LMFDB - Embedded newform 429.2.bn.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(4,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("429.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bn (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	429.4
Dual form			429.2.bn.a.322.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0803440 - 0.180456i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.31215 - 1.45729i) q^{4} +(0.296705 + 0.408379i) q^{5} +(-0.0803440 + 0.180456i) q^{6} +(3.31863 + 2.98811i) q^{7} +(-0.744131 - 0.241783i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.0803440 - 0.180456i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.31215 - 1.45729i) q^{4} +(0.296705 + 0.408379i) q^{5} +(-0.0803440 + 0.180456i) q^{6} +(3.31863 + 2.98811i) q^{7} +(-0.744131 - 0.241783i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0498559 - 0.0863529i) q^{10} +(3.08302 + 1.22269i) q^{11} -1.96098 q^{12} +(1.22351 + 3.39161i) q^{13} +(0.272589 - 0.838942i) q^{14} +(0.104951 - 0.493754i) q^{15} +(-0.393801 - 3.74677i) q^{16} +(-5.13747 - 2.28735i) q^{17} +(0.187865 - 0.0610411i) q^{18} +(1.21104 + 5.69749i) q^{19} +(0.984450 + 0.103470i) q^{20} -4.46566i q^{21} +(-0.0270621 - 0.654585i) q^{22} +(3.93702 - 6.81912i) q^{23} +(0.318241 + 0.714781i) q^{24} +(1.46635 - 4.51295i) q^{25} +(0.513734 - 0.493284i) q^{26} +(0.809017 - 0.587785i) q^{27} +(8.70909 - 0.915362i) q^{28} +(-3.68088 - 0.782395i) q^{29} +(-0.0975328 + 0.0207312i) q^{30} +(-2.46026 + 3.38626i) q^{31} +(-1.99969 + 1.15452i) q^{32} +(-1.15431 - 3.10927i) q^{33} +1.11086i q^{34} +(-0.235627 + 2.24184i) q^{35} +(1.31215 + 1.45729i) q^{36} +(0.900547 - 4.23674i) q^{37} +(0.930845 - 0.676298i) q^{38} +(1.70177 - 3.17867i) q^{39} +(-0.122048 - 0.375626i) q^{40} +(-2.50504 + 2.25555i) q^{41} +(-0.805853 + 0.358789i) q^{42} +(-4.97653 - 8.61961i) q^{43} +(5.82721 - 2.88852i) q^{44} +(-0.437156 + 0.252392i) q^{45} +(-1.54687 - 0.162582i) q^{46} +(-0.0570870 - 0.0185487i) q^{47} +(-2.52089 + 2.79973i) q^{48} +(1.35282 + 12.8712i) q^{49} +(-0.932199 + 0.0979780i) q^{50} +(1.73781 + 5.34842i) q^{51} +(6.54800 + 2.66731i) q^{52} +(8.92757 + 6.48626i) q^{53} +(-0.171069 - 0.0987667i) q^{54} +(0.415429 + 1.62182i) q^{55} +(-1.74702 - 3.02593i) q^{56} +(3.42372 - 4.71234i) q^{57} +(0.154549 + 0.727096i) q^{58} +(-8.58158 - 7.72689i) q^{59} +(-0.581832 - 0.800824i) q^{60} +(5.78470 + 2.57552i) q^{61} +(0.808737 + 0.171902i) q^{62} +(-3.31863 + 2.98811i) q^{63} +(-5.72679 - 4.16076i) q^{64} +(-1.02204 + 1.50596i) q^{65} +(-0.468343 + 0.458114i) q^{66} +(-5.27389 - 3.04488i) q^{67} +(-10.0745 + 4.48545i) q^{68} +(-7.70198 + 1.63711i) q^{69} +(0.423485 - 0.137599i) q^{70} +(-4.56789 + 10.2596i) q^{71} +(0.318241 - 0.714781i) q^{72} +(1.98896 - 0.646253i) q^{73} +(-0.836897 + 0.177888i) q^{74} +(-4.33495 + 1.93004i) q^{75} +(9.89198 + 5.71114i) q^{76} +(6.57790 + 13.2700i) q^{77} +(-0.710337 - 0.0517073i) q^{78} +(-2.63779 - 1.91647i) q^{79} +(1.41326 - 1.27250i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.608291 + 0.270829i) q^{82} +(-1.93221 - 2.65946i) q^{83} +(-6.50777 - 5.85962i) q^{84} +(-0.590206 - 2.77670i) q^{85} +(-1.15562 + 1.59058i) q^{86} +(1.88156 + 3.25895i) q^{87} +(-1.99855 - 1.65526i) q^{88} +(-2.22146 - 1.28256i) q^{89} +(0.0806685 + 0.0586091i) q^{90} +(-6.07414 + 14.9115i) q^{91} +(-4.77149 - 14.6851i) q^{92} +(4.16272 - 0.437519i) q^{93} +(0.00123938 + 0.0117919i) q^{94} +(-1.96742 + 2.18504i) q^{95} +(2.19603 + 0.713532i) q^{96} +(3.60949 + 0.379373i) q^{97} +(2.21399 - 1.27825i) q^{98} +(-1.53825 + 2.93833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9	$ 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9} + 21 q^{11} + 120 q^{12} - 15 q^{13} + 30 q^{14} - 6 q^{15} - 8 q^{16} - 12 q^{19} - 66 q^{20} - 17 q^{22} + 12 q^{23} + 14 q^{25} + 9 q^{26} + 28 q^{27} + 18 q^{28} - 2 q^{29} + 10 q^{30} - 30 q^{32} - 24 q^{33} + 16 q^{35} - 20 q^{36} + 38 q^{38} - 12 q^{39} - 60 q^{40} - 36 q^{41} + 12 q^{43} - 6 q^{45} + 54 q^{46} - 42 q^{48} - 40 q^{49} - 51 q^{50} - 30 q^{51} - 15 q^{52} - 22 q^{53} + 22 q^{55} - 76 q^{56} + 132 q^{58} + 72 q^{59} + 34 q^{61} + 17 q^{62} - 84 q^{64} + 28 q^{65} - 24 q^{66} - 48 q^{67} - 12 q^{68} - 7 q^{69} + 30 q^{71} + 20 q^{74} + 32 q^{75} - 48 q^{76} - 136 q^{77} - 14 q^{78} - 36 q^{79} + 18 q^{80} + 14 q^{81} - 5 q^{82} - 27 q^{84} - 66 q^{85} + 52 q^{87} + 52 q^{88} - 96 q^{89} - 20 q^{90} - 125 q^{91} - 10 q^{92} - 18 q^{93} + 22 q^{94} + 72 q^{95} - 93 q^{97} + 24 q^{98}+O(q^{100}) $ 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9 + 21 * q^11 + 120 * q^12 - 15 * q^13 + 30 * q^14 - 6 * q^15 - 8 * q^16 - 12 * q^19 - 66 * q^20 - 17 * q^22 + 12 * q^23 + 14 * q^25 + 9 * q^26 + 28 * q^27 + 18 * q^28 - 2 * q^29 + 10 * q^30 - 30 * q^32 - 24 * q^33 + 16 * q^35 - 20 * q^36 + 38 * q^38 - 12 * q^39 - 60 * q^40 - 36 * q^41 + 12 * q^43 - 6 * q^45 + 54 * q^46 - 42 * q^48 - 40 * q^49 - 51 * q^50 - 30 * q^51 - 15 * q^52 - 22 * q^53 + 22 * q^55 - 76 * q^56 + 132 * q^58 + 72 * q^59 + 34 * q^61 + 17 * q^62 - 84 * q^64 + 28 * q^65 - 24 * q^66 - 48 * q^67 - 12 * q^68 - 7 * q^69 + 30 * q^71 + 20 * q^74 + 32 * q^75 - 48 * q^76 - 136 * q^77 - 14 * q^78 - 36 * q^79 + 18 * q^80 + 14 * q^81 - 5 * q^82 - 27 * q^84 - 66 * q^85 + 52 * q^87 + 52 * q^88 - 96 * q^89 - 20 * q^90 - 125 * q^91 - 10 * q^92 - 18 * q^93 + 22 * q^94 + 72 * q^95 - 93 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0803440	−	0.180456i	−0.0568118	−	0.127601i	0.882909	−	0.469544i	$-0.155582\pi$
$2$	−0.0803440	−	0.180456i	−0.0568118	−	0.127601i	−0.939721	+	0.341943i	$0.888915\pi$
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	1.31215	−	1.45729i	0.656076	−	0.728646i
$5$	0.296705	+	0.408379i	0.132690	+	0.182633i	0.870192	−	0.492713i	$-0.163995\pi$
$5$	0.296705	+	0.408379i	0.132690	+	0.182633i	−0.737502	+	0.675345i	$0.763995\pi$
$6$	−0.0803440	+	0.180456i	−0.0328003	+	0.0736707i
$7$	3.31863	+	2.98811i	1.25432	+	1.12940i	0.986120	+	0.166036i	$0.0530969\pi$
$7$	3.31863	+	2.98811i	1.25432	+	1.12940i	0.268204	+	0.963362i	$0.413570\pi$
$8$	−0.744131	−	0.241783i	−0.263090	−	0.0854831i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.0498559	−	0.0863529i	0.0157658	−	0.0273072i
$11$	3.08302	+	1.22269i	0.929567	+	0.368654i
$11$	3.08302	+	1.22269i	0.929567	+	0.368654i
$12$	−1.96098			−0.566086
$13$	1.22351	+	3.39161i	0.339339	+	0.940664i
$13$	1.22351	+	3.39161i	0.339339	+	0.940664i
$14$	0.272589	−	0.838942i	0.0728524	−	0.224217i
$15$	0.104951	−	0.493754i	0.0270981	−	0.127487i
$16$	−0.393801	−	3.74677i	−0.0984503	−	0.936692i
$17$	−5.13747	−	2.28735i	−1.24602	−	0.554763i	−0.325530	−	0.945532i	$-0.605543\pi$
$17$	−5.13747	−	2.28735i	−1.24602	−	0.554763i	−0.920489	+	0.390768i	$0.872209\pi$
$18$	0.187865	−	0.0610411i	0.0442803	−	0.0143875i
$19$	1.21104	+	5.69749i	0.277831	+	1.30709i	0.866686	+	0.498855i	$0.166246\pi$
$19$	1.21104	+	5.69749i	0.277831	+	1.30709i	−0.588854	+	0.808239i	$0.700421\pi$
$20$	0.984450	+	0.103470i	0.220130	+	0.0231366i
$21$		−	4.46566i		−	0.974486i
$22$	−0.0270621	−	0.654585i	−0.00576966	−	0.139558i
$23$	3.93702	−	6.81912i	0.820926	−	1.42189i	−0.0840673	−	0.996460i	$-0.526791\pi$
$23$	3.93702	−	6.81912i	0.820926	−	1.42189i	0.904993	−	0.425426i	$-0.139876\pi$
$24$	0.318241	+	0.714781i	0.0649607	+	0.145904i
$25$	1.46635	−	4.51295i	0.293269	−	0.902589i
$26$	0.513734	−	0.493284i	0.100752	−	0.0967410i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	8.70909	−	0.915362i	1.64586	−	0.172987i
$29$	−3.68088	−	0.782395i	−0.683522	−	0.145287i	−0.146953	−	0.989143i	$-0.546947\pi$
$29$	−3.68088	−	0.782395i	−0.683522	−	0.145287i	−0.536569	+	0.843856i	$0.680280\pi$
$30$	−0.0975328	+	0.0207312i	−0.0178070	+	0.00378499i
$31$	−2.46026	+	3.38626i	−0.441876	+	0.608190i	−0.970628	−	0.240586i	$-0.922660\pi$
$31$	−2.46026	+	3.38626i	−0.441876	+	0.608190i	0.528752	+	0.848777i	$0.322660\pi$
$32$	−1.99969	+	1.15452i	−0.353498	+	0.204092i
$33$	−1.15431	−	3.10927i	−0.200940	−	0.541254i
$34$			1.11086i			0.190511i
$35$	−0.235627	+	2.24184i	−0.0398283	+	0.378941i
$36$	1.31215	+	1.45729i	0.218692	+	0.242882i
$37$	0.900547	−	4.23674i	0.148049	−	0.696516i	−0.840026	−	0.542545i	$-0.817461\pi$
$37$	0.900547	−	4.23674i	0.148049	−	0.696516i	0.988075	−	0.153970i	$-0.0492060\pi$
$38$	0.930845	−	0.676298i	0.151003	−	0.109710i
$39$	1.70177	−	3.17867i	0.272502	−	0.508995i
$40$	−0.122048	−	0.375626i	−0.0192975	−	0.0593916i
$41$	−2.50504	+	2.25555i	−0.391222	+	0.352257i	−0.841145	−	0.540810i	$-0.818118\pi$
$41$	−2.50504	+	2.25555i	−0.391222	+	0.352257i	0.449923	+	0.893067i	$0.351451\pi$
$42$	−0.805853	+	0.358789i	−0.124346	+	0.0553623i
$43$	−4.97653	−	8.61961i	−0.758914	−	1.31448i	−0.943405	−	0.331644i	$-0.892397\pi$
$43$	−4.97653	−	8.61961i	−0.758914	−	1.31448i	0.184490	−	0.982834i	$-0.440937\pi$
$44$	5.82721	−	2.88852i	0.878485	−	0.435461i
$45$	−0.437156	+	0.252392i	−0.0651674	+	0.0376244i
$46$	−1.54687	−	0.162582i	−0.228073	−	0.0239714i
$47$	−0.0570870	−	0.0185487i	−0.00832699	−	0.00270560i	0.304851	−	0.952400i	$-0.401393\pi$
$47$	−0.0570870	−	0.0185487i	−0.00832699	−	0.00270560i	−0.313178	+	0.949695i	$0.601393\pi$
$48$	−2.52089	+	2.79973i	−0.363859	+	0.404106i
$49$	1.35282	+	12.8712i	0.193259	+	1.83874i
$50$	−0.932199	+	0.0979780i	−0.131833	+	0.0138562i
$51$	1.73781	+	5.34842i	0.243342	+	0.748928i
$52$	6.54800	+	2.66731i	0.908044	+	0.369889i
$53$	8.92757	+	6.48626i	1.22630	+	0.890956i	0.996607	−	0.0823081i	$-0.0262292\pi$
$53$	8.92757	+	6.48626i	1.22630	+	0.890956i	0.229689	+	0.973264i	$0.426229\pi$
$54$	−0.171069	−	0.0987667i	−0.0232795	−	0.0134404i
$55$	0.415429	+	1.62182i	0.0560164	+	0.218686i
$56$	−1.74702	−	3.02593i	−0.233456	−	0.404357i
$57$	3.42372	−	4.71234i	0.453482	−	0.624165i
$58$	0.154549	+	0.727096i	0.0202933	+	0.0954724i
$59$	−8.58158	−	7.72689i	−1.11723	−	1.00596i	−0.999917	−	0.0128598i	$-0.995906\pi$
$59$	−8.58158	−	7.72689i	−1.11723	−	1.00596i	−0.117309	−	0.993095i	$-0.537427\pi$
$60$	−0.581832	−	0.800824i	−0.0751142	−	0.103386i
$61$	5.78470	+	2.57552i	0.740655	+	0.329761i	0.742146	−	0.670238i	$-0.233808\pi$
$61$	5.78470	+	2.57552i	0.740655	+	0.329761i	−0.00149104	+	0.999999i	$0.500475\pi$
$62$	0.808737	+	0.171902i	0.102710	+	0.0218316i
$63$	−3.31863	+	2.98811i	−0.418108	+	0.376466i
$64$	−5.72679	−	4.16076i	−0.715849	−	0.520094i
$65$	−1.02204	+	1.50596i	−0.126769	+	0.186792i
$66$	−0.468343	+	0.458114i	−0.0576491	+	0.0563899i
$67$	−5.27389	−	3.04488i	−0.644308	−	0.371992i	0.141964	−	0.989872i	$-0.454658\pi$
$67$	−5.27389	−	3.04488i	−0.644308	−	0.371992i	−0.786272	+	0.617880i	$0.787992\pi$
$68$	−10.0745	+	4.48545i	−1.22171	+	0.543940i
$69$	−7.70198	+	1.63711i	−0.927209	+	0.197084i
$70$	0.423485	−	0.137599i	0.0506161	−	0.0164462i
$71$	−4.56789	+	10.2596i	−0.542108	+	1.21760i	0.410070	+	0.912054i	$0.365504\pi$
$71$	−4.56789	+	10.2596i	−0.542108	+	1.21760i	−0.952179	+	0.305542i	$0.901162\pi$
$72$	0.318241	−	0.714781i	0.0375051	−	0.0842378i
$73$	1.98896	−	0.646253i	0.232790	−	0.0756382i	−0.190299	−	0.981726i	$-0.560946\pi$
$73$	1.98896	−	0.646253i	0.232790	−	0.0756382i	0.423089	+	0.906088i	$0.360946\pi$
$74$	−0.836897	+	0.177888i	−0.0972873	+	0.0206791i
$75$	−4.33495	+	1.93004i	−0.500557	+	0.222862i
$76$	9.89198	+	5.71114i	1.13469	+	0.655112i
$77$	6.57790	+	13.2700i	0.749621	+	1.51226i
$78$	−0.710337	−	0.0517073i	−0.0804298	−	0.00585469i
$79$	−2.63779	−	1.91647i	−0.296775	−	0.215619i	0.429426	−	0.903102i	$-0.358716\pi$
$79$	−2.63779	−	1.91647i	−0.296775	−	0.215619i	−0.726201	+	0.687483i	$0.758716\pi$
$80$	1.41326	−	1.27250i	0.158007	−	0.142270i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	0.608291	+	0.270829i	0.0671746	+	0.0299080i
$83$	−1.93221	−	2.65946i	−0.212088	−	0.291913i	0.689698	−	0.724097i	$-0.257743\pi$
$83$	−1.93221	−	2.65946i	−0.212088	−	0.291913i	−0.901786	+	0.432184i	$0.857743\pi$
$84$	−6.50777	−	5.85962i	−0.710056	−	0.639337i
$85$	−0.590206	−	2.77670i	−0.0640168	−	0.301176i
$86$	−1.15562	+	1.59058i	−0.124614	+	0.171516i
$87$	1.88156	+	3.25895i	0.201724	+	0.349396i
$88$	−1.99855	−	1.65526i	−0.213046	−	0.176451i
$89$	−2.22146	−	1.28256i	−0.235474	−	0.135951i	0.377621	−	0.925960i	$-0.376742\pi$
$89$	−2.22146	−	1.28256i	−0.235474	−	0.135951i	−0.613095	+	0.790009i	$0.710076\pi$
$90$	0.0806685	+	0.0586091i	0.00850320	+	0.00617794i
$91$	−6.07414	+	14.9115i	−0.636743	+	1.56315i
$92$	−4.77149	−	14.6851i	−0.497462	−	1.53103i
$93$	4.16272	−	0.437519i	0.431654	−	0.0453686i
$94$	0.00123938	+	0.0117919i	0.000127833	+	0.00121625i
$95$	−1.96742	+	2.18504i	−0.201853	+	0.224180i
$96$	2.19603	+	0.713532i	0.224131	+	0.0728246i
$97$	3.60949	+	0.379373i	0.366488	+	0.0385194i	0.285983	−	0.958235i	$-0.407680\pi$
$97$	3.60949	+	0.379373i	0.366488	+	0.0385194i	0.0805052	+	0.996754i	$0.474347\pi$
$98$	2.21399	−	1.27825i	0.223646	−	0.129122i
$99$	−1.53825	+	2.93833i	−0.154600	+	0.295313i
$100$	−4.65262	−	8.05857i	−0.465262	−	0.805857i
$101$	−14.7769	+	6.57909i	−1.47036	+	0.654644i	−0.976621	−	0.214968i	$-0.931035\pi$
$101$	−14.7769	+	6.57909i	−1.47036	+	0.654644i	−0.493734	+	0.869613i	$0.664368\pi$
$102$	0.825530	−	0.743310i	0.0817396	−	0.0735987i
$103$	−3.94524	−	12.1422i	−0.388736	−	1.19641i	−0.933734	−	0.357968i	$-0.883470\pi$
$103$	−3.94524	−	12.1422i	−0.388736	−	1.19641i	0.544998	−	0.838437i	$-0.316530\pi$
$104$	−0.0904150	−	2.81963i	−0.00886592	−	0.276487i
$105$	1.82368	−	1.32498i	0.177973	−	0.129305i
$106$	0.453205	−	2.13216i	0.0440192	−	0.207094i
$107$	0.0855540	+	0.0950174i	0.00827082	+	0.00918568i	0.747266	−	0.664525i	$-0.231366\pi$
$107$	0.0855540	+	0.0950174i	0.00827082	+	0.00918568i	−0.738995	+	0.673711i	$0.764699\pi$
$108$	0.204978	−	1.95024i	0.0197240	−	0.187662i
$109$			6.68536i			0.640341i	0.947360	+	0.320171i	$0.103740\pi$
$109$			6.68536i			0.640341i	−0.947360	+	0.320171i	$0.896260\pi$
$110$	0.259289	−	0.205270i	0.0247223	−	0.0195717i
$111$	−3.75109	+	2.16570i	−0.356038	+	0.205559i
$112$	9.88886	−	13.6109i	0.934410	−	1.28610i
$113$	−10.1674	+	2.16115i	−0.956470	+	0.203304i	−0.659603	−	0.751615i	$-0.729275\pi$
$113$	−10.1674	+	2.16115i	−0.956470	+	0.203304i	−0.296868	+	0.954919i	$0.595942\pi$
$114$	−1.12544	−	0.239221i	−0.105408	−	0.0224051i
$115$	3.95292	−	0.415469i	0.368612	−	0.0387427i
$116$	−5.97005	+	4.33750i	−0.554306	+	0.402727i
$117$	−3.50092	+	0.862283i	−0.323661	+	0.0797181i
$118$	−0.704882	+	2.16940i	−0.0648897	+	0.199710i
$119$	−10.2145	−	22.9422i	−0.936362	−	2.10310i
$120$	−0.197478	+	0.342042i	−0.0180272	+	0.0312240i
$121$	8.01008	+	7.53914i	0.728189	+	0.685376i
$122$		−	1.25081i		−	0.113243i
$123$	3.35240	+	0.352351i	0.302276	+	0.0317704i
$124$	1.70653	+	8.02861i	0.153251	+	0.720990i
$125$	4.67846	−	1.52012i	0.418454	−	0.135964i
$126$	0.805853	+	0.358789i	0.0717911	+	0.0319634i
$127$	−0.433677	−	4.12616i	−0.0384826	−	0.366137i	−0.996769	−	0.0803265i	$-0.974404\pi$
$127$	−0.433677	−	4.12616i	−0.0384826	−	0.366137i	0.958286	−	0.285811i	$-0.0922629\pi$
$128$	−1.25087	+	5.88489i	−0.110562	+	0.520155i
$129$	−3.07567	+	9.46593i	−0.270797	+	0.833429i
$130$	0.353874	+	0.0634385i	0.0310368	+	0.00556392i
$131$	18.6191			1.62676			0.813381	−	0.581731i	$-0.197625\pi$
$131$	18.6191			1.62676			0.813381	+	0.581731i	$0.197625\pi$
$132$	−6.04575	−	2.39766i	−0.526215	−	0.208690i
$133$	−13.0057	+	22.5266i	−1.12774	+	1.95330i
$134$	−0.125741	+	1.19634i	−0.0108623	+	0.103348i
$135$	0.480078	+	0.155987i	0.0413186	+	0.0134252i
$136$	3.26991	+	2.94424i	0.280392	+	0.252466i
$137$	−4.46622	+	10.0313i	−0.381575	+	0.857032i	0.616021	+	0.787730i	$0.288744\pi$
$137$	−4.46622	+	10.0313i	−0.381575	+	0.857032i	−0.997596	+	0.0693016i	$0.977923\pi$
$138$	0.914233	+	1.25833i	0.0778247	+	0.107117i
$139$	−6.91913	+	7.68447i	−0.586873	+	0.651788i	−0.961312	−	0.275463i	$-0.911169\pi$
$139$	−6.91913	+	7.68447i	−0.586873	+	0.651788i	0.374439	+	0.927252i	$0.377835\pi$
$140$	2.95784	+	3.28502i	0.249983	+	0.277635i
$141$	0.0244143	+	0.0548354i	0.00205605	+	0.00461797i
$142$	2.21841			0.186165
$143$	−0.374777	+	11.9524i	−0.0313404	+	0.999509i
$144$	3.76741			0.313951
$145$	−0.772621	−	1.73533i	−0.0641627	−	0.144112i
$146$	−0.276421	−	0.306997i	−0.0228768	−	0.0254072i
$147$	8.65994	−	9.61784i	0.714260	−	0.793266i
$148$	−4.99252	−	6.87161i	−0.410382	−	0.564843i
$149$	6.90173	−	15.5015i	0.565412	−	1.26994i	−0.374090	−	0.927393i	$-0.622045\pi$
$149$	6.90173	−	15.5015i	0.565412	−	1.26994i	0.939502	−	0.342544i	$-0.111289\pi$
$150$	0.696575	+	0.627199i	0.0568751	+	0.0512106i
$151$	4.97985	+	1.61805i	0.405255	+	0.131675i	0.504549	−	0.863383i	$-0.331659\pi$
$151$	4.97985	+	1.61805i	0.405255	+	0.131675i	−0.0992947	+	0.995058i	$0.531659\pi$
$152$	0.476384	−	4.53249i	0.0386398	−	0.367633i
$153$	2.81183	−	4.87023i	0.227323	−	0.393735i
$154$	1.86616	−	2.25319i	0.150379	−	0.181567i
$155$	−2.11285			−0.169708
$156$	−2.39927	−	6.65089i	−0.192095	−	0.532497i
$157$	−0.556837	+	1.71377i	−0.0444405	+	0.136774i	−0.970815	−	0.239830i	$-0.922908\pi$
$157$	−0.556837	+	1.71377i	−0.0444405	+	0.136774i	0.926374	+	0.376604i	$0.122908\pi$
$158$	−0.133907	+	0.629981i	−0.0106530	+	0.0501186i
$159$	−1.15348	−	10.9746i	−0.0914769	−	0.870345i
$160$	−1.06480	−	0.474079i	−0.0841797	−	0.0374792i
$161$	33.4418	−	10.8659i	2.63558	−	0.856353i
$162$	0.0410695	+	0.193217i	0.00322672	+	0.0151805i
$163$	−9.98708	−	1.04968i	−0.782249	−	0.0822177i	−0.295019	−	0.955491i	$-0.595326\pi$
$163$	−9.98708	−	1.04968i	−0.782249	−	0.0822177i	−0.487230	+	0.873274i	$0.661993\pi$
$164$			6.61020i			0.516170i
$165$	0.927271	−	1.39393i	0.0721879	−	0.108518i
$166$	−0.324673	+	0.562350i	−0.0251995	+	0.0436468i
$167$	0.140444	+	0.315442i	0.0108679	+	0.0244096i	0.918898	−	0.394496i	$-0.129081\pi$
$167$	0.140444	+	0.315442i	0.0108679	+	0.0244096i	−0.908030	+	0.418905i	$0.862414\pi$
$168$	−1.07972	+	3.32303i	−0.0833021	+	0.256378i
$169$	−10.0061	+	8.29931i	−0.769697	+	0.638409i
$170$	−0.453652	+	0.329597i	−0.0347935	+	0.0252790i
$171$	−5.79287	+	0.608855i	−0.442992	+	0.0465603i
$172$	−19.0913	−	4.05797i	−1.45570	−	0.309418i
$173$	20.7225	−	4.40471i	1.57551	−	0.334884i	0.664504	−	0.747285i	$-0.268643\pi$
$173$	20.7225	−	4.40471i	1.57551	−	0.334884i	0.911002	+	0.412401i	$0.135310\pi$
$174$	0.436924	−	0.601375i	0.0331232	−	0.0455901i
$175$	18.3514	−	10.5952i	1.38724	−	0.800922i
$176$	3.36702	−	12.0329i	0.253799	−	0.907012i
$177$			11.5477i			0.867975i
$178$	−0.0529642	+	0.503921i	−0.00396983	+	0.0377705i
$179$	3.92311	+	4.35706i	0.293227	+	0.325662i	0.871700	−	0.490040i	$-0.163018\pi$
$179$	3.92311	+	4.35706i	0.293227	+	0.325662i	−0.578473	+	0.815702i	$0.696351\pi$
$180$	−0.205806	+	0.968241i	−0.0153399	+	0.0721684i
$181$	15.5945	−	11.3301i	1.15913	−	0.842159i	0.169464	−	0.985536i	$-0.445796\pi$
$181$	15.5945	−	11.3301i	1.15913	−	0.842159i	0.989668	+	0.143378i	$0.0457964\pi$
$182$	3.17888	−	0.101935i	0.235634	−	0.00755592i
$183$	−1.95674	−	6.02223i	−0.144646	−	0.445176i
$184$	−4.57841	+	4.12242i	−0.337525	+	0.303909i
$185$	1.99739	−	0.889297i	0.146851	−	0.0653824i
$186$	−0.413402	−	0.716034i	−0.0303121	−	0.0525022i
$187$	−13.0422	−	13.3335i	−0.953742	−	0.975039i
$188$	−0.101938	+	0.0588538i	−0.00743457	+	0.00429235i
$189$	4.44119	+	0.466788i	0.323049	+	0.0339538i
$190$	0.552372	+	0.179477i	0.0400733	+	0.0130206i
$191$	−7.66872	+	8.51697i	−0.554889	+	0.616266i	−0.953697	−	0.300768i	$-0.902757\pi$
$191$	−7.66872	+	8.51697i	−0.554889	+	0.616266i	0.398809	+	0.917034i	$0.369424\pi$
$192$	0.739926	+	7.03992i	0.0533995	+	0.508063i
$193$	−10.4938	+	1.10295i	−0.755362	+	0.0793917i	−0.474379	−	0.880321i	$-0.657327\pi$
$193$	−10.4938	+	1.10295i	−0.755362	+	0.0793917i	−0.280983	+	0.959713i	$0.590661\pi$
$194$	−0.221541	−	0.681833i	−0.0159057	−	0.0489528i
$195$	1.80303	−	0.248159i	0.129118	−	0.0177710i
$196$	20.5322	+	14.9175i	1.46658	+	1.06554i
$197$	10.8193	+	6.24651i	0.770841	+	0.445046i	0.833175	−	0.553010i	$-0.186521\pi$
$197$	10.8193	+	6.24651i	0.770841	+	0.445046i	−0.0623332	+	0.998055i	$0.519854\pi$
$198$	0.653828	+	0.0415089i	0.0464655	+	0.00294991i
$199$	−4.02163	−	6.96567i	−0.285086	−	0.493783i	0.687544	−	0.726143i	$-0.258689\pi$
$199$	−4.02163	−	6.96567i	−0.285086	−	0.493783i	−0.972630	+	0.232359i	$0.925355\pi$
$200$	−2.18231	+	3.00369i	−0.154312	+	0.212393i
$201$	1.26613	+	5.95669i	0.0893061	+	0.420152i
$202$	2.37447	+	2.13798i	0.167067	+	0.150428i
$203$	−9.87759	−	13.5953i	−0.693271	−	0.954206i
$204$	10.0745	+	4.48545i	0.705354	+	0.314044i
$205$	−1.66438	−	0.353774i	−0.116245	−	0.0247087i
$206$	−1.87415	+	1.68749i	−0.130578	+	0.117573i
$207$	6.37024	+	4.62825i	0.442762	+	0.321685i
$208$	12.2258	−	5.91981i	0.847704	−	0.410465i
$209$	−3.23258	+	19.0462i	−0.223602	+	1.31745i
$210$	−0.385622	−	0.222639i	−0.0266105	−	0.0153636i
$211$	−4.77649	+	2.12663i	−0.328827	+	0.146403i	−0.564509	−	0.825427i	$-0.690934\pi$
$211$	−4.77649	+	2.12663i	−0.328827	+	0.146403i	0.235682	+	0.971830i	$0.424268\pi$
$212$	21.1667	−	4.49912i	1.45374	−	0.309001i
$213$	10.6809	−	3.47044i	0.731844	−	0.237791i
$214$	0.0102727	−	0.0230728i	0.000702225	−	0.00157722i
$215$	2.04351	−	4.58979i	0.139366	−	0.313021i
$216$	−0.744131	+	0.241783i	−0.0506317	+	0.0164512i
$217$	−18.2832	+	3.88621i	−1.24114	+	0.263813i
$218$	1.20641	−	0.537129i	0.0817084	−	0.0363789i
$219$	−1.81114	−	1.04566i	−0.122385	−	0.0706591i
$220$	2.90857	+	1.52267i	0.196096	+	0.102659i
$221$	1.47208	−	20.2229i	0.0990225	−	1.36034i
$222$	0.692190	+	0.502906i	0.0464568	+	0.0337528i
$223$	0.602272	−	0.542288i	0.0403311	−	0.0363143i	−0.648719	−	0.761028i	$-0.724695\pi$
$223$	0.602272	−	0.542288i	0.0403311	−	0.0363143i	0.689050	+	0.724714i	$0.258028\pi$
$224$	−10.0860	−	2.14386i	−0.673902	−	0.143242i
$225$	4.33495	+	1.93004i	0.288997	+	0.128670i
$226$	1.20688	+	1.66113i	0.0802807	+	0.110497i
$227$	8.82649	+	7.94741i	0.585835	+	0.527488i	0.907877	−	0.419237i	$-0.137702\pi$
$227$	8.82649	+	7.94741i	0.585835	+	0.527488i	−0.322042	+	0.946725i	$0.604369\pi$
$228$	−2.37482	−	11.1727i	−0.157277	−	0.739928i
$229$	8.90594	−	12.2580i	0.588521	−	0.810030i	−0.406076	−	0.913839i	$-0.633103\pi$
$229$	8.90594	−	12.2580i	0.588521	−	0.810030i	0.994597	+	0.103810i	$0.0331033\pi$
$230$	−0.392567	−	0.679947i	−0.0258851	−	0.0448344i
$231$	5.46009	−	13.7677i	0.359248	−	0.905850i
$232$	2.54989	+	1.47218i	0.167408	+	0.0966532i
$233$	−12.2860	−	8.92633i	−0.804885	−	0.584783i	0.107458	−	0.994210i	$-0.465729\pi$
$233$	−12.2860	−	8.92633i	−0.804885	−	0.584783i	−0.912343	+	0.409426i	$0.865729\pi$
$234$	0.436882	+	0.562482i	0.0285599	+	0.0367706i
$235$	−0.00936309	−	0.0288166i	−0.000610781	−	0.00187979i
$236$	−22.5207	+	2.36702i	−1.46597	+	0.154080i
$237$	0.340814	+	3.24263i	0.0221382	+	0.210631i
$238$	−3.31937	+	3.68653i	−0.215163	+	0.238962i
$239$	−19.1449	−	6.22057i	−1.23838	−	0.402375i	−0.384639	−	0.923067i	$-0.625674\pi$
$239$	−19.1449	−	6.22057i	−1.23838	−	0.402375i	−0.853745	+	0.520692i	$0.825674\pi$
$240$	−1.89131	−	0.198785i	−0.122084	−	0.0128315i
$241$	−18.1216	+	10.4625i	−1.16732	+	0.673950i	−0.953046	−	0.302825i	$-0.902070\pi$
$241$	−18.1216	+	10.4625i	−1.16732	+	0.673950i	−0.214269	+	0.976775i	$0.568737\pi$
$242$	0.716918	−	2.05119i	0.0460852	−	0.131855i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	11.3437	−	5.05054i	0.726205	−	0.323327i
$245$	−4.85494	+	4.37140i	−0.310170	+	0.279279i
$246$	−0.205761	−	0.633268i	−0.0131189	−	0.0403757i
$247$	−17.8420	+	11.0783i	−1.13526	+	0.704895i
$248$	2.64950	−	1.92497i	0.168243	−	0.122236i
$249$	−0.683462	+	3.21544i	−0.0433127	+	0.203770i
$250$	−0.650201	−	0.722121i	−0.0411223	−	0.0456710i
$251$	−1.03019	+	9.80165i	−0.0650253	+	0.618675i	0.912677	+	0.408681i	$0.134011\pi$
$251$	−1.03019	+	9.80165i	−0.0650253	+	0.618675i	−0.977703	+	0.209994i	$0.932656\pi$
$252$			8.75706i			0.551643i
$253$	20.4756	−	16.2098i	1.28729	−	1.01910i
$254$	−0.709745	+	0.409772i	−0.0445334	+	0.0257114i
$255$	−1.66857	+	2.29658i	−0.104490	+	0.143818i
$256$	−12.6856	+	2.69640i	−0.792848	+	0.168525i
$257$	2.66268	+	0.565971i	0.166094	+	0.0353043i	0.290208	−	0.956964i	$-0.406276\pi$
$257$	2.66268	+	0.565971i	0.166094	+	0.0353043i	−0.124114	+	0.992268i	$0.539609\pi$
$258$	1.95529	−	0.205509i	0.121731	−	0.0127945i
$259$	15.6484	−	11.3692i	0.972345	−	0.706450i
$260$	0.853550	+	3.46547i	0.0529349	+	0.214919i
$261$	1.16287	−	3.57893i	0.0719796	−	0.221530i
$262$	−1.49594	−	3.35993i	−0.0924193	−	0.207577i
$263$	2.25359	−	3.90333i	0.138962	−	0.240690i	−0.788142	−	0.615494i	$-0.788957\pi$
$263$	2.25359	−	3.90333i	0.138962	−	0.240690i	0.927104	+	0.374804i	$0.122290\pi$
$264$	0.107193	+	2.59280i	0.00659724	+	0.159576i
$265$			5.57034i			0.342183i
$266$	5.10998	+	0.537081i	0.313313	+	0.0329305i
$267$	0.533318	+	2.50907i	0.0326385	+	0.153552i
$268$	−11.3574	+	3.69025i	−0.693765	+	0.225418i
$269$	28.0121	+	12.4718i	1.70793	+	0.760419i	0.998448	+	0.0556943i	$0.0177372\pi$
$269$	28.0121	+	12.4718i	1.70793	+	0.760419i	0.709481	+	0.704725i	$0.248929\pi$
$270$	−0.0104227	−	0.0991655i	−0.000634306	−	0.00603502i
$271$	−0.577861	+	2.71862i	−0.0351025	+	0.165144i	−0.992207	−	0.124597i	$-0.960236\pi$
$271$	−0.577861	+	2.71862i	−0.0351025	+	0.165144i	0.957105	+	0.289742i	$0.0935694\pi$
$272$	−6.54702	+	20.1497i	−0.396971	+	1.22175i
$273$	15.1458	−	5.46376i	0.916664	−	0.330682i
$274$	2.16904			0.131036
$275$	10.0387	−	12.1206i	0.605356	−	0.730902i
$276$	−7.72043	+	13.3722i	−0.464715	+	0.804910i
$277$	2.60406	−	24.7760i	0.156463	−	1.48865i	−0.581357	−	0.813649i	$-0.697478\pi$
$277$	2.60406	−	24.7760i	0.156463	−	1.48865i	0.737820	−	0.674998i	$-0.235856\pi$
$278$	1.94262	+	0.631195i	0.116510	+	0.0378565i
$279$	−3.11054	−	2.80074i	−0.186223	−	0.167676i
$280$	0.717377	−	1.61126i	0.0428715	−	0.0962909i
$281$	7.42038	+	10.2133i	0.442663	+	0.609273i	0.970801	−	0.239885i	$-0.0771098\pi$
$281$	7.42038	+	10.2133i	0.442663	+	0.609273i	−0.528138	+	0.849158i	$0.677110\pi$
$282$	0.00793382	−	0.00881140i	0.000472452	−	0.000524711i
$283$	−14.2825	−	15.8623i	−0.849007	−	0.942918i	0.149944	−	0.988694i	$-0.452091\pi$
$283$	−14.2825	−	15.8623i	−0.849007	−	0.942918i	−0.998952	+	0.0457762i	$0.985424\pi$
$284$	8.95754	+	20.1190i	0.531532	+	1.19384i
$285$	2.94026			0.174166
$286$	2.18699	−	0.892672i	0.129319	−	0.0527848i
$287$	−15.0531			−0.888557
$288$	−0.939171	−	2.10941i	−0.0553412	−	0.124298i
$289$	9.78639	+	10.8689i	0.575670	+	0.639347i
$290$	−0.251076	+	0.278848i	−0.0147437	+	0.0163745i
$291$	−2.13329	−	2.93622i	−0.125056	−	0.172124i
$292$	1.66804	−	3.74648i	0.0976147	−	0.219246i
$293$	−19.0985	−	17.1964i	−1.11575	−	1.00462i	−0.999936	−	0.0113515i	$-0.996387\pi$
$293$	−19.0985	−	17.1964i	−1.11575	−	1.00462i	−0.115811	−	0.993271i	$-0.536947\pi$
$294$	−2.43137	−	0.790000i	−0.141800	−	0.0460737i
$295$	0.609304	−	5.79714i	0.0354751	−	0.337523i
$296$	−1.69450	+	2.93495i	−0.0984906	+	0.170591i
$297$	3.21290	−	0.822983i	0.186431	−	0.0477543i
$298$	−3.35186			−0.194168
$299$	27.9448	+	5.00962i	1.61609	+	0.289714i
$300$	−2.87547	+	8.84980i	−0.166016	+	0.510943i
$301$	9.24105	−	43.4757i	0.532645	−	2.50590i
$302$	−0.108115	−	1.02864i	−0.00622131	−	0.0591918i
$303$	14.7769	+	6.57909i	0.848910	+	0.377959i
$304$	20.8703	−	6.78116i	1.19699	−	0.388926i
$305$	0.664562	+	3.12652i	0.0380527	+	0.179024i
$306$	−1.10477	−	0.116116i	−0.0631558	−	0.00663794i
$307$		−	23.2670i		−	1.32792i	−0.747768	−	0.663960i	$-0.768874\pi$
$307$		−	23.2670i		−	1.32792i	0.747768	−	0.663960i	$-0.231126\pi$
$308$	27.9695	+	7.82640i	1.59371	+	0.445950i
$309$	−6.38353	+	11.0566i	−0.363146	+	0.628988i
$310$	0.169755	+	0.381276i	0.00964143	+	0.0216550i
$311$	1.60885	−	4.95153i	0.0912295	−	0.280776i	−0.895023	−	0.446020i	$-0.852841\pi$
$311$	1.60885	−	4.95153i	0.0912295	−	0.280776i	0.986253	+	0.165244i	$0.0528412\pi$
$312$	−2.03489	+	1.95389i	−0.115203	+	0.110617i
$313$	−7.04837	+	5.12094i	−0.398398	+	0.289453i	−0.768888	−	0.639383i	$-0.779190\pi$
$313$	−7.04837	+	5.12094i	−0.398398	+	0.289453i	0.370490	+	0.928836i	$0.379190\pi$
$314$	0.353998	−	0.0372067i	0.0199773	−	0.00209969i
$315$	−2.20493	−	0.468673i	−0.124234	−	0.0264067i
$316$	−6.25404	+	1.32934i	−0.351817	+	0.0747810i
$317$	−9.86143	+	13.5731i	−0.553873	+	0.762341i	−0.990531	−	0.137287i	$-0.956162\pi$
$317$	−9.86143	+	13.5731i	−0.553873	+	0.762341i	0.436658	+	0.899627i	$0.356162\pi$
$318$	−1.88776	+	1.08990i	−0.105860	+	0.0611184i
$319$	−10.3916	−	6.91270i	−0.581819	−	0.387037i
$320$		−	3.57322i		−	0.199749i
$321$	0.0133649	−	0.127158i	0.000745953	−	0.00709727i
$322$	−4.64766	−	5.16175i	−0.259004	−	0.287653i
$323$	6.81047	−	32.0407i	0.378945	−	1.78279i
$324$	−1.58647	+	1.15264i	−0.0881370	+	0.0640353i
$325$	17.1002	−	0.548342i	0.948551	−	0.0304165i
$326$	0.612981	+	1.88656i	0.0339499	+	0.104487i
$327$	4.96819	−	4.47338i	0.274741	−	0.247378i
$328$	2.40943	−	1.07275i	0.133039	−	0.0592326i
$329$	−0.134025	−	0.232138i	−0.00738904	−	0.0127982i
$330$	−0.326044	−	0.0553370i	−0.0179481	−	0.00304620i
$331$	−4.18667	+	2.41718i	−0.230120	+	0.132860i	−0.610628	−	0.791918i	$-0.709083\pi$
$331$	−4.18667	+	2.41718i	−0.230120	+	0.132860i	0.380507	+	0.924778i	$0.375749\pi$
$332$	−6.41096	−	0.673819i	−0.351847	−	0.0369806i
$333$	4.11940	+	1.33847i	0.225742	+	0.0733479i
$334$	0.0456395	−	0.0506878i	0.00249728	−	0.00277351i
$335$	−0.321322	−	3.05718i	−0.0175557	−	0.167031i
$336$	−16.7318	+	1.75858i	−0.912793	+	0.0959384i
$337$	1.96392	+	6.04432i	0.106981	+	0.329255i	0.990190	−	0.139725i	$-0.0446217\pi$
$337$	1.96392	+	6.04432i	0.106981	+	0.329255i	−0.883209	+	0.468980i	$0.844622\pi$
$338$	2.30159	+	1.13885i	0.125190	+	0.0619453i
$339$	8.40938	+	6.10977i	0.456735	+	0.331837i
$340$	−4.82091	−	2.78335i	−0.261450	−	0.150948i
$341$	−11.7254	+	7.43180i	−0.634965	+	0.402454i
$342$	0.575294	+	0.996438i	0.0311083	+	0.0538812i
$343$	−15.5971	+	21.4675i	−0.842162	+	1.15914i
$344$	1.61912	+	7.61736i	0.0872971	+	0.410700i
$345$	−2.95377	−	2.65959i	−0.159026	−	0.143188i
$346$	−2.45979	−	3.38561i	−0.132239	−	0.182011i
$347$	2.45778	+	1.09427i	0.131940	+	0.0587437i	0.471645	−	0.881789i	$-0.343660\pi$
$347$	2.45778	+	1.09427i	0.131940	+	0.0587437i	−0.339705	+	0.940532i	$0.610327\pi$
$348$	7.21813	+	1.53426i	0.386933	+	0.0822451i
$349$	−21.8740	+	19.6954i	−1.17089	+	1.05427i	−0.173299	+	0.984869i	$0.555443\pi$
$349$	−21.8740	+	19.6954i	−1.17089	+	1.05427i	−0.997589	+	0.0694025i	$0.977891\pi$
$350$	−3.38639	−	2.46036i	−0.181010	−	0.131512i
$351$	2.98338	+	2.02471i	0.159241	+	0.108071i
$352$	−7.57670	+	1.11442i	−0.403839	+	0.0593990i
$353$	4.39228	+	2.53589i	0.233778	+	0.134972i	0.612314	−	0.790615i	$-0.290239\pi$
$353$	4.39228	+	2.53589i	0.233778	+	0.134972i	−0.378536	+	0.925587i	$0.623572\pi$
$354$	2.08384	−	0.927785i	0.110755	−	0.0493112i
$355$	−5.54514	+	1.17866i	−0.294305	+	0.0625565i
$356$	−4.78396	+	1.55440i	−0.253549	+	0.0823831i
$357$	−10.2145	+	22.9422i	−0.540609	+	1.21423i
$358$	0.471057	−	1.05801i	0.0248961	−	0.0559177i
$359$	6.89326	−	2.23976i	0.363812	−	0.118210i	−0.121406	−	0.992603i	$-0.538740\pi$
$359$	6.89326	−	2.23976i	0.363812	−	0.118210i	0.485218	+	0.874393i	$0.338740\pi$
$360$	0.386325	−	0.0821160i	0.0203611	−	0.00432789i
$361$	−13.6374	+	6.07177i	−0.717759	+	0.319567i
$362$	−3.29751	−	1.90382i	−0.173313	−	0.100062i
$363$	0.242882	−	10.9973i	0.0127480	−	0.577210i
$364$	13.7602	+	28.4179i	0.721229	+	1.48950i
$365$	0.854051	+	0.620504i	0.0447031	+	0.0324787i
$366$	−0.929533	+	0.836955i	−0.0485875	+	0.0437483i
$367$	−14.6749	−	3.11925i	−0.766023	−	0.162823i	−0.191702	−	0.981453i	$-0.561401\pi$
$367$	−14.6749	−	3.11925i	−0.766023	−	0.162823i	−0.574321	+	0.818630i	$0.694734\pi$
$368$	−27.1001	−	12.0657i	−1.41269	−	0.628970i
$369$	−1.98134	−	2.72709i	−0.103145	−	0.141966i
$370$	−0.320957	−	0.288991i	−0.0166858	−	0.0150239i
$371$	10.2457	+	48.2020i	0.531928	+	2.50252i
$372$	4.82453	−	6.64039i	0.250140	−	0.344288i
$373$	2.68639	+	4.65297i	0.139096	+	0.240922i	0.927155	−	0.374679i	$-0.122247\pi$
$373$	2.68639	+	4.65297i	0.139096	+	0.240922i	−0.788059	+	0.615600i	$0.788914\pi$
$374$	−1.35823	+	3.42481i	−0.0702325	+	0.177093i
$375$	−4.26017	−	2.45961i	−0.219994	−	0.127014i
$376$	0.0379955	+	0.0276053i	0.00195947	+	0.00142364i
$377$	−1.85000	−	13.4414i	−0.0952797	−	0.692266i
$378$	−0.272589	−	0.838942i	−0.0140205	−	0.0431505i
$379$	−17.8771	+	1.87896i	−0.918286	+	0.0965157i	−0.551865	−	0.833934i	$-0.686084\pi$
$379$	−17.8771	+	1.87896i	−0.918286	+	0.0965157i	−0.366421	+	0.930449i	$0.619417\pi$
$380$	0.602689	+	5.73420i	0.0309173	+	0.294158i
$381$	−2.77615	+	3.08322i	−0.142226	+	0.157958i
$382$	2.15307	+	0.699575i	0.110161	+	0.0357934i
$383$	−23.9331	−	2.51547i	−1.22292	−	0.128534i	−0.529024	−	0.848607i	$-0.677442\pi$
$383$	−23.9331	−	2.51547i	−1.22292	−	0.128534i	−0.693899	+	0.720072i	$0.744109\pi$
$384$	5.21032	−	3.00818i	0.265888	−	0.153510i
$385$	−3.46752	+	6.62356i	−0.176721	+	0.337568i
$386$	1.04215	+	1.80505i	0.0530440	+	0.0918748i
$387$	9.09258	−	4.04828i	0.462202	−	0.205786i
$388$	5.28905	−	4.76229i	0.268511	−	0.241768i
$389$	4.97239	+	15.3035i	0.252110	+	0.775916i	0.994385	+	0.105820i	$0.0337469\pi$
$389$	4.97239	+	15.3035i	0.252110	+	0.775916i	−0.742275	+	0.670096i	$0.766253\pi$
$390$	−0.189644	−	0.305429i	−0.00960301	−	0.0154660i
$391$	−35.8240	+	26.0277i	−1.81170	+	1.31628i
$392$	2.10536	−	9.90493i	0.106337	−	0.500275i
$393$	−12.4586	−	13.8367i	−0.628455	−	0.697970i
$394$	0.257954	−	2.45427i	0.0129955	−	0.123644i
$395$		−	1.64584i		−	0.0828114i
$396$	2.26359	+	6.09722i	0.113750	+	0.306397i
$397$	−14.7210	+	8.49915i	−0.738824	+	0.426560i	−0.821642	−	0.570004i	$-0.806941\pi$
$397$	−14.7210	+	8.49915i	−0.738824	+	0.426560i	0.0828175	+	0.996565i	$0.473608\pi$
$398$	−0.933880	+	1.28538i	−0.0468112	+	0.0644301i
$399$	25.4430	−	5.40808i	1.27374	−	0.270743i
$400$	−17.4864	−	3.71685i	−0.874321	−	0.185843i
$401$	15.7779	−	1.65832i	0.787909	−	0.0828126i	0.297977	−	0.954573i	$-0.403688\pi$
$401$	15.7779	−	1.65832i	0.787909	−	0.0828126i	0.489932	+	0.871760i	$0.337021\pi$
$402$	0.973192	−	0.707065i	0.0485384	−	0.0352652i
$403$	−14.4950	−	4.20115i	−0.722049	−	0.209274i
$404$	−9.80186	+	30.1670i	−0.487661	+	1.50087i
$405$	−0.205314	−	0.461143i	−0.0102021	−	0.0229144i
$406$	−1.65975	+	2.87477i	−0.0823720	+	0.142673i
$407$	7.95661	−	11.9609i	0.394394	−	0.592879i
$408$		−	4.40009i		−	0.217837i
$409$	−10.1543	−	1.06726i	−0.502098	−	0.0527726i	−0.149906	−	0.988700i	$-0.547897\pi$
$409$	−10.1543	−	1.06726i	−0.502098	−	0.0527726i	−0.352192	+	0.935928i	$0.614564\pi$
$410$	0.0698822	+	0.328770i	0.00345123	+	0.0162368i
$411$	10.4432	−	3.39320i	0.515125	−	0.167374i
$412$	−22.8715	−	10.1830i	−1.12680	−	0.501682i
$413$	−5.39031	−	51.2854i	−0.265240	−	2.52359i
$414$	0.323383	−	1.52140i	0.0158934	−	0.0747726i
$415$	0.512771	−	1.57815i	0.0251710	−	0.0774682i
$416$	−6.36231	−	5.36960i	−0.311938	−	0.263266i
$417$	10.3405			0.506375
$418$	3.69672	−	0.946914i	0.180812	−	0.0463151i
$419$	13.4138	−	23.2333i	0.655305	−	1.13502i	−0.326512	−	0.945193i	$-0.605873\pi$
$419$	13.4138	−	23.2333i	0.655305	−	1.13502i	0.981817	−	0.189828i	$-0.0607932\pi$
$420$	0.462061	−	4.39621i	0.0225463	−	0.214513i
$421$	17.7227	+	5.75845i	0.863751	+	0.280650i	0.707194	−	0.707019i	$-0.249961\pi$
$421$	17.7227	+	5.75845i	0.863751	+	0.280650i	0.156557	+	0.987669i	$0.449961\pi$
$422$	0.767525	+	0.691083i	0.0373625	+	0.0336414i
$423$	0.0244143	−	0.0548354i	0.00118706	−	0.00266619i
$424$	−5.07501	−	6.98516i	−0.246464	−	0.339229i
$425$	−17.8560	+	19.8311i	−0.866142	+	0.961948i
$426$	−1.48441	−	1.64860i	−0.0719198	−	0.0798750i
$427$	11.5014	+	25.8325i	0.556590	+	1.25012i
$428$	0.250728			0.0121194
$429$	9.13313	−	7.71919i	0.440952	−	0.372686i
$430$	−0.992438			−0.0478596
$431$	−2.93422	−	6.59038i	−0.141337	−	0.317447i	0.828983	−	0.559274i	$-0.188920\pi$
$431$	−2.93422	−	6.59038i	−0.141337	−	0.317447i	−0.970319	+	0.241827i	$0.922253\pi$
$432$	−2.52089	−	2.79973i	−0.121286	−	0.134702i
$433$	−8.26236	+	9.17629i	−0.397064	+	0.440984i	−0.908213	−	0.418508i	$-0.862553\pi$
$433$	−8.26236	+	9.17629i	−0.397064	+	0.440984i	0.511149	+	0.859492i	$0.329220\pi$
$434$	2.17024	+	2.98707i	0.104175	+	0.143384i
$435$	−0.772621	+	1.73533i	−0.0370443	+	0.0832029i
$436$	9.74252	+	8.77220i	0.466582	+	0.420112i
$437$	43.6198	+	14.1729i	2.08662	+	0.677983i
$438$	−0.0431812	+	0.410842i	−0.00206328	+	0.0196308i
$439$	−7.67266	+	13.2894i	−0.366196	+	0.634270i	−0.988967	−	0.148134i	$-0.952673\pi$
$439$	−7.67266	+	13.2894i	−0.366196	+	0.634270i	0.622771	+	0.782404i	$0.286007\pi$
$440$	0.0829945	−	1.30729i	0.00395661	−	0.0623226i
$441$	−12.9421			−0.616290
$442$	−3.76761	+	1.35914i	−0.179207	+	0.0646479i
$443$	−0.549575	+	1.69142i	−0.0261111	+	0.0803617i	−0.963263	−	0.268560i	$-0.913452\pi$
$443$	−0.549575	+	1.69142i	−0.0261111	+	0.0803617i	0.937152	+	0.348922i	$0.113452\pi$
$444$	−1.76595	+	8.30817i	−0.0838085	+	0.394288i
$445$	−0.135347	−	1.28774i	−0.00641605	−	0.0610447i
$446$	−0.146248	−	0.0651138i	−0.00692504	−	0.00308323i
$447$	−16.1381	+	5.24357i	−0.763304	+	0.248012i
$448$	−6.57230	−	30.9203i	−0.310512	−	1.46084i
$449$	−37.0522	−	3.89434i	−1.74860	−	0.183785i	−0.824481	−	0.565890i	$-0.808533\pi$
$449$	−37.0522	−	3.89434i	−1.74860	−	0.183785i	−0.924119	+	0.382105i	$0.875199\pi$
$450$		−	0.937334i		−	0.0441863i
$451$	−10.4809	+	3.89103i	−0.493528	+	0.183222i
$452$	−10.1918	+	17.6527i	−0.479381	+	0.830312i
$453$	−2.12972	−	4.78344i	−0.100063	−	0.224746i
$454$	0.724999	−	2.23132i	0.0340259	−	0.104721i
$455$	−7.89176	+	1.94375i	−0.369971	+	0.0911246i
$456$	−3.68706	+	2.67880i	−0.172662	+	0.125447i
$457$	34.0098	−	3.57457i	1.59091	−	0.167211i	0.732715	−	0.680536i	$-0.238253\pi$
$457$	34.0098	−	3.57457i	1.59091	−	0.167211i	0.858195	+	0.513325i	$0.171586\pi$
$458$	−2.92756	−	0.622272i	−0.136796	−	0.0290769i
$459$	−5.50077	+	1.16922i	−0.256754	+	0.0545747i
$460$	4.58137	−	6.30572i	0.213608	−	0.294006i
$461$	−17.3191	+	9.99916i	−0.806629	+	0.465707i	−0.845784	−	0.533526i	$-0.820867\pi$
$461$	−17.3191	+	9.99916i	−0.806629	+	0.465707i	0.0391551	+	0.999233i	$0.487533\pi$
$462$	−2.92315	+	0.120850i	−0.135997	+	0.00562246i
$463$		−	6.00568i		−	0.279108i	−0.990214	−	0.139554i	$-0.955433\pi$
$463$		−	6.00568i		−	0.279108i	0.990214	−	0.139554i	$-0.0445668\pi$
$464$	−1.48192	+	14.0995i	−0.0687963	+	0.654553i
$465$	1.41377	+	1.57015i	0.0655621	+	0.0728141i
$466$	−0.623697	+	2.93426i	−0.0288922	+	0.135927i
$467$	21.2318	−	15.4258i	0.982489	−	0.713820i	0.0242254	−	0.999707i	$-0.492288\pi$
$467$	21.2318	−	15.4258i	0.982489	−	0.713820i	0.958263	+	0.285887i	$0.0922881\pi$
$468$	−3.33715	+	6.23332i	−0.154260	+	0.288135i
$469$	−8.40365	−	25.8638i	−0.388045	−	1.19428i
$470$	−0.00444785	+	0.00400487i	−0.000205164	+	0.000184731i
$471$	1.64618	−	0.732925i	0.0758518	−	0.0337714i
$472$	4.51759	+	7.82470i	0.207939	+	0.360161i
$473$	−4.80370	−	32.6592i	−0.220875	−	1.50167i
$474$	0.557768	−	0.322028i	0.0256191	−	0.0147912i
$475$	27.4883	+	2.88913i	1.26125	+	0.132563i
$476$	−46.8364	−	15.2181i	−2.14674	−	0.697520i
$477$	−7.38391	+	8.20066i	−0.338086	+	0.375483i
$478$	0.415645	+	3.95460i	0.0190112	+	0.180879i
$479$	−17.0031	+	1.78710i	−0.776891	+	0.0816545i	−0.484671	−	0.874697i	$-0.661061\pi$
$479$	−17.0031	+	1.78710i	−0.776891	+	0.0816545i	−0.292220	+	0.956351i	$0.594394\pi$
$480$	0.360180	+	1.10852i	0.0164399	+	0.0505968i
$481$	15.4712	−	2.12937i	0.705426	−	0.0970909i
$482$	3.34398	+	2.42955i	0.152314	+	0.110663i
$483$	−30.4519	−	17.5814i	−1.38561	−	0.799981i
$484$	21.4972	−	1.78053i	0.977144	−	0.0809334i
$485$	0.916025	+	1.58660i	0.0415945	+	0.0720439i
$486$	0.116107	−	0.159808i	0.00526673	−	0.00724903i
$487$	2.15035	+	10.1166i	0.0974417	+	0.458427i	0.999633	+	0.0270910i	$0.00862439\pi$
$487$	2.15035	+	10.1166i	0.0974417	+	0.458427i	−0.902191	+	0.431336i	$0.858042\pi$
$488$	−3.68186	−	3.31516i	−0.166670	−	0.150070i
$489$	5.90260	+	8.12423i	0.266925	+	0.367390i
$490$	1.17891	+	0.524884i	0.0532577	+	0.0237119i
$491$	24.4679	+	5.20081i	1.10422	+	0.234709i	0.723735	−	0.690078i	$-0.242424\pi$
$491$	24.4679	+	5.20081i	1.10422	+	0.234709i	0.380484	+	0.924787i	$0.375757\pi$
$492$	4.91233	−	4.42309i	0.221465	−	0.199408i
$493$	17.1208	+	12.4390i	0.771082	+	0.560224i
$494$	3.43264	+	2.32961i	0.154442	+	0.104814i
$495$	−1.65636	+	0.243627i	−0.0744478	+	0.0109502i
$496$	13.6564	+	7.88452i	0.613190	+	0.354025i
$497$	−45.8160	+	20.3986i	−2.05513	+	0.915003i
$498$	0.635156	−	0.135007i	0.0284620	−	0.00604979i
$499$	42.2280	−	13.7207i	1.89038	−	0.614223i	0.910929	−	0.412562i	$-0.135366\pi$
$499$	42.2280	−	13.7207i	1.89038	−	0.614223i	0.979455	−	0.201661i	$-0.0646340\pi$
$500$	3.92358	−	8.81251i	0.175468	−	0.394108i
$501$	0.140444	−	0.315442i	0.00627457	−	0.0140929i
$502$	1.85153	−	0.601599i	0.0826380	−	0.0268507i
$503$	25.1937	−	5.35510i	1.12333	−	0.238772i	0.391449	−	0.920200i	$-0.371974\pi$
$503$	25.1937	−	5.35510i	1.12333	−	0.238772i	0.731885	+	0.681428i	$0.238641\pi$
$504$	3.19197	−	1.42116i	0.142182	−	0.0633033i
$505$	−7.07114	−	4.08252i	−0.314662	−	0.181670i
$506$	−4.57024	−	2.39258i	−0.203172	−	0.106363i
$507$	12.8630	+	1.88263i	0.571264	+	0.0836106i
$508$	−6.58207	−	4.78215i	−0.292032	−	0.212174i
$509$	−1.66472	+	1.49892i	−0.0737874	+	0.0664385i	−0.705199	−	0.709009i	$-0.749142\pi$
$509$	−1.66472	+	1.49892i	−0.0737874	+	0.0664385i	0.631412	+	0.775448i	$0.282476\pi$
$510$	0.548491	+	0.116585i	0.0242876	+	0.00516249i
$511$	8.53170	+	3.79856i	0.377420	+	0.168038i
$512$	8.57844	+	11.8072i	0.379117	+	0.521810i
$513$	4.32865	+	3.89754i	0.191115	+	0.172080i
$514$	−0.111798	−	0.525968i	−0.00493120	−	0.0231995i
$515$	3.78805	−	5.21380i	0.166921	−	0.229747i
$516$	9.75889	+	16.9029i	0.429611	+	0.744108i
$517$	−0.153321	−	0.126986i	−0.00674307	−	0.00558482i
$518$	−3.30890	−	1.91039i	−0.145385	−	0.0839379i
$519$	−17.1394	−	12.4525i	−0.752337	−	0.546605i
$520$	1.12465	−	0.873520i	0.0493192	−	0.0383064i
$521$	−2.73505	−	8.41761i	−0.119825	−	0.368782i	0.873098	−	0.487545i	$-0.162107\pi$
$521$	−2.73505	−	8.41761i	−0.119825	−	0.368782i	−0.992923	+	0.118762i	$0.962107\pi$
$522$	−0.739268	+	0.0777002i	−0.0323569	+	0.00340085i
$523$	3.79710	+	36.1270i	0.166036	+	1.57972i	0.687329	+	0.726347i	$0.258783\pi$
$523$	3.79710	+	36.1270i	0.166036	+	1.57972i	−0.521293	+	0.853378i	$0.674550\pi$
$524$	24.4311	−	27.1335i	1.06728	−	1.18533i
$525$	−20.1533	−	6.54819i	−0.879561	−	0.285787i
$526$	−0.885441	−	0.0930636i	−0.0386071	−	0.00405777i
$527$	20.3851	−	11.7693i	0.887988	−	0.512680i
$528$	−11.1951	+	5.54938i	−0.487206	+	0.241506i
$529$	−19.5003	−	33.7755i	−0.847839	−	1.46850i
$530$	1.00520	−	0.447543i	0.0436630	−	0.0194400i
$531$	8.58158	−	7.72689i	0.372409	−	0.335318i
$532$	15.7623	+	48.5114i	0.683383	+	2.10324i
$533$	−10.7149	−	5.73645i	−0.464113	−	0.248473i
$534$	0.409926	−	0.297829i	0.0177392	−	0.0128883i
$535$	−0.0134188	+	0.0631306i	−0.000580146	+	0.00272937i
$536$	3.18826	+	3.54093i	0.137712	+	0.152945i
$537$	0.612851	−	5.83088i	0.0264465	−	0.251621i
$538$		−	6.05698i		−	0.261135i
$539$	−11.5666	+	41.3362i	−0.498211	+	1.78048i
$540$	0.857255	−	0.494936i	0.0368904	−	0.0212987i
$541$	−4.15823	+	5.72331i	−0.178776	+	0.246064i	−0.888995	−	0.457916i	$-0.848596\pi$
$541$	−4.15823	+	5.72331i	−0.178776	+	0.246064i	0.710219	+	0.703981i	$0.248596\pi$
$542$	0.537018	−	0.114147i	0.0230669	−	0.00490302i
$543$	−18.8547	−	4.00768i	−0.809131	−	0.171986i
$544$	12.9141	−	1.35733i	0.553688	−	0.0581950i
$545$	−2.73016	+	1.98358i	−0.116947	+	0.0849671i
$546$	−2.20284	−	2.29416i	−0.0942728	−	0.0981810i
$547$	2.27539	−	7.00293i	0.0972887	−	0.299424i	−0.890555	−	0.454876i	$-0.849684\pi$
$547$	2.27539	−	7.00293i	0.0972887	−	0.299424i	0.987843	+	0.155452i	$0.0496835\pi$
$548$	8.75817	+	19.6712i	0.374131	+	0.840311i
$549$	−3.16607	+	5.48380i	−0.135125	+	0.234043i
$550$	−2.99379	−	0.837717i	−0.127656	−	0.0357204i
$551$		−	21.9193i		−	0.933793i
$552$	6.12711	+	0.643985i	0.260787	+	0.0274098i
$553$	−3.02724	−	14.2420i	−0.128731	−	0.605633i
$554$	−4.68019	+	1.52069i	−0.198842	+	0.0646078i
$555$	−1.99739	−	0.889297i	−0.0847846	−	0.0377485i
$556$	2.11957	+	20.1664i	0.0898899	+	0.855246i
$557$	−6.41802	+	30.1944i	−0.271940	+	1.27938i	0.604010	+	0.796976i	$0.293569\pi$
$557$	−6.41802	+	30.1944i	−0.271940	+	1.27938i	−0.875950	+	0.482401i	$0.839765\pi$
$558$	−0.255497	+	0.786338i	−0.0108160	+	0.0332883i
$559$	23.1456	−	27.4246i	0.978953	−	1.15994i
$560$	8.49246			0.358872
$561$	−1.18173	+	18.6141i	−0.0498928	+	0.785888i
$562$	1.24686	−	2.15963i	0.0525956	−	0.0910983i
$563$	1.19344	−	11.3549i	0.0502976	−	0.478550i	−0.940160	−	0.340733i	$-0.889325\pi$
$563$	1.19344	−	11.3549i	0.0502976	−	0.478550i	0.990458	−	0.137817i	$-0.0440086\pi$
$564$	0.111947	+	0.0363736i	0.00471380	+	0.00153161i
$565$	−3.89929	−	3.51094i	−0.164044	−	0.147706i
$566$	−1.71493	+	3.85180i	−0.0720841	+	0.161903i
$567$	−2.62485	−	3.61279i	−0.110233	−	0.151723i
$568$	5.87971	−	6.53008i	0.246707	−	0.273996i
$569$	4.66078	+	5.17632i	0.195390	+	0.217003i	0.832876	−	0.553459i	$-0.186692\pi$
$569$	4.66078	+	5.17632i	0.195390	+	0.217003i	−0.637486	+	0.770462i	$0.720026\pi$
$570$	−0.236232	−	0.530586i	−0.00989467	−	0.0222238i
$571$	30.4818			1.27562			0.637812	−	0.770192i	$-0.279840\pi$
$571$	30.4818			1.27562			0.637812	+	0.770192i	$0.279840\pi$
$572$	16.9264	+	16.2295i	0.707727	+	0.678590i
$573$	11.4607			0.478778
$574$	1.20943	+	2.71642i	0.0504806	+	0.113381i
$575$	−25.0013	−	27.7668i	−1.04263	−	1.15795i
$576$	4.73657	−	5.26050i	0.197357	−	0.219187i
$577$	24.4745	+	33.6863i	1.01889	+	1.40238i	0.912981	+	0.408003i	$0.133775\pi$
$577$	24.4745	+	33.6863i	1.01889	+	1.40238i	0.105907	+	0.994376i	$0.466225\pi$
$578$	1.17507	−	2.63926i	0.0488767	−	0.109779i
$579$	7.84138	+	7.06041i	0.325877	+	0.293421i
$580$	−3.54269	−	1.15109i	−0.147102	−	0.0477964i
$581$	1.53446	−	14.5994i	0.0636601	−	0.605685i
$582$	−0.358461	+	0.620872i	−0.0148587	+	0.0257360i
$583$	19.5933	+	30.9129i	0.811470	+	1.28028i
$584$	−1.63630			−0.0677106
$585$	−1.39088	−	1.17386i	−0.0575058	−	0.0485332i
$586$	−1.56873	+	4.82806i	−0.0648037	+	0.199445i
$587$	−2.74350	+	12.9071i	−0.113236	+	0.532734i	0.884563	+	0.466421i	$0.154457\pi$
$587$	−2.74350	+	12.9071i	−0.113236	+	0.532734i	−0.997799	+	0.0663130i	$0.978876\pi$
$588$	−2.65285	−	25.2401i	−0.109402	−	1.04089i
$589$	−22.2727	−	9.91643i	−0.917729	−	0.408599i
$590$	−1.09508	+	0.355813i	−0.0450838	+	0.0146486i
$591$	−2.59745	−	12.2200i	−0.106845	−	0.502664i
$592$	−16.2287	−	1.70571i	−0.666996	−	0.0701041i
$593$			14.4617i			0.593869i	0.954898	+	0.296934i	$0.0959643\pi$
$593$			14.4617i			0.593869i	−0.954898	+	0.296934i	$0.904036\pi$
$594$	−0.406649	−	0.513663i	−0.0166850	−	0.0210759i
$595$	6.33841	−	10.9784i	0.259849	−	0.450072i
$596$	−13.5342	−	30.3982i	−0.554381	−	1.24516i
$597$	−2.48550	+	7.64959i	−0.101725	+	0.313077i
$598$	−1.34118	−	5.44529i	−0.0548451	−	0.222674i
$599$	35.6067	−	25.8698i	1.45485	−	1.05701i	0.470185	−	0.882568i	$-0.344187\pi$
$599$	35.6067	−	25.8698i	1.45485	−	1.05701i	0.984667	−	0.174444i	$-0.0558129\pi$
$600$	3.69242	−	0.388089i	0.150742	−	0.0158437i
$601$	20.1693	+	4.28712i	0.822723	+	0.174875i	0.599993	−	0.800005i	$-0.295170\pi$
$601$	20.1693	+	4.28712i	0.822723	+	0.174875i	0.222730	+	0.974880i	$0.428503\pi$
$602$	−8.58790	+	1.82541i	−0.350017	+	0.0743983i
$603$	3.57947	−	4.92672i	0.145767	−	0.200632i
$604$	8.89230	−	5.13397i	0.361823	−	0.208898i
$605$	−0.702198	+	5.50805i	−0.0285484	+	0.223934i
$606$		−	3.19516i		−	0.129795i
$607$	0.0906937	−	0.862893i	0.00368114	−	0.0350237i	−0.992527	−	0.122024i	$-0.961061\pi$
$607$	0.0906937	−	0.862893i	0.00368114	−	0.0350237i	0.996208	+	0.0870004i	$0.0277281\pi$
$608$	−8.99956	−	9.99503i	−0.364981	−	0.405352i
$609$	−3.49391	+	16.4375i	−0.141580	+	0.666083i
$610$	0.510805	−	0.371121i	0.0206819	−	0.0150263i
$611$	−0.00693631	−	0.216311i	−0.000280613	−	0.00875102i
$612$	−3.40780	−	10.4881i	−0.137752	−	0.423958i
$613$	34.6420	−	31.1918i	1.39918	−	1.25983i	0.473878	−	0.880590i	$-0.342854\pi$
$613$	34.6420	−	31.1918i	1.39918	−	1.25983i	0.925300	−	0.379236i	$-0.123813\pi$
$614$	−4.19867	+	1.86937i	−0.169444	+	0.0754415i
$615$	0.850780	+	1.47359i	0.0343067	+	0.0594210i
$616$	−1.68635	−	11.4651i	−0.0679450	−	0.461941i
$617$	35.5491	−	20.5243i	1.43115	−	0.826277i	0.433944	−	0.900940i	$-0.357121\pi$
$617$	35.5491	−	20.5243i	1.43115	−	0.826277i	0.997209	+	0.0746630i	$0.0237881\pi$
$618$	2.50810	+	0.263612i	0.100891	+	0.0106040i
$619$	3.59572	+	1.16832i	0.144524	+	0.0469588i	0.380386	−	0.924828i	$-0.375791\pi$
$619$	3.59572	+	1.16832i	0.144524	+	0.0469588i	−0.235862	+	0.971787i	$0.575791\pi$
$620$	−2.77238	+	3.07904i	−0.111341	+	0.123657i
$621$	−0.823062	−	7.83091i	−0.0330283	−	0.314244i
$622$	−1.02279	+	0.107500i	−0.0410103	+	0.00431035i
$623$	−3.53977	−	10.8943i	−0.141818	−	0.436471i
$624$	−12.5799	−	5.12439i	−0.503600	−	0.205140i
$625$	−17.1858	−	12.4862i	−0.687432	−	0.499449i
$626$	1.49040	+	0.860482i	0.0595683	+	0.0343918i
$627$	16.3171	−	10.3421i	0.651643	−	0.413025i
$628$	1.76681	+	3.06020i	0.0705033	+	0.122115i
$629$	−14.3174	+	19.7063i	−0.570873	+	0.785740i
$630$	0.0925785	+	0.435548i	0.00368842	+	0.0173526i
$631$	7.74672	+	6.97518i	0.308392	+	0.277678i	0.808764	−	0.588133i	$-0.200137\pi$
$631$	7.74672	+	6.97518i	0.308392	+	0.277678i	−0.500372	+	0.865810i	$0.666803\pi$
$632$	1.49949	+	2.06387i	0.0596466	+	0.0820965i
$633$	4.77649	+	2.12663i	0.189848	+	0.0845260i
$634$	3.24165	+	0.689033i	0.128742	+	0.0273650i
$635$	1.55636	−	1.40136i	0.0617624	−	0.0556111i
$636$	−17.5068	−	12.7194i	−0.694189	−	0.504358i
$637$	−41.9989	+	20.3362i	−1.66406	+	0.805749i
$638$	−0.412532	+	2.43062i	−0.0163323	+	0.0962292i
$639$	−9.72596	−	5.61529i	−0.384753	−	0.222137i
$640$	−2.77440	+	1.23524i	−0.109668	+	0.0488273i
$641$	−3.40780	+	0.724351i	−0.134600	+	0.0286101i	−0.274719	−	0.961525i	$-0.588585\pi$
$641$	−3.40780	+	0.724351i	−0.134600	+	0.0286101i	0.140119	+	0.990135i	$0.455252\pi$
$642$	−0.0240202	+	0.00780463i	−0.000948001	+	0.000308024i
$643$	12.3681	−	27.7793i	0.487752	−	1.09551i	−0.487240	−	0.873268i	$-0.661996\pi$
$643$	12.3681	−	27.7793i	0.487752	−	1.09551i	0.974992	−	0.222241i	$-0.0713371\pi$
$644$	28.0459	−	62.9922i	1.10516	−	2.48224i
$645$	−4.77825	+	1.55255i	−0.188144	+	0.0611315i
$646$	−6.32911	+	1.34529i	−0.249016	+	0.0529299i
$647$	−12.6373	+	5.62649i	−0.496824	+	0.221200i	−0.639823	−	0.768523i	$-0.720992\pi$
$647$	−12.6373	+	5.62649i	−0.496824	+	0.221200i	0.142999	+	0.989723i	$0.454325\pi$
$648$	0.677600	+	0.391213i	0.0266187	+	0.0153683i
$649$	−17.0097	−	34.3148i	−0.667688	−	1.34697i
$650$	−1.47285	−	3.04178i	−0.0577701	−	0.119308i
$651$	15.1219	+	10.9867i	0.592673	+	0.430602i
$652$	−14.6343	+	13.1768i	−0.573122	+	0.516042i
$653$	43.3475	+	9.21380i	1.69632	+	0.360564i	0.951725	−	0.306952i	$-0.0993091\pi$
$653$	43.3475	+	9.21380i	1.69632	+	0.360564i	0.744595	+	0.667516i	$0.232642\pi$
$654$	−1.20641	−	0.537129i	−0.0471744	−	0.0210034i
$655$	5.52439	+	7.60367i	0.215856	+	0.297100i
$656$	9.43750	+	8.49757i	0.368473	+	0.331774i
$657$	0.434810	+	2.04562i	0.0169635	+	0.0798072i
$658$	−0.0311226	+	0.0428365i	−0.00121328	+	0.00166994i
$659$	−7.05760	−	12.2241i	−0.274925	−	0.476184i	0.695191	−	0.718825i	$-0.255320\pi$
$659$	−7.05760	−	12.2241i	−0.274925	−	0.476184i	−0.970116	+	0.242641i	$0.921986\pi$
$660$	−0.814648	−	3.18036i	−0.0317101	−	0.123795i
$661$	20.1360	+	11.6255i	0.783198	+	0.452179i	0.837562	−	0.546342i	$-0.183980\pi$
$661$	20.1360	+	11.6255i	0.783198	+	0.452179i	−0.0543646	+	0.998521i	$0.517313\pi$
$662$	0.772568	+	0.561303i	0.0300267	+	0.0218157i
$663$	−16.0135	+	12.4378i	−0.621914	+	0.483043i
$664$	0.794806	+	2.44616i	0.0308444	+	0.0949294i
$665$	−13.0582	+	1.37248i	−0.506377	+	0.0532224i
$666$	−0.0894339	−	0.850907i	−0.00346549	−	0.0329720i
$667$	−19.8270	+	22.0201i	−0.767703	+	0.852621i
$668$	0.643975	+	0.209240i	0.0249161	+	0.00809575i
$669$	−0.805998	−	0.0847138i	−0.0311617	−	0.00327522i
$670$	−0.525869	+	0.303610i	−0.0203161	+	0.0117295i
$671$	14.6853	+	15.0132i	0.566921	+	0.579580i
$672$	5.15569	+	8.92991i	0.198885	+	0.344479i
$673$	28.5117	−	12.6942i	1.09904	−	0.489326i	0.224600	−	0.974451i	$-0.427892\pi$
$673$	28.5117	−	12.6942i	1.09904	−	0.489326i	0.874445	+	0.485125i	$0.161226\pi$
$674$	0.932943	−	0.840026i	0.0359356	−	0.0323566i
$675$	−1.46635	−	4.51295i	−0.0564397	−	0.173703i
$676$	−1.03495	+	25.4717i	−0.0398059	+	0.979682i
$677$	−6.01199	+	4.36796i	−0.231059	+	0.167874i	−0.697291	−	0.716788i	$-0.745611\pi$
$677$	−6.01199	+	4.36796i	−0.231059	+	0.167874i	0.466231	+	0.884663i	$0.345611\pi$
$678$	0.426899	−	2.00840i	0.0163950	−	0.0771323i
$679$	10.8449	+	12.0445i	0.416191	+	0.462227i
$680$	−0.232168	+	2.20893i	−0.00890324	+	0.0847087i
$681$		−	11.8772i		−	0.455136i
$682$	2.28317	+	1.51881i	0.0874272	+	0.0581583i
$683$	29.9296	−	17.2798i	1.14522	−	0.661195i	0.197504	−	0.980302i	$-0.436716\pi$
$683$	29.9296	−	17.2798i	1.14522	−	0.661195i	0.947719	+	0.319107i	$0.103383\pi$
$684$	−6.71384	+	9.24081i	−0.256710	+	0.353331i
$685$	−5.42172	+	1.15242i	−0.207153	+	0.0440318i
$686$	5.12706	+	1.08979i	0.195752	+	0.0416084i
$687$	−15.0687	+	1.58378i	−0.574906	+	0.0604251i
$688$	−30.3359	+	22.0403i	−1.15655	+	0.840280i
$689$	−11.0759	+	38.2148i	−0.421960	+	1.45587i
$690$	−0.242620	+	0.746707i	−0.00923638	+	0.0284267i
$691$	7.71812	+	17.3352i	0.293611	+	0.659461i	0.998770	−	0.0495884i	$-0.0157910\pi$
$691$	7.71812	+	17.3352i	0.293611	+	0.659461i	−0.705159	+	0.709049i	$0.749124\pi$
$692$	20.7722	−	35.9785i	0.789640	−	1.36770i
$693$	−13.8849	+	5.15477i	−0.527445	+	0.195813i
$694$		−	0.531438i		−	0.0201731i
$695$	−5.19112	−	0.545608i	−0.196910	−	0.0206961i
$696$	−0.612166	−	2.88001i	−0.0232041	−	0.109167i
$697$	18.0288	−	5.85791i	0.682889	−	0.221884i
$698$	5.31159	+	2.36487i	0.201047	+	0.0895118i
$699$	1.58741	+	15.1032i	0.0600413	+	0.571255i
$700$	8.63955	−	40.6459i	0.326544	−	1.53627i
$701$	0.633969	−	1.95116i	0.0239447	−	0.0736942i	−0.938370	−	0.345632i	$-0.887665\pi$
$701$	0.633969	−	1.95116i	0.0239447	−	0.0736942i	0.962315	+	0.271938i	$0.0876645\pi$
$702$	0.125674	−	0.701041i	0.00474328	−	0.0264591i
$703$	25.2294			0.951544
$704$	−12.5685	−	19.8298i	−0.473694	−	0.747363i
$705$	−0.0151498	+	0.0262402i	−0.000570574	+	0.000988264i
$706$	0.104721	−	0.996356i	0.00394123	−	0.0374983i
$707$	−68.6980	−	22.3213i	−2.58366	−	0.839481i
$708$	16.8283	+	15.1523i	0.632447	+	0.569458i
$709$	13.9668	−	31.3698i	0.524533	−	1.17812i	−0.435999	−	0.899947i	$-0.643605\pi$
$709$	13.9668	−	31.3698i	0.524533	−	1.17812i	0.960531	−	0.278172i	$-0.0897285\pi$
$710$	0.658214	+	0.905954i	0.0247023	+	0.0339998i
$711$	2.18169	−	2.42301i	0.0818199	−	0.0908702i
$712$	1.34296	+	1.49150i	0.0503294	+	0.0558964i
$713$	13.4052	+	30.1086i	0.502029	+	1.12758i
$714$	4.96072			0.185650
$715$	−4.99230	+	3.39328i	−0.186702	+	0.126901i
$716$	11.4972			0.429672
$717$	8.18768	+	18.3898i	0.305775	+	0.686781i
$718$	−0.958009	−	1.06398i	−0.0357526	−	0.0397073i
$719$	−31.1341	+	34.5779i	−1.16111	+	1.28954i	−0.211043	+	0.977477i	$0.567686\pi$
$719$	−31.1341	+	34.5779i	−1.16111	+	1.28954i	−0.950062	+	0.312061i	$0.898981\pi$
$720$	1.11781	+	1.53853i	0.0416582	+	0.0573376i
$721$	23.1894	−	52.0842i	0.863618	−	1.93972i
$722$	2.19137	+	1.97312i	0.0815544	+	0.0734319i
$723$	19.9009	+	6.46619i	0.740122	+	0.240480i
$724$	3.95114	−	37.5926i	0.146843	−	1.39712i
$725$	−8.92835	+	15.4644i	−0.331591	+	0.574332i
$726$	−2.00404	+	0.839739i	−0.0743770	+	0.0311657i
$727$	−14.2638			−0.529016			−0.264508	−	0.964383i	$-0.585210\pi$
$727$	−14.2638			−0.529016			−0.264508	+	0.964383i	$0.585210\pi$
$728$	8.12529	−	9.62746i	0.301143	−	0.356818i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.0433556	−	0.203972i	0.00160466	−	0.00754935i
$731$	5.85074	+	55.6660i	0.216397	+	2.05888i
$732$	−11.3437	−	5.05054i	−0.419275	−	0.186673i
$733$	−7.66030	+	2.48898i	−0.282940	+	0.0919326i	−0.447049	−	0.894510i	$-0.647525\pi$
$733$	−7.66030	+	2.48898i	−0.282940	+	0.0919326i	0.164109	+	0.986442i	$0.447525\pi$
$734$	0.616155	+	2.89878i	0.0227427	+	0.106996i
$735$	6.49717	+	0.682880i	0.239652	+	0.0251884i
$736$			18.1815i			0.670178i
$737$	−12.5366	−	15.8358i	−0.461792	−	0.583317i
$738$	−0.332929	+	0.576650i	−0.0122553	+	0.0212268i
$739$	−4.76644	−	10.7056i	−0.175336	−	0.393811i	0.804404	−	0.594082i	$-0.202485\pi$
$739$	−4.76644	−	10.7056i	−0.175336	−	0.393811i	−0.979741	+	0.200271i	$0.935818\pi$
$740$	1.32492	−	4.07768i	0.0487049	−	0.149898i
$741$	20.1714	+	5.84634i	0.741014	+	0.214771i
$742$	7.87515	−	5.72163i	0.289106	−	0.210048i
$743$	−41.7337	+	4.38639i	−1.53106	+	0.160921i	−0.832257	−	0.554390i	$-0.812951\pi$
$743$	−41.7337	+	4.38639i	−1.53106	+	0.160921i	−0.698806	+	0.715312i	$0.746285\pi$
$744$	−3.20339	−	0.680902i	−0.117442	−	0.0249631i
$745$	8.37829	−	1.78086i	0.306957	−	0.0652457i
$746$	0.623819	−	0.858613i	0.0228396	−	0.0314361i
$747$	2.84686	−	1.64364i	0.104161	−	0.0601375i
$748$	−36.5441	+	1.51082i	−1.33619	+	0.0552412i
$749$			0.570972i			0.0208629i
$750$	−0.101571	+	0.966387i	−0.00370886	+	0.0352875i
$751$	27.4544	+	30.4912i	1.00183	+	1.11264i	0.993632	+	0.112675i	$0.0359419\pi$
$751$	27.4544	+	30.4912i	1.00183	+	1.11264i	0.00819489	+	0.999966i	$0.497391\pi$
$752$	−0.0470167	+	0.221196i	−0.00171452	+	0.00806620i
$753$	7.97338	−	5.79300i	0.290566	−	0.211109i
$754$	−2.27694	+	1.41378i	−0.0829212	+	0.0514867i
$755$	0.816768	+	2.51375i	0.0297252	+	0.0914848i
$756$	6.50777	−	5.85962i	0.236685	−	0.213112i
$757$	−10.5700	+	4.70606i	−0.384173	+	0.171045i	−0.589730	−	0.807600i	$-0.700766\pi$
$757$	−10.5700	+	4.70606i	−0.384173	+	0.171045i	0.205558	+	0.978645i	$0.434099\pi$
$758$	1.77539	+	3.07506i	0.0644850	+	0.111691i
$759$	−25.7471	−	4.36986i	−0.934559	−	0.158616i
$760$	1.99232	−	1.15027i	0.0722690	−	0.0417245i
$761$	30.4900	+	3.20462i	1.10526	+	0.116168i	0.639535	−	0.768762i	$-0.279127\pi$
$761$	30.4900	+	3.20462i	1.10526	+	0.116168i	0.465725	+	0.884929i	$0.345794\pi$
$762$	0.779432	+	0.253253i	0.0282358	+	0.00917438i
$763$	−19.9766	+	22.1862i	−0.723200	+	0.803195i
$764$	2.34920	+	22.3511i	0.0849910	+	0.808635i
$765$	2.82318	−	0.296729i	0.102072	−	0.0107282i
$766$	1.46895	+	4.52096i	0.0530753	+	0.163349i
$767$	15.7070	−	38.5593i	0.567147	−	1.39230i
$768$	10.4921	+	7.62297i	0.378602	+	0.275070i
$769$	−2.81977	−	1.62799i	−0.101683	−	0.0587070i	0.448296	−	0.893885i	$-0.352031\pi$
$769$	−2.81977	−	1.62799i	−0.101683	−	0.0587070i	−0.549979	+	0.835178i	$0.685364\pi$
$770$	1.47385	+	0.0935690i	0.0531140	+	0.00337199i
$771$	−1.36108	−	2.35747i	−0.0490183	−	0.0849021i
$772$	−12.1622	+	16.7398i	−0.437726	+	0.602479i
$773$	8.84505	+	41.6127i	0.318134	+	1.49670i	0.788942	+	0.614468i	$0.210629\pi$
$773$	8.84505	+	41.6127i	0.318134	+	1.49670i	−0.470807	+	0.882236i	$0.656037\pi$
$774$	−1.46107	−	1.31555i	−0.0525170	−	0.0472866i
$775$	11.6744	+	16.0685i	0.419357	+	0.577196i
$776$	−2.59421	−	1.15502i	−0.0931266	−	0.0414626i
$777$	−18.9198	−	4.02153i	−0.678745	−	0.144272i
$778$	2.36209	−	2.12684i	0.0846851	−	0.0762508i
$779$	−15.8847	−	11.5409i	−0.569127	−	0.413495i
$780$	2.00421	−	2.95316i	0.0717621	−	0.105740i
$781$	−26.6272	+	26.0456i	−0.952797	+	0.931986i
$782$	7.57509	+	4.37348i	0.270885	+	0.156395i
$783$	−3.43777	+	1.53060i	−0.122856	+	0.0546990i
$784$	47.6926	−	10.1374i	1.70331	−	0.362049i
$785$	−0.865084	+	0.281083i	−0.0308762	+	0.0100323i
$786$	−1.49594	+	3.35993i	−0.0533583	+	0.119845i
$787$	−13.7977	+	30.9902i	−0.491835	+	1.10468i	0.481740	+	0.876314i	$0.340005\pi$
$787$	−13.7977	+	30.9902i	−0.491835	+	1.10468i	−0.973575	+	0.228366i	$0.926662\pi$
$788$	23.2995	−	7.57048i	0.830011	−	0.269687i
$789$	−4.40869	+	0.937096i	−0.156953	+	0.0333615i
$790$	−0.297002	+	0.132234i	−0.0105668	+	0.00470466i
$791$	−40.1996	−	23.2093i	−1.42933	−	0.825227i
$792$	1.85510	−	1.81458i	0.0659180	−	0.0644783i
$793$	−1.65753	+	22.7706i	−0.0588607	+	0.808609i
$794$	2.71646	+	1.97363i	0.0964036	+	0.0700413i
$795$	4.13957	−	3.72728i	0.146815	−	0.132193i
$796$	−15.4280	−	3.27932i	−0.546831	−	0.116233i
$797$	−1.54195	−	0.686521i	−0.0546187	−	0.0243178i	0.379246	−	0.925296i	$-0.376184\pi$
$797$	−1.54195	−	0.686521i	−0.0546187	−	0.0243178i	−0.433864	+	0.900978i	$0.642850\pi$
$798$	−3.02012	−	4.15683i	−0.106911	−	0.147150i
$799$	0.250855	+	0.225871i	0.00887462	+	0.00799075i
$800$	2.27805	+	10.7174i	0.0805414	+	0.378917i
$801$	1.50774	−	2.07522i	0.0532733	−	0.0733245i
$802$	−1.56691	−	2.71397i	−0.0553296	−	0.0958336i
$803$	6.92218	+	0.439461i	0.244279	+	0.0155083i
$804$	10.3420	+	5.97095i	0.364734	+	0.210579i
$805$	14.3597	+	10.4330i	0.506115	+	0.367714i
$806$	0.406468	+	2.95325i	0.0143172	+	0.104024i
$807$	−9.47541	−	29.1623i	−0.333550	−	1.02656i
$808$	12.5867	−	1.32291i	0.442797	−	0.0465398i
$809$	1.61744	+	15.3889i	0.0568661	+	0.541045i	0.985455	+	0.169935i	$0.0543559\pi$
$809$	1.61744	+	15.3889i	0.0568661	+	0.541045i	−0.928589	+	0.371110i	$0.878977\pi$
$810$	−0.0667202	+	0.0741002i	−0.00234431	+	0.00260362i
$811$	−14.6542	−	4.76144i	−0.514579	−	0.167197i	0.0402048	−	0.999191i	$-0.487199\pi$
$811$	−14.6542	−	4.76144i	−0.514579	−	0.167197i	−0.554784	+	0.831995i	$0.687199\pi$
$812$	−32.7733	−	3.44461i	−1.15012	−	0.120882i
$813$	2.40699	−	1.38968i	0.0844170	−	0.0487382i
$814$	−2.79768	−	0.474829i	−0.0980585	−	0.0166428i
$815$	−2.53455	−	4.38996i	−0.0887813	−	0.153774i
$816$	19.3549	−	8.61737i	0.677558	−	0.301668i
$817$	43.0834	−	38.7924i	1.50730	−	1.35718i
$818$	0.623245	+	1.91815i	0.0217912	+	0.0670666i
$819$	−14.1949	−	7.59954i	−0.496009	−	0.265549i
$820$	−2.69947	+	1.96128i	−0.0942695	+	0.0684908i
$821$	−2.18435	+	10.2766i	−0.0762345	+	0.358655i	−0.999686	−	0.0250602i	$-0.992022\pi$
$821$	−2.18435	+	10.2766i	−0.0762345	+	0.358655i	0.923451	+	0.383715i	$0.125356\pi$
$822$	−1.45137	−	1.61191i	−0.0506223	−	0.0562218i
$823$	−0.609524	+	5.79923i	−0.0212467	+	0.202149i	−0.999996	−	0.00291295i	$-0.999073\pi$
$823$	−0.609524	+	5.79923i	−0.0212467	+	0.202149i	0.978749	+	0.205062i	$0.0657394\pi$
$824$			9.98927i			0.347993i
$825$	−15.7246	+	0.650093i	−0.547460	+	0.0226333i
$826$	−8.82165	+	5.09318i	−0.306945	+	0.177215i
$827$	−14.9940	+	20.6375i	−0.521392	+	0.717635i	−0.985788	−	0.167993i	$-0.946272\pi$
$827$	−14.9940	+	20.6375i	−0.521392	+	0.717635i	0.464396	+	0.885628i	$0.346272\pi$
$828$	15.1034	−	3.21033i	0.524881	−	0.111567i
$829$	27.3125	+	5.80545i	0.948601	+	0.201631i	0.656134	−	0.754644i	$-0.272190\pi$
$829$	27.3125	+	5.80545i	0.948601	+	0.201631i	0.292467	+	0.956276i	$0.405524\pi$
$830$	−0.325984	+	0.0342623i	−0.0113151	+	0.00118926i
$831$	−20.1546	+	14.6432i	−0.699156	+	0.507967i
$832$	7.10491	−	24.5138i	0.246318	−	0.849862i
$833$	22.4908	−	69.2196i	0.779261	−	2.39832i
$834$	−0.830796	−	1.86600i	−0.0287681	−	0.0646142i
$835$	−0.0871496	+	0.150948i	−0.00301594	+	0.00522375i
$836$	23.5143	+	29.7024i	0.813259	+	1.02728i
$837$			4.18565i			0.144677i
$838$	−5.27030	−	0.553931i	−0.182059	−	0.0191352i
$839$	−6.83080	−	32.1364i	−0.235825	−	1.10947i	−0.923544	−	0.383493i	$-0.874721\pi$
$839$	−6.83080	−	32.1364i	−0.235825	−	1.10947i	0.687718	−	0.725978i	$-0.258612\pi$
$840$	−1.67741	+	0.545025i	−0.0578763	+	0.0188052i
$841$	−13.5561	−	6.03556i	−0.467451	−	0.208123i
$842$	−0.384767	−	3.66082i	−0.0132600	−	0.126160i
$843$	2.62474	−	12.3484i	0.0904009	−	0.425303i
$844$	−3.16836	+	9.75121i	−0.109059	+	0.335650i
$845$	−6.35811	−	1.62382i	−0.218726	−	0.0558612i
$846$	−0.0118569			−0.000407649
$847$	4.05473	+	48.9546i	0.139322	+	1.68210i
$848$	20.7868	−	36.0038i	0.713822	−	1.23638i
$849$	−2.23115	+	21.2280i	−0.0765728	+	0.728541i
$850$	5.01325	+	1.62890i	0.171953	+	0.0558709i
$851$	−25.3454	−	22.8211i	−0.868829	−	0.782297i
$852$	8.95754	−	20.1190i	0.306880	−	0.689264i
$853$	−24.1087	−	33.1827i	−0.825465	−	1.13616i	−0.988750	−	0.149576i	$-0.952209\pi$
$853$	−24.1087	−	33.1827i	−0.825465	−	1.13616i	0.163285	−	0.986579i	$-0.447791\pi$
$854$	3.73755	−	4.15097i	0.127896	−	0.142043i
$855$	−1.96742	−	2.18504i	−0.0672842	−	0.0747267i
$856$	−0.0406898	−	0.0913909i	−0.00139075	−	0.00312368i
$857$	−20.6185			−0.704316			−0.352158	−	0.935941i	$-0.614552\pi$
$857$	−20.6185			−0.704316			−0.352158	+	0.935941i	$0.614552\pi$
$858$	−2.12676	−	1.02793i	−0.0726065	−	0.0350931i
$859$	15.3541			0.523876			0.261938	−	0.965085i	$-0.415638\pi$
$859$	15.3541			0.523876			0.261938	+	0.965085i	$0.415638\pi$
$860$	−4.00728	−	9.00049i	−0.136647	−	0.306914i
$861$	10.0725	+	11.1866i	0.343270	+	0.381240i
$862$	−0.953523	+	1.05899i	−0.0324771	+	0.0360695i
$863$	3.71509	+	5.11338i	0.126463	+	0.174061i	0.867554	−	0.497344i	$-0.165691\pi$
$863$	3.71509	+	5.11338i	0.126463	+	0.174061i	−0.741091	+	0.671405i	$0.765691\pi$
$864$	−0.939171	+	2.10941i	−0.0319512	+	0.0717637i
$865$	7.94727	+	7.15576i	0.270215	+	0.243303i
$866$	2.31974	+	0.753731i	0.0788281	+	0.0256128i
$867$	1.52878	−	14.5454i	0.0519203	−	0.493988i
$868$	−18.3270	+	31.7433i	−0.622059	+	1.07744i
$869$	−5.78914	−	9.13370i	−0.196383	−	0.309840i
$870$	0.375226			0.0127214
$871$	3.87442	−	21.6124i	0.131280	−	0.732309i
$872$	1.61640	−	4.97478i	0.0547384	−	0.168467i
$873$	−0.754589	+	3.55006i	−0.0255390	+	0.120151i
$874$	−0.947005	−	9.01015i	−0.0320329	−	0.304773i
$875$	20.0684	+	8.93501i	0.678434	+	0.302058i
$876$	−3.90032	+	1.26729i	−0.131779	+	0.0428178i
$877$	3.69366	+	17.3773i	0.124726	+	0.586791i	0.995472	+	0.0950569i	$0.0303033\pi$
$877$	3.69366	+	17.3773i	0.124726	+	0.586791i	−0.870746	+	0.491734i	$0.836363\pi$
$878$	3.01461	+	0.316848i	0.101738	+	0.0106931i
$879$			25.6996i			0.866825i
$880$	5.91298	−	2.19519i	0.199327	−	0.0739998i
$881$	15.1293	−	26.2048i	0.509720	−	0.882861i	−0.490216	−	0.871601i	$-0.663082\pi$
$881$	15.1293	−	26.2048i	0.509720	−	0.882861i	0.999937	−	0.0112605i	$-0.00358440\pi$
$882$	1.03982	+	2.33547i	0.0350125	+	0.0786394i
$883$	5.27729	−	16.2418i	0.177595	−	0.546581i	−0.822148	−	0.569274i	$-0.807224\pi$
$883$	5.27729	−	16.2418i	0.177595	−	0.546581i	0.999742	+	0.0226937i	$0.00722425\pi$
$884$	−27.5391	−	28.6807i	−0.926239	−	0.964638i
$885$	−4.71582	+	3.42624i	−0.158521	+	0.115172i
$886$	0.349381	−	0.0367214i	0.0117377	−	0.00123368i
$887$	−8.53598	−	1.81438i	−0.286610	−	0.0609209i	0.0623631	−	0.998054i	$-0.480136\pi$
$887$	−8.53598	−	1.81438i	−0.286610	−	0.0609209i	−0.348973	+	0.937133i	$0.613470\pi$
$888$	3.31493	−	0.704611i	0.111242	−	0.0236452i
$889$	10.8902	−	14.9891i	0.365245	−	0.502717i
$890$	−0.221505	+	0.127886i	−0.00742488	+	0.00428676i
$891$	−2.76144	−	1.83696i	−0.0925118	−	0.0615406i
$892$		−	1.58925i		−	0.0532121i
$893$	0.0365464	−	0.347716i	0.00122298	−	0.0116359i
$894$	2.24283	+	2.49091i	0.0750114	+	0.0833086i
$895$	−0.615325	+	2.89488i	−0.0205681	+	0.0967651i
$896$	−21.7358	+	15.7920i	−0.726144	+	0.527574i
$897$	−14.9758	−	24.1191i	−0.500029	−	0.805314i
$898$	2.27416	+	6.99916i	0.0758899	+	0.233565i
$899$	11.7053	−	10.5395i	0.390394	−	0.351513i
$900$	8.50075	−	3.78478i	0.283358	−	0.126159i
$901$	−31.0288	−	53.7434i	−1.03372	−	1.79045i
$902$	1.54424	+	1.57872i	0.0514175	+	0.0525657i
$903$	−38.4922	+	22.2235i	−1.28094	+	0.739551i
$904$	8.08842	+	0.850127i	0.269017	+	0.0282748i
$905$	9.25394	+	3.00679i	0.307611	+	0.0999490i
$906$	−0.692088	+	0.768642i	−0.0229931	+	0.0255364i
$907$	0.915520	+	8.71059i	0.0303994	+	0.289231i	0.999151	+	0.0411978i	$0.0131174\pi$
$907$	0.915520	+	8.71059i	0.0303994	+	0.289231i	−0.968752	+	0.248033i	$0.920216\pi$
$908$	23.1634	−	2.43457i	0.768704	−	0.0807941i
$909$	−4.99845	−	15.3836i	−0.165788	−	0.510243i
$910$	0.984817	+	1.26794i	0.0326464	+	0.0420319i
$911$	−3.01962	−	2.19388i	−0.100044	−	0.0726865i	0.536638	−	0.843812i	$-0.319694\pi$
$911$	−3.01962	−	2.19388i	−0.100044	−	0.0726865i	−0.636683	+	0.771126i	$0.719694\pi$
$912$	−19.0043	−	10.9721i	−0.629296	−	0.363324i
$913$	−2.70537	−	10.5617i	−0.0895346	−	0.349540i
$914$	−3.37753	−	5.85006i	−0.111719	−	0.193503i
$915$	1.87878	−	2.58592i	0.0621105	−	0.0854877i
$916$	−6.17751	−	29.0629i	−0.204111	−	0.960265i
$917$	61.7900	+	55.6360i	2.04049	+	1.83726i
$918$	0.652947	+	0.898705i	0.0215505	+	0.0296617i
$919$	−13.9650	−	6.21763i	−0.460663	−	0.205101i	0.163265	−	0.986582i	$-0.447798\pi$
$919$	−13.9650	−	6.21763i	−0.460663	−	0.205101i	−0.623928	+	0.781482i	$0.714464\pi$
$920$	−3.04194	−	0.646585i	−0.100290	−	0.0213173i
$921$	−17.2908	+	15.5687i	−0.569751	+	0.513006i
$922$	3.19589	+	2.32195i	0.105251	+	0.0764693i
$923$	−40.3856	−	2.93977i	−1.32931	−	0.0967637i
$924$	−12.8991	−	26.0223i	−0.424350	−	0.856071i
$925$	−17.7997	−	10.2766i	−0.585249	−	0.337894i
$926$	−1.08376	+	0.482520i	−0.0356145	+	0.0158566i
$927$	12.4881	−	2.65442i	0.410162	−	0.0871826i
$928$	8.26390	−	2.68510i	0.271276	−	0.0881428i
$929$	6.67255	−	14.9868i	0.218919	−	0.491701i	−0.770383	−	0.637582i	$-0.779935\pi$
$929$	6.67255	−	14.9868i	0.218919	−	0.491701i	0.989302	+	0.145881i	$0.0466015\pi$
$930$	0.169755	−	0.381276i	0.00556648	−	0.0125025i
$931$	−71.6951	+	23.2952i	−2.34971	+	0.763468i
$932$	−29.1294	+	6.19165i	−0.954166	+	0.202814i
$933$	−4.75624	+	2.11761i	−0.155712	+	0.0693275i
$934$	−4.48951	−	2.59202i	−0.146901	−	0.0848136i
$935$	1.57541	−	9.28228i	0.0515215	−	0.303563i
$936$	2.81363	+	0.204811i	0.0919664	+	0.00669447i
$937$	20.3091	+	14.7554i	0.663470	+	0.482039i	0.867833	−	0.496856i	$-0.165512\pi$
$937$	20.3091	+	14.7554i	0.663470	+	0.482039i	−0.204363	+	0.978895i	$0.565512\pi$
$938$	−3.99208	+	3.59449i	−0.130346	+	0.117364i
$939$	8.52189	+	1.81138i	0.278101	+	0.0591122i
$940$	−0.0542800	−	0.0241670i	−0.00177042	−	0.000788242i
$941$	27.1721	+	37.3992i	0.885786	+	1.21918i	0.974785	+	0.223148i	$0.0716332\pi$
$941$	27.1721	+	37.3992i	0.885786	+	1.21918i	−0.0889991	+	0.996032i	$0.528367\pi$
$942$	−0.264521	−	0.238176i	−0.00861855	−	0.00776018i
$943$	5.51846	+	25.9623i	0.179706	+	0.845450i
$944$	−25.5714	+	35.1960i	−0.832279	+	1.14553i
$945$	1.12710	+	1.95219i	0.0366645	+	0.0635047i
$946$	−5.50759	+	3.49083i	−0.179067	+	0.113497i
$947$	−0.658587	−	0.380235i	−0.0214012	−	0.0123560i	0.489261	−	0.872137i	$-0.337266\pi$
$947$	−0.658587	−	0.380235i	−0.0214012	−	0.0123560i	−0.510662	+	0.859781i	$0.670600\pi$
$948$	5.17266	+	3.75815i	0.168000	+	0.122059i
$949$	4.62535	+	5.95509i	0.150145	+	0.193311i
$950$	−1.68716	−	5.19254i	−0.0547386	−	0.168468i
$951$	16.6854	−	1.75370i	0.541060	−	0.0568677i
$952$	2.05391	+	19.5417i	0.0665677	+	0.633349i
$953$	−10.7898	+	11.9833i	−0.349516	+	0.388176i	−0.892110	−	0.451819i	$-0.850775\pi$
$953$	−10.7898	+	11.9833i	−0.349516	+	0.388176i	0.542594	+	0.839995i	$0.317442\pi$
$954$	2.07311	+	0.673594i	0.0671194	+	0.0218084i
$955$	−5.75350	−	0.604717i	−0.186179	−	0.0195682i
$956$	−34.1863	+	19.7374i	−1.10566	+	0.638355i
$957$	1.81621	+	12.3480i	0.0587098	+	0.399153i
$958$	1.68859	+	2.92472i	0.0545558	+	0.0944934i
$959$	−44.7963	+	19.9446i	−1.44655	+	0.644045i
$960$	−2.65542	+	2.39095i	−0.0857032	+	0.0771675i
$961$	4.16566	+	12.8206i	0.134376	+	0.413567i
$962$	−1.62728	−	2.62078i	−0.0524655	−	0.0844975i
$963$	−0.103440	+	0.0751534i	−0.00333330	+	0.00242178i
$964$	−8.53136	+	40.1369i	−0.274777	+	1.29272i
$965$	−3.56399	−	3.95821i	−0.114729	−	0.127419i
$966$	−0.726036	+	6.90777i	−0.0233598	+	0.222254i
$967$		−	6.05836i		−	0.194824i	−0.995244	−	0.0974119i	$-0.968944\pi$
$967$		−	6.05836i		−	0.194824i	0.995244	−	0.0974119i	$-0.0310564\pi$
$968$	−4.13771	−	7.54681i	−0.132991	−	0.242564i
$969$	−28.3680	+	16.3783i	−0.911312	+	0.526146i
$970$	0.212714	−	0.292776i	0.00682984	−	0.00940046i
$971$	6.24502	−	1.32742i	0.200412	−	0.0425990i	−0.106612	−	0.994301i	$-0.534000\pi$
$971$	6.24502	−	1.32742i	0.200412	−	0.0425990i	0.307024	+	0.951702i	$0.400667\pi$
$972$	1.91813	+	0.407711i	0.0615240	+	0.0130773i
$973$	−45.9241	+	4.82681i	−1.47226	+	0.154740i
$974$	1.65283	−	1.20085i	0.0529601	−	0.0384778i
$975$	−11.8498	−	12.3410i	−0.379497	−	0.395230i
$976$	7.37184	−	22.6882i	0.235967	−	0.726231i
$977$	8.95927	+	20.1228i	0.286632	+	0.643787i	0.998272	−	0.0587575i	$-0.0187139\pi$
$977$	8.95927	+	20.1228i	0.286632	+	0.643787i	−0.711640	+	0.702544i	$0.752047\pi$
$978$	0.991824	−	1.71789i	0.0317150	−	0.0549321i
$979$	−5.28064	−	6.67031i	−0.168770	−	0.213184i
$980$			12.8110i			0.409233i
$981$	−6.64873	−	0.698810i	−0.212278	−	0.0223113i
$982$	−1.02733	−	4.83322i	−0.0327835	−	0.154234i
$983$	−1.75586	+	0.570513i	−0.0560031	+	0.0181965i	−0.336885	−	0.941546i	$-0.609373\pi$
$983$	−1.75586	+	0.570513i	−0.0560031	+	0.0181965i	0.280881	+	0.959742i	$0.409373\pi$
$984$	−2.40943	−	1.07275i	−0.0768098	−	0.0341979i
$985$	0.659186	+	6.27174i	0.0210034	+	0.199834i
$986$	0.869131	−	4.08894i	0.0276788	−	0.130218i
$987$	−0.0828321	+	0.254931i	−0.00263657	+	0.00811454i
$988$	−7.26707	+	40.5374i	−0.231196	+	1.28967i
$989$	−78.3709			−2.49205
$990$	0.177042	+	0.279325i	0.00562678	+	0.00887754i
$991$	3.76060	−	6.51355i	0.119459	−	0.206910i	−0.800094	−	0.599874i	$-0.795217\pi$
$991$	3.76060	−	6.51355i	0.119459	−	0.206910i	0.919554	+	0.392965i	$0.128551\pi$
$992$	1.01025	−	9.61188i	0.0320754	−	0.305177i
$993$	4.59774	+	1.49390i	0.145905	+	0.0474074i
$994$	7.36209	+	6.62886i	0.233511	+	0.210255i
$995$	1.65140	−	3.70910i	0.0523528	−	0.117586i
$996$	3.78903	+	5.21515i	0.120060	+	0.165248i
$997$	14.3611	−	15.9496i	0.454821	−	0.505130i	−0.471500	−	0.881866i	$-0.656287\pi$
$997$	14.3611	−	15.9496i	0.454821	−	0.505130i	0.926320	+	0.376737i	$0.122954\pi$
$998$	−5.86875	−	6.51790i	−0.185772	−	0.206321i
$999$	−1.76174	−	3.95692i	−0.0557388	−	0.125192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bn.a.4.7	✓	112
11.3	even	5	inner	429.2.bn.a.355.7	yes	112
13.10	even	6	inner	429.2.bn.a.400.7	yes	112
143.36	even	30	inner	429.2.bn.a.322.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bn.a.4.7	✓	112	1.1	even	1	trivial
429.2.bn.a.322.7	yes	112	143.36	even	30	inner
429.2.bn.a.355.7	yes	112	11.3	even	5	inner
429.2.bn.a.400.7	yes	112	13.10	even	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0803440 - 0.180456i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.31215 - 1.45729i) q^{4} +(0.296705 + 0.408379i) q^{5} +(-0.0803440 + 0.180456i) q^{6} +(3.31863 + 2.98811i) q^{7} +(-0.744131 - 0.241783i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.0803440 - 0.180456i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.31215 - 1.45729i) q^{4} +(0.296705 + 0.408379i) q^{5} +(-0.0803440 + 0.180456i) q^{6} +(3.31863 + 2.98811i) q^{7} +(-0.744131 - 0.241783i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0498559 - 0.0863529i) q^{10} +(3.08302 + 1.22269i) q^{11} -1.96098 q^{12} +(1.22351 + 3.39161i) q^{13} +(0.272589 - 0.838942i) q^{14} +(0.104951 - 0.493754i) q^{15} +(-0.393801 - 3.74677i) q^{16} +(-5.13747 - 2.28735i) q^{17} +(0.187865 - 0.0610411i) q^{18} +(1.21104 + 5.69749i) q^{19} +(0.984450 + 0.103470i) q^{20} -4.46566i q^{21} +(-0.0270621 - 0.654585i) q^{22} +(3.93702 - 6.81912i) q^{23} +(0.318241 + 0.714781i) q^{24} +(1.46635 - 4.51295i) q^{25} +(0.513734 - 0.493284i) q^{26} +(0.809017 - 0.587785i) q^{27} +(8.70909 - 0.915362i) q^{28} +(-3.68088 - 0.782395i) q^{29} +(-0.0975328 + 0.0207312i) q^{30} +(-2.46026 + 3.38626i) q^{31} +(-1.99969 + 1.15452i) q^{32} +(-1.15431 - 3.10927i) q^{33} +1.11086i q^{34} +(-0.235627 + 2.24184i) q^{35} +(1.31215 + 1.45729i) q^{36} +(0.900547 - 4.23674i) q^{37} +(0.930845 - 0.676298i) q^{38} +(1.70177 - 3.17867i) q^{39} +(-0.122048 - 0.375626i) q^{40} +(-2.50504 + 2.25555i) q^{41} +(-0.805853 + 0.358789i) q^{42} +(-4.97653 - 8.61961i) q^{43} +(5.82721 - 2.88852i) q^{44} +(-0.437156 + 0.252392i) q^{45} +(-1.54687 - 0.162582i) q^{46} +(-0.0570870 - 0.0185487i) q^{47} +(-2.52089 + 2.79973i) q^{48} +(1.35282 + 12.8712i) q^{49} +(-0.932199 + 0.0979780i) q^{50} +(1.73781 + 5.34842i) q^{51} +(6.54800 + 2.66731i) q^{52} +(8.92757 + 6.48626i) q^{53} +(-0.171069 - 0.0987667i) q^{54} +(0.415429 + 1.62182i) q^{55} +(-1.74702 - 3.02593i) q^{56} +(3.42372 - 4.71234i) q^{57} +(0.154549 + 0.727096i) q^{58} +(-8.58158 - 7.72689i) q^{59} +(-0.581832 - 0.800824i) q^{60} +(5.78470 + 2.57552i) q^{61} +(0.808737 + 0.171902i) q^{62} +(-3.31863 + 2.98811i) q^{63} +(-5.72679 - 4.16076i) q^{64} +(-1.02204 + 1.50596i) q^{65} +(-0.468343 + 0.458114i) q^{66} +(-5.27389 - 3.04488i) q^{67} +(-10.0745 + 4.48545i) q^{68} +(-7.70198 + 1.63711i) q^{69} +(0.423485 - 0.137599i) q^{70} +(-4.56789 + 10.2596i) q^{71} +(0.318241 - 0.714781i) q^{72} +(1.98896 - 0.646253i) q^{73} +(-0.836897 + 0.177888i) q^{74} +(-4.33495 + 1.93004i) q^{75} +(9.89198 + 5.71114i) q^{76} +(6.57790 + 13.2700i) q^{77} +(-0.710337 - 0.0517073i) q^{78} +(-2.63779 - 1.91647i) q^{79} +(1.41326 - 1.27250i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.608291 + 0.270829i) q^{82} +(-1.93221 - 2.65946i) q^{83} +(-6.50777 - 5.85962i) q^{84} +(-0.590206 - 2.77670i) q^{85} +(-1.15562 + 1.59058i) q^{86} +(1.88156 + 3.25895i) q^{87} +(-1.99855 - 1.65526i) q^{88} +(-2.22146 - 1.28256i) q^{89} +(0.0806685 + 0.0586091i) q^{90} +(-6.07414 + 14.9115i) q^{91} +(-4.77149 - 14.6851i) q^{92} +(4.16272 - 0.437519i) q^{93} +(0.00123938 + 0.0117919i) q^{94} +(-1.96742 + 2.18504i) q^{95} +(2.19603 + 0.713532i) q^{96} +(3.60949 + 0.379373i) q^{97} +(2.21399 - 1.27825i) q^{98} +(-1.53825 + 2.93833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9	\( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9} + 21 q^{11} + 120 q^{12} - 15 q^{13} + 30 q^{14} - 6 q^{15} - 8 q^{16} - 12 q^{19} - 66 q^{20} - 17 q^{22} + 12 q^{23} + 14 q^{25} + 9 q^{26} + 28 q^{27} + 18 q^{28} - 2 q^{29} + 10 q^{30} - 30 q^{32} - 24 q^{33} + 16 q^{35} - 20 q^{36} + 38 q^{38} - 12 q^{39} - 60 q^{40} - 36 q^{41} + 12 q^{43} - 6 q^{45} + 54 q^{46} - 42 q^{48} - 40 q^{49} - 51 q^{50} - 30 q^{51} - 15 q^{52} - 22 q^{53} + 22 q^{55} - 76 q^{56} + 132 q^{58} + 72 q^{59} + 34 q^{61} + 17 q^{62} - 84 q^{64} + 28 q^{65} - 24 q^{66} - 48 q^{67} - 12 q^{68} - 7 q^{69} + 30 q^{71} + 20 q^{74} + 32 q^{75} - 48 q^{76} - 136 q^{77} - 14 q^{78} - 36 q^{79} + 18 q^{80} + 14 q^{81} - 5 q^{82} - 27 q^{84} - 66 q^{85} + 52 q^{87} + 52 q^{88} - 96 q^{89} - 20 q^{90} - 125 q^{91} - 10 q^{92} - 18 q^{93} + 22 q^{94} + 72 q^{95} - 93 q^{97} + 24 q^{98}+O(q^{100}) \) 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9 + 21 * q^11 + 120 * q^12 - 15 * q^13 + 30 * q^14 - 6 * q^15 - 8 * q^16 - 12 * q^19 - 66 * q^20 - 17 * q^22 + 12 * q^23 + 14 * q^25 + 9 * q^26 + 28 * q^27 + 18 * q^28 - 2 * q^29 + 10 * q^30 - 30 * q^32 - 24 * q^33 + 16 * q^35 - 20 * q^36 + 38 * q^38 - 12 * q^39 - 60 * q^40 - 36 * q^41 + 12 * q^43 - 6 * q^45 + 54 * q^46 - 42 * q^48 - 40 * q^49 - 51 * q^50 - 30 * q^51 - 15 * q^52 - 22 * q^53 + 22 * q^55 - 76 * q^56 + 132 * q^58 + 72 * q^59 + 34 * q^61 + 17 * q^62 - 84 * q^64 + 28 * q^65 - 24 * q^66 - 48 * q^67 - 12 * q^68 - 7 * q^69 + 30 * q^71 + 20 * q^74 + 32 * q^75 - 48 * q^76 - 136 * q^77 - 14 * q^78 - 36 * q^79 + 18 * q^80 + 14 * q^81 - 5 * q^82 - 27 * q^84 - 66 * q^85 + 52 * q^87 + 52 * q^88 - 96 * q^89 - 20 * q^90 - 125 * q^91 - 10 * q^92 - 18 * q^93 + 22 * q^94 + 72 * q^95 - 93 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more