LMFDB - Embedded newform 552.2.t.a.235.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			235.5
Character	$\chi$	$=$	552.235
Dual form			552.2.t.a.451.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01188 - 0.987982i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.0477826 + 1.99943i) q^{4} +(-0.131847 + 0.917018i) q^{5} +(-1.40930 + 0.117734i) q^{6} +(0.0841231 + 0.184204i) q^{7} +(1.92705 - 2.07038i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.01188 - 0.987982i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.0477826 + 1.99943i) q^{4} +(-0.131847 + 0.917018i) q^{5} +(-1.40930 + 0.117734i) q^{6} +(0.0841231 + 0.184204i) q^{7} +(1.92705 - 2.07038i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.03941 - 0.797645i) q^{10} +(1.60270 + 5.45831i) q^{11} +(1.54236 + 1.27324i) q^{12} +(-2.77492 - 1.26726i) q^{13} +(0.0968681 - 0.269503i) q^{14} +(0.606695 + 0.700163i) q^{15} +(-3.99543 + 0.191076i) q^{16} +(2.86746 + 4.46186i) q^{17} +(-0.833921 + 1.14218i) q^{18} +(2.36103 - 3.67383i) q^{19} +(-1.83981 - 0.219802i) q^{20} +(0.194301 + 0.0570519i) q^{21} +(3.77098 - 7.10657i) q^{22} +(-1.13343 + 4.65997i) q^{23} +(-0.302740 - 2.81218i) q^{24} +(3.97393 + 1.16685i) q^{25} +(1.55584 + 4.02388i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.364283 + 0.177000i) q^{28} +(2.14129 + 3.33191i) q^{29} +(0.0778492 - 1.30788i) q^{30} +(1.22207 - 1.05893i) q^{31} +(4.23166 + 3.75407i) q^{32} +(5.17466 + 2.36319i) q^{33} +(1.50672 - 7.34784i) q^{34} +(-0.180010 + 0.0528556i) q^{35} +(1.97228 - 0.331845i) q^{36} +(1.42570 + 9.91599i) q^{37} +(-6.01875 + 1.38481i) q^{38} +(-2.77492 + 1.26726i) q^{39} +(1.64450 + 2.04011i) q^{40} +(0.414389 - 2.88214i) q^{41} +(-0.140242 - 0.249695i) q^{42} +(-1.13709 - 0.985294i) q^{43} +(-10.8369 + 3.46531i) q^{44} +0.926448 q^{45} +(5.75086 - 3.59550i) q^{46} -12.0701i q^{47} +(-2.47205 + 3.14468i) q^{48} +(4.55717 - 5.25926i) q^{49} +(-2.86829 - 5.10687i) q^{50} +(5.24983 + 0.754812i) q^{51} +(2.40121 - 5.60880i) q^{52} +(5.69226 + 12.4643i) q^{53} +(0.317100 + 1.37820i) q^{54} +(-5.21668 + 0.750046i) q^{55} +(0.543482 + 0.180803i) q^{56} +(-1.23035 - 4.19020i) q^{57} +(1.12515 - 5.48703i) q^{58} +(2.40581 - 5.26800i) q^{59} +(-1.37094 + 1.24650i) q^{60} +(-9.48472 - 10.9460i) q^{61} +(-2.28278 - 0.135878i) q^{62} +(0.170357 - 0.109482i) q^{63} +(-0.572955 - 7.97946i) q^{64} +(1.52797 - 2.37756i) q^{65} +(-2.90132 - 7.50373i) q^{66} +(-1.82054 + 6.20017i) q^{67} +(-8.78415 + 5.94648i) q^{68} +(2.77953 + 3.90822i) q^{69} +(0.234368 + 0.124363i) q^{70} +(1.62908 - 5.54815i) q^{71} +(-2.32356 - 1.61279i) q^{72} +(7.53405 + 4.84184i) q^{73} +(8.35418 - 11.4423i) q^{74} +(3.48421 - 2.23917i) q^{75} +(7.45839 + 4.54517i) q^{76} +(-0.870617 + 0.754394i) q^{77} +(4.05990 + 1.45926i) q^{78} +(1.72521 - 3.77767i) q^{79} +(0.351567 - 3.68908i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.26681 + 2.50695i) q^{82} +(-6.47236 + 0.930585i) q^{83} +(-0.104787 + 0.391217i) q^{84} +(-4.46967 + 2.04123i) q^{85} +(0.177140 + 2.12042i) q^{86} +(3.92033 + 0.563659i) q^{87} +(14.3893 + 7.20023i) q^{88} +(8.71852 + 7.55464i) q^{89} +(-0.937450 - 0.915314i) q^{90} -0.617756i q^{91} +(-9.37144 - 2.04354i) q^{92} -1.61703i q^{93} +(-11.9251 + 12.2135i) q^{94} +(3.05768 + 2.64949i) q^{95} +(5.60829 - 0.739681i) q^{96} +(-12.3742 - 1.77914i) q^{97} +(-9.80734 + 0.819307i) q^{98} +(5.17466 - 2.36319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.01188	−	0.987982i	−0.715504	−	0.698609i
$2$	−1.01188	−	0.987982i	−0.715504	−	0.698609i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	0.0477826	+	1.99943i	0.0238913	+	0.999715i
$5$	−0.131847	+	0.917018i	−0.0589639	+	0.410103i	0.938867	+	0.344279i	$0.111877\pi$
$5$	−0.131847	+	0.917018i	−0.0589639	+	0.410103i	−0.997831	+	0.0658239i	$0.979032\pi$
$6$	−1.40930	+	0.117734i	−0.575346	+	0.0480645i
$7$	0.0841231	+	0.184204i	0.0317955	+	0.0696225i	0.924863	−	0.380299i	$-0.124179\pi$
$7$	0.0841231	+	0.184204i	0.0317955	+	0.0696225i	−0.893068	+	0.449922i	$0.851452\pi$
$8$	1.92705	−	2.07038i	0.681315	−	0.731990i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	1.03941	−	0.797645i	0.328691	−	0.252238i
$11$	1.60270	+	5.45831i	0.483233	+	1.64574i	0.735084	+	0.677976i	$0.237143\pi$
$11$	1.60270	+	5.45831i	0.483233	+	1.64574i	−0.251851	+	0.967766i	$0.581039\pi$
$12$	1.54236	+	1.27324i	0.445241	+	0.367552i
$13$	−2.77492	−	1.26726i	−0.769623	−	0.351475i	−0.00839962	−	0.999965i	$-0.502674\pi$
$13$	−2.77492	−	1.26726i	−0.769623	−	0.351475i	−0.761223	+	0.648490i	$0.775401\pi$
$14$	0.0968681	−	0.269503i	0.0258891	−	0.0720278i
$15$	0.606695	+	0.700163i	0.156648	+	0.180781i
$16$	−3.99543	+	0.191076i	−0.998858	+	0.0477690i
$17$	2.86746	+	4.46186i	0.695461	+	1.08216i	0.991889	+	0.127104i	$0.0405681\pi$
$17$	2.86746	+	4.46186i	0.695461	+	1.08216i	−0.296428	+	0.955055i	$0.595795\pi$
$18$	−0.833921	+	1.14218i	−0.196557	+	0.269214i
$19$	2.36103	−	3.67383i	0.541658	−	0.842836i	−0.457261	−	0.889333i	$-0.651169\pi$
$19$	2.36103	−	3.67383i	0.541658	−	0.842836i	0.998918	+	0.0464970i	$0.0148058\pi$
$20$	−1.83981	−	0.219802i	−0.411395	−	0.0491492i
$21$	0.194301	+	0.0570519i	0.0423999	+	0.0124497i
$22$	3.77098	−	7.10657i	0.803975	−	1.51513i
$23$	−1.13343	+	4.65997i	−0.236336	+	0.971671i
$23$	−1.13343	+	4.65997i	−0.236336	+	0.971671i
$24$	−0.302740	−	2.81218i	−0.0617966	−	0.574034i
$25$	3.97393	+	1.16685i	0.794785	+	0.233370i
$26$	1.55584	+	4.02388i	0.305125	+	0.789147i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.364283	+	0.177000i	−0.0688430	+	0.0334498i
$29$	2.14129	+	3.33191i	0.397627	+	0.618720i	0.981120	−	0.193398i	$-0.0619509\pi$
$29$	2.14129	+	3.33191i	0.397627	+	0.618720i	−0.583493	+	0.812118i	$0.698315\pi$
$30$	0.0778492	−	1.30788i	0.0142133	−	0.238785i
$31$	1.22207	−	1.05893i	0.219490	−	0.190189i	−0.538175	−	0.842833i	$-0.680886\pi$
$31$	1.22207	−	1.05893i	0.219490	−	0.190189i	0.757664	+	0.652645i	$0.226340\pi$
$32$	4.23166	+	3.75407i	0.748059	+	0.663632i
$33$	5.17466	+	2.36319i	0.900793	+	0.411378i
$34$	1.50672	−	7.34784i	0.258401	−	1.26014i
$35$	−0.180010	+	0.0528556i	−0.0304272	+	0.00893423i
$36$	1.97228	−	0.331845i	0.328713	−	0.0553074i
$37$	1.42570	+	9.91599i	0.234384	+	1.63018i	0.678776	+	0.734345i	$0.262511\pi$
$37$	1.42570	+	9.91599i	0.234384	+	1.63018i	−0.444392	+	0.895833i	$0.646580\pi$
$38$	−6.01875	+	1.38481i	−0.976370	+	0.224645i
$39$	−2.77492	+	1.26726i	−0.444342	+	0.202924i
$40$	1.64450	+	2.04011i	0.260018	+	0.322570i
$41$	0.414389	−	2.88214i	0.0647166	−	0.450114i	−0.931538	−	0.363644i	$-0.881532\pi$
$41$	0.414389	−	2.88214i	0.0647166	−	0.450114i	0.996254	−	0.0864697i	$-0.0275586\pi$
$42$	−0.140242	−	0.249695i	−0.0216398	−	0.0385288i
$43$	−1.13709	−	0.985294i	−0.173405	−	0.150256i	0.563835	−	0.825888i	$-0.309325\pi$
$43$	−1.13709	−	0.985294i	−0.173405	−	0.150256i	−0.737239	+	0.675632i	$0.763871\pi$
$44$	−10.8369	+	3.46531i	−1.63373	+	0.522414i
$45$	0.926448			0.138107
$46$	5.75086	−	3.59550i	0.847918	−	0.530128i
$47$		−	12.0701i		−	1.76061i	−0.474410	−	0.880304i	$-0.657338\pi$
$47$		−	12.0701i		−	1.76061i	0.474410	−	0.880304i	$-0.342662\pi$
$48$	−2.47205	+	3.14468i	−0.356809	+	0.453895i
$49$	4.55717	−	5.25926i	0.651024	−	0.751322i
$50$	−2.86829	−	5.10687i	−0.405637	−	0.722221i
$51$	5.24983	+	0.754812i	0.735124	+	0.105695i
$52$	2.40121	−	5.60880i	0.332987	−	0.777801i
$53$	5.69226	+	12.4643i	0.781892	+	1.71210i	0.698525	+	0.715586i	$0.253840\pi$
$53$	5.69226	+	12.4643i	0.781892	+	1.71210i	0.0833675	+	0.996519i	$0.473432\pi$
$54$	0.317100	+	1.37820i	0.0431519	+	0.187550i
$55$	−5.21668	+	0.750046i	−0.703417	+	0.101136i
$56$	0.543482	+	0.180803i	0.0726258	+	0.0241609i
$57$	−1.23035	−	4.19020i	−0.162964	−	0.555005i
$58$	1.12515	−	5.48703i	0.147740	−	0.720482i
$59$	2.40581	−	5.26800i	0.313210	−	0.685835i	−0.685914	−	0.727683i	$-0.740597\pi$
$59$	2.40581	−	5.26800i	0.313210	−	0.685835i	0.999124	+	0.0418481i	$0.0133245\pi$
$60$	−1.37094	+	1.24650i	−0.176987	+	0.160922i
$61$	−9.48472	−	10.9460i	−1.21439	−	1.40149i	−0.890247	−	0.455479i	$-0.849468\pi$
$61$	−9.48472	−	10.9460i	−1.21439	−	1.40149i	−0.324148	−	0.946007i	$-0.605077\pi$
$62$	−2.28278	−	0.135878i	−0.289913	−	0.0172566i
$63$	0.170357	−	0.109482i	0.0214630	−	0.0137934i
$64$	−0.572955	−	7.97946i	−0.0716194	−	0.997432i
$65$	1.52797	−	2.37756i	0.189521	−	0.294900i
$66$	−2.90132	−	7.50373i	−0.357128	−	0.923645i
$67$	−1.82054	+	6.20017i	−0.222414	+	0.757472i	0.770375	+	0.637592i	$0.220069\pi$
$67$	−1.82054	+	6.20017i	−0.222414	+	0.757472i	−0.992788	+	0.119880i	$0.961749\pi$
$68$	−8.78415	+	5.94648i	−1.06523	+	0.721117i
$69$	2.77953	+	3.90822i	0.334617	+	0.470494i
$70$	0.234368	+	0.124363i	0.0280123	+	0.0148642i
$71$	1.62908	−	5.54815i	0.193337	−	0.658444i	−0.804575	−	0.593851i	$-0.797607\pi$
$71$	1.62908	−	5.54815i	0.193337	−	0.658444i	0.997912	−	0.0645931i	$-0.0205749\pi$
$72$	−2.32356	−	1.61279i	−0.273834	−	0.190069i
$73$	7.53405	+	4.84184i	0.881794	+	0.566694i	0.901339	−	0.433115i	$-0.142585\pi$
$73$	7.53405	+	4.84184i	0.881794	+	0.566694i	−0.0195451	+	0.999809i	$0.506222\pi$
$74$	8.35418	−	11.4423i	0.971154	−	1.33014i
$75$	3.48421	−	2.23917i	0.402322	−	0.258557i
$76$	7.45839	+	4.54517i	0.855536	+	0.521366i
$77$	−0.870617	+	0.754394i	−0.0992160	+	0.0859712i
$78$	4.05990	+	1.45926i	0.459693	+	0.165228i
$79$	1.72521	−	3.77767i	0.194101	−	0.425021i	−0.787410	−	0.616430i	$-0.788578\pi$
$79$	1.72521	−	3.77767i	0.194101	−	0.425021i	0.981510	+	0.191409i	$0.0613056\pi$
$80$	0.351567	−	3.68908i	0.0393064	−	0.412452i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−3.26681	+	2.50695i	−0.360759	+	0.276847i
$83$	−6.47236	+	0.930585i	−0.710434	+	0.102145i	−0.488052	−	0.872815i	$-0.662292\pi$
$83$	−6.47236	+	0.930585i	−0.710434	+	0.102145i	−0.222382	+	0.974960i	$0.571383\pi$
$84$	−0.104787	+	0.391217i	−0.0114332	+	0.0426853i
$85$	−4.46967	+	2.04123i	−0.484804	+	0.221403i
$86$	0.177140	+	2.12042i	0.0191015	+	0.228651i
$87$	3.92033	+	0.563659i	0.420304	+	0.0604306i
$88$	14.3893	+	7.20023i	1.53390	+	0.767547i
$89$	8.71852	+	7.55464i	0.924162	+	0.800791i	0.980276	−	0.197634i	$-0.0633256\pi$
$89$	8.71852	+	7.55464i	0.924162	+	0.800791i	−0.0561142	+	0.998424i	$0.517871\pi$
$90$	−0.937450	−	0.915314i	−0.0988159	−	0.0964826i
$91$		−	0.617756i		−	0.0647584i
$92$	−9.37144	−	2.04354i	−0.977040	−	0.213054i
$93$		−	1.61703i		−	0.167678i
$94$	−11.9251	+	12.2135i	−1.22998	+	1.25972i
$95$	3.05768	+	2.64949i	0.313711	+	0.271832i
$96$	5.60829	−	0.739681i	0.572393	−	0.0754933i
$97$	−12.3742	−	1.77914i	−1.25641	−	0.180644i	−0.518224	−	0.855245i	$-0.673407\pi$
$97$	−12.3742	−	1.77914i	−1.25641	−	0.180644i	−0.738182	+	0.674601i	$0.764316\pi$
$98$	−9.80734	+	0.819307i	−0.990691	+	0.0827625i
$99$	5.17466	−	2.36319i	0.520073	−	0.237509i
$100$	−2.14315	+	8.00134i	−0.214315	+	0.800134i
$101$	−14.8941	+	2.14145i	−1.48202	+	0.213083i	−0.835364	−	0.549698i	$-0.814743\pi$
$101$	−14.8941	+	2.14145i	−1.48202	+	0.213083i	−0.646658	+	0.762780i	$0.723834\pi$
$102$	−4.56643	−	5.95052i	−0.452144	−	0.589189i
$103$	13.6803	−	4.01689i	1.34796	−	0.395796i	0.473455	−	0.880818i	$-0.343007\pi$
$103$	13.6803	−	4.01689i	1.34796	−	0.395796i	0.874502	+	0.485022i	$0.161189\pi$
$104$	−7.97112	+	3.30306i	−0.781632	+	0.323891i
$105$	−0.0779357	+	0.170655i	−0.00760574	+	0.0166543i
$106$	6.55466	−	18.2362i	0.636645	−	1.77125i
$107$	−9.32118	+	8.07685i	−0.901113	+	0.780818i	−0.976316	−	0.216350i	$-0.930585\pi$
$107$	−9.32118	+	8.07685i	−0.901113	+	0.780818i	0.0752034	+	0.997168i	$0.476039\pi$
$108$	1.04078	−	1.70786i	0.100149	−	0.164339i
$109$	1.13664	−	0.730474i	0.108870	−	0.0699667i	−0.485073	−	0.874474i	$-0.661207\pi$
$109$	1.13664	−	0.730474i	0.108870	−	0.0699667i	0.593943	+	0.804507i	$0.297570\pi$
$110$	6.01966	+	4.39504i	0.573952	+	0.419050i
$111$	8.42764	+	5.41611i	0.799916	+	0.514075i
$112$	−0.371305	−	0.719900i	−0.0350850	−	0.0680242i
$113$	−1.11414	+	3.79442i	−0.104810	+	0.356949i	−0.995153	−	0.0983413i	$-0.968646\pi$
$113$	−1.11414	+	3.79442i	−0.104810	+	0.356949i	0.890343	+	0.455290i	$0.150465\pi$
$114$	−2.89488	+	5.45552i	−0.271130	+	0.510957i
$115$	−4.12384	−	1.65378i	−0.384550	−	0.154216i
$116$	−6.55960	+	4.44056i	−0.609044	+	0.412296i
$117$	−0.859451	+	2.92702i	−0.0794563	+	0.270603i
$118$	−7.63907	+	2.95365i	−0.703233	+	0.271906i
$119$	−0.580671	+	0.903542i	−0.0532301	+	0.0828276i
$120$	2.61873	+	0.0931601i	0.239057	+	0.00850431i
$121$	−17.9707	+	11.5491i	−1.63370	+	1.04991i
$122$	−1.21705	+	20.4467i	−0.110187	+	1.85115i
$123$	−1.90681	−	2.20057i	−0.171931	−	0.198419i
$124$	2.17564	+	2.39284i	0.195378	+	0.214883i
$125$	−3.51828	+	7.70395i	−0.314684	+	0.689062i
$126$	−0.280546	−	0.0575278i	−0.0249930	−	0.00512498i
$127$	0.662112	+	2.25495i	0.0587530	+	0.200094i	0.983639	−	0.180150i	$-0.0576582\pi$
$127$	0.662112	+	2.25495i	0.0587530	+	0.200094i	−0.924886	+	0.380244i	$0.875840\pi$
$128$	−7.30380	+	8.64028i	−0.645571	+	0.763700i
$129$	−1.48927	+	0.214125i	−0.131123	+	0.0188526i
$130$	−3.89510	+	0.896193i	−0.341623	+	0.0786013i
$131$	−6.92425	−	15.1620i	−0.604974	−	1.32471i	−0.925959	−	0.377625i	$-0.876741\pi$
$131$	−6.92425	−	15.1620i	−0.604974	−	1.32471i	0.320984	−	0.947085i	$-0.395986\pi$
$132$	−4.47777	+	10.4593i	−0.389740	+	0.910364i
$133$	0.875352	+	0.125857i	0.0759026	+	0.0109131i
$134$	7.96781	−	4.47514i	0.688314	−	0.386594i
$135$	0.606695	−	0.700163i	0.0522160	−	0.0602604i
$136$	14.7635	+	2.66148i	1.26596	+	0.228220i
$137$		−	3.60894i		−	0.308332i	−0.988045	−	0.154166i	$-0.950731\pi$
$137$		−	3.60894i		−	0.308332i	0.988045	−	0.154166i	$-0.0492691\pi$
$138$	1.04871	−	6.70076i	0.0892721	−	0.570407i
$139$	−7.40138			−0.627777			−0.313888	−	0.949460i	$-0.601632\pi$
$139$	−7.40138			−0.627777			−0.313888	+	0.949460i	$0.601632\pi$
$140$	−0.114282	−	0.357391i	−0.00965863	−	0.0302051i
$141$	−9.12199	−	7.90425i	−0.768210	−	0.665658i
$142$	−7.12990	+	4.00453i	−0.598328	+	0.336053i
$143$	2.46974	−	17.1774i	0.206530	−	1.43645i
$144$	0.757741	+	3.92757i	0.0631450	+	0.327298i
$145$	−3.33775	+	1.52430i	−0.277185	+	0.126586i
$146$	−2.83987	−	12.3428i	−0.235029	−	1.02150i
$147$	−0.990368	−	6.88816i	−0.0816842	−	0.568126i
$148$	−19.7582	+	3.32440i	−1.62411	+	0.273264i
$149$	3.51005	−	1.03064i	0.287555	−	0.0844337i	−0.134774	−	0.990876i	$-0.543031\pi$
$149$	3.51005	−	1.03064i	0.287555	−	0.0844337i	0.422329	+	0.906443i	$0.361213\pi$
$150$	−5.73785	−	1.17658i	−0.468493	−	0.0960676i
$151$	−9.33698	−	4.26406i	−0.759833	−	0.347004i	−0.00246886	−	0.999997i	$-0.500786\pi$
$151$	−9.33698	−	4.26406i	−0.759833	−	0.347004i	−0.757364	+	0.652993i	$0.773513\pi$
$152$	−3.05641	−	11.9679i	−0.247908	−	0.970725i
$153$	4.00836	−	3.47326i	0.324057	−	0.280797i
$154$	1.62628	+	0.0968016i	0.131050	+	0.00780049i
$155$	0.809929	+	1.26027i	0.0650550	+	0.101228i
$156$	−2.66639	−	5.48769i	−0.213482	−	0.439367i
$157$	2.74069	+	1.76134i	0.218731	+	0.140570i	0.645418	−	0.763829i	$-0.276683\pi$
$157$	2.74069	+	1.76134i	0.218731	+	0.140570i	−0.426687	+	0.904399i	$0.640319\pi$
$158$	−5.47797	+	2.11806i	−0.435804	+	0.168504i
$159$	13.1475	+	3.86046i	1.04267	+	0.306155i
$160$	−4.00049	+	3.38555i	−0.316266	+	0.267651i
$161$	−0.953732	+	0.183229i	−0.0751646	+	0.0144405i
$162$	1.24923	+	0.662884i	0.0981491	+	0.0520811i
$163$	0.225888	+	0.0663267i	0.0176929	+	0.00519510i	0.290567	−	0.956855i	$-0.406156\pi$
$163$	0.225888	+	0.0663267i	0.0176929	+	0.00519510i	−0.272874	+	0.962050i	$0.587974\pi$
$164$	5.78243	+	0.690825i	0.451532	+	0.0539444i
$165$	−2.84935	+	4.43368i	−0.221822	+	0.345162i
$166$	7.46862	+	5.45294i	0.579678	+	0.423230i
$167$	−1.18789	−	1.84840i	−0.0919218	−	0.143033i	0.792247	−	0.610200i	$-0.208911\pi$
$167$	−1.18789	−	1.84840i	−0.0919218	−	0.143033i	−0.884169	+	0.467167i	$0.845275\pi$
$168$	0.492547	−	0.292335i	0.0380008	−	0.0225541i
$169$	−2.41898	−	2.79166i	−0.186076	−	0.214743i
$170$	6.53945	+	2.35048i	0.501553	+	0.180274i
$171$	−3.97245	−	1.81416i	−0.303781	−	0.138732i
$172$	1.91569	−	2.32061i	0.146070	−	0.176945i
$173$	6.57650	+	22.3975i	0.500002	+	1.70285i	0.692382	+	0.721531i	$0.256561\pi$
$173$	6.57650	+	22.3975i	0.500002	+	1.70285i	−0.192380	+	0.981321i	$0.561620\pi$
$174$	−3.41000	−	4.44357i	−0.258512	−	0.336866i
$175$	0.119361	+	0.830172i	0.00902282	+	0.0627551i
$176$	−7.44645	−	21.5021i	−0.561297	−	1.62078i
$177$	−2.40581	−	5.26800i	−0.180832	−	0.395967i
$178$	−1.35820	−	16.2581i	−0.101802	−	1.21860i
$179$	−0.695910	+	4.84016i	−0.0520148	+	0.361771i	0.947146	+	0.320804i	$0.103953\pi$
$179$	−0.695910	+	4.84016i	−0.0520148	+	0.361771i	−0.999161	+	0.0409670i	$0.986956\pi$
$180$	0.0442681	+	1.85237i	0.00329955	+	0.138067i
$181$	6.96415	−	8.03706i	0.517641	−	0.597390i	−0.435397	−	0.900238i	$-0.643392\pi$
$181$	6.96415	−	8.03706i	0.517641	−	0.597390i	0.953039	+	0.302848i	$0.0979376\pi$
$182$	−0.610332	+	0.625092i	−0.0452408	+	0.0463349i
$183$	−14.4836			−1.07066
$184$	7.46375	+	11.3266i	0.550235	+	0.835010i
$185$	−9.28112			−0.682361
$186$	−1.59759	+	1.63623i	−0.117141	+	0.119974i
$187$	−19.7585	+	22.8025i	−1.44488	+	1.66749i
$188$	24.1334	−	0.576742i	1.76011	−	0.0420632i
$189$	0.0288193	−	0.200443i	0.00209629	−	0.0145800i
$190$	−0.476337	−	5.70189i	−0.0345571	−	0.413658i
$191$	−5.13936	−	11.2536i	−0.371871	−	0.814284i	−0.999364	−	0.0356618i	$-0.988646\pi$
$191$	−5.13936	−	11.2536i	−0.371871	−	0.814284i	0.627493	−	0.778622i	$-0.284081\pi$
$192$	−6.40568	−	4.79242i	−0.462290	−	0.345863i
$193$	1.75833	+	12.2295i	0.126568	+	0.880297i	0.949859	+	0.312678i	$0.101226\pi$
$193$	1.75833	+	12.2295i	0.126568	+	0.880297i	−0.823291	+	0.567619i	$0.807865\pi$
$194$	10.7634	+	14.0257i	0.772764	+	1.00699i
$195$	−0.796237	−	2.71173i	−0.0570197	−	0.194191i
$196$	10.7333	+	8.86044i	0.766662	+	0.632888i
$197$	3.41496	+	1.55956i	0.243306	+	0.111114i	0.533336	−	0.845903i	$-0.320938\pi$
$197$	3.41496	+	1.55956i	0.243306	+	0.111114i	−0.290030	+	0.957017i	$0.593665\pi$
$198$	−7.57090	−	2.72122i	−0.538041	−	0.193389i
$199$	−9.72722	−	11.2258i	−0.689545	−	0.795777i	0.297756	−	0.954642i	$-0.403762\pi$
$199$	−9.72722	−	11.2258i	−0.689545	−	0.795777i	−0.987300	+	0.158865i	$0.949216\pi$
$200$	10.0738	−	5.97896i	0.712324	−	0.422776i
$201$	3.49358	+	5.43612i	0.246418	+	0.383434i
$202$	17.1867	+	12.5483i	1.20925	+	0.882892i
$203$	−0.433619	+	0.674724i	−0.0304341	+	0.0473563i
$204$	−1.25834	+	10.5327i	−0.0881016	+	0.737439i
$205$	2.58834	+	0.760004i	0.180777	+	0.0530810i
$206$	−17.8113	−	9.45127i	−1.24097	−	0.658501i
$207$	4.77384	+	0.458708i	0.331805	+	0.0318824i
$208$	11.3291	+	4.53304i	0.785534	+	0.314310i
$209$	23.8370	+	6.99916i	1.64884	+	0.484142i
$210$	0.247466	−	0.0956828i	0.0170767	−	0.00660274i
$211$	−8.36095	−	5.37326i	−0.575592	−	0.369910i	0.220224	−	0.975449i	$-0.429321\pi$
$211$	−8.36095	−	5.37326i	−0.575592	−	0.369910i	−0.795816	+	0.605539i	$0.792958\pi$
$212$	−24.6495	+	11.9768i	−1.69294	+	0.822573i
$213$	−3.12619	−	4.86444i	−0.214203	−	0.333306i
$214$	17.4117	+	1.03640i	1.19024	+	0.0708467i
$215$	1.05345	−	0.912824i	0.0718450	−	0.0622541i
$216$	−2.74047	+	0.699873i	−0.186465	+	0.0476203i
$217$	0.297862	+	0.136029i	0.0202202	+	0.00923426i
$218$	−1.87183	−	0.383831i	−0.126777	−	0.0259963i
$219$	8.59297	−	2.52312i	0.580659	−	0.170497i
$220$	−1.74893	−	10.3945i	−0.117913	−	0.700800i
$221$	−2.30262	−	16.0151i	−0.154891	−	1.07729i
$222$	−3.17669	−	13.8068i	−0.213206	−	0.926651i
$223$	7.86015	−	3.58961i	0.526354	−	0.240378i	−0.134471	−	0.990918i	$-0.542934\pi$
$223$	7.86015	−	3.58961i	0.526354	−	0.240378i	0.660826	+	0.750540i	$0.270206\pi$
$224$	−0.335534	+	1.09529i	−0.0224188	+	0.0731823i
$225$	0.589424	−	4.09954i	0.0392950	−	0.273302i
$226$	4.87619	−	2.73873i	0.324359	−	0.182177i
$227$	−8.55473	−	7.41271i	−0.567797	−	0.491999i	0.323001	−	0.946399i	$-0.395308\pi$
$227$	−8.55473	−	7.41271i	−0.567797	−	0.491999i	−0.890798	+	0.454400i	$0.849854\pi$
$228$	8.31921	−	2.66022i	0.550953	−	0.176178i
$229$	−1.17566			−0.0776901			−0.0388450	−	0.999245i	$-0.512368\pi$
$229$	−1.17566			−0.0776901			−0.0388450	+	0.999245i	$0.512368\pi$
$230$	2.53891	+	5.74770i	0.167411	+	0.378992i
$231$			1.15199i			0.0757955i
$232$	11.0247	+	1.98747i	0.723806	+	0.130484i
$233$	19.1153	−	22.0602i	1.25229	−	1.44521i	0.404792	−	0.914409i	$-0.367344\pi$
$233$	19.1153	−	22.0602i	1.25229	−	1.44521i	0.847493	−	0.530806i	$-0.178111\pi$
$234$	3.76150	−	2.11266i	0.245897	−	0.138109i
$235$	11.0685	+	1.59141i	0.722031	+	0.103812i
$236$	10.6479	+	4.55854i	0.693122	+	0.296735i
$237$	−1.72521	−	3.77767i	−0.112064	−	0.245386i
$238$	1.48025	−	0.340579i	0.0959504	−	0.0220765i
$239$	1.17241	−	0.168567i	0.0758369	−	0.0109037i	−0.104292	−	0.994547i	$-0.533258\pi$
$239$	1.17241	−	0.168567i	0.0758369	−	0.0109037i	0.180129	+	0.983643i	$0.442349\pi$
$240$	−2.55779	−	2.68153i	−0.165105	−	0.173092i
$241$	−0.232358	−	0.791338i	−0.0149675	−	0.0509746i	0.951671	−	0.307120i	$-0.0993654\pi$
$241$	−0.232358	−	0.791338i	−0.0149675	−	0.0509746i	−0.966638	+	0.256146i	$0.917547\pi$
$242$	29.5944	+	6.06851i	1.90240	+	0.390099i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	21.4324	−	19.4871i	1.37207	−	1.24753i
$245$	4.22198	+	4.87243i	0.269733	+	0.311288i
$246$	−0.244676	+	4.11060i	−0.0156000	+	0.262082i
$247$	−11.2074	+	7.20254i	−0.713108	+	0.458287i
$248$	0.162602	−	4.57075i	0.0103252	−	0.290243i
$249$	−3.53521	+	5.50089i	−0.224035	+	0.348605i
$250$	11.1714	−	4.31944i	0.706543	−	0.273186i
$251$	3.63523	−	12.3805i	0.229454	−	0.781448i	−0.761607	−	0.648039i	$-0.775589\pi$
$251$	3.63523	−	12.3805i	0.229454	−	0.781448i	0.991061	−	0.133409i	$-0.0425923\pi$
$252$	0.227041	+	0.335385i	0.0143022	+	0.0211273i
$253$	−27.2521	+	1.28196i	−1.71333	+	0.0805960i
$254$	1.55787	−	2.93588i	0.0977496	−	0.184213i
$255$	−1.38435	+	4.71467i	−0.0866915	+	0.295244i
$256$	15.9270	−	1.52686i	0.995436	−	0.0954289i
$257$	−23.8145	−	15.3047i	−1.48551	−	0.954679i	−0.996604	−	0.0823423i	$-0.973760\pi$
$257$	−23.8145	−	15.3047i	−1.48551	−	0.954679i	−0.488906	−	0.872337i	$-0.662604\pi$
$258$	1.71851	+	1.25471i	0.106990	+	0.0781145i
$259$	−1.70663	+	1.09678i	−0.106045	+	0.0681508i
$260$	4.82678	+	2.94146i	0.299344	+	0.182421i
$261$	2.99326	−	2.59367i	0.185278	−	0.160544i
$262$	−7.97330	+	22.1831i	−0.492592	+	1.37048i
$263$	3.77248	−	8.26057i	0.232621	−	0.509368i	−0.756940	−	0.653484i	$-0.773307\pi$
$263$	3.77248	−	8.26057i	0.232621	−	0.509368i	0.989561	+	0.144116i	$0.0460338\pi$
$264$	14.8645	−	6.15954i	0.914849	−	0.379093i
$265$	−12.1805	+	3.57652i	−0.748243	+	0.219704i
$266$	−0.761403	−	0.992183i	−0.0466846	−	0.0608346i
$267$	11.4188	−	1.64178i	0.698822	−	0.100475i
$268$	−12.4838	−	3.34377i	−0.762569	−	0.204253i
$269$	−3.94407	+	1.80120i	−0.240474	+	0.109821i	−0.532007	−	0.846740i	$-0.678562\pi$
$269$	−3.94407	+	1.80120i	−0.240474	+	0.109821i	0.291533	+	0.956561i	$0.405835\pi$
$270$	−1.30565	+	0.109074i	−0.0794592	+	0.00663803i
$271$	25.2208	+	3.62621i	1.53206	+	0.220277i	0.856157	−	0.516716i	$-0.172846\pi$
$271$	25.2208	+	3.62621i	1.53206	+	0.220277i	0.675901	+	0.736993i	$0.263755\pi$
$272$	−12.3093	−	17.2791i	−0.746361	−	1.04770i
$273$	−0.466869	−	0.404544i	−0.0282562	−	0.0244841i
$274$	−3.56557	+	3.65179i	−0.215404	+	0.220613i
$275$			23.5610i			1.42078i
$276$	−7.68140	+	5.74423i	−0.462366	+	0.345762i
$277$		−	22.2355i		−	1.33600i	−0.744161	−	0.668001i	$-0.767150\pi$
$277$		−	22.2355i		−	1.33600i	0.744161	−	0.668001i	$-0.232850\pi$
$278$	7.48927	+	7.31243i	0.449177	+	0.438570i
$279$	−1.22207	−	1.05893i	−0.0731632	−	0.0633963i
$280$	−0.237456	+	0.474544i	−0.0141907	+	0.0283594i
$281$	11.8734	+	1.70714i	0.708307	+	0.101839i	0.487047	−	0.873376i	$-0.338074\pi$
$281$	11.8734	+	1.70714i	0.708307	+	0.101839i	0.221260	+	0.975215i	$0.428983\pi$
$282$	1.42106	+	17.0105i	0.0846228	+	1.01296i
$283$	25.7931	−	11.7793i	1.53324	−	0.700208i	0.543021	−	0.839719i	$-0.317280\pi$
$283$	25.7931	−	11.7793i	1.53324	−	0.700208i	0.990221	+	0.139511i	$0.0445530\pi$
$284$	11.1710	+	2.99213i	0.662875	+	0.177550i
$285$	4.00471	−	0.575790i	0.237218	−	0.0341069i
$286$	−19.4700	+	14.9413i	−1.15129	+	0.883499i
$287$	0.565760	−	0.166122i	0.0333958	−	0.00980589i
$288$	3.11363	−	4.72285i	0.183473	−	0.278296i
$289$	−4.62377	+	10.1246i	−0.271987	+	0.595568i
$290$	4.88336	+	1.75523i	0.286761	+	0.103071i
$291$	−9.44794	+	8.18668i	−0.553848	+	0.479912i
$292$	−9.32092	+	15.2952i	−0.545465	+	0.895081i
$293$	9.15954	−	5.88648i	0.535106	−	0.343892i	−0.245016	−	0.969519i	$-0.578793\pi$
$293$	9.15954	−	5.88648i	0.535106	−	0.343892i	0.780122	+	0.625627i	$0.215157\pi$
$294$	−5.80325	+	7.94842i	−0.338452	+	0.463561i
$295$	4.51365	+	2.90075i	0.262795	+	0.168888i
$296$	23.2773	+	16.1569i	1.35296	+	0.939098i
$297$	1.60270	−	5.45831i	0.0929983	−	0.316723i
$298$	−4.56999	−	2.42499i	−0.264733	−	0.140476i
$299$	9.05057	−	11.4947i	0.523408	−	0.664755i
$300$	4.64354	+	6.85945i	0.268095	+	0.396030i
$301$	0.0858394	−	0.292342i	0.00494770	−	0.0168503i
$302$	5.23505	+	13.5395i	0.301243	+	0.779109i
$303$	−8.13518	+	12.6586i	−0.467354	+	0.727217i
$304$	−8.73136	+	15.1297i	−0.500778	+	0.867748i
$305$	11.2882	−	7.25447i	0.646359	−	0.415390i
$306$	−7.48748	−	0.445679i	−0.428031	−	0.0254778i
$307$	−5.47474	−	6.31818i	−0.312460	−	0.360598i	0.577698	−	0.816251i	$-0.303951\pi$
$307$	−5.47474	−	6.31818i	−0.312460	−	0.360598i	−0.890157	+	0.455653i	$0.849406\pi$
$308$	−1.54996	−	1.70469i	−0.0883170	−	0.0971337i
$309$	5.92291	−	12.9694i	0.336942	−	0.737801i
$310$	0.425581	−	2.07543i	0.0241714	−	0.117877i
$311$	6.16337	+	20.9905i	0.349493	+	1.19026i	0.927372	+	0.374141i	$0.122062\pi$
$311$	6.16337	+	20.9905i	0.349493	+	1.19026i	−0.577879	+	0.816122i	$0.696119\pi$
$312$	−2.72369	+	8.18721i	−0.154198	+	0.463509i
$313$	−13.1874	+	1.89606i	−0.745395	+	0.107172i	−0.504539	−	0.863389i	$-0.668337\pi$
$313$	−13.1874	+	1.89606i	−0.745395	+	0.107172i	−0.240857	+	0.970561i	$0.577428\pi$
$314$	−1.03307	−	4.49001i	−0.0582995	−	0.253386i
$315$	0.0779357	+	0.170655i	0.00439118	+	0.00961534i
$316$	7.63563	+	3.26892i	0.429537	+	0.183891i
$317$	22.9026	+	3.29290i	1.28634	+	0.184948i	0.751347	−	0.659908i	$-0.229405\pi$
$317$	22.9026	+	3.29290i	1.28634	+	0.184948i	0.534994	+	0.844856i	$0.320314\pi$
$318$	−9.48959	−	16.8958i	−0.532150	−	0.947472i
$319$	−14.7547	+	17.0279i	−0.826107	+	0.953378i
$320$	7.39285	+	0.526660i	0.413273	+	0.0294412i
$321$			12.3337i			0.688399i
$322$	1.14609	+	0.756865i	0.0638688	+	0.0421784i
$323$	23.1623			1.28878
$324$	−0.609151	−	1.90498i	−0.0338417	−	0.105832i
$325$	−9.54861	−	8.27391i	−0.529661	−	0.458954i
$326$	−0.163041	−	0.290287i	−0.00902999	−	0.0160775i
$327$	0.192285	−	1.33737i	0.0106334	−	0.0739569i
$328$	−5.16857	−	6.41196i	−0.285387	−	0.354042i
$329$	2.22336	−	1.01538i	0.122578	−	0.0559795i
$330$	7.26359	−	1.67122i	0.399847	−	0.0919977i
$331$	−2.51020	−	17.4588i	−0.137973	−	0.959625i	−0.934739	−	0.355336i	$-0.884366\pi$
$331$	−2.51020	−	17.4588i	−0.137973	−	0.959625i	0.796765	−	0.604289i	$-0.206543\pi$
$332$	−2.16991	−	12.8966i	−0.119089	−	0.707791i
$333$	9.61216	−	2.82238i	0.526743	−	0.154666i
$334$	−0.624184	+	3.04396i	−0.0341538	+	0.166558i
$335$	−5.44564	−	2.48694i	−0.297527	−	0.135876i
$336$	−0.787218	−	0.190821i	−0.0429462	−	0.0104101i
$337$	10.0810	−	8.73524i	0.549148	−	0.475839i	−0.335538	−	0.942027i	$-0.608918\pi$
$337$	10.0810	−	8.73524i	0.549148	−	0.475839i	0.884686	+	0.466187i	$0.154373\pi$
$338$	−0.310397	+	5.21472i	−0.0168834	+	0.283643i
$339$	2.13802	+	3.32683i	0.116121	+	0.180689i
$340$	−4.29487	−	8.83925i	−0.232922	−	0.479376i
$341$	7.73856	+	4.97327i	0.419066	+	0.269318i
$342$	2.22727	+	5.76041i	0.120437	+	0.311487i
$343$	2.71224	+	0.796387i	0.146447	+	0.0430009i
$344$	−4.23116	+	0.455498i	−0.228129	+	0.0245588i
$345$	−3.95038	+	2.03360i	−0.212682	+	0.109485i
$346$	15.4737	−	29.1610i	0.831874	−	1.56770i
$347$	−20.4584	−	6.00714i	−1.09827	−	0.322480i	−0.318103	−	0.948056i	$-0.603046\pi$
$347$	−20.4584	−	6.00714i	−1.09827	−	0.322480i	−0.780163	+	0.625576i	$0.784864\pi$
$348$	−0.939672	+	7.86536i	−0.0503717	+	0.421628i
$349$	8.77052	−	13.6472i	0.469475	−	0.730518i	−0.523084	−	0.852281i	$-0.675219\pi$
$349$	8.77052	−	13.6472i	0.469475	−	0.730518i	0.992559	+	0.121764i	$0.0388550\pi$
$350$	0.699417	−	0.957956i	0.0373854	−	0.0512049i
$351$	1.64927	+	2.56632i	0.0880317	+	0.136980i
$352$	−13.7088	+	29.1144i	−0.730681	+	1.55180i
$353$	−6.98861	−	8.06529i	−0.371966	−	0.429272i	0.538647	−	0.842532i	$-0.318936\pi$
$353$	−6.98861	−	8.06529i	−0.371966	−	0.429272i	−0.910613	+	0.413260i	$0.864390\pi$
$354$	−2.77030	+	7.70746i	−0.147240	+	0.409647i
$355$	4.87296	+	2.22541i	0.258630	+	0.118112i
$356$	−14.6884	+	17.7931i	−0.778483	+	0.943030i
$357$	0.302593	+	1.03054i	0.0160149	+	0.0545418i
$358$	5.48617	−	4.21009i	0.289953	−	0.222510i
$359$	−4.73808	−	32.9541i	−0.250066	−	1.73925i	−0.597790	−	0.801653i	$-0.703954\pi$
$359$	−4.73808	−	32.9541i	−0.250066	−	1.73925i	0.347723	−	0.937597i	$-0.386955\pi$
$360$	1.78531	−	1.91810i	0.0940942	−	0.101093i
$361$	−0.0297137	−	0.0650639i	−0.00156388	−	0.00342441i
$362$	−14.9873	+	1.25204i	−0.787716	+	0.0658059i
$363$	−3.04010	+	21.1444i	−0.159564	+	1.10979i
$364$	1.23516	−	0.0295180i	0.0647400	−	0.00154716i
$365$	−5.43340	+	6.27048i	−0.284397	+	0.328212i
$366$	14.6556	+	14.3095i	0.766059	+	0.747970i
$367$	12.3136			0.642763			0.321381	−	0.946950i	$-0.395853\pi$
$367$	12.3136			0.642763			0.321381	+	0.946950i	$0.395853\pi$
$368$	3.63813	−	18.8352i	0.189650	−	0.981852i
$369$	−2.91177			−0.151581
$370$	9.39133	+	9.16958i	0.488232	+	0.476704i
$371$	−1.81712	+	2.09707i	−0.0943404	+	0.108875i
$372$	3.23313	−	0.0772657i	0.167630	−	0.00400604i
$373$	4.34766	−	30.2386i	0.225113	−	1.56570i	−0.493161	−	0.869938i	$-0.664159\pi$
$373$	4.34766	−	30.2386i	0.225113	−	1.56570i	0.718275	−	0.695760i	$-0.244932\pi$
$374$	42.5216	−	3.55226i	2.19874	−	0.183683i
$375$	3.51828	+	7.70395i	0.181683	+	0.397830i
$376$	−24.9898	−	23.2597i	−1.28875	−	1.19953i
$377$	−1.71949	−	11.9593i	−0.0885584	−	0.615937i
$378$	−0.227195	+	0.174350i	−0.0116857	+	0.00896759i
$379$	4.46584	+	15.2092i	0.229395	+	0.781246i	0.991076	+	0.133295i	$0.0425558\pi$
$379$	4.46584	+	15.2092i	0.229395	+	0.781246i	−0.761682	+	0.647951i	$0.775626\pi$
$380$	−5.15137	+	6.24021i	−0.264260	+	0.320116i
$381$	2.13777	+	0.976285i	0.109521	+	0.0500166i
$382$	−5.91799	+	16.4649i	−0.302791	+	0.842416i
$383$	−8.62982	−	9.95935i	−0.440963	−	0.508899i	0.491145	−	0.871078i	$-0.336578\pi$
$383$	−8.62982	−	9.95935i	−0.440963	−	0.508899i	−0.932109	+	0.362179i	$0.882033\pi$
$384$	1.74692	+	11.1780i	0.0891470	+	0.570426i
$385$	−0.577005	−	0.897837i	−0.0294069	−	0.0457580i
$386$	10.3033	−	14.1119i	0.524424	−	0.718277i
$387$	−0.813440	+	1.26574i	−0.0413495	+	0.0643411i
$388$	2.96599	−	24.8263i	0.150575	−	1.26036i
$389$	10.2394	+	3.00657i	0.519160	+	0.152439i	0.530806	−	0.847493i	$-0.321889\pi$
$389$	10.2394	+	3.00657i	0.519160	+	0.152439i	−0.0116467	+	0.999932i	$0.503707\pi$
$390$	−1.87345	+	3.53060i	−0.0948659	+	0.178779i
$391$	−24.0422	+	8.30510i	−1.21587	+	0.420007i
$392$	−2.10677	−	19.5699i	−0.106408	−	0.988431i
$393$	−15.9931	−	4.69599i	−0.806745	−	0.236882i
$394$	−1.91470	−	4.95200i	−0.0964610	−	0.249478i
$395$	3.23673	+	2.08012i	0.162858	+	0.104662i
$396$	4.97229	+	10.2335i	0.249867	+	0.514250i
$397$	6.12814	+	9.53558i	0.307563	+	0.478577i	0.960285	−	0.279020i	$-0.0900096\pi$
$397$	6.12814	+	9.53558i	0.307563	+	0.478577i	−0.652723	+	0.757597i	$0.726373\pi$
$398$	−1.24817	+	20.9694i	−0.0625650	+	1.05110i
$399$	0.668350	−	0.579128i	0.0334593	−	0.0289927i
$400$	−16.1005	−	3.90275i	−0.805026	−	0.195138i
$401$	−23.4511	−	10.7098i	−1.17109	−	0.534820i	−0.267644	−	0.963518i	$-0.586245\pi$
$401$	−23.4511	−	10.7098i	−1.17109	−	0.534820i	−0.903448	+	0.428698i	$0.858972\pi$
$402$	1.83572	−	8.95227i	0.0915574	−	0.446499i
$403$	−4.73307	+	1.38975i	−0.235771	+	0.0692286i
$404$	−4.99336	−	29.6774i	−0.248429	−	1.47651i
$405$	−0.131847	−	0.917018i	−0.00655155	−	0.0455670i
$406$	1.10538	−	0.254329i	0.0548593	−	0.0126221i
$407$	−51.8395	+	23.6743i	−2.56959	+	1.17349i
$408$	11.6794	−	9.41459i	0.578218	−	0.466092i
$409$	0.443640	−	3.08558i	0.0219366	−	0.152572i	−0.975909	−	0.218178i	$-0.929989\pi$
$409$	0.443640	−	3.08558i	0.0219366	−	0.152572i	0.997846	+	0.0656054i	$0.0208979\pi$
$410$	−1.86820	−	3.32626i	−0.0922640	−	0.164272i
$411$	−2.72745	−	2.36335i	−0.134535	−	0.116576i
$412$	8.68516	+	27.1608i	0.427887	+	1.33812i
$413$	1.17277			0.0577082
$414$	−4.37734	−	5.18063i	−0.215134	−	0.254614i
$415$		−	6.05797i		−	0.297374i
$416$	−6.98511	−	15.7799i	−0.342473	−	0.773671i
$417$	−4.84687	+	5.59359i	−0.237352	+	0.273919i
$418$	−17.2050	−	30.6328i	−0.841523	−	1.49830i
$419$	−4.64869	−	0.668381i	−0.227104	−	0.0326526i	0.0278235	−	0.999613i	$-0.491142\pi$
$419$	−4.64869	−	0.668381i	−0.227104	−	0.0326526i	−0.254927	+	0.966960i	$0.582051\pi$
$420$	−0.344937	−	0.147673i	−0.0168312	−	0.00720568i
$421$	4.69325	+	10.2768i	0.228735	+	0.500860i	0.988848	−	0.148932i	$-0.0475834\pi$
$421$	4.69325	+	10.2768i	0.228735	+	0.500860i	−0.760112	+	0.649792i	$0.774856\pi$
$422$	3.15156	+	13.6975i	0.153415	+	0.666786i
$423$	−11.9473	+	1.71776i	−0.580896	+	0.0835202i
$424$	36.7751	+	12.2342i	1.78596	+	0.594146i
$425$	6.18876	+	21.0770i	0.300199	+	1.02238i
$426$	−1.64267	+	8.01083i	−0.0795877	+	0.388126i
$427$	1.21840	−	2.66793i	0.0589626	−	0.129110i
$428$	−16.5945	−	18.2511i	−0.802124	−	0.882201i
$429$	−11.3645	−	13.1153i	−0.548682	−	0.633213i
$430$	−1.96782	−	0.117131i	−0.0948966	−	0.00564855i
$431$	3.81303	−	2.45048i	0.183667	−	0.118036i	−0.445576	−	0.895244i	$-0.647001\pi$
$431$	3.81303	−	2.45048i	0.183667	−	0.118036i	0.629243	+	0.777208i	$0.283365\pi$
$432$	3.46448	+	1.99935i	0.166685	+	0.0961938i
$433$	−11.8404	+	18.4240i	−0.569012	+	0.885401i	−0.999855	−	0.0170265i	$-0.994580\pi$
$433$	−11.8404	+	18.4240i	−0.569012	+	0.885401i	0.430843	+	0.902427i	$0.358216\pi$
$434$	−0.167005	−	0.431927i	−0.00801650	−	0.0207332i
$435$	−1.03377	+	3.52070i	−0.0495655	+	0.168805i
$436$	1.51484	+	2.23773i	0.0725478	+	0.107168i
$437$	14.4439	+	15.1664i	0.690946	+	0.725505i
$438$	−11.1878	−	5.93662i	−0.534574	−	0.283662i
$439$	−1.53974	+	5.24387i	−0.0734877	+	0.250276i	−0.988042	−	0.154188i	$-0.950724\pi$
$439$	−1.53974	+	5.24387i	−0.0734877	+	0.250276i	0.914554	+	0.404464i	$0.132542\pi$
$440$	−8.49993	+	12.2459i	−0.405218	+	0.583800i
$441$	−5.85428	−	3.76232i	−0.278775	−	0.179158i
$442$	−13.4927	+	18.4802i	−0.641780	+	0.879015i
$443$	−25.8908	+	16.6390i	−1.23011	+	0.790542i	−0.983908	−	0.178677i	$-0.942818\pi$
$443$	−25.8908	+	16.6390i	−1.23011	+	0.790542i	−0.246200	+	0.969219i	$0.579182\pi$
$444$	−10.4264	+	17.1093i	−0.494817	+	0.811970i
$445$	−8.07726	+	6.99899i	−0.382899	+	0.331784i
$446$	−11.5000	−	4.13345i	−0.544539	−	0.195724i
$447$	1.51969	−	3.32765i	0.0718787	−	0.157392i
$448$	1.42165	−	0.776797i	0.0671666	−	0.0367002i
$449$	18.1997	−	5.34392i	0.858899	−	0.252195i	0.177512	−	0.984119i	$-0.443195\pi$
$449$	18.1997	−	5.34392i	0.858899	−	0.252195i	0.681387	+	0.731923i	$0.261377\pi$
$450$	−4.64669	+	3.56588i	−0.219047	+	0.168097i
$451$	16.3957	−	2.35735i	0.772045	−	0.111003i
$452$	−7.63991	−	2.04634i	−0.359351	−	0.0962518i
$453$	−9.33698	+	4.26406i	−0.438690	+	0.200343i
$454$	1.33269	+	15.9527i	0.0625461	+	0.748695i
$455$	0.566494	+	0.0814495i	0.0265576	+	0.00381841i
$456$	−11.0463	−	5.52742i	−0.517288	−	0.258845i
$457$	−12.8086	−	11.0987i	−0.599161	−	0.519176i	0.301632	−	0.953424i	$-0.402469\pi$
$457$	−12.8086	−	11.0987i	−0.599161	−	0.519176i	−0.900793	+	0.434248i	$0.857014\pi$
$458$	1.18963	+	1.16153i	0.0555875	+	0.0542750i
$459$		−	5.30382i		−	0.247561i
$460$	3.10957	−	8.32435i	0.144984	−	0.388125i
$461$			14.7348i			0.686267i	0.939287	+	0.343134i	$0.111488\pi$
$461$			14.7348i			0.686267i	−0.939287	+	0.343134i	$0.888512\pi$
$462$	1.13815	−	1.16567i	0.0529514	−	0.0542320i
$463$	22.4526	+	19.4553i	1.04346	+	0.904163i	0.995507	−	0.0946869i	$-0.0301850\pi$
$463$	22.4526	+	19.4553i	1.04346	+	0.904163i	0.0479523	+	0.998850i	$0.484730\pi$
$464$	−9.19202	−	12.9033i	−0.426729	−	0.599019i
$465$	1.48284	+	0.213200i	0.0687651	+	0.00988693i
$466$	−41.1374	+	3.43663i	−1.90565	+	0.159199i
$467$	10.2840	−	4.69653i	0.475885	−	0.217329i	−0.163008	−	0.986625i	$-0.552120\pi$
$467$	10.2840	−	4.69653i	0.475885	−	0.217329i	0.638893	+	0.769295i	$0.279392\pi$
$468$	−5.89344	−	1.57855i	−0.272424	−	0.0729685i
$469$	−1.29524	+	0.186228i	−0.0598088	+	0.00859921i
$470$	−9.62768	−	12.5458i	−0.444092	−	0.578695i
$471$	3.12590	−	0.917847i	0.144034	−	0.0422922i
$472$	−6.27064	−	15.1326i	−0.288629	−	0.696536i
$473$	3.55562	−	7.78572i	0.163488	−	0.357988i
$474$	−1.98658	+	5.52701i	−0.0912467	+	0.253864i
$475$	13.6694	−	11.8446i	0.627194	−	0.543467i
$476$	−1.83432	−	1.11784i	−0.0840757	−	0.0512360i
$477$	11.5274	−	7.40818i	0.527801	−	0.339197i
$478$	−1.35287	−	0.987751i	−0.0618790	−	0.0451787i
$479$	15.6550	+	10.0608i	0.715294	+	0.459692i	0.846997	−	0.531597i	$-0.178408\pi$
$479$	15.6550	+	10.0608i	0.715294	+	0.459692i	−0.131703	+	0.991289i	$0.542044\pi$
$480$	−0.0611370	+	5.24043i	−0.00279051	+	0.239192i
$481$	8.60994	−	29.3228i	0.392579	−	1.33700i
$482$	−0.546711	+	1.03030i	−0.0249020	+	0.0469289i
$483$	−0.486086	+	0.840773i	−0.0221177	+	0.0382565i
$484$	−23.9502	−	35.3793i	−1.08865	−	1.60815i
$485$	3.26300	−	11.1128i	0.148165	−	0.504605i
$486$	1.31905	−	0.510011i	0.0598332	−	0.0231346i
$487$	−6.59926	+	10.2686i	−0.299041	+	0.465317i	−0.957962	−	0.286895i	$-0.907377\pi$
$487$	−6.59926	+	10.2686i	−0.299041	+	0.465317i	0.658921	+	0.752212i	$0.271013\pi$
$488$	−40.9398	−	1.45641i	−1.85326	−	0.0659287i
$489$	0.198051	−	0.127280i	0.00895620	−	0.00575580i
$490$	0.541752	−	9.10153i	0.0244739	−	0.411165i
$491$	5.64089	+	6.50994i	0.254570	+	0.293789i	0.868621	−	0.495477i	$-0.165007\pi$
$491$	5.64089	+	6.50994i	0.254570	+	0.293789i	−0.614051	+	0.789266i	$0.710461\pi$
$492$	4.30878	−	3.91767i	0.194255	−	0.176622i
$493$	−8.72644	+	19.1082i	−0.393019	+	0.860592i
$494$	18.4564	+	3.78461i	0.830394	+	0.170278i
$495$	1.48482	+	5.05684i	0.0667378	+	0.227288i
$496$	−4.68035	+	4.46438i	−0.210154	+	0.200456i
$497$	1.15903	−	0.166644i	0.0519898	−	0.00747500i
$498$	9.01197	−	2.07349i	0.403836	−	0.0929154i
$499$	17.3321	+	37.9519i	0.775889	+	1.69896i	0.713235	+	0.700925i	$0.247229\pi$
$499$	17.3321	+	37.9519i	0.775889	+	1.69896i	0.0626546	+	0.998035i	$0.480043\pi$
$500$	−15.5716	−	6.66643i	−0.696384	−	0.298132i
$501$	−2.17483	−	0.312693i	−0.0971642	−	0.0139701i
$502$	−15.9101	+	8.93593i	−0.710101	+	0.398830i
$503$	−20.3881	+	23.5291i	−0.909060	+	1.04911i	0.0895274	+	0.995984i	$0.471464\pi$
$503$	−20.3881	+	23.5291i	−0.909060	+	1.04911i	−0.998588	+	0.0531272i	$0.983081\pi$
$504$	0.101617	−	0.563681i	0.00452640	−	0.0251083i
$505$		−	13.9405i		−	0.620346i
$506$	28.8423	+	25.6274i	1.28220	+	1.13928i
$507$	−3.69389			−0.164051
$508$	−4.47697	+	1.43159i	−0.198633	+	0.0635167i
$509$	−25.3473	−	21.9636i	−1.12350	−	0.973519i	−0.123678	−	0.992322i	$-0.539469\pi$
$509$	−25.3473	−	21.9636i	−1.12350	−	0.973519i	−0.999823	+	0.0188034i	$0.994014\pi$
$510$	6.05881	−	3.40294i	0.268288	−	0.150685i
$511$	−0.258098	+	1.79511i	−0.0114176	+	0.0794111i
$512$	−17.6246	−	14.1906i	−0.778906	−	0.627141i
$513$	−3.97245	+	1.81416i	−0.175388	+	0.0800970i
$514$	8.97659	+	39.0147i	0.395940	+	1.72087i
$515$	1.87985	+	13.0747i	0.0828362	+	0.576139i
$516$	−0.499289	−	2.96746i	−0.0219800	−	0.130635i
$517$	65.8825	−	19.3448i	2.89751	−	0.850785i
$518$	2.81050	+	0.576310i	0.123486	+	0.0253216i
$519$	21.2336	+	9.69706i	0.932052	+	0.425654i
$520$	−1.97799	−	7.74516i	−0.0867407	−	0.339648i
$521$	−11.2719	+	9.76715i	−0.493831	+	0.427907i	−0.865839	−	0.500323i	$-0.833215\pi$
$521$	−11.2719	+	9.76715i	−0.493831	+	0.427907i	0.372008	+	0.928229i	$0.378669\pi$
$522$	−5.59131	−	0.332812i	−0.244725	−	0.0145668i
$523$	5.46842	+	8.50903i	0.239117	+	0.372074i	0.939984	−	0.341218i	$-0.110840\pi$
$523$	5.46842	+	8.50903i	0.239117	+	0.372074i	−0.700867	+	0.713292i	$0.747203\pi$
$524$	29.9845	−	14.5690i	1.30988	−	0.636451i
$525$	0.705566	+	0.453440i	0.0307934	+	0.0197897i
$526$	−11.9786	+	4.63153i	−0.522290	+	0.201944i
$527$	8.22900	+	2.41625i	0.358461	+	0.105254i
$528$	−21.1266	−	8.45321i	−0.919416	−	0.367879i
$529$	−20.4307	−	10.5635i	−0.888291	−	0.459282i
$530$	15.8587	+	8.41514i	0.688858	+	0.365530i
$531$	−5.55676	−	1.63161i	−0.241143	−	0.0708059i
$532$	−0.209815	+	1.75622i	−0.00909662	+	0.0761417i
$533$	−4.80231	+	7.47255i	−0.208011	+	0.323672i
$534$	−13.1765	−	9.62033i	−0.570202	−	0.416312i
$535$	−6.17765	−	9.61260i	−0.267083	−	0.415589i
$536$	9.32846	+	15.7172i	0.402928	+	0.678882i
$537$	3.20223	+	3.69556i	0.138186	+	0.159475i
$538$	5.77045	+	2.07408i	0.248782	+	0.0894201i
$539$	36.0104	+	16.4454i	1.55108	+	0.708354i
$540$	1.42892	+	1.17959i	0.0614907	+	0.0507614i
$541$	5.20899	+	17.7402i	0.223952	+	0.762711i	0.992428	+	0.122832i	$0.0391975\pi$
$541$	5.20899	+	17.7402i	0.223952	+	0.762711i	−0.768475	+	0.639879i	$0.778984\pi$
$542$	−21.9377	−	28.5870i	−0.942306	−	1.22792i
$543$	−1.51346	−	10.5263i	−0.0649486	−	0.451727i
$544$	−4.61601	+	29.6457i	−0.197910	+	1.27105i
$545$	0.519995	+	1.13863i	0.0222741	+	0.0487736i
$546$	0.0727306	+	0.870606i	0.00311258	+	0.0372585i
$547$	4.24770	−	29.5434i	0.181619	−	1.26318i	−0.671318	−	0.741170i	$-0.734271\pi$
$547$	4.24770	−	29.5434i	0.181619	−	1.26318i	0.852936	−	0.522015i	$-0.174820\pi$
$548$	7.21581	−	0.172444i	0.308244	−	0.00736646i
$549$	−9.48472	+	10.9460i	−0.404798	+	0.467162i
$550$	23.2779	−	23.8408i	0.992572	−	1.01658i
$551$	17.2965			0.736857
$552$	13.4478	+	1.77664i	0.572377	+	0.0756189i
$553$	0.840992			0.0357626
$554$	−21.9683	+	22.4995i	−0.933342	+	0.955914i
$555$	−6.07784	+	7.01420i	−0.257990	+	0.297736i
$556$	−0.353657	−	14.7985i	−0.0149984	−	0.627597i
$557$	6.32433	−	43.9867i	0.267971	−	1.86378i	−0.199677	−	0.979862i	$-0.563989\pi$
$557$	6.32433	−	43.9867i	0.267971	−	1.86378i	0.467647	−	0.883915i	$-0.345102\pi$
$558$	0.190378	+	2.27888i	0.00805935	+	0.0964727i
$559$	1.90670	+	4.17510i	0.0806449	+	0.176588i
$560$	0.709117	−	0.245577i	0.0299657	−	0.0103775i
$561$	4.29393	+	29.8650i	0.181290	+	1.26090i
$562$	−10.3278	−	13.4581i	−0.435651	−	0.567696i
$563$	−8.01378	−	27.2924i	−0.337741	−	1.15024i	−0.936897	−	0.349607i	$-0.886315\pi$
$563$	−8.01378	−	27.2924i	−0.337741	−	1.15024i	0.599156	−	0.800632i	$-0.295503\pi$
$564$	15.3681	−	18.6165i	0.647114	−	0.783894i
$565$	−3.33266	−	1.52197i	−0.140206	−	0.0640299i
$566$	−37.7372	−	13.5639i	−1.58621	−	0.570135i
$567$	−0.132612	−	0.153042i	−0.00556917	−	0.00642716i
$568$	−8.34745	−	14.0644i	−0.350251	−	0.590128i
$569$	13.7727	+	21.4307i	0.577380	+	0.898421i	0.999969	−	0.00790039i	$-0.00251480\pi$
$569$	13.7727	+	21.4307i	0.577380	+	0.898421i	−0.422588	+	0.906322i	$0.638878\pi$
$570$	−4.62113	−	3.37395i	−0.193558	−	0.141319i
$571$	−3.36774	+	5.24030i	−0.140936	+	0.219300i	−0.904545	−	0.426379i	$-0.859789\pi$
$571$	−3.36774	+	5.24030i	−0.140936	+	0.219300i	0.763609	+	0.645679i	$0.223425\pi$
$572$	34.4630	+	4.11728i	1.44097	+	0.172152i
$573$	−11.8705	−	3.48549i	−0.495897	−	0.145608i
$574$	−0.736605	−	0.390866i	−0.0307453	−	0.0163144i
$575$	−9.94165	+	17.1958i	−0.414595	+	0.717116i
$576$	−7.81670	+	1.70272i	−0.325696	+	0.0709466i
$577$	28.2697	+	8.30075i	1.17689	+	0.345565i	0.810972	−	0.585085i	$-0.198939\pi$
$577$	28.2697	+	8.30075i	1.17689	+	0.345565i	0.365913	+	0.930649i	$0.380757\pi$
$578$	14.6817	−	5.67668i	0.610676	−	0.236119i
$579$	10.3939	+	6.67975i	0.431955	+	0.277601i
$580$	−3.20721	−	6.60075i	−0.133172	−	0.274081i
$581$	−0.715893	−	1.11395i	−0.0297002	−	0.0462145i
$582$	17.6484	+	1.05049i	0.731551	+	0.0435442i
$583$	−58.9111	+	51.0467i	−2.43985	+	2.11414i
$584$	24.5429	−	6.26788i	1.01559	−	0.259367i
$585$	−2.57082	−	1.17405i	−0.106290	−	0.0485411i
$586$	−15.0841	−	3.09308i	−0.623117	−	0.127774i
$587$	−3.94078	+	1.15712i	−0.162653	+	0.0477594i	−0.362045	−	0.932160i	$-0.617921\pi$
$587$	−3.94078	+	1.15712i	−0.162653	+	0.0477594i	0.199392	+	0.979920i	$0.436103\pi$
$588$	13.7251	−	2.30930i	0.566012	−	0.0952341i
$589$	−1.00499	−	6.98983i	−0.0414097	−	0.288011i
$590$	−1.70136	−	7.39460i	−0.0700441	−	0.304431i
$591$	3.41496	−	1.55956i	0.140473	−	0.0641517i
$592$	−7.59101	−	39.3462i	−0.311989	−	1.61712i
$593$	−5.45699	+	37.9542i	−0.224092	+	1.55859i	0.498237	+	0.867041i	$0.333981\pi$
$593$	−5.45699	+	37.9542i	−0.224092	+	1.55859i	−0.722329	+	0.691550i	$0.756928\pi$
$594$	−7.01445	+	3.93968i	−0.287806	+	0.161647i
$595$	−0.752005	−	0.651616i	−0.0308292	−	0.0267137i
$596$	2.22842	+	6.96886i	0.0912797	+	0.285455i
$597$	−14.8539			−0.607929
$598$	−20.5146	+	2.68938i	−0.838904	+	0.109977i
$599$			9.20302i			0.376025i	0.982167	+	0.188013i	$0.0602046\pi$
$599$			9.20302i			0.376025i	−0.982167	+	0.188013i	$0.939795\pi$
$600$	2.07832	−	11.5286i	0.0848472	−	0.470655i
$601$	13.0357	−	15.0440i	0.531739	−	0.613659i	−0.424792	−	0.905291i	$-0.639653\pi$
$601$	13.0357	−	15.0440i	0.531739	−	0.613659i	0.956531	+	0.291632i	$0.0941981\pi$
$602$	−0.375688	+	0.211006i	−0.0153119	+	0.00859996i
$603$	6.39615	+	0.919628i	0.260471	+	0.0374501i
$604$	8.07953	−	18.8724i	0.328752	−	0.767906i
$605$	−8.22131	−	18.0022i	−0.334244	−	0.731892i
$606$	20.7382	−	4.77150i	0.842434	−	0.193829i
$607$	−7.59528	+	1.09204i	−0.308283	+	0.0443244i	−0.294720	−	0.955584i	$-0.595226\pi$
$607$	−7.59528	+	1.09204i	−0.308283	+	0.0443244i	−0.0135629	+	0.999908i	$0.504317\pi$
$608$	23.7829	−	6.68294i	0.964525	−	0.271029i
$609$	0.225962	+	0.769558i	0.00915646	+	0.0311840i
$610$	−18.5895	−	3.81190i	−0.752667	−	0.154339i
$611$	−15.2960	+	33.4936i	−0.618810	+	1.35500i
$612$	7.13607	+	7.84847i	0.288459	+	0.317255i
$613$	−15.3094	−	17.6680i	−0.618341	−	0.713604i	0.357050	−	0.934085i	$-0.383783\pi$
$613$	−15.3094	−	17.6680i	−0.618341	−	0.713604i	−0.975391	+	0.220482i	$0.929237\pi$
$614$	−0.702502	+	11.8022i	−0.0283507	+	0.476296i
$615$	2.26937	−	1.45844i	0.0915099	−	0.0588099i
$616$	−0.115840	+	3.25626i	−0.00466732	+	0.131199i
$617$	−5.26780	+	8.19686i	−0.212074	+	0.329993i	−0.930951	−	0.365144i	$-0.881020\pi$
$617$	−5.26780	+	8.19686i	−0.212074	+	0.329993i	0.718877	+	0.695137i	$0.244656\pi$
$618$	−18.8067	+	7.27164i	−0.756518	+	0.292508i
$619$	4.76989	−	16.2448i	0.191718	−	0.652932i	−0.806386	−	0.591389i	$-0.798580\pi$
$619$	4.76989	−	16.2448i	0.191718	−	0.652932i	0.998104	−	0.0615428i	$-0.0196021\pi$
$620$	−2.48113	+	1.67961i	−0.0996445	+	0.0674549i
$621$	3.47287	−	3.30744i	0.139362	−	0.132723i
$622$	14.5017	−	27.3291i	0.581465	−	1.09580i
$623$	−0.658166	+	2.24151i	−0.0263688	+	0.0898040i
$624$	10.8448	−	5.59348i	0.434141	−	0.223918i
$625$	10.8203	+	6.95377i	0.432811	+	0.278151i
$626$	15.2173	+	11.1103i	0.608204	+	0.444058i
$627$	20.8995	−	13.4313i	0.834646	−	0.536394i
$628$	−3.39071	+	5.56398i	−0.135304	+	0.222027i
$629$	−40.1556	+	34.7950i	−1.60111	+	1.38737i
$630$	0.0897433	−	0.249681i	0.00357546	−	0.00994753i
$631$	−2.82529	+	6.18653i	−0.112473	+	0.246282i	−0.957495	−	0.288450i	$-0.906860\pi$
$631$	−2.82529	+	6.18653i	−0.112473	+	0.246282i	0.845022	+	0.534732i	$0.179587\pi$
$632$	−4.49667	−	10.8516i	−0.178868	−	0.431653i
$633$	−9.53610	+	2.80005i	−0.379026	+	0.111292i
$634$	−19.9213	−	25.9594i	−0.791175	−	1.03098i
$635$	−2.15513	+	0.309860i	−0.0855236	+	0.0122964i
$636$	−7.09050	+	26.4720i	−0.281157	+	1.04968i
$637$	−19.3106	+	8.81886i	−0.765114	+	0.349416i
$638$	31.7532	−	2.65267i	1.25712	−	0.105020i
$639$	−5.72352	−	0.822918i	−0.226419	−	0.0325541i
$640$	−6.96031	−	7.83692i	−0.275130	−	0.309781i
$641$	−2.91391	−	2.52492i	−0.115093	−	0.0997283i	0.595413	−	0.803420i	$-0.296988\pi$
$641$	−2.91391	−	2.52492i	−0.115093	−	0.0997283i	−0.710506	+	0.703691i	$0.751534\pi$
$642$	12.1855	−	12.4802i	0.480922	−	0.492552i
$643$			21.8728i			0.862580i	0.902213	+	0.431290i	$0.141941\pi$
$643$			21.8728i			0.862580i	−0.902213	+	0.431290i	$0.858059\pi$
$644$	−0.411926	−	1.89817i	−0.0162322	−	0.0747982i
$645$		−	1.39392i		−	0.0548856i
$646$	−23.4373	−	22.8839i	−0.922130	−	0.900356i
$647$	−18.4655	−	16.0005i	−0.725955	−	0.629044i	0.211408	−	0.977398i	$-0.432195\pi$
$647$	−18.4655	−	16.0005i	−0.725955	−	0.629044i	−0.937363	+	0.348354i	$0.886741\pi$
$648$	−1.26570	+	2.52943i	−0.0497213	+	0.0993653i
$649$	32.6102	+	4.68863i	1.28006	+	0.184045i
$650$	1.48752	+	17.8060i	0.0583452	+	0.698410i
$651$	0.297862	−	0.136029i	0.0116741	−	0.00533140i
$652$	−0.121822	+	0.454816i	−0.00477092	+	0.0178120i
$653$	41.5415	−	5.97276i	1.62564	−	0.233732i	0.731607	−	0.681726i	$-0.238770\pi$
$653$	41.5415	−	5.97276i	1.62564	−	0.233732i	0.894037	+	0.447994i	$0.147861\pi$
$654$	−1.51587	+	1.16328i	−0.0592752	+	0.0454879i
$655$	14.8168	−	4.35060i	0.578939	−	0.169992i
$656$	−1.10496	+	11.5946i	−0.0431413	+	0.452692i
$657$	3.72035	−	8.14643i	0.145145	−	0.317822i
$658$	−3.25294	−	1.16921i	−0.126813	−	0.0455805i
$659$	34.1982	−	29.6329i	1.33217	−	1.15434i	0.356700	−	0.934219i	$-0.383902\pi$
$659$	34.1982	−	29.6329i	1.33217	−	1.15434i	0.975474	−	0.220116i	$-0.0706436\pi$
$660$	−9.00098	−	5.48523i	−0.350363	−	0.213512i
$661$	7.90976	−	5.08329i	0.307654	−	0.197717i	−0.377699	−	0.925929i	$-0.623284\pi$
$661$	7.90976	−	5.08329i	0.307654	−	0.197717i	0.685353	+	0.728211i	$0.259648\pi$
$662$	−14.7090	+	20.1462i	−0.571682	+	0.783005i
$663$	−13.6113	−	8.74745i	−0.528619	−	0.339723i
$664$	−10.5459	+	15.1935i	−0.409260	+	0.589624i
$665$	−0.230826	+	0.786120i	−0.00895103	+	0.0304844i
$666$	−12.5148	−	6.64074i	−0.484937	−	0.257323i
$667$	−17.9536	+	6.20187i	−0.695166	+	0.240137i
$668$	3.63898	−	2.46343i	0.140796	−	0.0953128i
$669$	2.43446	−	8.29100i	0.0941215	−	0.320548i
$670$	3.05325	+	7.89667i	0.117958	+	0.305075i
$671$	44.5452	−	69.3137i	1.71965	−	2.67582i
$672$	0.608038	+	0.970844i	0.0234556	+	0.0374511i
$673$	18.1780	−	11.6823i	0.700711	−	0.450320i	−0.141168	−	0.989986i	$-0.545086\pi$
$673$	18.1780	−	11.6823i	0.700711	−	0.450320i	0.841879	+	0.539666i	$0.181450\pi$
$674$	−18.8310	−	1.12088i	−0.725343	−	0.0431747i
$675$	−2.71223	−	3.13008i	−0.104394	−	0.120477i
$676$	5.46613	−	4.96998i	0.210236	−	0.191153i
$677$	−4.25282	+	9.31238i	−0.163449	+	0.357904i	−0.973580	−	0.228345i	$-0.926669\pi$
$677$	−4.25282	+	9.31238i	−0.163449	+	0.357904i	0.810131	+	0.586249i	$0.199396\pi$
$678$	1.12344	−	5.47866i	0.0431453	−	0.210407i
$679$	−0.713229	−	2.42904i	−0.0273712	−	0.0932178i
$680$	−4.38716	+	13.1875i	−0.168240	+	0.505717i
$681$	−11.2043	+	1.61094i	−0.429350	+	0.0617312i
$682$	−2.91695	−	12.6779i	−0.111696	−	0.485461i
$683$	−9.28447	−	20.3301i	−0.355260	−	0.777911i	−0.999910	−	0.0134332i	$-0.995724\pi$
$683$	−9.28447	−	20.3301i	−0.355260	−	0.777911i	0.644649	−	0.764478i	$-0.277003\pi$
$684$	3.43746	−	8.02932i	0.131435	−	0.307009i
$685$	3.30946	+	0.475829i	0.126448	+	0.0181805i
$686$	−1.95764	−	3.48549i	−0.0747429	−	0.133077i
$687$	−0.769896	+	0.888507i	−0.0293734	+	0.0338987i
$688$	4.73143	+	3.71941i	0.180384	+	0.141801i
$689$		−	41.8010i		−	1.59249i
$690$	6.00645	+	1.84516i	0.228662	+	0.0702442i
$691$	−0.568566			−0.0216293			−0.0108146	−	0.999942i	$-0.503442\pi$
$691$	−0.568566			−0.0216293			−0.0108146	+	0.999942i	$0.503442\pi$
$692$	−44.4680	+	14.2195i	−1.69042	+	0.540543i
$693$	0.870617	+	0.754394i	0.0330720	+	0.0286571i
$694$	14.7664	+	26.2910i	0.560526	+	0.997994i
$695$	0.975852	−	6.78720i	0.0370162	−	0.257453i
$696$	8.72167	−	7.03039i	0.330594	−	0.266486i
$697$	14.0479	−	6.41547i	0.532103	−	0.243003i
$698$	−22.3579	+	5.14414i	−0.846257	+	0.194709i
$699$	−4.15415	−	28.8928i	−0.157125	−	1.09283i
$700$	−1.65417	+	0.278321i	−0.0625216	+	0.0105195i
$701$	−3.62813	+	1.06532i	−0.137033	+	0.0402364i	−0.349530	−	0.936925i	$-0.613659\pi$
$701$	−3.62813	+	1.06532i	−0.137033	+	0.0402364i	0.212497	+	0.977162i	$0.431840\pi$
$702$	0.866620	−	4.22625i	0.0327084	−	0.159510i
$703$	39.7958	+	18.1741i	1.50093	+	0.685451i
$704$	42.6361	−	15.9161i	1.60691	−	0.599860i
$705$	8.45105	−	7.32288i	0.318285	−	0.275796i
$706$	−0.896758	+	15.0657i	−0.0337499	+	0.567004i
$707$	−1.64740	−	2.56341i	−0.0619570	−	0.0964070i
$708$	10.4180	−	5.06197i	0.391534	−	0.190241i
$709$	25.6884	+	16.5090i	0.964750	+	0.620007i	0.925309	−	0.379215i	$-0.123806\pi$
$709$	25.6884	+	16.5090i	0.964750	+	0.620007i	0.0394411	+	0.999222i	$0.487442\pi$
$710$	−2.73217	−	7.06624i	−0.102536	−	0.265191i
$711$	−3.98474	−	1.17003i	−0.149440	−	0.0438794i
$712$	32.4420	−	3.49249i	1.21582	−	0.130887i
$713$	3.54944	+	6.89501i	0.132928	+	0.258220i
$714$	0.711966	−	1.34173i	0.0266446	−	0.0502130i
$715$	15.4264	+	4.52959i	0.576913	+	0.169397i
$716$	−9.71081	−	1.16015i	−0.362910	−	0.0433567i
$717$	0.640371	−	0.996436i	0.0239151	−	0.0372126i
$718$	−27.7637	+	38.0266i	−1.03613	+	1.41914i
$719$	23.4540	+	36.4952i	0.874688	+	1.36104i	0.931914	+	0.362680i	$0.118138\pi$
$719$	23.4540	+	36.4952i	0.874688	+	1.36104i	−0.0572253	+	0.998361i	$0.518225\pi$
$720$	−3.70156	+	0.177022i	−0.137949	+	0.00659722i
$721$	1.89075	+	2.18204i	0.0704153	+	0.0812636i
$722$	−0.0342154	+	0.0951931i	−0.00127337	+	0.00354272i
$723$	−0.750216	−	0.342612i	−0.0279008	−	0.0127419i
$724$	16.4023	+	13.5403i	0.609587	+	0.503221i
$725$	4.62148	+	15.7393i	0.171638	+	0.584544i
$726$	23.9665	−	18.3919i	0.889479	−	0.682587i
$727$	3.92252	+	27.2817i	0.145478	+	1.01182i	0.923503	+	0.383590i	$0.125313\pi$
$727$	3.92252	+	27.2817i	0.145478	+	1.01182i	−0.778025	+	0.628233i	$0.783778\pi$
$728$	−1.27899	−	1.19045i	−0.0474025	−	0.0441209i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	11.6930	−	0.976839i	0.432779	−	0.0361544i
$731$	1.13568	−	7.89882i	0.0420046	−	0.292148i
$732$	−0.692063	−	28.9589i	−0.0255794	−	1.07035i
$733$	−13.7356	+	15.8517i	−0.507334	+	0.585495i	−0.950414	−	0.310987i	$-0.899340\pi$
$733$	−13.7356	+	15.8517i	−0.507334	+	0.585495i	0.443080	+	0.896482i	$0.353886\pi$
$734$	−12.4598	−	12.1656i	−0.459899	−	0.449040i
$735$	6.44715			0.237807
$736$	−22.2902	+	15.4644i	−0.821626	+	0.570027i
$737$	−36.7602			−1.35408
$738$	2.94635	+	2.87678i	0.108457	+	0.105896i
$739$	26.7580	−	30.8803i	0.984308	−	1.13595i	−0.00640517	−	0.999979i	$-0.502039\pi$
$739$	26.7580	−	30.8803i	0.984308	−	1.13595i	0.990713	−	0.135972i	$-0.0434157\pi$
$740$	−0.443476	−	18.5569i	−0.0163025	−	0.682166i
$741$	−1.89595	+	13.1866i	−0.0696495	+	0.484423i
$742$	3.91057	−	0.326690i	0.143562	−	0.0119932i
$743$	−6.21396	−	13.6067i	−0.227968	−	0.499180i	0.760736	−	0.649061i	$-0.224838\pi$
$743$	−6.21396	−	13.6067i	−0.227968	−	0.499180i	−0.988704	+	0.149881i	$0.952111\pi$
$744$	−3.34786	−	3.11609i	−0.122738	−	0.114241i
$745$	0.482329	+	3.35467i	0.0176712	+	0.122906i
$746$	−34.2745	+	26.3023i	−1.25488	+	0.962996i
$747$	1.84223	+	6.27405i	0.0674035	+	0.229555i
$748$	−46.5361	−	38.4161i	−1.70153	−	1.40463i
$749$	−2.27191	−	1.03755i	−0.0830139	−	0.0379112i
$750$	4.05131	−	11.2714i	0.147933	−	0.411575i
$751$	−12.3102	−	14.2067i	−0.449204	−	0.518409i	0.485307	−	0.874344i	$-0.338708\pi$
$751$	−12.3102	−	14.2067i	−0.449204	−	0.518409i	−0.934511	+	0.355935i	$0.884163\pi$
$752$	2.30631	+	48.2254i	0.0841025	+	1.75860i
$753$	−6.97596	−	10.8548i	−0.254218	−	0.395571i
$754$	−10.0757	+	13.8002i	−0.366935	+	0.502573i
$755$	5.14127	−	7.99998i	0.187110	−	0.291149i
$756$	0.402148	+	0.0480444i	0.0146260	+	0.00174736i
$757$	−30.1973	−	8.86672i	−1.09754	−	0.322267i	−0.317665	−	0.948203i	$-0.602899\pi$
$757$	−30.1973	−	8.86672i	−1.09754	−	0.322267i	−0.779874	+	0.625936i	$0.784717\pi$
$758$	10.5076	−	19.8020i	0.381653	−	0.719242i
$759$	−16.8775	+	21.4353i	−0.612614	+	0.778051i
$760$	11.3778	−	1.22485i	0.412715	−	0.0444301i
$761$	−7.20792	−	2.11644i	−0.261287	−	0.0767208i	0.148465	−	0.988918i	$-0.452567\pi$
$761$	−7.20792	−	2.11644i	−0.261287	−	0.0767208i	−0.409752	+	0.912197i	$0.634385\pi$
$762$	−1.19860	−	3.09995i	−0.0434207	−	0.112299i
$763$	0.230174	+	0.147924i	0.00833285	+	0.00535520i
$764$	22.2553	−	10.8135i	0.805167	−	0.391219i
$765$	2.65655	+	4.13368i	0.0960479	+	0.149453i
$766$	−1.10735	+	18.6037i	−0.0400103	+	0.672180i
$767$	−13.3519	+	11.5695i	−0.482108	+	0.417749i
$768$	9.27603	−	13.0367i	0.334720	−	0.470421i
$769$	3.85070	+	1.75856i	0.138860	+	0.0634152i	0.483633	−	0.875271i	$-0.339317\pi$
$769$	3.85070	+	1.75856i	0.138860	+	0.0634152i	−0.344773	+	0.938686i	$0.612044\pi$
$770$	−0.303190	+	1.47857i	−0.0109262	+	0.0532839i
$771$	−27.1617	+	7.97539i	−0.978205	+	0.287227i
$772$	−24.3680	+	4.10002i	−0.877022	+	0.147563i
$773$	−1.99233	−	13.8569i	−0.0716590	−	0.498399i	−0.993768	−	0.111469i	$-0.964444\pi$
$773$	−1.99233	−	13.8569i	−0.0716590	−	0.498399i	0.922109	−	0.386930i	$-0.126465\pi$
$774$	2.07363	−	0.477104i	0.0745349	−	0.0171492i
$775$	6.09201	−	2.78213i	0.218831	−	0.0999370i
$776$	−27.5291	+	22.1908i	−0.988238	+	0.796602i
$777$	−0.288710	+	2.00802i	−0.0103574	+	0.0720375i
$778$	−7.39059	−	13.1586i	−0.264965	−	0.471760i
$779$	−9.61011	−	8.32721i	−0.344318	−	0.298353i
$780$	5.38387	−	1.72159i	0.192774	−	0.0616429i
$781$	32.8944			1.17706
$782$	32.5330	+	15.3495i	1.16338	+	0.548898i
$783$		−	3.96065i		−	0.141542i
$784$	−17.2030	+	21.8838i	−0.614391	+	0.781563i
$785$	−1.97653	+	2.28104i	−0.0705454	+	0.0814137i
$786$	11.5434	+	20.5526i	0.411741	+	0.733089i
$787$	19.4314	+	2.79381i	0.692654	+	0.0995886i	0.479646	−	0.877462i	$-0.340765\pi$
$787$	19.4314	+	2.79381i	0.692654	+	0.0995886i	0.213008	+	0.977051i	$0.431674\pi$
$788$	−2.95505	+	6.90249i	−0.105269	+	0.245891i
$789$	−3.77248	−	8.26057i	−0.134304	−	0.294084i
$790$	−1.22005	−	5.30266i	−0.0434073	−	0.188660i
$791$	−0.792672	+	0.113969i	−0.0281842	+	0.00405227i
$792$	5.07913	−	15.2675i	0.180479	−	0.542507i
$793$	12.4479	+	42.3937i	0.442039	+	1.50544i
$794$	3.22006	−	15.7033i	0.114276	−	0.557290i
$795$	−5.27358	+	11.5475i	−0.187035	+	0.409549i
$796$	21.9804	−	19.9853i	0.779076	−	0.708360i
$797$	7.00294	+	8.08183i	0.248057	+	0.286273i	0.866099	−	0.499872i	$-0.166619\pi$
$797$	7.00294	+	8.08183i	0.248057	+	0.286273i	−0.618043	+	0.786145i	$0.712074\pi$
$798$	−1.24845	−	0.0743120i	−0.0441948	−	0.00263062i
$799$	53.8551	−	34.6106i	1.90526	−	1.22444i
$800$	12.4359	+	19.8561i	0.439674	+	0.702020i
$801$	6.23697	−	9.70492i	0.220373	−	0.342907i
$802$	13.1485	+	34.0062i	0.464291	+	1.20080i
$803$	−14.3534	+	48.8832i	−0.506521	+	1.72505i
$804$	−10.7022	+	7.24492i	−0.377438	+	0.255509i
$805$	−0.0422777	−	0.898748i	−0.00149009	−	0.0316767i
$806$	6.16232	+	3.26993i	0.217059	+	0.115178i
$807$	−1.22156	+	4.16026i	−0.0430010	+	0.146448i
$808$	−24.2681	+	34.9632i	−0.853749	+	1.23000i
$809$	−15.3301	−	9.85208i	−0.538979	−	0.346381i	0.242661	−	0.970111i	$-0.421980\pi$
$809$	−15.3301	−	9.85208i	−0.538979	−	0.346381i	−0.781639	+	0.623731i	$0.785616\pi$
$810$	−0.772585	+	1.05817i	−0.0271459	+	0.0371803i
$811$	−7.99571	+	5.13853i	−0.280767	+	0.180438i	−0.673444	−	0.739238i	$-0.735186\pi$
$811$	−7.99571	+	5.13853i	−0.280767	+	0.180438i	0.392676	+	0.919677i	$0.371549\pi$
$812$	−1.36978	−	0.834750i	−0.0480699	−	0.0292940i
$813$	19.2567	−	16.6860i	0.675360	−	0.585203i
$814$	75.8449	+	27.2611i	2.65836	+	0.955500i
$815$	−0.0906055	+	0.198398i	−0.00317377	+	0.00694959i
$816$	−21.1196	−	2.01268i	−0.739333	−	0.0704581i
$817$	−6.30451	+	1.85117i	−0.220567	+	0.0647643i
$818$	−3.49741	+	2.68392i	−0.122284	+	0.0938409i
$819$	−0.611468	+	0.0879159i	−0.0213664	+	0.00307203i
$820$	−1.39590	+	5.21151i	−0.0487468	+	0.181994i
$821$	−24.6672	+	11.2651i	−0.860891	+	0.393156i	−0.796406	−	0.604763i	$-0.793268\pi$
$821$	−24.6672	+	11.2651i	−0.860891	+	0.393156i	−0.0644855	+	0.997919i	$0.520541\pi$
$822$	0.424893	+	5.08609i	0.0148198	+	0.177398i
$823$	14.1562	+	2.03536i	0.493455	+	0.0709481i	0.384550	−	0.923104i	$-0.374357\pi$
$823$	14.1562	+	2.03536i	0.493455	+	0.0709481i	0.108905	+	0.994052i	$0.465266\pi$
$824$	18.0461	−	36.0641i	0.628665	−	1.25635i
$825$	17.8062	+	15.4292i	0.619934	+	0.537176i
$826$	−1.18670	−	1.15868i	−0.0412905	−	0.0403155i
$827$			44.6603i			1.55299i	0.630123	+	0.776495i	$0.283004\pi$
$827$			44.6603i			1.55299i	−0.630123	+	0.776495i	$0.716996\pi$
$828$	−0.689047	+	9.56688i	−0.0239460	+	0.332472i
$829$		−	12.9797i		−	0.450805i	−0.974266	−	0.225402i	$-0.927630\pi$
$829$		−	12.9797i		−	0.450805i	0.974266	−	0.225402i	$-0.0723697\pi$
$830$	−5.98517	+	6.12991i	−0.207748	+	0.212772i
$831$	−16.8045	−	14.5612i	−0.582940	−	0.505121i
$832$	−8.52216	+	22.8684i	−0.295453	+	0.792819i
$833$	36.5335	+	5.25273i	1.26581	+	0.181996i
$834$	10.4308	−	0.871390i	0.361189	−	0.0301738i
$835$	1.85163	−	0.845613i	0.0640784	−	0.0292636i
$836$	−12.8553	+	47.9947i	−0.444611	+	1.65993i
$837$	−1.60057	+	0.230127i	−0.0553237	+	0.00795434i
$838$	4.04355	+	5.26914i	0.139682	+	0.182020i
$839$	−32.9246	+	9.66753i	−1.13668	+	0.333760i	−0.795331	−	0.606175i	$-0.792703\pi$
$839$	−32.9246	+	9.66753i	−1.13668	+	0.333760i	−0.341352	+	0.939936i	$0.610885\pi$
$840$	0.203136	+	0.490218i	0.00700884	+	0.0169141i
$841$	5.53053	−	12.1102i	0.190708	−	0.417592i
$842$	5.40430	−	15.0357i	0.186244	−	0.518164i
$843$	9.06559	−	7.85538i	0.312235	−	0.270554i
$844$	10.3439	−	16.9739i	0.356053	−	0.584265i
$845$	2.87894	−	1.85018i	0.0990385	−	0.0636482i
$846$	13.7863	+	10.0655i	0.473981	+	0.346060i
$847$	−3.63913	−	2.33873i	−0.125042	−	0.0803596i
$848$	−25.1247	−	48.7127i	−0.862785	−	1.67280i
$849$	7.98868	−	27.2070i	0.274171	−	0.933740i
$850$	14.5614	−	27.4417i	0.499453	−	0.941241i
$851$	−47.8242	−	4.59531i	−1.63939	−	0.157525i
$852$	9.57673	−	6.48303i	0.328093	−	0.222105i
$853$	2.99724	−	10.2077i	0.102623	−	0.349504i	−0.892133	−	0.451772i	$-0.850792\pi$
$853$	2.99724	−	10.2077i	0.102623	−	0.349504i	0.994757	+	0.102269i	$0.0326102\pi$
$854$	−3.86874	+	1.49585i	−0.132385	+	0.0511870i
$855$	2.18737	−	3.40362i	0.0748066	−	0.116401i
$856$	−1.24023	+	34.8629i	−0.0423901	+	1.19159i
$857$	−3.72477	+	2.39376i	−0.127236	+	0.0817694i	−0.602711	−	0.797960i	$-0.705913\pi$
$857$	−3.72477	+	2.39376i	−0.127236	+	0.0817694i	0.475475	+	0.879729i	$0.342276\pi$
$858$	−1.45826	+	24.4989i	−0.0497840	+	0.836380i
$859$	−14.7732	−	17.0492i	−0.504056	−	0.581712i	0.445511	−	0.895277i	$-0.353022\pi$
$859$	−14.7732	−	17.0492i	−0.504056	−	0.581712i	−0.949567	+	0.313565i	$0.898477\pi$
$860$	1.87546	+	2.06269i	0.0639528	+	0.0703372i
$861$	0.244947	−	0.536360i	0.00834779	−	0.0182791i
$862$	−6.27934	−	1.28762i	−0.213875	−	0.0438565i
$863$	−0.182807	−	0.622585i	−0.00622283	−	0.0211930i	0.956323	−	0.292312i	$-0.0944245\pi$
$863$	−0.182807	−	0.622585i	−0.00622283	−	0.0211930i	−0.962546	+	0.271119i	$0.912606\pi$
$864$	−1.53029	−	5.44593i	−0.0520617	−	0.185274i
$865$	−21.4060	+	3.07772i	−0.727827	+	0.104646i
$866$	30.1836	−	6.94470i	1.02568	−	0.235990i
$867$	4.62377	+	10.1246i	0.157032	+	0.343851i
$868$	−0.257748	+	0.602054i	−0.00874854	+	0.0204351i
$869$	23.3847	+	3.36221i	0.793272	+	0.114055i
$870$	4.52444	−	2.54116i	0.153393	−	0.0861535i
$871$	12.9091	−	14.8979i	0.437407	−	0.504795i
$872$	0.678002	−	3.76094i	0.0229601	−	0.127361i
$873$			12.5014i			0.423109i
$874$	0.368659	−	29.6168i	0.0124701	−	1.00180i
$875$	−1.71507			−0.0579798
$876$	5.45540	+	17.0605i	0.184321	+	0.576420i
$877$	24.6662	+	21.3734i	0.832920	+	0.721729i	0.962921	−	0.269785i	$-0.0869526\pi$
$877$	24.6662	+	21.3734i	0.832920	+	0.721729i	−0.130001	+	0.991514i	$0.541498\pi$
$878$	6.73887	−	3.78491i	0.227426	−	0.127734i
$879$	1.54952	−	10.7771i	0.0522640	−	0.363504i
$880$	20.6996	−	3.99354i	0.697783	−	0.134622i
$881$	−12.5823	+	5.74615i	−0.423909	+	0.193593i	−0.615935	−	0.787797i	$-0.711222\pi$
$881$	−12.5823	+	5.74615i	−0.423909	+	0.193593i	0.192026	+	0.981390i	$0.438494\pi$
$882$	2.20670	+	9.59091i	0.0743034	+	0.322943i
$883$	−6.37121	−	44.3128i	−0.214408	−	1.49124i	−0.758200	−	0.652022i	$-0.773921\pi$
$883$	−6.37121	−	44.3128i	−0.214408	−	1.49124i	0.543791	−	0.839220i	$-0.316988\pi$
$884$	31.9110	−	5.36918i	1.07328	−	0.180585i
$885$	5.14805	−	1.51160i	0.173050	−	0.0508120i
$886$	42.6373	+	8.74304i	1.43243	+	0.293728i
$887$	−28.3153	−	12.9312i	−0.950735	−	0.434186i	−0.121192	−	0.992629i	$-0.538672\pi$
$887$	−28.3153	−	12.9312i	−0.950735	−	0.434186i	−0.829543	+	0.558443i	$0.811399\pi$
$888$	27.4539	−	7.01130i	0.921293	−	0.235284i
$889$	−0.359671	+	0.311657i	−0.0120630	+	0.0104526i
$890$	15.0881	+	0.898089i	0.505753	+	0.0301040i
$891$	−3.07557	−	4.78567i	−0.103035	−	0.160326i
$892$	7.55275	+	15.5443i	0.252885	+	0.520461i
$893$	−44.3436	−	28.4979i	−1.48390	−	0.953647i
$894$	−4.82539	+	1.86574i	−0.161385	+	0.0623998i
$895$	−4.34676	−	1.27632i	−0.145296	−	0.0426628i
$896$	−2.20599	−	0.618541i	−0.0736970	−	0.0206640i
$897$	−2.76024	−	14.3674i	−0.0921616	−	0.479713i
$898$	−23.6956	−	12.5736i	−0.790731	−	0.419587i
$899$	6.14504	+	1.80435i	0.204949	+	0.0601783i
$900$	8.22490	+	0.982626i	0.274163	+	0.0327542i
$901$	−39.2916	+	61.1390i	−1.30899	+	2.03683i
$902$	−18.9195	−	13.8133i	−0.629949	−	0.459934i
$903$	−0.164725	−	0.256317i	−0.00548169	−	0.00852968i
$904$	5.70889	+	9.61874i	0.189875	+	0.319914i
$905$	6.45193	+	7.44592i	0.214469	+	0.247511i
$906$	13.6607	+	4.91008i	0.453845	+	0.163126i
$907$	−3.69688	−	1.68831i	−0.122753	−	0.0560593i	0.353092	−	0.935589i	$-0.385130\pi$
$907$	−3.69688	−	1.68831i	−0.122753	−	0.0560593i	−0.475845	+	0.879529i	$0.657858\pi$
$908$	14.4124	−	17.4588i	0.478293	−	0.579390i
$909$	4.23931	+	14.4378i	0.140609	+	0.478871i
$910$	−0.492750	−	0.642102i	−0.0163345	−	0.0212855i
$911$	3.32306	+	23.1124i	0.110098	+	0.765748i	0.967822	+	0.251637i	$0.0809690\pi$
$911$	3.32306	+	23.1124i	0.110098	+	0.765748i	−0.857724	+	0.514111i	$0.828122\pi$
$912$	5.71644	+	16.5066i	0.189290	+	0.546587i
$913$	−15.4527	−	33.8367i	−0.511410	−	1.11983i
$914$	1.99537	+	23.8852i	0.0660010	+	0.790052i
$915$	1.90962	−	13.2817i	0.0631301	−	0.439079i
$916$	−0.0561763	−	2.35066i	−0.00185612	−	0.0776679i
$917$	2.21041	−	2.55095i	0.0729941	−	0.0842397i
$918$	−5.24008	+	5.36680i	−0.172948	+	0.177131i
$919$	31.8285			1.04993			0.524963	−	0.851125i	$-0.324079\pi$
$919$	31.8285			1.04993			0.524963	+	0.851125i	$0.324079\pi$
$920$	−11.3708	+	5.35101i	−0.374884	+	0.176417i
$921$	−8.36015			−0.275476
$922$	14.5577	−	14.9098i	0.479432	−	0.491027i
$923$	−11.5515	+	13.3312i	−0.380223	+	0.438801i
$924$	−2.30333	+	0.0550452i	−0.0757738	+	0.00181085i
$925$	−5.90483	+	41.0690i	−0.194150	+	1.35034i
$926$	−3.49775	−	41.8690i	−0.114943	−	1.37590i
$927$	−5.92291	−	12.9694i	−0.194534	−	0.425970i
$928$	−3.44703	+	22.1381i	−0.113154	+	0.726717i
$929$	4.58388	+	31.8816i	0.150392	+	1.04600i	0.915563	+	0.402174i	$0.131745\pi$
$929$	4.58388	+	31.8816i	0.150392	+	1.04600i	−0.765171	+	0.643827i	$0.777346\pi$
$930$	−1.28981	−	1.68075i	−0.0422946	−	0.0551141i
$931$	−8.56202	−	29.1596i	−0.280609	−	0.955666i
$932$	45.0213	+	37.1656i	1.47472	+	1.21740i
$933$	19.8997	+	9.08790i	0.651488	+	0.297525i
$934$	−15.0462	−	5.40807i	−0.492326	−	0.176958i
$935$	−18.3052	−	21.1254i	−0.598645	−	0.690873i
$936$	4.40384	+	7.41991i	0.143944	+	0.242527i
$937$	−23.3062	−	36.2651i	−0.761380	−	1.18473i	−0.978027	−	0.208481i	$-0.933148\pi$
$937$	−23.3062	−	36.2651i	−0.761380	−	1.18473i	0.216646	−	0.976250i	$-0.430488\pi$
$938$	1.49462	+	1.09124i	0.0488009	+	0.0356302i
$939$	−7.20296	+	11.2080i	−0.235060	+	0.365760i
$940$	−2.65304	+	22.2068i	−0.0865325	+	0.724305i
$941$	−9.15269	−	2.68747i	−0.298369	−	0.0876091i	0.129122	−	0.991629i	$-0.458784\pi$
$941$	−9.15269	−	2.68747i	−0.298369	−	0.0876091i	−0.427491	+	0.904020i	$0.640602\pi$
$942$	−4.06984	−	2.15959i	−0.132602	−	0.0703631i
$943$	12.9610	+	5.19773i	0.422068	+	0.169261i
$944$	−8.60568	+	21.5076i	−0.280091	+	0.700014i
$945$	0.180010	+	0.0528556i	0.00585572	+	0.00171939i
$946$	−11.2900	+	4.36529i	−0.367069	+	0.141928i
$947$	40.7090	+	26.1621i	1.32286	+	0.850153i	0.995501	−	0.0947463i	$-0.0302040\pi$
$947$	40.7090	+	26.1621i	1.32286	+	0.850153i	0.327362	+	0.944899i	$0.393840\pi$
$948$	7.47076	−	3.62993i	0.242639	−	0.117895i
$949$	−14.7705	−	22.9833i	−0.479470	−	0.746070i
$950$	−25.5339	−	1.51986i	−0.828430	−	0.0493108i
$951$	17.4867	−	15.1523i	0.567044	−	0.491346i
$952$	0.751694	+	2.94338i	0.0243625	+	0.0953956i
$953$	−20.4063	−	9.31924i	−0.661024	−	0.301880i	0.0565108	−	0.998402i	$-0.482002\pi$
$953$	−20.4063	−	9.31924i	−0.661024	−	0.301880i	−0.717535	+	0.696522i	$0.754730\pi$
$954$	−18.9834	−	3.89266i	−0.614610	−	0.126030i
$955$	10.9974	−	3.22913i	0.355867	−	0.104492i
$956$	0.393059	+	2.33610i	0.0127124	+	0.0755547i
$957$	3.20651	+	22.3018i	0.103652	+	0.720914i
$958$	−5.90095	−	25.6472i	−0.190651	−	0.828622i
$959$	0.664780	−	0.303595i	0.0214669	−	0.00980359i
$960$	5.23931	−	5.24225i	0.169098	−	0.169193i
$961$	−4.03964	+	28.0963i	−0.130311	+	0.906333i
$962$	−37.6825	+	21.1645i	−1.21493	+	0.682371i
$963$	9.32118	+	8.07685i	0.300371	+	0.260273i
$964$	1.57112	−	0.502395i	0.0506024	−	0.0161811i
$965$	−11.4465			−0.368476
$966$	1.32253	−	0.370512i	0.0425516	−	0.0119210i
$967$		−	23.0585i		−	0.741511i	−0.928731	−	0.370755i	$-0.879099\pi$
$967$		−	23.0585i		−	0.741511i	0.928731	−	0.370755i	$-0.120901\pi$
$968$	−10.7195	+	59.4618i	−0.344537	+	1.91117i
$969$	15.1681	−	17.5049i	0.487269	−	0.562338i
$970$	−14.2810	+	8.02094i	−0.458534	+	0.257537i
$971$	−40.3931	−	5.80765i	−1.29628	−	0.186376i	−0.540577	−	0.841295i	$-0.681794\pi$
$971$	−40.3931	−	5.80765i	−1.29628	−	0.186376i	−0.755700	+	0.654918i	$0.772703\pi$
$972$	−1.83859	−	0.787128i	−0.0589729	−	0.0252472i
$973$	−0.622627	−	1.36336i	−0.0199605	−	0.0437074i
$974$	16.8229	−	3.87064i	0.539039	−	0.124023i
$975$	−12.5060	+	1.79809i	−0.400513	+	0.0575851i
$976$	39.9871	+	41.9215i	1.27996	+	1.34188i
$977$	8.77866	+	29.8974i	0.280854	+	0.956502i	0.972234	+	0.234010i	$0.0751849\pi$
$977$	8.77866	+	29.8974i	0.280854	+	0.956502i	−0.691380	+	0.722491i	$0.742997\pi$
$978$	−0.326154	−	0.0668799i	−0.0104292	−	0.00213858i
$979$	−27.2624	+	59.6963i	−0.871309	+	1.90790i
$980$	−9.54034	+	8.67437i	−0.304755	+	0.277093i
$981$	−0.884800	−	1.02111i	−0.0282495	−	0.0326016i
$982$	0.723822	−	12.1603i	0.0230981	−	0.388052i
$983$	4.25085	−	2.73186i	0.135581	−	0.0871327i	−0.471092	−	0.882084i	$-0.656140\pi$
$983$	4.25085	−	2.73186i	0.135581	−	0.0871327i	0.606673	+	0.794951i	$0.292504\pi$
$984$	−8.23054	−	0.292797i	−0.262380	−	0.00933402i
$985$	−1.88040	+	2.92596i	−0.0599145	+	0.0932288i
$986$	27.7087	−	10.7136i	0.882424	−	0.341190i
$987$	0.688623	−	2.34524i	0.0219191	−	0.0746497i
$988$	−14.9365	−	22.0642i	−0.475193	−	0.701955i
$989$	5.88025	−	4.18205i	0.186981	−	0.132981i
$990$	3.49361	−	6.58387i	0.111034	−	0.209249i
$991$	13.5619	−	46.1876i	0.430808	−	1.46720i	−0.403029	−	0.915187i	$-0.632043\pi$
$991$	13.5619	−	46.1876i	0.430808	−	1.46720i	0.833837	−	0.552010i	$-0.186139\pi$
$992$	9.14665	+	0.106709i	0.290407	+	0.00338800i
$993$	−14.8384	−	9.53603i	−0.470881	−	0.302617i
$994$	−1.33744	−	0.976482i	−0.0424210	−	0.0309721i
$995$	11.5768	−	7.43995i	0.367009	−	0.235862i
$996$	−11.1676	−	6.80555i	−0.353858	−	0.215642i
$997$	17.1200	−	14.8346i	0.542197	−	0.469816i	−0.340180	−	0.940360i	$-0.610488\pi$
$997$	17.1200	−	14.8346i	0.542197	−	0.469816i	0.882376	+	0.470544i	$0.155942\pi$
$998$	19.9579	−	55.5263i	0.631757	−	1.75766i
$999$	4.16161	−	9.11265i	0.131667	−	0.288312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.235.5	yes	240
8.3	odd	2	inner	552.2.t.a.235.2	✓	240
23.14	odd	22	inner	552.2.t.a.451.2	yes	240
184.83	even	22	inner	552.2.t.a.451.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.2	✓	240	8.3	odd	2	inner
552.2.t.a.235.5	yes	240	1.1	even	1	trivial
552.2.t.a.451.2	yes	240	23.14	odd	22	inner
552.2.t.a.451.5	yes	240	184.83	even	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01188 - 0.987982i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.0477826 + 1.99943i) q^{4} +(-0.131847 + 0.917018i) q^{5} +(-1.40930 + 0.117734i) q^{6} +(0.0841231 + 0.184204i) q^{7} +(1.92705 - 2.07038i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.01188 - 0.987982i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.0477826 + 1.99943i) q^{4} +(-0.131847 + 0.917018i) q^{5} +(-1.40930 + 0.117734i) q^{6} +(0.0841231 + 0.184204i) q^{7} +(1.92705 - 2.07038i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.03941 - 0.797645i) q^{10} +(1.60270 + 5.45831i) q^{11} +(1.54236 + 1.27324i) q^{12} +(-2.77492 - 1.26726i) q^{13} +(0.0968681 - 0.269503i) q^{14} +(0.606695 + 0.700163i) q^{15} +(-3.99543 + 0.191076i) q^{16} +(2.86746 + 4.46186i) q^{17} +(-0.833921 + 1.14218i) q^{18} +(2.36103 - 3.67383i) q^{19} +(-1.83981 - 0.219802i) q^{20} +(0.194301 + 0.0570519i) q^{21} +(3.77098 - 7.10657i) q^{22} +(-1.13343 + 4.65997i) q^{23} +(-0.302740 - 2.81218i) q^{24} +(3.97393 + 1.16685i) q^{25} +(1.55584 + 4.02388i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.364283 + 0.177000i) q^{28} +(2.14129 + 3.33191i) q^{29} +(0.0778492 - 1.30788i) q^{30} +(1.22207 - 1.05893i) q^{31} +(4.23166 + 3.75407i) q^{32} +(5.17466 + 2.36319i) q^{33} +(1.50672 - 7.34784i) q^{34} +(-0.180010 + 0.0528556i) q^{35} +(1.97228 - 0.331845i) q^{36} +(1.42570 + 9.91599i) q^{37} +(-6.01875 + 1.38481i) q^{38} +(-2.77492 + 1.26726i) q^{39} +(1.64450 + 2.04011i) q^{40} +(0.414389 - 2.88214i) q^{41} +(-0.140242 - 0.249695i) q^{42} +(-1.13709 - 0.985294i) q^{43} +(-10.8369 + 3.46531i) q^{44} +0.926448 q^{45} +(5.75086 - 3.59550i) q^{46} -12.0701i q^{47} +(-2.47205 + 3.14468i) q^{48} +(4.55717 - 5.25926i) q^{49} +(-2.86829 - 5.10687i) q^{50} +(5.24983 + 0.754812i) q^{51} +(2.40121 - 5.60880i) q^{52} +(5.69226 + 12.4643i) q^{53} +(0.317100 + 1.37820i) q^{54} +(-5.21668 + 0.750046i) q^{55} +(0.543482 + 0.180803i) q^{56} +(-1.23035 - 4.19020i) q^{57} +(1.12515 - 5.48703i) q^{58} +(2.40581 - 5.26800i) q^{59} +(-1.37094 + 1.24650i) q^{60} +(-9.48472 - 10.9460i) q^{61} +(-2.28278 - 0.135878i) q^{62} +(0.170357 - 0.109482i) q^{63} +(-0.572955 - 7.97946i) q^{64} +(1.52797 - 2.37756i) q^{65} +(-2.90132 - 7.50373i) q^{66} +(-1.82054 + 6.20017i) q^{67} +(-8.78415 + 5.94648i) q^{68} +(2.77953 + 3.90822i) q^{69} +(0.234368 + 0.124363i) q^{70} +(1.62908 - 5.54815i) q^{71} +(-2.32356 - 1.61279i) q^{72} +(7.53405 + 4.84184i) q^{73} +(8.35418 - 11.4423i) q^{74} +(3.48421 - 2.23917i) q^{75} +(7.45839 + 4.54517i) q^{76} +(-0.870617 + 0.754394i) q^{77} +(4.05990 + 1.45926i) q^{78} +(1.72521 - 3.77767i) q^{79} +(0.351567 - 3.68908i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.26681 + 2.50695i) q^{82} +(-6.47236 + 0.930585i) q^{83} +(-0.104787 + 0.391217i) q^{84} +(-4.46967 + 2.04123i) q^{85} +(0.177140 + 2.12042i) q^{86} +(3.92033 + 0.563659i) q^{87} +(14.3893 + 7.20023i) q^{88} +(8.71852 + 7.55464i) q^{89} +(-0.937450 - 0.915314i) q^{90} -0.617756i q^{91} +(-9.37144 - 2.04354i) q^{92} -1.61703i q^{93} +(-11.9251 + 12.2135i) q^{94} +(3.05768 + 2.64949i) q^{95} +(5.60829 - 0.739681i) q^{96} +(-12.3742 - 1.77914i) q^{97} +(-9.80734 + 0.819307i) q^{98} +(5.17466 - 2.36319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more