LMFDB - Embedded newform 99.2.f.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$-1.73855 - 1.26313i$ of defining polynomial
Character	$\chi$	$=$	99.37
Dual form			99.2.f.c.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73855 - 1.26313i) q^{2} +(0.809017 + 2.48990i) q^{4} +(1.73855 - 1.26313i) q^{5} +(-1.30902 - 4.02874i) q^{7} +(0.410415 - 1.26313i) q^{8} +O(q^{10})$	\(q+(-1.73855 - 1.26313i) q^{2} +(0.809017 + 2.48990i) q^{4} +(1.73855 - 1.26313i) q^{5} +(-1.30902 - 4.02874i) q^{7} +(0.410415 - 1.26313i) q^{8} -4.61803 q^{10} +(-3.22344 - 0.780656i) q^{11} +(-0.190983 - 0.138757i) q^{13} +(-2.81303 + 8.65761i) q^{14} +(1.92705 - 1.40008i) q^{16} +(4.96199 - 3.60510i) q^{17} +(-0.736068 + 2.26538i) q^{19} +(4.55157 + 3.30691i) q^{20} +(4.61803 + 5.42882i) q^{22} +3.98439 q^{23} +(-0.118034 + 0.363271i) q^{25} +(0.156765 + 0.482472i) q^{26} +(8.97214 - 6.51864i) q^{28} +(2.14896 + 6.61382i) q^{29} +(3.73607 + 2.71441i) q^{31} -7.77501 q^{32} -13.1803 q^{34} +(-7.36460 - 5.35069i) q^{35} +(0.545085 + 1.67760i) q^{37} +(4.14116 - 3.00873i) q^{38} +(-0.881966 - 2.71441i) q^{40} +(-0.917716 + 2.82444i) q^{41} +2.70820 q^{43} +(-0.664066 - 8.65761i) q^{44} +(-6.92705 - 5.03280i) q^{46} +(1.07448 - 3.30691i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(0.664066 - 0.482472i) q^{50} +(0.190983 - 0.587785i) q^{52} +(1.48490 + 1.07884i) q^{53} +(-6.59017 + 2.71441i) q^{55} -5.62605 q^{56} +(4.61803 - 14.2128i) q^{58} +(-2.30573 - 7.09629i) q^{59} +(9.16312 - 6.65740i) q^{61} +(-3.06668 - 9.43826i) q^{62} +(9.66312 + 7.02067i) q^{64} -0.507301 q^{65} -2.85410 q^{67} +(12.9907 + 9.43826i) q^{68} +(6.04508 + 18.6049i) q^{70} +(-8.69273 + 6.31564i) q^{71} +(0.763932 + 2.35114i) q^{73} +(1.17137 - 3.60510i) q^{74} -6.23607 q^{76} +(1.07448 + 14.0083i) q^{77} +(7.66312 + 5.56758i) q^{79} +(1.58178 - 4.86822i) q^{80} +(5.16312 - 3.75123i) q^{82} +(-6.70053 + 4.86822i) q^{83} +(4.07295 - 12.5352i) q^{85} +(-4.70834 - 3.42081i) q^{86} +(-2.30902 + 3.75123i) q^{88} +8.90937 q^{89} +(-0.309017 + 0.951057i) q^{91} +(3.22344 + 9.92073i) q^{92} +(-6.04508 + 4.39201i) q^{94} +(1.58178 + 4.86822i) q^{95} +(-9.54508 - 6.93491i) q^{97} +23.5188 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 28 q^{10} - 6 q^{13} + 2 q^{16} + 12 q^{19} + 28 q^{22} + 8 q^{25} + 36 q^{28} + 12 q^{31} - 16 q^{34} - 18 q^{37} - 16 q^{40} - 32 q^{43} - 42 q^{46} - 44 q^{49} + 6 q^{52} - 8 q^{55} + 28 q^{58} + 42 q^{61} + 46 q^{64} + 4 q^{67} + 26 q^{70} + 24 q^{73} - 32 q^{76} + 30 q^{79} + 10 q^{82} + 46 q^{85} - 14 q^{88} + 2 q^{91} - 26 q^{94} - 54 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 28 * q^10 - 6 * q^13 + 2 * q^16 + 12 * q^19 + 28 * q^22 + 8 * q^25 + 36 * q^28 + 12 * q^31 - 16 * q^34 - 18 * q^37 - 16 * q^40 - 32 * q^43 - 42 * q^46 - 44 * q^49 + 6 * q^52 - 8 * q^55 + 28 * q^58 + 42 * q^61 + 46 * q^64 + 4 * q^67 + 26 * q^70 + 24 * q^73 - 32 * q^76 + 30 * q^79 + 10 * q^82 + 46 * q^85 - 14 * q^88 + 2 * q^91 - 26 * q^94 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−1.73855	−	1.26313i	−1.22934	−	0.893166i	−0.232497	−	0.972597i	$-0.574690\pi$
$2$	−1.73855	−	1.26313i	−1.22934	−	0.893166i	−0.996840	+	0.0794309i	$0.974690\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	+	2.48990i	0.404508	+	1.24495i
$5$	1.73855	−	1.26313i	0.777501	−	0.564888i	−0.126727	−	0.991938i	$-0.540447\pi$
$5$	1.73855	−	1.26313i	0.777501	−	0.564888i	0.904228	+	0.427050i	$0.140447\pi$
$6$		0			0
$7$	−1.30902	−	4.02874i	−0.494762	−	1.52272i	−0.817327	−	0.576173i	$-0.804545\pi$
$7$	−1.30902	−	4.02874i	−0.494762	−	1.52272i	0.322566	−	0.946547i	$-0.395455\pi$
$8$	0.410415	−	1.26313i	0.145104	−	0.446583i
$9$		0			0
$10$	−4.61803			−1.46035
$11$	−3.22344	−	0.780656i	−0.971904	−	0.235377i
$11$	−3.22344	−	0.780656i	−0.971904	−	0.235377i
$12$		0			0
$13$	−0.190983	−	0.138757i	−0.0529692	−	0.0384843i	0.560986	−	0.827826i	$-0.310422\pi$
$13$	−0.190983	−	0.138757i	−0.0529692	−	0.0384843i	−0.613955	+	0.789341i	$0.710422\pi$
$14$	−2.81303	+	8.65761i	−0.751813	+	2.31384i
$15$		0			0
$16$	1.92705	−	1.40008i	0.481763	−	0.350021i
$17$	4.96199	−	3.60510i	1.20346	−	0.874364i	0.208838	−	0.977950i	$-0.433032\pi$
$17$	4.96199	−	3.60510i	1.20346	−	0.874364i	0.994620	+	0.103586i	$0.0330318\pi$
$18$		0			0
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	−0.999300	−	0.0374011i	$-0.988092\pi$
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	0.830435	+	0.557116i	$0.188092\pi$
$20$	4.55157	+	3.30691i	1.01776	+	0.739448i
$21$		0			0
$22$	4.61803	+	5.42882i	0.984568	+	1.15743i
$23$	3.98439			0.830803			0.415402	−	0.909638i	$-0.363641\pi$
$23$	3.98439			0.830803			0.415402	+	0.909638i	$0.363641\pi$
$24$		0			0
$25$	−0.118034	+	0.363271i	−0.0236068	+	0.0726543i
$26$	0.156765	+	0.482472i	0.0307441	+	0.0946205i
$27$		0			0
$28$	8.97214	−	6.51864i	1.69557	−	1.23191i
$29$	2.14896	+	6.61382i	0.399052	+	1.22816i	0.925761	+	0.378110i	$0.123426\pi$
$29$	2.14896	+	6.61382i	0.399052	+	1.22816i	−0.526709	+	0.850046i	$0.676574\pi$
$30$		0			0
$31$	3.73607	+	2.71441i	0.671018	+	0.487523i	0.870366	−	0.492406i	$-0.163882\pi$
$31$	3.73607	+	2.71441i	0.671018	+	0.487523i	−0.199348	+	0.979929i	$0.563882\pi$
$32$	−7.77501			−1.37444
$33$		0			0
$34$	−13.1803			−2.26041
$35$	−7.36460	−	5.35069i	−1.24484	−	0.904432i
$36$		0			0
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	0.985812	−	0.167854i	$-0.0536836\pi$
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	−0.896201	+	0.443649i	$0.853684\pi$
$38$	4.14116	−	3.00873i	0.671784	−	0.488080i
$39$		0			0
$40$	−0.881966	−	2.71441i	−0.139451	−	0.429186i
$41$	−0.917716	+	2.82444i	−0.143323	+	0.441103i	−0.996792	−	0.0800413i	$-0.974495\pi$
$41$	−0.917716	+	2.82444i	−0.143323	+	0.441103i	0.853468	+	0.521145i	$0.174495\pi$
$42$		0			0
$43$	2.70820			0.412997			0.206499	−	0.978447i	$-0.433793\pi$
$43$	2.70820			0.412997			0.206499	+	0.978447i	$0.433793\pi$
$44$	−0.664066	−	8.65761i	−0.100112	−	1.30518i
$45$		0			0
$46$	−6.92705	−	5.03280i	−1.02134	−	0.742045i
$47$	1.07448	−	3.30691i	0.156729	−	0.482363i	−0.841603	−	0.540097i	$-0.818388\pi$
$47$	1.07448	−	3.30691i	0.156729	−	0.482363i	0.998332	+	0.0577343i	$0.0183876\pi$
$48$		0			0
$49$	−8.85410	+	6.43288i	−1.26487	+	0.918983i
$50$	0.664066	−	0.482472i	0.0939130	−	0.0682318i
$51$		0			0
$52$	0.190983	−	0.587785i	0.0264846	−	0.0815111i
$53$	1.48490	+	1.07884i	0.203966	+	0.148190i	0.685079	−	0.728468i	$-0.259767\pi$
$53$	1.48490	+	1.07884i	0.203966	+	0.148190i	−0.481113	+	0.876658i	$0.659767\pi$
$54$		0			0
$55$	−6.59017	+	2.71441i	−0.888618	+	0.366011i
$56$	−5.62605			−0.751813
$57$		0			0
$58$	4.61803	−	14.2128i	0.606378	−	1.86624i
$59$	−2.30573	−	7.09629i	−0.300180	−	0.923859i	−0.981432	−	0.191810i	$-0.938564\pi$
$59$	−2.30573	−	7.09629i	−0.300180	−	0.923859i	0.681252	−	0.732049i	$-0.261436\pi$
$60$		0			0
$61$	9.16312	−	6.65740i	1.17322	−	0.852392i	0.181827	−	0.983331i	$-0.441799\pi$
$61$	9.16312	−	6.65740i	1.17322	−	0.852392i	0.991391	+	0.130938i	$0.0417990\pi$
$62$	−3.06668	−	9.43826i	−0.389468	−	1.19866i
$63$		0			0
$64$	9.66312	+	7.02067i	1.20789	+	0.877583i
$65$	−0.507301			−0.0629229
$66$		0			0
$67$	−2.85410			−0.348684			−0.174342	−	0.984685i	$-0.555780\pi$
$67$	−2.85410			−0.348684			−0.174342	+	0.984685i	$0.555780\pi$
$68$	12.9907	+	9.43826i	1.57535	+	1.14456i
$69$		0			0
$70$	6.04508	+	18.6049i	0.722526	+	2.22371i
$71$	−8.69273	+	6.31564i	−1.03164	+	0.749528i	−0.968636	−	0.248485i	$-0.920067\pi$
$71$	−8.69273	+	6.31564i	−1.03164	+	0.749528i	−0.0630016	+	0.998013i	$0.520067\pi$
$72$		0			0
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	0.985757	−	0.168176i	$-0.0537877\pi$
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	−0.896346	+	0.443356i	$0.853788\pi$
$74$	1.17137	−	3.60510i	0.136169	−	0.419084i
$75$		0			0
$76$	−6.23607			−0.715326
$77$	1.07448	+	14.0083i	0.122448	+	1.59639i
$78$		0			0
$79$	7.66312	+	5.56758i	0.862168	+	0.626402i	0.928474	−	0.371397i	$-0.121121\pi$
$79$	7.66312	+	5.56758i	0.862168	+	0.626402i	−0.0663057	+	0.997799i	$0.521121\pi$
$80$	1.58178	−	4.86822i	0.176849	−	0.544284i
$81$		0			0
$82$	5.16312	−	3.75123i	0.570171	−	0.414254i
$83$	−6.70053	+	4.86822i	−0.735479	+	0.534357i	−0.891292	−	0.453430i	$-0.850200\pi$
$83$	−6.70053	+	4.86822i	−0.735479	+	0.534357i	0.155813	+	0.987787i	$0.450200\pi$
$84$		0			0
$85$	4.07295	−	12.5352i	0.441773	−	1.35964i
$86$	−4.70834	−	3.42081i	−0.507713	−	0.368875i
$87$		0			0
$88$	−2.30902	+	3.75123i	−0.246142	+	0.399882i
$89$	8.90937			0.944392			0.472196	−	0.881494i	$-0.343462\pi$
$89$	8.90937			0.944392			0.472196	+	0.881494i	$0.343462\pi$
$90$		0			0
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$	3.22344	+	9.92073i	0.336067	+	1.03431i
$93$		0			0
$94$	−6.04508	+	4.39201i	−0.623503	+	0.453001i
$95$	1.58178	+	4.86822i	0.162287	+	0.499469i
$96$		0			0
$97$	−9.54508	−	6.93491i	−0.969157	−	0.704133i	−0.0138974	−	0.999903i	$-0.504424\pi$
$97$	−9.54508	−	6.93491i	−0.969157	−	0.704133i	−0.955259	+	0.295770i	$0.904424\pi$
$98$	23.5188			2.37576
$99$		0			0
$100$	−1.00000			−0.100000
$101$	0.253650	+	0.184288i	0.0252392	+	0.0183373i	0.600333	−	0.799750i	$-0.295035\pi$
$101$	0.253650	+	0.184288i	0.0252392	+	0.0183373i	−0.575094	+	0.818087i	$0.695035\pi$
$102$		0			0
$103$	−3.38197	−	10.4086i	−0.333235	−	1.02559i	−0.967585	−	0.252546i	$-0.918732\pi$
$103$	−3.38197	−	10.4086i	−0.333235	−	1.02559i	0.634350	−	0.773046i	$-0.281268\pi$
$104$	−0.253650	+	0.184288i	−0.0248725	+	0.0180709i
$105$		0			0
$106$	−1.21885	−	3.75123i	−0.118385	−	0.364351i
$107$	−3.38021	+	10.4032i	−0.326777	+	1.00572i	0.643855	+	0.765147i	$0.277334\pi$
$107$	−3.38021	+	10.4032i	−0.326777	+	1.00572i	−0.970632	+	0.240569i	$0.922666\pi$
$108$		0			0
$109$	−13.7082			−1.31301			−0.656504	−	0.754323i	$-0.727965\pi$
$109$	−13.7082			−1.31301			−0.656504	+	0.754323i	$0.727965\pi$
$110$	14.8860	+	3.60510i	1.41932	+	0.343732i
$111$		0			0
$112$	−8.16312	−	5.93085i	−0.771342	−	0.560413i
$113$	5.52917	−	17.0170i	0.520140	−	1.60083i	−0.253590	−	0.967312i	$-0.581611\pi$
$113$	5.52917	−	17.0170i	0.520140	−	1.60083i	0.773730	−	0.633515i	$-0.218389\pi$
$114$		0			0
$115$	6.92705	−	5.03280i	0.645951	−	0.469311i
$116$	−14.7292	+	10.7014i	−1.36757	+	0.993599i
$117$		0			0
$118$	−4.95492	+	15.2497i	−0.456137	+	1.40385i
$119$	−21.0193	−	15.2714i	−1.92684	−	1.39993i
$120$		0			0
$121$	9.78115	+	5.03280i	0.889196	+	0.457527i
$122$	−24.3396			−2.20361
$123$		0			0
$124$	−3.73607	+	11.4984i	−0.335509	+	1.03259i
$125$	3.57398	+	10.9996i	0.319666	+	0.983832i
$126$		0			0
$127$	2.23607	−	1.62460i	0.198419	−	0.144160i	−0.484139	−	0.874991i	$-0.660867\pi$
$127$	2.23607	−	1.62460i	0.198419	−	0.144160i	0.682558	+	0.730831i	$0.260867\pi$
$128$	−3.12656	−	9.62255i	−0.276351	−	0.850521i
$129$		0			0
$130$	0.881966	+	0.640786i	0.0773535	+	0.0562006i
$131$	2.46249			0.215149			0.107574	−	0.994197i	$-0.465692\pi$
$131$	2.46249			0.215149			0.107574	+	0.994197i	$0.465692\pi$
$132$		0			0
$133$	10.0902			0.874929
$134$	4.96199	+	3.60510i	0.428650	+	0.311433i
$135$		0			0
$136$	−2.51722	−	7.74721i	−0.215850	−	0.664318i
$137$	−0.253650	+	0.184288i	−0.0216708	+	0.0157448i	−0.598568	−	0.801072i	$-0.704263\pi$
$137$	−0.253650	+	0.184288i	−0.0216708	+	0.0157448i	0.576897	+	0.816817i	$0.304263\pi$
$138$		0			0
$139$	−3.51722	−	10.8249i	−0.298327	−	0.918155i	−0.982084	−	0.188446i	$-0.939655\pi$
$139$	−3.51722	−	10.8249i	−0.298327	−	0.918155i	0.683757	−	0.729710i	$-0.260345\pi$
$140$	7.36460	−	22.6659i	0.622422	−	1.91562i
$141$		0			0
$142$	23.0902			1.93768
$143$	0.507301	+	0.596368i	0.0424226	+	0.0498708i
$144$		0			0
$145$	12.0902	+	8.78402i	1.00403	+	0.729473i
$146$	1.64166	−	5.05251i	0.135865	−	0.418149i
$147$		0			0
$148$	−3.73607	+	2.71441i	−0.307103	+	0.223123i
$149$	3.73074	−	2.71054i	0.305634	−	0.222056i	−0.424387	−	0.905481i	$-0.639510\pi$
$149$	3.73074	−	2.71054i	0.305634	−	0.222056i	0.730021	+	0.683425i	$0.239510\pi$
$150$		0			0
$151$	−4.09017	+	12.5882i	−0.332853	+	1.02442i	0.634917	+	0.772581i	$0.281034\pi$
$151$	−4.09017	+	12.5882i	−0.332853	+	1.02442i	−0.967770	+	0.251836i	$0.918966\pi$
$152$	2.55938	+	1.85950i	0.207593	+	0.150825i
$153$		0			0
$154$	15.8262	−	25.7113i	1.27531	−	2.07187i
$155$	9.92398			0.797113
$156$		0			0
$157$	−6.38197	+	19.6417i	−0.509336	+	1.56758i	0.284020	+	0.958818i	$0.408332\pi$
$157$	−6.38197	+	19.6417i	−0.509336	+	1.56758i	−0.793356	+	0.608758i	$0.791668\pi$
$158$	−6.29012	−	19.3590i	−0.500415	−	1.54012i
$159$		0			0
$160$	−13.5172	+	9.82084i	−1.06863	+	0.776405i
$161$	−5.21564	−	16.0521i	−0.411050	−	1.26508i
$162$		0			0
$163$	−1.11803	−	0.812299i	−0.0875712	−	0.0636242i	0.543138	−	0.839643i	$-0.317236\pi$
$163$	−1.11803	−	0.812299i	−0.0875712	−	0.0636242i	−0.630709	+	0.776019i	$0.717236\pi$
$164$	−7.77501			−0.607127
$165$		0			0
$166$	17.7984			1.38142
$167$	8.69273	+	6.31564i	0.672664	+	0.488719i	0.870916	−	0.491432i	$-0.163526\pi$
$167$	8.69273	+	6.31564i	0.672664	+	0.488719i	−0.198252	+	0.980151i	$0.563526\pi$
$168$		0			0
$169$	−4.00000	−	12.3107i	−0.307692	−	0.946980i
$170$	−22.9146	+	16.6485i	−1.75747	+	1.27688i
$171$		0			0
$172$	2.19098	+	6.74315i	0.167061	+	0.514161i
$173$	−4.14116	+	12.7452i	−0.314846	+	0.968998i	0.660971	+	0.750411i	$0.270145\pi$
$173$	−4.14116	+	12.7452i	−0.314846	+	0.968998i	−0.975818	+	0.218586i	$0.929855\pi$
$174$		0			0
$175$	1.61803			0.122312
$176$	−7.30472	+	3.00873i	−0.550614	+	0.226791i
$177$		0			0
$178$	−15.4894	−	11.2537i	−1.16098	−	0.843499i
$179$	0.604187	−	1.85950i	0.0451590	−	0.138985i	−0.925935	−	0.377684i	$-0.876721\pi$
$179$	0.604187	−	1.85950i	0.0451590	−	0.138985i	0.971094	+	0.238698i	$0.0767207\pi$
$180$		0			0
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	−0.891393	−	0.453231i	$-0.850271\pi$
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	0.155592	+	0.987821i	$0.450271\pi$
$182$	1.73855	−	1.26313i	0.128870	−	0.0936293i
$183$		0			0
$184$	1.63525	−	5.03280i	0.120553	−	0.371023i
$185$	3.06668	+	2.22807i	0.225467	+	0.163811i
$186$		0			0
$187$	−18.8090	+	7.74721i	−1.37545	+	0.566532i
$188$	9.10315			0.663915
$189$		0			0
$190$	3.39919	−	10.4616i	0.246603	−	0.758966i
$191$	−3.06668	−	9.43826i	−0.221897	−	0.682929i	−0.998592	−	0.0530515i	$-0.983105\pi$
$191$	−3.06668	−	9.43826i	−0.221897	−	0.682929i	0.776695	−	0.629877i	$-0.216895\pi$
$192$		0			0
$193$	−5.97214	+	4.33901i	−0.429884	+	0.312329i	−0.781602	−	0.623777i	$-0.785597\pi$
$193$	−5.97214	+	4.33901i	−0.429884	+	0.312329i	0.351719	+	0.936106i	$0.385597\pi$
$194$	7.83489	+	24.1133i	0.562513	+	1.73124i
$195$		0			0
$196$	−23.1803	−	16.8415i	−1.65574	−	1.20296i
$197$	−2.46249			−0.175445			−0.0877226	−	0.996145i	$-0.527959\pi$
$197$	−2.46249			−0.175445			−0.0877226	+	0.996145i	$0.527959\pi$
$198$		0			0
$199$	0.416408			0.0295184			0.0147592	−	0.999891i	$-0.495302\pi$
$199$	0.416408			0.0295184			0.0147592	+	0.999891i	$0.495302\pi$
$200$	0.410415	+	0.298184i	0.0290207	+	0.0210848i
$201$		0			0
$202$	−0.208204	−	0.640786i	−0.0146492	−	0.0450855i
$203$	23.8323	−	17.3152i	1.67270	−	1.21529i
$204$		0			0
$205$	1.97214	+	6.06961i	0.137740	+	0.423920i
$206$	−7.26771	+	22.3677i	−0.506366	+	1.55843i
$207$		0			0
$208$	−0.562306			−0.0389889
$209$	4.14116	−	6.72772i	0.286450	−	0.465366i
$210$		0			0
$211$	14.5902	+	10.6004i	1.00443	+	0.729760i	0.963033	−	0.269383i	$-0.0868196\pi$
$211$	14.5902	+	10.6004i	1.00443	+	0.729760i	0.0413955	+	0.999143i	$0.486820\pi$
$212$	−1.48490	+	4.57004i	−0.101983	+	0.313872i
$213$		0			0
$214$	19.0172	−	13.8168i	1.29999	−	0.944498i
$215$	4.70834	−	3.42081i	0.321106	−	0.233297i
$216$		0			0
$217$	6.04508	−	18.6049i	0.410367	−	1.26298i
$218$	23.8323	+	17.3152i	1.61413	+	1.17273i
$219$		0			0
$220$	−12.0902	−	14.2128i	−0.815119	−	0.958230i
$221$	−1.44789			−0.0973955
$222$		0			0
$223$	0.982779	−	3.02468i	0.0658118	−	0.202548i	−0.912743	−	0.408534i	$-0.866040\pi$
$223$	0.982779	−	3.02468i	0.0658118	−	0.202548i	0.978555	+	0.205986i	$0.0660402\pi$
$224$	10.1776	+	31.3235i	0.680021	+	2.09289i
$225$		0			0
$226$	−31.1074	+	22.6008i	−2.06923	+	1.50339i
$227$	3.38021	+	10.4032i	0.224352	+	0.690485i	0.998357	+	0.0573050i	$0.0182507\pi$
$227$	3.38021	+	10.4032i	0.224352	+	0.690485i	−0.774005	+	0.633180i	$0.781749\pi$
$228$		0			0
$229$	14.9443	+	10.8576i	0.987545	+	0.717494i	0.959382	−	0.282110i	$-0.0910342\pi$
$229$	14.9443	+	10.8576i	0.987545	+	0.717494i	0.0281631	+	0.999603i	$0.491034\pi$
$230$	−18.4001			−1.21326
$231$		0			0
$232$	9.23607			0.606378
$233$	−18.6167	−	13.5258i	−1.21962	−	0.886106i	−0.223552	−	0.974692i	$-0.571765\pi$
$233$	−18.6167	−	13.5258i	−1.21962	−	0.886106i	−0.996069	+	0.0885854i	$0.971765\pi$
$234$		0			0
$235$	−2.30902	−	7.10642i	−0.150624	−	0.463572i
$236$	15.8037	−	11.4820i	1.02873	−	0.747417i
$237$		0			0
$238$	17.2533	+	53.1002i	1.11836	+	3.44197i
$239$	3.53697	−	10.8857i	0.228788	−	0.704136i	−0.769097	−	0.639132i	$-0.779294\pi$
$239$	3.53697	−	10.8857i	0.228788	−	0.704136i	0.997885	−	0.0650043i	$-0.0207061\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	−10.6479	−	21.1046i	−0.684474	−	1.35665i
$243$		0			0
$244$	23.9894	+	17.4293i	1.53576	+	1.11580i
$245$	−7.26771	+	22.3677i	−0.464317	+	1.42902i
$246$		0			0
$247$	0.454915	−	0.330515i	0.0289456	−	0.0210302i
$248$	4.96199	−	3.60510i	0.315087	−	0.228924i
$249$		0			0
$250$	7.68034	−	23.6377i	0.485747	−	1.49498i
$251$	18.3631	+	13.3415i	1.15907	+	0.842111i	0.989660	−	0.143436i	$-0.0458150\pi$
$251$	18.3631	+	13.3415i	1.15907	+	0.842111i	0.169406	+	0.985546i	$0.445815\pi$
$252$		0			0
$253$	−12.8435	−	3.11044i	−0.807461	−	0.195552i
$254$	−5.93958			−0.372683
$255$		0			0
$256$	0.663119	−	2.04087i	0.0414449	−	0.127554i
$257$	−3.82763	−	11.7802i	−0.238761	−	0.734831i	−0.996600	−	0.0823893i	$-0.973745\pi$
$257$	−3.82763	−	11.7802i	−0.238761	−	0.734831i	0.757839	−	0.652441i	$-0.226255\pi$
$258$		0			0
$259$	6.04508	−	4.39201i	0.375623	−	0.272906i
$260$	−0.410415	−	1.26313i	−0.0254529	−	0.0783359i
$261$		0			0
$262$	−4.28115	−	3.11044i	−0.264491	−	0.192164i
$263$	−6.44688			−0.397532			−0.198766	−	0.980047i	$-0.563693\pi$
$263$	−6.44688			−0.397532			−0.198766	+	0.980047i	$0.563693\pi$
$264$		0			0
$265$	3.94427			0.242295
$266$	−17.5422	−	12.7452i	−1.07558	−	0.781457i
$267$		0			0
$268$	−2.30902	−	7.10642i	−0.141046	−	0.434094i
$269$	−16.3709	+	11.8941i	−0.998149	+	0.725198i	−0.961690	−	0.274138i	$-0.911608\pi$
$269$	−16.3709	+	11.8941i	−0.998149	+	0.725198i	−0.0364584	+	0.999335i	$0.511608\pi$
$270$		0			0
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	0.941585	−	0.336775i	$-0.109336\pi$
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	−0.959710	+	0.280993i	$0.909336\pi$
$272$	4.51457	−	13.8944i	0.273736	−	0.842472i
$273$		0			0
$274$	0.673762			0.0407035
$275$	0.664066	−	1.07884i	0.0400447	−	0.0650565i
$276$		0			0
$277$	−15.6803	−	11.3924i	−0.942140	−	0.684505i	0.00679460	−	0.999977i	$-0.497837\pi$
$277$	−15.6803	−	11.3924i	−0.942140	−	0.684505i	−0.948935	+	0.315472i	$0.897837\pi$
$278$	−7.55837	+	23.2623i	−0.453321	+	1.39518i
$279$		0			0
$280$	−9.78115	+	7.10642i	−0.584536	+	0.424690i
$281$	13.4011	−	9.73645i	0.799441	−	0.580828i	−0.111309	−	0.993786i	$-0.535504\pi$
$281$	13.4011	−	9.73645i	0.799441	−	0.580828i	0.910750	+	0.412958i	$0.135504\pi$
$282$		0			0
$283$	−3.38197	+	10.4086i	−0.201037	+	0.618728i	0.798816	+	0.601576i	$0.205460\pi$
$283$	−3.38197	+	10.4086i	−0.201037	+	0.618728i	−0.999853	+	0.0171527i	$0.994540\pi$
$284$	−22.7579	−	16.5346i	−1.35043	−	0.981145i
$285$		0			0
$286$	−0.128677	−	1.67760i	−0.00760884	−	0.0991985i
$287$	12.5802			0.742588
$288$		0			0
$289$	6.37132	−	19.6089i	0.374784	−	1.15347i
$290$	−9.92398	−	30.5429i	−0.582756	−	1.79354i
$291$		0			0
$292$	−5.23607	+	3.80423i	−0.306418	+	0.222625i
$293$	−1.54477	−	4.75433i	−0.0902467	−	0.277751i	0.895739	−	0.444580i	$-0.146647\pi$
$293$	−1.54477	−	4.75433i	−0.0902467	−	0.277751i	−0.985986	+	0.166829i	$0.946647\pi$
$294$		0			0
$295$	−12.9721	−	9.42481i	−0.755267	−	0.548734i
$296$	2.34273			0.136169
$297$		0			0
$298$	−9.90983			−0.574061
$299$	−0.760951	−	0.552864i	−0.0440070	−	0.0319729i
$300$		0			0
$301$	−3.54508	−	10.9106i	−0.204335	−	0.628879i
$302$	23.0115	−	16.7188i	1.32416	−	0.962061i
$303$		0			0
$304$	1.75329	+	5.39607i	0.100558	+	0.309486i
$305$	7.52136	−	23.1484i	0.430672	−	1.32547i
$306$		0			0
$307$	17.2705			0.985680			0.492840	−	0.870120i	$-0.335959\pi$
$307$	17.2705			0.985680			0.492840	+	0.870120i	$0.335959\pi$
$308$	−34.0100	+	14.0083i	−1.93790	+	0.798197i
$309$		0			0
$310$	−17.2533	−	12.5352i	−0.979921	−	0.711954i
$311$	−8.88650	+	27.3498i	−0.503907	+	1.55087i	0.298693	+	0.954349i	$0.403449\pi$
$311$	−8.88650	+	27.3498i	−0.503907	+	1.55087i	−0.802600	+	0.596518i	$0.796551\pi$
$312$		0			0
$313$	−25.6074	+	18.6049i	−1.44742	+	1.05161i	−0.460989	+	0.887406i	$0.652505\pi$
$313$	−25.6074	+	18.6049i	−1.44742	+	1.05161i	−0.986427	+	0.164203i	$0.947495\pi$
$314$	35.9053	−	26.0867i	2.02625	−	1.47216i
$315$		0			0
$316$	−7.66312	+	23.5847i	−0.431084	+	1.32674i
$317$	0.253650	+	0.184288i	0.0142464	+	0.0103506i	0.594886	−	0.803810i	$-0.297197\pi$
$317$	0.253650	+	0.184288i	0.0142464	+	0.0103506i	−0.580639	+	0.814161i	$0.697197\pi$
$318$		0			0
$319$	−1.76393	−	22.9969i	−0.0987612	−	1.28758i
$320$	25.6678			1.43487
$321$		0			0
$322$	−11.2082	+	34.4953i	−0.624609	+	1.92235i
$323$	4.51457	+	13.8944i	0.251197	+	0.773105i
$324$		0			0
$325$	0.0729490	−	0.0530006i	0.00404648	−	0.00293994i
$326$	0.917716	+	2.82444i	0.0508276	+	0.156431i
$327$		0			0
$328$	3.19098	+	2.31838i	0.176193	+	0.128011i
$329$	−14.7292			−0.812047
$330$		0			0
$331$	7.29180			0.400793			0.200397	−	0.979715i	$-0.435777\pi$
$331$	7.29180			0.400793			0.200397	+	0.979715i	$0.435777\pi$
$332$	−17.5422	−	12.7452i	−0.962755	−	0.699482i
$333$		0			0
$334$	−7.13525	−	21.9601i	−0.390424	−	1.20160i
$335$	−4.96199	+	3.60510i	−0.271102	+	0.196967i
$336$		0			0
$337$	−8.23607	−	25.3480i	−0.448647	−	1.38079i	−0.878434	−	0.477864i	$-0.841411\pi$
$337$	−8.23607	−	25.3480i	−0.448647	−	1.38079i	0.429787	−	0.902930i	$-0.358589\pi$
$338$	−8.59584	+	26.4553i	−0.467552	+	1.43898i
$339$		0			0
$340$	34.5066			1.87138
$341$	−9.92398	−	11.6663i	−0.537413	−	0.631767i
$342$		0			0
$343$	13.5172	+	9.82084i	0.729861	+	0.530275i
$344$	1.11149	−	3.42081i	0.0599274	−	0.184438i
$345$		0			0
$346$	23.2984	−	16.9273i	1.25253	−	0.910015i
$347$	−20.3553	+	14.7890i	−1.09273	+	0.793913i	−0.979858	−	0.199697i	$-0.936004\pi$
$347$	−20.3553	+	14.7890i	−1.09273	+	0.793913i	−0.112869	+	0.993610i	$0.536004\pi$
$348$		0			0
$349$	2.83688	−	8.73102i	0.151855	−	0.467361i	−0.845974	−	0.533224i	$-0.820980\pi$
$349$	2.83688	−	8.73102i	0.151855	−	0.467361i	0.997829	+	0.0658634i	$0.0209802\pi$
$350$	−2.81303	−	2.04378i	−0.150363	−	0.109245i
$351$		0			0
$352$	25.0623	+	6.06961i	1.33583	+	0.323511i
$353$	−33.7563			−1.79667			−0.898334	−	0.439314i	$-0.855222\pi$
$353$	−33.7563			−1.79667			−0.898334	+	0.439314i	$0.855222\pi$
$354$		0			0
$355$	−7.13525	+	21.9601i	−0.378700	+	1.16552i
$356$	7.20783	+	22.1834i	0.382014	+	1.17572i
$357$		0			0
$358$	−3.39919	+	2.46965i	−0.179653	+	0.130525i
$359$	0.627058	+	1.92989i	0.0330949	+	0.101856i	0.966239	−	0.257646i	$-0.0829468\pi$
$359$	0.627058	+	1.92989i	0.0330949	+	0.101856i	−0.933145	+	0.359501i	$0.882947\pi$
$360$		0			0
$361$	10.7812	+	7.83297i	0.567429	+	0.412261i
$362$	26.2948			1.38203
$363$		0			0
$364$	−2.61803			−0.137222
$365$	4.29792	+	3.12262i	0.224964	+	0.163446i
$366$		0			0
$367$	7.11803	+	21.9071i	0.371558	+	1.14354i	0.945771	+	0.324833i	$0.105308\pi$
$367$	7.11803	+	21.9071i	0.371558	+	1.14354i	−0.574213	+	0.818706i	$0.694692\pi$
$368$	7.67813	−	5.57849i	0.400250	−	0.290799i
$369$		0			0
$370$	−2.51722	−	7.74721i	−0.130864	−	0.402758i
$371$	2.40261	−	7.39448i	0.124737	−	0.383902i
$372$		0			0
$373$	−14.4164			−0.746453			−0.373227	−	0.927740i	$-0.621749\pi$
$373$	−14.4164			−0.746453			−0.373227	+	0.927740i	$0.621749\pi$
$374$	42.4861	+	10.2893i	2.19690	+	0.532048i
$375$		0			0
$376$	−3.73607	−	2.71441i	−0.192673	−	0.139985i
$377$	0.507301	−	1.56131i	0.0261273	−	0.0804116i
$378$		0			0
$379$	−5.04508	+	3.66547i	−0.259149	+	0.188282i	−0.709772	−	0.704432i	$-0.751202\pi$
$379$	−5.04508	+	3.66547i	−0.259149	+	0.188282i	0.450623	+	0.892714i	$0.351202\pi$
$380$	−10.8417	+	7.87695i	−0.556167	+	0.404079i
$381$		0			0
$382$	−6.59017	+	20.2825i	−0.337182	+	1.03774i
$383$	27.5631	+	20.0258i	1.40841	+	1.02327i	0.993552	+	0.113381i	$0.0361682\pi$
$383$	27.5631	+	20.0258i	1.40841	+	1.02327i	0.414856	+	0.909887i	$0.363832\pi$
$384$		0			0
$385$	19.5623	+	22.9969i	0.996987	+	1.17203i
$386$	15.8636			0.807434
$387$		0			0
$388$	9.54508	−	29.3768i	0.484578	−	1.49138i
$389$	6.89431	+	21.2185i	0.349555	+	1.07582i	0.959100	+	0.283068i	$0.0913523\pi$
$389$	6.89431	+	21.2185i	0.349555	+	1.07582i	−0.609545	+	0.792752i	$0.708648\pi$
$390$		0			0
$391$	19.7705	−	14.3641i	0.999838	−	0.726425i
$392$	4.49169	+	13.8240i	0.226865	+	0.698218i
$393$		0			0
$394$	4.28115	+	3.11044i	0.215681	+	0.156702i
$395$	20.3553			1.02418
$396$		0			0
$397$	24.4164			1.22542			0.612712	−	0.790306i	$-0.290078\pi$
$397$	24.4164			1.22542			0.612712	+	0.790306i	$0.290078\pi$
$398$	−0.723944	−	0.525976i	−0.0362880	−	0.0263648i
$399$		0			0
$400$	0.281153	+	0.865300i	0.0140576	+	0.0432650i
$401$	15.3933	−	11.1839i	0.768703	−	0.558495i	−0.132864	−	0.991134i	$-0.542417\pi$
$401$	15.3933	−	11.1839i	0.768703	−	0.558495i	0.901567	+	0.432639i	$0.142417\pi$
$402$		0			0
$403$	−0.336881	−	1.03681i	−0.0167812	−	0.0516473i
$404$	−0.253650	+	0.780656i	−0.0126196	+	0.0388391i
$405$		0			0
$406$	−63.3050			−3.14177
$407$	−0.447422	−	5.83317i	−0.0221779	−	0.289139i
$408$		0			0
$409$	4.09017	+	2.97168i	0.202246	+	0.146940i	0.684298	−	0.729202i	$-0.260109\pi$
$409$	4.09017	+	2.97168i	0.202246	+	0.146940i	−0.482053	+	0.876142i	$0.660109\pi$
$410$	4.23804	−	13.0434i	0.209302	−	0.644165i
$411$		0			0
$412$	23.1803	−	16.8415i	1.14201	−	0.829721i
$413$	−25.5709	+	18.5783i	−1.25826	+	0.914180i
$414$		0			0
$415$	−5.50000	+	16.9273i	−0.269984	+	0.830926i
$416$	1.48490	+	1.07884i	0.0728030	+	0.0528945i
$417$		0			0
$418$	−15.6976	+	6.46564i	−0.767793	+	0.316245i
$419$	−35.2782			−1.72345			−0.861727	−	0.507372i	$-0.830617\pi$
$419$	−35.2782			−1.72345			−0.861727	+	0.507372i	$0.830617\pi$
$420$		0			0
$421$	−9.02786	+	27.7849i	−0.439991	+	1.35415i	0.447893	+	0.894087i	$0.352174\pi$
$421$	−9.02786	+	27.7849i	−0.439991	+	1.35415i	−0.887884	+	0.460067i	$0.847826\pi$
$422$	−11.9761	−	36.8585i	−0.582985	−	1.79424i
$423$		0			0
$424$	1.97214	−	1.43284i	0.0957754	−	0.0695849i
$425$	0.723944	+	2.22807i	0.0351165	+	0.108077i
$426$		0			0
$427$	−38.8156	−	28.2012i	−1.87842	−	1.36475i
$428$	−28.6376			−1.38425
$429$		0			0
$430$	−12.5066			−0.603121
$431$	28.7943	+	20.9203i	1.38697	+	1.00770i	0.996190	+	0.0872135i	$0.0277962\pi$
$431$	28.7943	+	20.9203i	1.38697	+	1.00770i	0.390785	+	0.920482i	$0.372204\pi$
$432$		0			0
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	0.929428	−	0.369004i	$-0.120301\pi$
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	−0.968818	+	0.247773i	$0.920301\pi$
$434$	−34.0100	+	24.7097i	−1.63253	+	1.18610i
$435$		0			0
$436$	−11.0902	−	34.1320i	−0.531123	−	1.63463i
$437$	−2.93278	+	9.02618i	−0.140294	+	0.431781i
$438$		0			0
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	0.723944	+	9.43826i	0.0345127	+	0.449951i
$441$		0			0
$442$	2.51722	+	1.82887i	0.119732	+	0.0869904i
$443$	6.76041	−	20.8064i	0.321197	−	0.988542i	−0.651931	−	0.758278i	$-0.726041\pi$
$443$	6.76041	−	20.8064i	0.321197	−	0.988542i	0.973128	−	0.230264i	$-0.0739591\pi$
$444$		0			0
$445$	15.4894	−	11.2537i	0.734266	−	0.533475i
$446$	−5.52917	+	4.01718i	−0.261814	+	0.190219i
$447$		0			0
$448$	15.6353	−	48.1204i	0.738696	−	2.27347i
$449$	−23.8323	−	17.3152i	−1.12472	−	0.817155i	−0.139800	−	0.990180i	$-0.544646\pi$
$449$	−23.8323	−	17.3152i	−1.12472	−	0.817155i	−0.984918	+	0.173024i	$0.944646\pi$
$450$		0			0
$451$	5.16312	−	8.38800i	0.243122	−	0.394975i
$452$	46.8439			2.20335
$453$		0			0
$454$	7.26393	−	22.3561i	0.340913	−	1.04922i
$455$	0.664066	+	2.04378i	0.0311319	+	0.0958140i
$456$		0			0
$457$	−28.3885	+	20.6255i	−1.32796	+	0.964819i	−0.328164	+	0.944621i	$0.606430\pi$
$457$	−28.3885	+	20.6255i	−1.32796	+	0.964819i	−0.999796	+	0.0201987i	$0.993570\pi$
$458$	−12.2667	−	37.7530i	−0.573186	−	1.76408i
$459$		0			0
$460$	18.1353	+	13.1760i	0.845561	+	0.614336i
$461$	1.52190			0.0708821			0.0354410	−	0.999372i	$-0.488716\pi$
$461$	1.52190			0.0708821			0.0354410	+	0.999372i	$0.488716\pi$
$462$		0			0
$463$	−21.5623			−1.00209			−0.501043	−	0.865423i	$-0.667050\pi$
$463$	−21.5623			−1.00209			−0.501043	+	0.865423i	$0.667050\pi$
$464$	13.4011	+	9.73645i	0.622129	+	0.452003i
$465$		0			0
$466$	15.2812	+	47.0306i	0.707886	+	2.17865i
$467$	−17.1318	+	12.4470i	−0.792766	+	0.575978i	−0.908783	−	0.417269i	$-0.862987\pi$
$467$	−17.1318	+	12.4470i	−0.792766	+	0.575978i	0.116017	+	0.993247i	$0.462987\pi$
$468$		0			0
$469$	3.73607	+	11.4984i	0.172516	+	0.530948i
$470$	−4.96199	+	15.2714i	−0.228879	+	0.704418i
$471$		0			0
$472$	−9.90983			−0.456137
$473$	−8.72974	−	2.11418i	−0.401394	−	0.0972099i
$474$		0			0
$475$	−0.736068	−	0.534785i	−0.0337731	−	0.0245376i
$476$	21.0193	−	64.6908i	0.963419	−	2.96510i
$477$		0			0
$478$	−19.8992	+	14.4576i	−0.910168	+	0.661275i
$479$	29.8089	−	21.6575i	1.36200	−	0.989555i	0.363690	−	0.931520i	$-0.381517\pi$
$479$	29.8089	−	21.6575i	1.36200	−	0.989555i	0.998315	−	0.0580346i	$-0.0184834\pi$
$480$		0			0
$481$	0.128677	−	0.396027i	0.00586717	−	0.0180573i
$482$	−24.3396	−	17.6838i	−1.10864	−	0.805474i
$483$		0			0
$484$	−4.61803	+	28.4257i	−0.209911	+	1.29208i
$485$	−25.3542			−1.15128
$486$		0			0
$487$	5.83688	−	17.9641i	0.264494	−	0.814030i	−0.727315	−	0.686304i	$-0.759232\pi$
$487$	5.83688	−	17.9641i	0.264494	−	0.814030i	0.991809	−	0.127726i	$-0.0407679\pi$
$488$	−4.64846	−	14.3065i	−0.210426	−	0.647624i
$489$		0			0
$490$	40.8885	−	29.7073i	1.84716	−	1.34204i
$491$	−5.99946	−	18.4644i	−0.270752	−	0.833289i	−0.990312	−	0.138859i	$-0.955657\pi$
$491$	−5.99946	−	18.4644i	−0.270752	−	0.833289i	0.719560	−	0.694430i	$-0.244343\pi$
$492$		0			0
$493$	34.5066	+	25.0705i	1.55410	+	1.12912i
$494$	−1.20837			−0.0543673
$495$		0			0
$496$	11.0000			0.493915
$497$	36.8230	+	26.7535i	1.65174	+	1.20006i
$498$		0			0
$499$	10.1180	+	31.1401i	0.452945	+	1.39402i	0.873530	+	0.486770i	$0.161825\pi$
$499$	10.1180	+	31.1401i	0.452945	+	1.39402i	−0.420585	+	0.907253i	$0.638175\pi$
$500$	−24.4964	+	17.7977i	−1.09551	+	0.795937i
$501$		0			0
$502$	−15.0729	−	46.3898i	−0.672739	−	2.07048i
$503$	1.83543	−	5.64888i	0.0818379	−	0.251871i	−0.901763	−	0.432231i	$-0.857726\pi$
$503$	1.83543	−	5.64888i	0.0818379	−	0.251871i	0.983601	+	0.180360i	$0.0577264\pi$
$504$		0			0
$505$	0.673762			0.0299820
$506$	18.4001	+	21.6306i	0.817983	+	0.961596i
$507$		0			0
$508$	5.85410	+	4.25325i	0.259734	+	0.188708i
$509$	5.05887	−	15.5696i	0.224231	−	0.690111i	−0.774138	−	0.633017i	$-0.781816\pi$
$509$	5.05887	−	15.5696i	0.224231	−	0.690111i	0.998369	−	0.0570943i	$-0.0181836\pi$
$510$		0			0
$511$	8.47214	−	6.15537i	0.374785	−	0.272297i
$512$	−20.1016	+	14.6047i	−0.888374	+	0.645441i
$513$		0			0
$514$	−8.22542	+	25.3153i	−0.362808	+	1.11661i
$515$	−19.0271	−	13.8240i	−0.838435	−	0.609159i
$516$		0			0
$517$	−6.04508	+	9.82084i	−0.265863	+	0.431920i
$518$	−16.0573			−0.705519
$519$		0			0
$520$	−0.208204	+	0.640786i	−0.00913035	+	0.0281003i
$521$	−8.28232	−	25.4903i	−0.362855	−	1.11675i	−0.951313	−	0.308225i	$-0.900265\pi$
$521$	−8.28232	−	25.4903i	−0.362855	−	1.11675i	0.588459	−	0.808527i	$-0.299735\pi$
$522$		0			0
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.324997	−	0.945715i	$-0.394637\pi$
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.999858	−	0.0168489i	$-0.00536341\pi$
$524$	1.99220	+	6.13135i	0.0870295	+	0.267849i
$525$		0			0
$526$	11.2082	+	8.14324i	0.488701	+	0.355062i
$527$	28.3240			1.23381
$528$		0			0
$529$	−7.12461			−0.309766
$530$	−6.85730	−	4.98212i	−0.297862	−	0.216409i
$531$		0			0
$532$	8.16312	+	25.1235i	0.353916	+	1.08924i
$533$	0.567180	−	0.412080i	0.0245673	−	0.0178492i
$534$		0			0
$535$	7.26393	+	22.3561i	0.314047	+	0.966538i
$536$	−1.17137	+	3.60510i	−0.0505953	+	0.155716i
$537$		0			0
$538$	43.4853			1.87478
$539$	33.5625	−	13.8240i	1.44564	−	0.595442i
$540$		0			0
$541$	−31.2533	−	22.7068i	−1.34368	−	0.976243i	−0.999300	−	0.0374146i	$-0.988088\pi$
$541$	−31.2533	−	22.7068i	−1.34368	−	0.976243i	−0.344384	−	0.938829i	$-0.611912\pi$
$542$	−0.641194	+	1.97339i	−0.0275416	+	0.0847644i
$543$		0			0
$544$	−38.5795	+	28.0297i	−1.65408	+	1.20176i
$545$	−23.8323	+	17.3152i	−1.02087	+	0.741702i
$546$		0			0
$547$	6.19098	−	19.0539i	0.264707	−	0.814685i	−0.727053	−	0.686581i	$-0.759111\pi$
$547$	6.19098	−	19.0539i	0.264707	−	0.814685i	0.991761	−	0.128104i	$-0.0408893\pi$
$548$	−0.664066	−	0.482472i	−0.0283675	−	0.0206102i
$549$		0			0
$550$	−2.51722	+	1.03681i	−0.107335	+	0.0442099i
$551$	−16.5646			−0.705677
$552$		0			0
$553$	12.3992	−	38.1608i	0.527267	−	1.62276i
$554$	12.8709	+	39.6125i	0.546832	+	1.68298i
$555$		0			0
$556$	24.1074	−	17.5150i	1.02238	−	0.742803i
$557$	1.67867	+	5.16641i	0.0711274	+	0.218908i	0.980301	−	0.197510i	$-0.0632855\pi$
$557$	1.67867	+	5.16641i	0.0711274	+	0.218908i	−0.909173	+	0.416418i	$0.863285\pi$
$558$		0			0
$559$	−0.517221	−	0.375783i	−0.0218761	−	0.0158939i
$560$	−21.6834			−0.916290
$561$		0			0
$562$	−35.5967			−1.50156
$563$	−12.6401	−	9.18358i	−0.532717	−	0.387042i	0.288656	−	0.957433i	$-0.406792\pi$
$563$	−12.6401	−	9.18358i	−0.532717	−	0.387042i	−0.821373	+	0.570391i	$0.806792\pi$
$564$		0			0
$565$	−11.8820	−	36.5689i	−0.499878	−	1.53847i
$566$	19.0271	−	13.8240i	0.799770	−	0.581067i
$567$		0			0
$568$	4.40983	+	13.5721i	0.185032	+	0.569471i
$569$	9.80422	−	30.1743i	0.411014	−	1.26497i	−0.504754	−	0.863263i	$-0.668417\pi$
$569$	9.80422	−	30.1743i	0.411014	−	1.26497i	0.915768	−	0.401708i	$-0.131583\pi$
$570$		0			0
$571$	11.9787			0.501294			0.250647	−	0.968079i	$-0.419357\pi$
$571$	11.9787			0.501294			0.250647	+	0.968079i	$0.419357\pi$
$572$	−1.07448	+	1.74560i	−0.0449263	+	0.0729872i
$573$		0			0
$574$	−21.8713	−	15.8904i	−0.912891	−	0.663254i
$575$	−0.470294	+	1.44742i	−0.0196126	+	0.0603614i
$576$		0			0
$577$	1.09017	−	0.792055i	0.0453844	−	0.0329737i	−0.564862	−	0.825186i	$-0.691071\pi$
$577$	1.09017	−	0.792055i	0.0453844	−	0.0329737i	0.610246	+	0.792212i	$0.291071\pi$
$578$	−35.8454	+	26.0432i	−1.49097	+	1.08325i
$579$		0			0
$580$	−12.0902	+	37.2097i	−0.502017	+	1.54505i
$581$	28.3839	+	20.6221i	1.17756	+	0.855550i
$582$		0			0
$583$	−3.94427	−	4.63677i	−0.163355	−	0.192035i
$584$	3.28332			0.135865
$585$		0			0
$586$	−3.31966	+	10.2169i	−0.137134	+	0.422055i
$587$	11.3490	+	34.9286i	0.468423	+	1.44166i	0.854626	+	0.519244i	$0.173786\pi$
$587$	11.3490	+	34.9286i	0.468423	+	1.44166i	−0.386203	+	0.922414i	$0.626214\pi$
$588$		0			0
$589$	−8.89919	+	6.46564i	−0.366685	+	0.266412i
$590$	10.6479	+	32.7709i	0.438368	+	1.34916i
$591$		0			0
$592$	3.39919	+	2.46965i	0.139706	+	0.101502i
$593$	27.3094			1.12146			0.560732	−	0.827997i	$-0.310520\pi$
$593$	27.3094			1.12146			0.560732	+	0.827997i	$0.310520\pi$
$594$		0			0
$595$	−55.8328			−2.28892
$596$	9.76721	+	7.09629i	0.400081	+	0.290676i
$597$		0			0
$598$	0.624612	+	1.92236i	0.0255423	+	0.0786110i
$599$	−13.9084	+	10.1050i	−0.568281	+	0.412880i	−0.834480	−	0.551038i	$-0.814232\pi$
$599$	−13.9084	+	10.1050i	−0.568281	+	0.412880i	0.266200	+	0.963918i	$0.414232\pi$
$600$		0			0
$601$	−2.89261	−	8.90254i	−0.117992	−	0.363142i	0.874567	−	0.484904i	$-0.161146\pi$
$601$	−2.89261	−	8.90254i	−0.117992	−	0.363142i	−0.992559	+	0.121762i	$0.961146\pi$
$602$	−7.61825	+	23.4466i	−0.310497	+	0.955611i
$603$		0			0
$604$	−34.6525			−1.40999
$605$	23.3621	−	3.60510i	0.949802	−	0.146568i
$606$		0			0
$607$	23.1525	+	16.8213i	0.939730	+	0.682754i	0.948356	−	0.317209i	$-0.102746\pi$
$607$	23.1525	+	16.8213i	0.939730	+	0.682754i	−0.00862566	+	0.999963i	$0.502746\pi$
$608$	5.72294	−	17.6134i	0.232096	−	0.714318i
$609$		0			0
$610$	−42.3156	+	30.7441i	−1.71331	+	1.24479i
$611$	−0.664066	+	0.482472i	−0.0268652	+	0.0195187i
$612$		0			0
$613$	7.74265	−	23.8294i	0.312723	−	0.962461i	−0.663959	−	0.747769i	$-0.731125\pi$
$613$	7.74265	−	23.8294i	0.312723	−	0.962461i	0.976682	−	0.214692i	$-0.0688748\pi$
$614$	−30.0256	−	21.8149i	−1.21173	−	0.880376i
$615$		0			0
$616$	18.1353	+	4.39201i	0.730690	+	0.176959i
$617$	16.8782			0.679489			0.339745	−	0.940518i	$-0.389659\pi$
$617$	16.8782			0.679489			0.339745	+	0.940518i	$0.389659\pi$
$618$		0			0
$619$	2.12868	−	6.55139i	0.0855588	−	0.263323i	−0.899120	−	0.437703i	$-0.855792\pi$
$619$	2.12868	−	6.55139i	0.0855588	−	0.263323i	0.984678	+	0.174380i	$0.0557922\pi$
$620$	8.02866	+	24.7097i	0.322439	+	0.992365i
$621$		0			0
$622$	49.9959	−	36.3242i	2.00465	−	1.45647i
$623$	−11.6625	−	35.8936i	−0.467249	−	1.43804i
$624$		0			0
$625$	18.5623	+	13.4863i	0.742492	+	0.539452i
$626$	68.0199			2.71862
$627$		0			0
$628$	−54.0689			−2.15758
$629$	8.75261	+	6.35914i	0.348989	+	0.253556i
$630$		0			0
$631$	−5.37132	−	16.5312i	−0.213829	−	0.658098i	−0.999235	−	0.0391166i	$-0.987546\pi$
$631$	−5.37132	−	16.5312i	−0.213829	−	0.658098i	0.785406	−	0.618981i	$-0.212454\pi$
$632$	10.1776	−	7.39448i	0.404844	−	0.294137i
$633$		0			0
$634$	−0.208204	−	0.640786i	−0.00826883	−	0.0254489i
$635$	1.83543	−	5.64888i	0.0728369	−	0.224169i
$636$		0			0
$637$	2.58359			0.102366
$638$	−25.9813	+	42.2092i	−1.02861	+	1.67108i
$639$		0			0
$640$	−17.5902	−	12.7800i	−0.695313	−	0.505174i
$641$	−6.60365	+	20.3239i	−0.260828	+	0.802747i	0.731797	+	0.681523i	$0.238682\pi$
$641$	−6.60365	+	20.3239i	−0.260828	+	0.802747i	−0.992625	+	0.121224i	$0.961318\pi$
$642$		0			0
$643$	33.2984	−	24.1927i	1.31316	−	0.954066i	0.313169	−	0.949697i	$-0.398609\pi$
$643$	33.2984	−	24.1927i	1.31316	−	0.954066i	0.999990	−	0.00436901i	$-0.00139070\pi$
$644$	35.7485	−	25.9728i	1.40869	−	1.02347i
$645$		0			0
$646$	9.70163	−	29.8585i	0.381705	−	1.17477i
$647$	9.45368	+	6.86850i	0.371663	+	0.270029i	0.757900	−	0.652371i	$-0.226225\pi$
$647$	9.45368	+	6.86850i	0.371663	+	0.270029i	−0.386237	+	0.922399i	$0.626225\pi$
$648$		0			0
$649$	1.89261	+	24.6745i	0.0742914	+	0.968558i
$650$	−0.193772			−0.00760035
$651$		0			0
$652$	1.11803	−	3.44095i	0.0437856	−	0.134758i
$653$	−10.5652	−	32.5162i	−0.413447	−	1.27246i	−0.913633	−	0.406541i	$-0.866735\pi$
$653$	−10.5652	−	32.5162i	−0.413447	−	1.27246i	0.500186	−	0.865918i	$-0.333265\pi$
$654$		0			0
$655$	4.28115	−	3.11044i	0.167278	−	0.121535i
$656$	2.18597	+	6.72772i	0.0853477	+	0.262673i
$657$		0			0
$658$	25.6074	+	18.6049i	0.998280	+	0.725293i
$659$	−33.7563			−1.31496			−0.657480	−	0.753472i	$-0.728377\pi$
$659$	−33.7563			−1.31496			−0.657480	+	0.753472i	$0.728377\pi$
$660$		0			0
$661$	2.43769			0.0948153			0.0474077	−	0.998876i	$-0.484904\pi$
$661$	2.43769			0.0948153			0.0474077	+	0.998876i	$0.484904\pi$
$662$	−12.6771	−	9.21047i	−0.492710	−	0.357975i
$663$		0			0
$664$	3.39919	+	10.4616i	0.131914	+	0.405990i
$665$	17.5422	−	12.7452i	0.680258	−	0.494237i
$666$		0			0
$667$	8.56231	+	26.3521i	0.331534	+	1.02036i
$668$	−8.69273	+	26.7535i	−0.336332	+	1.03512i
$669$		0			0
$670$	13.1803			0.509201
$671$	−34.7339	+	14.3065i	−1.34089	+	0.552296i
$672$		0			0
$673$	−14.7533	−	10.7189i	−0.568697	−	0.413183i	0.265934	−	0.963991i	$-0.414320\pi$
$673$	−14.7533	−	10.7189i	−0.568697	−	0.413183i	−0.834632	+	0.550808i	$0.814320\pi$
$674$	−17.6990	+	54.4719i	−0.681740	+	2.09818i
$675$		0			0
$676$	27.4164	−	19.9192i	1.05448	−	0.766123i
$677$	6.95418	−	5.05251i	0.267271	−	0.194184i	−0.446075	−	0.894995i	$-0.647179\pi$
$677$	6.95418	−	5.05251i	0.267271	−	0.194184i	0.713346	+	0.700812i	$0.247179\pi$
$678$		0			0
$679$	−15.4443	+	47.5326i	−0.592697	+	1.82413i
$680$	−14.1620	−	10.2893i	−0.543089	−	0.394577i
$681$		0			0
$682$	2.51722	+	32.8177i	0.0963894	+	1.25665i
$683$	−0.940588			−0.0359906			−0.0179953	−	0.999838i	$-0.505728\pi$
$683$	−0.940588			−0.0359906			−0.0179953	+	0.999838i	$0.505728\pi$
$684$		0			0
$685$	−0.208204	+	0.640786i	−0.00795506	+	0.0244832i
$686$	−11.0953	−	34.1480i	−0.423622	−	1.30377i
$687$		0			0
$688$	5.21885	−	3.79171i	0.198967	−	0.144558i
$689$	−0.133893	−	0.412080i	−0.00510092	−	0.0156990i
$690$		0			0
$691$	−26.1803	−	19.0211i	−0.995947	−	0.723598i	−0.0347317	−	0.999397i	$-0.511058\pi$
$691$	−26.1803	−	19.0211i	−0.995947	−	0.723598i	−0.961215	+	0.275799i	$0.911058\pi$
$692$	−35.0845			−1.33371
$693$		0			0
$694$	54.0689			2.05243
$695$	−19.7881	−	14.3769i	−0.750604	−	0.545346i
$696$		0			0
$697$	5.62868	+	17.3233i	0.213201	+	0.656166i
$698$	−15.9604	+	11.5959i	−0.604112	+	0.438913i
$699$		0			0
$700$	1.30902	+	4.02874i	0.0494762	+	0.152272i
$701$	7.23071	−	22.2538i	0.273100	−	0.840515i	−0.716616	−	0.697468i	$-0.754310\pi$
$701$	7.23071	−	22.2538i	0.273100	−	0.840515i	0.989716	−	0.143047i	$-0.0456901\pi$
$702$		0			0
$703$	−4.20163			−0.158467
$704$	−25.6678	−	30.1743i	−0.967391	−	1.13724i
$705$		0			0
$706$	58.6869	+	42.6385i	2.20871	+	1.60472i
$707$	0.410415	−	1.26313i	0.0154352	−	0.0475048i
$708$		0			0
$709$	12.2984	−	8.93529i	0.461875	−	0.335572i	−0.332391	−	0.943142i	$-0.607855\pi$
$709$	12.2984	−	8.93529i	0.461875	−	0.335572i	0.794266	+	0.607570i	$0.207855\pi$
$710$	40.1433	−	29.1658i	1.50655	−	1.09457i
$711$		0			0
$712$	3.65654	−	11.2537i	0.137035	−	0.421749i
$713$	14.8860	+	10.8153i	0.557484	+	0.405036i
$714$		0			0
$715$	1.63525	+	0.396027i	0.0611551	+	0.0148106i
$716$	5.11875			0.191297
$717$		0			0
$718$	1.34752	−	4.14725i	0.0502892	−	0.154774i
$719$	−4.00726	−	12.3331i	−0.149446	−	0.459947i	0.848110	−	0.529820i	$-0.177741\pi$
$719$	−4.00726	−	12.3331i	−0.149446	−	0.459947i	−0.997556	+	0.0698732i	$0.977741\pi$
$720$		0			0
$721$	−37.5066	+	27.2501i	−1.39682	+	1.01485i
$722$	−8.84950	−	27.2359i	−0.329344	−	1.01362i
$723$		0			0
$724$	−25.9164	−	18.8294i	−0.963176	−	0.699788i
$725$	−2.65626			−0.0986511
$726$		0			0
$727$	19.5623			0.725526			0.362763	−	0.931881i	$-0.381833\pi$
$727$	19.5623			0.725526			0.362763	+	0.931881i	$0.381833\pi$
$728$	1.07448	+	0.780656i	0.0398229	+	0.0289330i
$729$		0			0
$730$	−3.52786	−	10.8576i	−0.130572	−	0.401860i
$731$	13.4381	−	9.76333i	0.497025	−	0.361110i
$732$		0			0
$733$	−4.52786	−	13.9353i	−0.167240	−	0.514713i	0.831954	−	0.554845i	$-0.187222\pi$
$733$	−4.52786	−	13.9353i	−0.167240	−	0.514713i	−0.999194	+	0.0401315i	$0.987222\pi$
$734$	15.2964	−	47.0774i	0.564600	−	1.73766i
$735$		0			0
$736$	−30.9787			−1.14189
$737$	9.20003	+	2.22807i	0.338888	+	0.0820721i
$738$		0			0
$739$	−14.7533	−	10.7189i	−0.542709	−	0.394301i	0.282381	−	0.959302i	$-0.408876\pi$
$739$	−14.7533	−	10.7189i	−0.542709	−	0.394301i	−0.825090	+	0.565001i	$0.808876\pi$
$740$	−3.06668	+	9.43826i	−0.112733	+	0.346957i
$741$		0			0
$742$	−13.5172	+	9.82084i	−0.496233	+	0.360534i
$743$	−14.6693	+	10.6579i	−0.538165	+	0.391000i	−0.823403	−	0.567457i	$-0.807927\pi$
$743$	−14.6693	+	10.6579i	−0.538165	+	0.391000i	0.285238	+	0.958457i	$0.407927\pi$
$744$		0			0
$745$	3.06231	−	9.42481i	0.112194	−	0.345298i
$746$	25.0636	+	18.2098i	0.917643	+	0.666707i
$747$		0			0
$748$	−34.5066	−	40.5649i	−1.26169	−	1.48320i
$749$	46.3366			1.69310
$750$		0			0
$751$	−0.465558	+	1.43284i	−0.0169885	+	0.0522851i	−0.959191	−	0.282758i	$-0.908751\pi$
$751$	−0.465558	+	1.43284i	−0.0169885	+	0.0522851i	0.942203	+	0.335043i	$0.108751\pi$
$752$	−2.55938	−	7.87695i	−0.0933308	−	0.287243i
$753$		0			0
$754$	−2.85410	+	2.07363i	−0.103940	+	0.0755170i
$755$	8.78962	+	27.0517i	0.319887	+	0.984511i
$756$		0			0
$757$	33.0795	+	24.0337i	1.20230	+	0.873519i	0.994509	−	0.104655i	$-0.0333738\pi$
$757$	33.0795	+	24.0337i	1.20230	+	0.873519i	0.207787	+	0.978174i	$0.433374\pi$
$758$	13.4011			0.486749
$759$		0			0
$760$	6.79837			0.246603
$761$	−27.0558	−	19.6572i	−0.980771	−	0.712572i	−0.0228906	−	0.999738i	$-0.507287\pi$
$761$	−27.0558	−	19.6572i	−0.980771	−	0.712572i	−0.957881	+	0.287166i	$0.907287\pi$
$762$		0			0
$763$	17.9443	+	55.2268i	0.649626	+	1.99934i
$764$	21.0193	−	15.2714i	0.760452	−	0.552501i
$765$		0			0
$766$	−22.6246	−	69.6314i	−0.817460	−	2.51588i
$767$	−0.544308	+	1.67521i	−0.0196538	+	0.0604882i
$768$		0			0
$769$	−22.2705			−0.803095			−0.401548	−	0.915838i	$-0.631528\pi$
$769$	−22.2705			−0.803095			−0.401548	+	0.915838i	$0.631528\pi$
$770$	−4.96199	−	64.6908i	−0.178818	−	2.33129i
$771$		0			0
$772$	−15.6353	−	11.3597i	−0.562725	−	0.408844i
$773$	−10.4084	+	32.0338i	−0.374364	+	1.15217i	0.569542	+	0.821962i	$0.307121\pi$
$773$	−10.4084	+	32.0338i	−0.374364	+	1.15217i	−0.943907	+	0.330213i	$0.892879\pi$
$774$		0			0
$775$	−1.42705	+	1.03681i	−0.0512612	+	0.0372434i
$776$	−12.6771	+	9.21047i	−0.455082	+	0.330637i
$777$		0			0
$778$	14.8156	−	45.5977i	0.531165	−	1.63476i
$779$	−5.72294	−	4.15796i	−0.205046	−	0.148974i
$780$		0			0
$781$	32.9508	−	13.5721i	1.17907	−	0.485647i
$782$	−52.5157			−1.87796
$783$		0			0
$784$	−8.05573	+	24.7930i	−0.287705	+	0.885464i
$785$	13.7146	+	42.2092i	0.489495	+	1.50651i
$786$		0			0
$787$	−22.4721	+	16.3270i	−0.801045	+	0.581993i	−0.911221	−	0.411919i	$-0.864859\pi$
$787$	−22.4721	+	16.3270i	−0.801045	+	0.581993i	0.110175	+	0.993912i	$0.464859\pi$
$788$	−1.99220	−	6.13135i	−0.0709691	−	0.218420i
$789$		0			0
$790$	−35.3885	−	25.7113i	−1.25907	−	0.914766i
$791$	−75.7950			−2.69496
$792$		0			0
$793$	−2.67376			−0.0949481
$794$	−42.4491	−	30.8410i	−1.50646	−	1.09451i
$795$		0			0
$796$	0.336881	+	1.03681i	0.0119404	+	0.0367489i
$797$	−3.47709	+	2.52626i	−0.123165	+	0.0894846i	−0.647662	−	0.761927i	$-0.724253\pi$
$797$	−3.47709	+	2.52626i	−0.123165	+	0.0894846i	0.524497	+	0.851412i	$0.324253\pi$
$798$		0			0
$799$	−6.59017	−	20.2825i	−0.233143	−	0.717542i
$800$	0.917716	−	2.82444i	0.0324462	−	0.0998590i
$801$		0			0
$802$	−40.8885			−1.44382
$803$	−0.627058	−	8.17513i	−0.0221284	−	0.288494i
$804$		0			0
$805$	−29.3435	−	21.3193i	−1.03422	−	0.751406i
$806$	−0.723944	+	2.22807i	−0.0254998	+	0.0784805i
$807$		0			0
$808$	0.336881	−	0.244758i	0.0118514	−	0.00861057i
$809$	5.72294	−	4.15796i	0.201208	−	0.146186i	−0.482619	−	0.875830i	$-0.660314\pi$
$809$	5.72294	−	4.15796i	0.201208	−	0.146186i	0.683827	+	0.729644i	$0.260314\pi$
$810$		0			0
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	0.359628	+	0.933096i	$0.382904\pi$
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	−0.839405	+	0.543506i	$0.817096\pi$
$812$	62.3939	+	45.3318i	2.18960	+	1.59083i
$813$		0			0
$814$	−6.59017	+	10.7064i	−0.230985	+	0.375258i
$815$	−2.96979			−0.104027
$816$		0			0
$817$	−1.99342	+	6.13512i	−0.0697410	+	0.214641i
$818$	−3.35733	−	10.3328i	−0.117386	−	0.361278i
$819$		0			0
$820$	−13.5172	+	9.82084i	−0.472042	+	0.342958i
$821$	12.2896	+	37.8234i	0.428909	+	1.32005i	0.899201	+	0.437536i	$0.144149\pi$
$821$	12.2896	+	37.8234i	0.428909	+	1.32005i	−0.470292	+	0.882511i	$0.655851\pi$
$822$		0			0
$823$	−15.4615	−	11.2334i	−0.538954	−	0.391573i	0.284743	−	0.958604i	$-0.408092\pi$
$823$	−15.4615	−	11.2334i	−0.538954	−	0.391573i	−0.823696	+	0.567031i	$0.808092\pi$
$824$	−14.5354			−0.506366
$825$		0			0
$826$	67.9230			2.36334
$827$	−9.41667	−	6.84161i	−0.327450	−	0.237906i	0.411898	−	0.911230i	$-0.364866\pi$
$827$	−9.41667	−	6.84161i	−0.327450	−	0.237906i	−0.739348	+	0.673324i	$0.764866\pi$
$828$		0			0
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	0.999152	+	0.0411726i	$0.0131094\pi$
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	−0.784130	+	0.620596i	$0.786891\pi$
$830$	30.9433	−	22.4816i	1.07406	−	0.780348i
$831$		0			0
$832$	−0.871323	−	2.68166i	−0.0302077	−	0.0929697i
$833$	−20.7428	+	63.8398i	−0.718695	+	2.21192i
$834$		0			0
$835$	23.0902			0.799068
$836$	20.1016	+	4.86822i	0.695228	+	0.168371i
$837$		0			0
$838$	61.3328	+	44.5609i	2.11871	+	1.53933i
$839$	−4.32079	+	13.2980i	−0.149170	+	0.459099i	−0.997524	−	0.0703313i	$-0.977594\pi$
$839$	−4.32079	+	13.2980i	−0.149170	+	0.459099i	0.848353	+	0.529430i	$0.177594\pi$
$840$		0			0
$841$	−15.6631	+	11.3799i	−0.540108	+	0.392411i
$842$	50.7912	−	36.9020i	1.75038	−	1.27173i
$843$		0			0
$844$	−14.5902	+	44.9039i	−0.502214	+	1.54566i
$845$	−22.5042	−	16.3503i	−0.774168	−	0.562466i
$846$		0			0
$847$	7.47214	−	45.9937i	0.256746	−	1.58036i
$848$	4.37194			0.150133
$849$		0			0
$850$	1.55573	−	4.78804i	0.0533610	−	0.164228i
$851$	2.17183	+	6.68421i	0.0744495	+	0.229132i
$852$		0			0
$853$	0.954915	−	0.693786i	0.0326957	−	0.0237548i	−0.571317	−	0.820729i	$-0.693567\pi$
$853$	0.954915	−	0.693786i	0.0326957	−	0.0237548i	0.604013	+	0.796974i	$0.293567\pi$
$854$	31.8610	+	98.0581i	1.09026	+	3.35548i
$855$		0			0
$856$	11.7533	+	8.53926i	0.401719	+	0.291866i
$857$	13.8344			0.472573			0.236286	−	0.971683i	$-0.424070\pi$
$857$	13.8344			0.472573			0.236286	+	0.971683i	$0.424070\pi$
$858$		0			0
$859$	42.4164			1.44723			0.723615	−	0.690204i	$-0.242479\pi$
$859$	42.4164			1.44723			0.723615	+	0.690204i	$0.242479\pi$
$860$	12.3266	+	8.95579i	0.420333	+	0.305390i
$861$		0			0
$862$	−23.6353	−	72.7418i	−0.805020	−	2.47760i
$863$	27.8167	−	20.2100i	0.946893	−	0.687958i	−0.00317717	−	0.999995i	$-0.501011\pi$
$863$	27.8167	−	20.2100i	0.946893	−	0.687958i	0.950070	+	0.312037i	$0.101011\pi$
$864$		0			0
$865$	8.89919	+	27.3889i	0.302581	+	0.931250i
$866$	−1.76142	+	5.42109i	−0.0598554	+	0.184216i
$867$		0			0
$868$	51.2148			1.73834
$869$	−20.3553	−	23.9290i	−0.690505	−	0.811737i
$870$		0			0
$871$	0.545085	+	0.396027i	0.0184695	+	0.0134189i
$872$	−5.62605	+	17.3152i	−0.190522	+	0.586367i
$873$		0			0
$874$	16.5000	−	11.9880i	0.558121	−	0.405499i
$875$	39.6360	−	28.7973i	1.33994	−	0.973525i
$876$		0			0
$877$	3.54508	−	10.9106i	0.119709	−	0.368426i	−0.873191	−	0.487378i	$-0.837953\pi$
$877$	3.54508	−	10.9106i	0.119709	−	0.368426i	0.992900	+	0.118952i	$0.0379533\pi$
$878$	43.4637	+	31.5782i	1.46683	+	1.06571i
$879$		0			0
$880$	−8.89919	+	14.4576i	−0.299992	+	0.487366i
$881$	34.3376			1.15686			0.578432	−	0.815730i	$-0.303665\pi$
$881$	34.3376			1.15686			0.578432	+	0.815730i	$0.303665\pi$
$882$		0			0
$883$	−4.36068	+	13.4208i	−0.146749	+	0.451646i	−0.997232	−	0.0743567i	$-0.976310\pi$
$883$	−4.36068	+	13.4208i	−0.146749	+	0.451646i	0.850483	+	0.526002i	$0.176310\pi$
$884$	−1.17137	−	3.60510i	−0.0393973	−	0.121252i
$885$		0			0
$886$	−38.0344	+	27.6336i	−1.27779	+	0.928370i
$887$	−17.4823	−	53.8051i	−0.587000	−	1.80660i	−0.591087	−	0.806608i	$-0.701301\pi$
$887$	−17.4823	−	53.8051i	−0.587000	−	1.80660i	0.00408722	−	0.999992i	$-0.498699\pi$
$888$		0			0
$889$	−9.47214	−	6.88191i	−0.317685	−	0.230812i
$890$	−41.1438			−1.37914
$891$		0			0
$892$	8.32624			0.278783
$893$	6.70053	+	4.86822i	0.224225	+	0.162909i
$894$		0			0
$895$	−1.29837	−	3.99598i	−0.0433999	−	0.133571i
$896$	−34.6740	+	25.1922i	−1.15838	+	0.841611i
$897$		0			0
$898$	19.5623	+	60.2066i	0.652803	+	2.00912i
$899$	−9.92398	+	30.5429i	−0.330983	+	1.01866i
$900$		0			0
$901$	11.2574			0.375037
$902$	−19.5714	+	8.06124i	−0.651657	+	0.268410i
$903$		0			0
$904$	−19.2254	−	13.9681i	−0.639428	−	0.464572i
$905$	−8.12555	+	25.0079i	−0.270102	+	0.831290i
$906$		0			0
$907$	29.0172	−	21.0822i	0.963501	−	0.700024i	0.00953981	−	0.999954i	$-0.496963\pi$
$907$	29.0172	−	21.0822i	0.963501	−	0.700024i	0.953961	+	0.299930i	$0.0969633\pi$
$908$	−23.1683	+	16.8327i	−0.768866	+	0.558614i
$909$		0			0
$910$	1.42705	−	4.39201i	0.0473063	−	0.145594i
$911$	−7.71514	−	5.60537i	−0.255614	−	0.185714i	0.452597	−	0.891715i	$-0.350498\pi$
$911$	−7.71514	−	5.60537i	−0.255614	−	0.185714i	−0.708211	+	0.706001i	$0.750498\pi$
$912$		0			0
$913$	25.3992	−	10.4616i	0.840590	−	0.346229i
$914$	75.4074			2.49426
$915$		0			0
$916$	−14.9443	+	45.9937i	−0.493773	+	1.51968i
$917$	−3.22344	−	9.92073i	−0.106447	−	0.327611i
$918$		0			0
$919$	20.3713	−	14.8006i	0.671988	−	0.488228i	−0.198702	−	0.980060i	$-0.563673\pi$
$919$	20.3713	−	14.8006i	0.671988	−	0.488228i	0.870690	+	0.491832i	$0.163673\pi$
$920$	−3.51410	−	10.8153i	−0.115856	−	0.356569i
$921$		0			0
$922$	−2.64590	−	1.92236i	−0.0871380	−	0.0633095i
$923$	2.53650			0.0834901
$924$		0			0
$925$	−0.673762			−0.0221532
$926$	37.4871	+	27.2359i	1.23190	+	0.895029i
$927$		0			0
$928$	−16.7082	−	51.4226i	−0.548474	−	1.68803i
$929$	−34.0100	+	24.7097i	−1.11583	+	0.810699i	−0.983572	−	0.180517i	$-0.942223\pi$
$929$	−34.0100	+	24.7097i	−1.11583	+	0.810699i	−0.132259	+	0.991215i	$0.542223\pi$
$930$		0			0
$931$	−8.05573	−	24.7930i	−0.264016	−	0.812557i
$932$	18.6167	−	57.2963i	0.609810	−	1.87680i
$933$		0			0
$934$	45.5066			1.48902
$935$	−22.9146	+	37.2271i	−0.749388	+	1.21746i
$936$		0			0
$937$	−8.75329	−	6.35964i	−0.285957	−	0.207760i	0.435554	−	0.900162i	$-0.356552\pi$
$937$	−8.75329	−	6.35964i	−0.285957	−	0.207760i	−0.721512	+	0.692402i	$0.756552\pi$
$938$	8.02866	−	24.7097i	0.262145	−	0.806800i
$939$		0			0
$940$	15.8262	−	11.4984i	0.516195	−	0.375038i
$941$	7.42448	−	5.39420i	0.242031	−	0.175846i	−0.460157	−	0.887838i	$-0.652207\pi$
$941$	7.42448	−	5.39420i	0.242031	−	0.175846i	0.702188	+	0.711992i	$0.252207\pi$
$942$		0			0
$943$	−3.65654	+	11.2537i	−0.119073	+	0.366470i
$944$	−14.3787	−	10.4467i	−0.467986	−	0.340011i
$945$		0			0
$946$	12.5066	+	14.7024i	0.406624	+	0.478015i
$947$	−22.3845			−0.727397			−0.363699	−	0.931517i	$-0.618486\pi$
$947$	−22.3845			−0.727397			−0.363699	+	0.931517i	$0.618486\pi$
$948$		0			0
$949$	0.180340	−	0.555029i	0.00585408	−	0.0180170i
$950$	0.604187	+	1.85950i	0.0196024	+	0.0603300i
$951$		0			0
$952$	−27.9164	+	20.2825i	−0.904776	+	0.657358i
$953$	5.19277	+	15.9817i	0.168210	+	0.517698i	0.999259	−	0.0385025i	$-0.0122587\pi$
$953$	5.19277	+	15.9817i	0.168210	+	0.517698i	−0.831048	+	0.556200i	$0.812259\pi$
$954$		0			0
$955$	−17.2533	−	12.5352i	−0.558303	−	0.405631i
$956$	29.9657			0.969160
$957$		0			0
$958$	−79.1803			−2.55820
$959$	1.07448	+	0.780656i	0.0346968	+	0.0252087i
$960$		0			0
$961$	−2.98936	−	9.20029i	−0.0964309	−	0.296784i
$962$	−0.723944	+	0.525976i	−0.0233409	+	0.0169582i
$963$		0			0
$964$	11.3262	+	34.8586i	0.364794	+	1.12272i
$965$	−4.90211	+	15.0871i	−0.157804	+	0.485672i
$966$		0			0
$967$	−17.6869			−0.568773			−0.284386	−	0.958710i	$-0.591790\pi$
$967$	−17.6869			−0.568773			−0.284386	+	0.958710i	$0.591790\pi$
$968$	10.3714	−	10.2893i	0.333349	−	0.330711i
$969$		0			0
$970$	44.0795	+	32.0257i	1.41531	+	1.02828i
$971$	0.313529	−	0.964944i	0.0100616	−	0.0309665i	−0.945900	−	0.324459i	$-0.894818\pi$
$971$	0.313529	−	0.964944i	0.0100616	−	0.0309665i	0.955961	+	0.293493i	$0.0948177\pi$
$972$		0			0
$973$	−39.0066	+	28.3399i	−1.25049	+	0.908537i
$974$	−32.8386	+	23.8586i	−1.05222	+	0.764480i
$975$		0			0
$976$	8.33688	−	25.6583i	0.266857	−	0.821302i
$977$	2.71614	+	1.97339i	0.0868970	+	0.0631344i	0.630385	−	0.776282i	$-0.282897\pi$
$977$	2.71614	+	1.97339i	0.0868970	+	0.0631344i	−0.543488	+	0.839417i	$0.682897\pi$
$978$		0			0
$979$	−28.7188	−	6.95515i	−0.917858	−	0.222288i
$980$	−61.5731			−1.96688
$981$		0			0
$982$	−12.8926	+	39.6794i	−0.411420	+	1.26622i
$983$	−15.6698	−	48.2266i	−0.499789	−	1.53819i	−0.809359	−	0.587314i	$-0.800185\pi$
$983$	−15.6698	−	48.2266i	−0.499789	−	1.53819i	0.309570	−	0.950877i	$-0.399815\pi$
$984$		0			0
$985$	−4.28115	+	3.11044i	−0.136409	+	0.0991068i
$986$	−28.3240	−	87.1724i	−0.902021	−	2.77614i
$987$		0			0
$988$	1.19098	+	0.865300i	0.0378902	+	0.0275289i
$989$	10.7905			0.343119
$990$		0			0
$991$	−58.2705			−1.85102			−0.925512	−	0.378719i	$-0.876365\pi$
$991$	−58.2705			−1.85102			−0.925512	+	0.378719i	$0.876365\pi$
$992$	−29.0480	−	21.1046i	−0.922274	−	0.670072i
$993$		0			0
$994$	−30.2254	−	93.0243i	−0.958692	−	2.95055i
$995$	0.723944	−	0.525976i	0.0229506	−	0.0166746i
$996$		0			0
$997$	11.9721	+	36.8464i	0.379161	+	1.16694i	0.940628	+	0.339439i	$0.110237\pi$
$997$	11.9721	+	36.8464i	0.379161	+	1.16694i	−0.561467	+	0.827499i	$0.689763\pi$
$998$	21.7433	−	66.9189i	0.688271	−	2.11828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.c.37.1	✓	8
3.2	odd	2	inner	99.2.f.c.37.2	yes	8
9.2	odd	6		891.2.n.e.433.2		16
9.4	even	3		891.2.n.e.136.2		16
9.5	odd	6		891.2.n.e.136.1		16
9.7	even	3		891.2.n.e.433.1		16
11.3	even	5	inner	99.2.f.c.91.1	yes	8
11.5	even	5		1089.2.a.v.1.4		4
11.6	odd	10		1089.2.a.w.1.1		4
33.5	odd	10		1089.2.a.v.1.1		4
33.14	odd	10	inner	99.2.f.c.91.2	yes	8
33.17	even	10		1089.2.a.w.1.4		4
99.14	odd	30		891.2.n.e.784.2		16
99.25	even	15		891.2.n.e.190.2		16
99.47	odd	30		891.2.n.e.190.1		16
99.58	even	15		891.2.n.e.784.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.37.1	✓	8	1.1	even	1	trivial
99.2.f.c.37.2	yes	8	3.2	odd	2	inner
99.2.f.c.91.1	yes	8	11.3	even	5	inner
99.2.f.c.91.2	yes	8	33.14	odd	10	inner
891.2.n.e.136.1		16	9.5	odd	6
891.2.n.e.136.2		16	9.4	even	3
891.2.n.e.190.1		16	99.47	odd	30
891.2.n.e.190.2		16	99.25	even	15
891.2.n.e.433.1		16	9.7	even	3
891.2.n.e.433.2		16	9.2	odd	6
891.2.n.e.784.1		16	99.58	even	15
891.2.n.e.784.2		16	99.14	odd	30
1089.2.a.v.1.1		4	33.5	odd	10
1089.2.a.v.1.4		4	11.5	even	5
1089.2.a.w.1.1		4	11.6	odd	10
1089.2.a.w.1.4		4	33.17	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73855 - 1.26313i) q^{2} +(0.809017 + 2.48990i) q^{4} +(1.73855 - 1.26313i) q^{5} +(-1.30902 - 4.02874i) q^{7} +(0.410415 - 1.26313i) q^{8} +O(q^{10})\)	\(q+(-1.73855 - 1.26313i) q^{2} +(0.809017 + 2.48990i) q^{4} +(1.73855 - 1.26313i) q^{5} +(-1.30902 - 4.02874i) q^{7} +(0.410415 - 1.26313i) q^{8} -4.61803 q^{10} +(-3.22344 - 0.780656i) q^{11} +(-0.190983 - 0.138757i) q^{13} +(-2.81303 + 8.65761i) q^{14} +(1.92705 - 1.40008i) q^{16} +(4.96199 - 3.60510i) q^{17} +(-0.736068 + 2.26538i) q^{19} +(4.55157 + 3.30691i) q^{20} +(4.61803 + 5.42882i) q^{22} +3.98439 q^{23} +(-0.118034 + 0.363271i) q^{25} +(0.156765 + 0.482472i) q^{26} +(8.97214 - 6.51864i) q^{28} +(2.14896 + 6.61382i) q^{29} +(3.73607 + 2.71441i) q^{31} -7.77501 q^{32} -13.1803 q^{34} +(-7.36460 - 5.35069i) q^{35} +(0.545085 + 1.67760i) q^{37} +(4.14116 - 3.00873i) q^{38} +(-0.881966 - 2.71441i) q^{40} +(-0.917716 + 2.82444i) q^{41} +2.70820 q^{43} +(-0.664066 - 8.65761i) q^{44} +(-6.92705 - 5.03280i) q^{46} +(1.07448 - 3.30691i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(0.664066 - 0.482472i) q^{50} +(0.190983 - 0.587785i) q^{52} +(1.48490 + 1.07884i) q^{53} +(-6.59017 + 2.71441i) q^{55} -5.62605 q^{56} +(4.61803 - 14.2128i) q^{58} +(-2.30573 - 7.09629i) q^{59} +(9.16312 - 6.65740i) q^{61} +(-3.06668 - 9.43826i) q^{62} +(9.66312 + 7.02067i) q^{64} -0.507301 q^{65} -2.85410 q^{67} +(12.9907 + 9.43826i) q^{68} +(6.04508 + 18.6049i) q^{70} +(-8.69273 + 6.31564i) q^{71} +(0.763932 + 2.35114i) q^{73} +(1.17137 - 3.60510i) q^{74} -6.23607 q^{76} +(1.07448 + 14.0083i) q^{77} +(7.66312 + 5.56758i) q^{79} +(1.58178 - 4.86822i) q^{80} +(5.16312 - 3.75123i) q^{82} +(-6.70053 + 4.86822i) q^{83} +(4.07295 - 12.5352i) q^{85} +(-4.70834 - 3.42081i) q^{86} +(-2.30902 + 3.75123i) q^{88} +8.90937 q^{89} +(-0.309017 + 0.951057i) q^{91} +(3.22344 + 9.92073i) q^{92} +(-6.04508 + 4.39201i) q^{94} +(1.58178 + 4.86822i) q^{95} +(-9.54508 - 6.93491i) q^{97} +23.5188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 28 q^{10} - 6 q^{13} + 2 q^{16} + 12 q^{19} + 28 q^{22} + 8 q^{25} + 36 q^{28} + 12 q^{31} - 16 q^{34} - 18 q^{37} - 16 q^{40} - 32 q^{43} - 42 q^{46} - 44 q^{49} + 6 q^{52} - 8 q^{55} + 28 q^{58} + 42 q^{61} + 46 q^{64} + 4 q^{67} + 26 q^{70} + 24 q^{73} - 32 q^{76} + 30 q^{79} + 10 q^{82} + 46 q^{85} - 14 q^{88} + 2 q^{91} - 26 q^{94} - 54 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 28 * q^10 - 6 * q^13 + 2 * q^16 + 12 * q^19 + 28 * q^22 + 8 * q^25 + 36 * q^28 + 12 * q^31 - 16 * q^34 - 18 * q^37 - 16 * q^40 - 32 * q^43 - 42 * q^46 - 44 * q^49 + 6 * q^52 - 8 * q^55 + 28 * q^58 + 42 * q^61 + 46 * q^64 + 4 * q^67 + 26 * q^70 + 24 * q^73 - 32 * q^76 + 30 * q^79 + 10 * q^82 + 46 * q^85 - 14 * q^88 + 2 * q^91 - 26 * q^94 - 54 * q^97

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