LMFDB - Embedded newform 669.2.m.b.19.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(19,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([0, 172])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.m (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [1368] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$1368$
Relative dimension:	$19$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	669.19
Dual form			669.2.m.b.493.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.149953 - 1.17100i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(0.586706 - 0.152766i) q^{4} +(-0.239221 + 0.0340808i) q^{5} +(0.875091 + 0.792432i) q^{6} +(-2.71848 + 3.67563i) q^{7} +(-1.14723 - 2.85499i) q^{8} +(0.155037 - 0.987909i) q^{9} +(0.0757806 + 0.275018i) q^{10} +(0.357400 - 0.115009i) q^{11} +(-0.346569 + 0.497445i) q^{12} +(1.52686 - 0.539475i) q^{13} +(4.71181 + 2.63218i) q^{14} +(0.159643 - 0.181390i) q^{15} +(-2.11261 + 1.18017i) q^{16} +(-0.331401 + 1.53771i) q^{17} +(-1.18009 - 0.0334086i) q^{18} +(5.51339 + 5.91799i) q^{19} +(-0.135146 + 0.0565404i) q^{20} +(-0.323208 - 4.56026i) q^{21} +(-0.188269 - 0.401270i) q^{22} +(1.89422 + 2.41508i) q^{23} +(2.72754 + 1.42396i) q^{24} +(-4.74501 + 1.38001i) q^{25} +(-0.860684 - 1.70706i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-1.03344 + 2.57181i) q^{28} +(7.65291 + 4.56401i) q^{29} +(-0.236347 - 0.159743i) q^{30} +(-0.574495 + 5.78053i) q^{31} +(-1.96044 - 2.65068i) q^{32} +(-0.196850 + 0.319705i) q^{33} +(1.85035 + 0.157488i) q^{34} +(0.525051 - 0.971937i) q^{35} +(-0.0599583 - 0.603296i) q^{36} +(-2.32146 + 2.10218i) q^{37} +(6.10323 - 7.34361i) q^{38} +(-0.809683 + 1.40241i) q^{39} +(0.371742 + 0.643876i) q^{40} +(-2.76663 - 0.474386i) q^{41} +(-5.29160 + 1.06230i) q^{42} +(1.20290 + 4.90331i) q^{43} +(0.192119 - 0.122075i) q^{44} +(-0.00341937 + 0.241613i) q^{45} +(2.54402 - 2.58028i) q^{46} +(-5.41640 + 5.81388i) q^{47} +(0.838373 - 2.27004i) q^{48} +(-4.07035 - 13.2911i) q^{49} +(2.32752 + 5.34948i) q^{50} +(-0.747640 - 1.38398i) q^{51} +(0.813406 - 0.549766i) q^{52} +(1.66812 - 0.0945256i) q^{53} +(0.918521 - 0.741654i) q^{54} +(-0.0815781 + 0.0396931i) q^{55} +(13.6126 + 3.54445i) q^{56} +(-8.03649 - 0.913722i) q^{57} +(4.19689 - 9.64596i) q^{58} +(7.97548 - 0.678814i) q^{59} +(0.0659534 - 0.130811i) q^{60} +(-0.663942 + 3.56822i) q^{61} +(6.85516 - 0.194071i) q^{62} +(3.20972 + 3.25547i) q^{63} +(-6.30411 + 6.04200i) q^{64} +(-0.346873 + 0.181091i) q^{65} +(0.403894 + 0.182572i) q^{66} +(3.33508 - 12.1035i) q^{67} +(0.0404748 + 0.952807i) q^{68} +(-3.00927 - 0.604116i) q^{69} +(-1.21687 - 0.469091i) q^{70} +(6.74898 - 14.3846i) q^{71} +(-2.99833 + 0.690730i) q^{72} +(-1.94105 - 0.944446i) q^{73} +(2.80977 + 2.40321i) q^{74} +(2.70896 - 4.13292i) q^{75} +(4.13881 + 2.62986i) q^{76} +(-0.548854 + 1.62632i) q^{77} +(1.76364 + 0.737845i) q^{78} +(2.48902 + 6.73945i) q^{79} +(0.465160 - 0.354322i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(-0.140644 + 3.31086i) q^{82} +(-1.10205 + 4.49225i) q^{83} +(-0.886281 - 2.62615i) q^{84} +(0.0268720 - 0.379146i) q^{85} +(5.56141 - 2.14386i) q^{86} +(-8.78234 + 1.50588i) q^{87} +(-0.738369 - 0.888431i) q^{88} +(-0.0419446 - 0.00597566i) q^{89} +(0.283442 - 0.0322264i) q^{90} +(-2.16784 + 7.07874i) q^{91} +(1.48029 + 1.12757i) q^{92} +(-3.32068 - 4.76630i) q^{93} +(7.62027 + 5.47081i) q^{94} +(-1.52061 - 1.22781i) q^{95} +(3.21273 + 0.740122i) q^{96} +(-1.63197 + 2.08072i) q^{97} +(-14.9535 + 6.75943i) q^{98} +(-0.0582083 - 0.370909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{86}{111}\right)$

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 $

$2$	−0.149953	−	1.17100i	−0.106033	−	0.828024i	−0.954382	−	0.298587i	$-0.903485\pi$
$2$	−0.149953	−	1.17100i	−0.106033	−	0.828024i	0.848350	−	0.529436i	$-0.177596\pi$
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$4$	0.586706	−	0.152766i	0.293353	−	0.0763831i
$5$	−0.239221	+	0.0340808i	−0.106983	+	0.0152414i	−0.194327	−	0.980937i	$-0.562252\pi$
$5$	−0.239221	+	0.0340808i	−0.106983	+	0.0152414i	0.0873438	+	0.996178i	$0.472162\pi$
$6$	0.875091	+	0.792432i	0.357254	+	0.323509i
$7$	−2.71848	+	3.67563i	−1.02749	+	1.38926i	−0.108896	+	0.994053i	$0.534732\pi$
$7$	−2.71848	+	3.67563i	−1.02749	+	1.38926i	−0.918593	+	0.395204i	$0.870674\pi$
$8$	−1.14723	−	2.85499i	−0.405607	−	1.00939i
$9$	0.155037	−	0.987909i	0.0516789	−	0.329303i
$10$	0.0757806	+	0.275018i	0.0239639	+	0.0869684i
$11$	0.357400	−	0.115009i	0.107760	−	0.0346765i	−0.251953	−	0.967739i	$-0.581073\pi$
$11$	0.357400	−	0.115009i	0.107760	−	0.0346765i	0.359713	+	0.933063i	$0.382875\pi$
$12$	−0.346569	+	0.497445i	−0.100046	+	0.143600i
$13$	1.52686	−	0.539475i	0.423476	−	0.149623i	−0.112893	−	0.993607i	$-0.536012\pi$
$13$	1.52686	−	0.539475i	0.423476	−	0.149623i	0.536369	+	0.843984i	$0.319796\pi$
$14$	4.71181	+	2.63218i	1.25929	+	0.703479i
$15$	0.159643	−	0.181390i	0.0412197	−	0.0468347i
$16$	−2.11261	+	1.18017i	−0.528152	+	0.295044i
$17$	−0.331401	+	1.53771i	−0.0803765	+	0.372948i	−0.999793	−	0.0203365i	$-0.993526\pi$
$17$	−0.331401	+	1.53771i	−0.0803765	+	0.372948i	0.919417	+	0.393285i	$0.128661\pi$
$18$	−1.18009	−	0.0334086i	−0.278150	−	0.00787449i
$19$	5.51339	+	5.91799i	1.26486	+	1.35768i	0.905424	+	0.424509i	$0.139553\pi$
$19$	5.51339	+	5.91799i	1.26486	+	1.35768i	0.359436	+	0.933170i	$0.382969\pi$
$20$	−0.135146	+	0.0565404i	−0.0302196	+	0.0126428i
$21$	−0.323208	−	4.56026i	−0.0705297	−	0.995129i
$22$	−0.188269	−	0.401270i	−0.0401390	−	0.0855510i
$23$	1.89422	+	2.41508i	0.394971	+	0.503579i	0.942960	−	0.332907i	$-0.108030\pi$
$23$	1.89422	+	2.41508i	0.394971	+	0.503579i	−0.547988	+	0.836486i	$0.684606\pi$
$24$	2.72754	+	1.42396i	0.556756	+	0.290664i
$25$	−4.74501	+	1.38001i	−0.949002	+	0.276002i
$26$	−0.860684	−	1.70706i	−0.168794	−	0.334783i
$27$	0.524307	+	0.851529i	0.100903	+	0.163877i
$28$	−1.03344	+	2.57181i	−0.195301	+	0.486025i
$29$	7.65291	+	4.56401i	1.42111	+	0.847515i	0.998276	−	0.0586930i	$-0.0186933\pi$
$29$	7.65291	+	4.56401i	1.42111	+	0.847515i	0.422833	+	0.906208i	$0.361036\pi$
$30$	−0.236347	−	0.159743i	−0.0431509	−	0.0291649i
$31$	−0.574495	+	5.78053i	−0.103182	+	1.03821i	0.797377	+	0.603481i	$0.206220\pi$
$31$	−0.574495	+	5.78053i	−0.103182	+	1.03821i	−0.900560	+	0.434732i	$0.856843\pi$
$32$	−1.96044	−	2.65068i	−0.346559	−	0.468579i
$33$	−0.196850	+	0.319705i	−0.0342673	+	0.0556536i
$34$	1.85035	+	0.157488i	0.317332	+	0.0270090i
$35$	0.525051	−	0.971937i	0.0887497	−	0.164287i
$36$	−0.0599583	−	0.603296i	−0.00999305	−	0.100549i
$37$	−2.32146	+	2.10218i	−0.381646	+	0.345596i	−0.839431	−	0.543467i	$-0.817111\pi$
$37$	−2.32146	+	2.10218i	−0.381646	+	0.345596i	0.457785	+	0.889063i	$0.348643\pi$
$38$	6.10323	−	7.34361i	0.990074	−	1.19129i
$39$	−0.809683	+	1.40241i	−0.129653	+	0.224566i
$40$	0.371742	+	0.643876i	0.0587776	+	0.101806i
$41$	−2.76663	−	0.474386i	−0.432075	−	0.0740867i	−0.0511463	−	0.998691i	$-0.516287\pi$
$41$	−2.76663	−	0.474386i	−0.432075	−	0.0740867i	−0.380928	+	0.924605i	$0.624396\pi$
$42$	−5.29160	+	1.06230i	−0.816512	+	0.163916i
$43$	1.20290	+	4.90331i	0.183440	+	0.747748i	0.988074	+	0.153977i	$0.0492082\pi$
$43$	1.20290	+	4.90331i	0.183440	+	0.747748i	−0.804634	+	0.593771i	$0.797639\pi$
$44$	0.192119	−	0.122075i	0.0289630	−	0.0184035i
$45$	−0.00341937	+	0.241613i	−0.000509729	+	0.0360175i
$46$	2.54402	−	2.58028i	0.375095	−	0.380441i
$47$	−5.41640	+	5.81388i	−0.790063	+	0.848041i	−0.991316	−	0.131498i	$-0.958021\pi$
$47$	−5.41640	+	5.81388i	−0.790063	+	0.848041i	0.201253	+	0.979539i	$0.435499\pi$
$48$	0.838373	−	2.27004i	0.121009	−	0.327651i
$49$	−4.07035	−	13.2911i	−0.581479	−	1.89873i
$50$	2.32752	+	5.34948i	0.329161	+	0.756531i
$51$	−0.747640	−	1.38398i	−0.104691	−	0.193796i
$52$	0.813406	−	0.549766i	0.112799	−	0.0762389i
$53$	1.66812	−	0.0945256i	0.229135	−	0.0129841i	0.0583659	−	0.998295i	$-0.481411\pi$
$53$	1.66812	−	0.0945256i	0.229135	−	0.0129841i	0.170769	+	0.985311i	$0.445375\pi$
$54$	0.918521	−	0.741654i	0.124995	−	0.100926i
$55$	−0.0815781	+	0.0396931i	−0.0110000	+	0.00535221i
$56$	13.6126	+	3.54445i	1.81906	+	0.473647i
$57$	−8.03649	−	0.913722i	−1.06446	−	0.121026i
$58$	4.19689	−	9.64596i	0.551078	−	1.26658i
$59$	7.97548	−	0.678814i	1.03832	−	0.0883740i	0.446775	−	0.894646i	$-0.352572\pi$
$59$	7.97548	−	0.678814i	1.03832	−	0.0883740i	0.591545	+	0.806272i	$0.298518\pi$
$60$	0.0659534	−	0.130811i	0.00851454	−	0.0168876i
$61$	−0.663942	+	3.56822i	−0.0850090	+	0.456863i	0.913715	+	0.406356i	$0.133201\pi$
$61$	−0.663942	+	3.56822i	−0.0850090	+	0.456863i	−0.998724	+	0.0505070i	$0.983916\pi$
$62$	6.85516	−	0.194071i	0.870606	−	0.0246470i
$63$	3.20972	+	3.25547i	0.404387	+	0.410150i
$64$	−6.30411	+	6.04200i	−0.788014	+	0.755250i
$65$	−0.346873	+	0.181091i	−0.0430242	+	0.0224615i
$66$	0.403894	+	0.182572i	0.0497159	+	0.0224730i
$67$	3.33508	−	12.1035i	0.407445	−	1.47867i	−0.414996	−	0.909823i	$-0.636217\pi$
$67$	3.33508	−	12.1035i	0.407445	−	1.47867i	0.822441	−	0.568850i	$-0.192612\pi$
$68$	0.0404748	+	0.952807i	0.00490829	+	0.115545i
$69$	−3.00927	−	0.604116i	−0.362273	−	0.0727271i
$70$	−1.21687	−	0.469091i	−0.145444	−	0.0560671i
$71$	6.74898	−	14.3846i	0.800957	−	1.70713i	0.0988055	−	0.995107i	$-0.468498\pi$
$71$	6.74898	−	14.3846i	0.800957	−	1.70713i	0.702152	−	0.712028i	$-0.252223\pi$
$72$	−2.99833	+	0.690730i	−0.353357	+	0.0814033i
$73$	−1.94105	−	0.944446i	−0.227182	−	0.110539i	0.320427	−	0.947273i	$-0.396174\pi$
$73$	−1.94105	−	0.944446i	−0.227182	−	0.110539i	−0.547609	+	0.836734i	$0.684462\pi$
$74$	2.80977	+	2.40321i	0.326629	+	0.279367i
$75$	2.70896	−	4.13292i	0.312804	−	0.477229i
$76$	4.13881	+	2.62986i	0.474754	+	0.301665i
$77$	−0.548854	+	1.62632i	−0.0625478	+	0.185336i
$78$	1.76364	+	0.737845i	0.199693	+	0.0835445i
$79$	2.48902	+	6.73945i	0.280037	+	0.758247i	0.998062	+	0.0622296i	$0.0198211\pi$
$79$	2.48902	+	6.73945i	0.280037	+	0.758247i	−0.718025	+	0.696017i	$0.754954\pi$
$80$	0.465160	−	0.354322i	0.0520065	−	0.0396144i
$81$	−0.951927	−	0.306324i	−0.105770	−	0.0340360i
$82$	−0.140644	+	3.31086i	−0.0155315	+	0.365624i
$83$	−1.10205	+	4.49225i	−0.120966	+	0.493088i	0.878904	+	0.476998i	$0.158275\pi$
$83$	−1.10205	+	4.49225i	−0.120966	+	0.493088i	−0.999871	+	0.0160904i	$0.994878\pi$
$84$	−0.886281	−	2.62615i	−0.0967012	−	0.286537i
$85$	0.0268720	−	0.379146i	0.00291467	−	0.0411242i
$86$	5.56141	−	2.14386i	0.599702	−	0.231178i
$87$	−8.78234	+	1.50588i	−0.941565	+	0.161448i
$88$	−0.738369	−	0.888431i	−0.0787104	−	0.0947071i
$89$	−0.0419446	−	0.00597566i	−0.00444612	−	0.000633418i	0.138818	−	0.990318i	$-0.455670\pi$
$89$	−0.0419446	−	0.00597566i	−0.00444612	−	0.000633418i	−0.143264	+	0.989685i	$0.545760\pi$
$90$	0.283442	−	0.0322264i	0.0298774	−	0.00339696i
$91$	−2.16784	+	7.07874i	−0.227251	+	0.742053i
$92$	1.48029	+	1.12757i	0.154331	+	0.117557i
$93$	−3.32068	−	4.76630i	−0.344338	−	0.494243i
$94$	7.62027	+	5.47081i	0.785970	+	0.564271i
$95$	−1.52061	−	1.22781i	−0.156011	−	0.125970i
$96$	3.21273	+	0.740122i	0.327898	+	0.0755384i
$97$	−1.63197	+	2.08072i	−0.165701	+	0.211265i	−0.862576	−	0.505928i	$-0.831150\pi$
$97$	−1.63197	+	2.08072i	−0.165701	+	0.211265i	0.696874	+	0.717193i	$0.254573\pi$
$98$	−14.9535	+	6.75943i	−1.51054	+	0.682805i
$99$	−0.0582083	−	0.370909i	−0.00585015	−	0.0372777i
$100$	−2.57310	+	1.53454i	−0.257310	+	0.153454i
$101$	0.639827	+	0.0362563i	0.0636652	+	0.00360764i	0.0883789	−	0.996087i	$-0.471831\pi$
$101$	0.639827	+	0.0362563i	0.0636652	+	0.00360764i	−0.0247137	+	0.999695i	$0.507867\pi$
$102$	−1.50853	+	1.08302i	−0.149367	+	0.107235i
$103$	−6.84429	−	2.41824i	−0.674388	−	0.238276i	−0.0260857	−	0.999660i	$-0.508304\pi$
$103$	−6.84429	−	2.41824i	−0.674388	−	0.238276i	−0.648302	+	0.761383i	$0.724521\pi$
$104$	−3.29186	−	3.74028i	−0.322793	−	0.366764i
$105$	0.232735	+	1.07990i	0.0227126	+	0.105387i
$106$	−0.360829	−	1.93920i	−0.0350469	−	0.188352i
$107$	−2.55069	−	0.741828i	−0.246585	−	0.0717152i	0.153659	−	0.988124i	$-0.450894\pi$
$107$	−2.55069	−	0.741828i	−0.246585	−	0.0717152i	−0.400244	+	0.916409i	$0.631074\pi$
$108$	0.437699	+	0.419501i	0.0421176	+	0.0403665i
$109$	−0.163046	−	11.5208i	−0.0156170	−	1.10349i	−0.841700	−	0.539946i	$-0.818445\pi$
$109$	−0.163046	−	11.5208i	−0.0156170	−	1.10349i	0.826083	−	0.563549i	$-0.190564\pi$
$110$	0.0587135	+	0.0895760i	0.00559811	+	0.00854074i
$111$	0.397798	−	3.10646i	0.0377573	−	0.294852i
$112$	1.40521	−	10.9734i	0.132779	−	1.03689i
$113$	−8.74802	−	13.3464i	−0.822944	−	1.25552i	−0.964101	−	0.265534i	$-0.914452\pi$
$113$	−8.74802	−	13.3464i	−0.822944	−	1.25552i	0.141157	−	0.989987i	$-0.454918\pi$
$114$	0.135122	+	9.54776i	0.0126554	+	0.894230i
$115$	−0.535445	−	0.513182i	−0.0499305	−	0.0478545i
$116$	5.18723	+	1.50862i	0.481622	+	0.140072i
$117$	−0.296232	−	1.59204i	−0.0273867	−	0.147184i
$118$	−1.99084	−	9.23752i	−0.183271	−	0.850382i
$119$	−4.75113	−	5.39833i	−0.435535	−	0.494864i
$120$	−0.701015	−	0.247684i	−0.0639936	−	0.0226104i
$121$	−8.82114	+	6.33295i	−0.801921	+	0.575723i
$122$	4.27795	+	0.242414i	0.387307	+	0.0219471i
$123$	2.41083	−	1.43776i	0.217377	−	0.129639i
$124$	0.546010	+	3.47923i	0.0490332	+	0.312444i
$125$	2.18901	−	0.989494i	0.195791	−	0.0885030i
$126$	3.33085	−	4.24676i	0.296736	−	0.378331i
$127$	1.65166	+	0.380496i	0.146561	+	0.0337635i	0.297136	−	0.954835i	$-0.403968\pi$
$127$	1.65166	+	0.380496i	0.146561	+	0.0337635i	−0.150575	+	0.988599i	$0.548113\pi$
$128$	2.89033	+	2.33378i	0.255471	+	0.206279i
$129$	−4.10122	−	2.94439i	−0.361092	−	0.259239i
$130$	0.264072	+	0.379033i	0.0231606	+	0.0332434i
$131$	−5.84514	−	4.45237i	−0.510692	−	0.389005i	0.318540	−	0.947909i	$-0.396807\pi$
$131$	−5.84514	−	4.45237i	−0.510692	−	0.389005i	−0.829232	+	0.558904i	$0.811222\pi$
$132$	−0.0666531	+	0.217645i	−0.00580140	+	0.0189436i
$133$	−36.7404	+	4.17726i	−3.18580	+	0.362214i
$134$	−14.6733	−	2.09044i	−1.26758	−	0.180586i
$135$	−0.154446	−	0.185835i	−0.0132926	−	0.0159941i
$136$	4.77033	−	0.817955i	0.409052	−	0.0701390i
$137$	7.24109	−	2.79136i	0.618648	−	0.238482i	−0.0300247	−	0.999549i	$-0.509559\pi$
$137$	7.24109	−	2.79136i	0.618648	−	0.238482i	0.648673	+	0.761067i	$0.275324\pi$
$138$	−0.256174	+	3.61445i	−0.0218070	+	0.307682i
$139$	3.63264	+	10.7639i	0.308116	+	0.912983i	0.984339	+	0.176286i	$0.0564085\pi$
$139$	3.63264	+	10.7639i	0.308116	+	0.912983i	−0.676223	+	0.736697i	$0.736384\pi$
$140$	0.159571	−	0.650451i	0.0134862	−	0.0549731i
$141$	0.337237	−	7.93882i	0.0284005	−	0.668569i
$142$	−17.8564	−	5.74607i	−1.49847	−	0.482199i
$143$	0.483656	−	0.368411i	0.0404453	−	0.0308081i
$144$	0.838373	+	2.27004i	0.0698644	+	0.189170i
$145$	−1.98628	−	0.830991i	−0.164952	−	0.0690100i
$146$	−0.814883	+	2.41459i	−0.0674402	+	0.199833i
$147$	11.7323	+	7.45484i	0.967661	+	0.614865i
$148$	−1.04087	+	1.58800i	−0.0855592	+	0.130533i
$149$	−9.13032	−	7.80921i	−0.747985	−	0.639755i	0.191834	−	0.981427i	$-0.438556\pi$
$149$	−9.13032	−	7.80921i	−0.747985	−	0.639755i	−0.939819	+	0.341672i	$0.889007\pi$
$150$	−5.24588	−	2.55246i	−0.428324	−	0.208408i
$151$	7.64270	−	1.76066i	0.621954	−	0.143280i	0.0982233	−	0.995164i	$-0.468684\pi$
$151$	7.64270	−	1.76066i	0.621954	−	0.143280i	0.523730	+	0.851884i	$0.324540\pi$
$152$	10.5707	−	22.5300i	0.857394	−	1.82742i
$153$	1.46773	+	0.565794i	0.118659	+	0.0457418i
$154$	1.98672	+	0.398839i	0.160095	+	0.0321393i
$155$	−0.0595734	−	1.40240i	−0.00478505	−	0.112644i
$156$	−0.260804	+	0.946495i	−0.0208811	+	0.0757803i
$157$	9.34754	+	4.22535i	0.746015	+	0.337220i	0.748818	−	0.662776i	$-0.230622\pi$
$157$	9.34754	+	4.22535i	0.746015	+	0.337220i	−0.00280275	+	0.999996i	$0.500892\pi$
$158$	7.51867	−	3.92525i	0.598153	−	0.312276i
$159$	−1.20624	+	1.15609i	−0.0956614	+	0.0916840i
$160$	0.559316	+	0.567287i	0.0442178	+	0.0448480i
$161$	−14.0263	+	0.397088i	−1.10543	+	0.0312949i
$162$	−0.215962	+	1.16064i	−0.0169676	+	0.0911887i
$163$	−3.41099	+	6.76529i	−0.267169	+	0.529899i	−0.986297	−	0.164979i	$-0.947244\pi$
$163$	−3.41099	+	6.76529i	−0.267169	+	0.529899i	0.719128	+	0.694878i	$0.244542\pi$
$164$	−1.69567	+	0.144323i	−0.132409	+	0.0112697i
$165$	0.0361950	−	0.0831892i	0.00281778	−	0.00647627i
$166$	5.42569	+	0.616883i	0.421115	+	0.0478794i
$167$	15.3624	+	4.00005i	1.18878	+	0.309533i	0.793235	−	0.608916i	$-0.208395\pi$
$167$	15.3624	+	4.00005i	1.18878	+	0.309533i	0.395540	+	0.918449i	$0.370557\pi$
$168$	−12.6487	+	6.15442i	−0.975868	+	0.474823i
$169$	−8.07419	+	6.51945i	−0.621091	+	0.501496i
$170$	−0.448011	+	0.0253869i	−0.0343609	+	0.00194709i
$171$	6.70121	−	4.52923i	0.512454	−	0.346359i
$172$	1.45481	+	2.69304i	0.110928	+	0.205342i
$173$	−5.58759	−	12.8423i	−0.424817	−	0.976382i	−0.988615	−	0.150469i	$-0.951922\pi$
$173$	−5.58759	−	12.8423i	−0.424817	−	0.976382i	0.563798	−	0.825913i	$-0.309340\pi$
$174$	3.08033	+	10.0583i	0.233519	+	0.762520i
$175$	7.82682	−	21.1924i	0.591652	−	1.60200i
$176$	−0.619315	+	0.664763i	−0.0466827	+	0.0501084i
$177$	−5.61972	+	5.69981i	−0.422404	+	0.428424i
$178$	−0.000707801		0.0500133i	−5.30519e−5		0.00374865i
$179$	−14.0117	+	8.90325i	−1.04729	+	0.665460i	−0.944254	−	0.329218i	$-0.893215\pi$
$179$	−14.0117	+	8.90325i	−1.04729	+	0.665460i	−0.103032	+	0.994678i	$0.532854\pi$
$180$	0.0349041	+	0.142278i	0.00260160	+	0.0106048i
$181$	1.40141	−	0.281335i	0.104166	−	0.0209115i	−0.144464	−	0.989510i	$-0.546146\pi$
$181$	1.40141	−	0.281335i	0.104166	−	0.0209115i	0.248630	+	0.968599i	$0.420020\pi$
$182$	8.61429	+	1.47707i	0.638534	+	0.109488i
$183$	−1.81473	−	3.14321i	−0.134149	−	0.232353i
$184$	4.72193	−	8.17862i	0.348105	−	0.602936i
$185$	0.483699	−	0.582004i	0.0355623	−	0.0427898i
$186$	−5.08341	+	4.60324i	−0.372733	+	0.337526i
$187$	0.0584072	+	0.587689i	0.00427116	+	0.0429761i
$188$	−2.28967	+	4.23848i	−0.166991	+	0.309123i
$189$	−4.55523	−	0.387707i	−0.331344	−	0.0282015i
$190$	−1.20975	+	1.96475i	−0.0877642	+	0.142538i
$191$	−1.45692	−	1.96988i	−0.105419	−	0.142536i	0.748123	−	0.663560i	$-0.230955\pi$
$191$	−1.45692	−	1.96988i	−0.105419	−	0.142536i	−0.853542	+	0.521025i	$0.825550\pi$
$192$	0.863570	−	8.68918i	0.0623228	−	0.627088i
$193$	−11.4989	−	7.77190i	−0.827709	−	0.559434i	0.0712538	−	0.997458i	$-0.477300\pi$
$193$	−11.4989	−	7.77190i	−0.827709	−	0.559434i	−0.898963	+	0.438024i	$0.855678\pi$
$194$	2.68124	+	1.59903i	0.192502	+	0.114803i
$195$	0.145898	−	0.363081i	0.0104480	−	0.0260008i
$196$	−4.41853	−	7.17615i	−0.315609	−	0.512582i
$197$	7.77231	+	15.4155i	0.553754	+	1.09831i	0.980971	+	0.194156i	$0.0621969\pi$
$197$	7.77231	+	15.4155i	0.553754	+	1.09831i	−0.427217	+	0.904149i	$0.640506\pi$
$198$	−0.425607	+	0.123781i	−0.0302465	+	0.00879672i
$199$	0.0617066	+	0.0322150i	0.00437427	+	0.00228366i	0.464980	−	0.885321i	$-0.346061\pi$
$199$	0.0617066	+	0.0322150i	0.00437427	+	0.00228366i	−0.460606	+	0.887605i	$0.652368\pi$
$200$	9.38353	+	11.9638i	0.663516	+	0.845966i
$201$	5.33260	+	11.3657i	0.376133	+	0.801677i
$202$	−0.0534876	−	0.754676i	−0.00376337	−	0.0530988i
$203$	−37.5799	+	15.7221i	−2.63759	+	1.10347i
$204$	−0.650070	−	0.697774i	−0.0455140	−	0.0488540i
$205$	0.678004	+	0.0191944i	0.0473539	+	0.00134060i
$206$	−1.80545	+	8.37730i	−0.125791	+	0.583674i
$207$	2.67955	−	1.49689i	0.186242	−	0.104041i
$208$	−2.58899	+	2.94166i	−0.179514	+	0.203968i
$209$	2.65111	+	1.48100i	0.183381	+	0.102443i
$210$	1.22966	−	0.434467i	0.0848546	−	0.0299811i
$211$	5.84965	−	8.39625i	0.402707	−	0.578021i	−0.566564	−	0.824018i	$-0.691728\pi$
$211$	5.84965	−	8.39625i	0.402707	−	0.578021i	0.969271	+	0.245996i	$0.0791151\pi$
$212$	0.964258	−	0.310292i	0.0662255	−	0.0213109i
$213$	4.22090	+	15.3182i	0.289211	+	1.04959i
$214$	−0.486198	+	3.09811i	−0.0332358	+	0.211782i
$215$	−0.454867	−	1.13198i	−0.0310217	−	0.0772004i
$216$	1.82961	−	2.47379i	0.124489	−	0.168320i
$217$	−19.6853	−	17.8259i	−1.33633	−	1.21010i
$218$	−13.4665	+	1.91851i	−0.912064	+	0.129938i
$219$	2.08897	−	0.543925i	0.141159	−	0.0367550i
$220$	−0.0417986	+	0.0357505i	−0.00281806	+	0.00241030i
$221$	0.323550	+	2.52665i	0.0217643	+	0.169961i
$222$	−3.69732			−0.248148
$223$	14.9078	+	0.870376i	0.998300	+	0.0582847i
$223$	14.9078	+	0.870376i	0.998300	+	0.0582847i
$224$	15.0723			1.00706
$225$	0.627673	+	4.90159i	0.0418448	+	0.326772i
$226$	−14.3168	+	12.2453i	−0.952342	+	0.814543i
$227$	0.155952	−	0.0406067i	0.0103509	−	0.00269516i	−0.246799	−	0.969067i	$-0.579379\pi$
$227$	0.155952	−	0.0406067i	0.0103509	−	0.00269516i	0.257150	+	0.966372i	$0.417217\pi$
$228$	−4.85464	+	0.691619i	−0.321506	+	0.0458036i
$229$	15.4023	+	13.9475i	1.01782	+	0.921675i	0.996945	−	0.0781075i	$-0.0248877\pi$
$229$	15.4023	+	13.9475i	1.01782	+	0.921675i	0.0208706	+	0.999782i	$0.493356\pi$
$230$	−0.520646	+	0.703960i	−0.0343304	+	0.0464177i
$231$	−0.639984	−	1.59266i	−0.0421079	−	0.104789i
$232$	4.25055	−	27.0849i	0.279062	−	1.77821i
$233$	7.67057	+	27.8376i	0.502516	+	1.82370i	0.564247	+	0.825606i	$0.309167\pi$
$233$	7.67057	+	27.8376i	0.502516	+	1.82370i	−0.0617311	+	0.998093i	$0.519662\pi$
$234$	−1.81986	+	0.585619i	−0.118968	+	0.0382831i
$235$	1.09758	−	1.57540i	0.0715981	−	0.102768i
$236$	4.57556	−	1.61665i	0.297844	−	0.105235i
$237$	−6.27207	−	3.50379i	−0.407415	−	0.227595i
$238$	−5.60901	+	6.37307i	−0.363578	+	0.413105i
$239$	−18.4966	+	10.3328i	−1.19645	+	0.668376i	−0.953421	−	0.301644i	$-0.902465\pi$
$239$	−18.4966	+	10.3328i	−1.19645	+	0.668376i	−0.243027	+	0.970019i	$0.578140\pi$
$240$	−0.123192	+	0.571613i	−0.00795202	+	0.0368975i
$241$	28.0517	+	0.794148i	1.80697	+	0.0511556i	0.915591	−	0.402110i	$-0.131723\pi$
$241$	28.0517	+	0.794148i	1.80697	+	0.0511556i	0.891375	+	0.453266i	$0.149741\pi$
$242$	8.73865	+	9.37993i	0.561742	+	0.602964i
$243$	0.922520	−	0.385950i	0.0591797	−	0.0247587i
$244$	0.155565	+	2.19492i	0.00995902	+	0.140515i
$245$	1.42669	+	3.04079i	0.0911476	+	0.194269i
$246$	−2.04513	−	2.60749i	−0.130393	−	0.166248i
$247$	11.6108	+	6.06162i	0.738778	+	0.385691i
$248$	17.1624	−	4.99141i	1.08982	−	0.316955i
$249$	−2.08240	−	4.13019i	−0.131967	−	0.261740i
$250$	−1.48695	−	2.41496i	−0.0940428	−	0.152735i
$251$	−5.05506	+	12.5800i	−0.319073	+	0.794043i	0.679124	+	0.734023i	$0.262360\pi$
$251$	−5.05506	+	12.5800i	−0.319073	+	0.794043i	−0.998197	+	0.0600201i	$0.980884\pi$
$252$	2.38049	+	1.41966i	0.149957	+	0.0894305i
$253$	0.954748	+	0.645297i	0.0600245	+	0.0405695i
$254$	0.197890	−	1.99116i	0.0124167	−	0.124936i
$255$	0.226019	+	0.305597i	0.0141538	+	0.0191372i
$256$	−6.85704	+	11.1365i	−0.428565	+	0.696034i
$257$	−13.3288	−	1.13445i	−0.831427	−	0.0707649i	−0.338641	−	0.940915i	$-0.609967\pi$
$257$	−13.3288	−	1.13445i	−0.831427	−	0.0707649i	−0.492786	+	0.870151i	$0.664021\pi$
$258$	−2.83289	+	5.24405i	−0.176368	+	0.326481i
$259$	−1.41599	−	14.2476i	−0.0879852	−	0.885301i
$260$	−0.175848	+	0.159237i	−0.0109056	+	0.00987548i
$261$	5.69530	−	6.85279i	0.352530	−	0.424177i
$262$	−4.33724	+	7.51231i	−0.267955	+	0.464112i
$263$	−10.3852	−	17.9878i	−0.640381	−	1.10917i	−0.985348	−	0.170558i	$-0.945443\pi$
$263$	−10.3852	−	17.9878i	−0.640381	−	1.10917i	0.344966	−	0.938615i	$-0.387890\pi$
$264$	1.13859	+	0.195231i	0.0700753	+	0.0120156i
$265$	−0.395830	+	0.0794635i	−0.0243156	+	0.00488141i
$266$	10.4009	+	42.3967i	0.637720	+	2.59951i
$267$	0.0357597	−	0.0227222i	0.00218846	−	0.00139058i
$268$	0.107708	−	7.61066i	0.00657932	−	0.464895i
$269$	15.4785	−	15.6991i	0.943741	−	0.957192i	−0.0554065	−	0.998464i	$-0.517645\pi$
$269$	15.4785	−	15.6991i	0.943741	−	0.957192i	0.999148	+	0.0412719i	$0.0131410\pi$
$270$	−0.194454	+	0.208723i	−0.0118341	+	0.0127025i
$271$	6.87912	−	18.6264i	0.417877	−	1.13147i	−0.539337	−	0.842090i	$-0.681325\pi$
$271$	6.87912	−	18.6264i	0.417877	−	1.13147i	0.957214	−	0.289382i	$-0.0934497\pi$
$272$	−1.11464	−	3.63968i	−0.0675850	−	0.220688i
$273$	−2.95364	−	6.78852i	−0.178762	−	0.410860i
$274$	−4.35451	−	8.06076i	−0.263065	−	0.486968i
$275$	−1.53715	+	1.03893i	−0.0926937	+	0.0626500i
$276$	−1.85784	+	0.105276i	−0.111829	+	0.00633688i
$277$	−0.326780	+	0.263856i	−0.0196343	+	0.0158536i	−0.637987	−	0.770047i	$-0.720233\pi$
$277$	−0.326780	+	0.263856i	−0.0196343	+	0.0158536i	0.618353	+	0.785901i	$0.287800\pi$
$278$	12.0598	−	5.86790i	0.723301	−	0.351933i
$279$	5.62156	+	1.46374i	0.336554	+	0.0876319i
$280$	−3.37723	−	0.383979i	−0.201828	−	0.0229472i
$281$	9.62274	−	22.1165i	0.574044	−	1.31936i	−0.349883	−	0.936793i	$-0.613779\pi$
$281$	9.62274	−	22.1165i	0.574044	−	1.31936i	0.923928	−	0.382567i	$-0.124960\pi$
$282$	−9.34694	+	0.795542i	−0.556602	+	0.0473738i
$283$	12.8188	−	25.4245i	0.761997	−	1.51133i	−0.0946972	−	0.995506i	$-0.530188\pi$
$283$	12.8188	−	25.4245i	0.761997	−	1.51133i	0.856694	−	0.515825i	$-0.172514\pi$
$284$	1.76219	−	9.47053i	0.104567	−	0.561972i
$285$	1.95364	−	0.0553080i	0.115724	−	0.00327616i
$286$	−0.503936	−	0.511118i	−0.0297983	−	0.0302230i
$287$	9.26469	−	8.87949i	0.546878	−	0.524140i
$288$	−2.92257	+	1.52578i	−0.172214	+	0.0899074i
$289$	13.2362	+	5.98313i	0.778598	+	0.351949i
$290$	−0.675243	+	2.45055i	−0.0396516	+	0.143901i
$291$	−0.112230	−	2.64199i	−0.00657906	−	0.154876i
$292$	−1.28310	−	0.257585i	−0.0750879	−	0.0150740i
$293$	−11.9751	−	4.61625i	−0.699590	−	0.269684i	−0.0163381	−	0.999867i	$-0.505201\pi$
$293$	−11.9751	−	4.61625i	−0.699590	−	0.269684i	−0.683252	+	0.730182i	$0.739435\pi$
$294$	6.97035	−	14.8564i	0.406519	−	0.866442i
$295$	−1.88477	+	0.434197i	−0.109736	+	0.0252800i
$296$	8.66496	+	4.21607i	0.503640	+	0.245054i
$297$	0.285321	+	0.244036i	0.0165560	+	0.0141604i
$298$	−7.77549	+	11.8626i	−0.450422	+	0.687184i
$299$	4.19508	+	2.66561i	0.242608	+	0.154156i
$300$	0.957994	−	2.83865i	0.0553098	−	0.163889i
$301$	−21.2928	−	8.90815i	−1.22730	−	0.513457i
$302$	−3.20778	−	8.68560i	−0.184587	−	0.499800i
$303$	−0.509800	+	0.388326i	−0.0292873	+	0.0223087i
$304$	−18.6319	−	5.99562i	−1.06861	−	0.343873i
$305$	0.0372214	−	0.876222i	0.00213129	−	0.0501723i
$306$	0.442456	−	1.80356i	0.0252935	−	0.103103i
$307$	−2.41188	−	7.14668i	−0.137653	−	0.407882i	0.856462	−	0.516210i	$-0.172658\pi$
$307$	−2.41188	−	7.14668i	−0.137653	−	0.407882i	−0.994115	+	0.108328i	$0.965450\pi$
$308$	−0.0735693	+	1.03802i	−0.00419200	+	0.0591465i
$309$	6.77311	−	2.61096i	0.385309	−	0.148532i
$310$	−1.63329	+	0.280055i	−0.0927644	+	0.0159061i
$311$	15.3681	+	18.4914i	0.871442	+	1.04855i	0.998395	+	0.0566411i	$0.0180391\pi$
$311$	15.3681	+	18.4914i	0.871442	+	1.04855i	−0.126952	+	0.991909i	$0.540519\pi$
$312$	4.93276	+	0.702749i	0.279263	+	0.0397853i
$313$	25.7694	−	2.92990i	1.45657	−	0.165608i	0.651440	−	0.758701i	$-0.274165\pi$
$313$	25.7694	−	2.92990i	1.45657	−	0.165608i	0.805134	+	0.593093i	$0.202093\pi$
$314$	3.54621	−	11.5796i	0.200124	−	0.653474i
$315$	−0.878783	−	0.669388i	−0.0495138	−	0.0377157i
$316$	2.48988	+	3.57383i	0.140067	+	0.201044i
$317$	21.0482	+	15.1111i	1.18218	+	0.848724i	0.991135	−	0.132857i	$-0.0424152\pi$
$317$	21.0482	+	15.1111i	1.18218	+	0.848724i	0.191047	+	0.981581i	$0.438812\pi$
$318$	1.53467	+	1.23916i	0.0860598	+	0.0694884i
$319$	3.26005	+	0.751022i	0.182528	+	0.0420492i
$320$	1.30216	−	1.66023i	0.0727931	−	0.0928094i
$321$	2.42057	−	1.09417i	0.135103	−	0.0610703i
$322$	2.56828	+	16.3653i	0.143124	+	0.912003i
$323$	−10.9273	+	6.51675i	−0.608009	+	0.362602i
$324$	−0.605297	−	0.0342997i	−0.0336276	−	0.00190554i
$325$	−6.50050	+	4.66690i	−0.360583	+	0.258873i
$326$	8.43366	+	2.97980i	0.467097	+	0.165036i
$327$	7.61228	+	8.64923i	0.420960	+	0.478304i
$328$	1.81959	+	8.44293i	0.100470	+	0.466183i
$329$	−6.64527	−	35.7136i	−0.366365	−	1.96895i
$330$	−0.102842	−	0.0299100i	−0.00566128	−	0.00164649i
$331$	13.7952	+	13.2216i	0.758252	+	0.726725i	0.967978	−	0.251035i	$-0.0807709\pi$
$331$	13.7952	+	13.2216i	0.758252	+	0.726725i	−0.209726	+	0.977760i	$0.567257\pi$
$332$	0.0396827	+	2.80399i	0.00217787	+	0.153889i
$333$	1.71685	+	2.61931i	0.0940829	+	0.143537i
$334$	2.38044	−	18.5892i	0.130252	−	1.01715i
$335$	−0.385326	+	3.00907i	−0.0210526	+	0.164403i
$336$	6.06471	+	9.25260i	0.330857	+	0.504770i
$337$	−0.252890	−	17.8692i	−0.0137758	−	0.973398i	−0.880343	−	0.474338i	$-0.842688\pi$
$337$	−0.252890	−	17.8692i	−0.0137758	−	0.973398i	0.866567	−	0.499060i	$-0.166321\pi$
$338$	8.84504	+	8.47728i	0.481107	+	0.461103i
$339$	15.3230	+	4.45644i	0.832230	+	0.242041i
$340$	−0.0421548	−	0.226552i	−0.00228617	−	0.0122865i
$341$	0.459488	+	2.13203i	0.0248827	+	0.115456i
$342$	−6.30860	−	7.16796i	−0.341130	−	0.387599i
$343$	29.7445	+	10.5094i	1.60605	+	0.567454i
$344$	12.6189	−	9.05948i	0.680366	−	0.488454i
$345$	0.740470	+	0.0419593i	0.0398656	+	0.00225902i
$346$	−14.2005	+	8.46882i	−0.763423	+	0.455286i
$347$	−1.28791	−	8.20669i	−0.0691386	−	0.440558i	−0.997607	−	0.0691457i	$-0.977973\pi$
$347$	−1.28791	−	8.20669i	−0.0691386	−	0.440558i	0.928468	−	0.371412i	$-0.121126\pi$
$348$	−4.92260	+	2.22516i	−0.263879	+	0.119281i
$349$	17.5079	−	22.3222i	0.937178	−	1.19488i	−0.0434614	−	0.999055i	$-0.513839\pi$
$349$	17.5079	−	22.3222i	0.937178	−	1.19488i	0.980639	−	0.195824i	$-0.0627380\pi$
$350$	−25.9900	−	5.98736i	−1.38922	−	0.320038i
$351$	1.25992	+	1.01732i	0.0672498	+	0.0543004i
$352$	−1.00551	−	0.721886i	−0.0535940	−	0.0384767i
$353$	−10.0834	−	14.4731i	−0.536684	−	0.770324i	0.456141	−	0.889908i	$-0.349231\pi$
$353$	−10.0834	−	14.4731i	−0.536684	−	0.770324i	−0.992824	+	0.119584i	$0.961844\pi$
$354$	7.51719	+	5.72600i	0.399534	+	0.304334i
$355$	−1.12426	+	3.67111i	−0.0596697	+	0.194842i
$356$	−0.0255220	+	0.00290177i	−0.00135266	+	0.000153793i
$357$	7.11944	+	1.01427i	0.376801	+	0.0536811i
$358$	12.5268	+	15.0727i	0.662063	+	0.796617i
$359$	0.0515092	−	0.00883214i	0.00271855	−	0.000466143i	−0.167641	−	0.985848i	$-0.553615\pi$
$359$	0.0515092	−	0.00883214i	0.00271855	−	0.000466143i	0.170360	+	0.985382i	$0.445507\pi$
$360$	0.693725	−	0.267423i	0.0365625	−	0.0140944i
$361$	−3.28179	+	46.3039i	−0.172726	+	2.43705i
$362$	−0.539589	−	1.59886i	−0.0283602	−	0.0840345i
$363$	2.58726	−	10.5463i	0.135796	−	0.553538i
$364$	−0.190491	+	4.48431i	−0.00998444	+	0.235042i
$365$	0.496527	+	0.159779i	0.0259894	+	0.00836323i
$366$	−3.40858	+	2.59639i	−0.178169	+	0.135715i
$367$	9.40951	+	25.4778i	0.491172	+	1.32993i	0.907246	+	0.420601i	$0.138181\pi$
$367$	9.40951	+	25.4778i	0.491172	+	1.32993i	−0.416073	+	0.909331i	$0.636594\pi$
$368$	−6.85195	−	2.86661i	−0.357183	−	0.149433i
$369$	−0.897579	+	2.65963i	−0.0467261	+	0.138455i
$370$	−0.754060	−	0.479140i	−0.0392017	−	0.0249093i
$371$	−4.18732	+	6.38837i	−0.217395	+	0.331668i
$372$	−2.67639	−	2.28913i	−0.138764	−	0.118686i
$373$	0.621548	+	0.302424i	0.0321825	+	0.0156589i	0.453544	−	0.891234i	$-0.350159\pi$
$373$	0.621548	+	0.302424i	0.0321825	+	0.0156589i	−0.421362	+	0.906893i	$0.638448\pi$
$374$	0.679427	−	0.156521i	0.0351323	−	0.00809349i
$375$	−1.02037	+	2.17479i	−0.0526917	+	0.112305i
$376$	22.8124	+	8.79393i	1.17646	+	0.453512i
$377$	14.1471	+	2.84006i	0.728613	+	0.146270i
$378$	0.229063	+	5.39232i	0.0117817	+	0.277351i
$379$	6.39173	−	23.1965i	0.328321	−	1.19152i	−0.593797	−	0.804615i	$-0.702372\pi$
$379$	6.39173	−	23.1965i	0.328321	−	1.19152i	0.922118	−	0.386908i	$-0.126457\pi$
$380$	−1.07972	−	0.488064i	−0.0553884	−	0.0250371i
$381$	−1.50249	+	0.784401i	−0.0769749	+	0.0401861i
$382$	−2.08827	+	2.00144i	−0.106845	+	0.102403i
$383$	−9.34644	−	9.47965i	−0.477581	−	0.484388i	0.430849	−	0.902424i	$-0.358214\pi$
$383$	−9.34644	−	9.47965i	−0.477581	−	0.484388i	−0.908430	+	0.418036i	$0.862718\pi$
$384$	−3.71342	+	0.105128i	−0.189500	+	0.00536477i
$385$	0.0758715	−	0.407756i	0.00386677	−	0.0207811i
$386$	−7.37662	+	14.6307i	−0.375460	+	0.744681i
$387$	5.03051	−	0.428160i	0.255715	−	0.0217646i
$388$	−0.639620	+	1.47008i	−0.0324718	+	0.0746319i
$389$	−29.8526	−	3.39414i	−1.51359	−	0.172090i	−0.683594	−	0.729862i	$-0.739584\pi$
$389$	−29.8526	−	3.39414i	−1.51359	−	0.172090i	−0.829994	+	0.557772i	$0.811656\pi$
$390$	−0.447047	−	0.116402i	−0.0226371	−	0.00589424i
$391$	−4.34142	+	2.11239i	−0.219555	+	0.106828i
$392$	−33.2763	+	26.8688i	−1.68071	+	1.35708i
$393$	7.33597	−	0.415698i	0.370051	−	0.0209692i
$394$	16.8861	−	11.4130i	0.850707	−	0.574978i
$395$	−0.825113	−	1.52739i	−0.0415159	−	0.0768514i
$396$	−0.0908135	−	0.208722i	−0.00456355	−	0.0104887i
$397$	3.17786	+	10.3768i	0.159492	+	0.520797i	0.999772	−	0.0213564i	$-0.00679848\pi$
$397$	3.17786	+	10.3768i	0.159492	+	0.520797i	−0.840280	+	0.542153i	$0.817609\pi$
$398$	0.0284707	−	0.0770893i	0.00142711	−	0.00386414i
$399$	25.2056	−	27.0552i	1.26186	−	1.35446i
$400$	8.39570	−	8.51535i	0.419785	−	0.425768i
$401$	−0.000425962		0.0300985i	−2.12715e−5		0.00150305i	−0.999910	−	0.0133993i	$-0.995735\pi$
$401$	−0.000425962		0.0300985i	−2.12715e−5		0.00150305i	0.999889	+	0.0149024i	$0.00474375\pi$
$402$	12.5097	−	7.94881i	0.623925	−	0.396451i
$403$	2.24127	+	9.13600i	0.111646	+	0.455096i
$404$	0.380929	−	0.0764722i	0.0189519	−	0.00380463i
$405$	0.238161	+	0.0408368i	0.0118343	+	0.00202920i
$406$	24.0458	+	41.6485i	1.19337	+	2.06698i
$407$	−0.587920	+	1.01831i	−0.0291421	+	0.0504756i
$408$	−3.09353	+	3.72225i	−0.153153	+	0.184279i
$409$	9.08031	−	8.22260i	0.448992	−	0.406581i	−0.415210	−	0.909725i	$-0.636292\pi$
$409$	9.08031	−	8.22260i	0.448992	−	0.406581i	0.864203	+	0.503144i	$0.167824\pi$
$410$	−0.0791918	−	0.796822i	−0.00391101	−	0.0393523i
$411$	−3.68850	+	6.82789i	−0.181940	+	0.336795i
$412$	−4.38501	−	0.373219i	−0.216034	−	0.0183872i
$413$	−19.1861	+	31.1603i	−0.944088	+	1.53330i
$414$	−2.15466	−	2.91330i	−0.105896	−	0.143181i
$415$	0.110536	−	1.11220i	0.00542598	−	0.0545958i
$416$	−4.42330	−	2.98963i	−0.216870	−	0.146579i
$417$	−9.75700	−	5.81884i	−0.477802	−	0.284950i
$418$	1.33671	−	3.32653i	0.0653806	−	0.162706i
$419$	−15.4432	−	25.0814i	−0.754452	−	1.22531i	−0.968629	−	0.248513i	$-0.920058\pi$
$419$	−15.4432	−	25.0814i	−0.754452	−	1.22531i	0.214176	−	0.976795i	$-0.431293\pi$
$420$	0.301519	+	0.598027i	0.0147126	+	0.0291807i
$421$	−14.2432	+	4.14241i	−0.694172	+	0.201889i	−0.607466	−	0.794345i	$-0.707814\pi$
$421$	−14.2432	+	4.14241i	−0.694172	+	0.201889i	−0.0867053	+	0.996234i	$0.527634\pi$
$422$	−10.7092	−	5.59091i	−0.521315	−	0.272161i
$423$	4.90384	+	6.25227i	0.238433	+	0.303996i
$424$	−2.18359	−	4.65404i	−0.106045	−	0.226020i
$425$	−0.549547	−	7.75376i	−0.0266569	−	0.376113i
$426$	17.3048	−	7.23970i	0.838418	−	0.350764i
$427$	−11.3105	−	12.1405i	−0.547355	−	0.587522i
$428$	−1.60983	−	0.0455747i	−0.0778142	−	0.00220293i
$429$	−0.128091	+	0.594342i	−0.00618427	+	0.0286951i
$430$	−1.25734	+	0.702394i	−0.0606345	+	0.0338724i
$431$	8.07773	−	9.17808i	0.389090	−	0.442093i	−0.522844	−	0.852428i	$-0.675129\pi$
$431$	8.07773	−	9.17808i	0.389090	−	0.442093i	0.911935	+	0.410336i	$0.134588\pi$
$432$	−2.11261	−	1.18017i	−0.101643	−	0.0567812i
$433$	−17.9619	+	6.34635i	−0.863195	+	0.304986i	−0.727787	−	0.685804i	$-0.759451\pi$
$433$	−17.9619	+	6.34635i	−0.863195	+	0.304986i	−0.135409	+	0.990790i	$0.543235\pi$
$434$	−17.9223	+	25.7246i	−0.860297	+	1.23482i
$435$	2.04960	−	0.659548i	0.0982709	−	0.0316229i
$436$	−1.85565	−	6.73443i	−0.0888697	−	0.322521i
$437$	−3.84884	+	24.5252i	−0.184115	+	1.17320i
$438$	−0.950183	−	2.36462i	−0.0454015	−	0.112986i
$439$	−21.1244	+	28.5621i	−1.00821	+	1.36320i	−0.0776850	+	0.996978i	$0.524753\pi$
$439$	−21.1244	+	28.5621i	−1.00821	+	1.36320i	−0.930529	+	0.366218i	$0.880653\pi$
$440$	0.206912	+	0.187368i	0.00986415	+	0.00893240i
$441$	−13.7614	+	1.96053i	−0.655307	+	0.0933586i
$442$	2.91019	−	0.757755i	0.138424	−	0.0360427i
$443$	−17.4352	+	14.9124i	−0.828372	+	0.708511i	−0.959149	−	0.282901i	$-0.908703\pi$
$443$	−17.4352	+	14.9124i	−0.828372	+	0.708511i	0.130777	+	0.991412i	$0.458253\pi$
$444$	−0.241172	−	1.88335i	−0.0114455	−	0.0893798i
$445$	0.0102377			0.000485313
$446$	−1.21625	−	17.5876i	−0.0575912	−	0.832796i
$447$	12.0144			0.568263
$448$	−5.07055	−	39.5966i	−0.239561	−	1.87077i
$449$	−21.4878	+	18.3787i	−1.01407	+	0.867342i	−0.991197	−	0.132396i	$-0.957733\pi$
$449$	−21.4878	+	18.3787i	−1.01407	+	0.867342i	−0.0228768	+	0.999738i	$0.507283\pi$
$450$	5.64565	−	1.47001i	0.266138	−	0.0692970i
$451$	−1.04335	+	0.148641i	−0.0491295	+	0.00699925i
$452$	−7.17139	−	6.49399i	−0.337314	−	0.305452i
$453$	−4.66364	+	6.30565i	−0.219117	+	0.296265i
$454$	−0.0709360	−	0.176531i	−0.00332919	−	0.00828501i
$455$	0.277344	−	1.76727i	0.0130021	−	0.0828507i
$456$	6.61103	+	23.9924i	0.309590	+	1.12355i
$457$	−25.6398	+	8.25073i	−1.19938	+	0.385953i	−0.837587	−	0.546305i	$-0.816034\pi$
$457$	−25.6398	+	8.25073i	−1.19938	+	0.385953i	−0.361795	+	0.932258i	$0.617836\pi$
$458$	14.0229	−	20.1276i	0.655247	−	0.940503i
$459$	−1.48316	+	0.524033i	−0.0692278	+	0.0244597i
$460$	−0.392545	−	0.219289i	−0.0183025	−	0.0102244i
$461$	10.3686	−	11.7810i	0.482912	−	0.548694i	−0.457288	−	0.889319i	$-0.651179\pi$
$461$	10.3686	−	11.7810i	0.482912	−	0.548694i	0.940199	+	0.340624i	$0.110638\pi$
$462$	−1.76904	+	0.988247i	−0.0823034	+	0.0459774i
$463$	−1.95429	+	9.06791i	−0.0908233	+	0.421422i	0.909164	+	0.416438i	$0.136722\pi$
$463$	−1.95429	+	9.06791i	−0.0908233	+	0.421422i	−0.999988	+	0.00498402i	$0.998414\pi$
$464$	−21.5539	−	0.610196i	−1.00062	−	0.0283276i
$465$	0.956816	+	1.02703i	0.0443713	+	0.0476274i
$466$	31.4476	−	13.1566i	1.45678	−	0.609466i
$467$	0.0459608	+	0.648477i	0.00212681	+	0.0300079i	0.998448	−	0.0556856i	$-0.0177344\pi$
$467$	0.0459608	+	0.648477i	0.00212681	+	0.0300079i	−0.996322	+	0.0856935i	$0.972689\pi$
$468$	−0.417011	−	0.888804i	−0.0192764	−	0.0410850i
$469$	35.4215	+	45.1616i	1.63561	+	2.08537i
$470$	−2.00938	−	1.04903i	−0.0926858	−	0.0483882i
$471$	−9.85005	+	2.86473i	−0.453866	+	0.132000i
$472$	−11.0877	−	21.9912i	−0.510354	−	1.01223i
$473$	0.993839	+	1.61410i	0.0456968	+	0.0742163i
$474$	−3.16243	+	7.87001i	−0.145255	+	0.361481i
$475$	−34.3280	−	20.4724i	−1.57508	−	0.939336i
$476$	−3.61220	−	2.44142i	−0.165565	−	0.111902i
$477$	0.165238	−	1.66261i	0.00756571	−	0.0761257i
$478$	14.8734	+	20.1102i	0.680293	+	0.919817i
$479$	22.7853	−	37.0056i	1.04108	−	1.69083i	0.418679	−	0.908134i	$-0.362493\pi$
$479$	22.7853	−	37.0056i	1.04108	−	1.69083i	0.622405	−	0.782695i	$-0.286156\pi$
$480$	−0.793779	−	0.0675605i	−0.0362309	−	0.00308370i
$481$	−2.41048	+	4.46211i	−0.109908	+	0.203455i
$482$	−3.27647	−	32.9676i	−0.149239	−	1.50164i
$483$	10.4011	−	9.41868i	0.473269	−	0.428565i
$484$	−4.20795	+	5.06315i	−0.191270	+	0.230143i
$485$	0.319489	−	0.553371i	0.0145072	−	0.0251273i
$486$	−0.590282	−	1.02240i	−0.0267757	−	0.0463769i
$487$	38.6717	+	6.63092i	1.75238	+	0.300476i	0.953584	−	0.301126i	$-0.0973626\pi$
$487$	38.6717	+	6.63092i	1.75238	+	0.300476i	0.798796	+	0.601602i	$0.205471\pi$
$488$	10.9489	−	2.19802i	0.495634	−	0.0994996i
$489$	−1.80518	−	7.35836i	−0.0816329	−	0.332756i
$490$	3.34684	−	2.12663i	0.151195	−	0.0960712i
$491$	−0.0718680	+	5.07820i	−0.00324336	+	0.229176i	0.991691	+	0.128646i	$0.0410629\pi$
$491$	−0.0718680	+	5.07820i	−0.00324336	+	0.229176i	−0.994934	+	0.100530i	$0.967946\pi$
$492$	1.19481	−	1.21184i	0.0538661	−	0.0546338i
$493$	−9.55427	+	10.2554i	−0.430303	+	0.461880i
$494$	5.35709	−	14.5052i	0.241027	−	0.652621i
$495$	0.0265655	+	0.0867456i	0.00119403	+	0.00389892i
$496$	−5.60835	−	12.8900i	−0.251822	−	0.578778i
$497$	34.5254	+	63.9109i	1.54867	+	2.86680i
$498$	−4.52420	+	3.05782i	−0.202734	+	0.137024i
$499$	34.6597	−	1.96402i	1.55158	−	0.0879216i	0.740179	−	0.672410i	$-0.234741\pi$
$499$	34.6597	−	1.96402i	1.55158	−	0.0879216i	0.811402	+	0.584488i	$0.198705\pi$
$500$	1.13314	−	0.914948i	0.0506756	−	0.0409177i
$501$	−14.2745	+	6.94550i	−0.637740	+	0.310302i
$502$	15.4892	+	4.03309i	0.691319	+	0.180005i
$503$	17.7118	+	2.01377i	0.789731	+	0.0897898i	0.498530	−	0.866872i	$-0.333873\pi$
$503$	17.7118	+	2.01377i	0.789731	+	0.0897898i	0.291200	+	0.956662i	$0.405945\pi$
$504$	5.61204	−	12.8985i	0.249980	−	0.574545i
$505$	−0.154296	+	0.0131325i	−0.00686608	+	0.000584389i
$506$	0.612477	−	1.21478i	0.0272279	−	0.0540034i
$507$	1.89840	−	10.2025i	0.0843108	−	0.453111i
$508$	1.02717	−	0.0290793i	0.0455731	−	0.00129018i
$509$	−23.5445	−	23.8801i	−1.04359	−	1.05846i	−0.998229	−	0.0594943i	$-0.981051\pi$
$509$	−23.5445	−	23.8801i	−1.04359	−	1.05846i	−0.0453626	−	0.998971i	$-0.514444\pi$
$510$	0.323963	−	0.310493i	0.0143453	−	0.0137489i
$511$	8.74813	−	4.56711i	0.386995	−	0.202037i
$512$	20.8394	+	9.42001i	0.920980	+	0.416309i
$513$	−2.14862	+	7.79766i	−0.0948641	+	0.344275i
$514$	0.670248	+	15.7782i	0.0295634	+	0.695945i
$515$	1.71972	+	0.345236i	0.0757797	+	0.0152129i
$516$	−2.85601	−	1.10096i	−0.125729	−	0.0484670i
$517$	−1.26717	+	2.70081i	−0.0557302	+	0.118782i
$518$	−16.4716	+	3.79459i	−0.723721	+	0.166725i
$519$	12.5936	+	6.12760i	0.552797	+	0.268972i
$520$	0.914955	+	0.782565i	0.0401234	+	0.0343178i
$521$	14.4479	−	22.0424i	0.632974	−	0.965695i	−0.366404	−	0.930456i	$-0.619411\pi$
$521$	14.4479	−	22.0424i	0.632974	−	0.965695i	0.999379	−	0.0352392i	$-0.0112193\pi$
$522$	−8.87865	−	5.64162i	−0.388608	−	0.246927i
$523$	−1.33809	+	3.96492i	−0.0585107	+	0.173374i	−0.972779	−	0.231736i	$-0.925559\pi$
$523$	−1.33809	+	3.96492i	−0.0585107	+	0.173374i	0.914268	+	0.405110i	$0.132767\pi$
$524$	−4.10955	−	1.71929i	−0.179526	−	0.0751075i
$525$	7.82682	+	21.1924i	0.341590	+	0.924913i
$526$	−19.5064	+	14.8585i	−0.850520	+	0.647859i
$527$	−8.69836	−	2.79907i	−0.378906	−	0.121930i
$528$	0.0385599	−	0.907730i	0.00167810	−	0.0395039i
$529$	3.23540	−	13.1883i	0.140669	−	0.573404i
$530$	0.152408	+	0.451601i	0.00662017	+	0.0196163i
$531$	0.565886	−	7.98429i	0.0245574	−	0.346489i
$532$	−20.9176	+	8.06351i	−0.906895	+	0.349598i
$533$	−4.48018	+	0.768204i	−0.194058	+	0.0332746i
$534$	−0.0319700	−	0.0384675i	−0.00138348	−	0.00166465i
$535$	0.635462	+	0.0905314i	0.0274734	+	0.00391401i
$536$	−38.3814	+	4.36384i	−1.65782	+	0.188489i
$537$	4.86118	−	15.8734i	0.209775	−	0.684988i
$538$	−20.7047	−	15.7712i	−0.892645	−	0.679947i
$539$	−2.98334	−	4.28211i	−0.128501	−	0.184443i
$540$	−0.119004	−	0.0854364i	−0.00512111	−	0.00367660i
$541$	31.2453	+	25.2288i	1.34334	+	1.08467i	0.988739	+	0.149652i	$0.0478154\pi$
$541$	31.2453	+	25.2288i	1.34334	+	1.08467i	0.354600	+	0.935018i	$0.384617\pi$
$542$	−22.8431	−	5.26239i	−0.981194	−	0.226039i
$543$	−0.882131	+	1.12470i	−0.0378559	+	0.0482653i
$544$	4.72566	−	2.13613i	0.202611	−	0.0915860i
$545$	0.431643	+	2.75047i	0.0184895	+	0.117817i
$546$	−7.50647	+	4.47667i	−0.321247	+	0.191584i
$547$	20.5664	+	1.16541i	0.879354	+	0.0498293i	0.490471	−	0.871458i	$-0.336825\pi$
$547$	20.5664	+	1.16541i	0.879354	+	0.0498293i	0.388883	+	0.921287i	$0.372861\pi$
$548$	3.82196	−	2.74390i	0.163266	−	0.117214i
$549$	3.42214	+	1.20912i	0.146053	+	0.0516039i
$550$	1.44709	+	1.64422i	0.0617042	+	0.0701096i
$551$	15.1838	+	70.4530i	0.646851	+	3.00140i
$552$	1.72758	+	9.28450i	0.0735305	+	0.395174i
$553$	−31.5381	−	9.17234i	−1.34114	−	0.390047i
$554$	0.357978	+	0.343094i	0.0152090	+	0.0145767i
$555$	0.0107089	+	0.756689i	0.000454566	+	0.0321197i
$556$	3.77565	+	5.76031i	0.160123	+	0.244291i
$557$	4.75901	−	37.1638i	0.201646	−	1.57468i	−0.502470	−	0.864594i	$-0.667575\pi$
$557$	4.75901	−	37.1638i	0.201646	−	1.57468i	0.704116	−	0.710085i	$-0.251343\pi$
$558$	0.871076	−	6.80236i	0.0368756	−	0.287967i
$559$	4.48187	+	6.83775i	0.189563	+	0.289206i
$560$	0.0378286	+	2.67297i	0.00159855	+	0.112954i
$561$	−0.426376	−	0.408649i	−0.0180016	−	0.0172532i
$562$	−27.3414	−	7.95182i	−1.15333	−	0.335427i
$563$	3.90326	+	20.9773i	0.164503	+	0.884086i	0.960394	+	0.278646i	$0.0898857\pi$
$563$	3.90326	+	20.9773i	0.164503	+	0.884086i	−0.795891	+	0.605440i	$0.792997\pi$
$564$	−1.01493	−	4.70927i	−0.0427361	−	0.198296i
$565$	2.54757	+	2.89460i	0.107177	+	0.121777i
$566$	−31.6944	−	11.1983i	−1.33221	−	0.470701i
$567$	3.71373	−	2.66620i	0.155962	−	0.111970i
$568$	−48.8105	−	2.76588i	−2.04804	−	0.116054i
$569$	−32.2479	+	19.2318i	−1.35190	+	0.806241i	−0.991938	−	0.126725i	$-0.959553\pi$
$569$	−32.2479	+	19.2318i	−1.35190	+	0.806241i	−0.359964	+	0.932966i	$0.617211\pi$
$570$	−0.357719	−	2.27942i	−0.0149832	−	0.0954746i
$571$	−5.90345	+	2.66853i	−0.247052	+	0.111674i	−0.531625	−	0.846980i	$-0.678418\pi$
$571$	−5.90345	+	2.66853i	−0.247052	+	0.111674i	0.284573	+	0.958654i	$0.408148\pi$
$572$	0.227483	−	0.290035i	0.00951154	−	0.0121270i
$573$	2.38758	+	0.550029i	0.0997424	+	0.0229778i
$574$	−11.7872	−	9.51747i	−0.491987	−	0.397252i
$575$	−12.3209	−	8.84553i	−0.513817	−	0.368884i
$576$	4.99158	+	7.16462i	0.207982	+	0.298526i
$577$	−19.1157	−	14.5609i	−0.795798	−	0.606176i	0.126805	−	0.991928i	$-0.459528\pi$
$577$	−19.1157	−	14.5609i	−0.795798	−	0.606176i	−0.922603	+	0.385751i	$0.873942\pi$
$578$	5.02146	−	16.3968i	0.208865	−	0.682016i
$579$	13.7902	−	1.56790i	0.573100	−	0.0651596i
$580$	−1.29231	−	0.184110i	−0.0536603	−	0.00764474i
$581$	−13.5159	−	16.2628i	−0.560735	−	0.674696i
$582$	−3.07694	+	0.527595i	−0.127543	+	0.0218695i
$583$	0.585316	−	0.225633i	0.0242413	−	0.00934475i
$584$	−0.469558	+	6.62517i	−0.0194304	+	0.274151i
$585$	0.125123	+	0.370754i	0.00517320	+	0.0153288i
$586$	−3.60994	+	14.7150i	−0.149125	+	0.607873i
$587$	−0.543375	+	12.7915i	−0.0224275	+	0.527961i	0.952380	+	0.304913i	$0.0986275\pi$
$587$	−0.543375	+	12.7915i	−0.0224275	+	0.527961i	−0.974808	+	0.223047i	$0.928400\pi$
$588$	8.02224	+	2.58150i	0.330832	+	0.106459i
$589$	−37.3765	+	28.4705i	−1.54007	+	1.17311i
$590$	0.791073	+	2.14196i	0.0325679	+	0.0881832i
$591$	−15.9264	−	6.66303i	−0.655123	−	0.274080i
$592$	2.42340	−	7.18081i	0.0996012	−	0.295130i
$593$	21.2516	+	13.5035i	0.872698	+	0.554524i	0.895422	−	0.445218i	$-0.146874\pi$
$593$	21.2516	+	13.5035i	0.872698	+	0.554524i	−0.0227245	+	0.999742i	$0.507234\pi$
$594$	0.242982	−	0.370705i	0.00996969	−	0.0152102i
$595$	1.32055	+	1.12947i	0.0541373	+	0.0463039i
$596$	−6.54980	−	3.18690i	−0.268290	−	0.130541i
$597$	−0.0678330	+	0.0156268i	−0.00277622	+	0.000639562i
$598$	2.49237	−	5.31217i	0.101921	−	0.217231i
$599$	24.7864	+	9.55486i	1.01274	+	0.390401i	0.808485	−	0.588516i	$-0.200288\pi$
$599$	24.7864	+	9.55486i	1.01274	+	0.390401i	0.204258	+	0.978917i	$0.434522\pi$
$600$	−14.9073	−	2.99266i	−0.608586	−	0.122175i
$601$	−0.389482	−	9.16871i	−0.0158873	−	0.373999i	−0.989386	−	0.145308i	$-0.953583\pi$
$601$	−0.389482	−	9.16871i	−0.0158873	−	0.373999i	0.973499	−	0.228691i	$-0.0734445\pi$
$602$	−7.23855	+	26.2697i	−0.295021	+	1.07067i
$603$	−11.4401	−	5.17123i	−0.465875	−	0.210589i
$604$	4.21504	−	2.20053i	0.171508	−	0.0895385i
$605$	1.89437	−	1.81561i	0.0770172	−	0.0738150i
$606$	0.531176	+	0.538747i	0.0215776	+	0.0218851i
$607$	1.11611	−	0.0315972i	0.0453014	−	0.00128249i	−0.00564091	−	0.999984i	$-0.501796\pi$
$607$	1.11611	−	0.0315972i	0.0453014	−	0.00128249i	0.0509423	+	0.998702i	$0.483778\pi$
$608$	4.87806	−	26.2161i	0.197831	−	1.06320i
$609$	18.3396	−	36.3743i	0.743156	−	1.47396i
$610$	−1.03164	+	0.0878054i	−0.0417698	+	0.00355514i
$611$	−5.13366	+	11.7990i	−0.207686	+	0.477337i
$612$	0.947562	+	0.107735i	0.0383029	+	0.00435491i
$613$	−2.94565	−	0.766987i	−0.118974	−	0.0309783i	0.192015	−	0.981392i	$-0.438498\pi$
$613$	−2.94565	−	0.766987i	−0.118974	−	0.0309783i	−0.310988	+	0.950414i	$0.600660\pi$
$614$	−8.00711	+	3.89598i	−0.323141	+	0.157229i
$615$	−0.527723	+	0.426106i	−0.0212798	+	0.0171823i
$616$	5.27279	−	0.298787i	0.212447	−	0.0120385i
$617$	−34.2206	+	23.1291i	−1.37767	+	0.931141i	−0.377682	+	0.925935i	$0.623279\pi$
$617$	−34.2206	+	23.1291i	−1.37767	+	0.931141i	−0.999986	+	0.00520598i	$0.998343\pi$
$618$	−4.07308	−	7.53981i	−0.163843	−	0.303296i
$619$	2.54637	+	5.85249i	0.102347	+	0.235231i	0.960565	−	0.278054i	$-0.0896895\pi$
$619$	2.54637	+	5.85249i	0.102347	+	0.235231i	−0.858218	+	0.513285i	$0.828428\pi$
$620$	−0.249192	−	0.813698i	−0.0100078	−	0.0326789i
$621$	−1.06336	+	2.87922i	−0.0426711	+	0.115539i
$622$	19.3490	−	20.7689i	0.775823	−	0.832755i
$623$	0.135990	−	0.137928i	0.00544832	−	0.00552597i
$624$	0.0554530	−	3.91831i	0.00221990	−	0.156858i
$625$	20.3643	−	12.9397i	0.814571	−	0.517589i
$626$	−7.29511	−	29.7367i	−0.291571	−	1.18852i
$627$	−2.97733	+	0.597704i	−0.118903	+	0.0238700i
$628$	6.12975	+	1.05105i	0.244604	+	0.0419415i
$629$	−2.46320	−	4.26639i	−0.0982142	−	0.170112i
$630$	−0.652079	+	1.12943i	−0.0259794	+	0.0449977i
$631$	2.29078	−	2.75635i	0.0911945	−	0.109728i	−0.721511	−	0.692403i	$-0.756552\pi$
$631$	2.29078	−	2.75635i	0.0911945	−	0.109728i	0.812706	+	0.582674i	$0.197994\pi$
$632$	16.3856	−	14.8378i	0.651783	−	0.590217i
$633$	1.01202	+	10.1829i	0.0402242	+	0.404733i
$634$	14.5389	−	26.9134i	0.577413	−	1.06887i
$635$	−0.408080	−	0.0347328i	−0.0161942	−	0.00137833i
$636$	−0.531099	+	0.862559i	−0.0210594	+	0.0342027i
$637$	−13.3851	−	18.0978i	−0.530336	−	0.717062i
$638$	0.390595	−	3.93014i	0.0154638	−	0.155596i
$639$	−13.1643	−	8.89752i	−0.520772	−	0.351980i
$640$	−0.770965	−	0.459785i	−0.0304751	−	0.0181746i
$641$	12.8554	−	31.9919i	0.507759	−	1.26361i	−0.425682	−	0.904873i	$-0.639966\pi$
$641$	12.8554	−	31.9919i	0.507759	−	1.26361i	0.933440	−	0.358733i	$-0.116791\pi$
$642$	−1.64424	−	2.67042i	−0.0648930	−	0.105393i
$643$	−5.75694	−	11.4182i	−0.227032	−	0.450290i	0.750560	−	0.660803i	$-0.229784\pi$
$643$	−5.75694	−	11.4182i	−0.227032	−	0.450290i	−0.977591	+	0.210512i	$0.932487\pi$
$644$	−8.16866	+	2.37572i	−0.321890	+	0.0936166i
$645$	1.08145	+	0.564587i	0.0425819	+	0.0222306i
$646$	9.26970	+	11.8186i	0.364711	+	0.464998i
$647$	15.6451	+	33.3455i	0.615074	+	1.31095i	0.931986	+	0.362494i	$0.118075\pi$
$647$	15.6451	+	33.3455i	0.615074	+	1.31095i	−0.316912	+	0.948455i	$0.602646\pi$
$648$	0.217527	+	3.06917i	0.00854527	+	0.120568i
$649$	2.77237	−	1.15986i	0.108825	−	0.0455285i
$650$	6.43971	+	6.91228i	0.252586	+	0.271122i
$651$	26.5464	+	0.751533i	1.04043	+	0.0294549i
$652$	−0.967738	+	4.49032i	−0.0378996	+	0.175855i
$653$	0.576364	−	0.321976i	0.0225548	−	0.0125999i	−0.476377	−	0.879241i	$-0.658050\pi$
$653$	0.576364	−	0.321976i	0.0225548	−	0.0125999i	0.498932	+	0.866641i	$0.333726\pi$
$654$	8.98679	−	10.2110i	0.351411	−	0.399281i
$655$	1.55002	+	0.865894i	0.0605644	+	0.0338333i
$656$	6.40466	−	2.26291i	0.250060	−	0.0883518i
$657$	−1.23396	+	1.77115i	−0.0481413	+	0.0690993i
$658$	−40.8242	+	13.1370i	−1.59149	+	0.512132i
$659$	−1.40885	−	5.11291i	−0.0548809	−	0.199171i	0.931473	−	0.363811i	$-0.118525\pi$
$659$	−1.40885	−	5.11291i	−0.0548809	−	0.199171i	−0.986354	+	0.164641i	$0.947354\pi$
$660$	0.00852732	−	0.0543369i	0.000331926	−	0.00211506i
$661$	−17.7359	−	44.1375i	−0.689847	−	1.71675i	−0.697301	−	0.716779i	$-0.745616\pi$
$661$	−17.7359	−	44.1375i	−0.689847	−	1.71675i	0.00745363	−	0.999972i	$-0.497627\pi$
$662$	13.4139	−	18.1368i	0.521346	−	0.704907i
$663$	−1.88817	−	1.70981i	−0.0733303	−	0.0664037i
$664$	14.0896	−	2.00729i	0.546784	−	0.0778979i
$665$	8.64672	−	2.25143i	0.335305	−	0.0873067i
$666$	2.80977	−	2.40321i	0.108876	−	0.0931224i
$667$	3.47382	+	27.1276i	0.134507	+	1.05038i
$668$	9.62426			0.372374
$669$	−11.8949	+	9.02842i	−0.459882	+	0.349059i
$670$	3.58141			0.138362
$671$	0.173084	+	1.35164i	0.00668184	+	0.0521795i
$672$	−11.4542	+	9.79681i	−0.441854	+	0.377920i
$673$	17.9687	−	4.67869i	0.692643	−	0.180350i	0.111032	−	0.993817i	$-0.464584\pi$
$673$	17.9687	−	4.67869i	0.692643	−	0.180350i	0.581612	+	0.813467i	$0.302422\pi$
$674$	−20.8870	+	2.97567i	−0.804536	+	0.114619i
$675$	−3.66296	−	3.31696i	−0.140987	−	0.127670i
$676$	−3.74122	+	5.05846i	−0.143893	+	0.194556i
$677$	12.4265	+	30.9246i	0.477591	+	1.18853i	0.951415	+	0.307911i	$0.0996299\pi$
$677$	12.4265	+	30.9246i	0.477591	+	1.18853i	−0.473824	+	0.880619i	$0.657127\pi$
$678$	2.92078	−	18.6115i	0.112172	−	0.714770i
$679$	−3.21148	−	11.6549i	−0.123245	−	0.447274i
$680$	−1.11329	+	0.358249i	−0.0426926	+	0.0137382i
$681$	−0.0921213	+	0.132225i	−0.00353010	+	0.00506689i
$682$	2.42771	−	0.857765i	0.0929619	−	0.0328455i
$683$	−3.14864	−	1.75893i	−0.120479	−	0.0673037i	0.426293	−	0.904585i	$-0.359819\pi$
$683$	−3.14864	−	1.75893i	−0.120479	−	0.0673037i	−0.546772	+	0.837281i	$0.684144\pi$
$684$	3.23972	−	3.68104i	0.123874	−	0.140748i
$685$	−1.63709	+	0.914534i	−0.0625501	+	0.0349426i
$686$	7.84625	−	36.4067i	0.299571	−	1.39002i
$687$	−20.7706	−	0.588020i	−0.792448	−	0.0224344i
$688$	−8.32801	−	8.93915i	−0.317502	−	0.340802i
$689$	2.49600	−	1.04424i	0.0950902	−	0.0397823i
$690$	−0.0619010	−	0.873384i	−0.00235653	−	0.0332492i
$691$	−6.74075	−	14.3670i	−0.256430	−	0.546548i	0.734864	−	0.678215i	$-0.237246\pi$
$691$	−6.74075	−	14.3670i	−0.256430	−	0.546548i	−0.991294	+	0.131667i	$0.957967\pi$
$692$	−5.24014	−	6.68105i	−0.199200	−	0.253975i
$693$	1.52156	+	0.794357i	0.0577994	+	0.0301751i
$694$	−9.41692	+	2.73876i	−0.357462	+	0.103962i
$695$	−1.23585	−	2.45116i	−0.0468783	−	0.0929776i
$696$	14.3746	+	23.3459i	0.544869	+	0.884924i
$697$	1.64633	−	4.09705i	0.0623591	−	0.155187i
$698$	−28.7647	−	17.1545i	−1.08876	−	0.649309i
$699$	−23.9232	−	16.1693i	−0.904860	−	0.611579i
$700$	1.35455	−	13.6294i	0.0511972	−	0.515142i
$701$	−23.3489	−	31.5698i	−0.881875	−	1.19237i	−0.980356	−	0.197235i	$-0.936804\pi$
$701$	−23.3489	−	31.5698i	−0.881875	−	1.19237i	0.0984811	−	0.995139i	$-0.468602\pi$
$702$	1.00235	−	1.62792i	0.0378313	−	0.0614420i
$703$	−25.2398	−	2.14822i	−0.951937	−	0.0810218i
$704$	−1.55820	+	2.88444i	−0.0587270	+	0.108711i
$705$	0.189887	+	1.91063i	0.00715155	+	0.0719584i
$706$	−15.4360	+	13.9779i	−0.580941	+	0.526066i
$707$	−1.87262	+	2.25320i	−0.0704272	+	0.0847405i
$708$	−2.42638	+	4.20262i	−0.0911890	+	0.157944i
$709$	−15.4249	−	26.7167i	−0.579294	−	1.00337i	−0.995561	−	0.0941236i	$-0.969995\pi$
$709$	−15.4249	−	26.7167i	−0.579294	−	1.00337i	0.416267	−	0.909243i	$-0.363338\pi$
$710$	4.46746	+	0.766023i	0.167661	+	0.0287483i
$711$	7.04385	−	1.41407i	0.264165	−	0.0530316i
$712$	0.0310596	+	0.126607i	0.00116401	+	0.00474479i
$713$	−15.0486	+	9.56211i	−0.563576	+	0.358104i
$714$	0.120138	−	8.48897i	0.00449606	−	0.317692i
$715$	−0.103145	+	0.104615i	−0.00385741	+	0.00391239i
$716$	−6.86065	+	7.36410i	−0.256394	+	0.275210i
$717$	7.34025	−	19.8750i	0.274127	−	0.742244i
$718$	−0.0180664	−	0.0589930i	−0.000674232	−	0.00220160i
$719$	−11.0502	−	25.3974i	−0.412104	−	0.947164i	−0.991257	−	0.131945i	$-0.957878\pi$
$719$	−11.0502	−	25.3974i	−0.412104	−	0.947164i	0.579153	−	0.815219i	$-0.303384\pi$
$720$	−0.277921	−	0.514469i	−0.0103575	−	0.0191731i
$721$	27.4946	−	18.5831i	1.02395	−	0.692072i
$722$	54.7141	−	3.10042i	2.03625	−	0.115386i
$723$	−21.8339	+	17.6297i	−0.812013	+	0.655655i
$724$	0.779235	−	0.379149i	0.0289601	−	0.0140910i
$725$	−42.6115	−	11.0952i	−1.58255	−	0.412064i
$726$	−12.7377	−	1.44824i	−0.472741	−	0.0537491i
$727$	2.54514	−	5.84964i	0.0943939	−	0.216951i	−0.863330	−	0.504639i	$-0.831625\pi$
$727$	2.54514	−	5.84964i	0.0943939	−	0.216951i	0.957724	+	0.287688i	$0.0928867\pi$
$728$	22.6967	−	1.93178i	0.841197	−	0.0715964i
$729$	−0.450204	+	0.892926i	−0.0166742	+	0.0330713i
$730$	0.112646	−	0.605394i	0.00416922	−	0.0224066i
$731$	−7.93848	+	0.224740i	−0.293615	+	0.00831231i
$732$	−1.54489	−	1.56691i	−0.0571007	−	0.0579146i
$733$	25.9336	−	24.8553i	0.957879	−	0.918052i	−0.0388195	−	0.999246i	$-0.512360\pi$
$733$	25.9336	−	24.8553i	0.957879	−	0.918052i	0.996698	+	0.0811938i	$0.0258733\pi$
$734$	28.4236	−	14.8390i	1.04913	−	0.547718i
$735$	−3.06068	−	1.38351i	−0.112895	−	0.0510317i
$736$	2.68812	−	9.75558i	0.0990855	−	0.359595i
$737$	−0.200050	−	4.70934i	−0.00736895	−	0.173471i
$738$	3.24903	+	0.652248i	0.119598	+	0.0240096i
$739$	6.14459	+	2.36867i	0.226032	+	0.0871328i	0.470057	−	0.882636i	$-0.344233\pi$
$739$	6.14459	+	2.36867i	0.226032	+	0.0871328i	−0.244024	+	0.969769i	$0.578468\pi$
$740$	0.194879	−	0.415358i	0.00716388	−	0.0152689i
$741$	−12.7636	+	2.94036i	−0.468881	+	0.108017i
$742$	8.10870	+	3.94541i	0.297680	+	0.144841i
$743$	24.3074	+	20.7902i	0.891751	+	0.762719i	0.972228	−	0.234037i	$-0.0751937\pi$
$743$	24.3074	+	20.7902i	0.891751	+	0.762719i	−0.0804764	+	0.996757i	$0.525644\pi$
$744$	−9.79817	+	14.9485i	−0.359218	+	0.548040i
$745$	2.45031	+	1.55696i	0.0897725	+	0.0570427i
$746$	0.260936	−	0.773183i	0.00955354	−	0.0283082i
$747$	4.26707	+	1.78519i	0.156124	+	0.0653168i
$748$	0.124047	+	0.335878i	0.00453561	+	0.0122809i
$749$	9.66069	−	7.35876i	0.352994	−	0.268883i
$750$	2.69969	+	0.868742i	0.0985786	+	0.0317220i
$751$	−0.266265	+	6.26809i	−0.00971615	+	0.228726i	0.987674	+	0.156525i	$0.0500292\pi$
$751$	−0.266265	+	6.26809i	−0.00971615	+	0.228726i	−0.997390	+	0.0722006i	$0.976998\pi$
$752$	4.58135	−	18.6747i	0.167065	−	0.680998i
$753$	−4.33525	−	12.8459i	−0.157985	−	0.468129i
$754$	1.20432	−	16.9922i	0.0438587	−	0.618818i
$755$	−1.76829	+	0.681656i	−0.0643547	+	0.0248080i
$756$	−2.73181	+	0.468415i	−0.0993548	+	0.0170361i
$757$	−14.0010	−	16.8465i	−0.508874	−	0.612295i	0.451069	−	0.892489i	$-0.351043\pi$
$757$	−14.0010	−	16.8465i	−0.508874	−	0.612295i	−0.959943	+	0.280194i	$0.909601\pi$
$758$	−28.1216	−	4.00635i	−1.02142	−	0.145517i
$759$	−1.14499	+	0.130182i	−0.0415605	+	0.00472529i
$760$	−1.76089	+	5.74991i	−0.0638742	+	0.208571i
$761$	6.49529	+	4.94760i	0.235454	+	0.179351i	0.717006	−	0.697067i	$-0.245512\pi$
$761$	6.49529	+	4.94760i	0.235454	+	0.179351i	−0.481551	+	0.876418i	$0.659927\pi$
$762$	1.14384	+	1.64180i	0.0414369	+	0.0594760i
$763$	42.7895	+	30.7199i	1.54908	+	1.11213i
$764$	−1.15571	−	0.933174i	−0.0418123	−	0.0337611i
$765$	−0.370396	−	0.0853286i	−0.0133917	−	0.00308506i
$766$	−9.69917	+	12.3662i	−0.350445	+	0.446809i
$767$	11.8113	−	5.33903i	0.426480	−	0.192781i
$768$	−2.02761	−	12.9202i	−0.0731652	−	0.466216i
$769$	6.54507	−	3.90332i	0.236021	−	0.140757i	−0.389336	−	0.921096i	$-0.627296\pi$
$769$	6.54507	−	3.90332i	0.236021	−	0.140757i	0.625357	+	0.780338i	$0.284953\pi$
$770$	−0.488860	−	0.0277016i	−0.0176173	−	0.000998298i
$771$	10.8665	−	7.80141i	0.391349	−	0.280961i
$772$	−7.93376	−	2.80318i	−0.285542	−	0.100888i
$773$	22.6209	+	25.7023i	0.813617	+	0.924449i	0.998296	−	0.0583502i	$-0.0185840\pi$
$773$	22.6209	+	25.7023i	0.813617	+	0.924449i	−0.184679	+	0.982799i	$0.559125\pi$
$774$	−1.25572	−	5.82654i	−0.0451358	−	0.209431i
$775$	−5.25119	−	28.2215i	−0.188628	−	1.01374i
$776$	7.81267	+	2.27219i	0.280458	+	0.0815668i
$777$	10.3368	+	9.90702i	0.370830	+	0.355412i
$778$	0.501931	+	35.4664i	0.0179951	+	1.27153i
$779$	−12.4461	−	18.9883i	−0.445928	−	0.680328i
$780$	0.0301327	−	0.235310i	0.00107892	−	0.00842546i
$781$	0.757732	−	5.91723i	0.0271138	−	0.211735i
$782$	3.12462	+	4.76706i	0.111736	+	0.170470i
$783$	0.126091	+	8.90961i	0.00450613	+	0.318404i
$784$	24.2849	+	23.2752i	0.867317	+	0.831256i
$785$	−2.38013	−	0.692224i	−0.0849507	−	0.0247065i
$786$	−1.58683	−	8.52810i	−0.0566004	−	0.304187i
$787$	8.03507	+	37.2829i	0.286419	+	1.32899i	0.860190	+	0.509974i	$0.170345\pi$
$787$	8.03507	+	37.2829i	0.286419	+	1.32899i	−0.573770	+	0.819016i	$0.694520\pi$
$788$	6.91502	+	7.85699i	0.246337	+	0.279894i
$789$	19.5840	+	6.91947i	0.697209	+	0.246340i
$790$	−1.66485	+	1.19525i	−0.0592327	+	0.0425249i
$791$	72.8376	+	4.12740i	2.58981	+	0.146754i
$792$	−0.992163	+	0.591702i	−0.0352550	+	0.0210252i
$793$	0.911216	+	5.80636i	0.0323582	+	0.206190i
$794$	11.6747	−	5.27731i	0.414321	−	0.187285i
$795$	0.249159	−	0.317672i	0.00883676	−	0.0112667i
$796$	0.0411250	+	0.00947402i	0.00145764	+	0.000335798i
$797$	14.4679	+	11.6820i	0.512479	+	0.413798i	0.849412	−	0.527731i	$-0.176957\pi$
$797$	14.4679	+	11.6820i	0.512479	+	0.413798i	−0.336933	+	0.941529i	$0.609390\pi$
$798$	−35.4614	−	25.4588i	−1.25532	−	0.901230i
$799$	−7.14503	−	10.2556i	−0.252773	−	0.362815i
$800$	12.9603	+	9.87210i	0.458214	+	0.349032i
$801$	−0.0124063	+	0.0405110i	−0.000438357	+	0.00143139i
$802$	0.0353093	−	0.00401455i	0.00124682	−	0.000141759i
$803$	−0.802349	−	0.114307i	−0.0283143	−	0.00403381i
$804$	4.86497	+	5.85370i	0.171574	+	0.206444i
$805$	3.34186	−	0.573020i	0.117785	−	0.0201963i
$806$	10.3622	−	3.99451i	0.364993	−	0.140700i
$807$	−1.55863	+	21.9913i	−0.0548664	+	0.774130i
$808$	−0.630517	−	1.86829i	−0.0221815	−	0.0657264i
$809$	6.94495	−	28.3094i	0.244172	−	0.995304i	−0.711926	−	0.702255i	$-0.752177\pi$
$809$	6.94495	−	28.3094i	0.244172	−	0.995304i	0.956097	−	0.293050i	$-0.0946701\pi$
$810$	0.0121071	−	0.285011i	0.000425400	−	0.0100143i
$811$	−39.3628	−	12.6667i	−1.38221	−	0.444787i	−0.480452	−	0.877021i	$-0.659527\pi$
$811$	−39.3628	−	12.6667i	−1.38221	−	0.444787i	−0.901762	+	0.432234i	$0.857726\pi$
$812$	−19.6465	+	14.9652i	−0.689458	+	0.525175i
$813$	6.87912	+	18.6264i	0.241261	+	0.653255i
$814$	1.28060	+	0.535758i	0.0448850	+	0.0187783i
$815$	0.585415	−	1.73465i	0.0205062	−	0.0607622i
$816$	3.21281	+	2.04146i	0.112471	+	0.0714654i
$817$	−22.3857	+	34.1526i	−0.783175	+	1.19485i
$818$	−10.9903	−	9.40006i	−0.384267	−	0.328665i
$819$	6.65705	+	3.23909i	0.232616	+	0.113183i
$820$	0.400721	−	0.0923147i	0.0139938	−	0.00322377i
$821$	9.82286	−	20.9361i	0.342820	−	0.730676i	−0.656908	−	0.753970i	$-0.728136\pi$
$821$	9.82286	−	20.9361i	0.342820	−	0.730676i	0.999729	+	0.0232943i	$0.00741547\pi$
$822$	8.54857	+	3.29538i	0.298166	+	0.114939i
$823$	−50.3887	−	10.1156i	−1.75644	−	0.352608i	−0.790716	−	0.612184i	$-0.790291\pi$
$823$	−50.3887	−	10.1156i	−1.75644	−	0.352608i	−0.965723	+	0.259575i	$0.916417\pi$
$824$	0.947915	+	22.3147i	0.0330222	+	0.777368i
$825$	0.492861	−	1.78866i	0.0171592	−	0.0622731i
$826$	39.3657	+	17.7944i	1.36971	+	0.619148i
$827$	−12.2490	+	6.39481i	−0.425941	+	0.222369i	−0.662210	−	0.749318i	$-0.730381\pi$
$827$	−12.2490	+	6.39481i	−0.425941	+	0.222369i	0.236270	+	0.971688i	$0.424075\pi$
$828$	1.34343	−	1.28758i	0.0466875	−	0.0447464i
$829$	6.35681	+	6.44741i	0.220781	+	0.223928i	0.813626	−	0.581389i	$-0.197491\pi$
$829$	6.35681	+	6.44741i	0.220781	+	0.223928i	−0.592844	+	0.805317i	$0.701995\pi$
$830$	−1.31896	+	0.0373402i	−0.0457819	+	0.00129610i
$831$	0.0768323	−	0.412919i	0.00266528	−	0.0143240i
$832$	−6.36601	+	12.6262i	−0.220702	+	0.437735i
$833$	21.7867	−	1.85432i	0.754864	−	0.0642484i
$834$	−5.35078	+	12.2980i	−0.185282	+	0.425846i
$835$	−3.81133	−	0.433336i	−0.131897	−	0.0149962i
$836$	1.78167	+	0.463910i	0.0616202	+	0.0160447i
$837$	−5.22350	+	2.54157i	−0.180551	+	0.0878496i
$838$	−27.0547	+	21.8451i	−0.934587	+	0.754627i
$839$	10.7953	−	0.611726i	0.372696	−	0.0211191i	0.130767	−	0.991413i	$-0.458256\pi$
$839$	10.7953	−	0.611726i	0.372696	−	0.0211191i	0.241929	+	0.970294i	$0.422220\pi$
$840$	2.81609	−	1.90335i	0.0971644	−	0.0656716i
$841$	23.9534	+	44.3408i	0.825978	+	1.52899i
$842$	6.98657	+	16.0577i	0.240773	+	0.553384i
$843$	7.06266	+	23.0620i	0.243251	+	0.794298i
$844$	2.14936	−	5.81975i	0.0739840	−	0.200324i
$845$	1.70933	−	1.83477i	0.0588027	−	0.0631179i
$846$	6.58608	−	6.67995i	0.226434	−	0.229661i
$847$	0.702508	−	49.6392i	0.0241384	−	1.70562i
$848$	−3.41254	+	2.16837i	−0.117187	+	0.0744622i
$849$	6.78400	+	27.6533i	0.232826	+	0.949058i
$850$	−8.99726	+	1.80622i	−0.308604	+	0.0619528i
$851$	−9.47428	−	1.62453i	−0.324774	−	0.0556881i
$852$	4.81654	+	8.34249i	0.165012	+	0.285809i
$853$	−16.6942	+	28.9152i	−0.571598	+	0.990037i	0.424804	+	0.905286i	$0.360343\pi$
$853$	−16.6942	+	28.9152i	−0.571598	+	0.990037i	−0.996402	+	0.0847520i	$0.972990\pi$
$854$	−12.5206	+	15.0652i	−0.428444	+	0.515519i
$855$	−1.44871	+	1.31187i	−0.0495449	+	0.0448650i
$856$	0.808319	+	8.13325i	0.0276278	+	0.277989i
$857$	21.7506	−	40.2632i	0.742986	−	1.37536i	−0.177315	−	0.984154i	$-0.556741\pi$
$857$	21.7506	−	40.2632i	0.742986	−	1.37536i	0.920301	−	0.391211i	$-0.127944\pi$
$858$	0.715184	+	0.0608711i	0.0244160	+	0.00207810i
$859$	−16.8893	+	27.4299i	−0.576254	+	0.935896i	0.423299	+	0.905990i	$0.360872\pi$
$859$	−16.8893	+	27.4299i	−0.576254	+	0.935896i	−0.999553	+	0.0299057i	$0.990479\pi$
$860$	−0.439802	−	0.594651i	−0.0149971	−	0.0202774i
$861$	−1.26913	+	12.7699i	−0.0432517	+	0.435196i
$862$	−11.9588	−	8.08276i	−0.407319	−	0.275300i
$863$	−20.3937	−	12.1623i	−0.694210	−	0.414010i	0.121406	−	0.992603i	$-0.461260\pi$
$863$	−20.3937	−	12.1623i	−0.694210	−	0.414010i	−0.815616	+	0.578593i	$0.803602\pi$
$864$	1.22926	−	3.05914i	0.0418204	−	0.104074i
$865$	1.77435	+	2.88172i	0.0603296	+	0.0979815i
$866$	10.1250	+	20.0818i	0.344063	+	0.682407i
$867$	−13.9477	+	4.05647i	−0.473690	+	0.137765i
$868$	−14.2727	−	7.45129i	−0.484446	−	0.252913i
$869$	1.66467	+	2.12242i	0.0564701	+	0.0719981i
$870$	−1.07968	−	2.30119i	−0.0366044	−	0.0780175i
$871$	−1.43731	−	20.2795i	−0.0487014	−	0.687145i
$872$	−32.7048	+	13.6825i	−1.10752	+	0.463349i
$873$	1.80254	+	1.93482i	0.0610069	+	0.0654838i
$874$	29.2962	+	0.829382i	0.990960	+	0.0280543i
$875$	−2.31376	+	10.7359i	−0.0782195	+	0.362940i
$876$	1.14252	−	0.638248i	0.0386020	−	0.0215644i
$877$	30.7651	−	34.9560i	1.03887	−	1.18038i	0.0555527	−	0.998456i	$-0.482308\pi$
$877$	30.7651	−	34.9560i	1.03887	−	1.18038i	0.983313	−	0.181924i	$-0.0582326\pi$
$878$	36.6140	+	20.4538i	1.23566	+	0.690282i
$879$	12.1009	−	4.27552i	0.408153	−	0.144210i
$880$	0.125498	−	0.180132i	0.00423053	−	0.00607226i
$881$	−3.48245	+	1.12063i	−0.117327	+	0.0377550i	−0.364405	−	0.931240i	$-0.618728\pi$
$881$	−3.48245	+	1.12063i	−0.117327	+	0.0377550i	0.247078	+	0.968995i	$0.420529\pi$
$882$	4.35935	+	15.8207i	0.146787	+	0.532710i
$883$	−7.87386	+	50.1731i	−0.264977	+	1.68846i	0.380582	+	0.924747i	$0.375724\pi$
$883$	−7.87386	+	50.1731i	−0.264977	+	1.68846i	−0.645559	+	0.763711i	$0.723375\pi$
$884$	0.575815	+	1.43297i	0.0193668	+	0.0481960i
$885$	1.15010	−	1.55504i	0.0386603	−	0.0522722i
$886$	20.0769	+	18.1805i	0.674498	+	0.610787i
$887$	18.5566	−	2.64367i	0.623068	−	0.0887657i	0.177658	−	0.984092i	$-0.443148\pi$
$887$	18.5566	−	2.64367i	0.623068	−	0.0887657i	0.445410	+	0.895327i	$0.353058\pi$
$888$	−9.32529	+	2.42812i	−0.312936	+	0.0814822i
$889$	−5.88857	+	5.03653i	−0.197496	+	0.168920i
$890$	−0.00153517	−	0.0119884i	−5.14590e−5	−	0.000401851i
$891$	−0.375449			−0.0125780
$892$	8.87945	−	1.76675i	0.297306	−	0.0591553i
$893$	−64.2692			−2.15069
$894$	−1.80160	−	14.0689i	−0.0602544	−	0.470535i
$895$	3.04848	−	2.60738i	0.101899	−	0.0871550i
$896$	−16.4354	+	4.27945i	−0.549068	+	0.142966i
$897$	−4.92065	+	0.701022i	−0.164296	+	0.0234065i
$898$	24.7436	+	22.4064i	0.825705	+	0.747710i
$899$	−30.7789	+	41.6158i	−1.02653	+	1.38797i
$900$	1.11706	+	2.77990i	0.0372352	+	0.0926634i
$901$	−0.407465	+	2.59641i	−0.0135746	+	0.0864989i
$902$	0.330513	+	1.19948i	0.0110049	+	0.0399382i
$903$	21.9716	−	7.07030i	0.731168	−	0.235285i
$904$	−28.0678	+	40.2869i	−0.933521	+	1.33992i
$905$	−0.325659	+	0.115063i	−0.0108253	+	0.00382481i
$906$	8.08326	+	4.51558i	0.268548	+	0.150020i
$907$	15.9659	−	18.1408i	0.530139	−	0.602355i	−0.422536	−	0.906346i	$-0.638860\pi$
$907$	15.9659	−	18.1408i	0.530139	−	0.602355i	0.952675	+	0.303992i	$0.0983195\pi$
$908$	0.0852946	−	0.0476484i	0.00283060	−	0.00158127i
$909$	0.135015	−	0.626470i	0.00447815	−	0.0207787i
$910$	−2.11106	−	0.0597646i	−0.0699810	−	0.00198118i
$911$	23.0667	+	24.7594i	0.764235	+	0.820317i	0.988021	−	0.154322i	$-0.0493192\pi$
$911$	23.0667	+	24.7594i	0.764235	+	0.820317i	−0.223786	+	0.974638i	$0.571842\pi$
$912$	18.0563	−	7.55412i	0.597904	−	0.250142i
$913$	0.122775	+	1.73227i	0.00406325	+	0.0573299i
$914$	13.5064	+	28.7871i	0.446752	+	0.952192i
$915$	0.541245	+	0.690075i	0.0178930	+	0.0228132i
$916$	11.1673	+	5.83010i	0.368980	+	0.192632i
$917$	32.2551	−	9.38089i	1.06516	−	0.309784i
$918$	0.836047	+	1.65820i	0.0275936	+	0.0547287i
$919$	16.6016	+	26.9628i	0.547637	+	0.889420i	0.999997	−	0.00241599i	$-0.000769035\pi$
$919$	16.6016	+	26.9628i	0.547637	+	0.889420i	−0.452360	+	0.891836i	$0.649418\pi$
$920$	−0.850852	+	2.11743i	−0.0280518	+	0.0698095i
$921$	6.47814	+	3.86340i	0.213462	+	0.127303i
$922$	−15.3503	−	10.3750i	−0.505536	−	0.341683i
$923$	2.54466	−	25.6042i	0.0837585	−	0.842772i
$924$	−0.618788	−	0.836656i	−0.0203566	−	0.0275240i
$925$	8.11433	−	13.1785i	0.266797	−	0.433306i
$926$	10.9116	+	0.928714i	0.358577	+	0.0305194i
$927$	−3.45012	+	6.38661i	−0.113317	+	0.209764i
$928$	−2.90530	−	29.2329i	−0.0953710	−	0.959617i
$929$	−23.9021	+	21.6444i	−0.784203	+	0.710129i	−0.961734	−	0.273986i	$-0.911658\pi$
$929$	−23.9021	+	21.6444i	−0.784203	+	0.710129i	0.177530	+	0.984115i	$0.443189\pi$
$930$	1.05918	−	1.27444i	0.0347318	−	0.0417905i
$931$	56.2150	−	97.3673i	1.84237	−	3.19108i
$932$	8.75301	+	15.1607i	0.286714	+	0.496604i
$933$	−23.6980	−	4.06344i	−0.775839	−	0.133031i
$934$	0.752476	−	0.151061i	0.0246218	−	0.00494287i
$935$	−0.0340012	−	0.138597i	−0.00111196	−	0.00453262i
$936$	−4.20541	+	2.67218i	−0.137458	+	0.0873428i
$937$	0.400021	−	28.2655i	0.0130681	−	0.923395i	−0.880390	−	0.474250i	$-0.842719\pi$
$937$	0.400021	−	28.2655i	0.0130681	−	0.923395i	0.893459	−	0.449146i	$-0.148272\pi$
$938$	47.5727	−	48.2507i	1.55330	−	1.57544i
$939$	−17.6790	+	18.9763i	−0.576932	+	0.619269i
$940$	0.403287	−	1.09197i	0.0131538	−	0.0356161i
$941$	4.05459	+	13.2396i	0.132176	+	0.431599i	0.997584	−	0.0694680i	$-0.0221302\pi$
$941$	4.05459	+	13.2396i	0.132176	+	0.431599i	−0.865408	+	0.501067i	$0.832941\pi$
$942$	4.83164	+	11.1049i	0.157423	+	0.361816i
$943$	−4.09491	−	7.58021i	−0.133349	−	0.246846i
$944$	−16.0480	+	10.8465i	−0.522317	+	0.353024i
$945$	1.10292	−	0.0624979i	0.0358780	−	0.00203306i
$946$	1.74108	−	1.40583i	0.0566075	−	0.0457073i
$947$	−19.8721	+	9.66907i	−0.645756	+	0.314202i	−0.731223	−	0.682139i	$-0.761050\pi$
$947$	−19.8721	+	9.66907i	−0.645756	+	0.314202i	0.0854669	+	0.996341i	$0.472762\pi$
$948$	−4.21512	−	1.09753i	−0.136901	−	0.0356462i
$949$	−3.47322	−	0.394893i	−0.112745	−	0.0128188i
$950$	−18.8256	+	43.2680i	−0.610783	+	1.40380i
$951$	−25.8175	+	2.19739i	−0.837189	+	0.0712553i
$952$	−9.96155	+	19.7576i	−0.322856	+	0.640346i
$953$	6.43309	−	34.5733i	0.208388	−	1.11994i	−0.703871	−	0.710327i	$-0.748547\pi$
$953$	6.43309	−	34.5733i	0.208388	−	1.11994i	0.912260	−	0.409612i	$-0.134336\pi$
$954$	−1.97170	+	0.0558191i	−0.0638361	+	0.00180721i
$955$	0.415661	+	0.421585i	0.0134505	+	0.0136422i
$956$	−9.27357	+	8.88800i	−0.299929	+	0.287458i
$957$	−2.96562	+	1.54825i	−0.0958647	+	0.0500478i
$958$	−46.7503	−	21.1325i	−1.51044	−	0.682760i
$959$	−9.42477	+	34.2038i	−0.304342	+	1.10450i
$960$	0.0895497	+	2.10807i	0.00289020	+	0.0680376i
$961$	−2.69084	−	0.540192i	−0.0868014	−	0.0174255i
$962$	5.58660	+	2.15357i	0.180119	+	0.0694339i
$963$	−1.12831	+	2.40484i	−0.0363592	+	0.0774949i
$964$	16.5794	−	3.81942i	0.533986	−	0.123015i
$965$	3.01566	+	1.46731i	0.0970774	+	0.0472345i
$966$	−12.5890	−	10.7674i	−0.405044	−	0.346436i
$967$	27.4284	−	41.8460i	0.882037	−	1.34568i	−0.0557434	−	0.998445i	$-0.517753\pi$
$967$	27.4284	−	41.8460i	0.882037	−	1.34568i	0.937780	−	0.347230i	$-0.112878\pi$
$968$	28.2004	+	17.9189i	0.906395	+	0.575936i
$969$	4.06834	−	12.0549i	0.130694	−	0.387261i
$970$	−0.695907	−	0.291143i	−0.0223442	−	0.00934802i
$971$	−6.35184	−	17.1987i	−0.203840	−	0.551932i	0.794638	−	0.607084i	$-0.207661\pi$
$971$	−6.35184	−	17.1987i	−0.203840	−	0.551932i	−0.998478	+	0.0551522i	$0.982436\pi$
$972$	0.482288	−	0.367369i	0.0154694	−	0.0117834i
$973$	−49.4394	−	15.9093i	−1.58496	−	0.510028i
$974$	1.96590	−	46.2789i	0.0629916	−	1.48287i
$975$	1.90661	−	7.77182i	0.0610604	−	0.248898i
$976$	−2.80847	−	8.32182i	−0.0898969	−	0.266375i
$977$	−0.805844	+	11.3699i	−0.0257812	+	0.363757i	0.967886	+	0.251391i	$0.0808879\pi$
$977$	−0.805844	+	11.3699i	−0.0257812	+	0.363757i	−0.993667	+	0.112366i	$0.964157\pi$
$978$	−8.34596	+	3.21727i	−0.266874	+	0.102877i
$979$	−0.0156782	+	0.00268830i	−0.000501079	+	8.59186e-5i
$980$	1.30158	+	1.56610i	0.0415773	+	0.0500273i
$981$	−11.4068	−	1.62508i	−0.364191	−	0.0518847i
$982$	5.95736	−	0.677332i	0.190107	−	0.0216145i
$983$	−5.66454	+	18.4967i	−0.180671	+	0.589952i	0.819194	+	0.573516i	$0.194421\pi$
$983$	−5.66454	+	18.4967i	−0.180671	+	0.589952i	−0.999865	+	0.0164356i	$0.994768\pi$
$984$	−6.87058	−	5.23346i	−0.219026	−	0.166837i
$985$	−2.38467	−	3.42282i	−0.0759820	−	0.109060i
$986$	13.4418	+	9.65025i	0.428074	+	0.307327i
$987$	28.2634	+	22.8211i	0.899633	+	0.726403i
$988$	7.73814	+	1.78265i	0.246183	+	0.0567135i
$989$	−9.56333	+	12.1930i	−0.304096	+	0.387715i
$990$	0.0975957	−	0.0441160i	0.00310179	−	0.00140210i
$991$	4.66934	+	29.7535i	0.148327	+	0.945152i	0.941709	+	0.336429i	$0.109219\pi$
$991$	4.66934	+	29.7535i	0.148327	+	0.945152i	−0.793382	+	0.608724i	$0.791682\pi$
$992$	16.4486	−	9.80955i	0.522244	−	0.311454i
$993$	−19.0775	−	1.08104i	−0.605405	−	0.0343057i
$994$	69.6627	−	50.0129i	2.20957	−	1.58631i
$995$	−0.0158595	−	0.00560350i	−0.000502779	−	0.000177643i
$996$	−1.85271	−	2.10508i	−0.0587053	−	0.0667022i
$997$	2.42073	+	11.2322i	0.0766652	+	0.355728i	0.999571	−	0.0292988i	$-0.00932745\pi$
$997$	2.42073	+	11.2322i	0.0766652	+	0.355728i	−0.922906	+	0.385026i	$0.874192\pi$
$998$	−7.49719	−	40.2921i	−0.237319	−	1.27542i
$999$	−3.00723	−	0.874603i	−0.0951445	−	0.0276712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.m.b.19.7	✓	1368
223.47	even	111	inner	669.2.m.b.493.7	yes	1368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.m.b.19.7	✓	1368	1.1	even	1	trivial
669.2.m.b.493.7	yes	1368	223.47	even	111	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.m (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.149953 - 1.17100i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(0.586706 - 0.152766i) q^{4} +(-0.239221 + 0.0340808i) q^{5} +(0.875091 + 0.792432i) q^{6} +(-2.71848 + 3.67563i) q^{7} +(-1.14723 - 2.85499i) q^{8} +(0.155037 - 0.987909i) q^{9} +(0.0757806 + 0.275018i) q^{10} +(0.357400 - 0.115009i) q^{11} +(-0.346569 + 0.497445i) q^{12} +(1.52686 - 0.539475i) q^{13} +(4.71181 + 2.63218i) q^{14} +(0.159643 - 0.181390i) q^{15} +(-2.11261 + 1.18017i) q^{16} +(-0.331401 + 1.53771i) q^{17} +(-1.18009 - 0.0334086i) q^{18} +(5.51339 + 5.91799i) q^{19} +(-0.135146 + 0.0565404i) q^{20} +(-0.323208 - 4.56026i) q^{21} +(-0.188269 - 0.401270i) q^{22} +(1.89422 + 2.41508i) q^{23} +(2.72754 + 1.42396i) q^{24} +(-4.74501 + 1.38001i) q^{25} +(-0.860684 - 1.70706i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-1.03344 + 2.57181i) q^{28} +(7.65291 + 4.56401i) q^{29} +(-0.236347 - 0.159743i) q^{30} +(-0.574495 + 5.78053i) q^{31} +(-1.96044 - 2.65068i) q^{32} +(-0.196850 + 0.319705i) q^{33} +(1.85035 + 0.157488i) q^{34} +(0.525051 - 0.971937i) q^{35} +(-0.0599583 - 0.603296i) q^{36} +(-2.32146 + 2.10218i) q^{37} +(6.10323 - 7.34361i) q^{38} +(-0.809683 + 1.40241i) q^{39} +(0.371742 + 0.643876i) q^{40} +(-2.76663 - 0.474386i) q^{41} +(-5.29160 + 1.06230i) q^{42} +(1.20290 + 4.90331i) q^{43} +(0.192119 - 0.122075i) q^{44} +(-0.00341937 + 0.241613i) q^{45} +(2.54402 - 2.58028i) q^{46} +(-5.41640 + 5.81388i) q^{47} +(0.838373 - 2.27004i) q^{48} +(-4.07035 - 13.2911i) q^{49} +(2.32752 + 5.34948i) q^{50} +(-0.747640 - 1.38398i) q^{51} +(0.813406 - 0.549766i) q^{52} +(1.66812 - 0.0945256i) q^{53} +(0.918521 - 0.741654i) q^{54} +(-0.0815781 + 0.0396931i) q^{55} +(13.6126 + 3.54445i) q^{56} +(-8.03649 - 0.913722i) q^{57} +(4.19689 - 9.64596i) q^{58} +(7.97548 - 0.678814i) q^{59} +(0.0659534 - 0.130811i) q^{60} +(-0.663942 + 3.56822i) q^{61} +(6.85516 - 0.194071i) q^{62} +(3.20972 + 3.25547i) q^{63} +(-6.30411 + 6.04200i) q^{64} +(-0.346873 + 0.181091i) q^{65} +(0.403894 + 0.182572i) q^{66} +(3.33508 - 12.1035i) q^{67} +(0.0404748 + 0.952807i) q^{68} +(-3.00927 - 0.604116i) q^{69} +(-1.21687 - 0.469091i) q^{70} +(6.74898 - 14.3846i) q^{71} +(-2.99833 + 0.690730i) q^{72} +(-1.94105 - 0.944446i) q^{73} +(2.80977 + 2.40321i) q^{74} +(2.70896 - 4.13292i) q^{75} +(4.13881 + 2.62986i) q^{76} +(-0.548854 + 1.62632i) q^{77} +(1.76364 + 0.737845i) q^{78} +(2.48902 + 6.73945i) q^{79} +(0.465160 - 0.354322i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(-0.140644 + 3.31086i) q^{82} +(-1.10205 + 4.49225i) q^{83} +(-0.886281 - 2.62615i) q^{84} +(0.0268720 - 0.379146i) q^{85} +(5.56141 - 2.14386i) q^{86} +(-8.78234 + 1.50588i) q^{87} +(-0.738369 - 0.888431i) q^{88} +(-0.0419446 - 0.00597566i) q^{89} +(0.283442 - 0.0322264i) q^{90} +(-2.16784 + 7.07874i) q^{91} +(1.48029 + 1.12757i) q^{92} +(-3.32068 - 4.76630i) q^{93} +(7.62027 + 5.47081i) q^{94} +(-1.52061 - 1.22781i) q^{95} +(3.21273 + 0.740122i) q^{96} +(-1.63197 + 2.08072i) q^{97} +(-14.9535 + 6.75943i) q^{98} +(-0.0582083 - 0.370909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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