LMFDB - Embedded newform 891.2.n.a.136.1

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			136.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	891.136
Dual form			891.2.n.a.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47815 + 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(0.348943 + 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})$	\(q+(-1.47815 + 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(0.348943 + 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} -0.618034 q^{10} +(2.93162 - 1.55100i) q^{11} +(-0.651847 + 6.20191i) q^{13} +(4.74803 - 1.00922i) q^{14} +(0.507392 + 4.82751i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(0.215659 - 0.0960175i) q^{20} +(-3.31263 + 4.22195i) q^{22} +(-2.73607 - 4.73901i) q^{23} +(-3.24803 - 3.60730i) q^{25} +(-3.11803 - 9.59632i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(-4.37441 - 0.929809i) q^{29} +(0.402863 - 3.83299i) q^{31} +(-1.69098 - 2.92887i) q^{32} +(0.500000 - 0.866025i) q^{34} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(-0.144455 - 1.37440i) q^{38} +(0.571506 - 0.634721i) q^{40} +(5.81438 - 1.23588i) q^{41} +(-0.881966 + 1.52761i) q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.413545 + 0.459289i) q^{47} +(1.82709 + 0.813473i) q^{49} +(7.17508 + 3.19455i) q^{50} +(2.57890 + 2.86416i) q^{52} +(-5.97214 - 4.33901i) q^{53} +(1.26393 - 0.0857567i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(7.07794 - 1.50446i) q^{58} +(3.56395 - 3.95817i) q^{59} +(-0.119779 - 1.13962i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-3.42705 - 2.48990i) q^{64} +(-1.19098 + 2.06284i) q^{65} +(-5.28115 - 9.14723i) q^{67} +(-0.0399263 + 0.379874i) q^{68} +(1.81359 + 0.385489i) q^{70} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(4.58629 + 5.09359i) q^{74} +(0.263932 + 0.457144i) q^{76} +(-9.57008 + 2.72277i) q^{77} +(0.482228 - 0.214702i) q^{79} +(-0.572949 + 1.76336i) q^{80} +(-7.78115 + 5.65334i) q^{82} +(-1.32837 - 12.6386i) q^{83} +(-0.230909 + 0.0490813i) q^{85} +(0.298335 - 2.83847i) q^{86} +(-1.27270 - 7.30618i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(-3.30806 - 0.703150i) q^{92} +(-0.913545 - 0.406737i) q^{94} +(-0.218296 + 0.242442i) q^{95} +(13.7346 - 6.11506i) q^{97} -3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.47815	+	0.658114i	−1.04521	+	0.465357i	−0.856214	−	0.516622i	$-0.827189\pi$
$2$	−1.47815	+	0.658114i	−1.04521	+	0.465357i	−0.188994	+	0.981978i	$0.560523\pi$
$3$		0			0
$3$		0			0
$4$	0.413545	−	0.459289i	0.206773	−	0.229644i
$5$	0.348943	+	0.155360i	0.156052	+	0.0694789i	0.483276	−	0.875468i	$-0.339447\pi$
$5$	0.348943	+	0.155360i	0.156052	+	0.0694789i	−0.327224	+	0.944947i	$0.606113\pi$
$6$		0			0
$7$	−2.93444	−	0.623735i	−1.10912	−	0.235750i	−0.383289	−	0.923628i	$-0.625209\pi$
$7$	−2.93444	−	0.623735i	−1.10912	−	0.235750i	−0.725826	+	0.687879i	$0.758542\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	2.93162	−	1.55100i	0.883917	−	0.467645i
$11$	2.93162	−	1.55100i	0.883917	−	0.467645i
$12$		0			0
$13$	−0.651847	+	6.20191i	−0.180790	+	1.72010i	0.408993	+	0.912537i	$0.365880\pi$
$13$	−0.651847	+	6.20191i	−0.180790	+	1.72010i	−0.589783	+	0.807562i	$0.700787\pi$
$14$	4.74803	−	1.00922i	1.26896	−	0.269727i
$15$		0			0
$16$	0.507392	+	4.82751i	0.126848	+	1.20688i
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	−0.646766	−	0.762688i	$-0.723879\pi$
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	0.525498	+	0.850795i	$0.323879\pi$
$18$		0			0
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$	0.215659	−	0.0960175i	0.0482228	−	0.0214702i
$21$		0			0
$22$	−3.31263	+	4.22195i	−0.706255	+	0.900123i
$23$	−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
$25$	−3.24803	−	3.60730i	−0.649606	−	0.721460i
$26$	−3.11803	−	9.59632i	−0.611497	−	1.88199i
$27$		0			0
$28$	−1.50000	+	1.08981i	−0.283473	+	0.205955i
$29$	−4.37441	−	0.929809i	−0.812307	−	0.172661i	−0.217013	−	0.976169i	$-0.569631\pi$
$29$	−4.37441	−	0.929809i	−0.812307	−	0.172661i	−0.595295	+	0.803508i	$0.702965\pi$
$30$		0			0
$31$	0.402863	−	3.83299i	0.0723564	−	0.688425i	−0.896877	−	0.442281i	$-0.854170\pi$
$31$	0.402863	−	3.83299i	0.0723564	−	0.688425i	0.969233	−	0.246145i	$-0.0791638\pi$
$32$	−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	−0.999139	−	0.0414819i	$-0.986792\pi$
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	0.783938	−	0.620839i	$-0.213208\pi$
$38$	−0.144455	−	1.37440i	−0.0234337	−	0.222956i
$39$		0			0
$40$	0.571506	−	0.634721i	0.0903630	−	0.100358i
$41$	5.81438	−	1.23588i	0.908053	−	0.193013i	0.269869	−	0.962897i	$-0.413019\pi$
$41$	5.81438	−	1.23588i	0.908053	−	0.193013i	0.638183	+	0.769884i	$0.279686\pi$
$42$		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
$47$	0.413545	+	0.459289i	0.0603218	+	0.0669942i	0.772550	−	0.634953i	$-0.218981\pi$
$47$	0.413545	+	0.459289i	0.0603218	+	0.0669942i	−0.712229	+	0.701948i	$0.752314\pi$
$48$		0			0
$49$	1.82709	+	0.813473i	0.261013	+	0.116210i
$50$	7.17508	+	3.19455i	1.01471	+	0.451778i
$51$		0			0
$52$	2.57890	+	2.86416i	0.357629	+	0.397187i
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	0.0964728	−	0.995336i	$-0.469244\pi$
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	−0.916809	+	0.399327i	$0.869244\pi$
$54$		0			0
$55$	1.26393	−	0.0857567i	0.170429	−	0.0115634i
$56$	−3.35410	+	5.80948i	−0.448211	+	0.776324i
$57$		0			0
$58$	7.07794	−	1.50446i	0.929379	−	0.197546i
$59$	3.56395	−	3.95817i	0.463987	−	0.515309i	−0.465056	−	0.885281i	$-0.653966\pi$
$59$	3.56395	−	3.95817i	0.463987	−	0.515309i	0.929043	+	0.369972i	$0.120633\pi$
$60$		0			0
$61$	−0.119779	−	1.13962i	−0.0153361	−	0.145913i	0.984174	−	0.177204i	$-0.0567051\pi$
$61$	−0.119779	−	1.13962i	−0.0153361	−	0.145913i	−0.999510	+	0.0312901i	$0.990038\pi$
$62$	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	$-0.389891\pi$
$68$	−0.0399263	+	0.379874i	−0.00484178	+	0.0460664i
$69$		0			0
$70$	1.81359	+	0.385489i	0.216765	+	0.0460748i
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.403253	−	0.915089i	$-0.367880\pi$
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.994913	−	0.100738i	$-0.0321204\pi$
$72$		0			0
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	0.970918	−	0.239412i	$-0.0769548\pi$
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	−0.926212	+	0.377003i	$0.876955\pi$
$74$	4.58629	+	5.09359i	0.533145	+	0.592118i
$75$		0			0
$76$	0.263932	+	0.457144i	0.0302751	+	0.0524380i
$77$	−9.57008	+	2.72277i	−1.09061	+	0.310289i
$78$		0			0
$79$	0.482228	−	0.214702i	0.0542549	−	0.0241558i	−0.379430	−	0.925221i	$-0.623880\pi$
$79$	0.482228	−	0.214702i	0.0542549	−	0.0241558i	0.433685	+	0.901065i	$0.357213\pi$
$80$	−0.572949	+	1.76336i	−0.0640576	+	0.197149i
$81$		0			0
$82$	−7.78115	+	5.65334i	−0.859285	+	0.624307i
$83$	−1.32837	−	12.6386i	−0.145807	−	1.38727i	−0.785608	−	0.618724i	$-0.787650\pi$
$83$	−1.32837	−	12.6386i	−0.145807	−	1.38727i	0.639801	−	0.768541i	$-0.279017\pi$
$84$		0			0
$85$	−0.230909	+	0.0490813i	−0.0250456	+	0.00532361i
$86$	0.298335	−	2.83847i	0.0321703	−	0.306080i
$87$		0			0
$88$	−1.27270	−	7.30618i	−0.135671	−	0.778841i
$89$	−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
$92$	−3.30806	−	0.703150i	−0.344889	−	0.0733085i
$93$		0			0
$94$	−0.913545	−	0.406737i	−0.0942250	−	0.0419517i
$95$	−0.218296	+	0.242442i	−0.0223967	+	0.0248740i
$96$		0			0
$97$	13.7346	−	6.11506i	1.39454	−	0.620890i	0.434481	−	0.900681i	$-0.356932\pi$
$97$	13.7346	−	6.11506i	1.39454	−	0.620890i	0.960061	+	0.279791i	$0.0902651\pi$
$98$	−3.23607			−0.326892
$99$		0			0
$100$	−3.00000			−0.300000
$101$	2.74064	−	1.22021i	0.272704	−	0.121415i	−0.265829	−	0.964020i	$-0.585646\pi$
$101$	2.74064	−	1.22021i	0.272704	−	0.121415i	0.538532	+	0.842605i	$0.318979\pi$
$102$		0			0
$103$	−4.01478	+	4.45887i	−0.395588	+	0.439345i	−0.907729	−	0.419556i	$-0.862186\pi$
$103$	−4.01478	+	4.45887i	−0.395588	+	0.439345i	0.512141	+	0.858901i	$0.328852\pi$
$104$	12.7387	+	5.67165i	1.24913	+	0.556151i
$105$		0			0
$106$	11.6833	+	2.48335i	1.13478	+	0.241205i
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−1.81184	+	0.958572i	−0.172752	+	0.0913963i
$111$		0			0
$112$	1.52218	−	14.4825i	0.143832	−	1.36847i
$113$	−12.4305	+	2.64218i	−1.16936	+	0.248556i	−0.751362	−	0.659891i	$-0.770603\pi$
$113$	−12.4305	+	2.64218i	−1.16936	+	0.248556i	−0.418001	+	0.908446i	$0.637269\pi$
$114$		0			0
$115$	−0.218482	−	2.07872i	−0.0203736	−	0.193842i
$116$	−2.23607	+	1.62460i	−0.207614	+	0.150840i
$117$		0			0
$118$	−2.66312	+	8.19624i	−0.245160	+	0.754525i
$119$	1.69381	−	0.754131i	0.155271	−	0.0691311i
$120$		0			0
$121$	6.18878	−	9.09390i	0.562617	−	0.826718i
$122$	0.927051	+	1.60570i	0.0839313	+	0.145373i
$123$		0			0
$124$	−1.59385	−	1.77015i	−0.143132	−	0.158964i
$125$	−1.16312	−	3.57971i	−0.104033	−	0.320179i
$126$		0			0
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	−0.878934	−	0.476944i	$-0.841745\pi$
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	0.181995	+	0.983299i	$0.441745\pi$
$128$	13.3204	+	2.83135i	1.17737	+	0.250258i
$129$		0			0
$130$	0.402863	−	3.83299i	0.0353335	−	0.336175i
$131$	−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
$137$	−0.153880	−	1.46407i	−0.0131469	−	0.125084i	0.985980	−	0.166864i	$-0.0533640\pi$
$137$	−0.153880	−	1.46407i	−0.0131469	−	0.125084i	−0.999127	+	0.0417795i	$0.986697\pi$
$138$		0			0
$139$	3.91716	−	4.35045i	0.332249	−	0.369000i	−0.553753	−	0.832681i	$-0.686805\pi$
$139$	3.91716	−	4.35045i	0.332249	−	0.369000i	0.886002	+	0.463681i	$0.153472\pi$
$140$	−0.692728	+	0.147244i	−0.0585462	+	0.0124444i
$141$		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
$146$	−1.33826	−	1.48629i	−0.110755	−	0.123006i
$147$		0			0
$148$	−2.39169	−	1.06485i	−0.196596	−	0.0875302i
$149$	−13.7032	−	6.10105i	−1.12261	−	0.499817i	−0.240399	−	0.970674i	$-0.577278\pi$
$149$	−13.7032	−	6.10105i	−1.12261	−	0.499817i	−0.882210	+	0.470857i	$0.843945\pi$
$150$		0			0
$151$	1.33826	+	1.48629i	0.108906	+	0.120953i	0.795133	−	0.606435i	$-0.207401\pi$
$151$	1.33826	+	1.48629i	0.108906	+	0.120953i	−0.686227	+	0.727388i	$0.740734\pi$
$152$	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
$157$	−9.49606	+	2.01845i	−0.757868	+	0.161090i	−0.570610	−	0.821221i	$-0.693293\pi$
$157$	−9.49606	+	2.01845i	−0.757868	+	0.161090i	−0.187258	+	0.982311i	$0.559960\pi$
$158$	−0.571506	+	0.634721i	−0.0454666	+	0.0504957i
$159$		0			0
$160$	−0.135029	−	1.28472i	−0.0106750	−	0.101566i
$161$	5.07295	+	15.6129i	0.399804	+	1.23047i
$162$		0			0
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.954914	−	0.296882i	$-0.0959467\pi$
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.0127336	+	0.999919i	$0.495947\pi$
$164$	1.83688	−	3.18157i	0.143436	−	0.248439i
$165$		0			0
$166$	10.2812	+	17.8075i	0.797972	+	1.38213i
$167$	−1.98964	+	18.9302i	−0.153963	+	1.46486i	0.595789	+	0.803141i	$0.296840\pi$
$167$	−1.98964	+	18.9302i	−0.153963	+	1.46486i	−0.749752	+	0.661719i	$0.769827\pi$
$168$		0			0
$169$	−25.3228	−	5.38253i	−1.94791	−	0.414041i
$170$	0.309017	−	0.224514i	0.0237005	−	0.0172194i
$171$		0			0
$172$	0.336881	+	1.03681i	0.0256869	+	0.0790563i
$173$	−11.7888	−	13.0928i	−0.896283	−	0.995423i	−1.00000		0.000816499i	$-0.999740\pi$
$173$	−11.7888	−	13.0928i	−0.896283	−	0.995423i	0.103716	−	0.994607i	$-0.466927\pi$
$174$		0			0
$175$	7.28115	+	12.6113i	0.550403	+	0.953327i
$176$	8.97496	+	13.3655i	0.676513	+	1.00746i
$177$		0			0
$178$	14.0012	−	6.23374i	1.04944	−	0.467239i
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$		0			0
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$	3.16413	+	30.1047i	0.234541	+	2.23151i
$183$		0			0
$184$	−11.9687	+	2.54402i	−0.882343	+	0.187548i
$185$	0.169131	−	1.60917i	0.0124347	−	0.118309i
$186$		0			0
$187$	−0.902375	+	1.84047i	−0.0659882	+	0.134589i
$188$	0.381966			0.0278577
$189$		0			0
$190$	0.163119	−	0.502029i	0.0118339	−	0.0364210i
$191$	1.43997	+	0.306074i	0.104192	+	0.0221468i	0.259713	−	0.965686i	$-0.416372\pi$
$191$	1.43997	+	0.306074i	0.104192	+	0.0221468i	−0.155520	+	0.987833i	$0.549705\pi$
$192$		0			0
$193$	1.42724	+	0.635447i	0.102735	+	0.0457405i	0.457461	−	0.889230i	$-0.348759\pi$
$193$	1.42724	+	0.635447i	0.102735	+	0.0457405i	−0.354726	+	0.934970i	$0.615426\pi$
$194$	−16.2774	+	18.0779i	−1.16865	+	1.29792i
$195$		0			0
$196$	1.12920	−	0.502754i	0.0806574	−	0.0359110i
$197$	−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	$0.537223\pi$
$200$	−9.91572	+	4.41476i	−0.701147	+	0.312171i
$201$		0			0
$202$	−3.24803	+	3.60730i	−0.228530	+	0.253809i
$203$	12.2565	+	5.45694i	0.860238	+	0.383002i
$204$		0			0
$205$	2.22089	+	0.472066i	0.155114	+	0.0329705i
$206$	3.00000	−	9.23305i	0.209020	−	0.643297i
$207$		0			0
$208$	−30.2705			−2.09888
$209$	0.486130	+	2.79071i	0.0336263	+	0.193038i
$210$		0			0
$211$	−1.17809	+	11.2088i	−0.0811030	+	0.771643i	0.876081	+	0.482164i	$0.160149\pi$
$211$	−1.17809	+	11.2088i	−0.0811030	+	0.771643i	−0.957184	+	0.289480i	$0.906518\pi$
$212$	−4.46261	+	0.948557i	−0.306493	+	0.0651471i
$213$		0			0
$214$	−0.0399263	−	0.379874i	−0.00272931	−	0.0259676i
$215$	−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
$220$	0.483306	−	0.615974i	0.0325845	−	0.0415290i
$221$	−1.92705	−	3.33775i	−0.129627	−	0.224521i
$222$		0			0
$223$	−8.50345	−	9.44404i	−0.569433	−	0.632419i	0.387798	−	0.921744i	$-0.373236\pi$
$223$	−8.50345	−	9.44404i	−0.569433	−	0.632419i	−0.957231	+	0.289325i	$0.906569\pi$
$224$	3.13525	+	9.64932i	0.209483	+	0.644722i
$225$		0			0
$226$	16.6353	−	12.0862i	1.10656	−	0.803963i
$227$	10.6506	+	2.26386i	0.706905	+	0.150257i	0.547316	−	0.836926i	$-0.315650\pi$
$227$	10.6506	+	2.26386i	0.706905	+	0.150257i	0.159589	+	0.987183i	$0.448983\pi$
$228$		0			0
$229$	−1.04528	+	9.94522i	−0.0690744	+	0.657199i	0.904130	+	0.427257i	$0.140520\pi$
$229$	−1.04528	+	9.94522i	−0.0690744	+	0.657199i	−0.973204	+	0.229941i	$0.926147\pi$
$230$	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	0.793419	−	0.608676i	$-0.208299\pi$
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	−0.333705	+	0.942677i	$0.608299\pi$
$234$		0			0
$235$	0.0729490	+	0.224514i	0.00475867	+	0.0146457i
$236$	−0.344086	−	3.27376i	−0.0223981	−	0.213104i
$237$		0			0
$238$	−2.00739	+	2.22943i	−0.130120	+	0.144513i
$239$	−17.1785	+	3.65141i	−1.11119	+	0.236190i	−0.726710	−	0.686945i	$-0.758951\pi$
$239$	−17.1785	+	3.65141i	−1.11119	+	0.236190i	−0.384477	+	0.923135i	$0.625618\pi$
$240$		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
$245$	0.511170	+	0.567712i	0.0326575	+	0.0362698i
$246$		0			0
$247$	−4.86576	−	2.16638i	−0.309601	−	0.137843i
$248$	−7.87297	−	3.50527i	−0.499934	−	0.222585i
$249$		0			0
$250$	4.07512	+	4.52588i	0.257733	+	0.286242i
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	0.927287	−	0.374352i	$-0.122135\pi$
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	−0.0694827	+	0.997583i	$0.522135\pi$
$252$		0			0
$253$	−15.3713	−	9.64932i	−0.966387	−	0.606648i
$254$	7.85410	−	13.6037i	0.492810	−	0.853572i
$255$		0			0
$256$	−13.2659	+	2.81976i	−0.829121	+	0.176235i
$257$	18.2848	−	20.3074i	1.14058	−	1.26674i	0.181562	−	0.983380i	$-0.441885\pi$
$257$	18.2848	−	20.3074i	1.14058	−	1.26674i	0.959014	−	0.283358i	$-0.0914486\pi$
$258$		0			0
$259$	1.32837	+	12.6386i	0.0825408	+	0.785324i
$260$	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
$266$	−0.433364	+	4.12319i	−0.0265713	+	0.252809i
$267$		0			0
$268$	−6.38521	−	1.35722i	−0.390039	−	0.0829054i
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.212161	−	0.977235i	$-0.431950\pi$
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.994967	+	0.100205i	$0.0319498\pi$
$270$		0			0
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	0.992502	−	0.122229i	$-0.0390043\pi$
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	−0.874795	+	0.484493i	$0.839004\pi$
$272$	−2.00739	−	2.22943i	−0.121716	−	0.135179i
$273$		0			0
$274$	1.19098	+	2.06284i	0.0719499	+	0.124621i
$275$	−15.1169	−	5.53753i	−0.911584	−	0.333926i
$276$		0			0
$277$	9.53531	−	4.24539i	0.572921	−	0.255081i	−0.0997623	−	0.995011i	$-0.531808\pi$
$277$	9.53531	−	4.24539i	0.572921	−	0.255081i	0.672683	+	0.739930i	$0.265142\pi$
$278$	−2.92705	+	9.00854i	−0.175553	+	0.540296i
$279$		0			0
$280$	−2.07295	+	1.50609i	−0.123882	+	0.0900058i
$281$	−0.547318	−	5.20738i	−0.0326503	−	0.310647i	−0.998643	−	0.0520775i	$-0.983416\pi$
$281$	−0.547318	−	5.20738i	−0.0326503	−	0.310647i	0.965993	−	0.258569i	$-0.0832509\pi$
$282$		0			0
$283$	21.6956	−	4.61155i	1.28967	−	0.274128i	0.488501	−	0.872563i	$-0.337544\pi$
$283$	21.6956	−	4.61155i	1.28967	−	0.274128i	0.801171	+	0.598435i	$0.204211\pi$
$284$	0.940756	−	8.95070i	0.0558236	−	0.531126i
$285$		0			0
$286$	−24.0248	−	23.2967i	−1.42062	−	1.37756i
$287$	−17.8328			−1.05264
$288$		0			0
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$	2.70353	+	0.574654i	0.158757	+	0.0337448i
$291$		0			0
$292$	0.697887	+	0.310719i	0.0408407	+	0.0181835i
$293$	−12.0071	+	13.3352i	−0.701460	+	0.779050i	−0.983608	−	0.180321i	$-0.942286\pi$
$293$	−12.0071	+	13.3352i	−0.701460	+	0.779050i	0.282148	+	0.959371i	$0.408953\pi$
$294$		0			0
$295$	1.85856	−	0.827482i	0.108209	−	0.0481779i
$296$	−9.47214			−0.550557
$297$		0			0
$298$	24.2705			1.40595
$299$	31.1744	−	13.8797i	1.80286	−	0.802686i
$300$		0			0
$301$	3.54090	−	3.93257i	0.204094	−	0.226670i
$302$	−2.95630	−	1.31623i	−0.170116	−	0.0757404i
$303$		0			0
$304$	−4.05530	−	0.861981i	−0.232587	−	0.0494380i
$305$	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	$0.688523\pi$
$308$	−2.70713	+	5.52142i	−0.154253	+	0.314612i
$309$		0			0
$310$	−0.248983	+	2.36892i	−0.0141413	+	0.134545i
$311$	11.2214	−	2.38519i	0.636310	−	0.135252i	0.121549	−	0.992585i	$-0.461214\pi$
$311$	11.2214	−	2.38519i	0.636310	−	0.135252i	0.514761	+	0.857334i	$0.327881\pi$
$312$		0			0
$313$	2.90932	+	27.6803i	0.164445	+	1.56459i	0.696300	+	0.717751i	$0.254828\pi$
$313$	2.90932	+	27.6803i	0.164445	+	1.56459i	−0.531856	+	0.846835i	$0.678505\pi$
$314$	12.7082	−	9.23305i	0.717165	−	0.521051i
$315$		0			0
$316$	0.100813	−	0.310271i	0.00567118	−	0.0174541i
$317$	−23.1681	+	10.3151i	−1.30125	+	0.579355i	−0.936146	−	0.351611i	$-0.885634\pi$
$317$	−23.1681	+	10.3151i	−1.30125	+	0.579355i	−0.365106	+	0.930966i	$0.618967\pi$
$318$		0			0
$319$	−14.2662	+	4.05887i	−0.798756	+	0.227253i
$320$	−0.809017	−	1.40126i	−0.0452254	−	0.0783327i
$321$		0			0
$322$	−17.7737	−	19.7396i	−0.990487	−	1.10005i
$323$	−0.163119	−	0.502029i	−0.00907618	−	0.0279336i
$324$		0			0
$325$	24.4894	−	17.7926i	1.35843	−	0.986954i
$326$	−24.1683	−	5.13712i	−1.33856	−	0.284519i
$327$		0			0
$328$	1.38937	−	13.2190i	0.0767152	−	0.729896i
$329$	−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
$335$	−0.421714	−	4.01234i	−0.0230407	−	0.219218i
$336$		0			0
$337$	−9.17258	+	10.1872i	−0.499662	+	0.554931i	−0.939235	−	0.343276i	$-0.888463\pi$
$337$	−9.17258	+	10.1872i	−0.499662	+	0.554931i	0.439572	+	0.898207i	$0.355130\pi$
$338$	40.9732	−	8.70912i	2.22865	−	0.473714i
$339$		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
$344$	2.63923	+	2.93117i	0.142298	+	0.158038i
$345$		0			0
$346$	26.0421	+	11.5947i	1.40003	+	0.623333i
$347$	2.79155	+	1.24288i	0.149858	+	0.0667211i	0.480295	−	0.877107i	$-0.340530\pi$
$347$	2.79155	+	1.24288i	0.149858	+	0.0667211i	−0.330437	+	0.943828i	$0.607196\pi$
$348$		0			0
$349$	20.1573	+	22.3869i	1.07900	+	1.19835i	0.979107	+	0.203347i	$0.0651821\pi$
$349$	20.1573	+	22.3869i	1.07900	+	1.19835i	0.0998889	+	0.994999i	$0.468151\pi$
$350$	−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
$355$	5.44076	−	1.15647i	0.288765	−	0.0613790i
$356$	−3.91716	+	4.35045i	−0.207609	+	0.230573i
$357$		0			0
$358$	−0.378188	−	3.59821i	−0.0199878	−	0.190172i
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$		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
$365$	−0.0493516	+	0.469550i	−0.00258318	+	0.0245773i
$366$		0			0
$367$	14.2441	+	3.02767i	0.743535	+	0.158043i	0.564077	−	0.825722i	$-0.309232\pi$
$367$	14.2441	+	3.02767i	0.743535	+	0.158043i	0.179458	+	0.983766i	$0.442565\pi$
$368$	21.4894	−	15.6129i	1.12021	−	0.813880i
$369$		0			0
$370$	0.809017	+	2.48990i	0.0420588	+	0.129444i
$371$	14.8185	+	16.4576i	0.769338	+	0.854437i
$372$		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	$-0.363747\pi$
$374$	0.122602	−	3.31436i	0.00633962	−	0.171381i
$375$		0			0
$376$	1.26249	−	0.562096i	0.0651079	−	0.0289879i
$377$	8.61803	−	26.5236i	0.443851	−	1.36603i
$378$		0			0
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.992271	−	0.124089i	$-0.960399\pi$
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.188613	+	0.982052i	$0.560399\pi$
$380$	0.0210757	+	0.200522i	0.00108116	+	0.0102865i
$381$		0			0
$382$	−2.32991	+	0.495239i	−0.119209	+	0.0253386i
$383$	−0.929106	+	8.83985i	−0.0474751	+	0.451695i	0.944801	+	0.327645i	$0.106255\pi$
$383$	−0.929106	+	8.83985i	−0.0474751	+	0.451695i	−0.992276	+	0.124050i	$0.960412\pi$
$384$		0			0
$385$	−3.76243	−	0.536711i	−0.191751	−	0.0273533i
$386$	−2.52786			−0.128665
$387$		0			0
$388$	2.87132	−	8.83702i	0.145769	−	0.448632i
$389$	−9.06793	−	1.92745i	−0.459762	−	0.0977255i	−0.0277927	−	0.999614i	$-0.508848\pi$
$389$	−9.06793	−	1.92745i	−0.459762	−	0.0977255i	−0.431969	+	0.901888i	$0.642181\pi$
$390$		0			0
$391$	3.08958	+	1.37557i	0.156247	+	0.0695655i
$392$	2.99244	−	3.32344i	0.151141	−	0.167859i
$393$		0			0
$394$	39.3454	−	17.5177i	1.98219	−	0.882529i
$395$	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	$0.718868\pi$
$398$	4.86576	−	2.16638i	0.243899	−	0.108591i
$399$		0			0
$400$	15.7663	−	17.5102i	0.788313	−	0.875510i
$401$	13.6208	+	6.06437i	0.680191	+	0.302840i	0.717596	−	0.696460i	$-0.245243\pi$
$401$	13.6208	+	6.06437i	0.680191	+	0.302840i	−0.0374052	+	0.999300i	$0.511909\pi$
$402$		0			0
$403$	23.5092	+	4.99704i	1.17108	+	0.248920i
$404$	0.572949	−	1.76336i	0.0285053	−	0.0877302i
$405$		0			0
$406$	−21.7082			−1.07736
$407$	−10.0861	−	9.78044i	−0.499951	−	0.484799i
$408$		0			0
$409$	3.02550	−	28.7857i	0.149601	−	1.42336i	−0.619882	−	0.784695i	$-0.712820\pi$
$409$	3.02550	−	28.7857i	0.149601	−	1.42336i	0.769483	−	0.638667i	$-0.220514\pi$
$410$	−3.59348	+	0.763818i	−0.177469	+	0.0377223i
$411$		0			0
$412$	0.387613	+	3.68789i	0.0190963	+	0.181689i
$413$	−12.9271	+	9.39205i	−0.636099	+	0.462153i
$414$		0			0
$415$	1.50000	−	4.61653i	0.0736321	−	0.226616i
$416$	19.2668	−	8.57814i	0.944634	−	0.420578i
$417$		0			0
$418$	−2.55518	−	3.80515i	−0.124978	−	0.186116i
$419$	−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
$421$	−2.49552	−	2.77155i	−0.121624	−	0.135077i	0.679257	−	0.733900i	$-0.262302\pi$
$421$	−2.49552	−	2.77155i	−0.121624	−	0.135077i	−0.800881	+	0.598823i	$0.795635\pi$
$422$	−5.63525	−	17.3435i	−0.274320	−	0.844270i
$423$		0			0
$424$	−13.3541	+	9.70232i	−0.648533	+	0.471186i
$425$	2.93444	+	0.623735i	0.142341	+	0.0302556i
$426$		0			0
$427$	−0.359337	+	3.41886i	−0.0173895	+	0.165450i
$428$	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	0.558306	−	0.829635i	$-0.311451\pi$
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	−0.616503	+	0.787352i	$0.711451\pi$
$432$		0			0
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$	−1.95554	−	18.6057i	−0.0938689	−	0.893103i
$435$		0			0
$436$		0			0
$437$	4.57163	−	0.971730i	0.218691	−	0.0464841i
$438$		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
$443$	0.585749	+	0.650540i	0.0278298	+	0.0309081i	0.756899	−	0.653532i	$-0.226713\pi$
$443$	0.585749	+	0.650540i	0.0278298	+	0.0309081i	−0.729069	+	0.684440i	$0.760047\pi$
$444$		0			0
$445$	−3.30524	−	1.47159i	−0.156683	−	0.0697599i
$446$	18.7846	+	8.36344i	0.889477	+	0.396021i
$447$		0			0
$448$	8.50345	+	9.44404i	0.401750	+	0.446189i
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	0.250483	−	0.968121i	$-0.419411\pi$
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	−0.843334	+	0.537389i	$0.819411\pi$
$450$		0			0
$451$	15.1287	−	12.6412i	0.712382	−	0.595253i
$452$	−3.92705	+	6.80185i	−0.184713	+	0.319932i
$453$		0			0
$454$	−17.2330	+	3.66300i	−0.808787	+	0.171913i
$455$	4.78154	−	5.31044i	0.224162	−	0.248957i
$456$		0			0
$457$	−3.42836	−	32.6187i	−0.160372	−	1.52584i	−0.718174	−	0.695864i	$-0.755022\pi$
$457$	−3.42836	−	32.6187i	−0.160372	−	1.52584i	0.557801	−	0.829974i	$-0.311645\pi$
$458$	−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	$0.898873\pi$
$464$	2.26913	−	21.5893i	0.105341	−	1.00226i
$465$		0			0
$466$	−13.7278	−	2.91792i	−0.635926	−	0.135170i
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	−0.821461	−	0.570264i	$-0.806841\pi$
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	0.288508	+	0.957478i	$0.406841\pi$
$468$		0			0
$469$	9.79180	+	30.1360i	0.452143	+	1.39155i
$470$	−0.255585	−	0.283856i	−0.0117893	−	0.0130933i
$471$		0			0
$472$	−5.95492	−	10.3142i	−0.274097	−	0.474750i
$473$	−0.216262	+	5.84630i	−0.00994375	+	0.268813i
$474$		0			0
$475$	3.78747	−	1.68629i	0.173781	−	0.0773722i
$476$	0.354102	−	1.08981i	0.0162302	−	0.0499515i
$477$		0			0
$478$	22.9894	−	16.7027i	1.05151	−	0.763966i
$479$	−1.76756	−	16.8172i	−0.0807618	−	0.768397i	−0.957695	−	0.287785i	$-0.907081\pi$
$479$	−1.76756	−	16.8172i	−0.0807618	−	0.768397i	0.876933	−	0.480612i	$-0.159586\pi$
$480$		0			0
$481$	25.8391	−	5.49228i	1.17816	−	0.250426i
$482$	2.89630	−	27.5564i	0.131923	−	1.25516i
$483$		0			0
$484$	−1.61738	−	6.60318i	−0.0735173	−	0.300144i
$485$	5.74265			0.260760
$486$		0			0
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	−0.163540	−	0.986537i	$-0.552291\pi$
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	0.712179	−	0.701998i	$-0.247709\pi$
$488$	−2.50631	−	0.532733i	−0.113455	−	0.0241157i
$489$		0			0
$490$	−1.12920	−	0.502754i	−0.0510122	−	0.0227121i
$491$	17.5411	−	19.4814i	0.791619	−	0.879182i	−0.203376	−	0.979101i	$-0.565191\pi$
$491$	17.5411	−	19.4814i	0.791619	−	0.879182i	0.994996	+	0.0999183i	$0.0318581\pi$
$492$		0			0
$493$	2.52498	−	1.12419i	0.113719	−	0.0506311i
$494$	8.61803			0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	−39.9100	+	17.7691i	−1.79021	+	0.797052i
$498$		0			0
$499$	1.71452	−	1.90416i	0.0767523	−	0.0852421i	−0.703545	−	0.710650i	$-0.748401\pi$
$499$	1.71452	−	1.90416i	0.0767523	−	0.0852421i	0.780298	+	0.625408i	$0.215068\pi$
$500$	−2.12512	−	0.946166i	−0.0950384	−	0.0423138i
$501$		0			0
$502$	−26.5864	−	5.65111i	−1.18661	−	0.252221i
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	−0.498574	−	0.866847i	$-0.666143\pi$
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	0.912875	−	0.408239i	$-0.133857\pi$
$504$		0			0
$505$	1.14590			0.0509918
$506$	29.0714	+	4.14704i	1.29238	+	0.184359i
$507$		0			0
$508$	−0.627171	+	5.96713i	−0.0278262	+	0.264749i
$509$	20.9147	−	4.44556i	0.927029	−	0.197046i	0.280428	−	0.959875i	$-0.409524\pi$
$509$	20.9147	−	4.44556i	0.927029	−	0.197046i	0.646600	+	0.762829i	$0.276190\pi$
$510$		0			0
$511$	−0.387613	−	3.68789i	−0.0171470	−	0.163143i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$		0			0
$514$	−13.6631	+	42.0508i	−0.602654	+	1.85478i
$515$	−2.09366	+	0.932157i	−0.0922577	+	0.0410758i
$516$		0			0
$517$	1.92472	+	0.705050i	0.0846489	+	0.0310081i
$518$	−10.2812	−	17.8075i	−0.451728	−	0.782416i
$519$		0			0
$520$	3.56395	+	3.95817i	0.156289	+	0.173577i
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	−0.762869	−	0.646553i	$-0.776210\pi$
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	0.237139	−	0.971476i	$-0.423790\pi$
$522$		0			0
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.997422	−	0.0717533i	$-0.977141\pi$
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.239979	+	0.970778i	$0.577141\pi$
$524$	−8.37520	−	1.78020i	−0.365872	−	0.0777686i
$525$		0			0
$526$	0.113954	−	1.08420i	0.00496862	−	0.0472733i
$527$	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
$533$	3.87475	+	36.8658i	0.167834	+	1.59684i
$534$		0			0
$535$	−0.0603355	+	0.0670093i	−0.00260853	+	0.00289707i
$536$	−23.1019	+	4.91047i	−0.997851	+	0.212100i
$537$		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	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$	−6.78893	−	7.53987i	−0.291610	−	0.323865i
$543$		0			0
$544$	1.90947	+	0.850149i	0.0818676	+	0.0364498i
$545$		0			0
$546$		0			0
$547$	12.9691	+	14.4036i	0.554517	+	0.615854i	0.953606	−	0.301059i	$-0.0973400\pi$
$547$	12.9691	+	14.4036i	0.554517	+	0.615854i	−0.399088	+	0.916912i	$0.630673\pi$
$548$	−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
$553$	−1.54899	+	0.329247i	−0.0658696	+	0.0140010i
$554$	−11.3006	+	12.5506i	−0.480118	+	0.533225i
$555$		0			0
$556$	−0.378188	−	3.59821i	−0.0160387	−	0.152598i
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	−0.963373	−	0.268164i	$-0.913583\pi$
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	0.621762	−	0.783206i	$-0.286417\pi$
$558$		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
$563$	2.81062	−	26.7412i	0.118453	−	1.12701i	−0.760247	−	0.649635i	$-0.774922\pi$
$563$	2.81062	−	26.7412i	0.118453	−	1.12701i	0.878700	−	0.477374i	$-0.158411\pi$
$564$		0			0
$565$	−4.74803	−	1.00922i	−0.199751	−	0.0424584i
$566$	−29.0344	+	21.0948i	−1.22041	+	0.886679i
$567$		0			0
$568$	−10.0623	−	30.9686i	−0.422205	−	1.29941i
$569$	−22.7965	−	25.3181i	−0.955680	−	1.06139i	−0.998058	−	0.0622889i	$-0.980160\pi$
$569$	−22.7965	−	25.3181i	−0.955680	−	1.06139i	0.0423778	−	0.999102i	$-0.486507\pi$
$570$		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	$0.652709\pi$
$572$	12.0027	+	4.39674i	0.501856	+	0.183837i
$573$		0			0
$574$	26.3595	−	11.7360i	1.10023	−	0.489852i
$575$	−8.20820	+	25.2623i	−0.342306	+	1.05351i
$576$		0			0
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	−0.814016	−	0.580842i	$-0.802723\pi$
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	0.300868	+	0.953666i	$0.402723\pi$
$578$	−2.81062	−	26.7412i	−0.116906	−	1.11229i
$579$		0			0
$580$	−1.03266	+	0.219498i	−0.0428788	+	0.00911417i
$581$	−3.98511	+	37.9158i	−0.165330	+	1.57301i
$582$		0			0
$583$	−24.2378	−	3.45753i	−1.00383	−	0.143196i
$584$	2.76393			0.114372
$585$		0			0
$586$	8.97214	−	27.6134i	0.370636	−	1.14070i
$587$	23.7738	+	5.05328i	0.981251	+	0.208571i	0.670491	−	0.741917i	$-0.266083\pi$
$587$	23.7738	+	5.05328i	0.981251	+	0.208571i	0.310760	+	0.950489i	$0.399417\pi$
$588$		0			0
$589$	3.00721	+	1.33889i	0.123910	+	0.0551682i
$590$	−2.20264	+	2.44628i	−0.0906813	+	0.100712i
$591$		0			0
$592$	18.7846	−	8.36344i	0.772042	−	0.343735i
$593$	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
$596$	−8.46903	+	3.77066i	−0.346905	+	0.154452i
$597$		0			0
$598$	−36.9459	+	41.0326i	−1.51083	+	1.67795i
$599$	19.8314	+	8.82952i	0.810290	+	0.360764i	0.769695	−	0.638411i	$-0.220408\pi$
$599$	19.8314	+	8.82952i	0.810290	+	0.360764i	0.0405948	+	0.999176i	$0.487075\pi$
$600$		0			0
$601$	19.3994	+	4.12347i	0.791319	+	0.168200i	0.585803	−	0.810454i	$-0.300779\pi$
$601$	19.3994	+	4.12347i	0.791319	+	0.168200i	0.205516	+	0.978654i	$0.434113\pi$
$602$	−2.64590	+	8.14324i	−0.107839	+	0.331894i
$603$		0			0
$604$	1.23607			0.0502949
$605$	3.57236	−	2.21177i	0.145237	−	0.0899211i
$606$		0			0
$607$	0.243158	−	2.31349i	0.00986948	−	0.0939018i	−0.988478	−	0.151363i	$-0.951634\pi$
$607$	0.243158	−	2.31349i	0.00986948	−	0.0939018i	0.998348	+	0.0574610i	$0.0183005\pi$
$608$	2.82542	−	0.600562i	0.114586	−	0.0243560i
$609$		0			0
$610$	0.0740275	+	0.704324i	0.00299728	+	0.0285173i
$611$	−3.11803	+	2.26538i	−0.126142	+	0.0916476i
$612$		0			0
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$	28.9160	−	12.8742i	1.16695	−	0.519561i
$615$		0			0
$616$	−0.822442	+	22.2334i	−0.0331371	+	0.895809i
$617$	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
$619$	−20.8637	−	23.1715i	−0.838584	−	0.931342i	0.159858	−	0.987140i	$-0.448896\pi$
$619$	−20.8637	−	23.1715i	−0.838584	−	0.931342i	−0.998442	+	0.0557984i	$0.982230\pi$
$620$	−0.281153	−	0.865300i	−0.0112914	−	0.0347513i
$621$		0			0
$622$	−15.0172	+	10.9106i	−0.602136	+	0.437477i
$623$	27.7954	+	5.90810i	1.11360	+	0.236703i
$624$		0			0
$625$	−2.38668	+	22.7077i	−0.0954672	+	0.908309i
$626$	−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	0.998319	−	0.0579577i	$-0.0184589\pi$
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	−0.841724	+	0.539908i	$0.818459\pi$
$632$	−0.123379	−	1.17387i	−0.00490776	−	0.0466942i
$633$		0			0
$634$	27.4574	−	30.4945i	1.09047	−	1.21109i
$635$	−3.62717	+	0.770979i	−0.143940	+	0.0305954i
$636$		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
$641$	4.51171	+	5.01076i	0.178202	+	0.197913i	0.825628	−	0.564215i	$-0.190821\pi$
$641$	4.51171	+	5.01076i	0.178202	+	0.197913i	−0.647426	+	0.762128i	$0.724154\pi$
$642$		0			0
$643$	−16.8437	−	7.49929i	−0.664250	−	0.295743i	0.0467798	−	0.998905i	$-0.485104\pi$
$643$	−16.8437	−	7.49929i	−0.664250	−	0.295743i	−0.711029	+	0.703162i	$0.751771\pi$
$644$	9.26874	+	4.12671i	0.365239	+	0.162615i
$645$		0			0
$646$	0.571506	+	0.634721i	0.0224856	+	0.0249728i
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	0.637535	−	0.770421i	$-0.279954\pi$
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	−0.535705	+	0.844405i	$0.679954\pi$
$648$		0			0
$649$	4.30902	−	17.1315i	0.169144	−	0.672471i
$650$	−24.4894	+	42.4168i	−0.960552	+	1.66372i
$651$		0			0
$652$	9.23146	−	1.96221i	0.361532	−	0.0768460i
$653$	−14.6978	+	16.3236i	−0.575170	+	0.638791i	−0.958592	−	0.284782i	$-0.908079\pi$
$653$	−14.6978	+	16.3236i	−0.575170	+	0.638791i	0.383422	+	0.923573i	$0.374746\pi$
$654$		0			0
$655$	−0.553143	−	5.26281i	−0.0216131	−	0.205635i
$656$	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	$0.698807\pi$
$662$	−3.82180	+	36.3620i	−0.148539	+	1.41325i
$663$		0			0
$664$	−27.7954	−	5.90810i	−1.07867	−	0.229279i
$665$	0.791796	−	0.575274i	0.0307045	−	0.0223082i
$666$		0			0
$667$	7.56231	+	23.2744i	0.292814	+	0.901188i
$668$	7.87161	+	8.74231i	0.304562	+	0.338250i
$669$		0			0
$670$	3.26393	+	5.65330i	0.126097	+	0.218406i
$671$	−2.11870	−	3.15516i	−0.0817915	−	0.121803i
$672$		0			0
$673$	−13.1700	+	5.86368i	−0.507668	+	0.226028i	−0.644554	−	0.764558i	$-0.722957\pi$
$673$	−13.1700	+	5.86368i	−0.507668	+	0.226028i	0.136887	+	0.990587i	$0.456290\pi$
$674$	6.85410	−	21.0948i	0.264010	−	0.812540i
$675$		0			0
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	2.34898	+	22.3490i	0.0902786	+	0.858943i	0.942150	+	0.335192i	$0.108801\pi$
$677$	2.34898	+	22.3490i	0.0902786	+	0.858943i	−0.851871	+	0.523751i	$0.824532\pi$
$678$		0			0
$679$	−44.1177	+	9.37751i	−1.69308	+	0.359876i
$680$	−0.0551768	+	0.524972i	−0.00211593	+	0.0201318i
$681$		0			0
$682$	14.8481	+	14.3981i	0.568565	+	0.551333i
$683$	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
$686$	−23.7401	−	5.04612i	−0.906403	−	0.192662i
$687$		0			0
$688$	−7.82206	−	3.48260i	−0.298213	−	0.132773i
$689$	30.8031	−	34.2103i	1.17350	−	1.30331i
$690$		0			0
$691$	−36.2752	+	16.1508i	−1.37998	+	0.614405i	−0.956561	−	0.291531i	$-0.905835\pi$
$691$	−36.2752	+	16.1508i	−1.37998	+	0.614405i	−0.423414	+	0.905936i	$0.639169\pi$
$692$	−10.8885			−0.413920
$693$		0			0
$694$	−4.94427			−0.187682
$695$	2.04275	−	0.909491i	0.0774859	−	0.0344990i
$696$		0			0
$697$	−2.45823	+	2.73014i	−0.0931120	+	0.103411i
$698$	−44.5286	−	19.8254i	−1.68543	−	0.750403i
$699$		0			0
$700$	8.80333	+	1.87121i	0.332735	+	0.0707249i
$701$	−15.3541	+	47.2551i	−0.579916	+	1.78480i	0.0388752	+	0.999244i	$0.487623\pi$
$701$	−15.3541	+	47.2551i	−0.579916	+	1.78480i	−0.618792	+	0.785555i	$0.712377\pi$
$702$		0			0
$703$	3.61803			0.136457
$704$	−13.9086	−	1.98407i	−0.524202	−	0.0747775i
$705$		0			0
$706$	0.258409	−	2.45859i	0.00972533	−	0.0925304i
$707$	−8.80333	+	1.87121i	−0.331083	+	0.0703739i
$708$		0			0
$709$	−0.654072	−	6.22308i	−0.0245642	−	0.233713i	−0.999915	−	0.0130519i	$-0.995845\pi$
$709$	−0.654072	−	6.22308i	−0.0245642	−	0.233713i	0.975351	−	0.220661i	$-0.0708213\pi$
$710$	−7.28115	+	5.29007i	−0.273257	+	0.198533i
$711$		0			0
$712$	−6.54508	+	20.1437i	−0.245287	+	0.754917i
$713$	−19.2668	+	8.57814i	−0.721548	+	0.321254i
$714$		0			0
$715$	−0.292035	+	7.89469i	−0.0109215	+	0.295245i
$716$	0.690983	+	1.19682i	0.0258232	+	0.0447272i
$717$		0			0
$718$	−18.6611	−	20.7252i	−0.696425	−	0.773459i
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	0.970308	+	0.241873i	$0.0777618\pi$
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	−0.642826	+	0.766012i	$0.722238\pi$
$720$		0			0
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$	−28.9163	−	6.14635i	−1.07615	−	0.228743i
$723$		0			0
$724$	0.550918	−	5.24164i	0.0204747	−	0.194804i
$725$	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
$731$	−0.113954	−	1.08420i	−0.00421473	−	0.0401005i
$732$		0			0
$733$	−16.2544	+	18.0523i	−0.600369	+	0.666778i	−0.964350	−	0.264629i	$-0.914751\pi$
$733$	−16.2544	+	18.0523i	−0.600369	+	0.666778i	0.363981	+	0.931406i	$0.381417\pi$
$734$	−23.0474	+	4.89888i	−0.850696	+	0.180821i
$735$		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	0.893963	−	0.448142i	$-0.147914\pi$
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	−0.149958	+	0.988692i	$0.547914\pi$
$740$	−0.669131	−	0.743145i	−0.0245977	−	0.0273185i
$741$		0			0
$742$	−32.7349	−	14.5745i	−1.20174	−	0.535047i
$743$	−11.7113	−	5.21423i	−0.429647	−	0.191291i	0.180507	−	0.983574i	$-0.442226\pi$
$743$	−11.7113	−	5.21423i	−0.429647	−	0.191291i	−0.610155	+	0.792282i	$0.708893\pi$
$744$		0			0
$745$	−3.83378	−	4.25784i	−0.140459	−	0.155995i
$746$	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
$751$	51.7665	−	11.0033i	1.88899	−	0.401516i	0.890424	−	0.455131i	$-0.150408\pi$
$751$	51.7665	−	11.0033i	1.88899	−	0.401516i	0.998562	+	0.0536148i	$0.0170743\pi$
$752$	−2.00739	+	2.22943i	−0.0732020	+	0.0812991i
$753$		0			0
$754$	4.71681	+	44.8774i	0.171776	+	1.63434i
$755$	0.236068	+	0.726543i	0.00859139	+	0.0264416i
$756$		0			0
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	0.796985	−	0.603999i	$-0.206427\pi$
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	−0.328156	+	0.944624i	$0.606427\pi$
$758$	22.9894	−	39.8187i	0.835011	−	1.44628i
$759$		0			0
$760$	0.364745	+	0.631757i	0.0132307	+	0.0229162i
$761$	0.510992	−	4.86176i	0.0185234	−	0.176239i	−0.981349	−	0.192237i	$-0.938426\pi$
$761$	0.510992	−	4.86176i	0.0185234	−	0.176239i	0.999872	+	0.0159979i	$0.00509252\pi$
$762$		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
$767$	22.2250	+	24.6834i	0.802499	+	0.891266i
$768$		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	$0.503911\pi$
$770$	5.91464	−	1.68277i	0.213149	−	0.0606427i
$771$		0			0
$772$	0.882081	−	0.392728i	0.0317468	−	0.0141346i
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	0.167870	+	0.985809i	$0.446311\pi$
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	−0.715253	+	0.698865i	$0.753689\pi$
$774$		0			0
$775$	−15.1353	+	10.9964i	−0.543674	+	0.395003i
$776$	−3.51404	−	33.4339i	−0.126147	−	1.20021i
$777$		0			0
$778$	14.6722	−	3.11868i	0.526024	−	0.111810i
$779$	−0.530693	+	5.04920i	−0.0190140	+	0.180906i
$780$		0			0
$781$	21.2620	−	43.3658i	0.760816	−	1.55175i
$782$	−5.47214			−0.195683
$783$		0			0
$784$	−3.00000	+	9.23305i	−0.107143	+	0.329752i
$785$	−3.62717	−	0.770979i	−0.129459	−	0.0275174i
$786$		0			0
$787$	−21.6585	−	9.64300i	−0.772043	−	0.343736i	−0.0173805	−	0.999849i	$-0.505533\pi$
$787$	−21.6585	−	9.64300i	−0.772043	−	0.343736i	−0.754662	+	0.656113i	$0.772199\pi$
$788$	−11.0078	+	12.2254i	−0.392135	+	0.435511i
$789$		0			0
$790$	−0.298033	+	0.132693i	−0.0106035	+	0.00472100i
$791$	38.1246			1.35556
$792$		0			0
$793$	7.14590			0.253758
$794$	37.3850	−	16.6449i	1.32674	−	0.590705i
$795$		0			0
$796$	−1.36131	+	1.51188i	−0.0482503	+	0.0535873i
$797$	−13.9188	−	6.19707i	−0.493031	−	0.219511i	0.145133	−	0.989412i	$-0.453639\pi$
$797$	−13.9188	−	6.19707i	−0.493031	−	0.219511i	−0.638164	+	0.769901i	$0.720306\pi$
$798$		0			0
$799$	−0.373619	−	0.0794152i	−0.0132177	−	0.00280951i
$800$	−5.07295	+	15.6129i	−0.179356	+	0.552000i
$801$		0			0
$802$	−24.1246			−0.851870
$803$	2.94309	+	2.85390i	0.103859	+	0.100712i
$804$		0			0
$805$	−0.655447	+	6.23616i	−0.0231015	+	0.219796i
$806$	−38.0387	+	8.08538i	−1.33986	+	0.284795i
$807$		0			0
$808$	−0.701198	−	6.67146i	−0.0246681	−	0.234701i
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	−0.166134	−	0.986103i	$-0.553128\pi$
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	0.886502	+	0.462726i	$0.153128\pi$
$810$		0			0
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	−0.318477	−	0.947931i	$-0.603171\pi$
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	0.814833	−	0.579696i	$-0.196829\pi$
$812$	7.57493	−	3.37258i	0.265828	−	0.118354i
$813$		0			0
$814$	21.3454	+	7.81912i	0.748157	+	0.274060i
$815$	2.91641	+	5.05137i	0.102157	+	0.176942i
$816$		0			0
$817$	−1.00810	−	1.11961i	−0.0352689	−	0.0391700i
$818$	14.4721	+	44.5407i	0.506006	+	1.55733i
$819$		0			0
$820$	1.13525	−	0.824811i	0.0396448	−	0.0288036i
$821$	13.2868	+	2.82419i	0.463711	+	0.0985648i	0.433842	−	0.900989i	$-0.357158\pi$
$821$	13.2868	+	2.82419i	0.463711	+	0.0985648i	0.0298691	+	0.999554i	$0.490491\pi$
$822$		0			0
$823$	2.77292	−	26.3825i	0.0966578	−	0.919638i	−0.833510	−	0.552504i	$-0.813672\pi$
$823$	2.77292	−	26.3825i	0.0966578	−	0.919638i	0.930168	−	0.367134i	$-0.119661\pi$
$824$	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	0.753975	−	0.656903i	$-0.228134\pi$
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	−0.391761	+	0.920067i	$0.628134\pi$
$828$		0			0
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	−0.867407	−	0.497600i	$-0.834215\pi$
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	0.409265	−	0.912416i	$-0.365785\pi$
$830$	0.820977	+	7.81108i	0.0284965	+	0.271126i
$831$		0			0
$832$	17.6760	−	19.6312i	0.612806	−	0.680590i
$833$	−1.20906	+	0.256993i	−0.0418913	+	0.00890428i
$834$		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
$839$	15.5853	+	17.3092i	0.538063	+	0.597579i	0.949464	−	0.313875i	$-0.101627\pi$
$839$	15.5853	+	17.3092i	0.538063	+	0.597579i	−0.411402	+	0.911454i	$0.634961\pi$
$840$		0			0
$841$	−8.22191	−	3.66063i	−0.283514	−	0.126229i
$842$	5.51274	+	2.45443i	0.189981	+	0.0845852i
$843$		0			0
$844$	4.66087	+	5.17642i	0.160434	+	0.178180i
$845$	−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
$850$	−4.74803	+	1.00922i	−0.162856	+	0.0346161i
$851$	−15.5107	+	17.2263i	−0.531699	+	0.590512i
$852$		0			0
$853$	−0.830403	−	7.90075i	−0.0284324	−	0.270517i	−0.999497	−	0.0317011i	$-0.989908\pi$
$853$	−0.830403	−	7.90075i	−0.0284324	−	0.270517i	0.971065	−	0.238816i	$-0.0767591\pi$
$854$	−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	$-0.427925\pi$
$860$	−0.0435265	+	0.414127i	−0.00148424	+	0.0141216i
$861$		0			0
$862$	2.36360	+	0.502399i	0.0805047	+	0.0171118i
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	−0.865944	−	0.500141i	$-0.833281\pi$
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	0.208071	+	0.978114i	$0.433281\pi$
$864$		0			0
$865$	−2.07953	−	6.40013i	−0.0707060	−	0.217611i
$866$	6.49606	+	7.21460i	0.220745	+	0.245162i
$867$		0			0
$868$	3.57295	+	6.18853i	0.121274	+	0.210052i
$869$	1.08071	−	1.37736i	0.0366604	−	0.0467237i
$870$		0			0
$871$	60.1727	−	26.7906i	2.03888	−	0.907766i
$872$		0			0
$873$		0			0
$874$	−6.11803	+	4.44501i	−0.206946	+	0.150355i
$875$	1.18031	+	11.2299i	0.0399019	+	0.379641i
$876$		0			0
$877$	19.9703	−	4.24481i	0.674348	−	0.143337i	0.142005	−	0.989866i	$-0.454645\pi$
$877$	19.9703	−	4.24481i	0.674348	−	0.143337i	0.532343	+	0.846529i	$0.321312\pi$
$878$	2.82587	−	26.8863i	0.0953684	−	0.907370i
$879$		0			0
$880$	1.05530	+	6.05813i	0.0355742	+	0.204220i
$881$	−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	−0.544358	−	0.838853i	$-0.683226\pi$
$883$	11.5623	−	35.5851i	0.389103	−	1.19753i	0.933460	−	0.358681i	$-0.116774\pi$
$884$	−2.32991	−	0.495239i	−0.0783635	−	0.0166567i
$885$		0			0
$886$	−1.29395	−	0.576105i	−0.0434712	−	0.0193546i
$887$	−2.00739	+	2.22943i	−0.0674016	+	0.0748571i	−0.775902	−	0.630853i	$-0.782705\pi$
$887$	−2.00739	+	2.22943i	−0.0674016	+	0.0748571i	0.708501	+	0.705710i	$0.249372\pi$
$888$		0			0
$889$	26.6067	−	11.8460i	0.892359	−	0.397304i
$890$	5.85410			0.196230
$891$		0			0
$892$	−7.85410			−0.262975
$893$	−0.482228	+	0.214702i	−0.0161371	+	0.00718472i
$894$		0			0
$895$	−0.571506	+	0.634721i	−0.0191033	+	0.0212164i
$896$	−37.3221	−	16.6169i	−1.24684	−	0.555130i
$897$		0			0
$898$	24.5756	+	5.22370i	0.820098	+	0.174317i
$899$	−5.32624	+	16.3925i	−0.177640	+	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$	−14.0430	+	28.6420i	−0.467582	+	0.953675i
$903$		0			0
$904$	−2.97032	+	28.2607i	−0.0987915	+	0.939938i
$905$	3.18617	−	0.677242i	0.105912	−	0.0225123i
$906$		0			0
$907$	−0.415889	−	3.95692i	−0.0138094	−	0.131387i	0.985445	−	0.169994i	$-0.0543748\pi$
$907$	−0.415889	−	3.95692i	−0.0138094	−	0.131387i	−0.999254	+	0.0386065i	$0.987708\pi$
$908$	5.44427	−	3.95550i	0.180675	−	0.131268i
$909$		0			0
$910$	−3.57295	+	10.9964i	−0.118442	+	0.364527i
$911$	−32.8367	+	14.6199i	−1.08793	+	0.484377i	−0.870736	−	0.491751i	$-0.836357\pi$
$911$	−32.8367	+	14.6199i	−1.08793	+	0.484377i	−0.217194	+	0.976129i	$0.569690\pi$
$912$		0			0
$913$	−23.4967	−	34.9912i	−0.777629	−	1.15804i
$914$	26.5344	+	45.9590i	0.877681	+	1.52019i
$915$		0			0
$916$	4.13545	+	4.59289i	0.136639	+	0.151753i
$917$	12.8435	+	39.5281i	0.424128	+	1.30533i
$918$		0			0
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.254753	−	0.967006i	$-0.418006\pi$
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.998400	+	0.0565371i	$0.0180059\pi$
$920$	−4.57163	−	0.971730i	−0.150722	−	0.0320370i
$921$		0			0
$922$	1.67606	−	15.9466i	0.0551980	−	0.525173i
$923$	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
$929$	0.301935	+	2.87272i	0.00990617	+	0.0942509i	0.998358	−	0.0572856i	$-0.0182446\pi$
$929$	0.301935	+	2.87272i	0.00990617	+	0.0942509i	−0.988452	+	0.151536i	$0.951578\pi$
$930$		0			0
$931$	−1.14301	+	1.26944i	−0.0374607	+	0.0416043i
$932$	5.24354	−	1.11455i	0.171758	−	0.0365082i
$933$		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	0.0667827	−	0.997768i	$-0.478727\pi$
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	−0.928296	+	0.371841i	$0.878727\pi$
$938$	−34.3067	−	38.1014i	−1.12015	−	1.24406i
$939$		0			0
$940$	0.133284	+	0.0593421i	0.00434726	+	0.00193553i
$941$	−30.7236	−	13.6790i	−1.00156	−	0.445924i	−0.160600	−	0.987020i	$-0.551343\pi$
$941$	−30.7236	−	13.6790i	−1.00156	−	0.445924i	−0.840961	+	0.541096i	$0.818010\pi$
$942$		0			0
$943$	−21.7654	−	24.1729i	−0.708779	−	0.787178i
$944$	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
$949$	−7.53976	+	1.60263i	−0.244751	+	0.0520234i
$950$	−4.48866	+	4.98517i	−0.145632	+	0.161740i
$951$		0			0
$952$	−0.433364	−	4.12319i	−0.0140454	−	0.133633i
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.513714	−	0.857961i	$-0.671731\pi$
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.0886937	−	0.996059i	$-0.528269\pi$
$954$		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
$959$	−0.461640	+	4.39221i	−0.0149071	+	0.141832i
$960$		0			0
$961$	15.7931	+	3.35692i	0.509454	+	0.108288i
$962$	−34.5795	+	25.1235i	−1.11489	+	0.810014i
$963$		0			0
$964$	3.27051	+	10.0656i	0.105336	+	0.324191i
$965$	0.399302	+	0.443470i	0.0128540	+	0.0142758i
$966$		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	$0.968859\pi$
$968$	−15.0630	−	19.4450i	−0.484143	−	0.624985i
$969$		0			0
$970$	−8.48848	+	3.77931i	−0.272549	+	0.121346i
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	−0.631779	−	0.775148i	$-0.717675\pi$
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	0.966741	−	0.255757i	$-0.0823248\pi$
$972$		0			0
$973$	−14.2082	+	10.3229i	−0.455494	+	0.330936i
$974$	6.62659	+	63.0478i	0.212330	+	2.02018i
$975$		0			0
$976$	5.44076	−	1.15647i	0.174154	−	0.0370177i
$977$	−5.15960	+	49.0903i	−0.165070	+	1.57054i	0.527733	+	0.849410i	$0.323042\pi$
$977$	−5.15960	+	49.0903i	−0.165070	+	1.57054i	−0.692803	+	0.721127i	$0.743625\pi$
$978$		0			0
$979$	−27.7687	+	14.6913i	−0.887491	+	0.469536i
$980$	0.472136			0.0150818
$981$		0			0
$982$	−13.1074	+	40.3404i	−0.418274	+	1.28731i
$983$	34.5335	+	7.34031i	1.10145	+	0.234120i	0.722549	−	0.691319i	$-0.242970\pi$
$983$	34.5335	+	7.34031i	1.10145	+	0.234120i	0.378897	+	0.925439i	$0.376304\pi$
$984$		0			0
$985$	−9.28819	−	4.13537i	−0.295946	−	0.131764i
$986$	−2.99244	+	3.32344i	−0.0952988	+	0.105840i
$987$		0			0
$988$	−3.00721	+	1.33889i	−0.0956719	+	0.0425959i
$989$	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	$0.562436\pi$
$992$	−11.9076	+	5.30159i	−0.378065	+	0.168325i
$993$		0			0
$994$	47.2988	−	52.5306i	1.50023	−	1.66617i
$995$	−1.14865	−	0.511412i	−0.0364147	−	0.0162129i
$996$		0			0
$997$	−33.2362	−	7.06457i	−1.05260	−	0.223737i	−0.351050	−	0.936357i	$-0.614175\pi$
$997$	−33.2362	−	7.06457i	−1.05260	−	0.223737i	−0.701551	+	0.712619i	$0.747509\pi$
$998$	−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.136.1		8
3.2	odd	2		891.2.n.d.136.1		8
9.2	odd	6		33.2.e.a.4.1	✓	4
9.4	even	3	inner	891.2.n.a.433.1		8
9.5	odd	6		891.2.n.d.433.1		8
9.7	even	3		99.2.f.b.37.1		4
11.3	even	5	inner	891.2.n.a.784.1		8
33.14	odd	10		891.2.n.d.784.1		8
36.11	even	6		528.2.y.f.433.1		4
45.2	even	12		825.2.bx.b.499.2		8
45.29	odd	6		825.2.n.f.301.1		4
45.38	even	12		825.2.bx.b.499.1		8
99.2	even	30		363.2.e.c.148.1		4
99.14	odd	30		891.2.n.d.190.1		8
99.16	even	15		1089.2.a.m.1.1		2
99.20	odd	30		363.2.e.h.148.1		4
99.25	even	15		99.2.f.b.91.1		4
99.29	even	30		363.2.e.c.130.1		4
99.38	odd	30		363.2.a.h.1.2		2
99.47	odd	30		33.2.e.a.25.1	yes	4
99.58	even	15	inner	891.2.n.a.190.1		8
99.61	odd	30		1089.2.a.s.1.2		2
99.65	even	6		363.2.e.j.202.1		4
99.74	even	30		363.2.e.j.124.1		4
99.83	even	30		363.2.a.e.1.1		2
99.92	odd	30		363.2.e.h.130.1		4
396.47	even	30		528.2.y.f.289.1		4
396.83	odd	30		5808.2.a.bm.1.2		2
396.335	even	30		5808.2.a.bl.1.2		2
495.47	even	60		825.2.bx.b.124.1		8
495.344	odd	30		825.2.n.f.751.1		4
495.434	odd	30		9075.2.a.x.1.1		2
495.443	even	60		825.2.bx.b.124.2		8
495.479	even	30		9075.2.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	9.2	odd	6
33.2.e.a.25.1	yes	4	99.47	odd	30
99.2.f.b.37.1		4	9.7	even	3
99.2.f.b.91.1		4	99.25	even	15
363.2.a.e.1.1		2	99.83	even	30
363.2.a.h.1.2		2	99.38	odd	30
363.2.e.c.130.1		4	99.29	even	30
363.2.e.c.148.1		4	99.2	even	30
363.2.e.h.130.1		4	99.92	odd	30
363.2.e.h.148.1		4	99.20	odd	30
363.2.e.j.124.1		4	99.74	even	30
363.2.e.j.202.1		4	99.65	even	6
528.2.y.f.289.1		4	396.47	even	30
528.2.y.f.433.1		4	36.11	even	6
825.2.n.f.301.1		4	45.29	odd	6
825.2.n.f.751.1		4	495.344	odd	30
825.2.bx.b.124.1		8	495.47	even	60
825.2.bx.b.124.2		8	495.443	even	60
825.2.bx.b.499.1		8	45.38	even	12
825.2.bx.b.499.2		8	45.2	even	12
891.2.n.a.136.1		8	1.1	even	1	trivial
891.2.n.a.190.1		8	99.58	even	15	inner
891.2.n.a.433.1		8	9.4	even	3	inner
891.2.n.a.784.1		8	11.3	even	5	inner
891.2.n.d.136.1		8	3.2	odd	2
891.2.n.d.190.1		8	99.14	odd	30
891.2.n.d.433.1		8	9.5	odd	6
891.2.n.d.784.1		8	33.14	odd	10
1089.2.a.m.1.1		2	99.16	even	15
1089.2.a.s.1.2		2	99.61	odd	30
5808.2.a.bl.1.2		2	396.335	even	30
5808.2.a.bm.1.2		2	396.83	odd	30
9075.2.a.x.1.1		2	495.434	odd	30
9075.2.a.bv.1.2		2	495.479	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)

\(f(q)\)	\(=\)	\(q+(-1.47815 + 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(0.348943 + 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})\)	\(q+(-1.47815 + 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(0.348943 + 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} -0.618034 q^{10} +(2.93162 - 1.55100i) q^{11} +(-0.651847 + 6.20191i) q^{13} +(4.74803 - 1.00922i) q^{14} +(0.507392 + 4.82751i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(0.215659 - 0.0960175i) q^{20} +(-3.31263 + 4.22195i) q^{22} +(-2.73607 - 4.73901i) q^{23} +(-3.24803 - 3.60730i) q^{25} +(-3.11803 - 9.59632i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(-4.37441 - 0.929809i) q^{29} +(0.402863 - 3.83299i) q^{31} +(-1.69098 - 2.92887i) q^{32} +(0.500000 - 0.866025i) q^{34} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(-0.144455 - 1.37440i) q^{38} +(0.571506 - 0.634721i) q^{40} +(5.81438 - 1.23588i) q^{41} +(-0.881966 + 1.52761i) q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.413545 + 0.459289i) q^{47} +(1.82709 + 0.813473i) q^{49} +(7.17508 + 3.19455i) q^{50} +(2.57890 + 2.86416i) q^{52} +(-5.97214 - 4.33901i) q^{53} +(1.26393 - 0.0857567i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(7.07794 - 1.50446i) q^{58} +(3.56395 - 3.95817i) q^{59} +(-0.119779 - 1.13962i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-3.42705 - 2.48990i) q^{64} +(-1.19098 + 2.06284i) q^{65} +(-5.28115 - 9.14723i) q^{67} +(-0.0399263 + 0.379874i) q^{68} +(1.81359 + 0.385489i) q^{70} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(4.58629 + 5.09359i) q^{74} +(0.263932 + 0.457144i) q^{76} +(-9.57008 + 2.72277i) q^{77} +(0.482228 - 0.214702i) q^{79} +(-0.572949 + 1.76336i) q^{80} +(-7.78115 + 5.65334i) q^{82} +(-1.32837 - 12.6386i) q^{83} +(-0.230909 + 0.0490813i) q^{85} +(0.298335 - 2.83847i) q^{86} +(-1.27270 - 7.30618i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(-3.30806 - 0.703150i) q^{92} +(-0.913545 - 0.406737i) q^{94} +(-0.218296 + 0.242442i) q^{95} +(13.7346 - 6.11506i) q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8}+O(q^{10}) \) 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

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