820	+	0.877812i	−0.0581971	+	0.0422827i	−0.616503	−	0.787352i	$-0.711451\pi$
$431$	−1.20820	+	0.877812i	−0.0581971	+	0.0422827i	0.558306	+	0.829635i	$0.311451\pi$
$432$		0			0
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	−0.985672	−	0.168674i	$-0.946051\pi$
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	0.896569	+	0.442903i	$0.146051\pi$
$434$	17.0908	−	7.60931i	0.820384	−	0.365259i
$435$		0			0
$436$		0			0
$437$	−3.12736	+	3.47328i	−0.149602	+	0.166150i
$438$		0			0
$439$	−8.35410	+	14.4697i	−0.398720	+	0.690602i	−0.993568	−	0.113235i	$-0.963879\pi$
$439$	−8.35410	+	14.4697i	−0.398720	+	0.690602i	0.594849	+	0.803838i	$0.297212\pi$
$440$	0.690983	+	2.74717i	0.0329413	+	0.130966i
$441$		0			0
$442$	5.04508	−	3.66547i	0.239970	−	0.174349i
$443$	−0.856259	−	0.182003i	−0.0406821	−	0.00864724i	0.187526	−	0.982260i	$-0.439953\pi$
$443$	−0.856259	−	0.182003i	−0.0406821	−	0.00864724i	−0.228208	+	0.973612i	$0.573287\pi$
$444$		0			0
$445$	0.378188	−	3.59821i	0.0179278	−	0.170572i
$446$	−2.14935	+	20.4497i	−0.101774	+	0.968320i
$447$		0			0
$448$	−12.4305	−	2.64218i	−0.587286	−	0.124831i
$449$	−12.5623	+	9.12705i	−0.592852	+	0.430732i	−0.843334	−	0.537389i	$-0.819411\pi$
$449$	−12.5623	+	9.12705i	−0.592852	+	0.430732i	0.250483	+	0.968121i	$0.419411\pi$
$450$		0			0
$451$	15.1287	+	12.6412i	0.712382	+	0.595253i
$452$	−3.92705	+	6.80185i	−0.184713	+	0.319932i
$453$		0			0
$454$	11.7888	−	13.0928i	0.553274	−	0.614473i
$455$	−6.98974	+	1.48572i	−0.327684	+	0.0696514i
$456$		0			0
$457$	29.9628	−	13.3403i	1.40160	−	0.624033i	0.439878	−	0.898057i	$-0.355022\pi$
$457$	29.9628	−	13.3403i	1.40160	−	0.624033i	0.961723	+	0.274025i	$0.0883549\pi$
$458$	−5.00000	+	15.3884i	−0.233635	+	0.719054i
$459$		0			0
$460$	−1.04508	+	0.759299i	−0.0487273	+	0.0354025i
$461$	−4.95492	+	8.58216i	−0.230773	+	0.399711i	−0.958036	−	0.286648i	$-0.907459\pi$
$461$	−4.95492	+	8.58216i	−0.230773	+	0.399711i	0.727263	+	0.686359i	$0.240792\pi$
$462$		0			0
$463$	−4.39919	−	7.61962i	−0.204448	−	0.354114i	0.745509	−	0.666496i	$-0.232206\pi$
$463$	−4.39919	−	7.61962i	−0.204448	−	0.354114i	−0.949957	+	0.312382i	$0.898873\pi$
$464$	−19.8314	−	8.82952i	−0.920651	−	0.409900i
$465$		0			0
$466$	9.39087	+	10.4296i	0.435024	+	0.483143i
$467$	−11.5172	−	8.36775i	−0.532953	−	0.387213i	0.288508	−	0.957478i	$-0.406841\pi$
$467$	−11.5172	−	8.36775i	−0.532953	−	0.387213i	−0.821461	+	0.570264i	$0.806841\pi$
$468$		0			0
$469$	9.79180	−	30.1360i	0.452143	−	1.39155i
$470$	0.373619	+	0.0794152i	0.0172338	+	0.00366315i
$471$		0			0
$472$	−5.95492	−	10.3142i	−0.274097	−	0.474750i
$473$	5.17118	+	2.73586i	0.237771	+	0.125795i
$474$		0			0
$475$	−0.433364	−	4.12319i	−0.0198841	−	0.189185i
$476$	0.354102	+	1.08981i	0.0162302	+	0.0499515i
$477$		0			0
$478$	22.9894	+	16.7027i	1.05151	+	0.763966i
$479$	15.4479	−	6.87785i	0.705832	−	0.314257i	−0.0222442	−	0.999753i	$-0.507081\pi$
$479$	15.4479	−	6.87785i	0.705832	−	0.314257i	0.728077	+	0.685496i	$0.240414\pi$
$480$		0			0
$481$	−17.6760	+	19.6312i	−0.805957	+	0.895106i
$482$	−25.3127	−	11.2699i	−1.15296	−	0.513332i
$483$		0			0
$484$	6.52721	−	1.90090i	0.296691	−	0.0864044i
$485$	5.74265			0.260760
$486$		0			0
$487$	12.1074	+	37.2627i	0.548638	+	1.68853i	0.712179	+	0.701998i	$0.247709\pi$
$487$	12.1074	+	37.2627i	0.548638	+	1.68853i	−0.163540	+	0.986537i	$0.552291\pi$
$488$	1.71452	+	1.90416i	0.0776126	+	0.0861975i
$489$		0			0
$490$	0.129204	−	1.22930i	0.00583685	−	0.0555340i
$491$	−25.6419	+	5.45036i	−1.15720	+	0.245971i	−0.746238	−	0.665679i	$-0.768142\pi$
$491$	−25.6419	+	5.45036i	−1.15720	+	0.245971i	−0.410966	+	0.911651i	$0.634809\pi$
$492$		0			0
$493$	−0.288910	−	2.74879i	−0.0130118	−	0.123799i
$494$	8.61803			0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	4.56653	+	43.4476i	0.204837	+	1.94889i
$498$		0			0
$499$	−2.50631	+	0.532733i	−0.112198	+	0.0238484i	−0.263668	−	0.964613i	$-0.584932\pi$
$499$	−2.50631	+	0.532733i	−0.112198	+	0.0238484i	0.151470	+	0.988462i	$0.451599\pi$
$500$	0.243158	−	2.31349i	0.0108744	−	0.103463i
$501$		0			0
$502$	18.1872	+	20.1989i	0.811734	+	0.901522i
$503$	9.29180	+	28.5972i	0.414301	+	1.27509i	0.912875	+	0.408239i	$0.133857\pi$
$503$	9.29180	+	28.5972i	0.414301	+	1.27509i	−0.498574	+	0.866847i	$0.666143\pi$
$504$		0			0
$505$	1.14590			0.0509918
$506$	−18.1272	−	23.1031i	−0.805851	−	1.02706i
$507$		0			0
$508$	5.48127	+	2.44042i	0.243192	+	0.108276i
$509$	−14.3073	+	15.8899i	−0.634161	+	0.704307i	−0.971490	−	0.237079i	$-0.923810\pi$
$509$	−14.3073	+	15.8899i	−0.634161	+	0.704307i	0.337329	+	0.941387i	$0.390476\pi$
$510$		0			0
$511$	3.38761	−	1.50826i	0.149859	−	0.0667216i
$512$	−4.28115	−	3.11044i	−0.189202	−	0.137463i
$513$		0			0
$514$	−13.6631	−	42.0508i	−0.602654	−	1.85478i
$515$	0.239558	+	2.27924i	0.0105562	+	0.100435i
$516$		0			0
$517$	−0.351767	+	2.01938i	−0.0154707	+	0.0888121i
$518$	−10.2812	−	17.8075i	−0.451728	−	0.782416i
$519$		0			0
$520$	−5.20985	−	1.10739i	−0.228467	−	0.0485621i
$521$	−12.0000	+	36.9322i	−0.525730	+	1.61803i	0.237139	+	0.971476i	$0.423790\pi$
$521$	−12.0000	+	36.9322i	−0.525730	+	1.61803i	−0.762869	+	0.646553i	$0.776210\pi$
$522$		0			0
$523$	−28.2984	−	20.5600i	−1.23740	−	0.899025i	−0.239979	−	0.970778i	$-0.577141\pi$
$523$	−28.2984	−	20.5600i	−1.23740	−	0.899025i	−0.997422	+	0.0717533i	$0.977141\pi$
$524$	5.72930	+	6.36303i	0.250286	+	0.277970i
$525$		0			0
$526$	−0.995920	−	0.443412i	−0.0434242	−	0.0193337i
$527$	1.19098	+	2.06284i	0.0518800	+	0.0898589i
$528$		0			0
$529$	−3.47214	+	6.01392i	−0.150962	+	0.261475i
$530$	3.69098	−	2.68166i	0.160326	−	0.116484i
$531$		0			0
$532$	−0.489357	+	1.50609i	−0.0212163	+	0.0652971i
$533$	−33.8641	+	15.0773i	−1.46682	+	0.653069i
$534$		0			0
$535$	0.0881995	−	0.0187474i	0.00381320	−	0.000810520i
$536$	15.8035	−	17.5516i	0.682609	−	0.758115i
$537$		0			0
$538$	−19.7984	+	34.2918i	−0.853569	+	1.47842i
$539$	6.61803	+	0.449028i	0.285059	+	0.0193410i
$540$		0			0
$541$	0.454915	−	0.330515i	0.0195583	−	0.0142100i	−0.577963	−	0.816063i	$-0.696152\pi$
$541$	0.454915	−	0.330515i	0.0195583	−	0.0142100i	0.597521	+	0.801853i	$0.296152\pi$
$542$	9.92419	+	2.10945i	0.426280	+	0.0906087i
$543$		0			0
$544$	−0.218482	+	2.07872i	−0.00936735	+	0.0891244i
$545$		0			0
$546$		0			0
$547$	−18.9584	−	4.02974i	−0.810604	−	0.172299i	−0.216078	−	0.976376i	$-0.569327\pi$
$547$	−18.9584	−	4.02974i	−0.810604	−	0.172299i	−0.594525	+	0.804077i	$0.702660\pi$
$548$	−0.736068	+	0.534785i	−0.0314433	+	0.0228449i
$549$		0			0
$550$	25.9894	+	1.76336i	1.10819	+	0.0751897i
$551$	1.90983	−	3.30792i	0.0813615	−	0.140922i
$552$		0			0
$553$	1.05963	−	1.17684i	0.0450600	−	0.0500443i
$554$	16.5195	−	3.51133i	0.701846	−	0.149182i
$555$		0			0
$556$	3.30524	−	1.47159i	0.140173	−	0.0624092i
$557$	−8.06231	+	24.8132i	−0.341611	+	1.05137i	0.621762	+	0.783206i	$0.286417\pi$
$557$	−8.06231	+	24.8132i	−0.341611	+	1.05137i	−0.963373	+	0.268164i	$0.913583\pi$
$558$		0			0
$559$	−8.89919	+	6.46564i	−0.376396	+	0.273467i
$560$	2.78115	−	4.81710i	0.117525	−	0.203560i
$561$		0			0
$562$	4.23607	+	7.33708i	0.178688	+	0.309496i
$563$	−24.5639	−	10.9366i	−1.03525	−	0.460921i	−0.182477	−	0.983210i	$-0.558411\pi$
$563$	−24.5639	−	10.9366i	−1.03525	−	0.460921i	−0.852768	+	0.522289i	$0.825078\pi$
$564$		0			0
$565$	3.24803	+	3.60730i	0.136646	+	0.151760i
$566$	−29.0344	−	21.0948i	−1.22041	−	0.886679i
$567$		0			0
$568$	−10.0623	+	30.9686i	−0.422205	+	1.29941i
$569$	33.3244	+	7.08332i	1.39703	+	0.296948i	0.844059	−	0.536251i	$-0.180160\pi$
$569$	33.3244	+	7.08332i	1.39703	+	0.296948i	0.552973	+	0.833199i	$0.313493\pi$
$570$		0			0
$571$	12.8435	+	22.2455i	0.537482	+	0.930946i	0.999039	+	0.0438355i	$0.0139577\pi$
$571$	12.8435	+	22.2455i	0.537482	+	0.930946i	−0.461557	+	0.887111i	$0.652709\pi$
$572$	−2.19364	+	12.5930i	−0.0917208	+	0.526539i
$573$		0			0
$574$	−3.01607	−	28.6960i	−0.125889	−	1.19775i
$575$	−8.20820	−	25.2623i	−0.342306	−	1.05351i
$576$		0			0
$577$	−12.3262	−	8.95554i	−0.513148	−	0.372824i	0.300868	−	0.953666i	$-0.402723\pi$
$577$	−12.3262	−	8.95554i	−0.513148	−	0.372824i	−0.814016	+	0.580842i	$0.802723\pi$
$578$	24.5639	−	10.9366i	1.02172	−	0.454901i
$579$		0			0
$580$	0.706420	−	0.784559i	0.0293325	−	0.0325770i
$581$	34.8286	+	15.5067i	1.44493	+	0.643325i
$582$		0			0
$583$	15.1132	+	19.2618i	0.625926	+	0.797743i
$584$	2.76393			0.114372
$585$		0			0
$586$	8.97214	+	27.6134i	0.370636	+	1.14070i
$587$	−16.2632	−	18.0621i	−0.671254	−	0.745503i	0.307273	−	0.951621i	$-0.400583\pi$
$587$	−16.2632	−	18.0621i	−0.671254	−	0.745503i	−0.978527	+	0.206119i	$0.933917\pi$
$588$		0			0
$589$	−0.344086	+	3.27376i	−0.0141778	+	0.134893i
$590$	3.21986	−	0.684403i	0.132560	−	0.0281764i
$591$		0			0
$592$	−2.14935	−	20.4497i	−0.0883376	−	0.840476i
$593$	29.2148			1.19971			0.599854	−	0.800110i	$-0.295225\pi$
$593$	29.2148			1.19971			0.599854	+	0.800110i	$0.295225\pi$
$594$		0			0
$595$	0.708204			0.0290335
$596$	0.969032	+	9.21973i	0.0396931	+	0.377655i
$597$		0			0
$598$	54.0082	−	11.4798i	2.20856	−	0.469444i
$599$	−2.26913	+	21.5893i	−0.0927139	+	0.882114i	0.845014	+	0.534744i	$0.179592\pi$
$599$	−2.26913	+	21.5893i	−0.0927139	+	0.882114i	−0.937728	+	0.347370i	$0.887075\pi$
$600$		0			0
$601$	−13.2707	−	14.7387i	−0.541325	−	0.601202i	0.408972	−	0.912547i	$-0.365887\pi$
$601$	−13.2707	−	14.7387i	−0.541325	−	0.601202i	−0.950297	+	0.311345i	$0.899221\pi$
$602$	−2.64590	−	8.14324i	−0.107839	−	0.331894i
$603$		0			0
$604$	1.23607			0.0502949
$605$	0.129267	−	4.19964i	0.00525547	−	0.170740i
$606$		0			0
$607$	−2.12512	−	0.946166i	−0.0862561	−	0.0384037i	0.363155	−	0.931729i	$-0.381700\pi$
$607$	−2.12512	−	0.946166i	−0.0862561	−	0.0384037i	−0.449411	+	0.893325i	$0.648366\pi$
$608$	−1.93281	+	2.14661i	−0.0783859	+	0.0870564i
$609$		0			0
$610$	−0.646976	+	0.288052i	−0.0261953	+	0.0116629i
$611$	−3.11803	−	2.26538i	−0.126142	−	0.0916476i
$612$		0			0
$613$	1.03444	+	3.18368i	0.0417807	+	0.128588i	0.969771	−	0.244016i	$-0.0784650\pi$
$613$	1.03444	+	3.18368i	0.0417807	+	0.128588i	−0.927990	+	0.372604i	$0.878465\pi$
$614$	−3.30858	−	31.4791i	−0.133524	−	1.27039i
$615$		0			0
$616$	19.6659	+	10.4044i	0.792362	+	0.419207i
$617$	23.2082	+	40.1978i	0.934327	+	1.61830i	0.775829	+	0.630943i	$0.217332\pi$
$617$	23.2082	+	40.1978i	0.934327	+	1.61830i	0.158498	+	0.987359i	$0.449335\pi$
$618$		0			0
$619$	30.4990	+	6.48276i	1.22586	+	0.260564i	0.774959	−	0.632011i	$-0.217770\pi$
$619$	30.4990	+	6.48276i	1.22586	+	0.260564i	0.450898	+	0.892575i	$0.351104\pi$
$620$	−0.281153	+	0.865300i	−0.0112914	+	0.0347513i
$621$		0			0
$622$	−15.0172	−	10.9106i	−0.602136	−	0.437477i
$623$	−19.0143	−	21.1175i	−0.761791	−	0.846055i
$624$		0			0
$625$	20.8588	+	9.28694i	0.834353	+	0.371478i
$626$	−22.5172	−	39.0010i	−0.899969	−	1.55879i
$627$		0			0
$628$	−3.00000	+	5.19615i	−0.119713	+	0.207349i
$629$	2.11803	−	1.53884i	0.0844515	−	0.0613576i
$630$		0			0
$631$	3.93363	−	12.1065i	0.156595	−	0.481951i	−0.841724	−	0.539908i	$-0.818459\pi$
$631$	3.93363	−	12.1065i	0.156595	−	0.481951i	0.998319	+	0.0579577i	$0.0184589\pi$
$632$	1.07829	−	0.480087i	0.0428922	−	0.0190969i
$633$		0			0
$634$	−40.1377	+	8.53154i	−1.59407	+	0.338831i
$635$	2.48127	−	2.75573i	0.0984663	−	0.109358i
$636$		0			0
$637$	−6.23607	+	10.8012i	−0.247082	+	0.427959i
$638$	18.4164	+	15.3884i	0.729113	+	0.609233i
$639$		0			0
$640$	4.20820	−	3.05744i	0.166344	−	0.120856i
$641$	−6.59530	−	1.40187i	−0.260499	−	0.0553707i	0.0758108	−	0.997122i	$-0.475846\pi$
$641$	−6.59530	−	1.40187i	−0.260499	−	0.0553707i	−0.336310	+	0.941751i	$0.609179\pi$
$642$		0			0
$643$	1.92726	−	18.3367i	0.0760039	−	0.723128i	−0.888467	−	0.458940i	$-0.848229\pi$
$643$	1.92726	−	18.3367i	0.0760039	−	0.723128i	0.964471	−	0.264188i	$-0.0851041\pi$
$644$	−1.06054	+	10.0903i	−0.0417909	+	0.397614i
$645$		0			0
$646$	−0.835438	−	0.177578i	−0.0328699	−	0.00698670i
$647$	2.59017	−	1.88187i	0.101830	−	0.0739839i	−0.535705	−	0.844405i	$-0.679954\pi$
$647$	2.59017	−	1.88187i	0.101830	−	0.0739839i	0.637535	+	0.770421i	$0.279954\pi$
$648$		0			0
$649$	4.30902	+	17.1315i	0.169144	+	0.672471i
$650$	−24.4894	+	42.4168i	−0.960552	+	1.66372i
$651$		0			0
$652$	−6.31505	+	7.01357i	−0.247316	+	0.274673i
$653$	21.4856	−	4.56690i	0.840795	−	0.178716i	0.232668	−	0.972556i	$-0.425254\pi$
$653$	21.4856	−	4.56690i	0.840795	−	0.178716i	0.608127	+	0.793840i	$0.291921\pi$
$654$		0			0
$655$	4.83430	−	2.15237i	0.188892	−	0.0841000i
$656$	8.91641	−	27.4419i	0.348127	−	1.07143i
$657$		0			0
$658$	2.42705	−	1.76336i	0.0946163	−	0.0687428i
$659$	10.3262	−	17.8856i	0.402253	−	0.696723i	−0.591744	−	0.806126i	$-0.701561\pi$
$659$	10.3262	−	17.8856i	0.402253	−	0.696723i	0.993997	+	0.109403i	$0.0348938\pi$
$660$		0			0
$661$	10.5451	+	18.2646i	0.410156	+	0.710411i	0.994907	−	0.100802i	$-0.0321408\pi$
$661$	10.5451	+	18.2646i	0.410156	+	0.710411i	−0.584750	+	0.811213i	$0.698807\pi$
$662$	33.4013	+	14.8712i	1.29818	+	0.577987i
$663$		0			0
$664$	19.0143	+	21.1175i	0.737897	+	0.819518i
$665$	0.791796	+	0.575274i	0.0307045	+	0.0223082i
$666$		0			0
$667$	7.56231	−	23.2744i	0.292814	−	0.901188i
$668$	−11.5069	−	2.44586i	−0.445214	−	0.0946331i
$669$		0			0
$670$	3.26393	+	5.65330i	0.126097	+	0.218406i
$671$	−1.67310	−	3.41243i	−0.0645891	−	0.131735i
$672$		0			0
$673$	1.50692	+	14.3374i	0.0580877	+	0.552667i	0.984404	+	0.175921i	$0.0562904\pi$
$673$	1.50692	+	14.3374i	0.0580877	+	0.552667i	−0.926317	+	0.376746i	$0.877043\pi$
$674$	6.85410	+	21.0948i	0.264010	+	0.812540i
$675$		0			0
$676$	−12.9443	−	9.40456i	−0.497857	−	0.361714i
$677$	−20.5293	+	9.14024i	−0.789006	+	0.351288i	−0.761360	−	0.648330i	$-0.775468\pi$
$677$	−20.5293	+	9.14024i	−0.789006	+	0.351288i	−0.0276461	+	0.999618i	$0.508801\pi$
$678$		0			0
$679$	30.1800	−	33.5183i	1.15820	−	1.28631i
$680$	0.482228	+	0.214702i	0.0184926	+	0.00823343i
$681$		0			0
$682$	−19.8932	−	5.65980i	−0.761751	−	0.216725i
$683$	38.8885			1.48803			0.744014	−	0.668164i	$-0.232919\pi$
$683$	38.8885			1.48803			0.744014	+	0.668164i	$0.232919\pi$
$684$		0			0
$685$	0.173762	+	0.534785i	0.00663911	+	0.0204331i
$686$	16.2401	+	18.0365i	0.620051	+	0.688637i
$687$		0			0
$688$	0.895005	−	8.51540i	0.0341217	−	0.324647i
$689$	−45.0285	+	9.57110i	−1.71545	+	0.364630i
$690$		0			0
$691$	4.15064	+	39.4907i	0.157898	+	1.50230i	0.730754	+	0.682641i	$0.239169\pi$
$691$	4.15064	+	39.4907i	0.157898	+	1.50230i	−0.572857	+	0.819656i	$0.694165\pi$
$692$	−10.8885			−0.413920
$693$		0			0
$694$	−4.94427			−0.187682
$695$	−0.233733	−	2.22382i	−0.00886599	−	0.0843542i
$696$		0			0
$697$	3.59348	−	0.763818i	0.136113	−	0.0289317i
$698$	5.09499	−	48.4756i	0.192848	−	1.83483i
$699$		0			0
$700$	−6.02218	−	6.68830i	−0.227617	−	0.252794i
$701$	−15.3541	−	47.2551i	−0.579916	−	1.78480i	−0.618792	−	0.785555i	$-0.712377\pi$
$701$	−15.3541	−	47.2551i	−0.579916	−	1.78480i	0.0388752	−	0.999244i	$-0.487623\pi$
$702$		0			0
$703$	3.61803			0.136457
$704$	8.67258	+	11.0532i	0.326860	+	0.416583i
$705$		0			0
$706$	−2.25841	−	1.00551i	−0.0849963	−	0.0378428i
$707$	6.02218	−	6.68830i	0.226487	−	0.251540i
$708$		0			0
$709$	5.71638	−	2.54510i	0.214683	−	0.0955831i	−0.296578	−	0.955009i	$-0.595845\pi$
$709$	5.71638	−	2.54510i	0.214683	−	0.0955831i	0.511261	+	0.859426i	$0.329179\pi$
$710$	−7.28115	−	5.29007i	−0.273257	−	0.198533i
$711$		0			0
$712$	−6.54508	−	20.1437i	−0.245287	−	0.754917i
$713$	2.20452	+	20.9746i	0.0825600	+	0.785506i
$714$		0			0
$715$	6.98302	+	3.69443i	0.261150	+	0.138164i
$716$	0.690983	+	1.19682i	0.0258232	+	0.0447272i
$717$		0			0
$718$	27.2791	+	5.79835i	1.01805	+	0.216393i
$719$	8.78115	−	27.0256i	0.327482	−	1.00789i	−0.642826	−	0.766012i	$-0.722238\pi$
$719$	8.78115	−	27.0256i	0.327482	−	1.00789i	0.970308	−	0.241873i	$-0.0777618\pi$
$720$		0			0
$721$	14.5623	+	10.5801i	0.542329	+	0.394025i
$722$	19.7810	+	21.9691i	0.736174	+	0.817604i
$723$		0			0
$724$	−4.81485	−	2.14371i	−0.178943	−	0.0796703i
$725$	10.8541	+	18.7999i	0.403111	+	0.698209i
$726$		0			0
$727$	−16.0729	+	27.8392i	−0.596113	+	1.03250i	0.397276	+	0.917699i	$0.369956\pi$
$727$	−16.0729	+	27.8392i	−0.596113	+	1.03250i	−0.993389	+	0.114798i	$0.963378\pi$
$728$	−33.8435	+	24.5887i	−1.25432	+	0.911318i
$729$		0			0
$730$	−0.236068	+	0.726543i	−0.00873727	+	0.0268905i
$731$	0.995920	−	0.443412i	0.0368354	−	0.0164002i
$732$		0			0
$733$	23.7610	−	5.05055i	0.877631	−	0.186546i	0.253000	−	0.967466i	$-0.418583\pi$
$733$	23.7610	−	5.05055i	0.877631	−	0.186546i	0.624631	+	0.780920i	$0.285249\pi$
$734$	15.7663	−	17.5102i	0.581943	−	0.646313i
$735$		0			0
$736$	−9.25329	+	16.0272i	−0.341081	+	0.590769i
$737$	−29.6697	+	18.6251i	−1.09290	+	0.686064i
$738$		0			0
$739$	20.2254	−	14.6946i	0.744004	−	0.540551i	−0.149958	−	0.988692i	$-0.547914\pi$
$739$	20.2254	−	14.6946i	0.744004	−	0.540551i	0.893963	+	0.448142i	$0.147914\pi$
$740$	0.978148	+	0.207912i	0.0359574	+	0.00764299i
$741$		0			0
$742$	3.74555	−	35.6365i	0.137503	−	1.30826i
$743$	1.34002	−	12.7494i	0.0491605	−	0.467731i	−0.942053	−	0.335463i	$-0.891107\pi$
$743$	1.34002	−	12.7494i	0.0491605	−	0.467731i	0.991214	−	0.132268i	$-0.0422261\pi$
$744$		0			0
$745$	5.60429	+	1.19123i	0.205325	+	0.0436432i
$746$	29.3435	−	21.3193i	1.07434	−	0.780554i
$747$		0			0
$748$	0.472136	−	1.17557i	0.0172630	−	0.0429831i
$749$	0.354102	−	0.613323i	0.0129386	−	0.0224103i
$750$		0			0
$751$	−35.4124	+	39.3294i	−1.29222	+	1.43515i	−0.452849	+	0.891587i	$0.649592\pi$
$751$	−35.4124	+	39.3294i	−1.29222	+	1.43515i	−0.839367	+	0.543565i	$0.817074\pi$
$752$	2.93444	−	0.623735i	0.107008	−	0.0227453i
$753$		0			0
$754$	−41.2234	+	18.3538i	−1.50127	+	0.668407i
$755$	0.236068	−	0.726543i	0.00859139	−	0.0264416i
$756$		0			0
$757$	12.8992	−	9.37181i	0.468829	−	0.340624i	−0.328156	−	0.944624i	$-0.606427\pi$
$757$	12.8992	−	9.37181i	0.468829	−	0.340624i	0.796985	+	0.603999i	$0.206427\pi$
$758$	22.9894	−	39.8187i	0.835011	−	1.44628i
$759$		0			0
$760$	0.364745	+	0.631757i	0.0132307	+	0.0229162i
$761$	−4.46591	−	1.98835i	−0.161889	−	0.0720776i	0.324192	−	0.945991i	$-0.394907\pi$
$761$	−4.46591	−	1.98835i	−0.161889	−	0.0720776i	−0.486081	+	0.873914i	$0.661574\pi$
$762$		0			0
$763$		0			0
$764$	0.736068	+	0.534785i	0.0266300	+	0.0193478i
$765$		0			0
$766$	−4.44427	+	13.6781i	−0.160578	+	0.494208i
$767$	−32.4890	−	6.90574i	−1.17311	−	0.249352i
$768$		0			0
$769$	23.8435	+	41.2981i	0.859817	+	1.48925i	0.872103	+	0.489322i	$0.162756\pi$
$769$	23.8435	+	41.2981i	0.859817	+	1.48925i	−0.0122858	+	0.999925i	$0.503911\pi$
$770$	−4.41464	+	4.28084i	−0.159092	+	0.154271i
$771$		0			0
$772$	−0.100928	−	0.960269i	−0.00363249	−	0.0345608i
$773$	−15.2188	−	46.8388i	−0.547384	−	1.68467i	−0.715253	−	0.698865i	$-0.753689\pi$
$773$	−15.2188	−	46.8388i	−0.547384	−	1.68467i	0.167870	−	0.985809i	$-0.446311\pi$
$774$		0			0
$775$	−15.1353	−	10.9964i	−0.543674	−	0.395003i
$776$	30.7116	−	13.6737i	1.10248	−	0.490857i
$777$		0			0
$778$	−10.0370	+	11.1472i	−0.359842	+	0.399645i
$779$	4.63808	+	2.06501i	0.166177	+	0.0739866i
$780$		0			0
$781$	26.9249	−	40.0964i	0.963448	−	1.43476i
$782$	−5.47214			−0.195683
$783$		0			0
$784$	−3.00000	−	9.23305i	−0.107143	−	0.329752i
$785$	2.48127	+	2.75573i	0.0885604	+	0.0983563i
$786$		0			0
$787$	2.47818	−	23.5783i	0.0883377	−	0.840477i	−0.857204	−	0.514976i	$-0.827801\pi$
$787$	2.47818	−	23.5783i	0.0883377	−	0.840477i	0.945542	−	0.325500i	$-0.105533\pi$
$788$	16.0914	−	3.42032i	0.573231	−	0.121844i
$789$		0			0
$790$	0.0341011	+	0.324451i	0.00121326	+	0.0115434i
$791$	38.1246			1.35556
$792$		0			0
$793$	7.14590			0.253758
$794$	−4.27762	−	40.6988i	−0.151807	−	1.44435i
$795$		0			0
$796$	1.98998	−	0.422984i	0.0705331	−	0.0149923i
$797$	1.59260	−	15.1526i	0.0564129	−	0.536733i	−0.929423	−	0.369017i	$-0.879694\pi$
$797$	1.59260	−	15.1526i	0.0564129	−	0.536733i	0.985835	−	0.167716i	$-0.0536390\pi$
$798$		0			0
$799$	0.255585	+	0.283856i	0.00904195	+	0.0100421i
$800$	−5.07295	−	15.6129i	−0.179356	−	0.552000i
$801$		0			0
$802$	−24.1246			−0.851870
$803$	−3.94309	−	1.12184i	−0.139149	−	0.0395890i
$804$		0			0
$805$	5.72840	+	2.55045i	0.201899	+	0.0898914i
$806$	26.0215	−	28.8998i	0.916569	−	1.01795i
$807$		0			0
$808$	6.12825	−	2.72847i	0.215591	−	0.0959873i
$809$	20.4894	+	14.8864i	0.720367	+	0.523378i	0.886502	−	0.462726i	$-0.153128\pi$
$809$	20.4894	+	14.8864i	0.720367	+	0.523378i	−0.166134	+	0.986103i	$0.553128\pi$
$810$		0			0
$811$	14.1353	+	43.5038i	0.496356	+	1.52763i	0.814833	+	0.579696i	$0.196829\pi$
$811$	14.1353	+	43.5038i	0.496356	+	1.52763i	−0.318477	+	0.947931i	$0.603171\pi$
$812$	−0.866729	−	8.24637i	−0.0304162	−	0.289391i
$813$		0			0
$814$	−3.90115	+	22.3952i	−0.136735	+	0.784953i
$815$	2.91641	+	5.05137i	0.102157	+	0.176942i
$816$		0			0
$817$	1.47366	+	0.313235i	0.0515567	+	0.0109587i
$818$	14.4721	−	44.5407i	0.506006	−	1.55733i
$819$		0			0
$820$	1.13525	+	0.824811i	0.0396448	+	0.0288036i
$821$	−9.08920	−	10.0946i	−0.317215	−	0.352303i	0.563358	−	0.826213i	$-0.309509\pi$
$821$	−9.08920	−	10.0946i	−0.317215	−	0.352303i	−0.880574	+	0.473910i	$0.842842\pi$
$822$		0			0
$823$	−24.2344	−	10.7899i	−0.844758	−	0.376111i	−0.0617272	−	0.998093i	$-0.519661\pi$
$823$	−24.2344	−	10.7899i	−0.844758	−	0.376111i	−0.783031	+	0.621982i	$0.786328\pi$
$824$	6.70820	+	11.6190i	0.233691	+	0.404765i
$825$		0			0
$826$	12.9271	−	22.3903i	0.449790	−	0.779058i
$827$	10.4164	−	7.56796i	0.362214	−	0.263164i	−0.391761	−	0.920067i	$-0.628134\pi$
$827$	10.4164	−	7.56796i	0.362214	−	0.263164i	0.753975	+	0.656903i	$0.228134\pi$
$828$		0			0
$829$	−13.1910	+	40.5977i	−0.458142	+	1.41002i	0.409265	+	0.912416i	$0.365785\pi$
$829$	−13.1910	+	40.5977i	−0.458142	+	1.41002i	−0.867407	+	0.497600i	$0.834215\pi$
$830$	−7.17508	+	3.19455i	−0.249051	+	0.110884i
$831$		0			0
$832$	−25.8391	+	5.49228i	−0.895811	+	0.190411i
$833$	0.827091	−	0.918578i	0.0286570	−	0.0318268i
$834$		0			0
$835$	−3.63525	+	6.29645i	−0.125803	+	0.217898i
$836$	1.48278	−	0.930812i	0.0512830	−	0.0321928i
$837$		0			0
$838$	28.1525	−	20.4540i	0.972511	−	0.706571i
$839$	−22.7828	−	4.84264i	−0.786550	−	0.167186i	−0.202908	−	0.979198i	$-0.565039\pi$
$839$	−22.7828	−	4.84264i	−0.786550	−	0.167186i	−0.583642	+	0.812011i	$0.698373\pi$
$840$		0			0
$841$	0.940756	−	8.95070i	0.0324399	−	0.308645i
$842$	−0.630771	+	6.00138i	−0.0217378	+	0.206821i
$843$		0			0
$844$	−6.81334	−	1.44822i	−0.234525	−	0.0498498i
$845$	−8.00000	+	5.81234i	−0.275208	+	0.199951i
$846$		0			0
$847$	−23.8328	−	22.8254i	−0.818905	−	0.784289i
$848$	17.9164	−	31.0321i	0.615252	−	1.06565i
$849$		0			0
$850$	3.24803	−	3.60730i	0.111406	−	0.123729i
$851$	22.6738	−	4.81946i	0.777248	−	0.165209i
$852$		0			0
$853$	7.25745	−	3.23123i	0.248490	−	0.110635i	−0.278712	−	0.960375i	$-0.589908\pi$
$853$	7.25745	−	3.23123i	0.248490	−	0.110635i	0.527203	+	0.849740i	$0.323241\pi$
$854$	−1.71885	+	5.29007i	−0.0588177	+	0.181022i
$855$		0			0
$856$	0.427051	−	0.310271i	0.0145963	−	0.0106048i
$857$	−20.8607	+	36.1318i	−0.712587	+	1.23424i	0.251296	+	0.967910i	$0.419143\pi$
$857$	−20.8607	+	36.1318i	−0.712587	+	1.23424i	−0.963883	+	0.266327i	$0.914190\pi$
$858$		0			0
$859$	−21.4443	−	37.1426i	−0.731669	−	1.26729i	−0.956169	−	0.292814i	$-0.905408\pi$
$859$	−21.4443	−	37.1426i	−0.731669	−	1.26729i	0.224500	−	0.974474i	$-0.427925\pi$
$860$	0.380408	+	0.169368i	0.0129718	+	0.00577541i
$861$		0			0
$862$	−1.61689	−	1.79574i	−0.0550716	−	0.0611632i
$863$	−19.3262	−	14.0413i	−0.657873	−	0.477973i	0.208071	−	0.978114i	$-0.433281\pi$
$863$	−19.3262	−	14.0413i	−0.657873	−	0.477973i	−0.865944	+	0.500141i	$0.833281\pi$
$864$		0			0
$865$	−2.07953	+	6.40013i	−0.0707060	+	0.217611i
$866$	−9.49606	−	2.01845i	−0.322689	−	0.0685897i
$867$		0			0
$868$	3.57295	+	6.18853i	0.121274	+	0.210052i
$869$	−1.73318	+	0.247239i	−0.0587942	+	0.00838699i
$870$		0			0
$871$	−6.88500	−	65.5064i	−0.233289	−	2.21960i
$872$		0			0
$873$		0			0
$874$	−6.11803	−	4.44501i	−0.206946	−	0.150355i
$875$	−10.3156	+	4.59279i	−0.348730	+	0.155265i
$876$		0			0
$877$	−13.6612	+	15.1723i	−0.461307	+	0.512334i	−0.928252	−	0.371953i	$-0.878688\pi$
$877$	−13.6612	+	15.1723i	−0.461307	+	0.512334i	0.466944	+	0.884287i	$0.345355\pi$
$878$	−24.6972	−	10.9959i	−0.833490	−	0.371094i
$879$		0			0
$880$	−5.77415	+	2.11515i	−0.194646	+	0.0713017i
$881$	−25.0902			−0.845309			−0.422655	−	0.906291i	$-0.638902\pi$
$881$	−25.0902			−0.845309			−0.422655	+	0.906291i	$0.638902\pi$
$882$		0			0
$883$	11.5623	+	35.5851i	0.389103	+	1.19753i	0.933460	+	0.358681i	$0.116774\pi$
$883$	11.5623	+	35.5851i	0.389103	+	1.19753i	−0.544358	+	0.838853i	$0.683226\pi$
$884$	1.59385	+	1.77015i	0.0536069	+	0.0595364i
$885$		0			0
$886$	0.148055	−	1.40865i	0.00497400	−	0.0473245i
$887$	2.93444	−	0.623735i	0.0985289	−	0.0209430i	−0.158383	−	0.987378i	$-0.550628\pi$
$887$	2.93444	−	0.623735i	0.0985289	−	0.0209430i	0.256912	+	0.966435i	$0.417295\pi$
$888$		0			0
$889$	−3.04435	−	28.9651i	−0.102104	−	0.971457i
$890$	5.85410			0.196230
$891$		0			0
$892$	−7.85410			−0.262975
$893$	0.0551768	+	0.524972i	0.00184642	+	0.0175675i
$894$		0			0
$895$	0.835438	−	0.177578i	0.0279256	−	0.00593577i
$896$	4.27042	−	40.6303i	0.142665	−	1.35736i
$897$		0			0
$898$	−16.8116	−	18.6712i	−0.561012	−	0.623067i
$899$	−5.32624	−	16.3925i	−0.177640	−	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$	−17.7832	+	26.4826i	−0.592116	+	0.881775i
$903$		0			0
$904$	25.9597	+	11.5580i	0.863406	+	0.384413i
$905$	−2.17960	+	2.42069i	−0.0724522	+	0.0804663i
$906$		0			0
$907$	3.63474	−	1.61829i	0.120689	−	0.0537344i	−0.345504	−	0.938417i	$-0.612292\pi$
$907$	3.63474	−	1.61829i	0.120689	−	0.0537344i	0.466193	+	0.884683i	$0.345625\pi$
$908$	5.44427	+	3.95550i	0.180675	+	0.131268i
$909$		0			0
$910$	−3.57295	−	10.9964i	−0.118442	−	0.364527i
$911$	3.75720	+	35.7474i	0.124482	+	1.18436i	0.861237	+	0.508204i	$0.169690\pi$
$911$	3.75720	+	35.7474i	0.124482	+	1.18436i	−0.736755	+	0.676159i	$0.763643\pi$
$912$		0			0
$913$	−18.5549	−	37.8444i	−0.614078	−	1.25247i
$914$	26.5344	+	45.9590i	0.877681	+	1.52019i
$915$		0			0
$916$	−6.04528	−	1.28496i	−0.199742	−	0.0424564i
$917$	12.8435	−	39.5281i	0.424128	−	1.30533i
$918$		0			0
$919$	37.9894	+	27.6009i	1.25315	+	0.910469i	0.998400	−	0.0565371i	$-0.0180059\pi$
$919$	37.9894	+	27.6009i	1.25315	+	0.910469i	0.254753	+	0.967006i	$0.418006\pi$
$920$	3.12736	+	3.47328i	0.103106	+	0.114511i
$921$		0			0
$922$	−14.6482	−	6.52180i	−0.482412	−	0.214784i
$923$	45.4058	+	78.6451i	1.49455	+	2.58863i
$924$		0			0
$925$	−10.2812	+	17.8075i	−0.338042	+	0.585506i
$926$	11.5172	−	8.36775i	0.378479	−	0.274981i
$927$		0			0
$928$	4.67376	−	14.3844i	0.153424	−	0.472190i
$929$	−2.63882	+	1.17488i	−0.0865767	+	0.0385465i	−0.449568	−	0.893246i	$-0.648422\pi$
$929$	−2.63882	+	1.17488i	−0.0865767	+	0.0385465i	0.362991	+	0.931792i	$0.381755\pi$
$930$		0			0
$931$	1.67088	−	0.355156i	0.0547607	−	0.0116398i
$932$	−3.58699	+	3.98376i	−0.117496	+	0.130492i
$933$		0			0
$934$	11.5172	−	19.9484i	0.376855	−	0.652732i
$935$	−0.600813	−	0.502029i	−0.0196487	−	0.0164181i
$936$		0			0
$937$	−26.3713	+	19.1599i	−0.861514	+	0.625926i	−0.928296	−	0.371841i	$-0.878727\pi$
$937$	−26.3713	+	19.1599i	−0.861514	+	0.625926i	0.0667827	+	0.997768i	$0.478727\pi$
$938$	50.1501	+	10.6597i	1.63746	+	0.348053i
$939$		0			0
$940$	−0.0152505	+	0.145099i	−0.000497416	+	0.00473260i
$941$	3.51542	−	33.4470i	0.114599	−	1.09034i	−0.774484	−	0.632594i	$-0.781990\pi$
$941$	3.51542	−	33.4470i	0.114599	−	1.09034i	0.889083	−	0.457746i	$-0.151343\pi$
$942$		0			0
$943$	31.8171	+	6.76292i	1.03611	+	0.220231i
$944$	20.9164	−	15.1967i	0.680771	−	0.494609i
$945$		0			0
$946$	−3.52786	+	8.78402i	−0.114701	+	0.285593i
$947$	1.33688	−	2.31555i	0.0434428	−	0.0752451i	−0.843486	−	0.537151i	$-0.819501\pi$
$947$	1.33688	−	2.31555i	0.0434428	−	0.0752451i	0.886929	+	0.461905i	$0.152834\pi$
$948$		0			0
$949$	5.15780	−	5.72831i	0.167429	−	0.185949i
$950$	6.56161	−	1.39471i	0.212887	−	0.0452505i
$951$		0			0
$952$	3.78747	−	1.68629i	0.122752	−	0.0546529i
$953$	−18.5967	+	57.2349i	−0.602408	+	1.85402i	−0.0886937	+	0.996059i	$0.528269\pi$
$953$	−18.5967	+	57.2349i	−0.602408	+	1.85402i	−0.513714	+	0.857961i	$0.671731\pi$
$954$		0			0
$955$	0.454915	−	0.330515i	0.0147207	−	0.0106952i
$956$	−5.42705	+	9.39993i	−0.175523	+	0.304015i
$957$		0			0
$958$	13.6803	+	23.6950i	0.441992	+	0.765552i
$959$	4.03459	+	1.79631i	0.130284	+	0.0580060i
$960$		0			0
$961$	−10.8037	−	11.9987i	−0.348507	−	0.387056i
$962$	−34.5795	−	25.1235i	−1.11489	−	0.810014i
$963$		0			0
$964$	3.27051	−	10.0656i	0.105336	−	0.324191i
$965$	−0.583707	−	0.124071i	−0.0187902	−	0.00399398i
$966$		0			0
$967$	−12.8435	−	22.2455i	−0.413018	−	0.715368i	0.582200	−	0.813045i	$-0.302192\pi$
$967$	−12.8435	−	22.2455i	−0.413018	−	0.715368i	−0.995218	+	0.0976776i	$0.968859\pi$
$968$	−9.30834	−	22.7674i	−0.299181	−	0.731772i
$969$		0			0
$970$	0.971257	+	9.24089i	0.0311852	+	0.296707i
$971$	10.4377	+	32.1239i	0.334962	+	1.03091i	0.966741	+	0.255757i	$0.0823248\pi$
$971$	10.4377	+	32.1239i	0.334962	+	1.03091i	−0.631779	+	0.775148i	$0.717675\pi$
$972$		0			0
$973$	−14.2082	−	10.3229i	−0.455494	−	0.330936i
$974$	−57.9143	+	25.7851i	−1.85569	+	0.826209i
$975$		0			0
$976$	−3.72191	+	4.13360i	−0.119135	+	0.132313i
$977$	45.0932	+	20.0768i	1.44266	+	0.642314i	0.970916	−	0.239422i	$-0.0769578\pi$
$977$	45.0932	+	20.0768i	1.44266	+	0.642314i	0.471744	+	0.881735i	$0.343625\pi$
$978$		0			0
$979$	1.16131	+	31.3940i	0.0371155	+	1.00336i
$980$	0.472136			0.0150818
$981$		0			0
$982$	−13.1074	−	40.3404i	−0.418274	−	1.28731i
$983$	−23.6236	−	26.2367i	−0.753477	−	0.836821i	0.237425	−	0.971406i	$-0.423696\pi$
$983$	−23.6236	−	26.2367i	−0.753477	−	0.836821i	−0.990902	+	0.134585i	$0.957030\pi$
$984$		0			0
$985$	1.06276	−	10.1115i	0.0338624	−	0.322179i
$986$	4.37441	−	0.929809i	0.139310	−	0.0296112i
$987$		0			0
$988$	0.344086	+	3.27376i	0.0109468	+	0.104152i
$989$	9.65248			0.306931
$990$		0			0
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	1.36247	+	12.9630i	0.0432585	+	0.411577i
$993$		0			0
$994$	−69.1422	+	14.6966i	−2.19306	+	0.466149i
$995$	0.131429	−	1.25047i	0.00416659	−	0.0396424i
$996$		0			0
$997$	22.7362	+	25.2511i	0.720063	+	0.799711i	0.986434	−	0.164160i	$-0.0524913\pi$
$997$	22.7362	+	25.2511i	0.720063	+	0.799711i	−0.266371	+	0.963871i	$0.585825\pi$
$998$	−1.28115	−	3.94298i	−0.0405542	−	0.124813i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.a.784.1		8
3.2	odd	2		891.2.n.d.784.1		8
9.2	odd	6		33.2.e.a.25.1	yes	4
9.4	even	3	inner	891.2.n.a.190.1		8
9.5	odd	6		891.2.n.d.190.1		8
9.7	even	3		99.2.f.b.91.1		4
11.4	even	5	inner	891.2.n.a.136.1		8
33.26	odd	10		891.2.n.d.136.1		8
36.11	even	6		528.2.y.f.289.1		4
45.2	even	12		825.2.bx.b.124.1		8
45.29	odd	6		825.2.n.f.751.1		4
45.38	even	12		825.2.bx.b.124.2		8
99.2	even	30		363.2.a.e.1.1		2
99.4	even	15	inner	891.2.n.a.433.1		8
99.20	odd	30		363.2.a.h.1.2		2
99.29	even	30		363.2.e.j.202.1		4
99.38	odd	30		363.2.e.h.130.1		4
99.47	odd	30		363.2.e.h.148.1		4
99.59	odd	30		891.2.n.d.433.1		8
99.65	even	6		363.2.e.j.124.1		4
99.70	even	15		99.2.f.b.37.1		4
99.74	even	30		363.2.e.c.148.1		4
99.79	odd	30		1089.2.a.s.1.2		2
99.83	even	30		363.2.e.c.130.1		4
99.92	odd	30		33.2.e.a.4.1	✓	4
99.97	even	15		1089.2.a.m.1.1		2
396.119	even	30		5808.2.a.bl.1.2		2
396.191	even	30		528.2.y.f.433.1		4
396.299	odd	30		5808.2.a.bm.1.2		2
495.92	even	60		825.2.bx.b.499.2		8
495.119	odd	30		9075.2.a.x.1.1		2
495.299	even	30		9075.2.a.bv.1.2		2
495.389	odd	30		825.2.n.f.301.1		4
495.488	even	60		825.2.bx.b.499.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	99.92	odd	30
33.2.e.a.25.1	yes	4	9.2	odd	6
99.2.f.b.37.1		4	99.70	even	15
99.2.f.b.91.1		4	9.7	even	3
363.2.a.e.1.1		2	99.2	even	30
363.2.a.h.1.2		2	99.20	odd	30
363.2.e.c.130.1		4	99.83	even	30
363.2.e.c.148.1		4	99.74	even	30
363.2.e.h.130.1		4	99.38	odd	30
363.2.e.h.148.1		4	99.47	odd	30
363.2.e.j.124.1		4	99.65	even	6
363.2.e.j.202.1		4	99.29	even	30
528.2.y.f.289.1		4	36.11	even	6
528.2.y.f.433.1		4	396.191	even	30
825.2.n.f.301.1		4	495.389	odd	30
825.2.n.f.751.1		4	45.29	odd	6
825.2.bx.b.124.1		8	45.2	even	12
825.2.bx.b.124.2		8	45.38	even	12
825.2.bx.b.499.1		8	495.488	even	60
825.2.bx.b.499.2		8	495.92	even	60
891.2.n.a.136.1		8	11.4	even	5	inner
891.2.n.a.190.1		8	9.4	even	3	inner
891.2.n.a.433.1		8	99.4	even	15	inner
891.2.n.a.784.1		8	1.1	even	1	trivial
891.2.n.d.136.1		8	33.26	odd	10
891.2.n.d.190.1		8	9.5	odd	6
891.2.n.d.433.1		8	99.59	odd	30
891.2.n.d.784.1		8	3.2	odd	2
1089.2.a.m.1.1		2	99.97	even	15
1089.2.a.s.1.2		2	99.79	odd	30
5808.2.a.bl.1.2		2	396.119	even	30
5808.2.a.bm.1.2		2	396.299	odd	30
9075.2.a.x.1.1		2	495.119	odd	30
9075.2.a.bv.1.2		2	495.299	even	30

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.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.169131 + 1.60917i) q^{2} +(-0.604528 + 0.128496i) q^{4} +(-0.0399263 + 0.379874i) q^{5} +(2.00739 + 2.22943i) q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})\)	\(q+(0.169131 + 1.60917i) q^{2} +(-0.604528 + 0.128496i) q^{4} +(-0.0399263 + 0.379874i) q^{5} +(2.00739 + 2.22943i) q^{7} +(0.690983 + 2.12663i) q^{8} -0.618034 q^{10} +(-0.122602 - 3.31436i) q^{11} +(5.69693 + 2.53644i) q^{13} +(-3.24803 + 3.60730i) q^{14} +(-4.43444 + 1.97434i) q^{16} +(-0.500000 - 0.363271i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(-0.0246758 - 0.234775i) q^{20} +(5.31263 - 0.757847i) q^{22} +(-2.73607 - 4.73901i) q^{23} +(4.74803 + 1.00922i) q^{25} +(-3.11803 + 9.59632i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(2.99244 + 3.32344i) q^{29} +(-3.52090 - 1.56760i) q^{31} +(-1.69098 - 2.92887i) q^{32} +(0.500000 - 0.866025i) q^{34} +(-0.927051 + 0.673542i) q^{35} +(-1.30902 + 4.02874i) q^{37} +(1.26249 - 0.562096i) q^{38} +(-0.835438 + 0.177578i) q^{40} +(-3.97749 + 4.41745i) q^{41} +(-0.881966 + 1.52761i) q^{43} +(0.500000 + 1.98787i) q^{44} +(7.16312 - 5.20431i) q^{46} +(-0.604528 - 0.128496i) q^{47} +(-0.209057 + 1.98904i) q^{49} +(-0.820977 + 7.81108i) q^{50} +(-3.76988 - 0.801313i) q^{52} +(-5.97214 + 4.33901i) q^{53} +(1.26393 + 0.0857567i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(-4.84187 + 5.37745i) q^{58} +(-5.20985 + 1.10739i) q^{59} +(1.04683 - 0.466079i) q^{61} +(1.92705 - 5.93085i) q^{62} +(-3.42705 + 2.48990i) q^{64} +(-1.19098 + 2.06284i) q^{65} +(-5.28115 - 9.14723i) q^{67} +(0.348943 + 0.155360i) q^{68} +(-1.24064 - 1.37787i) q^{70} +(11.7812 + 8.55951i) q^{71} +(0.381966 - 1.17557i) q^{73} +(-6.70432 - 1.42505i) q^{74} +(0.263932 + 0.457144i) q^{76} +(7.14303 - 6.92655i) q^{77} +(-0.0551768 - 0.524972i) q^{79} +(-0.572949 - 1.76336i) q^{80} +(-7.78115 - 5.65334i) q^{82} +(11.6095 - 5.16889i) q^{83} +(0.157960 - 0.175433i) q^{85} +(-2.60735 - 1.16087i) q^{86} +(6.96369 - 2.55089i) q^{88} -9.47214 q^{89} +(5.78115 + 17.7926i) q^{91} +(2.26298 + 2.51329i) q^{92} +(0.104528 - 0.994522i) q^{94} +(0.319109 - 0.0678287i) q^{95} +(-1.57153 - 14.9521i) q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8}+O(q^{10}) \) 8 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 + 10 * q^8	\( 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8} + 4 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} - 9 q^{16} - 4 q^{17} - 20 q^{19} + 3 q^{20} + 8 q^{22} - 4 q^{23} + 6 q^{25} - 16 q^{26} - 12 q^{28} - 10 q^{29} - 8 q^{31} - 18 q^{32} + 4 q^{34} + 6 q^{35} - 6 q^{37} - 10 q^{40} + 23 q^{41} - 16 q^{43} + 4 q^{44} + 26 q^{46} - 3 q^{47} + 2 q^{49} + 12 q^{50} - 7 q^{52} - 12 q^{53} + 28 q^{55} - 20 q^{59} - 3 q^{61} + 2 q^{62} - 14 q^{64} - 14 q^{65} - 2 q^{67} - q^{68} + 9 q^{70} + 54 q^{71} + 12 q^{73} - 4 q^{74} + 20 q^{76} - 3 q^{77} - 5 q^{79} - 18 q^{80} - 22 q^{82} + 21 q^{83} - 7 q^{85} - 7 q^{86} + 25 q^{88} - 40 q^{89} + 6 q^{91} + 7 q^{92} - q^{94} + 25 q^{95} + 33 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 + 10 * q^8 + 4 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 - 9 * q^16 - 4 * q^17 - 20 * q^19 + 3 * q^20 + 8 * q^22 - 4 * q^23 + 6 * q^25 - 16 * q^26 - 12 * q^28 - 10 * q^29 - 8 * q^31 - 18 * q^32 + 4 * q^34 + 6 * q^35 - 6 * q^37 - 10 * q^40 + 23 * q^41 - 16 * q^43 + 4 * q^44 + 26 * q^46 - 3 * q^47 + 2 * q^49 + 12 * q^50 - 7 * q^52 - 12 * q^53 + 28 * q^55 - 20 * q^59 - 3 * q^61 + 2 * q^62 - 14 * q^64 - 14 * q^65 - 2 * q^67 - q^68 + 9 * q^70 + 54 * q^71 + 12 * q^73 - 4 * q^74 + 20 * q^76 - 3 * q^77 - 5 * q^79 - 18 * q^80 - 22 * q^82 + 21 * q^83 - 7 * q^85 - 7 * q^86 + 25 * q^88 - 40 * q^89 + 6 * q^91 + 7 * q^92 - q^94 + 25 * q^95 + 33 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more