LMFDB - Embedded newform 966.2.bd.a.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(59,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 11, 42]))

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

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

chi := DirichletCharacter("966.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bd (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	966.59
Dual form			966.2.bd.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.945001 - 0.327068i) q^{2} +(-1.71282 - 0.257380i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-0.220141 + 0.0210209i) q^{5} +(1.53444 + 0.803434i) q^{6} +(2.60042 + 0.487642i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(2.86751 + 0.881693i) q^{9} +O(q^{10})$	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.71282 - 0.257380i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-0.220141 + 0.0210209i) q^{5} +(1.53444 + 0.803434i) q^{6} +(2.60042 + 0.487642i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(2.86751 + 0.881693i) q^{9} +(0.214909 + 0.0521363i) q^{10} +(-3.06997 + 1.06253i) q^{11} +(-1.18727 - 1.26111i) q^{12} +(1.42090 + 4.83914i) q^{13} +(-2.29791 - 1.31134i) q^{14} +(0.382473 + 0.0206549i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.358224 - 0.143411i) q^{17} +(-2.42143 - 1.77107i) q^{18} +(-1.54146 - 3.85037i) q^{19} +(-0.186037 - 0.119559i) q^{20} +(-4.32855 - 1.50454i) q^{21} +3.24865 q^{22} +(4.69989 - 0.954502i) q^{23} +(0.709499 + 1.58007i) q^{24} +(-4.86162 + 0.937001i) q^{25} +(0.239976 - 5.03772i) q^{26} +(-4.68460 - 2.24822i) q^{27} +(1.74263 + 1.99079i) q^{28} +(-6.62779 + 0.952933i) q^{29} +(-0.354681 - 0.144613i) q^{30} +(4.89407 - 0.233133i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(5.53179 - 1.02977i) q^{33} +(0.291617 + 0.252687i) q^{34} +(-0.582711 - 0.0526867i) q^{35} +(1.70899 + 2.46564i) q^{36} +(-0.876210 + 1.23046i) q^{37} +(0.197344 + 4.14277i) q^{38} +(-1.18825 - 8.65429i) q^{39} +(0.136701 + 0.173830i) q^{40} +(-0.886283 + 1.94069i) q^{41} +(3.59840 + 2.83752i) q^{42} +(-3.43131 - 2.20517i) q^{43} +(-3.06997 - 1.06253i) q^{44} +(-0.649791 - 0.133819i) q^{45} +(-4.75358 - 0.635177i) q^{46} +(4.94958 + 8.57293i) q^{47} +(-0.153688 - 1.72522i) q^{48} +(6.52441 + 2.53615i) q^{49} +(4.90070 + 0.704614i) q^{50} +(0.576662 + 0.337838i) q^{51} +(-1.87445 + 4.68216i) q^{52} +(-3.25516 - 3.41392i) q^{53} +(3.69163 + 3.65676i) q^{54} +(0.653492 - 0.298440i) q^{55} +(-0.995665 - 2.45125i) q^{56} +(1.64923 + 6.99174i) q^{57} +(6.57494 + 1.26722i) q^{58} +(-3.14709 + 12.9725i) q^{59} +(0.287876 + 0.252665i) q^{60} +(-4.14199 + 8.03434i) q^{61} +(-4.70115 - 1.38038i) q^{62} +(7.02679 + 3.69109i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.414522 - 1.03542i) q^{65} +(-5.56435 - 0.836138i) q^{66} +(-6.55809 + 1.26397i) q^{67} +(-0.192932 - 0.334168i) q^{68} +(-8.29573 + 0.425232i) q^{69} +(0.533430 + 0.240375i) q^{70} +(3.24815 - 2.81454i) q^{71} +(-0.808566 - 2.88898i) q^{72} +(-7.69186 + 9.78100i) q^{73} +(1.23046 - 0.876210i) q^{74} +(8.56826 - 0.353628i) q^{75} +(1.16848 - 3.97946i) q^{76} +(-8.50137 + 1.26598i) q^{77} +(-1.70765 + 8.56695i) q^{78} +(10.0689 + 9.60066i) q^{79} +(-0.0723286 - 0.208980i) q^{80} +(7.44523 + 5.05653i) q^{81} +(1.47227 - 1.54408i) q^{82} +(2.11936 + 4.64074i) q^{83} +(-2.47243 - 3.85838i) q^{84} +(0.0818745 + 0.0240405i) q^{85} +(2.52135 + 3.20616i) q^{86} +(11.5975 + 0.0736611i) q^{87} +(2.55361 + 2.00818i) q^{88} +(-0.770433 + 16.1734i) q^{89} +(0.570285 + 0.338985i) q^{90} +(1.33518 + 13.2767i) q^{91} +(4.28439 + 2.15499i) q^{92} +(-8.44267 - 0.860323i) q^{93} +(-1.87343 - 9.72028i) q^{94} +(0.420276 + 0.815223i) q^{95} +(-0.419029 + 1.68060i) q^{96} +(-11.4565 - 5.23201i) q^{97} +(-5.33608 - 4.53059i) q^{98} +(-9.74001 + 0.340036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 + 4 * q^9	$ 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$3$	−1.71282	−	0.257380i	−0.988898	−	0.148599i
$3$	−1.71282	−	0.257380i	−0.988898	−	0.148599i
$4$	0.786053	+	0.618159i	0.393027	+	0.309079i
$5$	−0.220141	+	0.0210209i	−0.0984501	+	0.00940085i	−0.144165	−	0.989554i	$-0.546050\pi$
$5$	−0.220141	+	0.0210209i	−0.0984501	+	0.00940085i	0.0457147	+	0.998955i	$0.485443\pi$
$6$	1.53444	+	0.803434i	0.626431	+	0.328000i
$7$	2.60042	+	0.487642i	0.982868	+	0.184311i
$7$	2.60042	+	0.487642i	0.982868	+	0.184311i
$8$	−0.540641	−	0.841254i	−0.191145	−	0.297428i
$9$	2.86751	+	0.881693i	0.955837	+	0.293898i
$10$	0.214909	+	0.0521363i	0.0679601	+	0.0164870i
$11$	−3.06997	+	1.06253i	−0.925632	+	0.320364i	−0.747974	−	0.663728i	$-0.768973\pi$
$11$	−3.06997	+	1.06253i	−0.925632	+	0.320364i	−0.177658	+	0.984092i	$0.556852\pi$
$12$	−1.18727	−	1.26111i	−0.342734	−	0.364051i
$13$	1.42090	+	4.83914i	0.394087	+	1.34214i	0.882824	+	0.469705i	$0.155640\pi$
$13$	1.42090	+	4.83914i	0.394087	+	1.34214i	−0.488737	+	0.872431i	$0.662542\pi$
$14$	−2.29791	−	1.31134i	−0.614143	−	0.350470i
$15$	0.382473	+	0.0206549i	0.0987540	+	0.00533308i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.358224	−	0.143411i	−0.0868821	−	0.0347823i	0.327814	−	0.944742i	$-0.393688\pi$
$17$	−0.358224	−	0.143411i	−0.0868821	−	0.0347823i	−0.414696	+	0.909960i	$0.636112\pi$
$18$	−2.42143	−	1.77107i	−0.570736	−	0.417446i
$19$	−1.54146	−	3.85037i	−0.353634	−	0.883336i	−0.993393	−	0.114760i	$-0.963390\pi$
$19$	−1.54146	−	3.85037i	−0.353634	−	0.883336i	0.639759	−	0.768576i	$-0.279034\pi$
$20$	−0.186037	−	0.119559i	−0.0415991	−	0.0267341i
$21$	−4.32855	−	1.50454i	−0.944567	−	0.328318i
$22$	3.24865			0.692614
$23$	4.69989	−	0.954502i	0.979994	−	0.199027i
$23$	4.69989	−	0.954502i	0.979994	−	0.199027i
$24$	0.709499	+	1.58007i	0.144826	+	0.322530i
$25$	−4.86162	+	0.937001i	−0.972325	+	0.187400i
$26$	0.239976	−	5.03772i	0.0470632	−	0.987978i
$27$	−4.68460	−	2.24822i	−0.901552	−	0.432671i
$28$	1.74263	+	1.99079i	0.329326	+	0.376224i
$29$	−6.62779	+	0.952933i	−1.23075	+	0.176955i	−0.726844	−	0.686803i	$-0.759014\pi$
$29$	−6.62779	+	0.952933i	−1.23075	+	0.176955i	−0.503907	+	0.863758i	$0.668104\pi$
$30$	−0.354681	−	0.144613i	−0.0647557	−	0.0264027i
$31$	4.89407	−	0.233133i	0.879001	−	0.0418720i	0.396772	−	0.917917i	$-0.370130\pi$
$31$	4.89407	−	0.233133i	0.879001	−	0.0418720i	0.482229	+	0.876045i	$0.339827\pi$
$32$	0.0950560	−	0.995472i	0.0168037	−	0.175976i
$33$	5.53179	−	1.02977i	0.962961	−	0.179260i
$34$	0.291617	+	0.252687i	0.0500118	+	0.0433355i
$35$	−0.582711	−	0.0526867i	−0.0984961	−	0.00890567i
$36$	1.70899	+	2.46564i	0.284832	+	0.410939i
$37$	−0.876210	+	1.23046i	−0.144048	+	0.202287i	−0.880296	−	0.474424i	$-0.842656\pi$
$37$	−0.876210	+	1.23046i	−0.144048	+	0.202287i	0.736248	+	0.676712i	$0.236596\pi$
$38$	0.197344	+	4.14277i	0.0320135	+	0.672046i
$39$	−1.18825	−	8.65429i	−0.190272	−	1.38580i
$40$	0.136701	+	0.173830i	0.0216144	+	0.0274849i
$41$	−0.886283	+	1.94069i	−0.138414	+	0.303085i	−0.966127	−	0.258067i	$-0.916914\pi$
$41$	−0.886283	+	1.94069i	−0.138414	+	0.303085i	0.827713	+	0.561152i	$0.189642\pi$
$42$	3.59840	+	2.83752i	0.555245	+	0.437839i
$43$	−3.43131	−	2.20517i	−0.523270	−	0.336285i	0.252194	−	0.967677i	$-0.418848\pi$
$43$	−3.43131	−	2.20517i	−0.523270	−	0.336285i	−0.775464	+	0.631391i	$0.782484\pi$
$44$	−3.06997	−	1.06253i	−0.462816	−	0.160182i
$45$	−0.649791	−	0.133819i	−0.0968651	−	0.0199486i
$46$	−4.75358	−	0.635177i	−0.700878	−	0.0936517i
$47$	4.94958	+	8.57293i	0.721971	+	1.25049i	0.960209	+	0.279284i	$0.0900970\pi$
$47$	4.94958	+	8.57293i	0.721971	+	1.25049i	−0.238238	+	0.971207i	$0.576570\pi$
$48$	−0.153688	−	1.72522i	−0.0221829	−	0.249014i
$49$	6.52441	+	2.53615i	0.932059	+	0.362307i
$50$	4.90070	+	0.704614i	0.693064	+	0.0996475i
$51$	0.576662	+	0.337838i	0.0807489	+	0.0473067i
$52$	−1.87445	+	4.68216i	−0.259940	+	0.649299i
$53$	−3.25516	−	3.41392i	−0.447131	−	0.468937i	0.461135	−	0.887330i	$-0.347442\pi$
$53$	−3.25516	−	3.41392i	−0.447131	−	0.468937i	−0.908266	+	0.418392i	$0.862594\pi$
$54$	3.69163	+	3.65676i	0.502367	+	0.497621i
$55$	0.653492	−	0.298440i	0.0881169	−	0.0402416i
$56$	−0.995665	−	2.45125i	−0.133051	−	0.327563i
$57$	1.64923	+	6.99174i	0.218446	+	0.926079i
$58$	6.57494	+	1.26722i	0.863332	+	0.166394i
$59$	−3.14709	+	12.9725i	−0.409716	+	1.68887i	0.276124	+	0.961122i	$0.410950\pi$
$59$	−3.14709	+	12.9725i	−0.409716	+	1.68887i	−0.685840	+	0.727752i	$0.740565\pi$
$60$	0.287876	+	0.252665i	0.0371646	+	0.0326189i
$61$	−4.14199	+	8.03434i	−0.530327	+	1.02869i	0.459734	+	0.888057i	$0.347945\pi$
$61$	−4.14199	+	8.03434i	−0.530327	+	1.02869i	−0.990062	+	0.140635i	$0.955086\pi$
$62$	−4.70115	−	1.38038i	−0.597047	−	0.175309i
$63$	7.02679	+	3.69109i	0.885293	+	0.465034i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	−0.414522	−	1.03542i	−0.0514151	−	0.128429i
$66$	−5.56435	−	0.836138i	−0.684924	−	0.102922i
$67$	−6.55809	+	1.26397i	−0.801198	+	0.154418i	−0.573385	−	0.819286i	$-0.694370\pi$
$67$	−6.55809	+	1.26397i	−0.801198	+	0.154418i	−0.227814	+	0.973705i	$0.573158\pi$
$68$	−0.192932	−	0.334168i	−0.0233965	−	0.0405238i
$69$	−8.29573	+	0.425232i	−0.998689	+	0.0511920i
$70$	0.533430	+	0.240375i	0.0637571	+	0.0287303i
$71$	3.24815	−	2.81454i	0.385484	−	0.334024i	−0.440464	−	0.897770i	$-0.645186\pi$
$71$	3.24815	−	2.81454i	0.385484	−	0.334024i	0.825948	+	0.563747i	$0.190641\pi$
$72$	−0.808566	−	2.88898i	−0.0952904	−	0.340470i
$73$	−7.69186	+	9.78100i	−0.900264	+	1.14478i	0.0886159	+	0.996066i	$0.471756\pi$
$73$	−7.69186	+	9.78100i	−0.900264	+	1.14478i	−0.988880	+	0.148713i	$0.952487\pi$
$74$	1.23046	−	0.876210i	0.143039	−	0.101857i
$75$	8.56826	−	0.353628i	0.989377	−	0.0408335i
$76$	1.16848	−	3.97946i	0.134033	−	0.456476i
$77$	−8.50137	+	1.26598i	−0.968821	+	0.144271i
$78$	−1.70765	+	8.56695i	−0.193353	+	0.970016i
$79$	10.0689	+	9.60066i	1.13284	+	1.08016i	0.995981	+	0.0895675i	$0.0285485\pi$
$79$	10.0689	+	9.60066i	1.13284	+	1.08016i	0.136857	+	0.990591i	$0.456300\pi$
$80$	−0.0723286	−	0.208980i	−0.00808659	−	0.0233647i
$81$	7.44523	+	5.05653i	0.827248	+	0.561837i
$82$	1.47227	−	1.54408i	0.162586	−	0.170515i
$83$	2.11936	+	4.64074i	0.232630	+	0.509388i	0.989562	−	0.144105i	$-0.0460303\pi$
$83$	2.11936	+	4.64074i	0.232630	+	0.509388i	−0.756933	+	0.653493i	$0.773303\pi$
$84$	−2.47243	−	3.85838i	−0.269764	−	0.420984i
$85$	0.0818745	+	0.0240405i	0.00888053	+	0.00260756i
$86$	2.52135	+	3.20616i	0.271884	+	0.345729i
$87$	11.5975	+	0.0736611i	1.24338	+	0.00789730i
$88$	2.55361	+	2.00818i	0.272216	+	0.214073i
$89$	−0.770433	+	16.1734i	−0.0816657	+	1.71437i	0.471969	+	0.881615i	$0.343543\pi$
$89$	−0.770433	+	16.1734i	−0.0816657	+	1.71437i	−0.553635	+	0.832760i	$0.686760\pi$
$90$	0.570285	+	0.338985i	0.0601133	+	0.0357322i
$91$	1.33518	+	13.2767i	0.139964	+	1.39178i
$92$	4.28439	+	2.15499i	0.446679	+	0.224673i
$93$	−8.44267	−	0.860323i	−0.875464	−	0.0892113i
$94$	−1.87343	−	9.72028i	−0.193230	−	1.00257i
$95$	0.420276	+	0.815223i	0.0431195	+	0.0836401i
$96$	−0.419029	+	1.68060i	−0.0427670	+	0.171525i
$97$	−11.4565	−	5.23201i	−1.16323	−	0.531230i	−0.262212	−	0.965010i	$-0.584452\pi$
$97$	−11.4565	−	5.23201i	−1.16323	−	0.531230i	−0.901019	+	0.433780i	$0.857179\pi$
$98$	−5.33608	−	4.53059i	−0.539026	−	0.457659i
$99$	−9.74001	+	0.340036i	−0.978908	+	0.0341749i
$100$	−4.40071	−	2.26872i	−0.440071	−	0.226872i
$101$	17.2588	+	1.64802i	1.71732	+	0.163984i	0.906751	−	0.421666i	$-0.138554\pi$
$101$	17.2588	+	1.64802i	1.71732	+	0.163984i	0.810564	+	0.585650i	$0.199161\pi$
$102$	−0.434450	−	0.507865i	−0.0430170	−	0.0502861i
$103$	2.68648	−	13.9388i	0.264707	−	1.37343i	−0.569506	−	0.821987i	$-0.692865\pi$
$103$	2.68648	−	13.9388i	0.264707	−	1.37343i	0.834213	−	0.551443i	$-0.185923\pi$
$104$	3.30275	−	3.81157i	0.323861	−	0.373755i
$105$	0.984519	+	0.240221i	0.0960792	+	0.0234432i
$106$	1.95955	+	4.29081i	0.190328	+	0.416761i
$107$	8.21000	−	15.9252i	0.793691	−	1.53955i	−0.0475397	−	0.998869i	$-0.515138\pi$
$107$	8.21000	−	15.9252i	0.793691	−	1.53955i	0.841231	−	0.540676i	$-0.181832\pi$
$108$	−2.29259	−	4.66305i	−0.220604	−	0.448702i
$109$	11.9978	+	4.80319i	1.14918	+	0.460062i	0.866512	−	0.499156i	$-0.166357\pi$
$109$	11.9978	+	4.80319i	1.14918	+	0.460062i	0.282667	+	0.959218i	$0.408781\pi$
$110$	−0.715161	+	0.0682896i	−0.0681879	+	0.00651116i
$111$	1.81749	−	1.88205i	0.172508	−	0.178636i
$112$	0.139177	+	2.64209i	0.0131510	+	0.249654i
$113$	−3.01683	+	2.61410i	−0.283799	+	0.245913i	−0.785114	−	0.619352i	$-0.787395\pi$
$113$	−3.01683	+	2.61410i	−0.283799	+	0.245913i	0.501314	+	0.865265i	$0.332850\pi$
$114$	0.728252	−	7.14661i	0.0682070	−	0.669341i
$115$	−1.01457	+	0.308921i	−0.0946095	+	0.0288070i
$116$	−5.79886	−	3.34797i	−0.538411	−	0.310852i
$117$	−0.192192	+	15.1291i	−0.0177681	+	1.39868i
$118$	7.21689	−	11.2297i	0.664368	−	1.03378i
$119$	−0.861601	−	0.547615i	−0.0789828	−	0.0501998i
$120$	−0.189404	−	0.332923i	−0.0172902	−	0.0303916i
$121$	−0.350805	+	0.275876i	−0.0318914	+	0.0250797i
$122$	6.54196	−	6.23774i	0.592281	−	0.564739i
$123$	2.01754	−	3.09594i	0.181915	−	0.279152i
$124$	3.99111	+	2.84206i	0.358413	+	0.255224i
$125$	2.11147	−	0.619983i	0.188856	−	0.0554530i
$126$	−5.43309	−	5.78633i	−0.484018	−	0.515487i
$127$	−11.2870	+	13.0259i	−1.00156	+	1.15586i	−0.0137932	+	0.999905i	$0.504391\pi$
$127$	−11.2870	+	13.0259i	−1.00156	+	1.15586i	−0.987764	+	0.155954i	$0.950155\pi$
$128$	0.690079	−	0.723734i	0.0609949	−	0.0639697i
$129$	5.30965	+	4.66021i	0.467489	+	0.410309i
$130$	0.0530689	+	1.11405i	0.00465445	+	0.0977090i
$131$	−0.270902	−	1.11667i	−0.0236688	−	0.0975640i	0.958752	−	0.284244i	$-0.0917425\pi$
$131$	−0.270902	−	1.11667i	−0.0236688	−	0.0975640i	−0.982421	+	0.186680i	$0.940227\pi$
$132$	4.98484	+	2.61007i	0.433875	+	0.227178i
$133$	−2.13084	−	10.7643i	−0.184767	−	0.933382i
$134$	6.61081	+	0.950490i	0.571087	+	0.0821099i
$135$	1.07853	+	0.396452i	0.0928254	+	0.0341211i
$136$	0.0730253	+	0.378891i	0.00626187	+	0.0324896i
$137$	−17.2264	−	9.94569i	−1.47175	−	0.849718i	−0.472258	−	0.881460i	$-0.656561\pi$
$137$	−17.2264	−	9.94569i	−1.47175	−	0.849718i	−0.999496	+	0.0317422i	$0.989894\pi$
$138$	7.97855	+	2.31142i	0.679180	+	0.196761i
$139$			19.1490i			1.62419i	0.583522	+	0.812097i	$0.301674\pi$
$139$			19.1490i			1.62419i	−0.583522	+	0.812097i	$0.698326\pi$
$140$	−0.425473	−	0.401623i	−0.0359590	−	0.0339433i
$141$	−6.27125	−	15.9578i	−0.528134	−	1.34389i
$142$	−3.99005	+	1.59737i	−0.334837	+	0.134049i
$143$	−9.50385	−	13.3463i	−0.794752	−	1.11607i
$144$	−0.180798	+	2.99455i	−0.0150665	+	0.249546i
$145$	1.43902	−	0.349102i	0.119504	−	0.0289913i
$146$	10.4679	−	6.72729i	0.866327	−	0.556754i
$147$	−10.5224	−	6.02323i	−0.867872	−	0.496787i
$148$	−1.44937	+	0.425573i	−0.119137	+	0.0349819i
$149$	2.46445	−	12.7868i	0.201895	−	1.04753i	−0.729626	−	0.683846i	$-0.760306\pi$
$149$	2.46445	−	12.7868i	0.201895	−	1.04753i	0.931521	−	0.363687i	$-0.118482\pi$
$150$	−8.21267	−	2.46822i	−0.670562	−	0.201530i
$151$	−1.47397	+	6.07578i	−0.119950	+	0.494440i	0.879865	+	0.475223i	$0.157633\pi$
$151$	−1.47397	+	6.07578i	−0.119950	+	0.494440i	−0.999815	+	0.0192173i	$0.993883\pi$
$152$	−2.40577	+	3.37843i	−0.195133	+	0.274026i
$153$	−0.900766	−	0.727077i	−0.0728226	−	0.0587807i
$154$	8.44786	+	1.58418i	0.680748	+	0.127657i
$155$	−1.07249	+	0.154200i	−0.0861441	+	0.0123857i
$156$	4.41570	−	7.53726i	0.353539	−	0.603464i
$157$	−3.09867	+	3.94028i	−0.247301	+	0.314469i	−0.893817	−	0.448431i	$-0.851983\pi$
$157$	−3.09867	+	3.94028i	−0.247301	+	0.314469i	0.646516	+	0.762900i	$0.276225\pi$
$158$	−6.37503	−	12.3658i	−0.507170	−	0.983773i
$159$	4.69684	+	6.68524i	0.372483	+	0.530174i
$160$			0.221142i			0.0174828i
$161$	12.6872	−	0.190250i	0.999888	−	0.0149938i
$162$	−5.38192	−	7.21352i	−0.422844	−	0.566748i
$163$	0.482638	−	1.39449i	0.0378032	−	0.109225i	−0.924520	−	0.381134i	$-0.875534\pi$
$163$	0.482638	−	1.39449i	0.0378032	−	0.109225i	0.962323	+	0.271909i	$0.0876549\pi$
$164$	−1.89632	+	0.977621i	−0.148078	+	0.0763393i
$165$	−1.19613	+	0.342978i	−0.0931184	+	0.0267008i
$166$	−0.484955	−	5.07868i	−0.0376398	−	0.394182i
$167$	0.199493	+	1.38750i	0.0154372	+	0.107368i	0.996083	−	0.0884213i	$-0.0281822\pi$
$167$	0.199493	+	1.38750i	0.0154372	+	0.107368i	−0.980646	+	0.195789i	$0.937273\pi$
$168$	1.07449	+	4.45483i	0.0828988	+	0.343697i
$169$	−10.4620	+	6.72353i	−0.804770	+	0.517195i
$170$	−0.0695085	−	0.0494968i	−0.00533106	−	0.00379623i
$171$	−1.02530	−	12.4001i	−0.0784064	−	0.948258i
$172$	−1.33405	−	3.85448i	−0.101720	−	0.293901i
$173$	6.67460	+	1.28642i	0.507460	+	0.0978049i	0.436554	−	0.899678i	$-0.356199\pi$
$173$	6.67460	+	1.28642i	0.507460	+	0.0978049i	0.0709062	+	0.997483i	$0.477411\pi$
$174$	−10.9355	−	3.86278i	−0.829021	−	0.292836i
$175$	−13.0992	+	0.0658699i	−0.990207	+	0.00497930i
$176$	−1.75635	−	2.73294i	−0.132390	−	0.206003i
$177$	8.72927	−	21.4095i	0.656132	−	1.60924i
$178$	6.01785	−	15.0319i	0.451057	−	1.12669i
$179$	−9.51462	+	6.77533i	−0.711156	+	0.506412i	−0.877452	−	0.479664i	$-0.840759\pi$
$179$	−9.51462	+	6.77533i	−0.711156	+	0.506412i	0.166296	+	0.986076i	$0.446819\pi$
$180$	−0.428049	−	0.506863i	−0.0319049	−	0.0377793i
$181$	−5.56252	+	8.65545i	−0.413459	+	0.643355i	−0.984053	−	0.177878i	$-0.943077\pi$
$181$	−5.56252	+	8.65545i	−0.413459	+	0.643355i	0.570594	+	0.821233i	$0.306713\pi$
$182$	3.08064	−	12.9832i	0.228352	−	0.962378i
$183$	9.16237	−	12.6953i	0.677302	−	0.938465i
$184$	−3.34393	−	3.43775i	−0.246518	−	0.253434i
$185$	0.167024	−	0.289295i	0.0122799	−	0.0212694i
$186$	7.69695	+	3.57433i	0.564368	+	0.262083i
$187$	1.25212	+	0.0596457i	0.0915639	+	0.00436172i
$188$	−1.40880	+	9.79841i	−0.102747	+	0.714622i
$189$	−11.0856	−	8.13074i	−0.806360	−	0.591424i
$190$	−0.130528	−	0.907845i	−0.00946953	−	0.0658620i
$191$	4.95281	−	1.20154i	0.358373	−	0.0869403i	−0.0525303	−	0.998619i	$-0.516729\pi$
$191$	4.95281	−	1.20154i	0.358373	−	0.0869403i	0.410903	+	0.911679i	$0.365213\pi$
$192$	0.945653	−	1.45112i	0.0682466	−	0.104725i
$193$	−19.9694	−	1.90685i	−1.43743	−	0.137258i	−0.652946	−	0.757404i	$-0.726467\pi$
$193$	−19.9694	−	1.90685i	−1.43743	−	0.137258i	−0.784486	+	0.620146i	$0.787073\pi$
$194$	9.11518	+	8.69130i	0.654432	+	0.623999i
$195$	0.443503	+	1.88019i	0.0317599	+	0.134643i
$196$	3.56079	+	6.02667i	0.254342	+	0.430477i
$197$	2.72343	+	9.27514i	0.194036	+	0.660826i	0.997825	+	0.0659121i	$0.0209957\pi$
$197$	2.72343	+	9.27514i	0.194036	+	0.660826i	−0.803789	+	0.594914i	$0.797186\pi$
$198$	9.31553	+	2.86431i	0.662026	+	0.203558i
$199$	14.1665	−	0.674833i	1.00424	−	0.0478377i	0.460985	−	0.887408i	$-0.347496\pi$
$199$	14.1665	−	0.674833i	1.00424	−	0.0478377i	0.543251	+	0.839570i	$0.317193\pi$
$200$	3.41665	+	3.58328i	0.241593	+	0.253376i
$201$	11.5582	−	0.477027i	0.815249	−	0.0336469i
$202$	−15.7706	−	7.20218i	−1.10961	−	0.506744i
$203$	−17.6998	−	0.753959i	−1.24228	−	0.0529175i
$204$	0.244450	+	0.622027i	0.0171149	+	0.0435506i
$205$	0.154312	−	0.445856i	0.0107776	−	0.0311399i
$206$	−7.09766	+	12.2935i	−0.494517	+	0.856529i
$207$	14.3186	+	1.40681i	0.995208	+	0.0977802i
$208$	−4.36774	+	2.52172i	−0.302848	+	0.174850i
$209$	8.82337	+	10.1827i	0.610325	+	0.704353i
$210$	−0.851803	−	0.549014i	−0.0587800	−	0.0378856i
$211$	2.07018	−	14.3984i	0.142517	−	0.991227i	−0.785546	−	0.618804i	$-0.787618\pi$
$211$	2.07018	−	14.3984i	0.142517	−	0.991227i	0.928063	−	0.372424i	$-0.121473\pi$
$212$	−0.448388	−	4.69573i	−0.0307954	−	0.322504i
$213$	−6.28790	+	3.98479i	−0.430840	+	0.273033i
$214$	−12.9671	+	12.3641i	−0.886411	+	0.845191i
$215$	0.801727	+	0.413319i	0.0546773	+	0.0281881i
$216$	0.641361	+	5.15642i	0.0436391	+	0.350850i
$217$	12.8403	+	1.78031i	0.871660	+	0.120855i
$218$	−9.76695	−	8.46311i	−0.661501	−	0.573194i
$219$	15.6922	−	14.7734i	1.06038	−	0.998291i
$220$	0.698163	+	0.169373i	0.0470701	+	0.0114191i
$221$	0.184987	−	1.93727i	0.0124436	−	0.130315i
$222$	−2.33308	+	1.18409i	−0.156586	+	0.0794711i
$223$	6.69429	−	22.7986i	0.448283	−	1.52671i	−0.357164	−	0.934042i	$-0.616256\pi$
$223$	6.69429	−	22.7986i	0.448283	−	1.52671i	0.805446	−	0.592669i	$-0.201926\pi$
$224$	0.732620	−	2.54230i	0.0489502	−	0.169864i
$225$	−14.7669	−	1.59960i	−0.984460	−	0.106640i
$226$	3.70589	−	1.48361i	0.246512	−	0.0986886i
$227$	2.08709	−	1.07597i	0.138525	−	0.0714145i	−0.387571	−	0.921840i	$-0.626686\pi$
$227$	2.08709	−	1.07597i	0.138525	−	0.0714145i	0.526096	+	0.850425i	$0.323655\pi$
$228$	−3.02563	+	6.51537i	−0.200377	+	0.431491i
$229$	6.65617	−	3.84294i	0.439852	−	0.253949i	−0.263683	−	0.964609i	$-0.584937\pi$
$229$	6.65617	−	3.84294i	0.439852	−	0.253949i	0.703535	+	0.710661i	$0.251604\pi$
$230$	1.05981	+	0.0399038i	0.0698819	+	0.00263118i
$231$	14.8872	+	0.0196940i	0.979503	+	0.00129577i
$232$	4.38491	+	5.06046i	0.287884	+	0.332235i
$233$	10.1847	+	0.485159i	0.667225	+	0.0317839i	0.378462	−	0.925617i	$-0.376453\pi$
$233$	10.1847	+	0.485159i	0.667225	+	0.0317839i	0.288763	+	0.957401i	$0.406756\pi$
$234$	5.12986	−	14.2341i	0.335349	−	0.930514i
$235$	−1.26982	−	1.78321i	−0.0828338	−	0.116324i
$236$	−10.4928	+	8.25166i	−0.683026	+	0.537137i
$237$	−14.7752	−	19.0357i	−0.959750	−	1.23650i
$238$	0.635106	+	0.799299i	0.0411678	+	0.0518108i
$239$	5.39988	−	2.46604i	0.349289	−	0.159515i	−0.233042	−	0.972467i	$-0.574868\pi$
$239$	5.39988	−	2.46604i	0.349289	−	0.159515i	0.582331	+	0.812952i	$0.302141\pi$
$240$	0.0700987	+	0.376561i	0.00452485	+	0.0243069i
$241$	−13.5229	+	4.68034i	−0.871089	+	0.301487i	−0.725803	−	0.687903i	$-0.758532\pi$
$241$	−13.5229	+	4.68034i	−0.871089	+	0.301487i	−0.145286	+	0.989390i	$0.546410\pi$
$242$	0.421742	−	0.145966i	0.0271106	−	0.00938307i
$243$	−11.4509	−	10.5772i	−0.734576	−	0.678527i
$244$	−8.22232	+	3.75501i	−0.526380	+	0.240390i
$245$	−1.48960	−	0.421162i	−0.0951673	−	0.0269070i
$246$	−2.91916	+	2.26579i	−0.186119	+	0.144462i
$247$	16.4422	−	12.9303i	1.04619	−	0.822736i
$248$	−2.84206	−	3.99111i	−0.180471	−	0.253436i
$249$	−2.43564	−	8.49424i	−0.154352	−	0.538301i
$250$	−2.19812	−	0.104709i	−0.139021	−	0.00662239i
$251$	−14.2203	−	16.4111i	−0.897577	−	1.03586i	−0.999158	−	0.0410321i	$-0.986935\pi$
$251$	−14.2203	−	16.4111i	−0.897577	−	1.03586i	0.101581	−	0.994827i	$-0.467610\pi$
$252$	3.24175	+	7.24507i	0.204211	+	0.456397i
$253$	−13.4143	+	7.92406i	−0.843353	+	0.498181i
$254$	14.9266	−	8.61785i	0.936575	−	0.540732i
$255$	−0.134049	−	0.0622500i	−0.00839446	−	0.00389824i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	11.9717	−	4.79276i	0.746776	−	0.298964i	0.0331113	−	0.999452i	$-0.489458\pi$
$257$	11.9717	−	4.79276i	0.746776	−	0.298964i	0.713664	+	0.700488i	$0.247034\pi$
$258$	−3.49342	−	6.14052i	−0.217491	−	0.382292i
$259$	−2.87854	+	2.77245i	−0.178864	+	0.172272i
$260$	0.314221	−	1.07014i	0.0194872	−	0.0663672i
$261$	−19.8455	−	3.11113i	−1.22840	−	0.192574i
$262$	−0.109225	+	1.14386i	−0.00674796	+	0.0706678i
$263$	−14.3750	−	3.48734i	−0.886402	−	0.215039i	−0.233387	−	0.972384i	$-0.574981\pi$
$263$	−14.3750	−	3.48734i	−0.886402	−	0.215039i	−0.653015	+	0.757345i	$0.726496\pi$
$264$	−3.85701	−	4.09690i	−0.237383	−	0.252147i
$265$	0.788359	+	0.683117i	0.0484285	+	0.0419635i
$266$	−1.50701	+	10.8692i	−0.0924005	+	0.666432i
$267$	5.48232	−	27.5038i	0.335513	−	1.68321i
$268$	−5.93634	−	3.06040i	−0.362620	−	0.186943i
$269$	−6.93783	+	6.61521i	−0.423007	+	0.403337i	−0.871457	−	0.490471i	$-0.836825\pi$
$269$	−6.93783	+	6.61521i	−0.423007	+	0.403337i	0.448450	+	0.893808i	$0.351976\pi$
$270$	−0.889548	−	0.727401i	−0.0541362	−	0.0442682i
$271$	−0.0108180	−	0.113291i	−0.000657148	−	0.00688196i	0.995137	−	0.0984965i	$-0.0314033\pi$
$271$	−0.0108180	−	0.113291i	−0.000657148	−	0.00688196i	−0.995795	+	0.0916145i	$0.970797\pi$
$272$	0.0549142	−	0.381937i	0.00332966	−	0.0231583i
$273$	1.13025	−	23.0843i	0.0684057	−	1.39712i
$274$	13.0261	+	15.0329i	0.786935	+	0.908171i
$275$	13.9295	−	8.04218i	0.839979	−	0.484962i
$276$	−6.78375	−	4.79383i	−0.408334	−	0.288554i
$277$	1.09496	−	1.89653i	0.0657901	−	0.113952i	−0.831254	−	0.555893i	$-0.812377\pi$
$277$	1.09496	−	1.89653i	0.0657901	−	0.113952i	0.897044	+	0.441941i	$0.145710\pi$
$278$	6.26301	−	18.0958i	0.375631	−	1.08531i
$279$	14.2394	+	3.64656i	0.852488	+	0.218314i
$280$	0.270714	+	0.518692i	0.0161783	+	0.0309978i
$281$	−2.24468	−	1.02511i	−0.133907	−	0.0611531i	0.347335	−	0.937741i	$-0.387087\pi$
$281$	−2.24468	−	1.02511i	−0.133907	−	0.0611531i	−0.481241	+	0.876588i	$0.659814\pi$
$282$	0.707041	+	17.1313i	0.0421037	+	1.02015i
$283$	8.07131	+	8.46494i	0.479789	+	0.503189i	0.918490	−	0.395445i	$-0.129410\pi$
$283$	8.07131	+	8.46494i	0.479789	+	0.503189i	−0.438700	+	0.898633i	$0.644561\pi$
$284$	4.29305	−	0.204503i	0.254745	−	0.0121350i
$285$	−0.510036	−	1.50450i	−0.0302119	−	0.0891190i
$286$	4.61600	+	15.7207i	0.272950	+	0.929582i
$287$	−3.25107	+	4.61442i	−0.191905	+	0.272381i
$288$	1.15027	−	2.77072i	0.0677806	−	0.163266i
$289$	−12.1957	−	11.6286i	−0.717395	−	0.684035i
$290$	−1.47405	−	0.140755i	−0.0865594	−	0.00826542i
$291$	18.2763	+	11.9102i	1.07138	+	0.698187i
$292$	−12.0924	+	2.93359i	−0.707656	+	0.171675i
$293$	1.71517	+	11.9293i	0.100201	+	0.696914i	0.976558	+	0.215253i	$0.0690575\pi$
$293$	1.71517	+	11.9293i	0.100201	+	0.696914i	−0.876357	+	0.481662i	$0.840033\pi$
$294$	7.97366	+	9.13349i	0.465034	+	0.532676i
$295$	0.420111	−	2.92193i	0.0244598	−	0.170122i
$296$	1.50885	+	0.0718753i	0.0877000	+	0.00417766i
$297$	16.7704	+	1.92447i	0.973118	+	0.111669i
$298$	−6.51105	+	11.2775i	−0.377175	+	0.653286i
$299$	11.2970	+	21.3871i	0.653324	+	1.23685i
$300$	6.95370	+	5.01857i	0.401472	+	0.289747i
$301$	−7.84753	−	7.40762i	−0.452324	−	0.426968i
$302$	3.38010	−	5.25953i	0.194503	−	0.302652i
$303$	−29.1371	−	7.26484i	−1.67388	−	0.417354i
$304$	3.37843	−	2.40577i	0.193766	−	0.137980i
$305$	0.742933	−	1.85576i	0.0425402	−	0.106260i
$306$	0.613421	+	0.981700i	0.0350670	+	0.0561201i
$307$	−10.0281	−	15.6040i	−0.572333	−	0.890567i	0.427577	−	0.903979i	$-0.359367\pi$
$307$	−10.0281	−	15.6040i	−0.572333	−	0.890567i	−0.999910	+	0.0134115i	$0.995731\pi$
$308$	−7.46510	−	4.26007i	−0.425364	−	0.242740i
$309$	−8.18904	+	23.1832i	−0.465858	+	1.31885i
$310$	1.06393	+	0.205056i	0.0604274	+	0.0116464i
$311$	−1.34288	−	3.88001i	−0.0761479	−	0.220015i	0.900502	−	0.434852i	$-0.143199\pi$
$311$	−1.34288	−	3.88001i	−0.0761479	−	0.220015i	−0.976650	+	0.214837i	$0.931078\pi$
$312$	−6.63804	+	5.67848i	−0.375805	+	0.321481i
$313$	22.0479	+	15.7002i	1.24622	+	0.887428i	0.996718	−	0.0809466i	$-0.0257943\pi$
$313$	22.0479	+	15.7002i	1.24622	+	0.887428i	0.249500	+	0.968375i	$0.419734\pi$
$314$	4.21699	−	2.71010i	0.237979	−	0.152940i
$315$	−1.62448	−	0.664852i	−0.0915289	−	0.0374602i
$316$	1.97994	+	13.7708i	0.111380	+	0.774668i
$317$	2.12429	+	22.2465i	0.119312	+	1.24949i	0.834677	+	0.550740i	$0.185654\pi$
$317$	2.12429	+	22.2465i	0.119312	+	1.24949i	−0.715365	+	0.698751i	$0.753740\pi$
$318$	−2.25198	−	7.85374i	−0.126285	−	0.440416i
$319$	19.3346	−	9.96770i	1.08253	−	0.558084i
$320$	0.0723286	−	0.208980i	0.00404329	−	0.0116823i
$321$	−18.1611	+	25.1639i	−1.01365	+	1.40451i
$322$	−12.0516	−	3.96977i	−0.671609	−	0.221227i
$323$			1.60036i			0.0890463i
$324$	2.72661	+	8.57704i	0.151478	+	0.476502i
$325$	−11.4422	−	22.1947i	−0.634697	−	1.23114i
$326$	−0.912187	+	1.15994i	−0.0505214	+	0.0642432i
$327$	−19.3138	−	11.3150i	−1.06806	−	0.625721i
$328$	2.11177	−	0.303627i	0.116603	−	0.0167650i
$329$	8.69050	+	24.7069i	0.479123	+	1.36213i
$330$	1.24252	+	0.0671006i	0.0683984	+	0.00369377i
$331$	11.0935	−	15.5787i	0.609756	−	0.856283i	−0.388108	−	0.921614i	$-0.626871\pi$
$331$	11.0935	−	15.5787i	0.609756	−	0.856283i	0.997864	+	0.0653315i	$0.0208105\pi$
$332$	−1.20279	+	4.95797i	−0.0660117	+	0.272104i
$333$	−3.59743	+	2.75582i	−0.197138	+	0.151018i
$334$	0.265287	−	1.37644i	0.0145159	−	0.0753154i
$335$	1.41714	−	0.416109i	0.0774264	−	0.0227344i
$336$	0.441636	−	4.56125i	0.0240932	−	0.248836i
$337$	2.12287	−	1.36429i	0.115640	−	0.0743175i	−0.481542	−	0.876423i	$-0.659923\pi$
$337$	2.12287	−	1.36429i	0.115640	−	0.0743175i	0.597182	+	0.802105i	$0.296287\pi$
$338$	12.0857	−	2.93195i	0.657373	−	0.159477i
$339$	5.84010	−	3.70100i	0.317191	−	0.201011i
$340$	0.0494968	+	0.0695085i	0.00268434	+	0.00376963i
$341$	−14.7770	+	5.91581i	−0.800218	+	0.320359i
$342$	−3.08676	+	12.0534i	−0.166913	+	0.651775i
$343$	15.7295	+	9.77664i	0.849313	+	0.527889i
$344$			4.07881i			0.219914i
$345$	1.81729	−	0.267995i	0.0978398	−	0.0144284i
$346$	−5.88675	−	3.39872i	−0.316474	−	0.182716i
$347$	−1.23893	−	6.42820i	−0.0665095	−	0.345084i	0.933396	−	0.358849i	$-0.116831\pi$
$347$	−1.23893	−	6.42820i	−0.0665095	−	0.345084i	−0.999905	+	0.0137646i	$0.995618\pi$
$348$	9.07071	+	7.22699i	0.486241	+	0.387407i
$349$	21.8133	+	3.13628i	1.16764	+	0.167881i	0.698743	−	0.715373i	$-0.253743\pi$
$349$	21.8133	+	3.13628i	1.16764	+	0.167881i	0.468895	+	0.883254i	$0.344652\pi$
$350$	12.4003	+	4.22208i	0.662824	+	0.225680i
$351$	4.22312	−	25.8639i	0.225413	−	1.38051i
$352$	0.765898	+	3.15707i	0.0408225	+	0.168273i
$353$	0.380113	+	7.97955i	0.0202314	+	0.424709i	0.986149	+	0.165860i	$0.0530400\pi$
$353$	0.380113	+	7.97955i	0.0202314	+	0.424709i	−0.965918	+	0.258849i	$0.916657\pi$
$354$	−15.2515	+	17.3770i	−0.810610	+	0.923576i
$355$	−0.655887	+	0.687874i	−0.0348108	+	0.0365086i
$356$	−10.6033	+	12.2369i	−0.561975	+	0.648554i
$357$	1.33482	+	1.15973i	0.0706463	+	0.0613792i
$358$	11.2073	−	3.29077i	0.592325	−	0.173922i
$359$	3.85013	+	2.74167i	0.203202	+	0.144700i	0.677128	−	0.735865i	$-0.263224\pi$
$359$	3.85013	+	2.74167i	0.203202	+	0.144700i	−0.473926	+	0.880565i	$0.657164\pi$
$360$	0.238728	+	0.618987i	0.0125821	+	0.0326235i
$361$	1.30166	−	1.24113i	0.0685085	−	0.0653227i
$362$	8.08751	−	6.36009i	0.425070	−	0.334279i
$363$	0.671872	−	0.382237i	0.0352641	−	0.0200622i
$364$	−7.15760	+	11.2615i	−0.375160	+	0.590265i
$365$	1.48769	−	2.31489i	0.0778692	−	0.121167i
$366$	−12.8107	+	9.00037i	−0.669625	+	0.470457i
$367$	7.24857	+	4.18496i	0.378372	+	0.218453i	0.677110	−	0.735882i	$-0.263232\pi$
$367$	7.24857	+	4.18496i	0.378372	+	0.218453i	−0.298738	+	0.954335i	$0.596566\pi$
$368$	2.03564	+	4.34237i	0.106115	+	0.226362i
$369$	−4.25252	+	4.78352i	−0.221377	+	0.249020i
$370$	−0.252457	+	0.218755i	−0.0131246	+	0.0113725i
$371$	−6.80004	−	10.4650i	−0.353040	−	0.543315i
$372$	−6.10457	−	5.89517i	−0.316507	−	0.305651i
$373$	−29.8883	+	2.85399i	−1.54756	+	0.147774i	−0.833583	−	0.552395i	$-0.813714\pi$
$373$	−29.8883	+	2.85399i	−1.54756	+	0.147774i	−0.713977	+	0.700169i	$0.753108\pi$
$374$	−1.16374	−	0.465893i	−0.0601757	−	0.0240907i
$375$	−3.77614	+	0.518470i	−0.194999	+	0.0267737i
$376$	4.53606	−	8.79873i	0.233930	−	0.453760i
$377$	−14.0288	−	30.7188i	−0.722520	−	1.58210i
$378$	7.81662	+	11.3093i	0.402043	+	0.581688i
$379$	8.15410	−	9.41034i	0.418848	−	0.483377i	−0.506638	−	0.862159i	$-0.669112\pi$
$379$	8.15410	−	9.41034i	0.418848	−	0.483377i	0.925486	+	0.378783i	$0.123657\pi$
$380$	−0.173578	+	0.900606i	−0.00890434	+	0.0462001i
$381$	22.6852	−	19.4059i	1.16220	−	0.994196i
$382$	−5.07339	−	0.484450i	−0.259577	−	0.0247866i
$383$	13.1174	+	6.76251i	0.670270	+	0.345548i	0.759541	−	0.650459i	$-0.225423\pi$
$383$	13.1174	+	6.76251i	0.670270	+	0.345548i	−0.0892711	+	0.996007i	$0.528454\pi$
$384$	−1.36826	+	1.06201i	−0.0698236	+	0.0541957i
$385$	1.84489	−	0.457400i	0.0940243	−	0.0233113i
$386$	18.2475	+	8.33334i	0.928772	+	0.424156i
$387$	−7.89504	−	9.34871i	−0.401327	−	0.475222i
$388$	−5.77120	−	11.1946i	−0.292988	−	0.568318i
$389$	3.02184	+	15.6788i	0.153213	+	0.794946i	0.974493	+	0.224420i	$0.0720487\pi$
$389$	3.02184	+	15.6788i	0.153213	+	0.794946i	−0.821279	+	0.570526i	$0.806739\pi$
$390$	0.195838	−	1.92183i	0.00991665	−	0.0973158i
$391$	−1.82050	−	0.332091i	−0.0920665	−	0.0167946i
$392$	−1.39382	−	6.85983i	−0.0703984	−	0.346474i
$393$	0.176596	+	1.98238i	0.00890811	+	0.0999980i
$394$	0.459960	−	9.65576i	0.0231725	−	0.486450i
$395$	−2.41839	−	1.90184i	−0.121682	−	0.0956921i
$396$	−7.86636	−	5.75359i	−0.395300	−	0.289129i
$397$	−14.2689	−	18.1443i	−0.716134	−	0.910639i	0.282686	−	0.959213i	$-0.408775\pi$
$397$	−14.2689	−	18.1443i	−0.716134	−	0.910639i	−0.998820	+	0.0485741i	$0.984532\pi$
$398$	−13.6081	−	3.99569i	−0.682111	−	0.200286i
$399$	0.879230	+	18.9857i	0.0440166	+	0.950475i
$400$	−2.05676	−	4.50368i	−0.102838	−	0.225184i
$401$	−20.9304	+	21.9512i	−1.04522	+	1.09619i	−0.0499736	+	0.998751i	$0.515914\pi$
$401$	−20.9304	+	21.9512i	−1.04522	+	1.09619i	−0.995241	+	0.0974394i	$0.968935\pi$
$402$	−11.0785	−	3.32951i	−0.552545	−	0.166061i
$403$	8.08215	+	23.3518i	0.402601	+	1.16324i
$404$	12.5476	+	11.9641i	0.624267	+	0.595237i
$405$	−1.74530	−	0.956644i	−0.0867244	−	0.0475360i
$406$	16.4797	+	6.50152i	0.817873	+	0.322665i
$407$	1.38254	−	4.70849i	0.0685299	−	0.233391i
$408$	−0.0275601	−	0.667768i	−0.00136443	−	0.0330594i
$409$	−15.3695	+	10.9446i	−0.759975	+	0.541176i	−0.893065	−	0.449928i	$-0.851450\pi$
$409$	−15.3695	+	10.9446i	−0.759975	+	0.541176i	0.133090	+	0.991104i	$0.457510\pi$
$410$	−0.291650	+	0.370864i	−0.0144036	+	0.0183156i
$411$	26.9460	+	21.4689i	1.32915	+	1.05898i
$412$	10.7281	−	9.29596i	0.528536	−	0.457979i
$413$	−14.5097	+	32.1993i	−0.713976	+	1.58442i
$414$	−13.0709	−	6.01258i	−0.642401	−	0.295502i
$415$	−0.564110	−	0.977067i	−0.0276911	−	0.0479623i
$416$	4.95229	−	0.954476i	0.242806	−	0.0467970i
$417$	4.92857	−	32.7988i	0.241353	−	1.60616i
$418$	−5.00765	−	12.5085i	−0.244932	−	0.611811i
$419$	−12.8696	+	28.1804i	−0.628719	+	1.37670i	0.280286	+	0.959917i	$0.409571\pi$
$419$	−12.8696	+	28.1804i	−0.628719	+	1.37670i	−0.909005	+	0.416786i	$0.863156\pi$
$420$	0.625389	+	0.797416i	0.0305159	+	0.0389099i
$421$	16.2979	+	4.78549i	0.794311	+	0.233231i	0.653620	−	0.756823i	$-0.273250\pi$
$421$	16.2979	+	4.78549i	0.794311	+	0.233231i	0.140691	+	0.990054i	$0.455068\pi$
$422$	−6.66558	+	12.9294i	−0.324475	+	0.629394i
$423$	6.63429	+	28.9470i	0.322570	+	1.40745i
$424$	−1.11210	+	4.58412i	−0.0540081	+	0.222625i
$425$	1.87593	+	0.361555i	0.0909958	+	0.0175380i
$426$	7.24537	−	1.70905i	0.351039	−	0.0828040i
$427$	−14.6888	+	18.8729i	−0.710841	+	0.913323i
$428$	16.2978	−	7.44295i	0.787784	−	0.359769i
$429$	12.8433	+	25.3059i	0.620081	+	1.22178i
$430$	−0.622449	−	0.652806i	−0.0300172	−	0.0314811i
$431$	9.21187	−	23.0101i	0.443720	−	1.10836i	−0.522957	−	0.852359i	$-0.675171\pi$
$431$	9.21187	−	23.0101i	0.443720	−	1.10836i	0.966677	−	0.256000i	$-0.0824046\pi$
$432$	1.08041	−	5.08259i	0.0519814	−	0.244536i
$433$	26.6023	+	3.82483i	1.27842	+	0.183810i	0.747872	−	0.663843i	$-0.231076\pi$
$433$	26.6023	+	3.82483i	1.27842	+	0.183810i	0.530552	+	0.847653i	$0.321985\pi$
$434$	−11.5519	−	5.88206i	−0.554507	−	0.282348i
$435$	−2.55463	+	0.227574i	−0.122485	+	0.0109113i
$436$	6.46176	+	11.1921i	0.309462	+	0.536004i
$437$	−10.9199	−	16.6250i	−0.522368	−	0.795281i
$438$	−19.6611	+	8.82842i	−0.939442	+	0.421838i
$439$	16.7811	+	5.80800i	0.800918	+	0.277201i	0.696708	−	0.717355i	$-0.254647\pi$
$439$	16.7811	+	5.80800i	0.800918	+	0.277201i	0.104210	+	0.994555i	$0.466769\pi$
$440$	−0.604368	−	0.388404i	−0.0288121	−	0.0185164i
$441$	16.4727	+	13.0250i	0.784415	+	0.620237i
$442$	−0.808431	+	1.77022i	−0.0384531	+	0.0842006i
$443$	7.67677	+	9.76181i	0.364735	+	0.463798i	0.933435	−	0.358747i	$-0.116796\pi$
$443$	7.67677	+	9.76181i	0.364735	+	0.463798i	−0.568700	+	0.822545i	$0.692554\pi$
$444$	2.59205	−	0.355892i	0.123013	−	0.0168899i
$445$	−0.170375	−	3.57662i	−0.00807657	−	0.169548i
$446$	−13.7828	+	19.3553i	−0.652635	+	0.916498i
$447$	−7.51222	+	21.2671i	−0.355316	+	1.00590i
$448$	−1.52383	+	2.16286i	−0.0719942	+	0.102185i
$449$	−10.2883	−	8.91486i	−0.485535	−	0.420718i	0.377387	−	0.926056i	$-0.376823\pi$
$449$	−10.2883	−	8.91486i	−0.485535	−	0.420718i	−0.862922	+	0.505337i	$0.831368\pi$
$450$	13.4316	+	6.34140i	0.633170	+	0.298937i
$451$	0.658829	−	6.89957i	0.0310230	−	0.324888i
$452$	−3.98731	+	0.189939i	−0.187547	+	0.00893398i
$453$	4.08843	−	10.0274i	0.192091	−	0.471126i
$454$	−2.32421	+	0.334171i	−0.109081	+	0.0156834i
$455$	−0.573016	−	2.89468i	−0.0268634	−	0.135705i
$456$	4.99019	−	5.16744i	0.233687	−	0.241988i
$457$	1.30669	−	27.4308i	0.0611244	−	1.28316i	−0.735017	−	0.678048i	$-0.762826\pi$
$457$	1.30669	−	27.4308i	0.0611244	−	1.28316i	0.796142	−	0.605110i	$-0.206871\pi$
$458$	−7.54699	+	1.45456i	−0.352648	+	0.0679673i
$459$	1.35572	+	1.47719i	0.0632794	+	0.0689494i
$460$	−0.988471	−	0.384339i	−0.0460877	−	0.0179199i
$461$	27.3756			1.27501			0.637504	−	0.770447i	$-0.279967\pi$
$461$	27.3756			1.27501			0.637504	+	0.770447i	$0.279967\pi$
$462$	−14.0619	−	4.88772i	−0.654221	−	0.227398i
$463$	22.9813	+	14.7692i	1.06803	+	0.686383i	0.951763	−	0.306835i	$-0.0992700\pi$
$463$	22.9813	+	14.7692i	1.06803	+	0.686383i	0.116269	+	0.993218i	$0.462906\pi$
$464$	−2.48863	−	6.21630i	−0.115532	−	0.288585i
$465$	1.87666	+	0.0119196i	0.0870282	+	0.000552757i
$466$	−9.46592	−	3.78958i	−0.438500	−	0.175549i
$467$	−1.89107	−	7.79510i	−0.0875083	−	0.360714i	0.911175	−	0.412020i	$-0.135177\pi$
$467$	−1.89107	−	7.79510i	−0.0875083	−	0.360714i	−0.998683	+	0.0513061i	$0.983662\pi$
$468$	−9.50325	+	11.7735i	−0.439288	+	0.544228i
$469$	−17.6702	+	0.0888553i	−0.815933	+	0.00410295i
$470$	0.616748	+	2.10045i	0.0284485	+	0.0968866i
$471$	6.32163	−	5.95146i	0.291285	−	0.274229i
$472$	12.6146	−	4.36595i	0.580634	−	0.200959i
$473$	12.8771	+	3.12395i	0.592089	+	0.143639i
$474$	7.73656	+	22.8213i	0.355352	+	1.04822i
$475$	11.1018	+	17.2747i	0.509385	+	0.792618i
$476$	−0.338751	−	0.963061i	−0.0155266	−	0.0441418i
$477$	−6.32419	−	12.6595i	−0.289565	−	0.579639i
$478$	−5.90945	+	0.564284i	−0.270292	+	0.0258098i
$479$	−11.9424	−	9.39160i	−0.545662	−	0.429113i	0.306898	−	0.951742i	$-0.400709\pi$
$479$	−11.9424	−	9.39160i	−0.545662	−	0.429113i	−0.852560	+	0.522629i	$0.824951\pi$
$480$	0.0569177	−	0.378777i	0.00259793	−	0.0172887i
$481$	−7.19939	−	2.49173i	−0.328264	−	0.113613i
$482$	14.3100			0.651802
$483$	−21.7798	−	2.93956i	−0.991014	−	0.133755i
$484$	−0.446287			−0.0202858
$485$	2.63203	+	0.910954i	0.119514	+	0.0413643i
$486$	7.36165	+	13.7407i	0.333931	+	0.623290i
$487$	11.0309	+	8.67482i	0.499859	+	0.393094i	0.836010	−	0.548715i	$-0.184883\pi$
$487$	11.0309	+	8.67482i	0.499859	+	0.393094i	−0.336151	+	0.941808i	$0.609125\pi$
$488$	8.99824	−	0.859228i	0.407331	−	0.0388954i
$489$	−1.18559	+	2.26429i	−0.0536141	+	0.102395i
$490$	1.26993	+	0.885200i	0.0573695	+	0.0399893i
$491$	−13.7119	−	21.3362i	−0.618810	−	0.962888i	−0.999274	−	0.0380919i	$-0.987872\pi$
$491$	−13.7119	−	21.3362i	−0.618810	−	0.962888i	0.380464	−	0.924796i	$-0.375764\pi$
$492$	3.49968	−	1.18641i	0.157778	−	0.0534876i
$493$	2.51090	+	0.609137i	0.113085	+	0.0274341i
$494$	−19.7670	+	6.84143i	−0.889360	+	0.307811i
$495$	2.13703	−	0.279600i	0.0960523	−	0.0125671i
$496$	1.38038	+	4.70115i	0.0619810	+	0.211088i
$497$	9.81904	−	5.73505i	0.440444	−	0.257252i
$498$	−0.476511	+	8.82368i	−0.0213530	+	0.395399i
$499$	−6.38132	−	26.3041i	−0.285667	−	1.17754i	−0.915990	−	0.401202i	$-0.868593\pi$
$499$	−6.38132	−	26.3041i	−0.285667	−	1.17754i	0.630323	−	0.776333i	$-0.282923\pi$
$500$	2.04298	+	0.817884i	0.0913647	+	0.0365769i
$501$	0.0154207	−	2.42789i	0.000688945	−	0.108470i
$502$	8.07065	+	20.1595i	0.360211	+	0.899763i
$503$	−29.4112	−	18.9014i	−1.31138	−	0.842772i	−0.316977	−	0.948433i	$-0.602668\pi$
$503$	−29.4112	−	18.9014i	−1.31138	−	0.842772i	−0.994402	+	0.105661i	$0.966304\pi$
$504$	−0.693826	−	7.90687i	−0.0309054	−	0.352200i
$505$	−3.83402			−0.170611
$506$	15.2683	−	3.10084i	0.678758	−	0.137849i
$507$	19.6501	−	8.82348i	0.872690	−	0.391865i
$508$	−16.9242	+	3.26188i	−0.750891	+	0.144722i
$509$	0.212756	−	4.46630i	0.00943025	−	0.197965i	−0.989236	−	0.146330i	$-0.953254\pi$
$509$	0.212756	−	4.46630i	0.00943025	−	0.197965i	0.998666	−	0.0516349i	$-0.0164432\pi$
$510$	0.106316	+	0.102669i	0.00470776	+	0.00454627i
$511$	−24.7717	+	21.6839i	−1.09584	+	0.959238i
$512$	0.989821	−	0.142315i	0.0437443	−	0.00628949i
$513$	−1.43539	+	21.5030i	−0.0633740	+	0.949381i
$514$	−12.8808	+	0.613590i	−0.568150	+	0.0270643i
$515$	−0.298399	+	3.12497i	−0.0131490	+	0.137703i
$516$	1.29292	+	6.94538i	0.0569175	+	0.305753i
$517$	−24.3041	−	21.0596i	−1.06889	−	0.926201i
$518$	3.62701	−	1.67849i	0.159361	−	0.0737487i
$519$	−11.1013	−	3.92132i	−0.487293	−	0.172127i
$520$	−0.646948	+	0.908511i	−0.0283705	+	0.0398408i
$521$	0.343886	+	7.21906i	0.0150659	+	0.316273i	0.993803	+	0.111155i	$0.0354548\pi$
$521$	0.343886	+	7.21906i	0.0150659	+	0.316273i	−0.978737	+	0.205118i	$0.934242\pi$
$522$	17.7364	+	9.43084i	0.776302	+	0.412777i
$523$	−21.2919	−	27.0748i	−0.931028	−	1.18390i	−0.982694	−	0.185234i	$-0.940696\pi$
$523$	−21.2919	−	27.0748i	−0.931028	−	1.18390i	0.0516664	−	0.998664i	$-0.483547\pi$
$524$	0.477337	−	1.04522i	0.0208526	−	0.0456608i
$525$	22.4535	+	3.25866i	0.979953	+	0.142219i
$526$	12.4438	+	7.99715i	0.542576	+	0.348692i
$527$	−1.78661	−	0.618351i	−0.0778259	−	0.0269358i
$528$	2.30491	+	5.13308i	0.100308	+	0.223389i
$529$	21.1779	−	8.97210i	0.920776	−	0.390091i
$530$	−0.521574	−	0.903393i	−0.0226557	−	0.0392409i
$531$	−20.4621	+	34.4240i	−0.887978	+	1.49387i
$532$	4.97909	−	9.77849i	0.215871	−	0.423952i
$533$	−10.6506	−	1.53132i	−0.461328	−	0.0663289i
$534$	−14.1764	+	24.1980i	−0.613473	+	1.04715i
$535$	−1.47260	+	3.67837i	−0.0636659	+	0.159030i
$536$	4.60889	+	4.83366i	0.199074	+	0.208783i
$537$	18.0407	−	9.15605i	0.778513	−	0.395113i
$538$	8.71988	−	3.98224i	0.375941	−	0.171686i
$539$	−22.7245	−	0.853545i	−0.978814	−	0.0367648i
$540$	0.602714	+	0.978337i	0.0259367	+	0.0421009i
$541$	19.2865	+	3.71716i	0.829190	+	0.159813i	0.586149	−	0.810203i	$-0.300643\pi$
$541$	19.2865	+	3.71716i	0.829190	+	0.159813i	0.243040	+	0.970016i	$0.421855\pi$
$542$	−0.0268310	+	0.110599i	−0.00115249	+	0.00475062i
$543$	11.7553	−	13.3936i	0.504470	−	0.574772i
$544$	−0.176813	+	0.342970i	−0.00758080	+	0.0147047i
$545$	−2.74217	−	0.805175i	−0.117462	−	0.0344899i
$546$	−8.61821	+	21.4450i	−0.368825	+	0.917760i
$547$	5.67374	−	12.4238i	0.242591	−	0.531201i	−0.748697	−	0.662913i	$-0.769320\pi$
$547$	5.67374	−	12.4238i	0.242591	−	0.531201i	0.991288	+	0.131712i	$0.0420473\pi$
$548$	−7.39288	−	18.4665i	−0.315808	−	0.788851i
$549$	−18.9610	+	19.3866i	−0.809237	+	0.827399i
$550$	−15.7937	+	3.04399i	−0.673446	+	0.129796i
$551$	13.8856	+	24.0506i	0.591547	+	1.02459i
$552$	4.84274	+	6.74892i	0.206121	+	0.287253i
$553$	21.5017	+	29.8758i	0.914344	+	1.27045i
$554$	−1.65504	+	1.43410i	−0.0703158	+	0.0609290i
$555$	−0.360541	+	0.452521i	−0.0153041	+	0.0192084i
$556$	−11.8371	+	15.0521i	−0.502005	+	0.638351i
$557$	9.69755	−	6.90559i	0.410898	−	0.292599i	−0.355855	−	0.934541i	$-0.615810\pi$
$557$	9.69755	−	6.90559i	0.410898	−	0.292599i	0.766753	+	0.641942i	$0.221871\pi$
$558$	−12.2635	−	8.10324i	−0.519157	−	0.343037i
$559$	5.79557	−	19.7379i	0.245127	−	0.834825i
$560$	−0.0861778	−	0.578707i	−0.00364168	−	0.0244548i
$561$	−2.12930	−	0.424433i	−0.0898991	−	0.0179196i
$562$	1.78595	+	1.70290i	0.0753356	+	0.0718323i
$563$	7.41421	+	21.4219i	0.312472	+	0.902827i	0.986448	+	0.164074i	$0.0524637\pi$
$563$	7.41421	+	21.4219i	0.312472	+	0.902827i	−0.673976	+	0.738753i	$0.735415\pi$
$564$	4.93494	−	16.4203i	0.207798	−	0.691420i
$565$	0.609177	−	0.638886i	0.0256283	−	0.0268782i
$566$	−4.85878	−	10.6392i	−0.204230	−	0.447201i
$567$	16.8950	+	16.7797i	0.709523	+	0.704682i
$568$	−4.12382	−	1.21086i	−0.173032	−	0.0508067i
$569$	−11.3713	−	14.4598i	−0.476711	−	0.606188i	0.486912	−	0.873451i	$-0.338123\pi$
$569$	−11.3713	−	14.4598i	−0.476711	−	0.606188i	−0.963624	+	0.267263i	$0.913881\pi$
$570$	−0.0100898	+	1.58857i	−0.000422614	+	0.0665379i
$571$	17.3518	+	13.6456i	0.726149	+	0.571050i	0.911341	−	0.411652i	$-0.135048\pi$
$571$	17.3518	+	13.6456i	0.726149	+	0.571050i	−0.185192	+	0.982702i	$0.559291\pi$
$572$	0.779598	−	16.3658i	0.0325966	−	0.684288i
$573$	−8.79253	+	0.783264i	−0.367313	+	0.0327213i
$574$	4.58150	−	3.29731i	0.191228	−	0.137627i
$575$	−21.9547	+	9.04423i	−0.915574	+	0.377170i
$576$	−1.99322	+	2.24211i	−0.0830510	+	0.0934213i
$577$	−1.94567	−	10.0951i	−0.0809993	−	0.420264i	−0.999681	−	0.0252651i	$-0.991957\pi$
$577$	−1.94567	−	10.0951i	−0.0809993	−	0.420264i	0.918682	−	0.394999i	$-0.129255\pi$
$578$	7.72162	+	14.9779i	0.321177	+	0.622997i
$579$	33.7133	+	8.40584i	1.40108	+	0.349335i
$580$	1.34695	+	0.615129i	0.0559289	+	0.0255419i
$581$	3.24820	+	13.1014i	0.134758	+	0.543537i
$582$	−13.3757	−	17.2327i	−0.554440	−	0.714319i
$583$	13.6207	+	7.02193i	0.564110	+	0.290819i
$584$	12.3868	+	1.18280i	0.512571	+	0.0489446i
$585$	−0.275718	−	3.33457i	−0.0113995	−	0.137868i
$586$	2.28084	−	11.8341i	0.0942207	−	0.488863i
$587$	−0.335257	+	0.386907i	−0.0138375	+	0.0159693i	−0.762626	−	0.646840i	$-0.776090\pi$
$587$	−0.335257	+	0.386907i	−0.0138375	+	0.0159693i	0.748789	+	0.662809i	$0.230636\pi$
$588$	−4.54785	−	11.2391i	−0.187550	−	0.463492i
$589$	−8.44165	−	18.4846i	−0.347832	−	0.761646i
$590$	−1.35268	+	2.62382i	−0.0556888	+	0.108021i
$591$	−2.27750	−	16.5876i	−0.0936839	−	0.682323i
$592$	−1.40235	−	0.561418i	−0.0576364	−	0.0230741i
$593$	−12.9052	+	1.23230i	−0.529953	+	0.0506044i	−0.356603	−	0.934256i	$-0.616065\pi$
$593$	−12.9052	+	1.23230i	−0.529953	+	0.0506044i	−0.173350	+	0.984860i	$0.555459\pi$
$594$	−15.2186	−	7.30369i	−0.624428	−	0.299674i
$595$	0.201185	+	0.102441i	0.00824779	+	0.00419967i
$596$	9.84144	−	8.52766i	0.403121	−	0.349307i
$597$	−24.4384	−	2.49031i	−1.00020	−	0.101922i
$598$	−3.68065	−	23.9058i	−0.150513	−	0.977580i
$599$	−7.65586	−	4.42011i	−0.312810	−	0.180601i	0.335373	−	0.942085i	$-0.391138\pi$
$599$	−7.65586	−	4.42011i	−0.312810	−	0.180601i	−0.648183	+	0.761484i	$0.724471\pi$
$600$	−4.92984	−	7.01689i	−0.201260	−	0.286463i
$601$	20.7417	−	32.2748i	0.846073	−	1.31652i	−0.100800	−	0.994907i	$-0.532140\pi$
$601$	20.7417	−	32.2748i	0.846073	−	1.31652i	0.946873	−	0.321609i	$-0.104224\pi$
$602$	4.99312	+	9.56689i	0.203505	+	0.389917i
$603$	−19.9198	−	2.15778i	−0.811198	−	0.0878716i
$604$	−4.91442	+	3.86474i	−0.199965	+	0.157254i
$605$	0.0714275	−	0.0681060i	0.00290394	−	0.00276890i
$606$	25.1585	+	16.3951i	1.02199	+	0.666005i
$607$	−12.0044	−	8.54826i	−0.487242	−	0.346963i	0.309886	−	0.950774i	$-0.399709\pi$
$607$	−12.0044	−	8.54826i	−0.487242	−	0.346963i	−0.797128	+	0.603810i	$0.793648\pi$
$608$	−3.97946	+	1.16848i	−0.161389	+	0.0473880i
$609$	30.1225	+	5.84697i	1.22062	+	0.236931i
$610$	−1.30903	+	1.51070i	−0.0530011	+	0.0611665i
$611$	−34.4527	+	36.1330i	−1.39381	+	1.46178i
$612$	−0.258601	−	1.12834i	−0.0104533	−	0.0456103i
$613$	0.371050	+	7.78929i	0.0149866	+	0.314607i	0.993897	+	0.110315i	$0.0351860\pi$
$613$	0.371050	+	7.78929i	0.0149866	+	0.314607i	−0.978910	+	0.204291i	$0.934511\pi$
$614$	4.37298	+	18.0257i	0.176479	+	0.727456i
$615$	−0.379064	+	0.723954i	−0.0152853	+	0.0291927i
$616$	5.66120	+	6.46737i	0.228096	+	0.260578i
$617$	13.9891	+	2.01132i	0.563178	+	0.0809728i	0.418023	−	0.908436i	$-0.362723\pi$
$617$	13.9891	+	2.01132i	0.563178	+	0.0809728i	0.145154	+	0.989409i	$0.453632\pi$
$618$	15.3211	−	19.2298i	0.616306	−	0.773535i
$619$	5.18102	+	26.8817i	0.208243	+	1.08047i	0.924080	+	0.382199i	$0.124833\pi$
$619$	5.18102	+	26.8817i	0.208243	+	1.08047i	−0.715837	+	0.698267i	$0.753955\pi$
$620$	−0.938351	−	0.541757i	−0.0376851	−	0.0217575i
$621$	−24.1630	−	6.09493i	−0.969629	−	0.244581i
$622$			4.10582i			0.164629i
$623$	−9.89027	+	41.6819i	−0.396245	+	1.66995i
$624$	8.13020	−	3.19508i	0.325468	−	0.127905i
$625$	22.5304	−	9.01981i	0.901216	−	0.360793i
$626$	−15.7002	−	22.0479i	−0.627506	−	0.881210i
$627$	−12.4920	−	19.7121i	−0.498883	−	0.787226i
$628$	−4.87144	+	1.18180i	−0.194392	+	0.0471589i
$629$	0.490342	−	0.315123i	0.0195512	−	0.0125648i
$630$	1.31768	+	1.15960i	0.0524976	+	0.0461996i
$631$	17.3127	−	5.08345i	0.689206	−	0.202369i	0.0816677	−	0.996660i	$-0.473975\pi$
$631$	17.3127	−	5.08345i	0.689206	−	0.202369i	0.607538	+	0.794291i	$0.292157\pi$
$632$	2.63294	−	13.6610i	0.104733	−	0.543405i
$633$	−7.25171	+	24.1291i	−0.288230	+	0.959045i
$634$	5.26868	−	21.7178i	0.209246	−	0.862524i
$635$	2.21091	−	3.10479i	0.0877374	−	0.123210i
$636$	−0.440581	+	8.15835i	−0.0174702	+	0.323499i
$637$	−3.00225	+	35.1761i	−0.118954	+	1.39373i
$638$	−21.5314	+	3.09574i	−0.852435	+	0.122562i
$639$	11.7957	−	5.20684i	0.466629	−	0.205979i
$640$	−0.136701	+	0.173830i	−0.00540359	+	0.00687122i
$641$	−20.4174	−	39.6042i	−0.806439	−	1.56427i	−0.825464	−	0.564455i	$-0.809086\pi$
$641$	−20.4174	−	39.6042i	−0.806439	−	1.56427i	0.0190249	−	0.999819i	$-0.493944\pi$
$642$	25.3926	−	17.8400i	1.00216	−	0.704088i
$643$		−	16.1334i		−	0.636237i	−0.948051	−	0.318119i	$-0.896949\pi$
$643$		−	16.1334i		−	0.636237i	0.948051	−	0.318119i	$-0.103051\pi$
$644$	10.0904	+	7.69313i	0.397617	+	0.303152i
$645$	−1.26683	−	0.914290i	−0.0498816	−	0.0360002i
$646$	0.523426	−	1.51234i	0.0205939	−	0.0595022i
$647$	15.3184	−	7.89718i	0.602228	−	0.310470i	−0.130017	−	0.991512i	$-0.541503\pi$
$647$	15.3184	−	7.89718i	0.602228	−	0.310470i	0.732245	+	0.681042i	$0.238473\pi$
$648$	0.228625	−	8.99710i	0.00898125	−	0.353439i
$649$	−4.12215	−	43.1691i	−0.161808	−	1.69453i
$650$	3.55368	+	24.7164i	0.139387	+	0.969455i
$651$	−21.5350	−	6.35420i	−0.844023	−	0.249041i
$652$	1.24140	−	0.797798i	0.0486169	−	0.0312442i
$653$	26.9425	+	19.1857i	1.05434	+	0.750793i	0.969374	−	0.245591i	$-0.0789819\pi$
$653$	26.9425	+	19.1857i	1.05434	+	0.750793i	0.0849675	+	0.996384i	$0.472921\pi$
$654$	14.5508	+	17.0096i	0.568981	+	0.665128i
$655$	0.0831100	+	0.240131i	0.00324738	+	0.00938268i
$656$	−2.09493	−	0.403765i	−0.0817934	−	0.0157644i
$657$	−30.6803	+	21.2653i	−1.19695	+	0.829637i
$658$	−0.131700	−	26.1904i	−0.00513418	−	1.02101i
$659$	10.5908	+	16.4795i	0.412557	+	0.641952i	0.983892	−	0.178766i	$-0.0572104\pi$
$659$	10.5908	+	16.4795i	0.412557	+	0.641952i	−0.571334	+	0.820717i	$0.693574\pi$
$660$	−1.15224	−	0.469798i	−0.0448507	−	0.0182869i
$661$	0.651725	−	1.62793i	0.0253492	−	0.0633191i	−0.915153	−	0.403106i	$-0.867931\pi$
$661$	0.651725	−	1.62793i	0.0253492	−	0.0633191i	0.940503	+	0.339787i	$0.110355\pi$
$662$	−15.5787	+	11.0935i	−0.605483	+	0.431163i
$663$	−0.815464	+	3.27058i	−0.0316700	+	0.127019i
$664$	2.75823	−	4.29189i	0.107040	−	0.166558i
$665$	0.695361	+	2.32487i	0.0269649	+	0.0901546i
$666$	4.30092	−	1.42765i	0.166657	−	0.0553203i
$667$	−30.2403	+	10.8049i	−1.17091	+	0.418368i
$668$	−0.700885	+	1.21397i	−0.0271181	+	0.0469699i
$669$	−17.3340	+	37.3270i	−0.670173	+	1.44315i
$670$	−1.47529	−	0.0702767i	−0.0569954	−	0.00271503i
$671$	4.17909	−	29.0662i	0.161332	−	1.12209i
$672$	−1.90918	+	4.16594i	−0.0736484	+	0.160704i
$673$	5.04089	+	35.0601i	0.194312	+	1.35147i	0.820433	+	0.571743i	$0.193732\pi$
$673$	5.04089	+	35.0601i	0.194312	+	1.35147i	−0.626121	+	0.779726i	$0.715358\pi$
$674$	−2.45233	+	0.594929i	−0.0944603	+	0.0229158i
$675$	24.8814	+	6.54054i	0.957684	+	0.251745i
$676$	−12.3799	−	1.18214i	−0.476150	−	0.0454668i
$677$	−21.4301	−	20.4335i	−0.823625	−	0.785325i	0.155660	−	0.987811i	$-0.450250\pi$
$677$	−21.4301	−	20.4335i	−0.823625	−	0.785325i	−0.979285	+	0.202486i	$0.935098\pi$
$678$	−6.72938	+	1.58734i	−0.258440	+	0.0609615i
$679$	−27.2404	−	19.1921i	−1.04539	−	0.736525i
$680$	−0.0240405	−	0.0818745i	−0.000921911	−	0.00313974i
$681$	−3.85174	+	1.30576i	−0.147599	+	0.0500370i
$682$	15.8991	−	0.757368i	0.608809	−	0.0290011i
$683$	−16.6989	−	17.5133i	−0.638964	−	0.670126i	0.322019	−	0.946733i	$-0.395638\pi$
$683$	−16.6989	−	17.5133i	−0.638964	−	0.670126i	−0.960983	+	0.276607i	$0.910790\pi$
$684$	6.85928	−	10.3809i	0.262271	−	0.396924i
$685$	4.00132	+	1.82734i	0.152882	+	0.0698191i
$686$	−11.6668	−	14.3836i	−0.445439	−	0.549167i
$687$	−12.3899	+	4.86910i	−0.472705	+	0.185768i
$688$	1.33405	−	3.85448i	0.0508601	−	0.146950i
$689$	11.8952	−	20.6030i	0.453169	−	0.784912i
$690$	−1.80500	−	0.341123i	−0.0687150	−	0.0129863i
$691$	−27.2264	+	15.7192i	−1.03574	+	0.597986i	−0.918625	−	0.395132i	$-0.870699\pi$
$691$	−27.2264	+	15.7192i	−1.03574	+	0.597986i	−0.117118	+	0.993118i	$0.537366\pi$
$692$	4.45137	+	5.13716i	0.169216	+	0.195285i
$693$	−25.4940	−	3.86540i	−0.968436	−	0.146834i
$694$	−0.931665	+	6.47987i	−0.0353655	+	0.245973i
$695$	−0.402529	−	4.21548i	−0.0152688	−	0.159902i
$696$	−6.20811	−	9.79625i	−0.235318	−	0.371326i
$697$	0.595804	−	0.568098i	0.0225677	−	0.0215183i
$698$	−19.5878	−	10.0982i	−0.741409	−	0.382223i
$699$	−17.3198	−	3.45235i	−0.655094	−	0.130580i
$700$	−10.3374	−	8.04561i	−0.390717	−	0.304096i
$701$	16.2246	+	14.0587i	0.612794	+	0.530989i	0.905025	−	0.425359i	$-0.139852\pi$
$701$	16.2246	+	14.0587i	0.612794	+	0.530989i	−0.292231	+	0.956348i	$0.594397\pi$
$702$	−12.4501	+	23.0602i	−0.469899	+	0.870351i
$703$	6.08839	+	1.47703i	0.229628	+	0.0557071i
$704$	0.308804	−	3.23394i	0.0116385	−	0.121884i
$705$	1.71601	+	3.38115i	0.0646286	+	0.127341i
$706$	2.25065	−	7.66501i	0.0847043	−	0.288476i
$707$	44.0766	+	12.7017i	1.65767	+	0.477695i
$708$	20.0962	−	11.4330i	0.755260	−	0.429677i
$709$	10.2412	−	4.09996i	0.384616	−	0.153977i	−0.171293	−	0.985220i	$-0.554794\pi$
$709$	10.2412	−	4.09996i	0.384616	−	0.153977i	0.555909	+	0.831243i	$0.312370\pi$
$710$	0.844795	−	0.435522i	0.0317046	−	0.0163449i
$711$	20.4078	+	36.4076i	0.765352	+	1.36539i
$712$	14.0224	−	8.09586i	0.525513	−	0.303405i
$713$	22.7791	−	5.76710i	0.853082	−	0.215980i
$714$	−0.882099	−	1.53252i	−0.0330117	−	0.0573531i
$715$	2.37274	+	2.73829i	0.0887354	+	0.102406i
$716$	−11.6672	−	0.555779i	−0.436025	−	0.0207704i
$717$	−9.88374	+	2.83407i	−0.369115	+	0.105840i
$718$	−2.74167	−	3.85013i	−0.102318	−	0.143686i
$719$	−24.3123	+	19.1194i	−0.906697	+	0.713034i	−0.958340	−	0.285632i	$-0.907797\pi$
$719$	−24.3123	+	19.1194i	−0.906697	+	0.713034i	0.0516429	+	0.998666i	$0.483554\pi$
$720$	−0.0231470	−	0.663024i	−0.000862638	−	0.0247094i
$721$	13.7831	−	34.9367i	0.513311	−	1.30111i
$722$	−1.63601	+	0.747139i	−0.0608858	+	0.0278056i
$723$	24.3670	−	4.53604i	0.906219	−	0.168697i
$724$	−9.72288	+	3.36512i	−0.361348	+	0.125064i
$725$	31.3289	−	10.8430i	1.16353	−	0.402701i
$726$	−0.759937	+	0.141466i	−0.0282039	+	0.00525029i
$727$	22.0878	−	10.0872i	0.819192	−	0.374113i	0.0386789	−	0.999252i	$-0.487685\pi$
$727$	22.0878	−	10.0872i	0.819192	−	0.374113i	0.780513	+	0.625139i	$0.214958\pi$
$728$	10.4472	−	8.30115i	0.387200	−	0.307661i
$729$	16.8910	+	21.0641i	0.625592	+	0.780150i
$730$	−2.16299	+	1.70100i	−0.0800560	+	0.0629567i
$731$	0.912931	+	1.28203i	0.0337660	+	0.0474177i
$732$	15.0498	−	4.31539i	0.556258	−	0.159501i
$733$	8.35236	+	0.397872i	0.308501	+	0.0146957i	0.201262	−	0.979537i	$-0.435496\pi$
$733$	8.35236	+	0.397872i	0.308501	+	0.0146957i	0.107240	+	0.994233i	$0.465799\pi$
$734$	−5.48113	−	6.32556i	−0.202312	−	0.233481i
$735$	2.44303	+	1.10477i	0.0901123	+	0.0407500i
$736$	−0.503427	−	4.76934i	−0.0185566	−	0.175800i
$737$	18.7902	−	10.8485i	0.692145	−	0.399610i
$738$	5.58317	−	3.12956i	0.205519	−	0.115201i
$739$	1.96337	−	1.01219i	0.0722238	−	0.0372339i	−0.421736	−	0.906719i	$-0.638579\pi$
$739$	1.96337	−	1.01219i	0.0722238	−	0.0372339i	0.493960	+	0.869485i	$0.335549\pi$
$740$	0.310120	−	0.124153i	0.0114002	−	0.00456397i
$741$	−31.4906	+	17.9154i	−1.15684	+	0.658139i
$742$	3.00328	+	12.1135i	0.110254	+	0.444700i
$743$	−7.50474	+	25.5588i	−0.275322	+	0.937662i	0.699491	+	0.714641i	$0.253410\pi$
$743$	−7.50474	+	25.5588i	−0.275322	+	0.937662i	−0.974814	+	0.223021i	$0.928408\pi$
$744$	3.84070	+	7.56755i	0.140807	+	0.277440i
$745$	−0.273737	+	2.86670i	−0.0100289	+	0.105028i
$746$	29.1780	+	7.07850i	1.06828	+	0.259162i
$747$	1.98556	+	15.1760i	0.0726480	+	0.555261i
$748$	0.947360	+	0.820892i	0.0346389	+	0.0300148i
$749$	29.1153	−	37.4087i	1.06385	−	1.36688i
$750$	3.73803	+	0.745101i	0.136494	+	0.0272072i
$751$	5.04186	+	2.59926i	0.183980	+	0.0948484i	0.547756	−	0.836638i	$-0.315482\pi$
$751$	5.04186	+	2.59926i	0.183980	+	0.0948484i	−0.363776	+	0.931487i	$0.618513\pi$
$752$	−7.16436	+	6.83121i	−0.261258	+	0.249109i
$753$	20.1329	+	31.7693i	0.733685	+	1.15774i
$754$	3.21010	+	33.6177i	0.116905	+	1.22428i
$755$	0.196763	−	1.36851i	0.00716093	−	0.0498053i
$756$	−3.68780	−	13.2439i	−0.134124	−	0.481675i
$757$	−28.1475	−	32.4839i	−1.02304	−	1.18065i	−0.983403	−	0.181433i	$-0.941926\pi$
$757$	−28.1475	−	32.4839i	−1.02304	−	1.18065i	−0.0396336	−	0.999214i	$-0.512619\pi$
$758$	−10.7835	+	6.22583i	−0.391673	+	0.226132i
$759$	25.0159	−	10.1199i	0.908019	−	0.367329i
$760$	0.458590	−	0.794302i	0.0166348	−	0.0288124i
$761$	−4.28728	+	12.3873i	−0.155414	+	0.449039i	−0.995649	−	0.0931833i	$-0.970296\pi$
$761$	−4.28728	+	12.3873i	−0.155414	+	0.449039i	0.840235	+	0.542222i	$0.182417\pi$
$762$	−27.7846	+	10.9190i	−1.00653	+	0.395555i
$763$	28.8571	+	18.3409i	1.04470	+	0.663987i
$764$	4.63591	+	2.11715i	0.167721	+	0.0765958i
$765$	0.213580	+	0.141125i	0.00772198	+	0.00510237i
$766$	−10.1842	−	10.6809i	−0.367970	−	0.385916i
$767$	−67.2474	+	3.20339i	−2.42816	+	0.115668i
$768$	1.64035	−	0.556091i	0.0591912	−	0.0200662i
$769$	2.37495	+	8.08832i	0.0856427	+	0.291672i	0.991167	−	0.132623i	$-0.0423400\pi$
$769$	2.37495	+	8.08832i	0.0856427	+	0.291672i	−0.905524	+	0.424295i	$0.860522\pi$
$770$	−1.89302	−	0.171160i	−0.0682198	−	0.00616819i
$771$	−21.7390	+	5.12784i	−0.782910	+	0.184675i
$772$	−14.5183	−	13.8432i	−0.522525	−	0.498227i
$773$	10.3182	+	0.985270i	0.371120	+	0.0354377i	0.278950	−	0.960306i	$-0.410014\pi$
$773$	10.3182	+	0.985270i	0.371120	+	0.0354377i	0.0921701	+	0.995743i	$0.470620\pi$
$774$	4.40315	+	11.4168i	0.158268	+	0.410367i
$775$	−23.5747	+	5.71916i	−0.846828	+	0.205438i
$776$	1.79241	+	12.4665i	0.0643436	+	0.447520i
$777$	5.64400	−	4.00783i	0.202477	−	0.143780i
$778$	2.27239	−	15.8048i	0.0814691	−	0.566630i
$779$	8.83854	+	0.421032i	0.316674	+	0.0150850i
$780$	−0.813638	+	1.75208i	−0.0291329	+	0.0627346i
$781$	−6.98121	+	12.0918i	−0.249807	+	0.432679i
$782$	1.61176	+	0.909253i	0.0576363	+	0.0325148i
$783$	33.1910	+	10.4366i	1.18615	+	0.372975i
$784$	−0.926472	+	6.93842i	−0.0330883	+	0.247801i
$785$	0.599317	−	0.932556i	0.0213905	−	0.0332843i
$786$	0.481490	−	1.93111i	0.0171742	−	0.0688805i
$787$	12.7773	−	9.09865i	0.455460	−	0.324332i	−0.329197	−	0.944261i	$-0.606778\pi$
$787$	12.7773	−	9.09865i	0.455460	−	0.324332i	0.784658	+	0.619929i	$0.212839\pi$
$788$	−3.59275	+	8.97426i	−0.127986	+	0.319695i
$789$	23.7243	+	9.67304i	0.844606	+	0.344370i
$790$	1.66335	+	2.58822i	0.0591793	+	0.0920847i
$791$	−9.11977	+	5.32663i	−0.324262	+	0.189393i
$792$	5.55190	+	8.00998i	0.197278	+	0.284622i
$793$	−44.7646	−	8.62768i	−1.58964	−	0.306378i
$794$	7.54966	+	21.8133i	0.267927	+	0.774125i
$795$	−1.17450	−	1.37296i	−0.0416551	−	0.0486940i
$796$	11.5528	+	8.22669i	0.409477	+	0.291587i
$797$	20.8094	−	13.3734i	0.737108	−	0.473710i	−0.117442	−	0.993080i	$-0.537469\pi$
$797$	20.8094	−	13.3734i	0.737108	−	0.473710i	0.854550	+	0.519369i	$0.173833\pi$
$798$	5.37875	−	18.2291i	0.190406	−	0.645303i
$799$	−0.543605	−	3.78086i	−0.0192314	−	0.133757i
$800$	0.470632	+	4.92868i	0.0166393	+	0.174255i
$801$	−16.4692	+	45.6980i	−0.581910	+	1.61466i
$802$	26.9588	−	13.8982i	0.951948	−	0.490763i
$803$	13.2212	−	38.2002i	0.466567	−	1.34806i
$804$	9.38020	+	6.76981i	0.330814	+	0.238753i
$805$	−2.78896	+	0.308578i	−0.0982981	+	0.0108759i
$806$		−	24.7109i		−	0.870405i
$807$	13.5859	−	9.54501i	0.478246	−	0.336000i
$808$	−7.94442	−	15.4100i	−0.279484	−	0.542123i
$809$	5.14824	−	6.54652i	0.181002	−	0.230163i	−0.687082	−	0.726580i	$-0.741109\pi$
$809$	5.14824	−	6.54652i	0.181002	−	0.230163i	0.868084	+	0.496417i	$0.165351\pi$
$810$	1.33642	+	1.47486i	0.0469569	+	0.0518213i
$811$	−31.6159	+	4.54567i	−1.11018	+	0.159620i	−0.672921	−	0.739714i	$-0.734961\pi$
$811$	−31.6159	+	4.54567i	−1.11018	+	0.159620i	−0.437262	+	0.899334i	$0.644052\pi$
$812$	−13.4469	−	11.5339i	−0.471893	−	0.404761i
$813$	−0.0106297	+	0.196832i	−0.000372799	+	0.00690321i
$814$	−2.84650	+	3.99735i	−0.0997697	+	0.140107i
$815$	−0.0769350	+	0.317131i	−0.00269492	+	0.0111086i
$816$	−0.192361	+	0.640055i	−0.00673399	+	0.0224064i
$817$	−3.20151	+	16.6110i	−0.112007	+	0.581145i
$818$	18.1039	−	5.31577i	0.632987	−	0.185862i
$819$	−7.87735	+	39.2483i	−0.275257	+	1.37145i
$820$	0.396907	−	0.255077i	0.0138606	−	0.00890767i
$821$	42.1142	−	10.2168i	1.46979	−	0.356568i	0.580634	−	0.814165i	$-0.302805\pi$
$821$	42.1142	−	10.2168i	1.46979	−	0.356568i	0.889160	+	0.457596i	$0.151290\pi$
$822$	−18.4422	−	29.1013i	−0.643245	−	1.01503i
$823$	−25.3075	−	35.5394i	−0.882165	−	1.23883i	−0.970101	−	0.242701i	$-0.921967\pi$
$823$	−25.3075	−	35.5394i	−0.882165	−	1.23883i	0.0879362	−	0.996126i	$-0.471973\pi$
$824$	−13.1785	+	5.27587i	−0.459094	+	0.183794i
$825$	−25.9286	+	10.1896i	−0.902718	+	0.354758i
$826$	24.2430	−	25.6827i	0.843523	−	0.893616i
$827$		−	40.1031i		−	1.39452i	−0.716818	−	0.697260i	$-0.754402\pi$
$827$		−	40.1031i		−	1.39452i	0.716818	−	0.697260i	$-0.245598\pi$
$828$	10.3855	+	9.95697i	0.360921	+	0.346029i
$829$	−33.0815	−	19.0996i	−1.14897	−	0.663358i	−0.200333	−	0.979728i	$-0.564203\pi$
$829$	−33.0815	−	19.0996i	−1.14897	−	0.663358i	−0.948636	+	0.316370i	$0.897536\pi$
$830$	0.213517	+	1.10783i	0.00741129	+	0.0384534i
$831$	−2.36361	+	2.96660i	−0.0819927	+	0.102910i
$832$	−4.99210	−	0.717755i	−0.173070	−	0.0248837i
$833$	−1.97349	−	1.84418i	−0.0683773	−	0.0638972i
$834$	−15.3849	+	29.3829i	−0.532736	+	1.01745i
$835$	−0.0730832	−	0.301253i	−0.00252915	−	0.0104253i
$836$	0.641102	+	13.4584i	0.0221730	+	0.465468i
$837$	−23.4509	−	9.91083i	−0.810582	−	0.342568i
$838$	21.3786	−	22.4213i	0.738513	−	0.774530i
$839$	7.30805	−	8.43394i	0.252302	−	0.291172i	−0.615443	−	0.788181i	$-0.711023\pi$
$839$	7.30805	−	8.43394i	0.252302	−	0.291172i	0.867745	+	0.497009i	$0.165569\pi$
$840$	−0.330184	−	0.958103i	−0.0113924	−	0.0330577i
$841$	15.1943	−	4.46144i	0.523940	−	0.153843i
$842$	−13.8363	−	9.85281i	−0.476832	−	0.339550i
$843$	3.58090	+	2.33357i	0.123333	+	0.0803725i
$844$	10.5278	−	10.0382i	0.362381	−	0.345530i
$845$	2.16179	−	1.70005i	0.0743677	−	0.0584834i
$846$	3.19822	−	29.5248i	0.109957	−	1.01508i
$847$	−1.04677	+	0.546328i	−0.0359675	+	0.0187721i
$848$	2.55025	−	3.96827i	0.0875759	−	0.136271i
$849$	−11.6460	−	16.5763i	−0.399689	−	0.568898i
$850$	−1.65450	−	0.955225i	−0.0567488	−	0.0327640i
$851$	−2.94361	+	6.61939i	−0.100905	+	0.226910i
$852$	−7.40585	−	0.754669i	−0.253720	−	0.0258545i
$853$	18.0336	−	15.6262i	0.617458	−	0.535030i	−0.288998	−	0.957330i	$-0.593322\pi$
$853$	18.0336	−	15.6262i	0.617458	−	0.535030i	0.906457	+	0.422299i	$0.138777\pi$
$854$	20.0536	−	13.0306i	0.686222	−	0.445900i
$855$	0.486371	+	2.70821i	0.0166335	+	0.0926190i
$856$	−17.8358	+	1.70311i	−0.609614	+	0.0582111i
$857$	13.0160	+	5.21083i	0.444619	+	0.177999i	0.583159	−	0.812358i	$-0.301817\pi$
$857$	13.0160	+	5.21083i	0.444619	+	0.177999i	−0.138539	+	0.990357i	$0.544241\pi$
$858$	−3.86019	−	28.1147i	−0.131785	−	0.959821i
$859$	1.43778	−	2.78890i	0.0490563	−	0.0951560i	−0.863033	−	0.505148i	$-0.831438\pi$
$859$	1.43778	−	2.78890i	0.0490563	−	0.0951560i	0.912089	+	0.409992i	$0.134468\pi$
$860$	0.374703	+	0.820486i	0.0127773	+	0.0279783i
$861$	6.75617	−	7.06692i	0.230250	−	0.240840i
$862$	−16.2311	+	18.7317i	−0.552833	+	0.638004i
$863$	6.77969	−	35.1764i	0.230783	−	1.19742i	−0.662896	−	0.748711i	$-0.730673\pi$
$863$	6.77969	−	35.1764i	0.230783	−	1.19742i	0.893679	−	0.448706i	$-0.148115\pi$
$864$	−2.68334	+	4.44968i	−0.0912892	+	0.151381i
$865$	−1.49640	−	0.142888i	−0.0508790	−	0.00485835i
$866$	−23.8882	−	12.3152i	−0.811754	−	0.418488i
$867$	17.8961	+	23.0566i	0.607784	+	0.783045i
$868$	8.99268	+	9.33679i	0.305232	+	0.316911i
$869$	−41.1122	−	18.7753i	−1.39464	−	0.636909i
$870$	2.48856	+	0.620481i	0.0843701	+	0.0210363i
$871$	−15.4349	−	29.9395i	−0.522992	−	1.01446i
$872$	−2.44579	−	12.6900i	−0.0828250	−	0.429737i
$873$	−28.2386	−	25.1040i	−0.955732	−	0.849640i
$874$	4.88178	+	19.2822i	0.165129	+	0.652229i
$875$	5.79305	−	0.582579i	0.195841	−	0.0196948i
$876$	21.4672	−	1.91236i	0.725310	−	0.0646127i
$877$	1.48228	−	31.1168i	0.0500529	−	1.05074i	−0.824516	−	0.565839i	$-0.808552\pi$
$877$	1.48228	−	31.1168i	0.0500529	−	1.05074i	0.874569	−	0.484902i	$-0.161145\pi$
$878$	−13.9585	−	10.9771i	−0.471078	−	0.370460i
$879$	0.132581	−	20.8741i	0.00447186	−	0.704067i
$880$	0.444094	+	0.564712i	0.0149704	+	0.0190364i
$881$	36.8779	+	10.8283i	1.24245	+	0.364816i	0.835935	−	0.548829i	$-0.184926\pi$
$881$	36.8779	+	10.8283i	1.24245	+	0.364816i	0.406514	+	0.913645i	$0.366744\pi$
$882$	−11.3067	−	17.6963i	−0.380716	−	0.595865i
$883$	5.33296	+	11.6776i	0.179468	+	0.392981i	0.977891	−	0.209117i	$-0.0670590\pi$
$883$	5.33296	+	11.6776i	0.179468	+	0.392981i	−0.798422	+	0.602098i	$0.794332\pi$
$884$	1.34295	−	1.40844i	0.0451683	−	0.0473711i
$885$	−1.47162	+	4.89662i	−0.0494680	+	0.164598i
$886$	−4.06178	−	11.7357i	−0.136458	−	0.394270i
$887$	−2.18917	−	2.08737i	−0.0735051	−	0.0700870i	0.652436	−	0.757844i	$-0.273747\pi$
$887$	−2.18917	−	2.08737i	−0.0735051	−	0.0700870i	−0.725941	+	0.687757i	$0.758596\pi$
$888$	−2.56589	−	0.511457i	−0.0861055	−	0.0171634i
$889$	−35.7029	+	28.3688i	−1.19744	+	0.951458i
$890$	−1.00879	+	3.43563i	−0.0338148	+	0.115163i
$891$	−28.2294	−	7.61264i	−0.945720	−	0.255033i
$892$	19.3553	−	13.7828i	0.648062	−	0.461483i
$893$	25.3794	−	32.2726i	0.849290	−	1.07996i
$894$	14.0549	−	17.6405i	0.470065	−	0.589985i
$895$	1.95214	−	1.69154i	0.0652527	−	0.0565418i
$896$	2.14742	−	1.54550i	0.0717403	−	0.0516317i
$897$	−13.8452	−	39.5400i	−0.462276	−	1.32020i
$898$	6.80668	+	11.7895i	0.227142	+	0.393421i
$899$	−32.2147	+	6.20888i	−1.07442	+	0.207078i
$900$	−10.6188	−	10.3857i	−0.353959	−	0.346189i
$901$	0.676483	+	1.68977i	0.0225369	+	0.0562945i
$902$	−2.87922	+	6.30461i	−0.0958676	+	0.209921i
$903$	11.5348	+	14.7077i	0.383855	+	0.489443i
$904$	3.83014	+	1.12463i	0.127388	+	0.0374046i
$905$	1.04259	−	2.02235i	0.0346570	−	0.0672252i
$906$	−7.14320	+	8.13867i	−0.237317	+	0.270389i
$907$	−0.893080	+	3.68132i	−0.0296542	+	0.122236i	−0.984715	−	0.174174i	$-0.944274\pi$
$907$	−0.893080	+	3.68132i	−0.0296542	+	0.122236i	0.955061	+	0.296410i	$0.0957896\pi$
$908$	2.30568	+	0.444383i	0.0765167	+	0.0147474i
$909$	48.0368	+	19.9427i	1.59328	+	0.661457i
$910$	−0.405258	+	2.92289i	−0.0134342	+	0.0968929i
$911$	−29.8163	+	13.6166i	−0.987858	+	0.451140i	−0.842767	−	0.538279i	$-0.819075\pi$
$911$	−29.8163	+	13.6166i	−0.987858	+	0.451140i	−0.145091	+	0.989418i	$0.546347\pi$
$912$	−6.40583	+	3.25111i	−0.212118	+	0.107655i
$913$	−11.4373	−	11.9951i	−0.378519	−	0.396979i
$914$	−10.2066	+	25.4948i	−0.337603	+	0.843291i
$915$	−1.75015	+	2.98736i	−0.0578581	+	0.0987592i
$916$	7.60765	+	1.09382i	0.251364	+	0.0361407i
$917$	−0.159923	−	3.03592i	−0.00528113	−	0.100255i
$918$	−0.798010	−	1.83936i	−0.0263383	−	0.0607079i
$919$	−12.8508	−	22.2583i	−0.423910	−	0.734234i	0.572408	−	0.819969i	$-0.306009\pi$
$919$	−12.8508	−	22.2583i	−0.423910	−	0.734234i	−0.996318	+	0.0857354i	$0.972676\pi$
$920$	0.808401	+	0.686498i	0.0266522	+	0.0226332i
$921$	13.1601	+	29.3079i	0.433641	+	0.965728i
$922$	−25.8700	−	8.95368i	−0.851982	−	0.294874i
$923$	18.2352	+	11.7191i	0.600220	+	0.385738i
$924$	11.6899	+	9.21811i	0.384570	+	0.303254i
$925$	3.10686	−	6.80306i	0.102153	−	0.223683i
$926$	−16.8868	−	21.4733i	−0.554936	−	0.705658i
$927$	19.9933	−	37.6010i	0.656665	−	1.23498i
$928$	0.318606	+	6.68836i	0.0104588	+	0.219556i
$929$	27.1963	−	38.1918i	0.892281	−	1.25303i	−0.0744462	−	0.997225i	$-0.523719\pi$
$929$	27.1963	−	38.1918i	0.892281	−	1.25303i	0.966727	−	0.255809i	$-0.0823417\pi$
$930$	−1.76955	−	0.625061i	−0.0580259	−	0.0204966i
$931$	−0.291972	−	29.0308i	−0.00956901	−	0.951446i
$932$	7.70585	+	6.67716i	0.252413	+	0.218718i
$933$	1.30148	+	6.99139i	0.0426086	+	0.228888i
$934$	−0.762464	+	7.98489i	−0.0249486	+	0.261273i
$935$	−0.276896	+	0.0131902i	−0.00905548	+	0.000431365i
$936$	12.8313	−	8.01772i	0.419404	−	0.262067i
$937$	33.3210	−	4.79083i	1.08855	−	0.156510i	0.425406	−	0.905003i	$-0.360131\pi$
$937$	33.3210	−	4.79083i	1.08855	−	0.156510i	0.663143	+	0.748493i	$0.269222\pi$
$938$	16.7274	+	5.69538i	0.546169	+	0.185961i
$939$	−33.7231	−	32.5663i	−1.10051	−	1.06276i
$940$	0.104163	−	2.18665i	0.00339742	−	0.0713206i
$941$	−22.0483	+	4.24947i	−0.718756	+	0.138529i	−0.535498	−	0.844536i	$-0.679876\pi$
$941$	−22.0483	+	4.24947i	−0.718756	+	0.138529i	−0.183257	+	0.983065i	$0.558664\pi$
$942$	−7.92047	+	3.55654i	−0.258063	+	0.115878i
$943$	−2.31304	+	9.96697i	−0.0753228	+	0.324569i
$944$	−13.3488			−0.434465
$945$	2.61132	+	1.55688i	0.0849462	+	0.0506453i
$946$	−11.1471	−	7.16382i	−0.362424	−	0.232916i
$947$	−5.62687	−	14.0552i	−0.182849	−	0.456734i	0.808418	−	0.588609i	$-0.200324\pi$
$947$	−5.62687	−	14.0552i	−0.182849	−	0.456734i	−0.991266	+	0.131875i	$0.957900\pi$
$948$	0.153048	−	24.0965i	0.00497078	−	0.782618i
$949$	−58.2610	−	23.3242i	−1.89123	−	0.757135i
$950$	−4.84119	−	19.9557i	−0.157069	−	0.647447i
$951$	2.08730	−	38.6511i	0.0676854	−	1.25335i
$952$	0.00513358	+	1.02089i	0.000166380	+	0.0330872i
$953$	−10.5591	−	35.9611i	−0.342044	−	1.16489i	−0.933506	−	0.358561i	$-0.883267\pi$
$953$	−10.5591	−	35.9611i	−0.342044	−	1.16489i	0.591462	−	0.806333i	$-0.298551\pi$
$954$	1.83585	+	14.0317i	0.0594377	+	0.454292i
$955$	−1.06506	+	0.368621i	−0.0344645	+	0.0119283i
$956$	5.76900	+	1.39954i	0.186583	+	0.0452645i
$957$	−35.6823	+	12.0965i	−1.15344	+	0.391025i
$958$	8.21388	+	12.7810i	0.265378	+	0.412937i
$959$	−39.9461	−	34.2634i	−1.28993	−	1.10642i
$960$	−0.177673	+	0.339329i	−0.00573438	+	0.0109518i
$961$	−6.96204	+	0.664794i	−0.224582	+	0.0214450i
$962$	5.98847	+	4.70938i	0.193076	+	0.151837i
$963$	37.5834	−	38.4269i	1.21111	−	1.23829i
$964$	−13.5229	−	4.68034i	−0.435545	−	0.150743i
$965$	4.43618			0.142806
$966$	19.6205	+	9.90136i	0.631279	+	0.318571i
$967$	6.56023			0.210963			0.105481	−	0.994421i	$-0.466362\pi$
$967$	6.56023			0.210963			0.105481	+	0.994421i	$0.466362\pi$
$968$	0.421742	+	0.145966i	0.0135553	+	0.00469153i
$969$	0.411901	−	2.74113i	0.0132322	−	0.0880577i
$970$	−2.18932	−	1.72170i	−0.0702950	−	0.0552806i
$971$	12.8858	−	1.23044i	0.413524	−	0.0394868i	0.113779	−	0.993506i	$-0.463704\pi$
$971$	12.8858	−	1.23044i	0.413524	−	0.0394868i	0.299745	+	0.954019i	$0.403098\pi$
$972$	−2.46263	−	15.3927i	−0.0789890	−	0.493721i
$973$	−9.33784	+	49.7954i	−0.299357	+	1.59637i
$974$	−7.58698	−	11.8056i	−0.243103	−	0.378275i
$975$	13.8859	+	40.9605i	0.444704	+	1.31179i
$976$	−8.78437	−	2.13107i	−0.281181	−	0.0682138i
$977$	−22.6655	+	7.84460i	−0.725133	+	0.250971i	−0.664604	−	0.747195i	$-0.731400\pi$
$977$	−22.6655	+	7.84460i	−0.725133	+	0.250971i	−0.0605287	+	0.998166i	$0.519279\pi$
$978$	1.86096	−	1.75199i	0.0595069	−	0.0560225i
$979$	−14.8195	−	50.4705i	−0.473632	−	1.61304i
$980$	−0.910562	−	1.25187i	−0.0290868	−	0.0399894i
$981$	30.1688	+	24.3516i	0.963217	+	0.777485i
$982$	5.97940	+	24.6474i	0.190810	+	0.786531i
$983$	20.2997	+	8.12678i	0.647460	+	0.259204i	0.672064	−	0.740493i	$-0.265408\pi$
$983$	20.2997	+	8.12678i	0.647460	+	0.259204i	−0.0246035	+	0.999697i	$0.507832\pi$
$984$	−3.69523	−	0.0234702i	−0.117800	−	0.000748202i
$985$	−0.794510	−	1.98459i	−0.0253152	−	0.0632343i
$986$	−2.17357	−	1.39687i	−0.0692205	−	0.0444853i
$987$	−8.52620	−	44.5552i	−0.271392	−	1.41821i
$988$	20.9175			0.665473
$989$	−18.2316	−	7.08885i	−0.579731	−	0.225412i
$990$	−2.11094	−	0.434731i	−0.0670901	−	0.0138167i
$991$	−41.8906	+	8.07375i	−1.33070	+	0.256471i	−0.804531	−	0.593910i	$-0.797583\pi$
$991$	−41.8906	+	8.07375i	−1.33070	+	0.256471i	−0.526167	+	0.850381i	$0.676371\pi$
$992$	0.233133	−	4.89407i	0.00740199	−	0.155387i
$993$	−23.0109	+	23.8283i	−0.730229	+	0.756167i
$994$	−11.1548	+	2.20814i	−0.353807	+	0.0700378i
$995$	−3.10444	+	0.446351i	−0.0984174	+	0.0141503i
$996$	3.33625	−	8.18254i	0.105713	−	0.259274i
$997$	−1.21357	+	0.0578094i	−0.0384341	+	0.00183084i	−0.0667902	−	0.997767i	$-0.521276\pi$
$997$	−1.21357	+	0.0578094i	−0.0384341	+	0.00183084i	0.0283561	+	0.999598i	$0.490973\pi$
$998$	−2.57289	+	26.9446i	−0.0814435	+	0.852915i
$999$	6.87105	−	3.79432i	0.217390	−	0.120047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bd.a.59.3	✓	1280
3.2	odd	2	inner	966.2.bd.a.59.54	yes	1280
7.5	odd	6	inner	966.2.bd.a.887.41	yes	1280
21.5	even	6	inner	966.2.bd.a.887.9	yes	1280
23.16	even	11	inner	966.2.bd.a.269.9	yes	1280
69.62	odd	22	inner	966.2.bd.a.269.41	yes	1280
161.131	odd	66	inner	966.2.bd.a.131.54	yes	1280
483.131	even	66	inner	966.2.bd.a.131.3	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bd.a.59.3	✓	1280	1.1	even	1	trivial
966.2.bd.a.59.54	yes	1280	3.2	odd	2	inner
966.2.bd.a.131.3	yes	1280	483.131	even	66	inner
966.2.bd.a.131.54	yes	1280	161.131	odd	66	inner
966.2.bd.a.269.9	yes	1280	23.16	even	11	inner
966.2.bd.a.269.41	yes	1280	69.62	odd	22	inner
966.2.bd.a.887.9	yes	1280	21.5	even	6	inner
966.2.bd.a.887.41	yes	1280	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.71282 - 0.257380i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-0.220141 + 0.0210209i) q^{5} +(1.53444 + 0.803434i) q^{6} +(2.60042 + 0.487642i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(2.86751 + 0.881693i) q^{9} +O(q^{10})\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.71282 - 0.257380i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-0.220141 + 0.0210209i) q^{5} +(1.53444 + 0.803434i) q^{6} +(2.60042 + 0.487642i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(2.86751 + 0.881693i) q^{9} +(0.214909 + 0.0521363i) q^{10} +(-3.06997 + 1.06253i) q^{11} +(-1.18727 - 1.26111i) q^{12} +(1.42090 + 4.83914i) q^{13} +(-2.29791 - 1.31134i) q^{14} +(0.382473 + 0.0206549i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.358224 - 0.143411i) q^{17} +(-2.42143 - 1.77107i) q^{18} +(-1.54146 - 3.85037i) q^{19} +(-0.186037 - 0.119559i) q^{20} +(-4.32855 - 1.50454i) q^{21} +3.24865 q^{22} +(4.69989 - 0.954502i) q^{23} +(0.709499 + 1.58007i) q^{24} +(-4.86162 + 0.937001i) q^{25} +(0.239976 - 5.03772i) q^{26} +(-4.68460 - 2.24822i) q^{27} +(1.74263 + 1.99079i) q^{28} +(-6.62779 + 0.952933i) q^{29} +(-0.354681 - 0.144613i) q^{30} +(4.89407 - 0.233133i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(5.53179 - 1.02977i) q^{33} +(0.291617 + 0.252687i) q^{34} +(-0.582711 - 0.0526867i) q^{35} +(1.70899 + 2.46564i) q^{36} +(-0.876210 + 1.23046i) q^{37} +(0.197344 + 4.14277i) q^{38} +(-1.18825 - 8.65429i) q^{39} +(0.136701 + 0.173830i) q^{40} +(-0.886283 + 1.94069i) q^{41} +(3.59840 + 2.83752i) q^{42} +(-3.43131 - 2.20517i) q^{43} +(-3.06997 - 1.06253i) q^{44} +(-0.649791 - 0.133819i) q^{45} +(-4.75358 - 0.635177i) q^{46} +(4.94958 + 8.57293i) q^{47} +(-0.153688 - 1.72522i) q^{48} +(6.52441 + 2.53615i) q^{49} +(4.90070 + 0.704614i) q^{50} +(0.576662 + 0.337838i) q^{51} +(-1.87445 + 4.68216i) q^{52} +(-3.25516 - 3.41392i) q^{53} +(3.69163 + 3.65676i) q^{54} +(0.653492 - 0.298440i) q^{55} +(-0.995665 - 2.45125i) q^{56} +(1.64923 + 6.99174i) q^{57} +(6.57494 + 1.26722i) q^{58} +(-3.14709 + 12.9725i) q^{59} +(0.287876 + 0.252665i) q^{60} +(-4.14199 + 8.03434i) q^{61} +(-4.70115 - 1.38038i) q^{62} +(7.02679 + 3.69109i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.414522 - 1.03542i) q^{65} +(-5.56435 - 0.836138i) q^{66} +(-6.55809 + 1.26397i) q^{67} +(-0.192932 - 0.334168i) q^{68} +(-8.29573 + 0.425232i) q^{69} +(0.533430 + 0.240375i) q^{70} +(3.24815 - 2.81454i) q^{71} +(-0.808566 - 2.88898i) q^{72} +(-7.69186 + 9.78100i) q^{73} +(1.23046 - 0.876210i) q^{74} +(8.56826 - 0.353628i) q^{75} +(1.16848 - 3.97946i) q^{76} +(-8.50137 + 1.26598i) q^{77} +(-1.70765 + 8.56695i) q^{78} +(10.0689 + 9.60066i) q^{79} +(-0.0723286 - 0.208980i) q^{80} +(7.44523 + 5.05653i) q^{81} +(1.47227 - 1.54408i) q^{82} +(2.11936 + 4.64074i) q^{83} +(-2.47243 - 3.85838i) q^{84} +(0.0818745 + 0.0240405i) q^{85} +(2.52135 + 3.20616i) q^{86} +(11.5975 + 0.0736611i) q^{87} +(2.55361 + 2.00818i) q^{88} +(-0.770433 + 16.1734i) q^{89} +(0.570285 + 0.338985i) q^{90} +(1.33518 + 13.2767i) q^{91} +(4.28439 + 2.15499i) q^{92} +(-8.44267 - 0.860323i) q^{93} +(-1.87343 - 9.72028i) q^{94} +(0.420276 + 0.815223i) q^{95} +(-0.419029 + 1.68060i) q^{96} +(-11.4565 - 5.23201i) q^{97} +(-5.33608 - 4.53059i) q^{98} +(-9.74001 + 0.340036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 + 4 * q^9	\( 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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