LMFDB - Embedded newform 891.2.f.b.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(82,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	891.163
Dual form			891.2.f.b.82.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.118034 + 0.363271i) q^{2} +(1.50000 + 1.08981i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +0.472136 q^{10} +(0.309017 - 3.30220i) q^{11} +(-2.00000 + 6.15537i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(0.972136 + 2.99193i) q^{16} +(1.50000 + 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(0.708204 - 2.17963i) q^{20} +(1.16312 + 0.502029i) q^{22} +4.61803 q^{23} +(2.80902 - 2.04087i) q^{25} +(-2.00000 - 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(3.92705 + 2.85317i) q^{29} +(0.190983 - 0.587785i) q^{31} -4.14590 q^{32} -1.85410 q^{34} +(0.381966 - 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(-0.118034 - 0.363271i) q^{38} +(1.47214 + 1.06957i) q^{40} +(2.04508 - 1.48584i) q^{41} +1.85410 q^{43} +(4.06231 - 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-9.66312 + 7.02067i) q^{47} +(-1.85410 - 5.70634i) q^{49} +(0.409830 + 1.26133i) q^{50} +(-9.70820 + 7.05342i) q^{52} +(1.26393 - 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} -1.47214 q^{56} +(-1.50000 + 1.08981i) q^{58} +(-1.30902 - 0.951057i) q^{59} +(3.35410 + 10.3229i) q^{61} +(0.190983 + 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(-2.78115 + 8.55951i) q^{68} +(0.381966 + 0.277515i) q^{70} +(-0.899187 - 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.57295 + 1.14281i) q^{74} -1.85410 q^{76} +(2.19098 - 2.48990i) q^{77} +(3.26393 - 10.0453i) q^{79} +(3.14590 - 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(-3.01722 - 9.28605i) q^{83} +(4.85410 - 3.52671i) q^{85} +(-0.218847 + 0.673542i) q^{86} +(2.48936 + 4.20025i) q^{88} -6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(6.92705 + 5.03280i) q^{92} +(-1.40983 - 4.33901i) q^{94} +(1.00000 + 0.726543i) q^{95} +(1.85410 - 5.70634i) q^{97} +2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^4 - 6 * q^5 + q^7 - 7 * q^8 - 16 * q^10 - q^11 - 8 * q^13 + q^14 - 14 * q^16 + 6 * q^17 - q^19 - 24 * q^20 - 11 * q^22 + 14 * q^23 + 9 * q^25 - 8 * q^26 + 9 * q^28 + 9 * q^29 + 3 * q^31 - 30 * q^32 + 6 * q^34 + 6 * q^35 + 12 * q^37 + 4 * q^38 - 12 * q^40 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 9 * q^46 - 23 * q^47 + 6 * q^49 + 24 * q^50 - 12 * q^52 + 14 * q^53 - 16 * q^55 + 12 * q^56 - 6 * q^58 - 3 * q^59 + 3 * q^62 - 17 * q^64 + 32 * q^65 + 24 * q^67 + 9 * q^68 + 6 * q^70 + 21 * q^71 - 4 * q^73 - 13 * q^74 + 6 * q^76 + 11 * q^77 + 22 * q^79 + 26 * q^80 - 48 * q^82 + 17 * q^83 + 6 * q^85 - 21 * q^86 - 37 * q^88 - 36 * q^89 - 12 * q^91 + 21 * q^92 - 28 * q^94 + 4 * q^95 - 6 * q^97 + 36 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	−0.984076	−	0.177750i	$-0.943118\pi$
$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	0.900613	+	0.434622i	$0.143118\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	−0.381966	−	1.17557i	−0.170820	−	0.525731i	0.828598	−	0.559845i	$-0.189139\pi$
$5$	−0.381966	−	1.17557i	−0.170820	−	0.525731i	−0.999418	+	0.0341136i	$0.989139\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	0.730084	−	0.683358i	$-0.239481\pi$
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	−0.424304	+	0.905520i	$0.639481\pi$
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$		0			0
$10$	0.472136			0.149302
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$		0			0
$13$	−2.00000	+	6.15537i	−0.554700	+	1.70719i	0.142034	+	0.989862i	$0.454636\pi$
$13$	−2.00000	+	6.15537i	−0.554700	+	1.70719i	−0.696734	+	0.717330i	$0.745364\pi$
$14$	−0.309017	+	0.224514i	−0.0825883	+	0.0600039i
$15$		0			0
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	1.50000	+	4.61653i	0.363803	+	1.11967i	0.950727	+	0.310029i	$0.100339\pi$
$17$	1.50000	+	4.61653i	0.363803	+	1.11967i	−0.586924	+	0.809642i	$0.699661\pi$
$18$		0			0
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	−0.676706	−	0.736253i	$-0.736593\pi$
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	0.491105	+	0.871100i	$0.336593\pi$
$20$	0.708204	−	2.17963i	0.158359	−	0.487380i
$21$		0			0
$22$	1.16312	+	0.502029i	0.247978	+	0.107033i
$23$	4.61803			0.962927			0.481463	−	0.876466i	$-0.340105\pi$
$23$	4.61803			0.962927			0.481463	+	0.876466i	$0.340105\pi$
$24$		0			0
$25$	2.80902	−	2.04087i	0.561803	−	0.408174i
$26$	−2.00000	−	1.45309i	−0.392232	−	0.284973i
$27$		0			0
$28$	0.572949	+	1.76336i	0.108277	+	0.333243i
$29$	3.92705	+	2.85317i	0.729235	+	0.529820i	0.889321	−	0.457283i	$-0.151177\pi$
$29$	3.92705	+	2.85317i	0.729235	+	0.529820i	−0.160086	+	0.987103i	$0.551177\pi$
$30$		0			0
$31$	0.190983	−	0.587785i	0.0343016	−	0.105569i	−0.932440	−	0.361325i	$-0.882324\pi$
$31$	0.190983	−	0.587785i	0.0343016	−	0.105569i	0.966741	+	0.255756i	$0.0823244\pi$
$32$	−4.14590			−0.732898
$33$		0			0
$34$	−1.85410			−0.317976
$35$	0.381966	−	1.17557i	0.0645640	−	0.198708i
$36$		0			0
$37$	4.11803	+	2.99193i	0.677001	+	0.491870i	0.872361	−	0.488862i	$-0.162588\pi$
$37$	4.11803	+	2.99193i	0.677001	+	0.491870i	−0.195361	+	0.980731i	$0.562588\pi$
$38$	−0.118034	−	0.363271i	−0.0191476	−	0.0589304i
$39$		0			0
$40$	1.47214	+	1.06957i	0.232765	+	0.169114i
$41$	2.04508	−	1.48584i	0.319389	−	0.232049i	−0.416526	−	0.909124i	$-0.636752\pi$
$41$	2.04508	−	1.48584i	0.319389	−	0.232049i	0.735915	+	0.677074i	$0.236752\pi$
$42$		0			0
$43$	1.85410			0.282748			0.141374	−	0.989956i	$-0.454848\pi$
$43$	1.85410			0.282748			0.141374	+	0.989956i	$0.454848\pi$
$44$	4.06231	−	4.61653i	0.612416	−	0.695967i
$45$		0			0
$46$	−0.545085	+	1.67760i	−0.0803684	+	0.247348i
$47$	−9.66312	+	7.02067i	−1.40951	+	1.02407i	−0.416117	+	0.909311i	$0.636609\pi$
$47$	−9.66312	+	7.02067i	−1.40951	+	1.02407i	−0.993393	+	0.114759i	$0.963391\pi$
$48$		0			0
$49$	−1.85410	−	5.70634i	−0.264872	−	0.815191i
$50$	0.409830	+	1.26133i	0.0579587	+	0.178379i
$51$		0			0
$52$	−9.70820	+	7.05342i	−1.34629	+	0.978134i
$53$	1.26393	−	3.88998i	0.173614	−	0.534330i	−0.825953	−	0.563739i	$-0.809362\pi$
$53$	1.26393	−	3.88998i	0.173614	−	0.534330i	0.999567	+	0.0294087i	$0.00936242\pi$
$54$		0			0
$55$	−4.00000	+	0.898056i	−0.539360	+	0.121094i
$56$	−1.47214			−0.196722
$57$		0			0
$58$	−1.50000	+	1.08981i	−0.196960	+	0.143100i
$59$	−1.30902	−	0.951057i	−0.170419	−	0.123817i	0.499306	−	0.866426i	$-0.333588\pi$
$59$	−1.30902	−	0.951057i	−0.170419	−	0.123817i	−0.669726	+	0.742609i	$0.733588\pi$
$60$		0			0
$61$	3.35410	+	10.3229i	0.429449	+	1.32171i	0.898669	+	0.438626i	$0.144535\pi$
$61$	3.35410	+	10.3229i	0.429449	+	1.32171i	−0.469221	+	0.883081i	$0.655465\pi$
$62$	0.190983	+	0.138757i	0.0242549	+	0.0176222i
$63$		0			0
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	8.00000			0.992278
$66$		0			0
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	−2.78115	+	8.55951i	−0.337264	+	1.03799i
$69$		0			0
$70$	0.381966	+	0.277515i	0.0456537	+	0.0331693i
$71$	−0.899187	−	2.76741i	−0.106714	−	0.328431i	0.883415	−	0.468591i	$-0.155238\pi$
$71$	−0.899187	−	2.76741i	−0.106714	−	0.328431i	−0.990129	+	0.140160i	$0.955238\pi$
$72$		0			0
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	0.594671	−	0.803969i	$-0.297282\pi$
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	−0.580856	+	0.814006i	$0.697282\pi$
$74$	−1.57295	+	1.14281i	−0.182852	+	0.132849i
$75$		0			0
$76$	−1.85410			−0.212680
$77$	2.19098	−	2.48990i	0.249686	−	0.283750i
$78$		0			0
$79$	3.26393	−	10.0453i	0.367221	−	1.13019i	−0.581357	−	0.813648i	$-0.697478\pi$
$79$	3.26393	−	10.0453i	0.367221	−	1.13019i	0.948579	−	0.316542i	$-0.102522\pi$
$80$	3.14590	−	2.28563i	0.351722	−	0.255541i
$81$		0			0
$82$	0.298374	+	0.918300i	0.0329499	+	0.101409i
$83$	−3.01722	−	9.28605i	−0.331183	−	1.01928i	−0.968572	−	0.248734i	$-0.919985\pi$
$83$	−3.01722	−	9.28605i	−0.331183	−	1.01928i	0.637389	−	0.770542i	$-0.280015\pi$
$84$		0			0
$85$	4.85410	−	3.52671i	0.526501	−	0.382526i
$86$	−0.218847	+	0.673542i	−0.0235989	+	0.0726299i
$87$		0			0
$88$	2.48936	+	4.20025i	0.265366	+	0.447749i
$89$	−6.76393			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$89$	−6.76393			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$90$		0			0
$91$	−5.23607	+	3.80423i	−0.548889	+	0.398791i
$92$	6.92705	+	5.03280i	0.722195	+	0.524705i
$93$		0			0
$94$	−1.40983	−	4.33901i	−0.145413	−	0.447535i
$95$	1.00000	+	0.726543i	0.102598	+	0.0745417i
$96$		0			0
$97$	1.85410	−	5.70634i	0.188256	−	0.579391i	−0.811734	−	0.584028i	$-0.801476\pi$
$97$	1.85410	−	5.70634i	0.188256	−	0.579391i	0.999989	+	0.00463676i	$0.00147593\pi$
$98$	2.29180			0.231506
$99$		0			0
$100$	6.43769			0.643769
$101$	−2.61803	+	8.05748i	−0.260504	+	0.801749i	0.732191	+	0.681099i	$0.238498\pi$
$101$	−2.61803	+	8.05748i	−0.260504	+	0.801749i	−0.992695	+	0.120650i	$0.961502\pi$
$102$		0			0
$103$	8.28115	+	6.01661i	0.815966	+	0.592834i	0.915554	−	0.402195i	$-0.131752\pi$
$103$	8.28115	+	6.01661i	0.815966	+	0.592834i	−0.0995880	+	0.995029i	$0.531752\pi$
$104$	−2.94427	−	9.06154i	−0.288710	−	0.888557i
$105$		0			0
$106$	1.26393	+	0.918300i	0.122764	+	0.0891932i
$107$	−11.3541	+	8.24924i	−1.09764	+	0.797484i	−0.980673	−	0.195652i	$-0.937318\pi$
$107$	−11.3541	+	8.24924i	−1.09764	+	0.797484i	−0.116969	+	0.993136i	$0.537318\pi$
$108$		0			0
$109$	7.14590			0.684453			0.342226	−	0.939618i	$-0.388819\pi$
$109$	7.14590			0.684453			0.342226	+	0.939618i	$0.388819\pi$
$110$	0.145898	−	1.55909i	0.0139108	−	0.148653i
$111$		0			0
$112$	−0.972136	+	2.99193i	−0.0918582	+	0.282711i
$113$	−13.9443	+	10.1311i	−1.31177	+	0.953054i	−0.311771	+	0.950157i	$0.600922\pi$
$113$	−13.9443	+	10.1311i	−1.31177	+	0.953054i	−0.999996	+	0.00289705i	$0.999078\pi$
$114$		0			0
$115$	−1.76393	−	5.42882i	−0.164488	−	0.506240i
$116$	2.78115	+	8.55951i	0.258224	+	0.794730i
$117$		0			0
$118$	0.500000	−	0.363271i	0.0460287	−	0.0334418i
$119$	−1.50000	+	4.61653i	−0.137505	+	0.423196i
$120$		0			0
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−4.14590			−0.375352
$123$		0			0
$124$	0.927051	−	0.673542i	0.0832516	−	0.0604859i
$125$	−8.47214	−	6.15537i	−0.757771	−	0.550553i
$126$		0			0
$127$	−3.26393	−	10.0453i	−0.289627	−	0.891381i	−0.984973	−	0.172706i	$-0.944749\pi$
$127$	−3.26393	−	10.0453i	−0.289627	−	0.891381i	0.695346	−	0.718675i	$-0.255251\pi$
$128$	−8.16312	−	5.93085i	−0.721525	−	0.524218i
$129$		0			0
$130$	−0.944272	+	2.90617i	−0.0828181	+	0.254888i
$131$	21.2361			1.85540			0.927702	−	0.373322i	$-0.121781\pi$
$131$	21.2361			1.85540			0.927702	+	0.373322i	$0.121781\pi$
$132$		0			0
$133$	−1.00000			−0.0867110
$134$	−0.708204	+	2.17963i	−0.0611795	+	0.188291i
$135$		0			0
$136$	−5.78115	−	4.20025i	−0.495730	−	0.360169i
$137$	−2.66312	−	8.19624i	−0.227526	−	0.700252i	−0.998025	−	0.0628116i	$-0.979993\pi$
$137$	−2.66312	−	8.19624i	−0.227526	−	0.700252i	0.770500	−	0.637440i	$-0.220007\pi$
$138$		0			0
$139$	−7.85410	−	5.70634i	−0.666176	−	0.484005i	0.202567	−	0.979268i	$-0.435072\pi$
$139$	−7.85410	−	5.70634i	−0.666176	−	0.484005i	−0.868743	+	0.495263i	$0.835072\pi$
$140$	1.85410	−	1.34708i	0.156700	−	0.113849i
$141$		0			0
$142$	1.11146			0.0932713
$143$	19.7082	+	8.50651i	1.64808	+	0.711350i
$144$		0			0
$145$	1.85410	−	5.70634i	0.153975	−	0.473886i
$146$	−0.0450850	+	0.0327561i	−0.00373126	+	0.00271092i
$147$		0			0
$148$	2.91641	+	8.97578i	0.239727	+	0.737805i
$149$	−4.69098	−	14.4374i	−0.384300	−	1.18275i	−0.936987	−	0.349365i	$-0.886397\pi$
$149$	−4.69098	−	14.4374i	−0.384300	−	1.18275i	0.552686	−	0.833389i	$-0.313603\pi$
$150$		0			0
$151$	−3.50000	+	2.54290i	−0.284826	+	0.206938i	−0.721020	−	0.692915i	$-0.756326\pi$
$151$	−3.50000	+	2.54290i	−0.284826	+	0.206938i	0.436194	+	0.899853i	$0.356326\pi$
$152$	0.454915	−	1.40008i	0.0368985	−	0.113562i
$153$		0			0
$154$	0.645898	+	1.08981i	0.0520479	+	0.0878197i
$155$	−0.763932			−0.0613605
$156$		0			0
$157$	−5.78115	+	4.20025i	−0.461386	+	0.335217i	−0.794075	−	0.607820i	$-0.792044\pi$
$157$	−5.78115	+	4.20025i	−0.461386	+	0.335217i	0.332689	+	0.943037i	$0.392044\pi$
$158$	3.26393	+	2.37139i	0.259664	+	0.188657i
$159$		0			0
$160$	1.58359	+	4.87380i	0.125194	+	0.385307i
$161$	3.73607	+	2.71441i	0.294443	+	0.213926i
$162$		0			0
$163$	6.39919	−	19.6947i	0.501223	−	1.54261i	−0.305806	−	0.952094i	$-0.598926\pi$
$163$	6.39919	−	19.6947i	0.501223	−	1.54261i	0.807029	−	0.590512i	$-0.201074\pi$
$164$	4.68692			0.365987
$165$		0			0
$166$	3.72949			0.289465
$167$	−1.78115	+	5.48183i	−0.137830	+	0.424196i	−0.996019	−	0.0891363i	$-0.971589\pi$
$167$	−1.78115	+	5.48183i	−0.137830	+	0.424196i	0.858190	+	0.513333i	$0.171589\pi$
$168$		0			0
$169$	−23.3713	−	16.9803i	−1.79779	−	1.30617i
$170$	0.708204	+	2.17963i	0.0543168	+	0.167170i
$171$		0			0
$172$	2.78115	+	2.02063i	0.212061	+	0.154071i
$173$	18.6803	−	13.5721i	1.42024	−	1.03186i	0.428508	−	0.903538i	$-0.359039\pi$
$173$	18.6803	−	13.5721i	1.42024	−	1.03186i	0.991732	−	0.128327i	$-0.0409606\pi$
$174$		0			0
$175$	3.47214			0.262469
$176$	10.1803	−	2.28563i	0.767372	−	0.172286i
$177$		0			0
$178$	0.798374	−	2.45714i	0.0598407	−	0.184171i
$179$	4.09017	−	2.97168i	0.305714	−	0.222114i	−0.424341	−	0.905502i	$-0.639494\pi$
$179$	4.09017	−	2.97168i	0.305714	−	0.222114i	0.730055	+	0.683388i	$0.239494\pi$
$180$		0			0
$181$	−3.06231	−	9.42481i	−0.227619	−	0.700540i	−0.998015	−	0.0629745i	$-0.979941\pi$
$181$	−3.06231	−	9.42481i	−0.227619	−	0.700540i	0.770396	−	0.637566i	$-0.220059\pi$
$182$	−0.763932	−	2.35114i	−0.0566264	−	0.174278i
$183$		0			0
$184$	−5.50000	+	3.99598i	−0.405465	+	0.294588i
$185$	1.94427	−	5.98385i	0.142946	−	0.439942i
$186$		0			0
$187$	15.7082	−	3.52671i	1.14870	−	0.257899i
$188$	−22.1459			−1.61516
$189$		0			0
$190$	−0.381966	+	0.277515i	−0.0277107	+	0.0201330i
$191$	−4.80902	−	3.49396i	−0.347968	−	0.252814i	0.400048	−	0.916494i	$-0.368993\pi$
$191$	−4.80902	−	3.49396i	−0.347968	−	0.252814i	−0.748016	+	0.663680i	$0.768993\pi$
$192$		0			0
$193$	−3.39919	−	10.4616i	−0.244679	−	0.753044i	−0.995689	−	0.0927535i	$-0.970433\pi$
$193$	−3.39919	−	10.4616i	−0.244679	−	0.753044i	0.751010	−	0.660291i	$-0.229567\pi$
$194$	1.85410	+	1.34708i	0.133117	+	0.0967150i
$195$		0			0
$196$	3.43769	−	10.5801i	0.245550	−	0.755724i
$197$	8.23607			0.586796			0.293398	−	0.955990i	$-0.405214\pi$
$197$	8.23607			0.586796			0.293398	+	0.955990i	$0.405214\pi$
$198$		0			0
$199$	−7.14590			−0.506559			−0.253280	−	0.967393i	$-0.581509\pi$
$199$	−7.14590			−0.506559			−0.253280	+	0.967393i	$0.581509\pi$
$200$	−1.57953	+	4.86128i	−0.111689	+	0.343745i
$201$		0			0
$202$	−2.61803	−	1.90211i	−0.184204	−	0.133832i
$203$	1.50000	+	4.61653i	0.105279	+	0.324017i
$204$		0			0
$205$	−2.52786	−	1.83660i	−0.176554	−	0.128274i
$206$	−3.16312	+	2.29814i	−0.220385	+	0.160119i
$207$		0			0
$208$	−20.3607			−1.41176
$209$	1.69098	+	2.85317i	0.116968	+	0.197358i
$210$		0			0
$211$	6.32624	−	19.4702i	0.435516	−	1.34038i	−0.457041	−	0.889446i	$-0.651091\pi$
$211$	6.32624	−	19.4702i	0.435516	−	1.34038i	0.892557	−	0.450935i	$-0.148909\pi$
$212$	6.13525	−	4.45752i	0.421371	−	0.306144i
$213$		0			0
$214$	−1.65654	−	5.09831i	−0.113239	−	0.348513i
$215$	−0.708204	−	2.17963i	−0.0482991	−	0.148649i
$216$		0			0
$217$	0.500000	−	0.363271i	0.0339422	−	0.0246605i
$218$	−0.843459	+	2.59590i	−0.0571262	+	0.175816i
$219$		0			0
$220$	−6.97871	−	3.01217i	−0.470505	−	0.203081i
$221$	−31.4164			−2.11330
$222$		0			0
$223$	12.5451	−	9.11454i	0.840081	−	0.610355i	−0.0823123	−	0.996607i	$-0.526230\pi$
$223$	12.5451	−	9.11454i	0.840081	−	0.610355i	0.922393	+	0.386252i	$0.126230\pi$
$224$	−3.35410	−	2.43690i	−0.224105	−	0.162822i
$225$		0			0
$226$	−2.03444	−	6.26137i	−0.135329	−	0.416500i
$227$	13.4443	+	9.76784i	0.892328	+	0.648314i	0.936484	−	0.350711i	$-0.114060\pi$
$227$	13.4443	+	9.76784i	0.892328	+	0.648314i	−0.0441562	+	0.999025i	$0.514060\pi$
$228$		0			0
$229$	3.14590	−	9.68208i	0.207887	−	0.639810i	−0.791696	−	0.610916i	$-0.790801\pi$
$229$	3.14590	−	9.68208i	0.207887	−	0.639810i	0.999582	−	0.0288941i	$-0.00919856\pi$
$230$	2.18034			0.143767
$231$		0			0
$232$	−7.14590			−0.469151
$233$	−3.43769	+	10.5801i	−0.225211	+	0.693128i	0.773059	+	0.634334i	$0.218725\pi$
$233$	−3.43769	+	10.5801i	−0.225211	+	0.693128i	−0.998270	+	0.0587939i	$0.981275\pi$
$234$		0			0
$235$	11.9443	+	8.67802i	0.779158	+	0.566092i
$236$	−0.927051	−	2.85317i	−0.0603459	−	0.185726i
$237$		0			0
$238$	−1.50000	−	1.08981i	−0.0972306	−	0.0706421i
$239$	−8.47214	+	6.15537i	−0.548017	+	0.398158i	−0.827054	−	0.562123i	$-0.809985\pi$
$239$	−8.47214	+	6.15537i	−0.548017	+	0.398158i	0.279037	+	0.960280i	$0.409985\pi$
$240$		0			0
$241$	−26.8328			−1.72845			−0.864227	−	0.503102i	$-0.832192\pi$
$241$	−26.8328			−1.72845			−0.864227	+	0.503102i	$0.832192\pi$
$242$	2.01722	−	3.68571i	0.129672	−	0.236927i
$243$		0			0
$244$	−6.21885	+	19.1396i	−0.398121	+	1.22529i
$245$	−6.00000	+	4.35926i	−0.383326	+	0.278503i
$246$		0			0
$247$	−2.00000	−	6.15537i	−0.127257	−	0.391657i
$248$	0.281153	+	0.865300i	0.0178532	+	0.0549466i
$249$		0			0
$250$	3.23607	−	2.35114i	0.204667	−	0.148699i
$251$	6.35410	−	19.5559i	0.401067	−	1.23436i	−0.523067	−	0.852291i	$-0.675212\pi$
$251$	6.35410	−	19.5559i	0.401067	−	1.23436i	0.924135	−	0.382067i	$-0.124788\pi$
$252$		0			0
$253$	1.42705	−	15.2497i	0.0897179	−	0.958738i
$254$	4.03444			0.253143
$255$		0			0
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	12.0623	+	8.76378i	0.752426	+	0.546669i	0.896578	−	0.442886i	$-0.146045\pi$
$257$	12.0623	+	8.76378i	0.752426	+	0.546669i	−0.144152	+	0.989556i	$0.546045\pi$
$258$		0			0
$259$	1.57295	+	4.84104i	0.0977383	+	0.300808i
$260$	12.0000	+	8.71851i	0.744208	+	0.540699i
$261$		0			0
$262$	−2.50658	+	7.71445i	−0.154857	+	0.476601i
$263$	−12.7082			−0.783621			−0.391811	−	0.920046i	$-0.628151\pi$
$263$	−12.7082			−0.783621			−0.391811	+	0.920046i	$0.628151\pi$
$264$		0			0
$265$	−5.05573			−0.310571
$266$	0.118034	−	0.363271i	0.00723713	−	0.0222736i
$267$		0			0
$268$	9.00000	+	6.53888i	0.549762	+	0.399426i
$269$	−6.57295	−	20.2295i	−0.400760	−	1.23341i	−0.924384	−	0.381463i	$-0.875421\pi$
$269$	−6.57295	−	20.2295i	−0.400760	−	1.23341i	0.523625	−	0.851949i	$-0.324579\pi$
$270$		0			0
$271$	−8.70820	−	6.32688i	−0.528986	−	0.384331i	0.290993	−	0.956725i	$-0.406015\pi$
$271$	−8.70820	−	6.32688i	−0.528986	−	0.384331i	−0.819978	+	0.572395i	$0.806015\pi$
$272$	−12.3541	+	8.97578i	−0.749077	+	0.544237i
$273$		0			0
$274$	3.29180			0.198865
$275$	−5.87132	−	9.90659i	−0.354054	−	0.597390i
$276$		0			0
$277$	−5.94427	+	18.2946i	−0.357157	+	1.09922i	0.597592	+	0.801801i	$0.296124\pi$
$277$	−5.94427	+	18.2946i	−0.357157	+	1.09922i	−0.954748	+	0.297415i	$0.903876\pi$
$278$	3.00000	−	2.17963i	0.179928	−	0.130725i
$279$		0			0
$280$	0.562306	+	1.73060i	0.0336042	+	0.103423i
$281$	−2.88197	−	8.86978i	−0.171924	−	0.529127i	0.827556	−	0.561383i	$-0.189731\pi$
$281$	−2.88197	−	8.86978i	−0.171924	−	0.529127i	−0.999480	+	0.0322566i	$0.989731\pi$
$282$		0			0
$283$	13.7533	−	9.99235i	0.817548	−	0.593984i	−0.0984610	−	0.995141i	$-0.531392\pi$
$283$	13.7533	−	9.99235i	0.817548	−	0.593984i	0.916009	+	0.401157i	$0.131392\pi$
$284$	1.66718	−	5.13107i	0.0989292	−	0.304473i
$285$		0			0
$286$	−5.41641	+	6.15537i	−0.320279	+	0.363974i
$287$	2.52786			0.149215
$288$		0			0
$289$	−5.30902	+	3.85723i	−0.312295	+	0.226896i
$290$	1.85410	+	1.34708i	0.108877	+	0.0791035i
$291$		0			0
$292$	0.0835921	+	0.257270i	0.00489186	+	0.0150556i
$293$	23.6074	+	17.1518i	1.37916	+	1.00202i	0.996958	+	0.0779378i	$0.0248336\pi$
$293$	23.6074	+	17.1518i	1.37916	+	1.00202i	0.382200	+	0.924080i	$0.375166\pi$
$294$		0			0
$295$	−0.618034	+	1.90211i	−0.0359833	+	0.110745i
$296$	−7.49342			−0.435546
$297$		0			0
$298$	5.79837			0.335891
$299$	−9.23607	+	28.4257i	−0.534136	+	1.64390i
$300$		0			0
$301$	1.50000	+	1.08981i	0.0864586	+	0.0628158i
$302$	−0.510643	−	1.57160i	−0.0293842	−	0.0904353i
$303$		0			0
$304$	−2.54508	−	1.84911i	−0.145971	−	0.106054i
$305$	10.8541	−	7.88597i	0.621504	−	0.451549i
$306$		0			0
$307$	7.85410			0.448257			0.224129	−	0.974560i	$-0.428046\pi$
$307$	7.85410			0.448257			0.224129	+	0.974560i	$0.428046\pi$
$308$	6.00000	−	1.34708i	0.341882	−	0.0767572i
$309$		0			0
$310$	0.0901699	−	0.277515i	0.00512131	−	0.0157618i
$311$	−12.2812	+	8.92278i	−0.696400	+	0.505964i	−0.878758	−	0.477268i	$-0.841627\pi$
$311$	−12.2812	+	8.92278i	−0.696400	+	0.505964i	0.182358	+	0.983232i	$0.441627\pi$
$312$		0			0
$313$	1.07295	+	3.30220i	0.0606467	+	0.186651i	0.976790	−	0.214200i	$-0.0687144\pi$
$313$	1.07295	+	3.30220i	0.0606467	+	0.186651i	−0.916143	+	0.400851i	$0.868714\pi$
$314$	−0.843459	−	2.59590i	−0.0475991	−	0.146495i
$315$		0			0
$316$	15.8435	−	11.5109i	0.891264	−	0.647541i
$317$	6.47214	−	19.9192i	0.363511	−	1.11877i	−0.587397	−	0.809299i	$-0.699847\pi$
$317$	6.47214	−	19.9192i	0.363511	−	1.11877i	0.950908	−	0.309474i	$-0.100153\pi$
$318$		0			0
$319$	10.6353	−	12.0862i	0.595460	−	0.676698i
$320$	5.81966			0.325329
$321$		0			0
$322$	−1.42705	+	1.03681i	−0.0795264	+	0.0577793i
$323$	−3.92705	−	2.85317i	−0.218507	−	0.158755i
$324$		0			0
$325$	6.94427	+	21.3723i	0.385199	+	1.18552i
$326$	6.39919	+	4.64928i	0.354418	+	0.257500i
$327$		0			0
$328$	−1.14996	+	3.53922i	−0.0634961	+	0.195421i
$329$	−11.9443			−0.658509
$330$		0			0
$331$	14.4164			0.792397			0.396199	−	0.918165i	$-0.370329\pi$
$331$	14.4164			0.792397			0.396199	+	0.918165i	$0.370329\pi$
$332$	5.59424	−	17.2173i	0.307024	−	0.944921i
$333$		0			0
$334$	−1.78115	−	1.29408i	−0.0974604	−	0.0708091i
$335$	−2.29180	−	7.05342i	−0.125214	−	0.385370i
$336$		0			0
$337$	9.28115	+	6.74315i	0.505577	+	0.367323i	0.811143	−	0.584848i	$-0.198846\pi$
$337$	9.28115	+	6.74315i	0.505577	+	0.367323i	−0.305566	+	0.952171i	$0.598846\pi$
$338$	8.92705	−	6.48588i	0.485568	−	0.352785i
$339$		0			0
$340$	11.1246			0.603317
$341$	−1.88197	−	0.812299i	−0.101914	−	0.0439885i
$342$		0			0
$343$	4.01722	−	12.3637i	0.216910	−	0.667579i
$344$	−2.20820	+	1.60435i	−0.119058	+	0.0865010i
$345$		0			0
$346$	2.72542	+	8.38800i	0.146520	+	0.450941i
$347$	−2.74671	−	8.45351i	−0.147451	−	0.453808i	0.849867	−	0.526997i	$-0.176682\pi$
$347$	−2.74671	−	8.45351i	−0.147451	−	0.453808i	−0.997318	+	0.0731894i	$0.976682\pi$
$348$		0			0
$349$	3.35410	−	2.43690i	0.179541	−	0.130444i	−0.494385	−	0.869243i	$-0.664607\pi$
$349$	3.35410	−	2.43690i	0.179541	−	0.130444i	0.673926	+	0.738799i	$0.264607\pi$
$350$	−0.409830	+	1.26133i	−0.0219063	+	0.0674208i
$351$		0			0
$352$	−1.28115	+	13.6906i	−0.0682857	+	0.729710i
$353$	−16.4164			−0.873757			−0.436879	−	0.899520i	$-0.643916\pi$
$353$	−16.4164			−0.873757			−0.436879	+	0.899520i	$0.643916\pi$
$354$		0			0
$355$	−2.90983	+	2.11412i	−0.154438	+	0.112206i
$356$	−10.1459	−	7.37143i	−0.537732	−	0.390685i
$357$		0			0
$358$	0.596748	+	1.83660i	0.0315391	+	0.0970674i
$359$	18.4894	+	13.4333i	0.975831	+	0.708983i	0.956773	−	0.290836i	$-0.0939333\pi$
$359$	18.4894	+	13.4333i	0.975831	+	0.708983i	0.0190579	+	0.999818i	$0.493933\pi$
$360$		0			0
$361$	−5.56231	+	17.1190i	−0.292753	+	0.901001i
$362$	3.78522			0.198947
$363$		0			0
$364$	−12.0000			−0.628971
$365$	0.0557281	−	0.171513i	0.00291694	−	0.00897742i
$366$		0			0
$367$	10.2812	+	7.46969i	0.536672	+	0.389915i	0.822847	−	0.568262i	$-0.192384\pi$
$367$	10.2812	+	7.46969i	0.536672	+	0.389915i	−0.286176	+	0.958177i	$0.592384\pi$
$368$	4.48936	+	13.8168i	0.234024	+	0.720252i
$369$		0			0
$370$	1.94427	+	1.41260i	0.101078	+	0.0734374i
$371$	3.30902	−	2.40414i	0.171796	−	0.124817i
$372$		0			0
$373$	−5.65248			−0.292674			−0.146337	−	0.989235i	$-0.546748\pi$
$373$	−5.65248			−0.292674			−0.146337	+	0.989235i	$0.546748\pi$
$374$	−0.572949	+	6.12261i	−0.0296265	+	0.316593i
$375$		0			0
$376$	5.43363	−	16.7230i	0.280218	−	0.862422i
$377$	−25.4164	+	18.4661i	−1.30901	+	0.951053i
$378$		0			0
$379$	4.88197	+	15.0251i	0.250770	+	0.771790i	0.994634	+	0.103459i	$0.0329910\pi$
$379$	4.88197	+	15.0251i	0.250770	+	0.771790i	−0.743864	+	0.668331i	$0.767009\pi$
$380$	0.708204	+	2.17963i	0.0363301	+	0.111813i
$381$		0			0
$382$	1.83688	−	1.33457i	0.0939830	−	0.0682827i
$383$	6.13525	−	18.8824i	0.313497	−	0.964844i	−0.662872	−	0.748733i	$-0.730663\pi$
$383$	6.13525	−	18.8824i	0.313497	−	0.964844i	0.976369	−	0.216111i	$-0.0693374\pi$
$384$		0			0
$385$	−3.76393	−	1.62460i	−0.191828	−	0.0827972i
$386$	4.20163			0.213857
$387$		0			0
$388$	9.00000	−	6.53888i	0.456906	−	0.331961i
$389$	18.3262	+	13.3148i	0.929177	+	0.675087i	0.945791	−	0.324775i	$-0.105289\pi$
$389$	18.3262	+	13.3148i	0.929177	+	0.675087i	−0.0166141	+	0.999862i	$0.505289\pi$
$390$		0			0
$391$	6.92705	+	21.3193i	0.350316	+	1.07816i
$392$	7.14590	+	5.19180i	0.360922	+	0.262225i
$393$		0			0
$394$	−0.972136	+	2.99193i	−0.0489755	+	0.150731i
$395$	−13.0557			−0.656905
$396$		0			0
$397$	−2.12461			−0.106631			−0.0533156	−	0.998578i	$-0.516979\pi$
$397$	−2.12461			−0.106631			−0.0533156	+	0.998578i	$0.516979\pi$
$398$	0.843459	−	2.59590i	0.0422788	−	0.130121i
$399$		0			0
$400$	8.83688	+	6.42037i	0.441844	+	0.321018i
$401$	4.50000	+	13.8496i	0.224719	+	0.691615i	0.998320	+	0.0579414i	$0.0184537\pi$
$401$	4.50000	+	13.8496i	0.224719	+	0.691615i	−0.773601	+	0.633673i	$0.781546\pi$
$402$		0			0
$403$	3.23607	+	2.35114i	0.161200	+	0.117119i
$404$	−12.7082	+	9.23305i	−0.632257	+	0.459361i
$405$		0			0
$406$	−1.85410			−0.0920175
$407$	11.1525	−	12.6740i	0.552808	−	0.628227i
$408$		0			0
$409$	−10.4271	+	32.0912i	−0.515584	+	1.58681i	0.266631	+	0.963799i	$0.414089\pi$
$409$	−10.4271	+	32.0912i	−0.515584	+	1.58681i	−0.782216	+	0.623007i	$0.785911\pi$
$410$	0.965558	−	0.701519i	0.0476855	−	0.0346456i
$411$		0			0
$412$	5.86475	+	18.0498i	0.288935	+	0.889251i
$413$	−0.500000	−	1.53884i	−0.0246034	−	0.0757215i
$414$		0			0
$415$	−9.76393	+	7.09391i	−0.479293	+	0.348226i
$416$	8.29180	−	25.5195i	0.406539	−	1.25120i
$417$		0			0
$418$	−1.23607	+	0.277515i	−0.0604581	+	0.0135737i
$419$	8.09017			0.395231			0.197615	−	0.980280i	$-0.436680\pi$
$419$	8.09017			0.395231			0.197615	+	0.980280i	$0.436680\pi$
$420$		0			0
$421$	−8.28115	+	6.01661i	−0.403599	+	0.293232i	−0.771005	−	0.636829i	$-0.780246\pi$
$421$	−8.28115	+	6.01661i	−0.403599	+	0.293232i	0.367407	+	0.930060i	$0.380246\pi$
$422$	6.32624	+	4.59628i	0.307956	+	0.223743i
$423$		0			0
$424$	1.86068	+	5.72658i	0.0903626	+	0.278107i
$425$	13.6353	+	9.90659i	0.661407	+	0.480540i
$426$		0			0
$427$	−3.35410	+	10.3229i	−0.162316	+	0.499558i
$428$	−26.0213			−1.25779
$429$		0			0
$430$	0.875388			0.0422150
$431$	−10.5279	+	32.4014i	−0.507109	+	1.56072i	0.290086	+	0.957001i	$0.406316\pi$
$431$	−10.5279	+	32.4014i	−0.507109	+	1.56072i	−0.797195	+	0.603722i	$0.793684\pi$
$432$		0			0
$433$	−11.9271	−	8.66551i	−0.573177	−	0.416438i	0.263081	−	0.964774i	$-0.415261\pi$
$433$	−11.9271	−	8.66551i	−0.573177	−	0.416438i	−0.836258	+	0.548336i	$0.815261\pi$
$434$	0.0729490	+	0.224514i	0.00350166	+	0.0107770i
$435$		0			0
$436$	10.7188	+	7.78770i	0.513340	+	0.372963i
$437$	−3.73607	+	2.71441i	−0.178720	+	0.129848i
$438$		0			0
$439$	−0.708204			−0.0338007			−0.0169004	−	0.999857i	$-0.505380\pi$
$439$	−0.708204			−0.0338007			−0.0169004	+	0.999857i	$0.505380\pi$
$440$	3.98684	−	4.53077i	0.190065	−	0.215996i
$441$		0			0
$442$	3.70820	−	11.4127i	0.176381	−	0.542846i
$443$	1.00000	−	0.726543i	0.0475114	−	0.0345191i	−0.563776	−	0.825928i	$-0.690652\pi$
$443$	1.00000	−	0.726543i	0.0475114	−	0.0345191i	0.611288	+	0.791409i	$0.290652\pi$
$444$		0			0
$445$	2.58359	+	7.95148i	0.122474	+	0.376936i
$446$	1.83030	+	5.63309i	0.0866674	+	0.266735i
$447$		0			0
$448$	−3.80902	+	2.76741i	−0.179959	+	0.130748i
$449$	2.30902	−	7.10642i	0.108969	−	0.335373i	−0.881672	−	0.471862i	$-0.843582\pi$
$449$	2.30902	−	7.10642i	0.108969	−	0.335373i	0.990642	+	0.136489i	$0.0435820\pi$
$450$		0			0
$451$	−4.27458	−	7.21242i	−0.201282	−	0.339620i
$452$	−31.9574			−1.50315
$453$		0			0
$454$	−5.13525	+	3.73098i	−0.241009	+	0.175104i
$455$	6.47214	+	4.70228i	0.303418	+	0.220446i
$456$		0			0
$457$	−0.309017	−	0.951057i	−0.0144552	−	0.0444885i	0.943569	−	0.331177i	$-0.107446\pi$
$457$	−0.309017	−	0.951057i	−0.0144552	−	0.0444885i	−0.958024	+	0.286688i	$0.907446\pi$
$458$	3.14590	+	2.28563i	0.146998	+	0.106800i
$459$		0			0
$460$	3.27051	−	10.0656i	0.152488	−	0.469311i
$461$	−16.1459			−0.751989			−0.375995	−	0.926622i	$-0.622699\pi$
$461$	−16.1459			−0.751989			−0.375995	+	0.926622i	$0.622699\pi$
$462$		0			0
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$	−4.71885	+	14.5231i	−0.219067	+	0.674219i
$465$		0			0
$466$	−3.43769	−	2.49763i	−0.159248	−	0.115701i
$467$	−0.236068	−	0.726543i	−0.0109239	−	0.0336204i	0.945446	−	0.325779i	$-0.105627\pi$
$467$	−0.236068	−	0.726543i	−0.0109239	−	0.0336204i	−0.956370	+	0.292159i	$0.905627\pi$
$468$		0			0
$469$	4.85410	+	3.52671i	0.224142	+	0.162848i
$470$	−4.56231	+	3.31471i	−0.210443	+	0.152896i
$471$		0			0
$472$	2.38197			0.109639
$473$	0.572949	−	6.12261i	0.0263442	−	0.281518i
$474$		0			0
$475$	−1.07295	+	3.30220i	−0.0492303	+	0.151515i
$476$	−7.28115	+	5.29007i	−0.333731	+	0.242470i
$477$		0			0
$478$	−1.23607	−	3.80423i	−0.0565364	−	0.174001i
$479$	−3.63525	−	11.1882i	−0.166099	−	0.511200i	0.833017	−	0.553248i	$-0.186612\pi$
$479$	−3.63525	−	11.1882i	−0.166099	−	0.511200i	−0.999116	+	0.0420478i	$0.986612\pi$
$480$		0			0
$481$	−26.6525	+	19.3642i	−1.21525	+	0.882930i
$482$	3.16718	−	9.74759i	0.144261	−	0.443991i
$483$		0			0
$484$	−13.9894	−	14.8411i	−0.635880	−	0.674596i
$485$	−7.41641			−0.336762
$486$		0			0
$487$	10.5000	−	7.62870i	0.475800	−	0.345689i	−0.323897	−	0.946092i	$-0.604993\pi$
$487$	10.5000	−	7.62870i	0.475800	−	0.345689i	0.799698	+	0.600403i	$0.204993\pi$
$488$	−12.9271	−	9.39205i	−0.585180	−	0.425158i
$489$		0			0
$490$	−0.875388	−	2.69417i	−0.0395460	−	0.121710i
$491$	−5.92705	−	4.30625i	−0.267484	−	0.194339i	0.445956	−	0.895055i	$-0.352864\pi$
$491$	−5.92705	−	4.30625i	−0.267484	−	0.194339i	−0.713440	+	0.700716i	$0.752864\pi$
$492$		0			0
$493$	−7.28115	+	22.4091i	−0.327927	+	1.00925i
$494$	2.47214			0.111227
$495$		0			0
$496$	1.94427			0.0873004
$497$	0.899187	−	2.76741i	0.0403340	−	0.124135i
$498$		0			0
$499$	−31.0795	−	22.5806i	−1.39131	−	1.01085i	−0.995720	−	0.0924194i	$-0.970540\pi$
$499$	−31.0795	−	22.5806i	−1.39131	−	1.01085i	−0.395591	−	0.918427i	$-0.629460\pi$
$500$	−6.00000	−	18.4661i	−0.268328	−	0.825829i
$501$		0			0
$502$	6.35410	+	4.61653i	0.283597	+	0.206046i
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	−0.402526	−	0.915409i	$-0.631868\pi$
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	0.746218	+	0.665702i	$0.231868\pi$
$504$		0			0
$505$	10.4721			0.466004
$506$	5.37132	+	2.31838i	0.238784	+	0.103065i
$507$		0			0
$508$	6.05166	−	18.6251i	0.268499	−	0.826355i
$509$	21.9894	−	15.9762i	0.974661	−	0.708133i	0.0181520	−	0.999835i	$-0.494222\pi$
$509$	21.9894	−	15.9762i	0.974661	−	0.708133i	0.956509	+	0.291702i	$0.0942217\pi$
$510$		0			0
$511$	0.0450850	+	0.138757i	0.00199444	+	0.00613826i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$		0			0
$514$	−4.60739	+	3.34747i	−0.203223	+	0.147650i
$515$	3.90983	−	12.0332i	0.172288	−	0.530247i
$516$		0			0
$517$	20.1976	+	34.0790i	0.888288	+	1.49879i
$518$	−1.94427			−0.0854264
$519$		0			0
$520$	−9.52786	+	6.92240i	−0.417824	+	0.303567i
$521$	32.6525	+	23.7234i	1.43053	+	1.03934i	0.989918	+	0.141645i	$0.0452390\pi$
$521$	32.6525	+	23.7234i	1.43053	+	1.03934i	0.440613	+	0.897697i	$0.354761\pi$
$522$		0			0
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	31.8541	+	23.1434i	1.39155	+	1.01102i
$525$		0			0
$526$	1.50000	−	4.61653i	0.0654031	−	0.201290i
$527$	3.00000			0.130682
$528$		0			0
$529$	−1.67376			−0.0727723
$530$	0.596748	−	1.83660i	0.0259211	−	0.0797768i
$531$		0			0
$532$	−1.50000	−	1.08981i	−0.0650332	−	0.0472494i
$533$	5.05573	+	15.5599i	0.218988	+	0.673975i
$534$		0			0
$535$	14.0344	+	10.1966i	0.606762	+	0.440838i
$536$	−7.14590	+	5.19180i	−0.308656	+	0.224252i
$537$		0			0
$538$	8.12461			0.350277
$539$	−19.4164	+	4.35926i	−0.836324	+	0.187766i
$540$		0			0
$541$	−3.68034	+	11.3269i	−0.158230	+	0.486982i	−0.998474	−	0.0552266i	$-0.982412\pi$
$541$	−3.68034	+	11.3269i	−0.158230	+	0.486982i	0.840244	+	0.542209i	$0.182412\pi$
$542$	3.32624	−	2.41665i	0.142874	−	0.103804i
$543$		0			0
$544$	−6.21885	−	19.1396i	−0.266631	−	0.820605i
$545$	−2.72949	−	8.40051i	−0.116919	−	0.359838i
$546$		0			0
$547$	26.1525	−	19.0009i	1.11820	−	0.812419i	0.134264	−	0.990946i	$-0.457133\pi$
$547$	26.1525	−	19.0009i	1.11820	−	0.812419i	0.983935	+	0.178526i	$0.0571330\pi$
$548$	4.93769	−	15.1967i	0.210928	−	0.649169i
$549$		0			0
$550$	4.29180	−	0.963568i	0.183003	−	0.0410867i
$551$	−4.85410			−0.206792
$552$		0			0
$553$	8.54508	−	6.20837i	0.363374	−	0.264007i
$554$	−5.94427	−	4.31877i	−0.252548	−	0.183487i
$555$		0			0
$556$	−5.56231	−	17.1190i	−0.235894	−	0.726008i
$557$	0.527864	+	0.383516i	0.0223663	+	0.0162501i	0.598912	−	0.800815i	$-0.295600\pi$
$557$	0.527864	+	0.383516i	0.0223663	+	0.0162501i	−0.576546	+	0.817065i	$0.695600\pi$
$558$		0			0
$559$	−3.70820	+	11.4127i	−0.156840	+	0.482705i
$560$	3.88854			0.164321
$561$		0			0
$562$	3.56231			0.150267
$563$	−6.27458	+	19.3112i	−0.264442	+	0.813868i	0.727380	+	0.686235i	$0.240738\pi$
$563$	−6.27458	+	19.3112i	−0.264442	+	0.813868i	−0.991821	+	0.127633i	$0.959262\pi$
$564$		0			0
$565$	17.2361	+	12.5227i	0.725127	+	0.526835i
$566$	2.00658	+	6.17561i	0.0843428	+	0.259580i
$567$		0			0
$568$	3.46556	+	2.51788i	0.145412	+	0.105648i
$569$	−31.3885	+	22.8051i	−1.31588	+	0.956040i	−0.315902	+	0.948792i	$0.602307\pi$
$569$	−31.3885	+	22.8051i	−1.31588	+	0.956040i	−0.999974	+	0.00724836i	$0.997693\pi$
$570$		0			0
$571$	−18.5279			−0.775367			−0.387683	−	0.921793i	$-0.626725\pi$
$571$	−18.5279			−0.775367			−0.387683	+	0.921793i	$0.626725\pi$
$572$	20.2918	+	34.2380i	0.848443	+	1.43156i
$573$		0			0
$574$	−0.298374	+	0.918300i	−0.0124539	+	0.0383291i
$575$	12.9721	−	9.42481i	0.540975	−	0.393042i
$576$		0			0
$577$	10.9443	+	33.6830i	0.455616	+	1.40224i	0.870410	+	0.492327i	$0.163853\pi$
$577$	10.9443	+	33.6830i	0.455616	+	1.40224i	−0.414794	+	0.909915i	$0.636147\pi$
$578$	−0.774575	−	2.38390i	−0.0322181	−	0.0991570i
$579$		0			0
$580$	9.00000	−	6.53888i	0.373705	−	0.271512i
$581$	3.01722	−	9.28605i	0.125175	−	0.385250i
$582$		0			0
$583$	−12.4549	−	5.37582i	−0.515830	−	0.222644i
$584$	−0.214782			−0.00888773
$585$		0			0
$586$	−9.01722	+	6.55139i	−0.372498	+	0.270636i
$587$	−10.8541	−	7.88597i	−0.447997	−	0.325489i	0.340808	−	0.940133i	$-0.389300\pi$
$587$	−10.8541	−	7.88597i	−0.447997	−	0.325489i	−0.788804	+	0.614644i	$0.789300\pi$
$588$		0			0
$589$	0.190983	+	0.587785i	0.00786932	+	0.0242193i
$590$	−0.618034	−	0.449028i	−0.0254441	−	0.0184862i
$591$		0			0
$592$	−4.94834	+	15.2294i	−0.203375	+	0.625925i
$593$	−10.9443			−0.449427			−0.224714	−	0.974425i	$-0.572145\pi$
$593$	−10.9443			−0.449427			−0.224714	+	0.974425i	$0.572145\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	8.69756	−	26.7683i	0.356266	−	1.09647i
$597$		0			0
$598$	−9.23607	−	6.71040i	−0.377691	−	0.274409i
$599$	−4.12868	−	12.7068i	−0.168693	−	0.519184i	0.830596	−	0.556875i	$-0.188000\pi$
$599$	−4.12868	−	12.7068i	−0.168693	−	0.519184i	−0.999289	+	0.0376909i	$0.988000\pi$
$600$		0			0
$601$	14.1353	+	10.2699i	0.576589	+	0.418916i	0.837493	−	0.546448i	$-0.184021\pi$
$601$	14.1353	+	10.2699i	0.576589	+	0.418916i	−0.260904	+	0.965365i	$0.584021\pi$
$602$	−0.572949	+	0.416272i	−0.0233517	+	0.0169660i
$603$		0			0
$604$	−8.02129			−0.326382
$605$	1.72949	+	13.4863i	0.0703138	+	0.548296i
$606$		0			0
$607$	−1.10739	+	3.40820i	−0.0449476	+	0.138335i	−0.971012	−	0.239031i	$-0.923170\pi$
$607$	−1.10739	+	3.40820i	−0.0449476	+	0.138335i	0.926064	+	0.377366i	$0.123170\pi$
$608$	3.35410	−	2.43690i	0.136027	−	0.0988293i
$609$		0			0
$610$	1.58359	+	4.87380i	0.0641178	+	0.197334i
$611$	−23.8885	−	73.5214i	−0.966427	−	2.97436i
$612$		0			0
$613$	−16.0623	+	11.6699i	−0.648750	+	0.471345i	−0.862845	−	0.505468i	$-0.831320\pi$
$613$	−16.0623	+	11.6699i	−0.648750	+	0.471345i	0.214095	+	0.976813i	$0.431320\pi$
$614$	−0.927051	+	2.85317i	−0.0374127	+	0.115145i
$615$		0			0
$616$	−0.454915	+	4.86128i	−0.0183290	+	0.195867i
$617$	−27.1591			−1.09338			−0.546691	−	0.837334i	$-0.684113\pi$
$617$	−27.1591			−1.09338			−0.546691	+	0.837334i	$0.684113\pi$
$618$		0			0
$619$	−22.2984	+	16.2007i	−0.896247	+	0.651162i	−0.937499	−	0.347987i	$-0.886865\pi$
$619$	−22.2984	+	16.2007i	−0.896247	+	0.651162i	0.0412520	+	0.999149i	$0.486865\pi$
$620$	−1.14590	−	0.832544i	−0.0460204	−	0.0334358i
$621$		0			0
$622$	−1.79180	−	5.51458i	−0.0718445	−	0.221115i
$623$	−5.47214	−	3.97574i	−0.219236	−	0.159285i
$624$		0			0
$625$	1.36475	−	4.20025i	0.0545898	−	0.168010i
$626$	−1.32624			−0.0530071
$627$		0			0
$628$	−13.2492			−0.528702
$629$	−7.63525	+	23.4989i	−0.304438	+	0.936962i
$630$		0			0
$631$	8.80902	+	6.40013i	0.350681	+	0.254785i	0.749155	−	0.662395i	$-0.230460\pi$
$631$	8.80902	+	6.40013i	0.350681	+	0.254785i	−0.398473	+	0.917180i	$0.630460\pi$
$632$	4.80495	+	14.7881i	0.191131	+	0.588240i
$633$		0			0
$634$	6.47214	+	4.70228i	0.257041	+	0.186751i
$635$	−10.5623	+	7.67396i	−0.419152	+	0.304532i
$636$		0			0
$637$	38.8328			1.53861
$638$	3.13525	+	5.29007i	0.124126	+	0.209436i
$639$		0			0
$640$	−3.85410	+	11.8617i	−0.152347	+	0.468875i
$641$	16.5451	−	12.0207i	0.653492	−	0.474789i	−0.210967	−	0.977493i	$-0.567661\pi$
$641$	16.5451	−	12.0207i	0.653492	−	0.474789i	0.864459	+	0.502704i	$0.167661\pi$
$642$		0			0
$643$	−2.11803	−	6.51864i	−0.0835271	−	0.257070i	0.900567	−	0.434717i	$-0.143152\pi$
$643$	−2.11803	−	6.51864i	−0.0835271	−	0.257070i	−0.984094	+	0.177647i	$0.943152\pi$
$644$	2.64590	+	8.14324i	0.104263	+	0.320888i
$645$		0			0
$646$	1.50000	−	1.08981i	0.0590167	−	0.0428782i
$647$	−1.29180	+	3.97574i	−0.0507857	+	0.156302i	−0.973233	−	0.229821i	$-0.926186\pi$
$647$	−1.29180	+	3.97574i	−0.0507857	+	0.156302i	0.922447	+	0.386123i	$0.126186\pi$
$648$		0			0
$649$	−3.54508	+	4.02874i	−0.139157	+	0.158142i
$650$	−8.58359			−0.336676
$651$		0			0
$652$	31.0623	−	22.5681i	1.21649	−	0.883834i
$653$	1.10081	+	0.799788i	0.0430781	+	0.0312981i	0.609116	−	0.793081i	$-0.291524\pi$
$653$	1.10081	+	0.799788i	0.0430781	+	0.0312981i	−0.566038	+	0.824379i	$0.691524\pi$
$654$		0			0
$655$	−8.11146	−	24.9645i	−0.316941	−	0.975444i
$656$	6.43363	+	4.67430i	0.251191	+	0.182501i
$657$		0			0
$658$	1.40983	−	4.33901i	0.0549609	−	0.169152i
$659$	9.97871			0.388715			0.194358	−	0.980931i	$-0.437738\pi$
$659$	9.97871			0.388715			0.194358	+	0.980931i	$0.437738\pi$
$660$		0			0
$661$	−4.29180			−0.166932			−0.0834658	−	0.996511i	$-0.526599\pi$
$661$	−4.29180			−0.166932			−0.0834658	+	0.996511i	$0.526599\pi$
$662$	−1.70163	+	5.23707i	−0.0661356	+	0.203544i
$663$		0			0
$664$	11.6287	+	8.44873i	0.451280	+	0.327874i
$665$	0.381966	+	1.17557i	0.0148120	+	0.0455867i
$666$		0			0
$667$	18.1353	+	13.1760i	0.702200	+	0.510178i
$668$	−8.64590	+	6.28161i	−0.334520	+	0.243043i
$669$		0			0
$670$	2.83282			0.109441
$671$	35.1246	−	7.88597i	1.35597	−	0.304434i
$672$		0			0
$673$	−9.13525	+	28.1154i	−0.352138	+	1.08377i	0.605512	+	0.795836i	$0.292968\pi$
$673$	−9.13525	+	28.1154i	−0.352138	+	1.08377i	−0.957650	+	0.287934i	$0.907032\pi$
$674$	−3.54508	+	2.57565i	−0.136552	+	0.0992105i
$675$		0			0
$676$	−16.5517	−	50.9408i	−0.636602	−	1.95926i
$677$	1.87132	+	5.75934i	0.0719208	+	0.221349i	0.980555	−	0.196243i	$-0.0628741\pi$
$677$	1.87132	+	5.75934i	0.0719208	+	0.221349i	−0.908635	+	0.417592i	$0.862874\pi$
$678$		0			0
$679$	4.85410	−	3.52671i	0.186283	−	0.135343i
$680$	−2.72949	+	8.40051i	−0.104671	+	0.322145i
$681$		0			0
$682$	0.517221	−	0.587785i	0.0198054	−	0.0225075i
$683$	−5.52786			−0.211518			−0.105759	−	0.994392i	$-0.533727\pi$
$683$	−5.52786			−0.211518			−0.105759	+	0.994392i	$0.533727\pi$
$684$		0			0
$685$	−8.61803	+	6.26137i	−0.329278	+	0.239235i
$686$	4.01722	+	2.91868i	0.153378	+	0.111436i
$687$		0			0
$688$	1.80244	+	5.54734i	0.0687173	+	0.211490i
$689$	21.4164	+	15.5599i	0.815900	+	0.592786i
$690$		0			0
$691$	4.51064	−	13.8823i	0.171593	−	0.528109i	−0.827869	−	0.560922i	$-0.810447\pi$
$691$	4.51064	−	13.8823i	0.171593	−	0.528109i	0.999461	+	0.0328134i	$0.0104467\pi$
$692$	42.8115			1.62745
$693$		0			0
$694$	3.39512			0.128877
$695$	−3.70820	+	11.4127i	−0.140660	+	0.432908i
$696$		0			0
$697$	9.92705	+	7.21242i	0.376014	+	0.273190i
$698$	0.489357	+	1.50609i	0.0185224	+	0.0570062i
$699$		0			0
$700$	5.20820	+	3.78398i	0.196852	+	0.143021i
$701$	38.6074	−	28.0499i	1.45818	−	1.05943i	0.474349	−	0.880337i	$-0.342683\pi$
$701$	38.6074	−	28.0499i	1.45818	−	1.05943i	0.983832	−	0.179094i	$-0.0573165\pi$
$702$		0			0
$703$	−5.09017			−0.191979
$704$	14.3369	+	6.18812i	0.540342	+	0.233224i
$705$		0			0
$706$	1.93769	−	5.96361i	0.0729261	−	0.224443i
$707$	−6.85410	+	4.97980i	−0.257775	+	0.187285i
$708$		0			0
$709$	−7.96149	−	24.5030i	−0.299000	−	0.920228i	−0.981848	−	0.189668i	$-0.939259\pi$
$709$	−7.96149	−	24.5030i	−0.299000	−	0.920228i	0.682848	−	0.730560i	$-0.260741\pi$
$710$	−0.424538	−	1.30660i	−0.0159326	−	0.0490356i
$711$		0			0
$712$	8.05573	−	5.85283i	0.301901	−	0.219344i
$713$	0.881966	−	2.71441i	0.0330299	−	0.101656i
$714$		0			0
$715$	2.47214	−	26.4176i	0.0924526	−	0.987961i
$716$	9.37384			0.350317
$717$		0			0
$718$	−7.06231	+	5.13107i	−0.263563	+	0.191490i
$719$	15.8541	+	11.5187i	0.591258	+	0.429574i	0.842765	−	0.538281i	$-0.180926\pi$
$719$	15.8541	+	11.5187i	0.591258	+	0.429574i	−0.251507	+	0.967855i	$0.580926\pi$
$720$		0			0
$721$	3.16312	+	9.73508i	0.117801	+	0.362553i
$722$	−5.56231	−	4.04125i	−0.207008	−	0.150400i
$723$		0			0
$724$	5.67783	−	17.4746i	0.211015	−	0.649437i
$725$	16.8541			0.625946
$726$		0			0
$727$	18.8328			0.698470			0.349235	−	0.937035i	$-0.386441\pi$
$727$	18.8328			0.698470			0.349235	+	0.937035i	$0.386441\pi$
$728$	2.94427	−	9.06154i	0.109122	−	0.335843i
$729$		0			0
$730$	0.0557281	+	0.0404888i	0.00206259	+	0.00149856i
$731$	2.78115	+	8.55951i	0.102865	+	0.316585i
$732$		0			0
$733$	−39.2148	−	28.4912i	−1.44843	−	1.05235i	−0.986195	−	0.165590i	$-0.947047\pi$
$733$	−39.2148	−	28.4912i	−1.44843	−	1.05235i	−0.462236	−	0.886757i	$-0.652953\pi$
$734$	−3.92705	+	2.85317i	−0.144950	+	0.105312i
$735$		0			0
$736$	−19.1459			−0.705727
$737$	1.85410	−	19.8132i	0.0682967	−	0.729828i
$738$		0			0
$739$	13.1459	−	40.4589i	0.483580	−	1.48831i	−0.350448	−	0.936582i	$-0.613971\pi$
$739$	13.1459	−	40.4589i	0.483580	−	1.48831i	0.834027	−	0.551723i	$-0.186029\pi$
$740$	9.43769	−	6.85689i	0.346937	−	0.252064i
$741$		0			0
$742$	0.482779	+	1.48584i	0.0177234	+	0.0545469i
$743$	−13.0902	−	40.2874i	−0.480232	−	1.47800i	−0.838770	−	0.544486i	$-0.816725\pi$
$743$	−13.0902	−	40.2874i	−0.480232	−	1.47800i	0.358538	−	0.933515i	$-0.383275\pi$
$744$		0			0
$745$	−15.1803	+	11.0292i	−0.556165	+	0.404077i
$746$	0.667184	−	2.05338i	0.0244274	−	0.0751797i
$747$		0			0
$748$	27.4058	+	11.8290i	1.00205	+	0.432509i
$749$	−14.0344			−0.512807
$750$		0			0
$751$	25.2812	−	18.3678i	0.922522	−	0.670252i	−0.0216282	−	0.999766i	$-0.506885\pi$
$751$	25.2812	−	18.3678i	0.922522	−	0.670252i	0.944151	+	0.329514i	$0.106885\pi$
$752$	−30.3992	−	22.0863i	−1.10854	−	0.805405i
$753$		0			0
$754$	−3.70820	−	11.4127i	−0.135045	−	0.415625i
$755$	4.32624	+	3.14320i	0.157448	+	0.114393i
$756$		0			0
$757$	3.39919	−	10.4616i	0.123546	−	0.380234i	−0.870088	−	0.492897i	$-0.835938\pi$
$757$	3.39919	−	10.4616i	0.123546	−	0.380234i	0.993633	+	0.112663i	$0.0359380\pi$
$758$	−6.03444			−0.219181
$759$		0			0
$760$	−1.81966			−0.0660060
$761$	2.15654	−	6.63715i	0.0781746	−	0.240597i	−0.904330	−	0.426833i	$-0.859629\pi$
$761$	2.15654	−	6.63715i	0.0781746	−	0.240597i	0.982505	+	0.186237i	$0.0596291\pi$
$762$		0			0
$763$	5.78115	+	4.20025i	0.209292	+	0.152059i
$764$	−3.40576	−	10.4819i	−0.123216	−	0.379221i
$765$		0			0
$766$	6.13525	+	4.45752i	0.221676	+	0.161057i
$767$	8.47214	−	6.15537i	0.305911	−	0.222257i
$768$		0			0
$769$	−15.7984			−0.569704			−0.284852	−	0.958572i	$-0.591944\pi$
$769$	−15.7984			−0.569704			−0.284852	+	0.958572i	$0.591944\pi$
$770$	1.03444	−	1.17557i	0.0372787	−	0.0423646i
$771$		0			0
$772$	6.30244	−	19.3969i	0.226830	−	0.698110i
$773$	−19.1353	+	13.9026i	−0.688247	+	0.500041i	−0.876083	−	0.482159i	$-0.839853\pi$
$773$	−19.1353	+	13.9026i	−0.688247	+	0.500041i	0.187836	+	0.982200i	$0.439853\pi$
$774$		0			0
$775$	−0.663119	−	2.04087i	−0.0238199	−	0.0733102i
$776$	2.72949	+	8.40051i	0.0979830	+	0.301561i
$777$		0			0
$778$	−7.00000	+	5.08580i	−0.250962	+	0.182335i
$779$	−0.781153	+	2.40414i	−0.0279877	+	0.0861373i
$780$		0			0
$781$	−9.41641	+	2.11412i	−0.336946	+	0.0756490i
$782$	−8.56231			−0.306187
$783$		0			0
$784$	15.2705	−	11.0947i	0.545375	−	0.396238i
$785$	7.14590	+	5.19180i	0.255048	+	0.185303i
$786$		0			0
$787$	11.1246	+	34.2380i	0.396550	+	1.22045i	0.927748	+	0.373207i	$0.121742\pi$
$787$	11.1246	+	34.2380i	0.396550	+	1.22045i	−0.531199	+	0.847247i	$0.678258\pi$
$788$	12.3541	+	8.97578i	0.440097	+	0.319749i
$789$		0			0
$790$	1.54102	−	4.74277i	0.0548270	−	0.168740i
$791$	−17.2361			−0.612844
$792$		0			0
$793$	−70.2492			−2.49462
$794$	0.250776	−	0.771810i	0.00889972	−	0.0273905i
$795$		0			0
$796$	−10.7188	−	7.78770i	−0.379919	−	0.276028i
$797$	7.50000	+	23.0826i	0.265664	+	0.817629i	0.991540	+	0.129803i	$0.0414345\pi$
$797$	7.50000	+	23.0826i	0.265664	+	0.817629i	−0.725876	+	0.687825i	$0.758565\pi$
$798$		0			0
$799$	−46.9058	−	34.0790i	−1.65941	−	1.20563i
$800$	−11.6459	+	8.46124i	−0.411745	+	0.299150i
$801$		0			0
$802$	−5.56231			−0.196412
$803$	0.319660	−	0.363271i	0.0112806	−	0.0128196i
$804$		0			0
$805$	1.76393	−	5.42882i	0.0621704	−	0.191341i
$806$	−1.23607	+	0.898056i	−0.0435386	+	0.0316327i
$807$		0			0
$808$	−3.85410	−	11.8617i	−0.135587	−	0.417293i
$809$	−5.59017	−	17.2048i	−0.196540	−	0.604888i	−0.999955	−	0.00946853i	$-0.996986\pi$
$809$	−5.59017	−	17.2048i	−0.196540	−	0.604888i	0.803415	−	0.595419i	$-0.203014\pi$
$810$		0			0
$811$	−7.02786	+	5.10604i	−0.246782	+	0.179297i	−0.704299	−	0.709903i	$-0.748739\pi$
$811$	−7.02786	+	5.10604i	−0.246782	+	0.179297i	0.457518	+	0.889201i	$0.348739\pi$
$812$	−2.78115	+	8.55951i	−0.0975993	+	0.300380i
$813$		0			0
$814$	3.28773	+	5.54734i	0.115235	+	0.194434i
$815$	−25.5967			−0.896615
$816$		0			0
$817$	−1.50000	+	1.08981i	−0.0524784	+	0.0381278i
$818$	−10.4271	−	7.57570i	−0.364573	−	0.264878i
$819$		0			0
$820$	−1.79024	−	5.50980i	−0.0625180	−	0.192411i
$821$	−30.9164	−	22.4621i	−1.07899	−	0.783932i	−0.101484	−	0.994837i	$-0.532359\pi$
$821$	−30.9164	−	22.4621i	−1.07899	−	0.783932i	−0.977507	+	0.210905i	$0.932359\pi$
$822$		0			0
$823$	−13.0689	+	40.2219i	−0.455553	+	1.40205i	0.414932	+	0.909852i	$0.363805\pi$
$823$	−13.0689	+	40.2219i	−0.455553	+	1.40205i	−0.870485	+	0.492195i	$0.836195\pi$
$824$	−15.0689			−0.524949
$825$		0			0
$826$	0.618034			0.0215042
$827$	−17.6246	+	54.2430i	−0.612868	+	1.88621i	−0.183721	+	0.982978i	$0.558814\pi$
$827$	−17.6246	+	54.2430i	−0.612868	+	1.88621i	−0.429147	+	0.903235i	$0.641186\pi$
$828$		0			0
$829$	−35.2254	−	25.5928i	−1.22343	−	0.888874i	−0.227049	−	0.973883i	$-0.572908\pi$
$829$	−35.2254	−	25.5928i	−1.22343	−	0.888874i	−0.996380	+	0.0850096i	$0.972908\pi$
$830$	−1.42454	−	4.38428i	−0.0494465	−	0.152181i
$831$		0			0
$832$	−24.6525	−	17.9111i	−0.854671	−	0.620955i
$833$	23.5623	−	17.1190i	0.816386	−	0.593139i
$834$		0			0
$835$	7.12461			0.246557
$836$	−0.572949	+	6.12261i	−0.0198159	+	0.211755i
$837$		0			0
$838$	−0.954915	+	2.93893i	−0.0329870	+	0.101524i
$839$	13.9894	−	10.1639i	0.482966	−	0.350896i	−0.319507	−	0.947584i	$-0.603517\pi$
$839$	13.9894	−	10.1639i	0.482966	−	0.350896i	0.802473	+	0.596689i	$0.203517\pi$
$840$		0			0
$841$	−1.68034	−	5.17155i	−0.0579428	−	0.178329i
$842$	−1.20820	−	3.71847i	−0.0416375	−	0.128147i
$843$		0			0
$844$	30.7082	−	22.3108i	1.05702	−	0.767970i
$845$	−11.0344	+	33.9605i	−0.379596	+	1.16828i
$846$		0			0
$847$	−7.54508	−	8.00448i	−0.259252	−	0.275037i
$848$	12.8673			0.441863
$849$		0			0
$850$	−5.20820	+	3.78398i	−0.178640	+	0.129789i
$851$	19.0172	+	13.8168i	0.651902	+	0.473634i
$852$		0			0
$853$	−10.9508	−	33.7032i	−0.374950	−	1.15398i	−0.943512	−	0.331337i	$-0.892500\pi$
$853$	−10.9508	−	33.7032i	−0.374950	−	1.15398i	0.568562	−	0.822640i	$-0.307500\pi$
$854$	−3.35410	−	2.43690i	−0.114775	−	0.0833889i
$855$		0			0
$856$	6.38448	−	19.6494i	0.218217	−	0.671603i
$857$	25.3607			0.866304			0.433152	−	0.901321i	$-0.357401\pi$
$857$	25.3607			0.866304			0.433152	+	0.901321i	$0.357401\pi$
$858$		0			0
$859$	−32.5623			−1.11101			−0.555506	−	0.831513i	$-0.687475\pi$
$859$	−32.5623			−1.11101			−0.555506	+	0.831513i	$0.687475\pi$
$860$	1.31308	−	4.04125i	0.0447757	−	0.137806i
$861$		0			0
$862$	−10.5279	−	7.64894i	−0.358580	−	0.260524i
$863$	4.46556	+	13.7436i	0.152009	+	0.467837i	0.997846	−	0.0656059i	$-0.0208980\pi$
$863$	4.46556	+	13.7436i	0.152009	+	0.467837i	−0.845836	+	0.533443i	$0.820898\pi$
$864$		0			0
$865$	−23.0902	−	16.7760i	−0.785089	−	0.570401i
$866$	4.55573	−	3.30993i	0.154810	−	0.112476i
$867$		0			0
$868$	1.14590			0.0388943
$869$	−32.1631	−	13.8823i	−1.09106	−	0.470926i
$870$		0			0
$871$	−12.0000	+	36.9322i	−0.406604	+	1.25140i
$872$	−8.51064	+	6.18334i	−0.288207	+	0.209394i
$873$		0			0
$874$	−0.545085	−	1.67760i	−0.0184378	−	0.0567456i
$875$	−3.23607	−	9.95959i	−0.109399	−	0.336696i
$876$		0			0
$877$	−9.38197	+	6.81640i	−0.316806	+	0.230173i	−0.734812	−	0.678271i	$-0.762729\pi$
$877$	−9.38197	+	6.81640i	−0.316806	+	0.230173i	0.418005	+	0.908445i	$0.362729\pi$
$878$	0.0835921	−	0.257270i	0.00282110	−	0.00868245i
$879$		0			0
$880$	−6.57546	−	11.0947i	−0.221659	−	0.374001i
$881$	1.81966			0.0613059			0.0306530	−	0.999530i	$-0.490241\pi$
$881$	1.81966			0.0613059			0.0306530	+	0.999530i	$0.490241\pi$
$882$		0			0
$883$	28.8435	−	20.9560i	0.970660	−	0.705226i	0.0150579	−	0.999887i	$-0.495207\pi$
$883$	28.8435	−	20.9560i	0.970660	−	0.705226i	0.955602	+	0.294661i	$0.0952068\pi$
$884$	−47.1246	−	34.2380i	−1.58497	−	1.15155i
$885$		0			0
$886$	0.145898	+	0.449028i	0.00490154	+	0.0150854i
$887$	3.26393	+	2.37139i	0.109592	+	0.0796233i	0.641232	−	0.767347i	$-0.278424\pi$
$887$	3.26393	+	2.37139i	0.109592	+	0.0796233i	−0.531639	+	0.846971i	$0.678424\pi$
$888$		0			0
$889$	3.26393	−	10.0453i	0.109469	−	0.336910i
$890$	−3.19350			−0.107046
$891$		0			0
$892$	28.7508			0.962647
$893$	3.69098	−	11.3597i	0.123514	−	0.380137i
$894$		0			0
$895$	−5.05573	−	3.67320i	−0.168994	−	0.122782i
$896$	−3.11803	−	9.59632i	−0.104166	−	0.320591i
$897$		0			0
$898$	2.30902	+	1.67760i	0.0770529	+	0.0559822i
$899$	2.42705	−	1.76336i	0.0809467	−	0.0588112i
$900$		0			0
$901$	19.8541			0.661436
$902$	3.12461	−	0.701519i	0.104038	−	0.0233580i
$903$		0			0
$904$	7.84095	−	24.1320i	0.260786	−	0.802617i
$905$	−9.90983	+	7.19991i	−0.329414	+	0.239333i
$906$		0			0
$907$	−4.50658	−	13.8698i	−0.149638	−	0.460540i	0.847940	−	0.530093i	$-0.177843\pi$
$907$	−4.50658	−	13.8698i	−0.149638	−	0.460540i	−0.997578	+	0.0695527i	$0.977843\pi$
$908$	9.52129	+	29.3035i	0.315975	+	0.972471i
$909$		0			0
$910$	−2.47214	+	1.79611i	−0.0819505	+	0.0595405i
$911$	−5.92705	+	18.2416i	−0.196372	+	0.604371i	0.803586	+	0.595189i	$0.202923\pi$
$911$	−5.92705	+	18.2416i	−0.196372	+	0.604371i	−0.999958	+	0.00918193i	$0.997077\pi$
$912$		0			0
$913$	−31.5967	+	7.09391i	−1.04570	+	0.234774i
$914$	0.381966			0.0126343
$915$		0			0
$916$	15.2705	−	11.0947i	0.504552	−	0.366578i
$917$	17.1803	+	12.4822i	0.567345	+	0.412200i
$918$		0			0
$919$	−8.30244	−	25.5523i	−0.273872	−	0.842892i	−0.989516	−	0.144426i	$-0.953866\pi$
$919$	−8.30244	−	25.5523i	−0.273872	−	0.842892i	0.715643	−	0.698466i	$-0.246134\pi$
$920$	6.79837	+	4.93931i	0.224136	+	0.162844i
$921$		0			0
$922$	1.90576	−	5.86534i	0.0627630	−	0.193165i
$923$	18.8328			0.619890
$924$		0			0
$925$	17.6738			0.581110
$926$	−2.00658	+	6.17561i	−0.0659402	+	0.202943i
$927$		0			0
$928$	−16.2812	−	11.8290i	−0.534455	−	0.388304i
$929$	−14.9164	−	45.9080i	−0.489391	−	1.50619i	−0.825518	−	0.564375i	$-0.809117\pi$
$929$	−14.9164	−	45.9080i	−0.489391	−	1.50619i	0.336127	−	0.941817i	$-0.390883\pi$
$930$		0			0
$931$	4.85410	+	3.52671i	0.159087	+	0.115583i
$932$	−16.6869	+	12.1238i	−0.546598	+	0.397127i
$933$		0			0
$934$	0.291796			0.00954786
$935$	−10.1459	−	17.1190i	−0.331806	−	0.559852i
$936$		0			0
$937$	−7.11803	+	21.9071i	−0.232536	+	0.715672i	0.764903	+	0.644146i	$0.222787\pi$
$937$	−7.11803	+	21.9071i	−0.232536	+	0.715672i	−0.997439	+	0.0715265i	$0.977213\pi$
$938$	−1.85410	+	1.34708i	−0.0605386	+	0.0439838i
$939$		0			0
$940$	8.45898	+	26.0341i	0.275902	+	0.849138i
$941$	8.39261	+	25.8298i	0.273591	+	0.842027i	0.989589	+	0.143924i	$0.0459722\pi$
$941$	8.39261	+	25.8298i	0.273591	+	0.842027i	−0.715997	+	0.698103i	$0.754028\pi$
$942$		0			0
$943$	9.44427	−	6.86167i	0.307548	−	0.223447i
$944$	1.57295	−	4.84104i	0.0511951	−	0.157562i
$945$		0			0
$946$	2.15654	+	0.930812i	0.0701152	+	0.0302633i
$947$	36.7082			1.19286			0.596428	−	0.802666i	$-0.296586\pi$
$947$	36.7082			1.19286			0.596428	+	0.802666i	$0.296586\pi$
$948$		0			0
$949$	−0.763932	+	0.555029i	−0.0247983	+	0.0180170i
$950$	−1.07295	−	0.779543i	−0.0348111	−	0.0252917i
$951$		0			0
$952$	−2.20820	−	6.79615i	−0.0715683	−	0.220265i
$953$	7.68034	+	5.58009i	0.248791	+	0.180757i	0.705191	−	0.709018i	$-0.250861\pi$
$953$	7.68034	+	5.58009i	0.248791	+	0.180757i	−0.456400	+	0.889775i	$0.650861\pi$
$954$		0			0
$955$	−2.27051	+	6.98791i	−0.0734720	+	0.226123i
$956$	−19.4164			−0.627972
$957$		0			0
$958$	4.49342			0.145176
$959$	2.66312	−	8.19624i	0.0859966	−	0.264670i
$960$		0			0
$961$	24.7705	+	17.9968i	0.799049	+	0.580543i
$962$	−3.88854	−	11.9677i	−0.125372	−	0.385854i
$963$		0			0
$964$	−40.2492	−	29.2428i	−1.29634	−	0.941846i
$965$	−11.0000	+	7.99197i	−0.354103	+	0.257271i
$966$		0			0
$967$	52.4853			1.68781			0.843907	−	0.536490i	$-0.180250\pi$
$967$	52.4853			1.68781			0.843907	+	0.536490i	$0.180250\pi$
$968$	14.6393	−	6.92240i	0.470526	−	0.222494i
$969$		0			0
$970$	0.875388	−	2.69417i	0.0281070	−	0.0865045i
$971$	−7.50000	+	5.44907i	−0.240686	+	0.174869i	−0.701589	−	0.712582i	$-0.747526\pi$
$971$	−7.50000	+	5.44907i	−0.240686	+	0.174869i	0.460903	+	0.887451i	$0.347526\pi$
$972$		0			0
$973$	−3.00000	−	9.23305i	−0.0961756	−	0.295998i
$974$	1.53193	+	4.71479i	0.0490862	+	0.151072i
$975$		0			0
$976$	−27.6246	+	20.0705i	−0.884242	+	0.642440i
$977$	4.87132	−	14.9924i	0.155847	−	0.479649i	−0.842398	−	0.538855i	$-0.818857\pi$
$977$	4.87132	−	14.9924i	0.155847	−	0.479649i	0.998246	+	0.0592062i	$0.0188570\pi$
$978$		0			0
$979$	−2.09017	+	22.3358i	−0.0668021	+	0.713857i
$980$	−13.7508			−0.439252
$981$		0			0
$982$	2.26393	−	1.64484i	0.0722450	−	0.0524890i
$983$	−7.48936	−	5.44134i	−0.238873	−	0.173552i	0.461908	−	0.886928i	$-0.347165\pi$
$983$	−7.48936	−	5.44134i	−0.238873	−	0.173552i	−0.700781	+	0.713376i	$0.747165\pi$
$984$		0			0
$985$	−3.14590	−	9.68208i	−0.100237	−	0.308497i
$986$	−7.28115	−	5.29007i	−0.231879	−	0.168470i
$987$		0			0
$988$	3.70820	−	11.4127i	0.117974	−	0.363086i
$989$	8.56231			0.272265
$990$		0			0
$991$	20.5967			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$991$	20.5967			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$992$	−0.791796	+	2.43690i	−0.0251396	+	0.0773716i
$993$		0			0
$994$	0.899187	+	0.653298i	0.0285205	+	0.0207213i
$995$	2.72949	+	8.40051i	0.0865307	+	0.266314i
$996$		0			0
$997$	−5.97214	−	4.33901i	−0.189139	−	0.137418i	0.489186	−	0.872180i	$-0.337294\pi$
$997$	−5.97214	−	4.33901i	−0.189139	−	0.137418i	−0.678325	+	0.734762i	$0.737294\pi$
$998$	11.8713	−	8.62502i	0.375780	−	0.273020i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.b.163.1		4
3.2	odd	2		891.2.f.a.163.1		4
9.2	odd	6		297.2.n.a.64.1		8
9.4	even	3		99.2.m.a.97.1	yes	8
9.5	odd	6		297.2.n.a.262.1		8
9.7	even	3		99.2.m.a.31.1	yes	8
11.4	even	5		9801.2.a.n.1.2		2
11.5	even	5	inner	891.2.f.b.82.1		4
11.7	odd	10		9801.2.a.bc.1.1		2
33.5	odd	10		891.2.f.a.82.1		4
33.26	odd	10		9801.2.a.bb.1.1		2
33.29	even	10		9801.2.a.m.1.2		2
99.4	even	15		1089.2.e.g.727.1		4
99.5	odd	30		297.2.n.a.181.1		8
99.7	odd	30		1089.2.e.d.364.2		4
99.16	even	15		99.2.m.a.49.1	yes	8
99.38	odd	30		297.2.n.a.280.1		8
99.40	odd	30		1089.2.e.d.727.2		4
99.49	even	15		99.2.m.a.16.1	✓	8
99.70	even	15		1089.2.e.g.364.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	99.49	even	15
99.2.m.a.31.1	yes	8	9.7	even	3
99.2.m.a.49.1	yes	8	99.16	even	15
99.2.m.a.97.1	yes	8	9.4	even	3
297.2.n.a.64.1		8	9.2	odd	6
297.2.n.a.181.1		8	99.5	odd	30
297.2.n.a.262.1		8	9.5	odd	6
297.2.n.a.280.1		8	99.38	odd	30
891.2.f.a.82.1		4	33.5	odd	10
891.2.f.a.163.1		4	3.2	odd	2
891.2.f.b.82.1		4	11.5	even	5	inner
891.2.f.b.163.1		4	1.1	even	1	trivial
1089.2.e.d.364.2		4	99.7	odd	30
1089.2.e.d.727.2		4	99.40	odd	30
1089.2.e.g.364.1		4	99.70	even	15
1089.2.e.g.727.1		4	99.4	even	15
9801.2.a.m.1.2		2	33.29	even	10
9801.2.a.n.1.2		2	11.4	even	5
9801.2.a.bb.1.1		2	33.26	odd	10
9801.2.a.bc.1.1		2	11.7	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118034 + 0.363271i) q^{2} +(1.50000 + 1.08981i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +0.472136 q^{10} +(0.309017 - 3.30220i) q^{11} +(-2.00000 + 6.15537i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(0.972136 + 2.99193i) q^{16} +(1.50000 + 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(0.708204 - 2.17963i) q^{20} +(1.16312 + 0.502029i) q^{22} +4.61803 q^{23} +(2.80902 - 2.04087i) q^{25} +(-2.00000 - 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(3.92705 + 2.85317i) q^{29} +(0.190983 - 0.587785i) q^{31} -4.14590 q^{32} -1.85410 q^{34} +(0.381966 - 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(-0.118034 - 0.363271i) q^{38} +(1.47214 + 1.06957i) q^{40} +(2.04508 - 1.48584i) q^{41} +1.85410 q^{43} +(4.06231 - 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-9.66312 + 7.02067i) q^{47} +(-1.85410 - 5.70634i) q^{49} +(0.409830 + 1.26133i) q^{50} +(-9.70820 + 7.05342i) q^{52} +(1.26393 - 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} -1.47214 q^{56} +(-1.50000 + 1.08981i) q^{58} +(-1.30902 - 0.951057i) q^{59} +(3.35410 + 10.3229i) q^{61} +(0.190983 + 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(-2.78115 + 8.55951i) q^{68} +(0.381966 + 0.277515i) q^{70} +(-0.899187 - 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.57295 + 1.14281i) q^{74} -1.85410 q^{76} +(2.19098 - 2.48990i) q^{77} +(3.26393 - 10.0453i) q^{79} +(3.14590 - 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(-3.01722 - 9.28605i) q^{83} +(4.85410 - 3.52671i) q^{85} +(-0.218847 + 0.673542i) q^{86} +(2.48936 + 4.20025i) q^{88} -6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(6.92705 + 5.03280i) q^{92} +(-1.40983 - 4.33901i) q^{94} +(1.00000 + 0.726543i) q^{95} +(1.85410 - 5.70634i) q^{97} +2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^4 - 6 * q^5 + q^7 - 7 * q^8 - 16 * q^10 - q^11 - 8 * q^13 + q^14 - 14 * q^16 + 6 * q^17 - q^19 - 24 * q^20 - 11 * q^22 + 14 * q^23 + 9 * q^25 - 8 * q^26 + 9 * q^28 + 9 * q^29 + 3 * q^31 - 30 * q^32 + 6 * q^34 + 6 * q^35 + 12 * q^37 + 4 * q^38 - 12 * q^40 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 9 * q^46 - 23 * q^47 + 6 * q^49 + 24 * q^50 - 12 * q^52 + 14 * q^53 - 16 * q^55 + 12 * q^56 - 6 * q^58 - 3 * q^59 + 3 * q^62 - 17 * q^64 + 32 * q^65 + 24 * q^67 + 9 * q^68 + 6 * q^70 + 21 * q^71 - 4 * q^73 - 13 * q^74 + 6 * q^76 + 11 * q^77 + 22 * q^79 + 26 * q^80 - 48 * q^82 + 17 * q^83 + 6 * q^85 - 21 * q^86 - 37 * q^88 - 36 * q^89 - 12 * q^91 + 21 * q^92 - 28 * q^94 + 4 * q^95 - 6 * q^97 + 36 * q^98

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