LMFDB - Embedded newform 731.2.y.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(4,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 8]))

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

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

chi := DirichletCharacter("731.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.y (of order $28$, degree $12$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$64$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	731.4
Dual form			731.2.y.a.183.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69014 - 1.34784i) q^{2} +(-2.41916 - 0.272574i) q^{3} +(0.594855 + 2.60623i) q^{4} +(-2.17264 + 0.760238i) q^{5} +(3.72134 + 3.72134i) q^{6} +(-1.13454 - 1.13454i) q^{7} +(0.631484 - 1.31129i) q^{8} +(2.85326 + 0.651238i) q^{9} +O(q^{10})$	\(q+(-1.69014 - 1.34784i) q^{2} +(-2.41916 - 0.272574i) q^{3} +(0.594855 + 2.60623i) q^{4} +(-2.17264 + 0.760238i) q^{5} +(3.72134 + 3.72134i) q^{6} +(-1.13454 - 1.13454i) q^{7} +(0.631484 - 1.31129i) q^{8} +(2.85326 + 0.651238i) q^{9} +(4.69674 + 1.64346i) q^{10} +(4.81279 - 3.02408i) q^{11} +(-0.728660 - 6.46703i) q^{12} +(0.135477 + 0.0652424i) q^{13} +(0.388350 + 3.44670i) q^{14} +(5.46318 - 1.24693i) q^{15} +(1.98233 - 0.954640i) q^{16} +(-0.0598501 - 4.12267i) q^{17} +(-3.94465 - 4.94643i) q^{18} +(0.00556756 - 0.00127076i) q^{19} +(-3.27376 - 5.21016i) q^{20} +(2.43538 + 3.05387i) q^{21} +(-12.2103 - 1.37577i) q^{22} +(2.77101 - 1.74114i) q^{23} +(-1.88508 + 3.00009i) q^{24} +(0.233225 - 0.185991i) q^{25} +(-0.141039 - 0.292871i) q^{26} +(0.168573 + 0.0589863i) q^{27} +(2.28198 - 3.63175i) q^{28} +(-0.466677 - 4.14187i) q^{29} +(-10.9142 - 5.25601i) q^{30} +(1.00853 + 8.95099i) q^{31} +(-7.47498 - 1.70612i) q^{32} +(-12.4672 + 6.00389i) q^{33} +(-5.45556 + 7.04856i) q^{34} +(3.32745 + 1.60242i) q^{35} +7.82365i q^{36} +(3.42717 - 3.42717i) q^{37} +(-0.0111227 - 0.00535643i) q^{38} +(-0.309958 - 0.194759i) q^{39} +(-0.375092 + 3.32903i) q^{40} +(1.15054 - 0.129634i) q^{41} -8.44398i q^{42} +(-5.31833 - 3.83607i) q^{43} +(10.7444 + 10.7444i) q^{44} +(-6.69419 + 0.754254i) q^{45} +(-7.03018 - 0.792111i) q^{46} +(-1.17144 - 5.13243i) q^{47} +(-5.05579 + 1.76910i) q^{48} -4.42566i q^{49} -0.644869 q^{50} +(-0.978946 + 9.98972i) q^{51} +(-0.0894473 + 0.391894i) q^{52} +(0.923910 + 1.91852i) q^{53} +(-0.205408 - 0.326905i) q^{54} +(-8.15742 + 10.2291i) q^{55} +(-2.20415 + 0.771264i) q^{56} +(-0.0138152 + 0.00155660i) q^{57} +(-4.79384 + 7.62935i) q^{58} +(-2.93948 - 6.10388i) q^{59} +(6.49960 + 13.4966i) q^{60} +(-1.36249 + 12.0924i) q^{61} +(10.3600 - 16.4878i) q^{62} +(-2.49827 - 3.97598i) q^{63} +(7.59057 + 9.51827i) q^{64} +(-0.343942 - 0.0387530i) q^{65} +(29.1636 + 6.65641i) q^{66} +(1.86530 + 8.17240i) q^{67} +(10.7090 - 2.60837i) q^{68} +(-7.17811 + 3.45680i) q^{69} +(-3.46406 - 7.19318i) q^{70} +(-1.61162 - 1.01265i) q^{71} +(2.65575 - 3.33021i) q^{72} +(4.02151 - 1.40719i) q^{73} +(-10.4117 + 1.17312i) q^{74} +(-0.614905 + 0.386370i) q^{75} +(0.00662379 + 0.0137544i) q^{76} +(-8.89121 - 2.02936i) q^{77} +(0.261367 + 0.746945i) q^{78} +(1.93271 + 1.93271i) q^{79} +(-3.58113 + 3.58113i) q^{80} +(-8.30216 - 3.99811i) q^{81} +(-2.11929 - 1.33164i) q^{82} +(-7.87274 + 6.27830i) q^{83} +(-6.51039 + 8.16377i) q^{84} +(3.26424 + 8.91156i) q^{85} +(3.81831 + 13.6518i) q^{86} +10.1471i q^{87} +(-0.926241 - 8.22062i) q^{88} +(3.41605 + 4.28359i) q^{89} +(12.3307 + 7.74792i) q^{90} +(-0.0796839 - 0.227723i) q^{91} +(6.18617 + 6.18617i) q^{92} -21.9288i q^{93} +(-4.93781 + 10.2535i) q^{94} +(-0.0111302 + 0.00699357i) q^{95} +(17.6181 + 6.16486i) q^{96} +(-7.78042 - 12.3825i) q^{97} +(-5.96509 + 7.47998i) q^{98} +(15.7015 - 5.49421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 14 q^{3} + 104 q^{4} - 6 q^{5} - 36 q^{6} - 28 q^{7}+O(q^{10}) $ 768 * q - 14 * q^3 + 104 * q^4 - 6 * q^5 - 36 * q^6 - 28 * q^7	$ 768 q - 14 q^{3} + 104 q^{4} - 6 q^{5} - 36 q^{6} - 28 q^{7} - 18 q^{10} - 4 q^{11} + 34 q^{12} + 4 q^{13} + 26 q^{14} - 152 q^{16} - 10 q^{17} - 24 q^{18} + 22 q^{20} - 20 q^{21} + 12 q^{22} - 24 q^{23} - 100 q^{24} + 10 q^{27} - 42 q^{28} - 18 q^{29} + 48 q^{30} + 4 q^{31} + 36 q^{33} - 4 q^{34} - 60 q^{35} + 40 q^{37} + 12 q^{38} + 34 q^{39} + 6 q^{40} - 48 q^{41} - 104 q^{44} - 52 q^{45} - 74 q^{46} + 20 q^{47} + 94 q^{48} - 344 q^{50} + 80 q^{51} + 12 q^{52} + 60 q^{54} - 32 q^{55} - 50 q^{56} + 38 q^{57} + 112 q^{58} - 12 q^{61} + 10 q^{62} + 52 q^{63} + 144 q^{64} - 10 q^{65} - 20 q^{67} - 54 q^{68} - 12 q^{69} + 14 q^{71} - 208 q^{72} - 176 q^{73} + 46 q^{74} - 116 q^{75} + 140 q^{78} - 168 q^{79} + 32 q^{80} + 116 q^{81} + 186 q^{82} - 60 q^{84} - 184 q^{85} + 176 q^{86} + 24 q^{88} - 4 q^{89} - 58 q^{90} - 152 q^{91} - 136 q^{92} + 70 q^{95} - 332 q^{96} + 72 q^{97} + 104 q^{98} - 56 q^{99}+O(q^{100}) $ 768 * q - 14 * q^3 + 104 * q^4 - 6 * q^5 - 36 * q^6 - 28 * q^7 - 18 * q^10 - 4 * q^11 + 34 * q^12 + 4 * q^13 + 26 * q^14 - 152 * q^16 - 10 * q^17 - 24 * q^18 + 22 * q^20 - 20 * q^21 + 12 * q^22 - 24 * q^23 - 100 * q^24 + 10 * q^27 - 42 * q^28 - 18 * q^29 + 48 * q^30 + 4 * q^31 + 36 * q^33 - 4 * q^34 - 60 * q^35 + 40 * q^37 + 12 * q^38 + 34 * q^39 + 6 * q^40 - 48 * q^41 - 104 * q^44 - 52 * q^45 - 74 * q^46 + 20 * q^47 + 94 * q^48 - 344 * q^50 + 80 * q^51 + 12 * q^52 + 60 * q^54 - 32 * q^55 - 50 * q^56 + 38 * q^57 + 112 * q^58 - 12 * q^61 + 10 * q^62 + 52 * q^63 + 144 * q^64 - 10 * q^65 - 20 * q^67 - 54 * q^68 - 12 * q^69 + 14 * q^71 - 208 * q^72 - 176 * q^73 + 46 * q^74 - 116 * q^75 + 140 * q^78 - 168 * q^79 + 32 * q^80 + 116 * q^81 + 186 * q^82 - 60 * q^84 - 184 * q^85 + 176 * q^86 + 24 * q^88 - 4 * q^89 - 58 * q^90 - 152 * q^91 - 136 * q^92 + 70 * q^95 - 332 * q^96 + 72 * q^97 + 104 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−1.69014	−	1.34784i	−1.19511	−	0.953068i	−0.195492	−	0.980705i	$-0.562630\pi$
$2$	−1.69014	−	1.34784i	−1.19511	−	0.953068i	−0.999618	+	0.0276370i	$0.991202\pi$
$3$	−2.41916	−	0.272574i	−1.39670	−	0.157371i	−0.618698	−	0.785629i	$-0.712340\pi$
$3$	−2.41916	−	0.272574i	−1.39670	−	0.157371i	−0.778005	+	0.628258i	$0.783768\pi$
$4$	0.594855	+	2.60623i	0.297427	+	1.30312i
$5$	−2.17264	+	0.760238i	−0.971632	+	0.339989i	−0.768988	−	0.639264i	$-0.779239\pi$
$5$	−2.17264	+	0.760238i	−0.971632	+	0.339989i	−0.202644	+	0.979252i	$0.564954\pi$
$6$	3.72134	+	3.72134i	1.51923	+	1.51923i
$7$	−1.13454	−	1.13454i	−0.428814	−	0.428814i	0.459410	−	0.888224i	$-0.348061\pi$
$7$	−1.13454	−	1.13454i	−0.428814	−	0.428814i	−0.888224	+	0.459410i	$0.848061\pi$
$8$	0.631484	−	1.31129i	0.223263	−	0.463611i
$9$	2.85326	+	0.651238i	0.951087	+	0.217079i
$10$	4.69674	+	1.64346i	1.48524	+	0.519708i
$11$	4.81279	−	3.02408i	1.45111	−	0.911794i	0.451300	−	0.892372i	$-0.350961\pi$
$11$	4.81279	−	3.02408i	1.45111	−	0.911794i	0.999811	−	0.0194212i	$-0.00618234\pi$
$12$	−0.728660	−	6.46703i	−0.210346	−	1.86687i
$13$	0.135477	+	0.0652424i	0.0375746	+	0.0180950i	0.452577	−	0.891725i	$-0.350505\pi$
$13$	0.135477	+	0.0652424i	0.0375746	+	0.0180950i	−0.415002	+	0.909820i	$0.636219\pi$
$14$	0.388350	+	3.44670i	0.103791	+	0.921169i
$15$	5.46318	−	1.24693i	1.41059	−	0.321957i
$16$	1.98233	−	0.954640i	0.495583	−	0.238660i
$17$	−0.0598501	−	4.12267i	−0.0145158	−	0.999895i
$17$	−0.0598501	−	4.12267i	−0.0145158	−	0.999895i
$18$	−3.94465	−	4.94643i	−0.929762	−	1.16589i
$19$	0.00556756	−	0.00127076i	0.00127729	−	0.000291532i	−0.221882	−	0.975073i	$-0.571220\pi$
$19$	0.00556756	−	0.00127076i	0.00127729	−	0.000291532i	0.223160	+	0.974782i	$0.428363\pi$
$20$	−3.27376	−	5.21016i	−0.732035	−	1.16503i
$21$	2.43538	+	3.05387i	0.531444	+	0.666409i
$22$	−12.2103	−	1.37577i	−2.60324	−	0.293315i
$23$	2.77101	−	1.74114i	0.577796	−	0.363053i	−0.211208	−	0.977441i	$-0.567740\pi$
$23$	2.77101	−	1.74114i	0.577796	−	0.363053i	0.789004	+	0.614388i	$0.210597\pi$
$24$	−1.88508	+	3.00009i	−0.384791	+	0.612392i
$25$	0.233225	−	0.185991i	0.0466450	−	0.0371981i
$26$	−0.141039	−	0.292871i	−0.0276600	−	0.0574367i
$27$	0.168573	+	0.0589863i	0.0324419	+	0.0113519i
$28$	2.28198	−	3.63175i	0.431253	−	0.686335i
$29$	−0.466677	−	4.14187i	−0.0866597	−	0.769126i	−0.959613	−	0.281323i	$-0.909227\pi$
$29$	−0.466677	−	4.14187i	−0.0866597	−	0.769126i	0.872953	−	0.487803i	$-0.162202\pi$
$30$	−10.9142	−	5.25601i	−1.99265	−	0.959611i
$31$	1.00853	+	8.95099i	0.181138	+	1.60765i	0.674806	+	0.737995i	$0.264227\pi$
$31$	1.00853	+	8.95099i	0.181138	+	1.60765i	−0.493668	+	0.869650i	$0.664344\pi$
$32$	−7.47498	−	1.70612i	−1.32140	−	0.301602i
$33$	−12.4672	+	6.00389i	−2.17026	+	1.04514i
$34$	−5.45556	+	7.04856i	−0.935620	+	1.20882i
$35$	3.32745	+	1.60242i	0.562442	+	0.270858i
$36$			7.82365i			1.30394i
$37$	3.42717	−	3.42717i	0.563424	−	0.563424i	−0.366855	−	0.930278i	$-0.619565\pi$
$37$	3.42717	−	3.42717i	0.563424	−	0.563424i	0.930278	+	0.366855i	$0.119565\pi$
$38$	−0.0111227	−	0.00535643i	−0.00180435	−	0.000868928i
$39$	−0.309958	−	0.194759i	−0.0496330	−	0.0311865i
$40$	−0.375092	+	3.32903i	−0.0593072	+	0.526366i
$41$	1.15054	−	0.129634i	0.179684	−	0.0202455i	−0.0216642	−	0.999765i	$-0.506896\pi$
$41$	1.15054	−	0.129634i	0.179684	−	0.0202455i	0.201348	+	0.979520i	$0.435468\pi$
$42$		−	8.44398i		−	1.30293i
$43$	−5.31833	−	3.83607i	−0.811037	−	0.584995i
$43$	−5.31833	−	3.83607i	−0.811037	−	0.584995i
$44$	10.7444	+	10.7444i	1.61977	+	1.61977i
$45$	−6.69419	+	0.754254i	−0.997911	+	0.112438i
$46$	−7.03018	−	0.792111i	−1.03654	−	0.116790i
$47$	−1.17144	−	5.13243i	−0.170873	−	0.748643i	−0.985641	−	0.168855i	$-0.945993\pi$
$47$	−1.17144	−	5.13243i	−0.170873	−	0.748643i	0.814768	−	0.579787i	$-0.196864\pi$
$48$	−5.05579	+	1.76910i	−0.729740	+	0.255347i
$49$		−	4.42566i		−	0.632237i
$50$	−0.644869			−0.0911982
$51$	−0.978946	+	9.98972i	−0.137080	+	1.39884i
$52$	−0.0894473	+	0.391894i	−0.0124041	+	0.0543460i
$53$	0.923910	+	1.91852i	0.126909	+	0.263529i	0.954736	−	0.297454i	$-0.0961376\pi$
$53$	0.923910	+	1.91852i	0.126909	+	0.263529i	−0.827827	+	0.560983i	$0.810423\pi$
$54$	−0.205408	−	0.326905i	−0.0279525	−	0.0444862i
$55$	−8.15742	+	10.2291i	−1.09995	+	1.37929i
$56$	−2.20415	+	0.771264i	−0.294541	+	0.103064i
$57$	−0.0138152	+	0.00155660i	−0.00182987	+	0.000206177i
$58$	−4.79384	+	7.62935i	−0.629462	+	1.00178i
$59$	−2.93948	−	6.10388i	−0.382687	−	0.794658i	−0.999969	−	0.00791569i	$-0.997480\pi$
$59$	−2.93948	−	6.10388i	−0.382687	−	0.794658i	0.617282	−	0.786742i	$-0.288234\pi$
$60$	6.49960	+	13.4966i	0.839094	+	1.74240i
$61$	−1.36249	+	12.0924i	−0.174449	+	1.54827i	0.535813	+	0.844337i	$0.320005\pi$
$61$	−1.36249	+	12.0924i	−0.174449	+	1.54827i	−0.710262	+	0.703938i	$0.751423\pi$
$62$	10.3600	−	16.4878i	1.31572	−	2.09395i
$63$	−2.49827	−	3.97598i	−0.314753	−	0.500927i
$64$	7.59057	+	9.51827i	0.948821	+	1.18978i
$65$	−0.343942	−	0.0387530i	−0.0426608	−	0.00480672i
$66$	29.1636	+	6.65641i	3.58979	+	0.819347i
$67$	1.86530	+	8.17240i	0.227882	+	0.998417i	0.951363	+	0.308072i	$0.0996839\pi$
$67$	1.86530	+	8.17240i	0.227882	+	0.998417i	−0.723481	+	0.690345i	$0.757459\pi$
$68$	10.7090	−	2.60837i	1.29866	−	0.316312i
$69$	−7.17811	+	3.45680i	−0.864143	+	0.416149i
$70$	−3.46406	−	7.19318i	−0.414034	−	0.859750i
$71$	−1.61162	−	1.01265i	−0.191264	−	0.120179i	0.432996	−	0.901396i	$-0.357456\pi$
$71$	−1.61162	−	1.01265i	−0.191264	−	0.120179i	−0.624260	+	0.781217i	$0.714599\pi$
$72$	2.65575	−	3.33021i	0.312983	−	0.392468i
$73$	4.02151	−	1.40719i	0.470682	−	0.164699i	−0.0845070	−	0.996423i	$-0.526932\pi$
$73$	4.02151	−	1.40719i	0.470682	−	0.164699i	0.555189	+	0.831724i	$0.312646\pi$
$74$	−10.4117	+	1.17312i	−1.21033	+	0.136372i
$75$	−0.614905	+	0.386370i	−0.0710031	+	0.0446142i
$76$	0.00662379	+	0.0137544i	0.000759800	+	0.00157774i
$77$	−8.89121	−	2.02936i	−1.01325	−	0.231267i
$78$	0.261367	+	0.746945i	0.0295940	+	0.0845749i
$79$	1.93271	+	1.93271i	0.217447	+	0.217447i	0.807422	−	0.589975i	$-0.200862\pi$
$79$	1.93271	+	1.93271i	0.217447	+	0.217447i	−0.589975	+	0.807422i	$0.700862\pi$
$80$	−3.58113	+	3.58113i	−0.400382	+	0.400382i
$81$	−8.30216	−	3.99811i	−0.922462	−	0.444234i
$82$	−2.11929	−	1.33164i	−0.234037	−	0.147055i
$83$	−7.87274	+	6.27830i	−0.864145	+	0.689133i	−0.951701	−	0.307027i	$-0.900666\pi$
$83$	−7.87274	+	6.27830i	−0.864145	+	0.689133i	0.0875558	+	0.996160i	$0.472094\pi$
$84$	−6.51039	+	8.16377i	−0.710342	+	0.890741i
$85$	3.26424	+	8.91156i	0.354057	+	0.966594i
$86$	3.81831	+	13.6518i	0.411739	+	1.47211i
$87$			10.1471i			1.08788i
$88$	−0.926241	−	8.22062i	−0.0987376	−	0.876321i
$89$	3.41605	+	4.28359i	0.362101	+	0.454060i	0.929193	−	0.369594i	$-0.120503\pi$
$89$	3.41605	+	4.28359i	0.362101	+	0.454060i	−0.567093	+	0.823654i	$0.691932\pi$
$90$	12.3307	+	7.74792i	1.29977	+	0.816703i
$91$	−0.0796839	−	0.227723i	−0.00835314	−	0.0238719i
$92$	6.18617	+	6.18617i	0.644952	+	0.644952i
$93$		−	21.9288i		−	2.27391i
$94$	−4.93781	+	10.2535i	−0.509296	+	1.05756i
$95$	−0.0111302	+	0.00699357i	−0.00114193	+	0.000717525i
$96$	17.6181	+	6.16486i	1.79814	+	0.629198i
$97$	−7.78042	−	12.3825i	−0.789982	−	1.25725i	−0.962241	−	0.272198i	$-0.912250\pi$
$97$	−7.78042	−	12.3825i	−0.789982	−	1.25725i	0.172259	−	0.985052i	$-0.444893\pi$
$98$	−5.96509	+	7.47998i	−0.602565	+	0.755592i
$99$	15.7015	−	5.49421i	1.57807	−	0.552189i
$100$	0.623469	+	0.497200i	0.0623469	+	0.0497200i
$101$	−2.66653	−	11.6828i	−0.265330	−	1.16249i	−0.915379	−	0.402594i	$-0.868109\pi$
$101$	−2.66653	−	11.6828i	−0.265330	−	1.16249i	0.650049	−	0.759893i	$-0.274749\pi$
$102$	15.1191	−	15.5646i	1.49702	−	1.54112i
$103$	−11.4904	+	5.53349i	−1.13218	+	0.545231i	−0.903636	−	0.428302i	$-0.859112\pi$
$103$	−11.4904	+	5.53349i	−1.13218	+	0.545231i	−0.228547	+	0.973533i	$0.573398\pi$
$104$	0.171103	−	0.136450i	0.0167781	−	0.0133800i
$105$	−7.61286	−	4.78348i	−0.742939	−	0.466820i
$106$	1.02432	−	4.48785i	0.0994910	−	0.435898i
$107$	16.0553	+	1.80899i	1.55212	+	0.174882i	0.845990	−	0.533199i	$-0.179010\pi$
$107$	16.0553	+	1.80899i	1.55212	+	0.174882i	0.706131	+	0.708081i	$0.250439\pi$
$108$	−0.0534553	+	0.474429i	−0.00514374	+	0.0456519i
$109$	0.785333	−	0.493457i	0.0752213	−	0.0472646i	−0.493896	−	0.869521i	$-0.664428\pi$
$109$	0.785333	−	0.493457i	0.0752213	−	0.0472646i	0.569118	+	0.822256i	$0.307285\pi$
$110$	27.5744	−	6.29367i	2.62911	−	0.600078i
$111$	−9.22504	+	7.35673i	−0.875602	+	0.698269i
$112$	−3.33210	−	1.16595i	−0.314854	−	0.110172i
$113$	−16.8004	−	5.87872i	−1.58045	−	0.553024i	−0.609600	−	0.792709i	$-0.708670\pi$
$113$	−16.8004	−	5.87872i	−1.58045	−	0.553024i	−0.970851	+	0.239685i	$0.922956\pi$
$114$	0.0254477	+	0.0159899i	0.00238340	+	0.00149759i
$115$	−4.69671	+	5.88949i	−0.437971	+	0.549198i
$116$	10.5171	−	3.68008i	0.976485	−	0.341687i
$117$	0.344064	+	0.274381i	0.0318087	+	0.0253666i
$118$	−3.25895	+	14.2784i	−0.300010	+	1.31443i
$119$	−4.60942	+	4.74522i	−0.422544	+	0.434994i
$120$	1.81481	−	7.95122i	0.165669	−	0.725844i
$121$	9.24520	−	19.1978i	0.840472	−	1.74526i
$122$	18.6015	−	18.6015i	1.68410	−	1.68410i
$123$	−2.81867			−0.254151
$124$	−22.7284	+	7.95301i	−2.04107	+	0.714202i
$125$	5.75785	−	9.16357i	0.514998	−	0.819615i
$126$	−1.13656	+	10.0872i	−0.101253	+	0.898643i
$127$	−13.1754	−	10.5071i	−1.16913	−	0.932351i	−0.170536	−	0.985351i	$-0.554550\pi$
$127$	−13.1754	−	10.5071i	−1.16913	−	0.932351i	−0.998594	+	0.0530007i	$0.983121\pi$
$128$		−	10.9837i		−	0.970828i
$129$	11.8203	+	10.7297i	1.04072	+	0.944697i
$130$	0.529078	+	0.529078i	0.0464032	+	0.0464032i
$131$	−0.967583	−	8.58753i	−0.0845381	−	0.750296i	−0.962447	−	0.271469i	$-0.912491\pi$
$131$	−0.967583	−	8.58753i	−0.0845381	−	0.750296i	0.877909	−	0.478827i	$-0.158938\pi$
$132$	−23.0637	−	28.9210i	−2.00744	−	2.51725i
$133$	−0.00775832	−	0.00487488i	−0.000672732	−	0.000422705i
$134$	7.86249	−	16.3266i	0.679215	−	1.41041i
$135$	−0.411092			−0.0353811
$136$	−5.44381	−	2.52492i	−0.466803	−	0.216510i
$137$	−7.23684	−	3.48508i	−0.618285	−	0.297750i	0.0984007	−	0.995147i	$-0.468627\pi$
$137$	−7.23684	−	3.48508i	−0.618285	−	0.297750i	−0.716685	+	0.697397i	$0.754342\pi$
$138$	16.7912	+	3.83249i	1.42937	+	0.326243i
$139$	−5.89010	+	16.8329i	−0.499591	+	1.42775i	0.367698	+	0.929945i	$0.380146\pi$
$139$	−5.89010	+	16.8329i	−0.499591	+	1.42775i	−0.867289	+	0.497805i	$0.834140\pi$
$140$	−2.19691	+	9.62530i	−0.185673	+	0.813487i
$141$	1.43495	+	12.7355i	0.120844	+	1.07252i
$142$	1.35897	+	3.88372i	0.114042	+	0.325914i
$143$	0.849321	−	0.0956955i	0.0710238	−	0.00800246i
$144$	6.27781	−	1.43287i	0.523151	−	0.119406i
$145$	4.16273	+	8.64399i	0.345696	+	0.717844i
$146$	−8.69358	−	3.04202i	−0.719486	−	0.251759i
$147$	−1.20632	+	10.7064i	−0.0994955	+	0.883047i
$148$	10.9707	+	6.89333i	0.901784	+	0.566628i
$149$	3.87954	−	16.9974i	0.317824	−	1.39248i	−0.523536	−	0.852003i	$-0.675388\pi$
$149$	3.87954	−	16.9974i	0.317824	−	1.39248i	0.841360	−	0.540475i	$-0.181755\pi$
$150$	1.56004	+	0.175775i	0.127377	+	0.0143519i
$151$	7.08414	−	5.64942i	0.576500	−	0.459743i	−0.291318	−	0.956626i	$-0.594094\pi$
$151$	7.08414	−	5.64942i	0.576500	−	0.459743i	0.867817	+	0.496883i	$0.165522\pi$
$152$	0.00184949	−	0.00810315i	0.000150014	−	0.000657252i
$153$	2.51407	−	11.8020i	0.203251	−	0.954138i
$154$	12.2921	+	15.4138i	0.990528	+	1.24208i
$155$	−8.99606	−	18.6805i	−0.722581	−	1.50045i
$156$	0.323208	−	0.923675i	0.0258773	−	0.0739532i
$157$	−1.30995	−	5.73926i	−0.104545	−	0.458043i	−0.999919	−	0.0127275i	$-0.995949\pi$
$157$	−1.30995	−	5.73926i	−0.104545	−	0.458043i	0.895374	−	0.445316i	$-0.146909\pi$
$158$	−0.661564	−	5.87154i	−0.0526312	−	0.467115i
$159$	−1.71215	−	4.89304i	−0.135782	−	0.388043i
$160$	17.5375	−	1.97600i	1.38646	−	0.156216i
$161$	−5.11920	−	1.16842i	−0.403449	−	0.0920847i
$162$	8.64300	+	17.9474i	0.679058	+	1.41008i
$163$	0.670665	−	0.421407i	0.0525305	−	0.0330071i	−0.505511	−	0.862820i	$-0.668696\pi$
$163$	0.670665	−	0.421407i	0.0525305	−	0.0330071i	0.558041	+	0.829813i	$0.311553\pi$
$164$	1.02226	+	2.92145i	0.0798250	+	0.228127i
$165$	22.5223	−	22.5223i	1.75336	−	1.75336i
$166$	21.7682			1.68954
$167$	−16.6139	+	5.81346i	−1.28562	+	0.449859i	−0.884661	−	0.466235i	$-0.845610\pi$
$167$	−16.6139	+	5.81346i	−1.28562	+	0.449859i	−0.400963	+	0.916094i	$0.631324\pi$
$168$	5.54241	−	1.26502i	0.427606	−	0.0975983i
$169$	−8.09127	−	10.1461i	−0.622405	−	0.780472i
$170$	6.49435	−	19.4615i	0.498094	−	1.49263i
$171$	0.0167133			0.00127810
$172$	6.83404	−	16.1427i	0.521090	−	1.23087i
$173$	1.86847	−	1.86847i	0.142057	−	0.142057i	−0.632502	−	0.774559i	$-0.717972\pi$
$173$	1.86847	−	1.86847i	0.142057	−	0.142057i	0.774559	+	0.632502i	$0.217972\pi$
$174$	13.6766	−	17.1500i	1.03682	−	1.30014i
$175$	−0.475615	−	0.0535889i	−0.0359531	−	0.00405094i
$176$	6.65364	−	10.5892i	0.501537	−	0.798191i
$177$	5.44731	+	15.5675i	0.409445	+	1.17013i
$178$		−	11.8442i		−	0.887758i
$179$		−	2.84980i		−	0.213004i	−0.994312	−	0.106502i	$-0.966035\pi$
$179$		−	2.84980i		−	0.213004i	0.994312	−	0.106502i	$-0.0339651\pi$
$180$	−5.94784	−	16.9979i	−0.443325	−	1.26695i
$181$	−6.66354	+	4.18698i	−0.495297	+	0.311216i	−0.756416	−	0.654091i	$-0.773051\pi$
$181$	−6.66354	+	4.18698i	−0.495297	+	0.311216i	0.261119	+	0.965307i	$0.415908\pi$
$182$	−0.172258	+	0.492286i	−0.0127686	+	0.0364907i
$183$	6.59215	−	28.8821i	0.487306	−	2.13503i
$184$	−0.533292	−	4.73310i	−0.0393148	−	0.348929i
$185$	−4.84053	+	10.0515i	−0.355883	+	0.738998i
$186$	−29.5566	+	37.0627i	−2.16719	+	2.71757i
$187$	−12.7553	−	19.6606i	−0.932762	−	1.43772i
$188$	12.6795	−	6.10611i	0.924745	−	0.445334i
$189$	−0.124330	−	0.258174i	−0.00904369	−	0.0187794i
$190$	0.0282378	+	0.00318164i	0.00204859	+	0.000230820i
$191$	−0.940652	−	4.12127i	−0.0680632	−	0.298204i	0.929427	−	0.369005i	$-0.120302\pi$
$191$	−0.940652	−	4.12127i	−0.0680632	−	0.298204i	−0.997490	+	0.0708010i	$0.977444\pi$
$192$	−15.7684	−	25.0952i	−1.13798	−	1.81109i
$193$	−0.206412	+	1.83196i	−0.0148579	+	0.131867i	−0.998951	−	0.0457841i	$-0.985421\pi$
$193$	−0.206412	+	1.83196i	−0.0148579	+	0.131867i	0.984093	+	0.177651i	$0.0568499\pi$
$194$	−3.53961	+	31.4149i	−0.254129	+	2.25546i
$195$	0.821489	+	0.187499i	0.0588280	+	0.0134271i
$196$	11.5343	−	2.63262i	0.823877	−	0.188045i
$197$	−0.915917	+	8.12899i	−0.0652564	+	0.579167i	0.917953	+	0.396688i	$0.129841\pi$
$197$	−0.915917	+	8.12899i	−0.0652564	+	0.579167i	−0.983210	+	0.182478i	$0.941588\pi$
$198$	−33.9432	−	11.8772i	−2.41224	−	0.844078i
$199$	−3.30368	+	9.44138i	−0.234192	+	0.669282i	0.765475	+	0.643466i	$0.222504\pi$
$199$	−3.30368	+	9.44138i	−0.234192	+	0.669282i	−0.999667	+	0.0258161i	$0.991782\pi$
$200$	−0.0966098	−	0.423275i	−0.00683135	−	0.0299301i
$201$	−2.28487	−	20.2788i	−0.161162	−	1.43035i
$202$	−11.2398	+	23.3397i	−0.790831	+	1.64218i
$203$	−4.16964	+	5.22856i	−0.292651	+	0.366973i
$204$	−26.6178	+	3.39108i	−1.86362	+	0.237423i
$205$	−2.40114	+	1.15633i	−0.167703	+	0.0807615i
$206$	26.8787	+	6.13488i	1.87273	+	0.427437i
$207$	9.04032	−	3.16334i	0.628346	−	0.219868i
$208$	0.330843			0.0229399
$209$	0.0229526	−	0.0229526i	0.00158767	−	0.00158767i
$210$	6.41943	+	18.3457i	0.442983	+	1.26597i
$211$	−3.13680	+	4.99218i	−0.215946	+	0.343676i	−0.937077	−	0.349123i	$-0.886480\pi$
$211$	−3.13680	+	4.99218i	−0.215946	+	0.343676i	0.721131	+	0.692799i	$0.243623\pi$
$212$	−4.45051	+	3.54916i	−0.305662	+	0.243757i
$213$	3.62274	+	2.88904i	0.248226	+	0.197954i
$214$	−24.6974	−	24.6974i	−1.68828	−	1.68828i
$215$	14.4711	+	4.29118i	0.986921	+	0.292656i
$216$	0.183799	−	0.183799i	0.0125060	−	0.0125060i
$217$	9.01100	−	11.2994i	0.611707	−	0.767056i
$218$	−1.99243	−	0.224492i	−0.134944	−	0.0152046i
$219$	−10.1122	+	2.30805i	−0.683322	+	0.155964i
$220$	−31.5118	−	15.1753i	−2.12453	−	1.02312i
$221$	0.260864	−	0.562433i	0.0175476	−	0.0378333i
$222$	25.5073			1.71194
$223$	−10.4613	+	21.7230i	−0.700538	+	1.45468i	0.181444	+	0.983401i	$0.441923\pi$
$223$	−10.4613	+	21.7230i	−0.700538	+	1.45468i	−0.881983	+	0.471282i	$0.843791\pi$
$224$	6.54499	+	10.4163i	0.437305	+	0.695967i
$225$	0.786576	−	0.378795i	0.0524384	−	0.0252530i
$226$	20.4715	+	32.5802i	1.36174	+	2.16720i
$227$	−3.89799	+	0.439199i	−0.258719	+	0.0291506i	−0.240371	−	0.970681i	$-0.577269\pi$
$227$	−3.89799	+	0.439199i	−0.258719	+	0.0291506i	−0.0183478	+	0.999832i	$0.505841\pi$
$228$	−0.0122749	−	0.0350797i	−0.000812926	−	0.00232321i
$229$	17.0669	+	13.6104i	1.12781	+	0.899398i	0.995773	−	0.0918464i	$-0.0292769\pi$
$229$	17.0669	+	13.6104i	1.12781	+	0.899398i	0.132037	+	0.991245i	$0.457848\pi$
$230$	15.8762	−	3.62364i	1.04685	−	0.238936i
$231$	20.9561	+	7.33286i	1.37881	+	0.482467i
$232$	−5.72589	−	2.00358i	−0.375923	−	0.131541i
$233$	3.01673	+	0.339904i	0.197632	+	0.0222678i	0.210226	−	0.977653i	$-0.432580\pi$
$233$	3.01673	+	0.339904i	0.197632	+	0.0222678i	−0.0125933	+	0.999921i	$0.504009\pi$
$234$	−0.211693	−	0.927487i	−0.0138388	−	0.0606317i
$235$	6.44699	+	10.2603i	0.420556	+	0.669310i
$236$	14.1596	−	11.2919i	0.921709	−	0.735039i
$237$	−4.14873	−	5.20234i	−0.269489	−	0.337929i
$238$	14.1864	−	1.80732i	0.919566	−	0.117151i
$239$	2.89770	+	12.6957i	0.187437	+	0.821214i	0.977962	+	0.208784i	$0.0669506\pi$
$239$	2.89770	+	12.6957i	0.187437	+	0.821214i	−0.790525	+	0.612430i	$0.790192\pi$
$240$	9.63945	−	7.68720i	0.622224	−	0.496207i
$241$	2.81975	−	8.05839i	0.181636	−	0.519086i	−0.816680	−	0.577091i	$-0.804188\pi$
$241$	2.81975	−	8.05839i	0.181636	−	0.519086i	0.998316	+	0.0580043i	$0.0184737\pi$
$242$	−41.5014	+	19.9860i	−2.66781	+	1.28475i
$243$	18.5408	+	11.6500i	1.18939	+	0.747346i
$244$	−32.3261	+	3.64227i	−2.06947	+	0.233173i
$245$	3.36455	+	9.61534i	0.214953	+	0.614301i
$246$	4.76394	+	3.79912i	0.303738	+	0.242223i
$247$	0.000837185	0	0.000191082i	5.32688e−5	0	1.21583e-5i
$248$	12.3742	+	4.32992i	0.785763	+	0.274950i
$249$	20.7567	−	13.0423i	1.31540	−	0.826523i
$250$	−22.0826	+	7.72705i	−1.39663	+	0.488701i
$251$	−14.2302			−0.898205			−0.449102	−	0.893480i	$-0.648256\pi$
$251$	−14.2302			−0.898205			−0.449102	+	0.893480i	$0.648256\pi$
$252$	8.87621	−	8.87621i	0.559149	−	0.559149i
$253$	8.07095	−	16.7595i	0.507416	−	1.05366i
$254$	8.10648	+	35.5168i	0.508646	+	2.22852i
$255$	−5.46767	−	22.4483i	−0.342399	−	1.40576i
$256$	0.376881	−	0.472593i	0.0235550	−	0.0295371i
$257$			0.481971i			0.0300646i	0.999887	+	0.0150323i	$0.00478510\pi$
$257$			0.481971i			0.0300646i	−0.999887	+	0.0150323i	$0.995215\pi$
$258$	−5.51599	−	34.0666i	−0.343411	−	2.12089i
$259$	−7.77650			−0.483208
$260$	−0.103597	−	0.919445i	−0.00642479	−	0.0570216i
$261$	1.36579	−	12.1218i	0.0845406	−	0.750318i
$262$	−9.93929	+	15.8183i	−0.614051	+	0.977257i
$263$	−6.42501	+	13.3417i	−0.396183	+	0.822683i	0.603496	+	0.797366i	$0.293774\pi$
$263$	−6.42501	+	13.3417i	−0.396183	+	0.822683i	−0.999679	+	0.0253173i	$0.991940\pi$
$264$			20.1395i			1.23950i
$265$	−3.46585	−	3.46585i	−0.212905	−	0.212905i
$266$	0.00654209	+	0.0186962i	0.000401121	+	0.00114634i
$267$	−7.09638	−	11.2938i	−0.434292	−	0.691171i
$268$	−20.1896	+	9.72278i	−1.23327	+	0.593913i
$269$	8.33499	+	13.2651i	0.508193	+	0.808785i	0.998011	−	0.0630399i	$-0.0200795\pi$
$269$	8.33499	+	13.2651i	0.508193	+	0.808785i	−0.489818	+	0.871825i	$0.662937\pi$
$270$	0.694803	+	0.554087i	0.0422843	+	0.0337206i
$271$	−0.890681	−	0.428929i	−0.0541050	−	0.0260556i	0.406636	−	0.913590i	$-0.366702\pi$
$271$	−0.890681	−	0.428929i	−0.0541050	−	0.0260556i	−0.460741	+	0.887535i	$0.652416\pi$
$272$	−4.05431	−	8.11536i	−0.245829	−	0.492066i
$273$	0.130697	+	0.572620i	0.00791012	+	0.0346565i
$274$	7.53394	+	15.6444i	0.455142	+	0.945112i
$275$	0.560013	−	1.60042i	0.0337700	−	0.0965092i
$276$	−13.2791	−	16.6515i	−0.799311	−	1.00230i
$277$	16.0446	+	10.0815i	0.964027	+	0.605739i	0.919425	−	0.393266i	$-0.128655\pi$
$277$	16.0446	+	10.0815i	0.964027	+	0.605739i	0.0446028	+	0.999005i	$0.485798\pi$
$278$	32.6432	−	20.5111i	1.95781	−	1.23017i
$279$	−2.95162	+	26.1963i	−0.176709	+	1.56833i
$280$	4.20246	−	3.35135i	0.251145	−	0.200281i
$281$	−26.0513	−	5.94604i	−1.55409	−	0.354711i	−0.642655	−	0.766156i	$-0.722167\pi$
$281$	−26.0513	−	5.94604i	−1.55409	−	0.354711i	−0.911435	+	0.411445i	$0.865024\pi$
$282$	14.7402	−	23.4589i	0.877765	−	1.39695i
$283$	3.19780	−	28.3812i	0.190089	−	1.68709i	−0.430213	−	0.902727i	$-0.641562\pi$
$283$	3.19780	−	28.3812i	0.190089	−	1.68709i	0.620303	−	0.784363i	$-0.287010\pi$
$284$	1.68051	−	4.80262i	0.0997199	−	0.284983i
$285$	0.0288320	−	0.0138848i	0.00170786	−	0.000822463i
$286$	−1.56445	−	0.983012i	−0.0925082	−	0.0581267i
$287$	−1.45240	−	1.15825i	−0.0857324	−	0.0683693i
$288$	−20.2170	−	9.73599i	−1.19130	−	0.573699i
$289$	−16.9928	+	0.493484i	−0.999579	+	0.0290285i
$290$	4.61514	−	20.2203i	0.271011	−	1.18737i
$291$	15.4470	+	32.0759i	0.905517	+	1.88032i
$292$	6.05967	+	9.64391i	0.354615	+	0.564367i
$293$	3.20628	+	1.54406i	0.187313	+	0.0902050i	0.525189	−	0.850985i	$-0.323994\pi$
$293$	3.20628	+	1.54406i	0.187313	+	0.0902050i	−0.337877	+	0.941190i	$0.609709\pi$
$294$	16.4694	−	16.4694i	0.960512	−	0.960512i
$295$	11.0268	+	11.0268i	0.642006	+	0.642006i
$296$	−2.32981	−	6.65822i	−0.135418	−	0.387001i
$297$	0.989687	−	0.225889i	0.0574274	−	0.0131074i
$298$	−29.4667	+	23.4989i	−1.70696	+	1.36126i
$299$	0.489005	−	0.0550976i	0.0282799	−	0.00318638i
$300$	−1.37275	−	1.37275i	−0.0792557	−	0.0792557i
$301$	1.68168	+	10.3860i	0.0969303	+	0.598638i
$302$	−19.5877			−1.12715
$303$	3.26634	+	28.9895i	0.187646	+	1.66540i
$304$	0.00982363	−	0.00783409i	0.000563424	−	0.000449316i
$305$	−6.23292	−	27.3082i	−0.356896	−	1.56366i
$306$	−20.1564	+	16.5585i	−1.15227	+	0.946588i
$307$	5.65166			0.322557			0.161279	−	0.986909i	$-0.448438\pi$
$307$	5.65166			0.322557			0.161279	+	0.986909i	$0.448438\pi$
$308$		−	24.3797i		−	1.38916i
$309$	29.3054	−	10.2544i	1.66713	−	0.583353i
$310$	−9.97377	+	43.6980i	−0.566472	+	2.48188i
$311$	5.97773	−	17.0834i	0.338966	−	0.968709i	−0.640651	−	0.767833i	$-0.721335\pi$
$311$	5.97773	−	17.0834i	0.338966	−	0.968709i	0.979617	−	0.200877i	$-0.0643790\pi$
$312$	−0.451119	+	0.283457i	−0.0255396	+	0.0160476i
$313$	8.59511	−	0.968436i	0.485824	−	0.0547392i	0.134344	−	0.990935i	$-0.457107\pi$
$313$	8.59511	−	0.968436i	0.485824	−	0.0547392i	0.351480	+	0.936195i	$0.385679\pi$
$314$	−5.52162	+	11.4658i	−0.311603	+	0.647051i
$315$	8.45053	+	6.73907i	0.476134	+	0.379704i
$316$	−3.88740	+	6.18677i	−0.218684	+	0.348033i
$317$	18.0582	+	6.31883i	1.01425	+	0.354901i	0.785684	−	0.618628i	$-0.212311\pi$
$317$	18.0582	+	6.31883i	1.01425	+	0.354901i	0.228564	+	0.973529i	$0.426597\pi$
$318$	−3.70127	+	10.5776i	−0.207557	+	0.593164i
$319$	−14.7714	−	18.5227i	−0.827037	−	1.03707i
$320$	−23.7277	−	14.9091i	−1.32642	−	0.833444i
$321$	−38.3472	−	8.75250i	−2.14033	−	0.488517i
$322$	7.07732	+	8.87467i	0.394403	+	0.494566i
$323$	−0.00557215	−	0.0228772i	−0.000310042	−	0.00127292i
$324$	5.48141	−	24.0156i	0.304523	−	1.33420i
$325$	0.0437311	−	0.00998134i	0.00242577	−	0.000553665i
$326$	−1.70151	−	0.191714i	−0.0942378	−	0.0106181i
$327$	−2.03435	+	0.979692i	−0.112500	+	0.0541771i
$328$	0.556557	−	1.59055i	0.0307307	−	0.0878233i
$329$	−4.49389	+	7.15198i	−0.247756	+	0.394301i
$330$	−68.4224	+	7.70935i	−3.76653	+	0.424386i
$331$	0.187735	−	0.389837i	0.0103189	−	0.0214274i	−0.895746	−	0.444567i	$-0.853358\pi$
$331$	0.187735	−	0.389837i	0.0103189	−	0.0214274i	0.906065	+	0.423139i	$0.139072\pi$
$332$	−21.0458	−	16.7835i	−1.15504	−	0.921113i
$333$	12.0105	−	7.54671i	0.658173	−	0.413557i
$334$	35.9155	+	12.5674i	1.96521	+	0.687656i
$335$	−10.2656	−	16.3376i	−0.560868	−	0.892617i
$336$	7.74308	+	3.72887i	0.422419	+	0.203426i
$337$	23.4089	−	23.4089i	1.27517	−	1.27517i	0.331824	−	0.943341i	$-0.392336\pi$
$337$	23.4089	−	23.4089i	1.27517	−	1.27517i	0.943341	−	0.331824i	$-0.107664\pi$
$338$			28.0541i			1.52594i
$339$	39.0405	+	18.8009i	2.12039	+	1.02113i
$340$	−21.2838	+	13.8085i	−1.15428	+	0.748869i
$341$	31.9224	+	40.0294i	1.72869	+	2.16771i
$342$	−0.0282478	−	0.0225269i	−0.00152747	−	0.00121811i
$343$	−12.9628	+	12.9628i	−0.699926	+	0.699926i
$344$	−8.38863	+	4.55145i	−0.452284	+	0.245398i
$345$	12.9674	−	12.9674i	0.698143	−	0.698143i
$346$	−5.67639	+	0.639576i	−0.305165	+	0.0343838i
$347$	−0.630254	+	5.59366i	−0.0338338	+	0.300283i	0.965387	+	0.260821i	$0.0839931\pi$
$347$	−0.630254	+	5.59366i	−0.0338338	+	0.300283i	−0.999221	+	0.0394625i	$0.987435\pi$
$348$	−26.4456	+	6.03603i	−1.41763	+	0.323565i
$349$	4.53799	−	9.42324i	0.242913	−	0.504415i	−0.743492	−	0.668745i	$-0.766832\pi$
$349$	4.53799	−	9.42324i	0.242913	−	0.504415i	0.986405	+	0.164330i	$0.0525462\pi$
$350$	0.731627	+	0.731627i	0.0391071	+	0.0391071i
$351$	0.0189894	+	0.0189894i	0.00101358	+	0.00101358i
$352$	−41.1350	+	14.3937i	−2.19250	+	0.767189i
$353$	−7.86915	+	34.4770i	−0.418833	+	1.83503i	0.120211	+	0.992748i	$0.461643\pi$
$353$	−7.86915	+	34.4770i	−0.418833	+	1.83503i	−0.539043	+	0.842278i	$0.681214\pi$
$354$	11.7758	−	33.6534i	0.625878	−	1.78866i
$355$	4.27131	+	0.974898i	0.226697	+	0.0517422i
$356$	−9.13197	+	11.4511i	−0.483994	+	0.606909i
$357$	12.4443	−	10.2230i	0.658625	−	0.541061i
$358$	−3.84108	+	4.81656i	−0.203007	+	0.254563i
$359$	−16.4837	+	3.76229i	−0.869975	+	0.198566i	−0.634132	−	0.773225i	$-0.718642\pi$
$359$	−16.4837	+	3.76229i	−0.869975	+	0.198566i	−0.235843	+	0.971791i	$0.575785\pi$
$360$	−3.23823	+	9.25432i	−0.170670	+	0.487746i
$361$	−17.1184	+	8.24378i	−0.900967	+	0.433883i
$362$	16.9057	+	1.90481i	0.888544	+	0.100115i
$363$	−27.5985	+	43.9227i	−1.44854	+	2.30534i
$364$	0.546099	−	0.343137i	0.0286234	−	0.0179853i
$365$	−7.66748	+	6.11461i	−0.401334	+	0.320053i
$366$	−50.0702	+	39.9297i	−2.61721	+	2.08716i
$367$	−3.89439	+	2.44701i	−0.203285	+	0.127733i	−0.629828	−	0.776735i	$-0.716874\pi$
$367$	−3.89439	+	2.44701i	−0.203285	+	0.127733i	0.426542	+	0.904468i	$0.359732\pi$
$368$	3.83090	−	6.09684i	0.199699	−	0.317820i
$369$	3.36720	+	0.379393i	0.175290	+	0.0197504i
$370$	21.7290	−	10.4641i	1.12963	−	0.544003i
$371$	1.12842	−	3.22484i	0.0585846	−	0.167425i
$372$	57.1515	−	13.0445i	2.96317	−	0.676323i
$373$	−11.7811	+	14.7731i	−0.610003	+	0.764920i	−0.986900	−	0.161335i	$-0.948420\pi$
$373$	−11.7811	+	14.7731i	−0.610003	+	0.764920i	0.376896	+	0.926255i	$0.376991\pi$
$374$	−4.94105	+	50.4213i	−0.255496	+	2.60722i
$375$	−16.4269	+	20.5987i	−0.848283	+	1.06371i
$376$	−7.46985	−	1.70495i	−0.385228	−	0.0879259i
$377$	0.207001	−	0.591576i	0.0106611	−	0.0304677i
$378$	−0.137843	+	0.603928i	−0.00708987	+	0.0310627i
$379$	−10.3602	+	3.62520i	−0.532170	+	0.186214i	−0.582969	−	0.812495i	$-0.698109\pi$
$379$	−10.3602	+	3.62520i	−0.532170	+	0.186214i	0.0507989	+	0.998709i	$0.483823\pi$
$380$	−0.0248477	−	0.0248477i	−0.00127466	−	0.00127466i
$381$	29.0096	+	29.0096i	1.48620	+	1.48620i
$382$	−3.96498	+	8.23337i	−0.202866	+	0.421256i
$383$	23.7840	−	5.42854i	1.21531	−	0.277386i	0.433641	−	0.901085i	$-0.357228\pi$
$383$	23.7840	−	5.42854i	1.21531	−	0.277386i	0.781664	+	0.623700i	$0.214371\pi$
$384$	−2.99386	+	26.5713i	−0.152780	+	1.35596i
$385$	20.8601	−	2.35037i	1.06313	−	0.119786i
$386$	2.81806	−	2.81806i	0.143435	−	0.143435i
$387$	−12.6764	−	14.4088i	−0.644377	−	0.732440i
$388$	27.6433	−	27.6433i	1.40338	−	1.40338i
$389$	−12.4514	−	9.92968i	−0.631312	−	0.503455i	0.254759	−	0.967005i	$-0.418004\pi$
$389$	−12.4514	−	9.92968i	−0.631312	−	0.503455i	−0.886071	+	0.463550i	$0.846575\pi$
$390$	−1.13571	−	1.42414i	−0.0575090	−	0.0721140i
$391$	−7.34400	−	11.3198i	−0.371402	−	0.572465i
$392$	−5.80332	−	2.79473i	−0.293112	−	0.141155i
$393$			21.0384i			1.06125i
$394$	12.5046	−	12.5046i	0.629974	−	0.629974i
$395$	−5.66839	−	2.72975i	−0.285208	−	0.137349i
$396$	23.6593	+	37.6536i	1.18893	+	1.89216i
$397$	−3.57975	−	1.25261i	−0.179663	−	0.0628667i	0.238949	−	0.971032i	$-0.423197\pi$
$397$	−3.57975	−	1.25261i	−0.179663	−	0.0628667i	−0.418611	+	0.908166i	$0.637483\pi$
$398$	18.3092	−	11.5044i	0.917756	−	0.576665i
$399$	0.0174399	+	0.0139078i	0.000873086	+	0.000696263i
$400$	0.284775	−	0.591341i	0.0142387	−	0.0295670i
$401$	−36.4204	+	4.10360i	−1.81875	+	0.204924i	−0.954514	−	0.298165i	$-0.903625\pi$
$401$	−36.4204	+	4.10360i	−1.81875	+	0.204924i	−0.864234	+	0.503089i	$0.832197\pi$
$402$	−23.4708	+	37.3536i	−1.17062	+	1.86303i
$403$	−0.447350	+	1.27845i	−0.0222841	+	0.0636843i
$404$	28.8620	−	13.8992i	1.43594	−	0.691511i
$405$	21.0771	+	2.37482i	1.04733	+	0.118006i
$406$	14.0946	−	3.21699i	0.699501	−	0.159657i
$407$	6.13023	−	26.8583i	0.303864	−	1.33132i
$408$	12.4812	+	7.59203i	0.617913	+	0.375861i
$409$	−14.6236	−	18.3374i	−0.723090	−	0.906727i	0.275418	−	0.961325i	$-0.411184\pi$
$409$	−14.6236	−	18.3374i	−0.723090	−	0.906727i	−0.998508	+	0.0545978i	$0.982612\pi$
$410$	5.61682	+	1.28200i	0.277395	+	0.0633136i
$411$	16.5571	+	10.4035i	0.816703	+	0.513169i
$412$	−21.2567	−	26.6550i	−1.04724	−	1.31320i
$413$	−3.59013	+	10.2600i	−0.176659	+	0.504862i
$414$	−19.5431	−	6.83843i	−0.960491	−	0.336090i
$415$	12.3316	−	19.6256i	0.605334	−	0.963383i
$416$	−0.901378	−	0.718825i	−0.0441937	−	0.0352433i
$417$	18.8373	−	39.1161i	0.922467	−	1.91552i
$418$	−0.0697297	+	0.00785665i	−0.00341059	+	0.000384282i
$419$	−21.9005	+	13.7610i	−1.06991	+	0.672268i	−0.947352	−	0.320194i	$-0.896252\pi$
$419$	−21.9005	+	13.7610i	−1.06991	+	0.672268i	−0.122556	+	0.992462i	$0.539109\pi$
$420$	7.93830	−	22.6863i	0.387349	−	1.10698i
$421$	8.37098	−	36.6757i	0.407977	−	1.78746i	−0.185536	−	0.982637i	$-0.559402\pi$
$421$	8.37098	−	36.6757i	0.407977	−	1.78746i	0.593513	−	0.804825i	$-0.297741\pi$
$422$	12.0303	−	4.20958i	0.585626	−	0.204919i
$423$		−	15.4071i		−	0.749117i
$424$	3.09917			0.150509
$425$	−0.780737	−	0.950378i	−0.0378713	−	0.0461001i
$426$	−2.22897	−	9.76576i	−0.107994	−	0.473153i
$427$	15.2651	−	12.1735i	0.738728	−	0.589116i
$428$	4.83590	+	42.9198i	0.233752	+	2.07461i
$429$	−2.08073			−0.100459
$430$	−18.6744	−	26.7575i	−0.900558	−	1.29036i
$431$	2.48210	+	2.48210i	0.119558	+	0.119558i	0.764355	−	0.644796i	$-0.223058\pi$
$431$	2.48210	+	2.48210i	0.119558	+	0.119558i	−0.644796	+	0.764355i	$0.723058\pi$
$432$	0.390478	−	0.0439963i	0.0187869	−	0.00211678i
$433$	−15.8501	+	12.6400i	−0.761705	+	0.607440i	−0.925365	−	0.379077i	$-0.876241\pi$
$433$	−15.8501	+	12.6400i	−0.761705	+	0.607440i	0.163660	+	0.986517i	$0.447670\pi$
$434$	−30.4597	+	6.95223i	−1.46211	+	0.333718i
$435$	−7.71418	−	22.0459i	−0.369867	−	1.05702i
$436$	1.75322	+	1.75322i	0.0839641	+	0.0839641i
$437$	0.0132152	−	0.0132152i	0.000632169	−	0.000632169i
$438$	20.2020	+	9.72878i	0.965289	+	0.464859i
$439$	−1.35843	−	2.16194i	−0.0648345	−	0.103184i	0.812734	−	0.582635i	$-0.197978\pi$
$439$	−1.35843	−	2.16194i	−0.0648345	−	0.103184i	−0.877568	+	0.479452i	$0.840836\pi$
$440$	8.26201	+	17.1562i	0.393876	+	0.817892i
$441$	2.88216	−	12.6276i	0.137246	−	0.601312i
$442$	−1.19897	+	0.598986i	−0.0570291	+	0.0284909i
$443$	11.3479	+	5.46484i	0.539153	+	0.259643i	0.683583	−	0.729872i	$-0.260421\pi$
$443$	11.3479	+	5.46484i	0.539153	+	0.259643i	−0.144430	+	0.989515i	$0.546135\pi$
$444$	−24.6609	−	19.6664i	−1.17035	−	0.933326i
$445$	−10.6784	−	6.70967i	−0.506204	−	0.318069i
$446$	46.9603	−	22.6149i	2.22363	−	1.07085i
$447$	−14.0183	+	40.0619i	−0.663041	+	1.89486i
$448$	2.18705	−	19.4106i	0.103328	−	0.917064i
$449$	−0.345010	+	0.549080i	−0.0162820	+	0.0259127i	−0.854766	−	0.519013i	$-0.826299\pi$
$449$	−0.345010	+	0.549080i	−0.0162820	+	0.0259127i	0.838484	+	0.544926i	$0.183442\pi$
$450$	−1.83998	−	0.419963i	−0.0867375	−	0.0197973i
$451$	5.14527	−	4.10321i	0.242281	−	0.193213i
$452$	5.32749	−	47.2827i	0.250584	−	2.22399i
$453$	−18.6776	+	11.7359i	−0.877549	+	0.551401i
$454$	7.18013	+	4.51157i	0.336980	+	0.211739i
$455$	0.346248	+	0.434181i	0.0162324	+	0.0203547i
$456$	−0.00668293	+	0.0190987i	−0.000312957	+	0.000894379i
$457$	−16.4247	−	34.1063i	−0.768316	−	1.59542i	−0.802966	−	0.596025i	$-0.796746\pi$
$457$	−16.4247	−	34.1063i	−0.768316	−	1.59542i	0.0346505	−	0.999399i	$-0.488968\pi$
$458$	−10.5008	−	46.0069i	−0.490669	−	2.14976i
$459$	0.233092	−	0.698502i	0.0108798	−	0.0326033i
$460$	−18.1432	−	8.73732i	−0.845933	−	0.407380i
$461$	−14.4372	−	11.5133i	−0.672407	−	0.536226i	0.226695	−	0.973966i	$-0.427208\pi$
$461$	−14.4372	−	11.5133i	−0.672407	−	0.536226i	−0.899102	+	0.437739i	$0.855779\pi$
$462$	−25.5352	−	40.6391i	−1.18801	−	1.89070i
$463$	1.42767	−	0.687528i	0.0663493	−	0.0319521i	−0.400415	−	0.916334i	$-0.631134\pi$
$463$	1.42767	−	0.687528i	0.0663493	−	0.0319521i	0.466764	+	0.884382i	$0.345420\pi$
$464$	−4.87910	−	7.76505i	−0.226507	−	0.360483i
$465$	16.6711	+	47.6433i	0.773104	+	2.20940i
$466$	−4.64056	−	4.64056i	−0.214970	−	0.214970i
$467$			28.1282i			1.30162i	0.759241	+	0.650809i	$0.225570\pi$
$467$			28.1282i			1.30162i	−0.759241	+	0.650809i	$0.774430\pi$
$468$	−0.510433	+	1.05993i	−0.0235948	+	0.0489951i
$469$	7.15563	−	11.3881i	0.330416	−	0.525855i
$470$	2.93298	−	26.0309i	0.135288	−	1.20072i
$471$	1.60461	+	14.2413i	0.0739363	+	0.656203i
$472$	−9.86019			−0.453852
$473$	−37.1966	−	2.37915i	−1.71030	−	0.109394i
$474$			14.3845i			0.660703i
$475$	0.00106214	−	0.00133189i	4.87346e−5	−	6.11112e-5i
$476$	−15.1091	−	9.19048i	−0.692523	−	0.421245i
$477$	1.38674	+	6.07572i	0.0634946	+	0.278188i
$478$	12.2142	−	25.3631i	0.558665	−	1.16008i
$479$	6.11175	−	6.11175i	0.279253	−	0.279253i	−0.553558	−	0.832811i	$-0.686730\pi$
$479$	6.11175	−	6.11175i	0.279253	−	0.279253i	0.832811	+	0.553558i	$0.186730\pi$
$480$	−42.9646			−1.96106
$481$	0.687900	−	0.240707i	0.0313656	−	0.0109753i
$482$	−15.6272	+	9.81923i	−0.711800	+	0.447253i
$483$	12.0657	+	4.22197i	0.549008	+	0.192106i
$484$	55.5336	+	12.6752i	2.52425	+	0.576144i
$485$	26.3176	+	20.9876i	1.19502	+	0.952999i
$486$	−15.6343	−	44.6802i	−0.709185	−	2.02673i
$487$	36.0274	−	4.05932i	1.63256	−	0.183945i	0.752427	−	0.658675i	$-0.228883\pi$
$487$	36.0274	−	4.05932i	1.63256	−	0.183945i	0.880131	+	0.474730i	$0.157454\pi$
$488$	14.9963	+	9.42277i	0.678849	+	0.426549i
$489$	−1.73731	+	0.836645i	−0.0785639	+	0.0378344i
$490$	7.27339	−	20.7862i	0.328578	−	0.939023i
$491$	1.21026	−	0.965152i	0.0546183	−	0.0435567i	−0.595800	−	0.803133i	$-0.703165\pi$
$491$	1.21026	−	0.965152i	0.0546183	−	0.0435567i	0.650419	+	0.759576i	$0.274594\pi$
$492$	−1.67670	−	7.34610i	−0.0755914	−	0.331188i
$493$	−17.0476	+	2.17185i	−0.767787	+	0.0978151i
$494$	−0.00115741	−	0.00145135i	−5.20744e−5	−	6.52993e-5i
$495$	−29.9368	+	23.8738i	−1.34556	+	1.07305i
$496$	10.5442	+	16.7810i	0.473450	+	0.753491i
$497$	0.679554	+	2.97732i	0.0304822	+	0.133551i
$498$	−52.6608	−	5.93344i	−2.35978	−	0.265884i
$499$	−26.4864	−	9.26801i	−1.18570	−	0.414893i	−0.335846	−	0.941917i	$-0.609022\pi$
$499$	−26.4864	−	9.26801i	−1.18570	−	0.414893i	−0.849850	+	0.527024i	$0.823308\pi$
$500$	27.3075	+	9.55530i	1.22123	+	0.427326i
$501$	41.7764	−	9.53518i	1.86643	−	0.426000i
$502$	24.0511	+	19.1801i	1.07345	+	0.856050i
$503$	−11.8880	−	33.9739i	−0.530059	−	1.51482i	−0.828274	−	0.560324i	$-0.810677\pi$
$503$	−11.8880	−	33.9739i	−0.530059	−	1.51482i	0.298214	−	0.954499i	$-0.403609\pi$
$504$	−6.79128	+	0.765194i	−0.302508	+	0.0340844i
$505$	14.6752	+	23.3554i	0.653036	+	1.03930i
$506$	−36.2302	+	17.4475i	−1.61063	+	0.775638i
$507$	16.8085	+	26.7506i	0.746492	+	1.18804i
$508$	19.5463	−	40.5884i	0.867229	−	1.80082i
$509$	0.503720			0.0223270			0.0111635	−	0.999938i	$-0.496446\pi$
$509$	0.503720			0.0223270			0.0111635	+	0.999938i	$0.496446\pi$
$510$	−21.0156	+	45.3103i	−0.930585	+	2.00637i
$511$	−6.15905	−	2.96604i	−0.272460	−	0.131210i
$512$	−22.6905	+	5.17897i	−1.00279	+	0.228880i
$513$	0.00101350		0.000114194i	4.47471e−5		5.04179e-6i
$514$	0.649622	−	0.814600i	0.0286536	−	0.0359304i
$515$	20.7577	−	20.7577i	0.914693	−	0.914693i
$516$	−20.9327	+	37.1890i	−0.921511	+	1.63715i
$517$	−21.1588	−	21.1588i	−0.930563	−	0.930563i
$518$	13.1434	+	10.4815i	0.577487	+	0.460530i
$519$	−5.02944	+	4.01084i	−0.220768	+	0.176056i
$520$	−0.268010	+	0.426536i	−0.0117530	+	0.0187048i
$521$	−0.162587	−	0.464647i	−0.00712306	−	0.0203565i	0.940267	−	0.340438i	$-0.110575\pi$
$521$	−0.162587	−	0.464647i	−0.00712306	−	0.0203565i	−0.947390	+	0.320082i	$0.896290\pi$
$522$	−18.6466	+	18.6466i	−0.816140	+	0.816140i
$523$	22.5899			0.987785			0.493893	−	0.869523i	$-0.335574\pi$
$523$	22.5899			0.987785			0.493893	+	0.869523i	$0.335574\pi$
$524$	21.8055	−	7.63008i	0.952578	−	0.333322i
$525$	1.13598	+	0.259281i	0.0495784	+	0.0113159i
$526$	28.8417	−	13.8894i	1.25756	−	0.605607i
$527$	36.8416	−	4.69357i	1.60485	−	0.204455i
$528$	−18.9826	+	23.8034i	−0.826110	+	1.03591i
$529$	−5.33240	+	11.0728i	−0.231843	+	0.481428i
$530$	1.18635	+	10.5292i	0.0515320	+	0.457359i
$531$	−4.41201	−	19.3303i	−0.191465	−	0.838863i
$532$	0.00808997	−	0.0231198i	0.000350745	−	0.00100237i
$533$	0.164329	+	0.0575012i	0.00711788	+	0.00249065i
$534$	−3.22841	+	28.6530i	−0.139707	+	1.23993i
$535$	−36.2575	+	8.27554i	−1.56755	+	0.357783i
$536$	11.8943	+	2.71479i	0.513755	+	0.117261i
$537$	−0.776781	+	6.89412i	−0.0335206	+	0.297503i
$538$	3.79190	−	33.6541i	0.163481	−	1.45093i
$539$	−13.3835	−	21.2998i	−0.576469	−	0.917446i
$540$	−0.244540	−	1.07140i	−0.0105233	−	0.0461057i
$541$	31.7280	+	3.57489i	1.36409	+	0.153696i	0.763474	−	0.645839i	$-0.223492\pi$
$541$	31.7280	+	3.57489i	1.36409	+	0.153696i	0.600619	+	0.799535i	$0.294921\pi$
$542$	0.927247	+	1.92545i	0.0398287	+	0.0827051i
$543$	17.2614	−	8.31267i	0.740759	−	0.356731i
$544$	−6.58638	+	30.9190i	−0.282389	+	1.32564i
$545$	−1.33110	+	1.66914i	−0.0570179	+	0.0714982i
$546$	0.550905	−	1.14397i	0.0235766	−	0.0489572i
$547$	3.37859	+	29.9859i	0.144458	+	1.28210i	0.831516	+	0.555500i	$0.187473\pi$
$547$	3.37859	+	29.9859i	0.144458	+	1.28210i	−0.687058	+	0.726602i	$0.741098\pi$
$548$	4.77804	−	20.9340i	0.204108	−	0.894255i
$549$	−11.7626	+	33.6155i	−0.502014	+	1.43467i
$550$	−3.10362	+	1.95013i	−0.132339	+	0.0831540i
$551$	−0.00786158	−	0.0224671i	−0.000334915	−	0.000957131i
$552$			11.5955i			0.493537i
$553$		−	4.38546i		−	0.186489i
$554$	−13.5294	−	38.6648i	−0.574808	−	1.64271i
$555$	14.4498	−	22.9967i	0.613359	−	0.976156i
$556$	−47.3742	−	5.33779i	−2.00911	−	0.226373i
$557$	−9.80967	+	12.3009i	−0.415649	+	0.521207i	−0.944945	−	0.327230i	$-0.893885\pi$
$557$	−9.80967	+	12.3009i	−0.415649	+	0.521207i	0.529296	+	0.848437i	$0.322456\pi$
$558$	40.2971	−	40.2971i	1.70591	−	1.70591i
$559$	−0.470238	−	0.866680i	−0.0198889	−	0.0366566i
$560$	8.12583			0.343379
$561$	25.4982	+	51.0389i	1.07654	+	2.15486i
$562$	36.0160	+	45.1627i	1.51924	+	1.90507i
$563$	−35.0801	+	8.00680i	−1.47845	+	0.337446i	−0.884304	−	0.466912i	$-0.845367\pi$
$563$	−35.0801	+	8.00680i	−1.47845	+	0.337446i	−0.594145	+	0.804358i	$0.702509\pi$
$564$	−32.3380	+	11.3156i	−1.36168	+	0.476471i
$565$	40.9704			1.72364
$566$	−43.6582	+	43.6582i	−1.83509	+	1.83509i
$567$	4.88310	+	13.9551i	0.205071	+	0.586059i
$568$	−2.34558	+	1.47383i	−0.0984184	+	0.0618404i
$569$	−3.15175	−	6.54468i	−0.132128	−	0.274367i	0.824399	−	0.566008i	$-0.191513\pi$
$569$	−3.15175	−	6.54468i	−0.132128	−	0.274367i	−0.956528	+	0.291641i	$0.905799\pi$
$570$	−0.0674447	−	0.0153938i	−0.00282495	−	0.000644776i
$571$	−26.2506	+	2.95774i	−1.09856	+	0.123777i	−0.642583	−	0.766216i	$-0.722137\pi$
$571$	−26.2506	+	2.95774i	−1.09856	+	0.123777i	−0.455973	+	0.889994i	$0.650709\pi$
$572$	0.754628	+	2.15660i	0.0315526	+	0.0901720i
$573$	1.15224	+	10.2264i	0.0481355	+	0.427214i
$574$	0.893621	+	3.91521i	0.0372990	+	0.163418i
$575$	0.322433	−	0.921460i	0.0134464	−	0.0384275i
$576$	15.4592	+	32.1014i	0.644134	+	1.33756i
$577$	−29.5856	−	37.0991i	−1.23166	−	1.54446i	−0.737995	−	0.674806i	$-0.764227\pi$
$577$	−29.5856	−	37.0991i	−1.23166	−	1.54446i	−0.493668	−	0.869650i	$-0.664344\pi$
$578$	29.3854	+	22.0696i	1.22227	+	0.917974i
$579$	0.998688	−	4.37554i	0.0415041	−	0.181841i
$580$	−20.0520	+	15.9909i	−0.832614	+	0.663988i
$581$	16.0549	+	1.80895i	0.666068	+	0.0750478i
$582$	17.1258	−	75.0329i	0.709886	−	3.11021i
$583$	10.2483	+	6.43945i	0.424442	+	0.266695i
$584$	0.694288	−	6.16198i	0.0287299	−	0.254985i
$585$	−0.956120	−	0.334561i	−0.0395307	−	0.0138324i
$586$	−3.33791	−	6.93124i	−0.137888	−	0.286327i
$587$	29.1186	−	6.64612i	1.20185	−	0.274315i	0.425702	−	0.904863i	$-0.360027\pi$
$587$	29.1186	−	6.64612i	1.20185	−	0.274315i	0.776150	+	0.630548i	$0.217170\pi$
$588$	−28.6209	+	3.22480i	−1.18030	+	0.132988i
$589$	0.0169896	+	0.0485536i	0.000700046	+	0.00200062i
$590$	−3.77446	−	33.4993i	−0.155392	−	1.37914i
$591$	4.43150	−	19.4157i	0.182288	−	0.798655i
$592$	3.52207	−	10.0655i	0.144756	−	0.413690i
$593$	38.1613	+	8.71008i	1.56710	+	0.357680i	0.915957	−	0.401277i	$-0.131433\pi$
$593$	38.1613	+	8.71008i	1.56710	+	0.357680i	0.651141	+	0.758956i	$0.274290\pi$
$594$	−1.97717	−	0.952156i	−0.0811244	−	0.0390674i
$595$	6.40708	−	13.8139i	0.262665	−	0.566314i
$596$	46.6068			1.90909
$597$	10.5656	−	21.9397i	0.432422	−	0.897933i
$598$	−0.900750	−	0.565979i	−0.0368344	−	0.0231446i
$599$	7.19254	+	9.01916i	0.293879	+	0.368513i	0.906749	−	0.421671i	$-0.138556\pi$
$599$	7.19254	+	9.01916i	0.293879	+	0.368513i	−0.612870	+	0.790184i	$0.709985\pi$
$600$	0.118341	+	1.05030i	0.00483125	+	0.0428785i
$601$	−17.2474	−	17.2474i	−0.703536	−	0.703536i	0.261632	−	0.965168i	$-0.415739\pi$
$601$	−17.2474	−	17.2474i	−0.703536	−	0.703536i	−0.965168	+	0.261632i	$0.915739\pi$
$602$	11.1564	−	19.8204i	0.454701	−	0.807820i
$603$			24.5327i			0.999050i
$604$	18.9377	+	15.1023i	0.770565	+	0.614505i
$605$	−5.49151	+	48.7385i	−0.223261	+	1.98150i
$606$	33.5527	−	53.3989i	1.36299	−	2.16918i
$607$	−14.6881	+	5.13960i	−0.596172	+	0.208610i	−0.611463	−	0.791273i	$-0.709419\pi$
$607$	−14.6881	+	5.13960i	−0.596172	+	0.208610i	0.0152902	+	0.999883i	$0.495133\pi$
$608$	−0.0437855			−0.00177574
$609$	11.5122	−	11.5122i	0.466498	−	0.466498i
$610$	−26.2726	+	54.5557i	−1.06375	+	2.20890i
$611$	0.176148	−	0.771756i	0.00712619	−	0.0312219i
$612$	32.2543	−	0.468246i	1.30380	−	0.0189277i
$613$	7.95049	−	34.8334i	0.321117	−	1.40691i	−0.514451	−	0.857520i	$-0.672004\pi$
$613$	7.95049	−	34.8334i	0.321117	−	1.40691i	0.835568	−	0.549387i	$-0.185139\pi$
$614$	−9.55211	−	7.61755i	−0.385492	−	0.307419i
$615$	6.12394	−	2.14286i	0.246941	−	0.0864084i
$616$	−8.27573	+	10.3774i	−0.333439	+	0.418119i
$617$	−25.2786	−	15.8836i	−1.01768	−	0.639449i	−0.0835919	−	0.996500i	$-0.526639\pi$
$617$	−25.2786	−	15.8836i	−1.01768	−	0.639449i	−0.934085	+	0.357051i	$0.883782\pi$
$618$	−63.3516	−	22.1677i	−2.54838	−	0.891715i
$619$	14.3966	+	5.03759i	0.578648	+	0.202478i	0.603704	−	0.797208i	$-0.293691\pi$
$619$	14.3966	+	5.03759i	0.578648	+	0.202478i	−0.0250563	+	0.999686i	$0.507977\pi$
$620$	43.3344	−	34.5580i	1.74035	−	1.38788i
$621$	0.569822	−	0.130058i	0.0228662	−	0.00521905i
$622$	−33.1289	+	20.8163i	−1.32835	+	0.834656i
$623$	0.984257	−	8.73552i	0.0394334	−	0.349981i
$624$	−0.800364	−	0.0901793i	−0.0320402	−	0.00361006i
$625$	−5.87512	+	25.7406i	−0.235005	+	1.02962i
$626$	−15.8322	−	9.94806i	−0.632784	−	0.397604i
$627$	−0.0617824	+	0.0492699i	−0.00246735	+	0.00196765i
$628$	14.1786	−	6.82806i	0.565788	−	0.272469i
$629$	−14.3342	−	13.9240i	−0.571543	−	0.555186i
$630$	−5.19938	−	22.7800i	−0.207148	−	0.907576i
$631$	−22.7852	−	18.1706i	−0.907065	−	0.723360i	0.0543327	−	0.998523i	$-0.482697\pi$
$631$	−22.7852	−	18.1706i	−0.907065	−	0.723360i	−0.961398	+	0.275163i	$0.911268\pi$
$632$	3.75482	−	1.31387i	0.149359	−	0.0522628i
$633$	8.94915	−	11.2219i	0.355697	−	0.446030i
$634$	−22.0041	−	35.0193i	−0.873893	−	1.39079i
$635$	36.6133	+	12.8115i	1.45295	+	0.508410i
$636$	11.7339	−	7.37290i	0.465280	−	0.292355i
$637$	0.288740	−	0.599575i	0.0114403	−	0.0237560i
$638$			51.2154i			2.02764i
$639$	−3.93889	−	3.93889i	−0.155820	−	0.155820i
$640$	8.35020	+	23.8635i	0.330071	+	0.943288i
$641$	16.3147	+	10.2512i	0.644392	+	0.404898i	0.814204	−	0.580578i	$-0.197173\pi$
$641$	16.3147	+	10.2512i	0.644392	+	0.404898i	−0.169813	+	0.985476i	$0.554316\pi$
$642$	53.0152	+	66.4789i	2.09234	+	2.62371i
$643$	−1.16176	−	10.3109i	−0.0458154	−	0.406623i	−0.995599	−	0.0937154i	$-0.970126\pi$
$643$	−1.16176	−	10.3109i	−0.0458154	−	0.406623i	0.949784	−	0.312907i	$-0.101303\pi$
$644$		−	14.0369i		−	0.553130i
$645$	−33.8383	−	14.3255i	−1.33238	−	0.564066i
$646$	−0.0214171	+	0.0461760i	−0.000842645	+	0.00181677i
$647$	−21.6723	+	27.1762i	−0.852026	+	1.06841i	0.144852	+	0.989453i	$0.453729\pi$
$647$	−21.6723	+	27.1762i	−0.852026	+	1.06841i	−0.996878	+	0.0789540i	$0.974842\pi$
$648$	−10.4854	+	8.36179i	−0.411904	+	0.328482i
$649$	−32.6057	−	20.4875i	−1.27989	−	0.804205i
$650$	−0.0873650	−	0.0420728i	−0.00342674	−	0.00165023i
$651$	−24.8790	+	24.8790i	−0.975085	+	0.975085i
$652$	1.49723	+	1.49723i	0.0586361	+	0.0586361i
$653$	−6.72080	−	19.2069i	−0.263005	−	0.751626i	−0.997343	−	0.0728422i	$-0.976793\pi$
$653$	−6.72080	−	19.2069i	−0.263005	−	0.751626i	0.734338	−	0.678784i	$-0.237493\pi$
$654$	4.75881	+	1.08617i	0.186084	+	0.0424725i
$655$	8.63077	+	17.9220i	0.337232	+	0.700270i
$656$	2.15699	−	1.35533i	0.0842162	−	0.0529166i
$657$	12.3908	−	1.39611i	0.483413	−	0.0544675i
$658$	17.2350	−	6.03080i	0.671892	−	0.235105i
$659$	6.96642	−	8.73561i	0.271373	−	0.340291i	−0.627406	−	0.778692i	$-0.715884\pi$
$659$	6.96642	−	8.73561i	0.271373	−	0.340291i	0.898780	+	0.438401i	$0.144455\pi$
$660$	72.0958	+	45.3008i	2.80633	+	1.76333i
$661$	−15.4334	−	32.0477i	−0.600288	−	1.24651i	−0.950757	−	0.309937i	$-0.899692\pi$
$661$	−15.4334	−	32.0477i	−0.600288	−	1.24651i	0.350469	−	0.936575i	$-0.386022\pi$
$662$	−0.842737	+	0.405841i	−0.0327539	+	0.0157735i
$663$	−0.784378	+	1.28951i	−0.0304627	+	0.0500804i
$664$	3.26116	+	14.2881i	0.126558	+	0.554485i
$665$	0.0205621	+	0.00469316i	0.000797363	+	0.000181993i
$666$	−30.4713	−	3.43329i	−1.18074	−	0.133037i
$667$	−8.50475	−	10.6646i	−0.329305	−	0.412936i
$668$	−25.0341	−	39.8415i	−0.968598	−	1.54152i
$669$	31.2286	−	49.7001i	1.20737	−	1.92152i
$670$	−4.67020	+	41.4492i	−0.180426	+	1.60132i
$671$	30.0110	+	62.3185i	1.15856	+	2.40578i
$672$	−12.9942	−	26.9827i	−0.501261	−	1.04088i
$673$	−6.92379	+	11.0191i	−0.266892	+	0.424757i	−0.953103	−	0.302646i	$-0.902130\pi$
$673$	−6.92379	+	11.0191i	−0.266892	+	0.424757i	0.686211	+	0.727403i	$0.259273\pi$
$674$	−71.1159	+	8.01284i	−2.73928	+	0.308643i
$675$	0.0502864	−	0.0175960i	0.00193552	−	0.000677269i
$676$	21.6300	−	27.1232i	0.831924	−	1.04320i
$677$	10.8881	+	17.3283i	0.418464	+	0.665982i	0.987730	−	0.156172i	$-0.0499153\pi$
$677$	10.8881	+	17.3283i	0.418464	+	0.665982i	−0.569266	+	0.822154i	$0.692772\pi$
$678$	−40.6433	−	84.3967i	−1.56090	−	3.24124i
$679$	−5.22119	+	22.8755i	−0.200371	+	0.877882i
$680$	13.7469	+	1.34714i	0.527171	+	0.0516603i
$681$	9.54959			0.365941
$682$		−	110.682i		−	4.23822i
$683$	7.92523	−	2.77316i	0.303251	−	0.106112i	−0.174364	−	0.984681i	$-0.555787\pi$
$683$	7.92523	−	2.77316i	0.303251	−	0.106112i	0.477615	+	0.878569i	$0.341501\pi$
$684$	0.00994198	+	0.0435587i	0.000380141	+	0.00166551i
$685$	18.3725	+	2.07008i	0.701977	+	0.0790938i
$686$	39.3808	−	4.43715i	1.50357	−	0.169411i
$687$	−37.5777	−	37.5777i	−1.43368	−	1.43368i
$688$	−14.2047	−	2.52726i	−0.541551	−	0.0963510i
$689$			0.320193i			0.0121984i
$690$	−39.3948	+	4.43873i	−1.49974	+	0.168980i
$691$	2.62557	−	23.3026i	0.0998813	−	0.886471i	−0.839445	−	0.543445i	$-0.817120\pi$
$691$	2.62557	−	23.3026i	0.0998813	−	0.886471i	0.939326	−	0.343026i	$-0.111452\pi$
$692$	5.98115	+	3.75820i	0.227369	+	0.142865i
$693$	−24.0473	−	11.5806i	−0.913483	−	0.439910i
$694$	8.60458	−	8.60458i	0.326626	−	0.326626i
$695$		−	41.0497i		−	1.55710i
$696$	13.3057	+	6.40770i	0.504352	+	0.242883i
$697$	−0.603299	−	4.73552i	−0.0228516	−	0.179371i
$698$	−20.3709	+	9.81010i	−0.771050	+	0.371318i
$699$	−7.20530	−	1.64456i	−0.272530	−	0.0622031i
$700$	−0.143257	−	1.27144i	−0.00541460	−	0.0480559i
$701$	10.2312	+	4.92711i	0.386429	+	0.186094i	0.617004	−	0.786960i	$-0.288346\pi$
$701$	10.2312	+	4.92711i	0.386429	+	0.186094i	−0.230575	+	0.973055i	$0.574061\pi$
$702$	−0.00650004	−	0.0576895i	−0.000245328	−	0.00217735i
$703$	0.0147259	−	0.0234361i	0.000555397	−	0.000883910i
$704$	65.3158	+	22.8550i	2.46168	+	0.861380i
$705$	−12.7996	−	26.5787i	−0.482062	−	1.00101i
$706$	59.7696	−	47.6646i	2.24946	−	1.79388i
$707$	−10.2293	+	16.2799i	−0.384714	+	0.612268i
$708$	−37.3321	+	23.4573i	−1.40303	+	0.881581i
$709$	10.0733	+	1.13499i	0.378310	+	0.0426253i	0.299072	−	0.954230i	$-0.403323\pi$
$709$	10.0733	+	1.13499i	0.378310	+	0.0426253i	0.0792377	+	0.996856i	$0.474751\pi$
$710$	−5.90510	−	7.40476i	−0.221614	−	0.277896i
$711$	4.25587	+	6.77318i	0.159608	+	0.254014i
$712$	7.77421	−	1.77441i	0.291351	−	0.0664989i
$713$	18.3796	+	23.0473i	0.688322	+	0.863128i
$714$	−34.8117	+	0.505373i	−1.30280	+	0.0189131i
$715$	−1.77251	+	0.853598i	−0.0662883	+	0.0319227i
$716$	7.42723	−	1.69522i	0.277569	−	0.0633532i
$717$	−3.54950	−	31.5027i	−0.132559	−	1.17649i
$718$	32.9307	+	15.8586i	1.22896	+	0.591837i
$719$	−0.149803	−	1.32954i	−0.00558670	−	0.0495833i	0.990610	−	0.136721i	$-0.0436565\pi$
$719$	−0.149803	−	1.32954i	−0.00558670	−	0.0495833i	−0.996196	+	0.0871380i	$0.972228\pi$
$720$	−12.5501	+	7.88573i	−0.467713	+	0.293884i
$721$	19.3142	+	6.75834i	0.719299	+	0.251694i
$722$	40.0438	+	9.13973i	1.49028	+	0.340146i
$723$	−9.01794	+	18.7259i	−0.335381	+	0.696425i
$724$	−14.8761	−	14.8761i	−0.552865	−	0.552865i
$725$	−0.879190	−	0.879190i	−0.0326523	−	0.0326523i
$726$	105.846	−	37.0372i	3.92832	−	1.37458i
$727$	5.34010	+	23.3965i	0.198054	+	0.867729i	0.972094	+	0.234593i	$0.0753756\pi$
$727$	5.34010	+	23.3965i	0.198054	+	0.867729i	−0.774040	+	0.633136i	$0.781767\pi$
$728$	−0.348930	−	0.0393150i	−0.0129322	−	0.00145711i
$729$	−20.0647	−	16.0011i	−0.743138	−	0.592633i
$730$	21.2006			0.784671
$731$	−15.4965	+	22.1553i	−0.573160	+	0.819443i
$732$	79.1948			2.92712
$733$	0.399118	+	0.318286i	0.0147418	+	0.0117562i	0.630833	−	0.775919i	$-0.282713\pi$
$733$	0.399118	+	0.318286i	0.0147418	+	0.0117562i	−0.616091	+	0.787675i	$0.711285\pi$
$734$	9.88025	+	1.11324i	0.364687	+	0.0410903i
$735$	−5.51850	−	24.1781i	−0.203553	−	0.891824i
$736$	−23.6839	+	8.28734i	−0.872998	+	0.305475i
$737$	33.6912	+	33.6912i	1.24103	+	1.24103i
$738$	−5.17969	−	5.17969i	−0.190667	−	0.190667i
$739$	19.8885	−	41.2989i	0.731611	−	1.51921i	−0.118703	−	0.992930i	$-0.537874\pi$
$739$	19.8885	−	41.2989i	0.731611	−	1.51921i	0.850314	−	0.526276i	$-0.176412\pi$
$740$	−29.0758	−	6.63637i	−1.06885	−	0.243958i
$741$	−0.00197320		0.000690453i	−7.24874e−5		2.53644e-5i
$742$	−6.25376	+	3.92950i	−0.229583	+	0.144256i
$743$	−0.0642270	−	0.570030i	−0.00235626	−	0.0209124i	0.992479	−	0.122414i	$-0.0390637\pi$
$743$	−0.0642270	−	0.570030i	−0.00235626	−	0.0209124i	−0.994835	+	0.101502i	$0.967635\pi$
$744$	−28.7550	−	13.8477i	−1.05421	−	0.507680i
$745$	4.49322	+	39.8784i	0.164619	+	1.46103i
$746$	39.8235	−	9.08946i	1.45804	−	0.332789i
$747$	−26.5516	+	12.7866i	−0.971474	+	0.467837i
$748$	43.6524	−	44.9385i	1.59609	−	1.64311i
$749$	−16.1629	−	20.2676i	−0.590580	−	0.740564i
$750$	55.5277	−	12.6738i	2.02758	−	0.462783i
$751$	28.0998	+	44.7205i	1.02537	+	1.63187i	0.738935	+	0.673776i	$0.235329\pi$
$751$	28.0998	+	44.7205i	1.02537	+	1.63187i	0.286439	+	0.958098i	$0.407528\pi$
$752$	−7.22182	−	9.05587i	−0.263353	−	0.330234i
$753$	34.4252	+	3.87879i	1.25453	+	0.141351i
$754$	−1.14721	+	0.720842i	−0.0417790	+	0.0262515i
$755$	−11.0964	+	17.6598i	−0.403838	+	0.642704i
$756$	0.598903	−	0.477609i	0.0217819	−	0.0173705i
$757$	−18.7223	−	38.8773i	−0.680474	−	1.41302i	−0.899334	−	0.437263i	$-0.855948\pi$
$757$	−18.7223	−	38.8773i	−0.680474	−	1.41302i	0.218860	−	0.975756i	$-0.429766\pi$
$758$	22.3965	+	7.83686i	0.813476	+	0.284648i
$759$	−24.0931	+	38.3440i	−0.874526	+	1.39180i
$760$	0.00214205	+	0.0190112i	7.77004e−5	+	0.000689610i
$761$	−45.6871	−	22.0018i	−1.65616	−	0.797564i	−0.999041	−	0.0437745i	$-0.986062\pi$
$761$	−45.6871	−	22.0018i	−1.65616	−	0.797564i	−0.657116	−	0.753789i	$-0.728224\pi$
$762$	−9.92993	−	88.1305i	−0.359723	−	3.19263i
$763$	−1.45083	−	0.331143i	−0.0525237	−	0.0119882i
$764$	10.1814	−	4.90311i	0.368351	−	0.177388i
$765$	3.51019	+	27.5528i	0.126911	+	0.996174i
$766$	−47.5151	−	22.8821i	−1.71679	−	0.826763i
$767$		−	1.01872i		−	0.0367837i
$768$	−1.04055	+	1.04055i	−0.0375477	+	0.0375477i
$769$	24.5016	+	11.7993i	0.883550	+	0.425495i	0.819920	−	0.572478i	$-0.194018\pi$
$769$	24.5016	+	11.7993i	0.883550	+	0.425495i	0.0636300	+	0.997974i	$0.479732\pi$
$770$	−38.4245	−	24.1437i	−1.38472	−	0.870080i
$771$	0.131373	−	1.16597i	0.00473128	−	0.0419913i
$772$	−4.89729	+	0.551792i	−0.176257	+	0.0198594i
$773$			28.0221i			1.00788i	0.863738	+	0.503942i	$0.168117\pi$
$773$			28.0221i			1.00788i	−0.863738	+	0.503942i	$0.831883\pi$
$774$	2.00409	+	41.4387i	0.0720355	+	1.48948i
$775$	1.90002	+	1.90002i	0.0682506	+	0.0682506i
$776$	−21.1502	+	2.38306i	−0.759248	+	0.0855467i
$777$	18.8126	+	2.11967i	0.674899	+	0.0760428i
$778$	7.66101	+	33.5651i	0.274661	+	1.20337i
$779$	0.00624095	−	0.00218380i	0.000223605	−	7.82428e-5i
$780$			2.25252i			0.0806533i
$781$	−10.8187			−0.387123
$782$	−2.84486	+	29.0305i	−0.101732	+	1.03813i
$783$	0.165644	−	0.725736i	0.00591965	−	0.0259357i
$784$	−4.22491	−	8.77311i	−0.150890	−	0.313326i
$785$	7.20925	+	11.4735i	0.257309	+	0.409505i
$786$	28.3564	−	35.5578i	1.01144	−	1.26830i
$787$	16.8260	−	5.88768i	0.599783	−	0.209873i	−0.0132738	−	0.999912i	$-0.504225\pi$
$787$	16.8260	−	5.88768i	0.599783	−	0.209873i	0.613057	+	0.790039i	$0.289940\pi$
$788$	−21.7309	+	2.44848i	−0.774130	+	0.0872235i
$789$	19.1797	−	30.5244i	0.682817	−	1.08670i
$790$	5.90110	+	12.2538i	0.209952	+	0.435969i
$791$	12.3911	+	25.7303i	0.440575	+	0.914864i
$792$	2.71077	−	24.0588i	0.0963231	−	0.854891i
$793$	−0.973523	+	1.54935i	−0.0345708	+	0.0550192i
$794$	4.36196	+	6.94203i	0.154800	+	0.246363i
$795$	7.43975	+	9.32915i	0.263861	+	0.330871i
$796$	−26.5716	−	2.99390i	−0.941806	−	0.106116i
$797$	−16.1567	−	3.68765i	−0.572299	−	0.130623i	−0.0734290	−	0.997300i	$-0.523394\pi$
$797$	−16.1567	−	3.68765i	−0.572299	−	0.130623i	−0.498870	+	0.866677i	$0.666251\pi$
$798$	−0.0107303	−	0.0470124i	−0.000379847	−	0.00166422i
$799$	−21.0892	+	5.13666i	−0.746083	+	0.181722i
$800$	−2.06067	+	0.992368i	−0.0728558	+	0.0350855i
$801$	6.95725	+	14.4469i	0.245822	+	0.510455i
$802$	67.0866	+	42.1533i	2.36891	+	1.48849i
$803$	15.0992	−	18.9339i	0.532841	−	0.668161i
$804$	51.4920	−	18.0178i	1.81598	−	0.635440i
$805$	12.0104	−	1.35325i	0.423312	−	0.0476958i
$806$	2.47924	−	1.55781i	0.0873275	−	0.0548715i
$807$	−16.5480	−	34.3622i	−0.582516	−	1.20961i
$808$	−17.0035	−	3.88093i	−0.598180	−	0.136531i
$809$	−10.0963	−	28.8535i	−0.354967	−	1.01444i	−0.973502	−	0.228679i	$-0.926559\pi$
$809$	−10.0963	−	28.8535i	−0.354967	−	1.01444i	0.618535	−	0.785757i	$-0.287726\pi$
$810$	−32.4223	−	32.4223i	−1.13921	−	1.13921i
$811$	10.1537	−	10.1537i	0.356544	−	0.356544i	−0.505993	−	0.862537i	$-0.668874\pi$
$811$	10.1537	−	10.1537i	0.356544	−	0.356544i	0.862537	+	0.505993i	$0.168874\pi$
$812$	−16.1072	−	7.75681i	−0.565251	−	0.272210i
$813$	2.03779	+	1.28043i	0.0714683	+	0.0449065i
$814$	−46.5617	+	37.1317i	−1.63199	+	1.30147i
$815$	−1.13674	+	1.42543i	−0.0398183	+	0.0499306i
$816$	7.59599	+	20.7375i	0.265913	+	0.725957i
$817$	−0.0344848	−	0.0145992i	−0.00120647	−	0.000510762i
$818$			50.7031i			1.77279i
$819$	−0.0790567	−	0.701648i	−0.00276247	−	0.0245176i
$820$	−4.44199	−	5.57008i	−0.155121	−	0.194516i
$821$	−34.2792	−	21.5391i	−1.19635	−	0.751718i	−0.221629	−	0.975131i	$-0.571137\pi$
$821$	−34.2792	−	21.5391i	−1.19635	−	0.751718i	−0.974724	+	0.223413i	$0.928280\pi$
$822$	−13.9616	−	39.8998i	−0.486965	−	1.39167i
$823$	32.5431	+	32.5431i	1.13438	+	1.13438i	0.989440	+	0.144941i	$0.0462991\pi$
$823$	32.5431	+	32.5431i	1.13438	+	1.13438i	0.144941	+	0.989440i	$0.453701\pi$
$824$			18.5615i			0.646622i
$825$	−1.79100	+	3.71904i	−0.0623545	+	0.129480i
$826$	19.8967	−	12.5019i	0.692295	−	0.434998i
$827$	42.4125	+	14.8408i	1.47483	+	0.516064i	0.943578	−	0.331152i	$-0.107437\pi$
$827$	42.4125	+	14.8408i	1.47483	+	0.516064i	0.531249	+	0.847216i	$0.321723\pi$
$828$	13.6221	+	21.6794i	0.473400	+	0.753412i
$829$	1.83211	−	2.29740i	0.0636319	−	0.0797919i	−0.748997	−	0.662573i	$-0.769464\pi$
$829$	1.83211	−	2.29740i	0.0636319	−	0.0797919i	0.812629	+	0.582782i	$0.198036\pi$
$830$	−47.2943	+	16.5490i	−1.64161	+	0.574424i
$831$	−36.0666	−	28.7621i	−1.25113	−	0.997747i
$832$	0.407354	+	1.78473i	0.0141225	+	0.0618745i
$833$	−18.2455	+	0.264876i	−0.632170	+	0.00917741i
$834$	−84.5600	+	40.7220i	−2.92807	+	1.41009i
$835$	31.6764	−	25.2611i	1.09621	−	0.874195i
$836$	0.0734734	+	0.0461664i	0.00254113	+	0.00159670i
$837$	−0.357974	+	1.56839i	−0.0123734	+	0.0542114i
$838$	55.5625	+	6.26039i	1.91938	+	0.216262i
$839$	−1.51678	+	13.4618i	−0.0523652	+	0.464754i	0.939977	+	0.341237i	$0.110846\pi$
$839$	−1.51678	+	13.4618i	−0.0523652	+	0.464754i	−0.992342	+	0.123517i	$0.960583\pi$
$840$	−11.0799	+	6.96198i	−0.382294	+	0.240211i
$841$	11.3356	−	2.58728i	0.390883	−	0.0892164i
$842$	−63.5811	+	50.7043i	−2.19115	+	1.74738i
$843$	61.4016	+	21.4853i	2.11478	+	0.739994i
$844$	−14.8767	−	5.20559i	−0.512077	−	0.179184i
$845$	25.2929	+	15.8926i	0.870101	+	0.546720i
$846$	−20.7663	+	26.0401i	−0.713960	+	0.895278i
$847$	−32.2697	+	11.2916i	−1.10880	+	0.387985i
$848$	3.66299	+	2.92114i	0.125788	+	0.100312i
$849$	−15.4720	+	67.7872i	−0.530997	+	2.32645i
$850$	0.0385955	+	2.65858i	0.00132381	+	0.0911886i
$851$	3.52954	−	15.4639i	0.120991	−	0.530097i
$852$	−5.37449	+	11.1603i	−0.184127	+	0.382344i
$853$	−23.6371	+	23.6371i	−0.809319	+	0.809319i	−0.984531	−	0.175212i	$-0.943939\pi$
$853$	−23.6371	+	23.6371i	−0.809319	+	0.809319i	0.175212	+	0.984531i	$0.443939\pi$
$854$	−42.2080			−1.44433
$855$	−0.0363119	+	0.0127061i	−0.00124184	+	0.000434539i
$856$	12.5108	−	19.9107i	0.427609	−	0.680535i
$857$	1.12693	−	10.0018i	0.0384953	−	0.341655i	−0.959671	−	0.281125i	$-0.909292\pi$
$857$	1.12693	−	10.0018i	0.0384953	−	0.341655i	0.998166	−	0.0605300i	$-0.0192791\pi$
$858$	3.51673	+	2.80449i	0.120059	+	0.0957439i
$859$			26.5864i			0.907117i	0.891226	+	0.453559i	$0.149846\pi$
$859$			26.5864i			0.907117i	−0.891226	+	0.453559i	$0.850154\pi$
$860$	−2.57559	+	40.2677i	−0.0878267	+	1.37312i
$861$	3.19788	+	3.19788i	0.108983	+	0.108983i
$862$	−0.849618	−	7.54057i	−0.0289381	−	0.256833i
$863$	−18.2006	−	22.8228i	−0.619555	−	0.776898i	0.368727	−	0.929538i	$-0.379794\pi$
$863$	−18.2006	−	22.8228i	−0.619555	−	0.776898i	−0.988282	+	0.152640i	$0.951222\pi$
$864$	−1.15944	−	0.728527i	−0.0394451	−	0.0247850i
$865$	−2.63903	+	5.48000i	−0.0897297	+	0.186326i
$866$	43.8256			1.48925
$867$	41.2429	+	3.43799i	1.40068	+	0.116760i
$868$	34.8092	+	16.7632i	1.18150	+	0.568981i
$869$	15.1464	+	3.45707i	0.513806	+	0.117273i
$870$	−16.6763	+	47.6581i	−0.565379	+	1.61576i
$871$	−0.280481	+	1.22887i	−0.00950375	+	0.0416386i
$872$	−0.151140	−	1.34141i	−0.00511826	−	0.0454258i
$873$	−14.1356	−	40.3973i	−0.478419	−	1.36724i
$874$	−0.0401476	+	0.00452355i	−0.00135801	+	0.000153011i
$875$	−16.9289	+	3.86391i	−0.572301	+	0.130624i
$876$	−12.0306	−	24.9819i	−0.406478	−	0.844060i
$877$	−0.0561570	−	0.0196502i	−0.00189629	−	0.000663539i	0.329331	−	0.944215i	$-0.393177\pi$
$877$	−0.0561570	−	0.0196502i	−0.00189629	−	0.000663539i	−0.331227	+	0.943551i	$0.607463\pi$
$878$	−0.618003	+	5.48493i	−0.0208566	+	0.185107i
$879$	−7.33563	−	4.60928i	−0.247425	−	0.155467i
$880$	−6.40561	+	28.0648i	−0.215933	+	0.946065i
$881$	−53.4637	−	6.02391i	−1.80124	−	0.202951i	−0.853303	−	0.521415i	$-0.825404\pi$
$881$	−53.4637	−	6.02391i	−1.80124	−	0.202951i	−0.947935	+	0.318465i	$0.896833\pi$
$882$	−21.8912	+	17.4577i	−0.737115	+	0.587830i
$883$	−1.62409	+	7.11559i	−0.0546549	+	0.239459i	−0.994876	−	0.101107i	$-0.967762\pi$
$883$	−1.62409	+	7.11559i	−0.0546549	+	0.239459i	0.940221	+	0.340566i	$0.110619\pi$
$884$	1.62101	+	0.345307i	0.0545203	+	0.0116139i
$885$	−23.6700	−	29.6813i	−0.795659	−	0.997725i
$886$	−11.8137	−	24.5315i	−0.396890	−	0.824151i
$887$	10.6212	−	30.3537i	0.356626	−	1.01918i	−0.616190	−	0.787598i	$-0.711325\pi$
$887$	10.6212	−	30.3537i	0.356626	−	1.01918i	0.972816	−	0.231581i	$-0.0743897\pi$
$888$	3.82133	+	16.7423i	0.128236	+	0.561836i
$889$	3.02737	+	26.8686i	0.101535	+	0.901145i
$890$	9.00439	+	25.7331i	0.301828	+	0.862574i
$891$	−52.0472	+	5.86431i	−1.74365	+	0.196462i
$892$	−62.8382	−	14.3424i	−2.10398	−	0.480219i
$893$	−0.0130442	−	0.0270865i	−0.000436507	−	0.000906416i
$894$	77.6899	−	48.8158i	2.59834	−	1.63265i
$895$	2.16653	+	6.19157i	0.0724190	+	0.206962i
$896$	−12.4614	+	12.4614i	−0.416305	+	0.416305i
$897$	−1.19800			−0.0400001
$898$	1.32319	−	0.463004i	0.0441554	−	0.0154506i
$899$	36.6032	−	8.35444i	1.22078	−	0.278636i
$900$	1.45513	+	1.82467i	0.0485042	+	0.0608223i
$901$	7.85412	−	3.92380i	0.261659	−	0.130721i
$902$	−14.2267			−0.473697
$903$	−1.23730	−	25.5838i	−0.0411748	−	0.851374i
$904$	−18.3179	+	18.3179i	−0.609244	+	0.609244i
$905$	11.2943	−	14.1626i	0.375436	−	0.470782i
$906$	47.3859	+	5.33910i	1.57429	+	0.177380i
$907$	3.85189	−	6.13025i	0.127900	−	0.203552i	−0.776635	−	0.629950i	$-0.783075\pi$
$907$	3.85189	−	6.13025i	0.127900	−	0.203552i	0.904535	+	0.426399i	$0.140218\pi$
$908$	−3.46339	−	9.89781i	−0.114937	−	0.328470i
$909$		−	35.0708i		−	1.16322i
$910$		−	1.20052i		−	0.0397967i
$911$	−1.17913	−	3.36976i	−0.0390663	−	0.111645i	0.922698	−	0.385524i	$-0.125979\pi$
$911$	−1.17913	−	3.36976i	−0.0390663	−	0.111645i	−0.961764	+	0.273878i	$0.911693\pi$
$912$	−0.0259003	+	0.0162742i	−0.000857645	+	0.000538894i
$913$	−18.9038	+	54.0239i	−0.625624	+	1.78793i
$914$	−18.2098	+	79.7823i	−0.602326	+	2.63896i
$915$	7.63493	+	67.7619i	0.252403	+	2.24014i
$916$	−25.3194	+	52.5764i	−0.836578	+	1.73717i
$917$	−8.64511	+	10.8406i	−0.285487	+	0.357989i
$918$	−1.33543	+	0.866395i	−0.0440757	+	0.0285953i
$919$	−53.2174	+	25.6281i	−1.75548	+	0.845394i	−0.779851	+	0.625965i	$0.784705\pi$
$919$	−53.2174	+	25.6281i	−1.75548	+	0.845394i	−0.975628	+	0.219429i	$0.929581\pi$
$920$	4.75693	+	9.87787i	0.156831	+	0.325664i
$921$	−13.6723	−	1.54050i	−0.450517	−	0.0507611i
$922$	8.88280	+	38.9181i	0.292539	+	1.28170i
$923$	−0.152270	−	0.242336i	−0.00501202	−	0.00797659i
$924$	−6.64528	+	58.9785i	−0.218614	+	1.94025i
$925$	0.161880	−	1.43672i	0.00532258	−	0.0472392i
$926$	−3.33964	−	0.762250i	−0.109747	−	0.0250491i
$927$	−36.3887	+	8.30549i	−1.19516	+	0.272788i
$928$	−3.57811	+	31.7566i	−0.117457	+	1.04246i
$929$	−44.1846	−	15.4609i	−1.44965	−	0.507255i	−0.513266	−	0.858230i	$-0.671565\pi$
$929$	−44.1846	−	15.4609i	−1.44965	−	0.507255i	−0.936385	+	0.350975i	$0.885850\pi$
$930$	36.0391	−	102.994i	1.18177	−	3.37730i
$931$	−0.00562395	−	0.0246401i	−0.000184317	−	0.000807548i
$932$	0.908649	+	8.06448i	0.0297638	+	0.264161i
$933$	−19.1176	+	39.6981i	−0.625881	+	1.29966i
$934$	37.9124	−	47.5406i	1.24053	−	1.55558i
$935$	42.6594	+	33.0182i	1.39511	+	1.07981i
$936$	0.577064	−	0.277899i	0.0188619	−	0.00908342i
$937$	35.9635	+	8.20844i	1.17488	+	0.268158i	0.765029	−	0.643996i	$-0.222725\pi$
$937$	35.9635	+	8.20844i	1.17488	+	0.268158i	0.409848	+	0.912154i	$0.365582\pi$
$938$	−27.4434	+	9.60287i	−0.896059	+	0.313545i
$939$	−21.0569			−0.687167
$940$	−22.9058	+	22.9058i	−0.747103	+	0.747103i
$941$	−10.2310	−	29.2384i	−0.333520	−	0.953146i	−0.981496	−	0.191485i	$-0.938670\pi$
$941$	−10.2310	−	29.2384i	−0.333520	−	0.953146i	0.647975	−	0.761661i	$-0.275616\pi$
$942$	16.4830	−	26.2325i	0.537044	−	0.854701i
$943$	2.96244	−	2.36246i	0.0964702	−	0.0769324i
$944$	−11.6540	−	9.29377i	−0.379306	−	0.302487i
$945$	0.466398	+	0.466398i	0.0151719	+	0.0151719i
$946$	59.6607	+	54.1562i	1.93974	+	1.76077i
$947$	4.83335	−	4.83335i	0.157063	−	0.157063i	−0.624201	−	0.781264i	$-0.714575\pi$
$947$	4.83335	−	4.83335i	0.157063	−	0.157063i	0.781264	+	0.624201i	$0.214575\pi$
$948$	11.0906	−	13.9072i	0.360206	−	0.451684i
$949$	0.636631	+	0.0717311i	0.0206659	+	0.00232849i
$950$	−0.00359035		0.000819474i	−0.000116486		2.65872e-5i
$951$	−41.9633	−	20.2085i	−1.36075	−	0.655304i
$952$	3.31159	+	9.04081i	0.107329	+	0.293014i
$953$	36.1117			1.16977			0.584886	−	0.811116i	$-0.301139\pi$
$953$	36.1117			1.16977			0.584886	+	0.811116i	$0.301139\pi$
$954$	5.84532	−	12.1379i	0.189249	−	0.392980i
$955$	5.17684	+	8.23889i	0.167519	+	0.266604i
$956$	−31.3641	+	15.1042i	−1.01439	+	0.488503i
$957$	30.6855	+	48.8357i	0.991921	+	1.57863i
$958$	−18.5674	+	2.09204i	−0.599886	+	0.0675909i
$959$	4.25651	+	12.1644i	0.137450	+	0.392809i
$960$	53.3373	+	42.5351i	1.72145	+	1.37281i
$961$	−48.8803	+	11.1566i	−1.57678	+	0.359891i
$962$	−1.48708	−	0.520353i	−0.0479455	−	0.0167769i
$963$	44.6318	+	15.6173i	1.43824	+	0.503262i
$964$	22.6793	+	2.55535i	0.730453	+	0.0823023i
$965$	−0.944266	−	4.13710i	−0.0303970	−	0.133178i
$966$	−14.7022	−	23.3984i	−0.473034	−	0.752830i
$967$	−13.0483	+	10.4057i	−0.419606	+	0.334625i	−0.810424	−	0.585843i	$-0.800763\pi$
$967$	−13.0483	+	10.4057i	−0.419606	+	0.334625i	0.390818	+	0.920468i	$0.372192\pi$
$968$	−19.3357	−	24.2463i	−0.621474	−	0.779304i
$969$	0.00724419	+	0.0568624i	0.000232717	+	0.00182668i
$970$	−16.1925	−	70.9441i	−0.519910	−	2.27788i
$971$	−27.3118	+	21.7804i	−0.876478	+	0.698968i	−0.954573	−	0.297978i	$-0.903688\pi$
$971$	−27.3118	+	21.7804i	−0.876478	+	0.698968i	0.0780948	+	0.996946i	$0.475116\pi$
$972$	−19.3334	+	55.2517i	−0.620119	+	1.77220i
$973$	25.7801	−	12.4150i	0.826471	−	0.398008i
$974$	−66.3627	−	41.6985i	−2.12640	−	1.33611i
$975$	−0.108513	+	0.0122265i	−0.00347521	+	0.000391562i
$976$	8.84300	+	25.2718i	0.283057	+	0.808932i
$977$	−10.7110	−	8.54177i	−0.342676	−	0.273275i	0.436995	−	0.899464i	$-0.356043\pi$
$977$	−10.7110	−	8.54177i	−0.342676	−	0.273275i	−0.779672	+	0.626188i	$0.784614\pi$
$978$	4.06397	+	0.927574i	0.129951	+	0.0296605i
$979$	29.3947	+	10.2856i	0.939457	+	0.328730i
$980$	−23.0584	+	14.4885i	−0.736572	+	0.462819i
$981$	2.56212	−	0.896524i	0.0818022	−	0.0286238i
$982$	−3.34638			−0.106787
$983$	−31.7135	+	31.7135i	−1.01150	+	1.01150i	−0.0115719	+	0.999933i	$0.503684\pi$
$983$	−31.7135	+	31.7135i	−1.01150	+	1.01150i	−0.999933	+	0.0115719i	$0.996316\pi$
$984$	−1.77994	+	3.69609i	−0.0567425	+	0.117827i
$985$	−4.19001	−	18.3576i	−0.133505	−	0.584923i
$986$	31.7402	+	19.3068i	1.01081	+	0.614854i
$987$	12.8209	−	16.0769i	0.408093	−	0.511732i
$988$			0.00229556i			7.30316e-5i
$989$	−21.4163	−	1.36982i	−0.680998	−	0.0435577i
$990$	82.7756			2.63078
$991$	−2.08805	−	18.5320i	−0.0663291	−	0.588687i	−0.982283	−	0.187404i	$-0.939993\pi$
$991$	−2.08805	−	18.5320i	−0.0663291	−	0.588687i	0.915954	−	0.401284i	$-0.131436\pi$
$992$	7.73265	−	68.6292i	0.245512	−	2.17898i
$993$	−0.560422	+	0.891906i	−0.0177844	+	0.0283038i
$994$	2.86442	−	5.94802i	0.0908537	−	0.188660i
$995$		−	23.0243i		−	0.729918i
$996$	46.3385	+	46.3385i	1.46829	+	1.46829i
$997$	−17.1762	−	49.0869i	−0.543977	−	1.55460i	−0.807453	−	0.589931i	$-0.799155\pi$
$997$	−17.1762	−	49.0869i	−0.543977	−	1.55460i	0.263476	−	0.964666i	$-0.415131\pi$
$998$	32.2740	+	51.3638i	1.02162	+	1.62589i
$999$	0.779885	−	0.375573i	0.0246745	−	0.0118826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.y.a.4.9	✓	768
17.13	even	4	inner	731.2.y.a.47.56	yes	768
43.11	even	7	inner	731.2.y.a.140.56	yes	768
731.183	even	28	inner	731.2.y.a.183.9	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.y.a.4.9	✓	768	1.1	even	1	trivial
731.2.y.a.47.56	yes	768	17.13	even	4	inner
731.2.y.a.140.56	yes	768	43.11	even	7	inner
731.2.y.a.183.9	yes	768	731.183	even	28	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.y (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69014 - 1.34784i) q^{2} +(-2.41916 - 0.272574i) q^{3} +(0.594855 + 2.60623i) q^{4} +(-2.17264 + 0.760238i) q^{5} +(3.72134 + 3.72134i) q^{6} +(-1.13454 - 1.13454i) q^{7} +(0.631484 - 1.31129i) q^{8} +(2.85326 + 0.651238i) q^{9} +O(q^{10})\)	\(q+(-1.69014 - 1.34784i) q^{2} +(-2.41916 - 0.272574i) q^{3} +(0.594855 + 2.60623i) q^{4} +(-2.17264 + 0.760238i) q^{5} +(3.72134 + 3.72134i) q^{6} +(-1.13454 - 1.13454i) q^{7} +(0.631484 - 1.31129i) q^{8} +(2.85326 + 0.651238i) q^{9} +(4.69674 + 1.64346i) q^{10} +(4.81279 - 3.02408i) q^{11} +(-0.728660 - 6.46703i) q^{12} +(0.135477 + 0.0652424i) q^{13} +(0.388350 + 3.44670i) q^{14} +(5.46318 - 1.24693i) q^{15} +(1.98233 - 0.954640i) q^{16} +(-0.0598501 - 4.12267i) q^{17} +(-3.94465 - 4.94643i) q^{18} +(0.00556756 - 0.00127076i) q^{19} +(-3.27376 - 5.21016i) q^{20} +(2.43538 + 3.05387i) q^{21} +(-12.2103 - 1.37577i) q^{22} +(2.77101 - 1.74114i) q^{23} +(-1.88508 + 3.00009i) q^{24} +(0.233225 - 0.185991i) q^{25} +(-0.141039 - 0.292871i) q^{26} +(0.168573 + 0.0589863i) q^{27} +(2.28198 - 3.63175i) q^{28} +(-0.466677 - 4.14187i) q^{29} +(-10.9142 - 5.25601i) q^{30} +(1.00853 + 8.95099i) q^{31} +(-7.47498 - 1.70612i) q^{32} +(-12.4672 + 6.00389i) q^{33} +(-5.45556 + 7.04856i) q^{34} +(3.32745 + 1.60242i) q^{35} +7.82365i q^{36} +(3.42717 - 3.42717i) q^{37} +(-0.0111227 - 0.00535643i) q^{38} +(-0.309958 - 0.194759i) q^{39} +(-0.375092 + 3.32903i) q^{40} +(1.15054 - 0.129634i) q^{41} -8.44398i q^{42} +(-5.31833 - 3.83607i) q^{43} +(10.7444 + 10.7444i) q^{44} +(-6.69419 + 0.754254i) q^{45} +(-7.03018 - 0.792111i) q^{46} +(-1.17144 - 5.13243i) q^{47} +(-5.05579 + 1.76910i) q^{48} -4.42566i q^{49} -0.644869 q^{50} +(-0.978946 + 9.98972i) q^{51} +(-0.0894473 + 0.391894i) q^{52} +(0.923910 + 1.91852i) q^{53} +(-0.205408 - 0.326905i) q^{54} +(-8.15742 + 10.2291i) q^{55} +(-2.20415 + 0.771264i) q^{56} +(-0.0138152 + 0.00155660i) q^{57} +(-4.79384 + 7.62935i) q^{58} +(-2.93948 - 6.10388i) q^{59} +(6.49960 + 13.4966i) q^{60} +(-1.36249 + 12.0924i) q^{61} +(10.3600 - 16.4878i) q^{62} +(-2.49827 - 3.97598i) q^{63} +(7.59057 + 9.51827i) q^{64} +(-0.343942 - 0.0387530i) q^{65} +(29.1636 + 6.65641i) q^{66} +(1.86530 + 8.17240i) q^{67} +(10.7090 - 2.60837i) q^{68} +(-7.17811 + 3.45680i) q^{69} +(-3.46406 - 7.19318i) q^{70} +(-1.61162 - 1.01265i) q^{71} +(2.65575 - 3.33021i) q^{72} +(4.02151 - 1.40719i) q^{73} +(-10.4117 + 1.17312i) q^{74} +(-0.614905 + 0.386370i) q^{75} +(0.00662379 + 0.0137544i) q^{76} +(-8.89121 - 2.02936i) q^{77} +(0.261367 + 0.746945i) q^{78} +(1.93271 + 1.93271i) q^{79} +(-3.58113 + 3.58113i) q^{80} +(-8.30216 - 3.99811i) q^{81} +(-2.11929 - 1.33164i) q^{82} +(-7.87274 + 6.27830i) q^{83} +(-6.51039 + 8.16377i) q^{84} +(3.26424 + 8.91156i) q^{85} +(3.81831 + 13.6518i) q^{86} +10.1471i q^{87} +(-0.926241 - 8.22062i) q^{88} +(3.41605 + 4.28359i) q^{89} +(12.3307 + 7.74792i) q^{90} +(-0.0796839 - 0.227723i) q^{91} +(6.18617 + 6.18617i) q^{92} -21.9288i q^{93} +(-4.93781 + 10.2535i) q^{94} +(-0.0111302 + 0.00699357i) q^{95} +(17.6181 + 6.16486i) q^{96} +(-7.78042 - 12.3825i) q^{97} +(-5.96509 + 7.47998i) q^{98} +(15.7015 - 5.49421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 14 q^{3} + 104 q^{4} - 6 q^{5} - 36 q^{6} - 28 q^{7}+O(q^{10}) \) 768 * q - 14 * q^3 + 104 * q^4 - 6 * q^5 - 36 * q^6 - 28 * q^7	\( 768 q - 14 q^{3} + 104 q^{4} - 6 q^{5} - 36 q^{6} - 28 q^{7} - 18 q^{10} - 4 q^{11} + 34 q^{12} + 4 q^{13} + 26 q^{14} - 152 q^{16} - 10 q^{17} - 24 q^{18} + 22 q^{20} - 20 q^{21} + 12 q^{22} - 24 q^{23} - 100 q^{24} + 10 q^{27} - 42 q^{28} - 18 q^{29} + 48 q^{30} + 4 q^{31} + 36 q^{33} - 4 q^{34} - 60 q^{35} + 40 q^{37} + 12 q^{38} + 34 q^{39} + 6 q^{40} - 48 q^{41} - 104 q^{44} - 52 q^{45} - 74 q^{46} + 20 q^{47} + 94 q^{48} - 344 q^{50} + 80 q^{51} + 12 q^{52} + 60 q^{54} - 32 q^{55} - 50 q^{56} + 38 q^{57} + 112 q^{58} - 12 q^{61} + 10 q^{62} + 52 q^{63} + 144 q^{64} - 10 q^{65} - 20 q^{67} - 54 q^{68} - 12 q^{69} + 14 q^{71} - 208 q^{72} - 176 q^{73} + 46 q^{74} - 116 q^{75} + 140 q^{78} - 168 q^{79} + 32 q^{80} + 116 q^{81} + 186 q^{82} - 60 q^{84} - 184 q^{85} + 176 q^{86} + 24 q^{88} - 4 q^{89} - 58 q^{90} - 152 q^{91} - 136 q^{92} + 70 q^{95} - 332 q^{96} + 72 q^{97} + 104 q^{98} - 56 q^{99}+O(q^{100}) \) 768 * q - 14 * q^3 + 104 * q^4 - 6 * q^5 - 36 * q^6 - 28 * q^7 - 18 * q^10 - 4 * q^11 + 34 * q^12 + 4 * q^13 + 26 * q^14 - 152 * q^16 - 10 * q^17 - 24 * q^18 + 22 * q^20 - 20 * q^21 + 12 * q^22 - 24 * q^23 - 100 * q^24 + 10 * q^27 - 42 * q^28 - 18 * q^29 + 48 * q^30 + 4 * q^31 + 36 * q^33 - 4 * q^34 - 60 * q^35 + 40 * q^37 + 12 * q^38 + 34 * q^39 + 6 * q^40 - 48 * q^41 - 104 * q^44 - 52 * q^45 - 74 * q^46 + 20 * q^47 + 94 * q^48 - 344 * q^50 + 80 * q^51 + 12 * q^52 + 60 * q^54 - 32 * q^55 - 50 * q^56 + 38 * q^57 + 112 * q^58 - 12 * q^61 + 10 * q^62 + 52 * q^63 + 144 * q^64 - 10 * q^65 - 20 * q^67 - 54 * q^68 - 12 * q^69 + 14 * q^71 - 208 * q^72 - 176 * q^73 + 46 * q^74 - 116 * q^75 + 140 * q^78 - 168 * q^79 + 32 * q^80 + 116 * q^81 + 186 * q^82 - 60 * q^84 - 184 * q^85 + 176 * q^86 + 24 * q^88 - 4 * q^89 - 58 * q^90 - 152 * q^91 - 136 * q^92 + 70 * q^95 - 332 * q^96 + 72 * q^97 + 104 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

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