LMFDB - Embedded newform 460.2.q.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(11,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("460.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.q (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	460.11
Dual form			460.2.q.a.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39626 - 0.224613i) q^{2} +(1.77069 + 0.254587i) q^{3} +(1.89910 + 0.627237i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-2.41517 - 0.753191i) q^{6} +(-0.375831 - 0.433732i) q^{7} +(-2.51075 - 1.30235i) q^{8} +(0.192056 + 0.0563926i) q^{9} +O(q^{10})$	\(q+(-1.39626 - 0.224613i) q^{2} +(1.77069 + 0.254587i) q^{3} +(1.89910 + 0.627237i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-2.41517 - 0.753191i) q^{6} +(-0.375831 - 0.433732i) q^{7} +(-2.51075 - 1.30235i) q^{8} +(0.192056 + 0.0563926i) q^{9} +(-0.177858 - 1.40298i) q^{10} +(3.64615 + 2.34324i) q^{11} +(3.20303 + 1.59413i) q^{12} +(0.362789 - 0.418681i) q^{13} +(0.427337 + 0.690020i) q^{14} +(0.254587 + 1.77069i) q^{15} +(3.21315 + 2.38237i) q^{16} +(7.04896 - 3.21915i) q^{17} +(-0.255494 - 0.121877i) q^{18} +(-0.00868497 + 0.0190174i) q^{19} +(-0.0667921 + 1.99888i) q^{20} +(-0.555058 - 0.863687i) q^{21} +(-4.56467 - 4.09075i) q^{22} +(0.231288 + 4.79025i) q^{23} +(-4.11421 - 2.94527i) q^{24} +(-0.841254 + 0.540641i) q^{25} +(-0.600589 + 0.503101i) q^{26} +(-4.55601 - 2.08066i) q^{27} +(-0.441687 - 1.05943i) q^{28} +(4.07892 + 8.93158i) q^{29} +(0.0422500 - 2.52953i) q^{30} +(-6.11561 + 0.879291i) q^{31} +(-3.95129 - 4.04813i) q^{32} +(5.85966 + 5.07742i) q^{33} +(-10.5653 + 2.91150i) q^{34} +(0.310279 - 0.482803i) q^{35} +(0.329361 + 0.227560i) q^{36} +(1.92972 - 6.57204i) q^{37} +(0.0163981 - 0.0246026i) q^{38} +(0.748978 - 0.648993i) q^{39} +(0.542235 - 2.77596i) q^{40} +(3.29344 - 0.967042i) q^{41} +(0.581011 + 1.33061i) q^{42} +(-1.58179 + 11.0016i) q^{43} +(5.45464 + 6.73705i) q^{44} +0.200164i q^{45} +(0.753014 - 6.74040i) q^{46} -9.81404i q^{47} +(5.08297 + 5.03647i) q^{48} +(0.949329 - 6.60273i) q^{49} +(1.29605 - 0.565920i) q^{50} +(13.3011 - 3.90555i) q^{51} +(0.951583 - 0.567561i) q^{52} +(-0.409635 + 0.354951i) q^{53} +(5.89404 + 3.92848i) q^{54} +(-1.22108 + 4.15863i) q^{55} +(0.378748 + 1.57846i) q^{56} +(-0.0202200 + 0.0314629i) q^{57} +(-3.68909 - 13.3870i) q^{58} +(2.44039 + 2.11461i) q^{59} +(-0.627158 + 3.52240i) q^{60} +(-8.51202 + 1.22384i) q^{61} +(8.73649 + 0.145923i) q^{62} +(-0.0477212 - 0.104495i) q^{63} +(4.60777 + 6.53976i) q^{64} +(0.503930 + 0.230137i) q^{65} +(-7.04116 - 8.40557i) q^{66} +(-0.568059 + 0.365069i) q^{67} +(15.4058 - 1.69212i) q^{68} +(-0.809996 + 8.54094i) q^{69} +(-0.541675 + 0.604428i) q^{70} +(4.89074 + 7.61014i) q^{71} +(-0.408762 - 0.391712i) q^{72} +(6.44117 - 14.1042i) q^{73} +(-4.17057 + 8.74285i) q^{74} +(-1.62724 + 0.743136i) q^{75} +(-0.0284221 + 0.0306684i) q^{76} +(-0.353999 - 2.46212i) q^{77} +(-1.19154 + 0.737934i) q^{78} +(-0.702066 + 0.810228i) q^{79} +(-1.38062 + 3.75418i) q^{80} +(-8.04274 - 5.16876i) q^{81} +(-4.81572 + 0.610495i) q^{82} +(-6.33961 - 1.86148i) q^{83} +(-0.512373 - 1.98838i) q^{84} +(5.07468 + 5.85649i) q^{85} +(4.67968 - 15.0058i) q^{86} +(4.94864 + 16.8535i) q^{87} +(-6.10288 - 10.6319i) q^{88} +(-5.88789 - 0.846551i) q^{89} +(0.0449594 - 0.279481i) q^{90} -0.317942 q^{91} +(-2.56539 + 9.24223i) q^{92} -11.0527 q^{93} +(-2.20436 + 13.7030i) q^{94} +(-0.0206939 - 0.00297534i) q^{95} +(-5.96591 - 8.17393i) q^{96} +(-3.14195 - 10.7005i) q^{97} +(-2.80857 + 9.00591i) q^{98} +(0.568123 + 0.655649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q - 4 * q^2 + 2 * q^6 + 2 * q^8 + 48 * q^9	$ 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9} + 6 q^{12} - 24 q^{16} + 26 q^{18} + 4 q^{24} + 48 q^{25} - 14 q^{26} + 40 q^{29} + 16 q^{32} - 22 q^{34} - 152 q^{36} - 110 q^{38} - 88 q^{40} - 8 q^{41} - 22 q^{44} - 132 q^{46} - 190 q^{48} - 56 q^{49} - 18 q^{50} - 50 q^{52} - 90 q^{54} - 110 q^{56} - 136 q^{58} - 22 q^{60} + 30 q^{62} - 30 q^{64} + 4 q^{69} + 110 q^{72} + 22 q^{74} - 176 q^{77} + 66 q^{78} - 8 q^{81} + 154 q^{82} + 308 q^{84} + 32 q^{85} + 176 q^{88} - 88 q^{89} + 134 q^{92} - 448 q^{93} + 204 q^{94} + 6 q^{96} - 88 q^{97} + 132 q^{98}+O(q^{100}) $ 480 * q - 4 * q^2 + 2 * q^6 + 2 * q^8 + 48 * q^9 + 6 * q^12 - 24 * q^16 + 26 * q^18 + 4 * q^24 + 48 * q^25 - 14 * q^26 + 40 * q^29 + 16 * q^32 - 22 * q^34 - 152 * q^36 - 110 * q^38 - 88 * q^40 - 8 * q^41 - 22 * q^44 - 132 * q^46 - 190 * q^48 - 56 * q^49 - 18 * q^50 - 50 * q^52 - 90 * q^54 - 110 * q^56 - 136 * q^58 - 22 * q^60 + 30 * q^62 - 30 * q^64 + 4 * q^69 + 110 * q^72 + 22 * q^74 - 176 * q^77 + 66 * q^78 - 8 * q^81 + 154 * q^82 + 308 * q^84 + 32 * q^85 + 176 * q^88 - 88 * q^89 + 134 * q^92 - 448 * q^93 + 204 * q^94 + 6 * q^96 - 88 * q^97 + 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−1.39626	−	0.224613i	−0.987307	−	0.158825i
$2$	−1.39626	−	0.224613i	−0.987307	−	0.158825i
$3$	1.77069	+	0.254587i	1.02231	+	0.146986i	0.633025	−	0.774132i	$-0.281813\pi$
$3$	1.77069	+	0.254587i	1.02231	+	0.146986i	0.389285	+	0.921118i	$0.372722\pi$
$4$	1.89910	+	0.627237i	0.949549	+	0.313619i
$5$	0.281733	+	0.959493i	0.125995	+	0.429098i
$5$	0.281733	+	0.959493i	0.125995	+	0.429098i
$6$	−2.41517	−	0.753191i	−0.985988	−	0.307489i
$7$	−0.375831	−	0.433732i	−0.142051	−	0.163935i	0.680266	−	0.732965i	$-0.261864\pi$
$7$	−0.375831	−	0.433732i	−0.142051	−	0.163935i	−0.822317	+	0.569030i	$0.807319\pi$
$8$	−2.51075	−	1.30235i	−0.887686	−	0.460450i
$9$	0.192056	+	0.0563926i	0.0640186	+	0.0187975i
$10$	−0.177858	−	1.40298i	−0.0562437	−	0.443663i
$11$	3.64615	+	2.34324i	1.09936	+	0.706514i	0.958949	−	0.283580i	$-0.0915221\pi$
$11$	3.64615	+	2.34324i	1.09936	+	0.706514i	0.140408	+	0.990094i	$0.455158\pi$
$12$	3.20303	+	1.59413i	0.924635	+	0.460186i
$13$	0.362789	−	0.418681i	0.100619	−	0.116121i	−0.703206	−	0.710986i	$-0.748249\pi$
$13$	0.362789	−	0.418681i	0.100619	−	0.116121i	0.803826	+	0.594865i	$0.202794\pi$
$14$	0.427337	+	0.690020i	0.114211	+	0.184416i
$15$	0.254587	+	1.77069i	0.0657341	+	0.457191i
$16$	3.21315	+	2.38237i	0.803287	+	0.595593i
$17$	7.04896	−	3.21915i	1.70962	−	0.780759i	0.712780	−	0.701388i	$-0.247436\pi$
$17$	7.04896	−	3.21915i	1.70962	−	0.780759i	0.996845	−	0.0793715i	$-0.0252913\pi$
$18$	−0.255494	−	0.121877i	−0.0602204	−	0.0287267i
$19$	−0.00868497	+	0.0190174i	−0.00199247	+	0.00436290i	−0.910626	−	0.413232i	$-0.864400\pi$
$19$	−0.00868497	+	0.0190174i	−0.00199247	+	0.00436290i	0.908633	+	0.417595i	$0.137127\pi$
$20$	−0.0667921	+	1.99888i	−0.0149352	+	0.446964i
$21$	−0.555058	−	0.863687i	−0.121124	−	0.188472i
$22$	−4.56467	−	4.09075i	−0.973190	−	0.872152i
$23$	0.231288	+	4.79025i	0.0482268	+	0.998836i
$23$	0.231288	+	4.79025i	0.0482268	+	0.998836i
$24$	−4.11421	−	2.94527i	−0.839809	−	0.601200i
$25$	−0.841254	+	0.540641i	−0.168251	+	0.108128i
$26$	−0.600589	+	0.503101i	−0.117785	+	0.0986662i
$27$	−4.55601	−	2.08066i	−0.876804	−	0.400423i
$28$	−0.441687	−	1.05943i	−0.0834709	−	0.200214i
$29$	4.07892	+	8.93158i	0.757436	+	1.65855i	0.752523	+	0.658566i	$0.228836\pi$
$29$	4.07892	+	8.93158i	0.757436	+	1.65855i	0.00491268	+	0.999988i	$0.498436\pi$
$30$	0.0422500	−	2.52953i	0.00771376	−	0.461828i
$31$	−6.11561	+	0.879291i	−1.09840	+	0.157925i	−0.667597	−	0.744523i	$-0.732677\pi$
$31$	−6.11561	+	0.879291i	−1.09840	+	0.157925i	−0.430798	+	0.902448i	$0.641768\pi$
$32$	−3.95129	−	4.04813i	−0.698495	−	0.715615i
$33$	5.85966	+	5.07742i	1.02004	+	0.883866i
$34$	−10.5653	+	2.91150i	−1.81193	+	0.499317i
$35$	0.310279	−	0.482803i	0.0524467	−	0.0816087i
$36$	0.329361	+	0.227560i	0.0548935	+	0.0379266i
$37$	1.92972	−	6.57204i	0.317245	−	1.08044i	−0.634341	−	0.773053i	$-0.718729\pi$
$37$	1.92972	−	6.57204i	0.317245	−	1.08044i	0.951586	−	0.307383i	$-0.0994532\pi$
$38$	0.0163981	−	0.0246026i	0.00266012	−	0.00399106i
$39$	0.748978	−	0.648993i	0.119932	−	0.103922i
$40$	0.542235	−	2.77596i	0.0857348	−	0.438919i
$41$	3.29344	−	0.967042i	0.514350	−	0.151027i	−0.0142492	−	0.999898i	$-0.504536\pi$
$41$	3.29344	−	0.967042i	0.514350	−	0.151027i	0.528599	+	0.848872i	$0.322718\pi$
$42$	0.581011	+	1.33061i	0.0896520	+	0.205317i
$43$	−1.58179	+	11.0016i	−0.241220	+	1.67772i	0.404803	+	0.914404i	$0.367340\pi$
$43$	−1.58179	+	11.0016i	−0.241220	+	1.67772i	−0.646023	+	0.763318i	$0.723569\pi$
$44$	5.45464	+	6.73705i	0.822317	+	1.01565i
$45$			0.200164i			0.0298386i
$46$	0.753014	−	6.74040i	0.111026	−	0.993818i
$47$		−	9.81404i		−	1.43152i	−0.698344	−	0.715762i	$-0.746079\pi$
$47$		−	9.81404i		−	1.43152i	0.698344	−	0.715762i	$-0.253921\pi$
$48$	5.08297	+	5.03647i	0.733664	+	0.726952i
$49$	0.949329	−	6.60273i	0.135618	−	0.943247i
$50$	1.29605	−	0.565920i	0.183289	−	0.0800332i
$51$	13.3011	−	3.90555i	1.86253	−	0.546887i
$52$	0.951583	−	0.567561i	0.131961	−	0.0787065i
$53$	−0.409635	+	0.354951i	−0.0562678	+	0.0487563i	−0.682541	−	0.730848i	$-0.739125\pi$
$53$	−0.409635	+	0.354951i	−0.0562678	+	0.0487563i	0.626273	+	0.779604i	$0.284580\pi$
$54$	5.89404	+	3.92848i	0.802077	+	0.534599i
$55$	−1.22108	+	4.15863i	−0.164651	+	0.560749i
$56$	0.378748	+	1.57846i	0.0506123	+	0.210930i
$57$	−0.0202200	+	0.0314629i	−0.00267820	+	0.00416737i
$58$	−3.68909	−	13.3870i	−0.484401	−	1.75780i
$59$	2.44039	+	2.11461i	0.317711	+	0.275298i	0.799086	−	0.601216i	$-0.205317\pi$
$59$	2.44039	+	2.11461i	0.317711	+	0.275298i	−0.481375	+	0.876515i	$0.659863\pi$
$60$	−0.627158	+	3.52240i	−0.0809658	+	0.454740i
$61$	−8.51202	+	1.22384i	−1.08985	+	0.156697i	−0.663733	−	0.747970i	$-0.731029\pi$
$61$	−8.51202	+	1.22384i	−1.08985	+	0.156697i	−0.426119	+	0.904667i	$0.640120\pi$
$62$	8.73649	+	0.145923i	1.10954	+	0.0185322i
$63$	−0.0477212	−	0.104495i	−0.00601230	−	0.0131651i
$64$	4.60777	+	6.53976i	0.575971	+	0.817470i
$65$	0.503930	+	0.230137i	0.0625049	+	0.0285450i
$66$	−7.04116	−	8.40557i	−0.866707	−	1.03465i
$67$	−0.568059	+	0.365069i	−0.0693995	+	0.0446003i	−0.574880	−	0.818237i	$-0.694951\pi$
$67$	−0.568059	+	0.365069i	−0.0693995	+	0.0446003i	0.505481	+	0.862838i	$0.331315\pi$
$68$	15.4058	−	1.69212i	1.86823	−	0.205199i
$69$	−0.809996	+	8.54094i	−0.0975121	+	1.02821i
$70$	−0.541675	+	0.604428i	−0.0647425	+	0.0722429i
$71$	4.89074	+	7.61014i	0.580424	+	0.903157i	0.999990	−	0.00456761i	$-0.00145392\pi$
$71$	4.89074	+	7.61014i	0.580424	+	0.903157i	−0.419566	+	0.907725i	$0.637818\pi$
$72$	−0.408762	−	0.391712i	−0.0481730	−	0.0461637i
$73$	6.44117	−	14.1042i	0.753881	−	1.65077i	−0.00538086	−	0.999986i	$-0.501713\pi$
$73$	6.44117	−	14.1042i	0.753881	−	1.65077i	0.759262	−	0.650785i	$-0.225560\pi$
$74$	−4.17057	+	8.74285i	−0.484818	+	1.01634i
$75$	−1.62724	+	0.743136i	−0.187898	+	0.0858100i
$76$	−0.0284221	+	0.0306684i	−0.00326023	+	0.00351791i
$77$	−0.353999	−	2.46212i	−0.0403419	−	0.280584i
$78$	−1.19154	+	0.737934i	−0.134916	+	0.0835546i
$79$	−0.702066	+	0.810228i	−0.0789886	+	0.0911578i	−0.793868	−	0.608090i	$-0.791936\pi$
$79$	−0.702066	+	0.810228i	−0.0789886	+	0.0911578i	0.714880	+	0.699248i	$0.246481\pi$
$80$	−1.38062	+	3.75418i	−0.154358	+	0.419730i
$81$	−8.04274	−	5.16876i	−0.893638	−	0.574306i
$82$	−4.81572	+	0.610495i	−0.531808	+	0.0674179i
$83$	−6.33961	−	1.86148i	−0.695862	−	0.204324i	−0.0853740	−	0.996349i	$-0.527209\pi$
$83$	−6.33961	−	1.86148i	−0.695862	−	0.204324i	−0.610488	+	0.792025i	$0.709027\pi$
$84$	−0.512373	−	1.98838i	−0.0559044	−	0.216950i
$85$	5.07468	+	5.85649i	0.550426	+	0.635226i
$86$	4.67968	−	15.0058i	0.504623	−	1.61811i
$87$	4.94864	+	16.8535i	0.530550	+	1.80689i
$88$	−6.10288	−	10.6319i	−0.650569	−	1.13336i
$89$	−5.88789	−	0.846551i	−0.624115	−	0.0897342i	−0.177000	−	0.984211i	$-0.556639\pi$
$89$	−5.88789	−	0.846551i	−0.624115	−	0.0897342i	−0.447115	+	0.894477i	$0.647548\pi$
$90$	0.0449594	−	0.279481i	0.00473913	−	0.0294599i
$91$	−0.317942			−0.0333294
$92$	−2.56539	+	9.24223i	−0.267460	+	0.963569i
$93$	−11.0527			−1.14611
$94$	−2.20436	+	13.7030i	−0.227362	+	1.41335i
$95$	−0.0206939	−	0.00297534i	−0.00212315	−	0.000305263i
$96$	−5.96591	−	8.17393i	−0.608893	−	0.834249i
$97$	−3.14195	−	10.7005i	−0.319017	−	1.08647i	−0.950408	−	0.311007i	$-0.899334\pi$
$97$	−3.14195	−	10.7005i	−0.319017	−	1.08647i	0.631391	−	0.775465i	$-0.282485\pi$
$98$	−2.80857	+	9.00591i	−0.283709	+	0.909735i
$99$	0.568123	+	0.655649i	0.0570985	+	0.0658952i
$100$	−1.93673	+	0.499064i	−0.193673	+	0.0499064i
$101$	−10.2389	−	3.00641i	−1.01881	−	0.299149i	−0.270656	−	0.962676i	$-0.587241\pi$
$101$	−10.2389	−	3.00641i	−1.01881	−	0.299149i	−0.748152	+	0.663527i	$0.769059\pi$
$102$	−19.4491	+	2.46558i	−1.92574	+	0.244129i
$103$	−15.2672	−	9.81166i	−1.50433	−	0.966772i	−0.994301	−	0.106613i	$-0.965999\pi$
$103$	−15.2672	−	9.81166i	−1.50433	−	0.966772i	−0.510026	−	0.860159i	$-0.670364\pi$
$104$	−1.45614	+	0.578726i	−0.142786	+	0.0567487i
$105$	0.672324	−	0.775903i	0.0656121	−	0.0757204i
$106$	0.651685	−	0.403596i	0.0632973	−	0.0392007i
$107$	−1.52429	−	10.6016i	−0.147358	−	1.02490i	−0.920521	−	0.390693i	$-0.872236\pi$
$107$	−1.52429	−	10.6016i	−0.147358	−	1.02490i	0.773163	−	0.634208i	$-0.218674\pi$
$108$	−7.34724	−	6.80907i	−0.706988	−	0.655203i
$109$	−0.425797	+	0.194455i	−0.0407840	+	0.0186254i	−0.435703	−	0.900091i	$-0.643500\pi$
$109$	−0.425797	+	0.194455i	−0.0407840	+	0.0186254i	0.394919	+	0.918716i	$0.370773\pi$
$110$	2.63903	−	5.53226i	0.251622	−	0.527481i
$111$	5.09010	−	11.1458i	0.483131	−	1.05791i
$112$	−0.174290	−	2.28901i	−0.0164688	−	0.216291i
$113$	−1.32869	−	2.06748i	−0.124993	−	0.194493i	0.773118	−	0.634263i	$-0.218696\pi$
$113$	−1.32869	−	2.06748i	−0.124993	−	0.194493i	−0.898110	+	0.439770i	$0.855060\pi$
$114$	0.0352994	−	0.0393888i	0.00330609	−	0.00368910i
$115$	−4.53105	+	1.57149i	−0.422523	+	0.146542i
$116$	2.14404	+	19.5204i	0.199069	+	1.81242i
$117$	0.0932861	−	0.0599514i	0.00862431	−	0.00554250i
$118$	−2.93245	−	3.50069i	−0.269954	−	0.322264i
$119$	−4.04547	−	1.84750i	−0.370847	−	0.169360i
$120$	1.66685	−	4.77733i	0.152162	−	0.436109i
$121$	3.23410	+	7.08169i	0.294009	+	0.643790i
$122$	12.1599	+	0.203103i	1.10091	+	0.0183881i
$123$	6.07787	−	0.873866i	0.548023	−	0.0787938i
$124$	−12.1657	−	2.16608i	−1.09251	−	0.194519i
$125$	−0.755750	−	0.654861i	−0.0675963	−	0.0585725i
$126$	0.0431604	+	0.156621i	0.00384503	+	0.0139529i
$127$	−1.32056	+	2.05483i	−0.117180	+	0.182336i	−0.894889	−	0.446289i	$-0.852746\pi$
$127$	−1.32056	+	2.05483i	−0.117180	+	0.182336i	0.777709	+	0.628625i	$0.216382\pi$
$128$	−4.96474	−	10.1662i	−0.438825	−	0.898572i
$129$	−5.60171	+	19.0777i	−0.493203	+	1.67969i
$130$	−0.651927	−	0.434521i	−0.0571778	−	0.0381100i
$131$	3.79056	−	3.28454i	0.331183	−	0.286972i	−0.473356	−	0.880871i	$-0.656958\pi$
$131$	3.79056	−	3.28454i	0.331183	−	0.286972i	0.804539	+	0.593899i	$0.202412\pi$
$132$	7.94331	+	13.3179i	0.691377	+	1.15918i
$133$	0.0115125	−	0.00338039i	0.000998264	−	0.000293117i
$134$	0.875159	−	0.382139i	0.0756022	−	0.0330118i
$135$	0.712802	−	4.95765i	0.0613482	−	0.426686i
$136$	−21.8907	−	1.09772i	−1.87711	−	0.0941283i
$137$			5.17519i			0.442146i	0.975257	+	0.221073i	$0.0709560\pi$
$137$			5.17519i			0.442146i	−0.975257	+	0.221073i	$0.929044\pi$
$138$	3.04937	−	11.7435i	0.259580	−	0.999670i
$139$			14.5288i			1.23231i	0.787623	+	0.616157i	$0.211311\pi$
$139$			14.5288i			1.23231i	−0.787623	+	0.616157i	$0.788689\pi$
$140$	0.892082	−	0.722272i	0.0753947	−	0.0610432i
$141$	2.49853	−	17.3776i	0.210414	−	1.46346i
$142$	−5.11942	−	11.7243i	−0.429612	−	0.983879i
$143$	2.30385	−	0.676472i	0.192658	−	0.0565695i
$144$	0.482755	+	0.638746i	0.0402296	+	0.0532288i
$145$	−7.42063	+	6.43001i	−0.616250	+	0.533983i
$146$	−12.1615	+	18.2464i	−1.00650	+	1.51008i
$147$	3.36194	−	11.4497i	0.277288	−	0.944356i
$148$	7.78696	−	11.2705i	0.640084	−	0.926433i
$149$	4.66970	−	7.26620i	0.382557	−	0.595270i	−0.595564	−	0.803308i	$-0.703071\pi$
$149$	4.66970	−	7.26620i	0.382557	−	0.595270i	0.978121	+	0.208038i	$0.0667077\pi$
$150$	2.43897	−	0.672114i	0.199141	−	0.0548778i
$151$	−1.95837	−	1.69694i	−0.159370	−	0.138095i	0.571525	−	0.820584i	$-0.306352\pi$
$151$	−1.95837	−	1.69694i	−0.159370	−	0.138095i	−0.730895	+	0.682489i	$0.760897\pi$
$152$	0.0465732	−	0.0364372i	0.00377758	−	0.00295545i
$153$	1.53533	−	0.220747i	0.124124	−	0.0178463i
$154$	−0.0587478	+	3.51727i	−0.00473404	+	0.283430i
$155$	−2.56664	−	5.62016i	−0.206157	−	0.451422i
$156$	1.82945	−	0.762714i	0.146474	−	0.0610660i
$157$	−13.8952	−	6.34574i	−1.10896	−	0.506445i	−0.225165	−	0.974321i	$-0.572292\pi$
$157$	−13.8952	−	6.34574i	−1.10896	−	0.506445i	−0.883794	+	0.467876i	$0.845019\pi$
$158$	1.16226	−	0.973598i	0.0924642	−	0.0774553i
$159$	−0.815704	+	0.524221i	−0.0646895	+	0.0415734i
$160$	2.77095	−	4.93172i	0.219062	−	0.389887i
$161$	1.99076	−	1.90064i	0.156894	−	0.149791i
$162$	10.0688	+	9.02344i	0.791080	+	0.708949i
$163$	1.03965	+	1.61773i	0.0814317	+	0.126710i	0.879580	−	0.475750i	$-0.157823\pi$
$163$	1.03965	+	1.61773i	0.0814317	+	0.126710i	−0.798149	+	0.602461i	$0.794187\pi$
$164$	6.86114	+	0.229263i	0.535765	+	0.0179024i
$165$	−3.22089	+	7.05277i	−0.250746	+	0.549058i
$166$	8.43364	+	4.02307i	0.654578	+	0.312251i
$167$	−10.6479	+	4.86271i	−0.823956	+	0.376288i	−0.782345	−	0.622846i	$-0.785976\pi$
$167$	−10.6479	+	4.86271i	−0.823956	+	0.376288i	−0.0416113	+	0.999134i	$0.513249\pi$
$168$	0.268791	+	2.89139i	0.0207377	+	0.223075i
$169$	1.80642	+	12.5639i	0.138955	+	0.966453i
$170$	−5.77014	−	9.31704i	−0.442549	−	0.714584i
$171$	−0.00274044	+	0.00316264i	−0.000209567	+	0.000241853i
$172$	−9.90455	+	19.9009i	−0.755215	+	1.51743i
$173$	14.7258	+	9.46369i	1.11958	+	0.719511i	0.963360	−	0.268211i	$-0.0864325\pi$
$173$	14.7258	+	9.46369i	1.11958	+	0.719511i	0.156221	+	0.987722i	$0.450069\pi$
$174$	−3.12408	−	24.6435i	−0.236836	−	1.86822i
$175$	0.550662	+	0.161689i	0.0416261	+	0.0122225i
$176$	6.13316	+	16.2157i	0.462304	+	1.22230i
$177$	3.78282	+	4.36561i	0.284334	+	0.328139i
$178$	8.03090	+	2.50450i	0.601941	+	0.187721i
$179$	−4.44358	−	15.1334i	−0.332129	−	1.13113i	−0.941155	−	0.337976i	$-0.890258\pi$
$179$	−4.44358	−	15.1334i	−0.332129	−	1.13113i	0.609026	−	0.793150i	$-0.291561\pi$
$180$	−0.125550	+	0.380130i	−0.00935796	+	0.0283333i
$181$	−7.84181	−	1.12748i	−0.582877	−	0.0838051i	−0.155432	−	0.987847i	$-0.549677\pi$
$181$	−7.84181	−	1.12748i	−0.582877	−	0.0838051i	−0.427445	+	0.904041i	$0.640586\pi$
$182$	0.443931	+	0.0714139i	0.0329063	+	0.00529355i
$183$	−15.3837			−1.13720
$184$	5.65788	−	12.3284i	0.417104	−	0.908859i
$185$	6.84949			0.503584
$186$	15.4325	+	2.48258i	1.13156	+	0.182032i
$187$	33.2449	+	4.77989i	2.43111	+	0.349540i
$188$	6.15573	−	18.6378i	0.448953	−	1.35930i
$189$	0.809840	+	2.75806i	0.0589072	+	0.200619i
$190$	0.0282259	+	0.00880248i	0.00204772	+	0.000638599i
$191$	0.933061	+	1.07681i	0.0675139	+	0.0779152i	0.788502	−	0.615032i	$-0.210857\pi$
$191$	0.933061	+	1.07681i	0.0675139	+	0.0779152i	−0.720988	+	0.692948i	$0.756312\pi$
$192$	6.49400	+	12.7530i	0.468664	+	0.920367i
$193$	2.80196	+	0.822729i	0.201689	+	0.0592213i	0.381017	−	0.924568i	$-0.375574\pi$
$193$	2.80196	+	0.822729i	0.201689	+	0.0592213i	−0.179327	+	0.983789i	$0.557392\pi$
$194$	1.98352	+	15.6464i	0.142408	+	1.12335i
$195$	0.833715	+	0.535796i	0.0597036	+	0.0383692i
$196$	5.94435	−	11.9438i	0.424596	−	0.853127i
$197$	−11.8611	+	13.6884i	−0.845066	+	0.975258i	−0.999920	−	0.0126792i	$-0.995964\pi$
$197$	−11.8611	+	13.6884i	−0.845066	+	0.975258i	0.154854	+	0.987937i	$0.450509\pi$
$198$	−0.645982	−	1.04307i	−0.0459079	−	0.0741275i
$199$	−2.33511	−	16.2411i	−0.165532	−	1.15130i	−0.887983	−	0.459877i	$-0.847894\pi$
$199$	−2.33511	−	16.2411i	−0.165532	−	1.15130i	0.722451	−	0.691422i	$-0.243015\pi$
$200$	2.81628	−	0.261809i	0.199141	−	0.0185127i
$201$	−1.09880	+	0.501805i	−0.0775033	+	0.0353946i
$202$	13.6209	+	6.49753i	0.958364	+	0.457165i
$203$	2.34093	−	5.12592i	0.164301	−	0.359769i
$204$	27.7098	+	0.925914i	1.94007	+	0.0648269i
$205$	1.85574	+	2.88759i	0.129611	+	0.201678i
$206$	19.1133	+	17.1289i	1.33168	+	1.19343i
$207$	−0.225715	+	0.933038i	−0.0156883	+	0.0648506i
$208$	2.16315	−	0.480985i	0.149987	−	0.0333503i
$209$	−0.0762292	+	0.0489895i	−0.00527288	+	0.00338868i
$210$	−1.11302	+	0.932352i	−0.0768056	+	0.0643384i
$211$	1.61660	+	0.738278i	0.111292	+	0.0508251i	0.470283	−	0.882516i	$-0.344152\pi$
$211$	1.61660	+	0.738278i	0.111292	+	0.0508251i	−0.358991	+	0.933341i	$0.616879\pi$
$212$	−1.00058	+	0.417148i	−0.0687199	+	0.0286499i
$213$	6.72255	+	14.7203i	0.460622	+	1.00862i
$214$	−0.252963	+	15.1451i	−0.0172922	+	1.03530i
$215$	−11.0016	+	1.58179i	−0.750300	+	0.107877i
$216$	8.72927	+	11.1575i	0.593951	+	0.759174i
$217$	2.67981	+	2.32207i	0.181917	+	0.157632i
$218$	0.638201	−	0.175871i	0.0432245	−	0.0119115i
$219$	14.9961	−	23.3343i	1.01334	−	1.57679i
$220$	−4.92740	+	7.13173i	−0.332205	+	0.480821i
$221$	1.20949	−	4.11914i	0.0813589	−	0.277083i
$222$	−9.61060	+	14.4191i	−0.645021	+	0.967748i
$223$	−1.67380	+	1.45036i	−0.112086	+	0.0971232i	−0.709101	−	0.705107i	$-0.750899\pi$
$223$	−1.67380	+	1.45036i	−0.112086	+	0.0971232i	0.597015	+	0.802230i	$0.296353\pi$
$224$	−0.270788	+	3.23521i	−0.0180928	+	0.216162i
$225$	−0.192056	+	0.0563926i	−0.0128037	+	0.00375951i
$226$	1.39082	+	3.18519i	0.0925159	+	0.211876i
$227$	0.648808	−	4.51256i	0.0430629	−	0.299509i	−0.956896	−	0.290431i	$-0.906201\pi$
$227$	0.648808	−	4.51256i	0.0430629	−	0.299509i	0.999959	−	0.00907792i	$-0.00288963\pi$
$228$	−0.0581345	+	0.0470685i	−0.00385005	+	0.00311718i
$229$		−	15.4971i		−	1.02408i	−0.858961	−	0.512040i	$-0.828890\pi$
$229$		−	15.4971i		−	1.02408i	0.858961	−	0.512040i	$-0.171110\pi$
$230$	6.67951	−	1.17648i	0.440434	−	0.0775747i
$231$		−	4.44977i		−	0.292773i
$232$	1.39089	−	27.7372i	0.0913164	−	1.82104i
$233$	−0.0813275	+	0.565645i	−0.00532794	+	0.0370566i	−0.992312	−	0.123762i	$-0.960504\pi$
$233$	−0.0813275	+	0.565645i	−0.00532794	+	0.0370566i	0.986984	+	0.160818i	$0.0514133\pi$
$234$	−0.143718	+	0.0627546i	−0.00939512	+	0.00410239i
$235$	9.41650	−	2.76493i	0.614265	−	0.180364i
$236$	3.30817	+	5.54654i	0.215344	+	0.361049i
$237$	−1.44942	+	1.25593i	−0.0941497	+	0.0815812i
$238$	5.23356	+	3.48826i	0.339241	+	0.226111i
$239$	−1.84097	+	6.26975i	−0.119082	+	0.405556i	−0.997362	−	0.0725908i	$-0.976873\pi$
$239$	−1.84097	+	6.26975i	−0.119082	+	0.405556i	0.878280	+	0.478147i	$0.158691\pi$
$240$	−3.40042	+	6.29601i	−0.219496	+	0.406406i
$241$	8.39722	−	13.0663i	0.540913	−	0.841676i	−0.457969	−	0.888968i	$-0.651423\pi$
$241$	8.39722	−	13.0663i	0.540913	−	0.841676i	0.998881	+	0.0472920i	$0.0150591\pi$
$242$	−2.92501	−	10.6143i	−0.188027	−	0.682314i
$243$	−1.56951	−	1.35999i	−0.100684	−	0.0872435i
$244$	−16.9328	−	3.01486i	−1.08401	−	0.193006i
$245$	6.60273	−	0.949329i	0.421833	−	0.0606504i
$246$	−8.68258	−	0.145022i	−0.553581	−	0.00924629i
$247$	0.00481142	+	0.0105355i	0.000306143	+	0.000670360i
$248$	16.4999	+	5.75698i	1.04775	+	0.365568i
$249$	−10.7516	−	4.91008i	−0.681354	−	0.311164i
$250$	0.908135	+	1.08411i	0.0574355	+	0.0685651i
$251$	−4.02426	+	2.58624i	−0.254009	+	0.163242i	−0.661449	−	0.749990i	$-0.730058\pi$
$251$	−4.02426	+	2.58624i	−0.254009	+	0.163242i	0.407440	+	0.913232i	$0.366422\pi$
$252$	−0.0250841	−	0.228378i	−0.00158015	−	0.0143865i
$253$	−10.3814	+	18.0080i	−0.652673	+	1.13215i
$254$	2.30538	−	2.57246i	0.144653	−	0.161411i
$255$	7.49470	+	11.6620i	0.469337	+	0.730302i
$256$	4.64862	+	15.3098i	0.290539	+	0.956863i
$257$	−6.59377	+	14.4383i	−0.411308	+	0.900639i	0.584689	+	0.811257i	$0.301216\pi$
$257$	−6.59377	+	14.4383i	−0.411308	+	0.900639i	−0.995997	+	0.0893820i	$0.971511\pi$
$258$	12.1065	−	25.3792i	0.753721	−	1.58004i
$259$	−3.57575	+	1.63299i	−0.222186	+	0.101469i
$260$	0.812663	+	0.753137i	0.0503992	+	0.0467076i
$261$	0.279704	+	1.94538i	0.0173132	+	0.120416i
$262$	−6.03037	+	3.73467i	−0.372558	+	0.230729i
$263$	−18.3304	+	21.1544i	−1.13030	+	1.30443i	−0.183351	+	0.983048i	$0.558694\pi$
$263$	−18.3304	+	21.1544i	−1.13030	+	1.30443i	−0.946948	+	0.321387i	$0.895851\pi$
$264$	−8.09958	−	20.3795i	−0.498494	−	1.25427i
$265$	−0.455981	−	0.293041i	−0.0280107	−	0.0180014i
$266$	−0.0168338	+	0.00213404i	−0.00103215	+	0.000130847i
$267$	−10.2101	−	2.99796i	−0.624849	−	0.183472i
$268$	−1.30778	+	0.336995i	−0.0798857	+	0.0205852i
$269$	1.97848	+	2.28328i	0.120630	+	0.139214i	0.812852	−	0.582470i	$-0.197914\pi$
$269$	1.97848	+	2.28328i	0.120630	+	0.139214i	−0.692222	+	0.721684i	$0.743368\pi$
$270$	−2.10881	+	6.76207i	−0.128338	+	0.411527i
$271$	−1.93400	−	6.58660i	−0.117482	−	0.400108i	0.879665	−	0.475595i	$-0.157767\pi$
$271$	−1.93400	−	6.58660i	−0.117482	−	0.400108i	−0.997147	+	0.0754869i	$0.975949\pi$
$272$	30.3186	+	6.44963i	1.83833	+	0.391066i
$273$	−0.562978	−	0.0809440i	−0.0340730	−	0.00489895i
$274$	1.16242	−	7.22593i	0.0702241	−	0.436534i
$275$	−4.33419			−0.261362
$276$	−6.89546	+	15.7120i	−0.415058	+	0.945753i
$277$	29.8984			1.79642			0.898212	−	0.439563i	$-0.144867\pi$
$277$	29.8984			1.79642			0.898212	+	0.439563i	$0.144867\pi$
$278$	3.26335	−	20.2860i	0.195723	−	1.21667i
$279$	−1.22412	−	0.176002i	−0.0732863	−	0.0105370i
$280$	−1.40781	+	0.808109i	−0.0841329	+	0.0482937i
$281$	1.10994	+	3.78011i	0.0662134	+	0.225502i	0.985952	−	0.167030i	$-0.0534175\pi$
$281$	1.10994	+	3.78011i	0.0662134	+	0.225502i	−0.919738	+	0.392532i	$0.871599\pi$
$282$	−7.39184	+	23.7025i	−0.440178	+	1.41147i
$283$	5.99496	+	6.91856i	0.356364	+	0.411266i	0.905418	−	0.424521i	$-0.139557\pi$
$283$	5.99496	+	6.91856i	0.356364	+	0.411266i	−0.549054	+	0.835787i	$0.685012\pi$
$284$	4.51463	+	17.5201i	0.267894	+	1.03962i
$285$	−0.0358851	−	0.0105368i	−0.00212565	−	0.000624147i
$286$	−3.36873	+	0.427058i	−0.199197	+	0.0252524i
$287$	−1.65721	−	1.06503i	−0.0978223	−	0.0628666i
$288$	−0.530582	−	1.00029i	−0.0312648	−	0.0589426i
$289$	28.1923	−	32.5357i	1.65837	−	1.91386i
$290$	11.8054	−	7.31121i	0.693237	−	0.429329i
$291$	−2.83922	−	19.7472i	−0.166438	−	1.15760i
$292$	21.0791	−	22.7451i	1.23356	−	1.33106i
$293$	21.8507	−	9.97886i	1.27653	−	0.582971i	0.342282	−	0.939597i	$-0.388800\pi$
$293$	21.8507	−	9.97886i	1.27653	−	0.582971i	0.934247	+	0.356626i	$0.116073\pi$
$294$	−7.26590	+	15.2317i	−0.423756	+	0.888329i
$295$	−1.34141	+	2.93729i	−0.0781001	+	0.171015i
$296$	−13.4042	+	13.9876i	−0.779101	+	0.813012i
$297$	−11.7364	−	18.2622i	−0.681016	−	1.05968i
$298$	−8.15221	+	9.09664i	−0.472245	+	0.526954i
$299$	2.08949	+	1.64101i	0.120839	+	0.0949023i
$300$	−3.55641	+	0.390622i	−0.205330	+	0.0225526i
$301$	5.36621	−	3.44865i	0.309303	−	0.198777i
$302$	2.35325	+	2.80925i	0.135414	+	0.161654i
$303$	−17.3645	−	7.93012i	−0.997567	−	0.455573i
$304$	−0.0732127	+	0.0404150i	−0.00419903	+	0.00231796i
$305$	−3.57238	−	7.82242i	−0.204554	−	0.447911i
$306$	−2.19331	−	0.0366341i	−0.125383	−	0.00209423i
$307$	11.1313	−	1.60044i	0.635297	−	0.0913419i	0.182861	−	0.983139i	$-0.441464\pi$
$307$	11.1313	−	1.60044i	0.635297	−	0.0913419i	0.452436	+	0.891797i	$0.350555\pi$
$308$	0.872052	−	4.89784i	0.0496898	−	0.279080i
$309$	−24.5357	−	21.2603i	−1.39579	−	1.20945i
$310$	2.32134	+	8.42371i	0.131843	+	0.478435i
$311$	5.15279	−	8.01789i	0.292188	−	0.454653i	−0.663863	−	0.747854i	$-0.731084\pi$
$311$	5.15279	−	8.01789i	0.292188	−	0.454653i	0.956051	+	0.293201i	$0.0947206\pi$
$312$	−2.72571	+	0.654030i	−0.154313	+	0.0370272i
$313$	−8.46680	+	28.8353i	−0.478572	+	1.62987i	0.267183	+	0.963646i	$0.413907\pi$
$313$	−8.46680	+	28.8353i	−0.478572	+	1.62987i	−0.745755	+	0.666220i	$0.767911\pi$
$314$	17.9760	+	11.9814i	1.01445	+	0.676147i
$315$	0.0868174	−	0.0752277i	0.00489160	−	0.00423860i
$316$	−1.84150	+	1.09834i	−0.103592	+	0.0617864i
$317$	−20.6297	+	6.05742i	−1.15868	+	0.340219i	−0.803919	−	0.594739i	$-0.797255\pi$
$317$	−20.6297	+	6.05742i	−1.15868	+	0.340219i	−0.354760	+	0.934958i	$0.615437\pi$
$318$	1.25668	−	0.548733i	0.0704713	−	0.0307714i
$319$	−6.05649	+	42.1238i	−0.339098	+	2.35848i
$320$	−4.97670	+	6.26359i	−0.278206	+	0.350145i
$321$		−	19.1603i		−	1.06942i
$322$	−3.20653	+	2.20664i	−0.178693	+	0.122971i
$323$			0.162011i			0.00901456i
$324$	−12.0319	−	14.8607i	−0.668440	−	0.825593i
$325$	−0.0788415	+	0.548355i	−0.00437334	+	0.0304173i
$326$	−1.08826	−	2.49229i	−0.0602733	−	0.138035i
$327$	−0.803461	+	0.235917i	−0.0444315	+	0.0130463i
$328$	−9.52845	−	1.86121i	−0.526121	−	0.102768i
$329$	−4.25666	+	3.68842i	−0.234677	+	0.203349i
$330$	6.08136	−	9.12407i	0.334768	−	0.502264i
$331$	3.79189	−	12.9140i	0.208421	−	0.709818i	−0.787230	−	0.616660i	$-0.788486\pi$
$331$	3.79189	−	12.9140i	0.208421	−	0.709818i	0.995651	−	0.0931584i	$-0.0296963\pi$
$332$	−10.8719	−	7.51156i	−0.596675	−	0.412251i
$333$	0.741229	−	1.15337i	0.0406191	−	0.0632045i
$334$	15.9594	−	4.39798i	0.873261	−	0.240647i
$335$	−0.510322	−	0.442197i	−0.0278819	−	0.0241598i
$336$	0.274140	−	4.09751i	0.0149555	−	0.223537i
$337$	−21.4091	+	3.07816i	−1.16623	+	0.167678i	−0.698112	−	0.715989i	$-0.745976\pi$
$337$	−21.4091	+	3.07816i	−1.16623	+	0.167678i	−0.468116	+	0.883667i	$0.655067\pi$
$338$	0.299784	−	17.9482i	0.0163061	−	0.976255i
$339$	−1.82635	−	3.99915i	−0.0991936	−	0.217204i
$340$	5.96390	+	14.3051i	0.323438	+	0.775802i
$341$	−24.3588	−	11.1243i	−1.31911	−	0.602415i
$342$	0.00453674	−	0.00380033i	0.000245319	−	0.000205499i
$343$	−6.60023	+	4.24171i	−0.356379	+	0.229031i
$344$	18.2994	−	25.5622i	0.986635	−	1.37822i
$345$	−8.42318	+	1.62908i	−0.453489	+	0.0877065i
$346$	−18.4354	−	16.5214i	−0.991093	−	0.888196i
$347$	9.67109	+	15.0485i	0.519171	+	0.807847i	0.997524	−	0.0703211i	$-0.0224024\pi$
$347$	9.67109	+	15.0485i	0.519171	+	0.807847i	−0.478353	+	0.878168i	$0.658766\pi$
$348$	−1.17320	+	35.1105i	−0.0628904	+	1.88212i
$349$	−7.48765	+	16.3957i	−0.400805	+	0.877640i	0.596383	+	0.802700i	$0.296604\pi$
$349$	−7.48765	+	16.3957i	−0.400805	+	0.877640i	−0.997188	+	0.0749402i	$0.976123\pi$
$350$	−0.732551	−	0.349446i	−0.0391565	−	0.0186787i
$351$	−2.52400	+	1.15267i	−0.134721	+	0.0615251i
$352$	−4.92125	−	24.0189i	−0.262304	−	1.28021i
$353$	−2.41353	−	16.7865i	−0.128459	−	0.893454i	−0.947508	−	0.319731i	$-0.896408\pi$
$353$	−2.41353	−	16.7865i	−0.128459	−	0.893454i	0.819049	−	0.573723i	$-0.194502\pi$
$354$	−4.30124	−	6.94520i	−0.228608	−	0.369133i
$355$	−5.92400	+	6.83665i	−0.314413	+	0.362852i
$356$	−10.6507	−	5.30079i	−0.564486	−	0.280941i
$357$	−6.69292	−	4.30128i	−0.354227	−	0.227648i
$358$	2.80524	+	22.1283i	0.148261	+	1.16952i
$359$	−0.367672	−	0.107958i	−0.0194050	−	0.00569781i	0.272016	−	0.962293i	$-0.412310\pi$
$359$	−0.367672	−	0.107958i	−0.0194050	−	0.00569781i	−0.291421	+	0.956595i	$0.594128\pi$
$360$	0.260683	−	0.502562i	0.0137392	−	0.0264873i
$361$	12.4421	+	14.3589i	0.654846	+	0.755732i
$362$	10.6960	+	3.33563i	0.562168	+	0.175317i
$363$	3.92368	+	13.3628i	0.205940	+	0.701367i
$364$	−0.603803	−	0.199425i	−0.0316479	−	0.0104527i
$365$	15.3476	+	2.20665i	0.803328	+	0.115501i
$366$	21.4797	+	3.45539i	1.12276	+	0.180616i
$367$	−16.1600			−0.843544			−0.421772	−	0.906702i	$-0.638592\pi$
$367$	−16.1600			−0.843544			−0.421772	+	0.906702i	$0.638592\pi$
$368$	−10.6690	+	15.9428i	−0.556160	+	0.831076i
$369$	0.687059			0.0357668
$370$	−9.56368	−	1.53848i	−0.497192	−	0.0799820i
$371$	0.307907	+	0.0442704i	0.0159857	+	0.00229840i
$372$	−20.9902	−	6.93267i	−1.08829	−	0.359442i
$373$	−2.92421	−	9.95895i	−0.151410	−	0.515655i	0.848498	−	0.529198i	$-0.177507\pi$
$373$	−2.92421	−	9.95895i	−0.151410	−	0.515655i	−0.999908	+	0.0135431i	$0.995689\pi$
$374$	−45.3449	−	14.1412i	−2.34473	−	0.731224i
$375$	−1.17148	−	1.35196i	−0.0604950	−	0.0698149i
$376$	−12.7813	+	24.6406i	−0.659146	+	1.27074i
$377$	5.21927	+	1.53251i	0.268806	+	0.0789285i
$378$	−0.511253	−	4.03288i	−0.0262960	−	0.207429i
$379$	−23.8292	−	15.3141i	−1.22402	−	0.786632i	−0.241073	−	0.970507i	$-0.577499\pi$
$379$	−23.8292	−	15.3141i	−1.22402	−	0.786632i	−0.982950	+	0.183875i	$0.941136\pi$
$380$	−0.0374336	−	0.0186305i	−0.00192030	−	0.000955723i
$381$	−2.86143	+	3.30227i	−0.146595	+	0.169180i
$382$	−1.06093	−	1.71309i	−0.0542820	−	0.0876491i
$383$	−0.233065	−	1.62100i	−0.0119091	−	0.0828295i	0.983000	−	0.183605i	$-0.0587767\pi$
$383$	−0.233065	−	1.62100i	−0.0119091	−	0.0828295i	−0.994909	+	0.100775i	$0.967868\pi$
$384$	−6.20284	−	19.2651i	−0.316538	−	0.983120i
$385$	2.26265	−	1.03332i	0.115315	−	0.0526627i
$386$	−3.72747	−	1.77810i	−0.189723	−	0.0905030i
$387$	−0.924198	+	2.02371i	−0.0469796	+	0.102871i
$388$	0.744882	−	22.2921i	0.0378157	−	1.13171i
$389$	10.7799	+	16.7739i	0.546563	+	0.850468i	0.999149	−	0.0412527i	$-0.0131349\pi$
$389$	10.7799	+	16.7739i	0.546563	+	0.850468i	−0.452586	+	0.891721i	$0.649498\pi$
$390$	−1.04374	−	0.935376i	−0.0528518	−	0.0473646i
$391$	17.0509	+	33.0218i	0.862301	+	1.66998i
$392$	−10.9826	+	15.3415i	−0.554705	+	0.774861i
$393$	7.54812	−	4.85088i	0.380752	−	0.244695i
$394$	19.6358	−	16.4485i	0.989235	−	0.828661i
$395$	−0.975203	−	0.445360i	−0.0490678	−	0.0224085i
$396$	0.667674	+	1.60149i	0.0335519	+	0.0804779i
$397$	0.142841	+	0.312779i	0.00716899	+	0.0156979i	0.913183	−	0.407551i	$-0.133617\pi$
$397$	0.142841	+	0.312779i	0.00716899	+	0.0156979i	−0.906014	+	0.423249i	$0.860890\pi$
$398$	−0.387524	+	23.2013i	−0.0194248	+	1.16298i
$399$	0.0212458	−	0.00305468i	0.00106362	−	0.000152925i
$400$	−3.99108	−	0.267019i	−0.199554	−	0.0133510i
$401$	12.8868	+	11.1665i	0.643535	+	0.557626i	0.914309	−	0.405016i	$-0.132734\pi$
$401$	12.8868	+	11.1665i	0.643535	+	0.557626i	−0.270774	+	0.962643i	$0.587280\pi$
$402$	1.64692	−	0.453847i	0.0821411	−	0.0226358i
$403$	−1.85053	+	2.87948i	−0.0921815	+	0.143437i
$404$	−17.5589	−	12.1317i	−0.873590	−	0.603574i
$405$	2.69348	−	9.17316i	0.133840	−	0.455818i
$406$	−4.41990	+	6.63133i	−0.219356	+	0.329107i
$407$	22.4359	−	19.4409i	1.11211	−	0.963647i
$408$	−38.4822	−	7.51680i	−1.90515	−	0.372137i
$409$	19.9979	−	5.87191i	0.988832	−	0.290347i	0.252967	−	0.967475i	$-0.418594\pi$
$409$	19.9979	−	5.87191i	0.988832	−	0.290347i	0.735866	+	0.677128i	$0.236775\pi$
$410$	−1.94251	−	4.44866i	−0.0959338	−	0.219703i
$411$	−1.31754	+	9.16367i	−0.0649893	+	0.452010i
$412$	−22.8398	−	28.2095i	−1.12523	−	1.38978i
$413$		−	1.85321i		−	0.0911903i
$414$	0.524729	−	1.25207i	0.0257890	−	0.0615357i
$415$		−	6.60724i		−	0.324337i
$416$	−3.12835	+	0.185711i	−0.153380	+	0.00910521i
$417$	−3.69884	+	25.7260i	−0.181133	+	1.25981i
$418$	0.117440	−	0.0512802i	0.00574416	−	0.00250819i
$419$	30.3906	−	8.92349i	1.48468	−	0.435941i	0.563839	−	0.825884i	$-0.309324\pi$
$419$	30.3906	−	8.92349i	1.48468	−	0.435941i	0.920839	+	0.389944i	$0.127505\pi$
$420$	1.76348	−	1.05181i	0.0860492	−	0.0513230i
$421$	5.78018	−	5.00856i	0.281709	−	0.244102i	−0.502532	−	0.864559i	$-0.667598\pi$
$421$	5.78018	−	5.00856i	0.281709	−	0.244102i	0.784241	+	0.620456i	$0.213053\pi$
$422$	−2.09137	−	1.39394i	−0.101807	−	0.0678559i
$423$	0.553439	−	1.88484i	0.0269091	−	0.0916441i
$424$	1.49076	−	0.357706i	0.0723979	−	0.0173717i
$425$	−4.18956	+	6.51908i	−0.203223	+	0.316222i
$426$	−6.08007	−	22.0634i	−0.294580	−	1.06898i
$427$	3.72990	+	3.23197i	0.180502	+	0.156406i
$428$	3.75498	−	21.0897i	0.181504	−	1.01941i
$429$	4.25163	−	0.611293i	0.205271	−	0.0295135i
$430$	15.7164	+	0.262505i	0.757910	+	0.0126591i
$431$	−11.3455	−	24.8432i	−0.546494	−	1.19666i	−0.958400	−	0.285429i	$-0.907864\pi$
$431$	−11.3455	−	24.8432i	−0.546494	−	1.19666i	0.411905	−	0.911227i	$-0.364863\pi$
$432$	−9.68222	−	17.5396i	−0.465836	−	0.843873i
$433$	−15.3083	−	6.99107i	−0.735671	−	0.335970i	0.0120998	−	0.999927i	$-0.496148\pi$
$433$	−15.3083	−	6.99107i	−0.735671	−	0.335970i	−0.747771	+	0.663957i	$0.768876\pi$
$434$	−3.22015	−	3.84414i	−0.154572	−	0.184524i
$435$	−14.7766	+	9.49637i	−0.708486	+	0.455316i
$436$	−0.930600	+	0.102213i	−0.0445676	+	0.00489513i
$437$	−0.0931070	−	0.0372047i	−0.00445391	−	0.00177974i
$438$	−26.1796	+	29.2125i	−1.25091	+	1.39583i
$439$	22.2698	+	34.6525i	1.06288	+	1.65387i	0.685980	+	0.727620i	$0.259374\pi$
$439$	22.2698	+	34.6525i	1.06288	+	1.65387i	0.376900	+	0.926254i	$0.376990\pi$
$440$	8.48183	−	8.85101i	0.404355	−	0.421955i
$441$	0.554669	−	1.21456i	0.0264128	−	0.0578360i
$442$	−2.61397	+	5.47973i	−0.124334	+	0.260644i
$443$	16.4962	−	7.53355i	0.783757	−	0.357930i	0.0169903	−	0.999856i	$-0.494592\pi$
$443$	16.4962	−	7.53355i	0.783757	−	0.357930i	0.766767	+	0.641926i	$0.221864\pi$
$444$	16.6576	−	17.9742i	0.790537	−	0.853018i
$445$	−0.846551	−	5.88789i	−0.0401304	−	0.279113i
$446$	2.66284	−	1.64912i	0.126089	−	0.0780883i
$447$	10.1185	−	11.6774i	0.478588	−	0.552320i
$448$	1.10476	−	4.45638i	0.0521950	−	0.210544i
$449$	−17.2219	−	11.0678i	−0.812750	−	0.522323i	0.0670035	−	0.997753i	$-0.478656\pi$
$449$	−17.2219	−	11.0678i	−0.812750	−	0.522323i	−0.879754	+	0.475430i	$0.842293\pi$
$450$	0.280827	−	0.0356007i	0.0132383	−	0.00167823i
$451$	14.2744	+	4.19135i	0.672156	+	0.197363i
$452$	−1.22651	−	4.75976i	−0.0576903	−	0.223880i
$453$	−3.03565	−	3.50333i	−0.142627	−	0.164601i
$454$	−1.91949	+	6.15499i	−0.0900859	+	0.288868i
$455$	−0.0895747	−	0.305063i	−0.00419933	−	0.0143016i
$456$	0.0917432	−	0.0526622i	0.00429627	−	0.00246613i
$457$	25.0901	+	3.60742i	1.17367	+	0.168748i	0.701439	−	0.712729i	$-0.252541\pi$
$457$	25.0901	+	3.60742i	1.17367	+	0.168748i	0.472227	+	0.881477i	$0.343450\pi$
$458$	−3.48086	+	21.6381i	−0.162650	+	1.01108i
$459$	−38.8131			−1.81164
$460$	−9.59061	+	0.142367i	−0.447164	+	0.00663789i
$461$	8.36029			0.389377			0.194689	−	0.980865i	$-0.437630\pi$
$461$	8.36029			0.389377			0.194689	+	0.980865i	$0.437630\pi$
$462$	−0.999476	+	6.21305i	−0.0464998	+	0.289057i
$463$	28.4913	+	4.09642i	1.32410	+	0.190377i	0.767846	−	0.640635i	$-0.221329\pi$
$463$	28.4913	+	4.09642i	1.32410	+	0.190377i	0.556255	+	0.831012i	$0.312238\pi$
$464$	−8.17218	+	38.4160i	−0.379384	+	1.78342i
$465$	−3.11391	−	10.6050i	−0.144404	−	0.491795i
$466$	0.240606	−	0.771522i	0.0111458	−	0.0357401i
$467$	22.4589	+	25.9190i	1.03927	+	1.19939i	0.979556	+	0.201171i	$0.0644748\pi$
$467$	22.4589	+	25.9190i	1.03927	+	1.19939i	0.0597182	+	0.998215i	$0.480980\pi$
$468$	0.214763	−	0.0553410i	0.00992743	−	0.00255814i
$469$	0.371836	+	0.109181i	0.0171698	+	0.00504151i
$470$	−13.7689	+	1.74551i	−0.635114	+	0.0805142i
$471$	−22.9886	−	14.7739i	−1.05926	−	0.680745i
$472$	−3.37325	−	8.48749i	−0.155266	−	0.390668i
$473$	−31.5467	+	36.4069i	−1.45052	+	1.67399i
$474$	2.30586	−	1.42805i	0.105912	−	0.0655923i
$475$	−0.00297534	−	0.0206939i	−0.000136518	−	0.000949503i
$476$	−6.52392	−	6.04606i	−0.299023	−	0.277121i
$477$	−0.0986894	+	0.0450700i	−0.00451868	+	0.00206361i
$478$	3.97874	−	8.34071i	0.181983	−	0.381495i
$479$	3.75146	−	8.21456i	0.171409	−	0.375333i	−0.804358	−	0.594144i	$-0.797491\pi$
$479$	3.75146	−	8.21456i	0.171409	−	0.375333i	0.975767	+	0.218812i	$0.0702180\pi$
$480$	6.16204	−	8.02711i	0.281257	−	0.366386i
$481$	−2.05150	−	3.19220i	−0.0935404	−	0.145552i
$482$	−14.6596	+	16.3579i	−0.667726	+	0.745082i
$483$	4.00890	−	2.85863i	0.182411	−	0.130072i
$484$	1.69997	+	15.4774i	0.0772714	+	0.703517i
$485$	9.38187	−	6.02936i	0.426009	−	0.273779i
$486$	1.88598	+	2.25144i	0.0855498	+	0.102127i
$487$	−1.94584	−	0.888633i	−0.0881742	−	0.0402678i	0.370840	−	0.928697i	$-0.379070\pi$
$487$	−1.94584	−	0.888633i	−0.0881742	−	0.0402678i	−0.459014	+	0.888429i	$0.651797\pi$
$488$	22.9654	+	8.01285i	1.03960	+	0.362725i
$489$	1.42905	+	3.12918i	0.0646238	+	0.141506i
$490$	−9.43238	−	0.157546i	−0.426111	−	0.00711720i
$491$	21.3202	−	3.06538i	0.962168	−	0.138339i	0.356709	−	0.934216i	$-0.383899\pi$
$491$	21.3202	−	3.06538i	0.962168	−	0.138339i	0.605459	+	0.795877i	$0.292990\pi$
$492$	12.0906	+	2.15271i	0.545086	+	0.0970517i
$493$	57.5043	+	49.8277i	2.58986	+	2.24413i
$494$	−0.00435159	−	0.0157911i	−0.000195787	−	0.000710474i
$495$	−0.469032	+	0.729828i	−0.0210814	+	0.0328033i
$496$	−21.7451	−	11.7443i	−0.976386	−	0.527337i
$497$	1.46267	−	4.98139i	0.0656097	−	0.223446i
$498$	13.9092	+	9.27071i	0.623284	+	0.415430i
$499$	13.8198	−	11.9749i	0.618658	−	0.536070i	−0.288166	−	0.957581i	$-0.593045\pi$
$499$	13.8198	−	11.9749i	0.618658	−	0.536070i	0.906823	+	0.421511i	$0.138500\pi$
$500$	−1.02449	−	1.71768i	−0.0458166	−	0.0768169i
$501$	−20.0921	+	5.89956i	−0.897647	+	0.263573i
$502$	6.19983	−	2.70716i	0.276712	−	0.120827i
$503$	−2.24175	+	15.5917i	−0.0999548	+	0.695201i	0.876802	+	0.480851i	$0.159672\pi$
$503$	−2.24175	+	15.5917i	−0.0999548	+	0.695201i	−0.976757	+	0.214349i	$0.931237\pi$
$504$	−0.0162727	+	0.324510i	−0.000724842	+	0.0144548i
$505$		−	10.6712i		−	0.474860i
$506$	18.5400	−	22.8120i	0.824203	−	1.01412i
$507$			22.7067i			1.00844i
$508$	−3.79673	+	3.07401i	−0.168453	+	0.136387i
$509$	4.75646	−	33.0819i	0.210827	−	1.46633i	−0.559579	−	0.828777i	$-0.689037\pi$
$509$	4.75646	−	33.0819i	0.210827	−	1.46633i	0.770406	−	0.637554i	$-0.220054\pi$
$510$	−7.84514	−	17.9666i	−0.347389	−	0.795575i
$511$	−8.53822	+	2.50705i	−0.377709	+	0.110905i
$512$	−3.05192	−	22.4207i	−0.134877	−	0.990862i
$513$	0.0791376	−	0.0685731i	0.00349401	−	0.00302758i
$514$	12.4497	−	18.6787i	0.549132	−	0.823881i
$515$	5.11294	−	17.4131i	0.225303	−	0.767312i
$516$	−22.6044	+	32.7168i	−0.995104	+	1.44028i
$517$	22.9967	−	35.7835i	1.01139	−	1.57376i
$518$	5.35948	−	1.47692i	0.235482	−	0.0648923i
$519$	23.6655	+	20.5063i	1.03880	+	0.900125i
$520$	−0.965526	−	1.23411i	−0.0423411	−	0.0541194i
$521$	−16.8274	+	2.41941i	−0.737222	+	0.105996i	−0.500689	−	0.865627i	$-0.666920\pi$
$521$	−16.8274	+	2.41941i	−0.737222	+	0.105996i	−0.236532	+	0.971624i	$0.576011\pi$
$522$	0.0464182	−	2.77909i	0.00203167	−	0.121637i
$523$	18.0173	+	39.4525i	0.787843	+	1.72514i	0.682725	+	0.730675i	$0.260795\pi$
$523$	18.0173	+	39.4525i	0.787843	+	1.72514i	0.105118	+	0.994460i	$0.466478\pi$
$524$	9.25884	−	3.86009i	0.404474	−	0.168629i
$525$	0.933889	+	0.426493i	0.0407583	+	0.0186137i
$526$	30.3455	−	25.4198i	1.32313	−	1.10836i
$527$	−40.2781	+	25.8852i	−1.75454	+	1.12758i
$528$	6.73164	+	30.2744i	0.292957	+	1.31752i
$529$	−22.8930	+	2.21585i	−0.995348	+	0.0963414i
$530$	0.570848	+	0.511581i	0.0247961	+	0.0222217i
$531$	0.349442	+	0.543742i	0.0151645	+	0.0235964i
$532$	0.0239838		0.000801409i	0.00103983		3.47455e-5i
$533$	0.789943	−	1.72973i	0.0342162	−	0.0749231i
$534$	13.5826	+	6.47927i	0.587778	+	0.280385i
$535$	9.74277	−	4.44937i	0.421217	−	0.192363i
$536$	1.90170	−	0.176788i	0.0821411	−	0.00763606i
$537$	−4.01543	−	27.9279i	−0.173279	−	1.20518i
$538$	−2.24962	−	3.63246i	−0.0969879	−	0.156606i
$539$	18.9332	−	21.8501i	0.815510	−	0.941149i
$540$	4.46330	−	8.96796i	0.192070	−	0.385920i
$541$	17.8107	+	11.4463i	0.765744	+	0.492114i	0.864274	−	0.503020i	$-0.167778\pi$
$541$	17.8107	+	11.4463i	0.765744	+	0.492114i	−0.0985309	+	0.995134i	$0.531414\pi$
$542$	1.22094	+	9.63103i	0.0524437	+	0.413688i
$543$	−13.5984	−	3.99285i	−0.583563	−	0.171350i
$544$	−40.8840	−	15.8153i	−1.75289	−	0.678076i
$545$	−0.306539	−	0.353765i	−0.0131307	−	0.0151536i
$546$	0.767884	+	0.239471i	0.0328624	+	0.0102484i
$547$	−8.45507	−	28.7953i	−0.361513	−	1.23120i	−0.916734	−	0.399497i	$-0.869185\pi$
$547$	−8.45507	−	28.7953i	−0.361513	−	1.23120i	0.555222	−	0.831702i	$-0.312633\pi$
$548$	−3.24607	+	9.82820i	−0.138665	+	0.419840i
$549$	−1.70380	−	0.244969i	−0.0727163	−	0.0104550i
$550$	6.05167	+	0.973516i	0.258044	+	0.0415109i
$551$	−0.205281			−0.00874527
$552$	13.1570	−	20.3893i	0.559999	−	0.867826i
$553$	0.615280			0.0261644
$554$	−41.7461	−	6.71558i	−1.77362	−	0.285318i
$555$	12.1283	+	1.74379i	0.514819	+	0.0740198i
$556$	−9.11298	+	27.5916i	−0.386477	+	1.17014i
$557$	8.96072	+	30.5174i	0.379678	+	1.29306i	0.898798	+	0.438363i	$0.144441\pi$
$557$	8.96072	+	30.5174i	0.379678	+	1.29306i	−0.519120	+	0.854701i	$0.673740\pi$
$558$	1.66966	+	0.520699i	0.0706825	+	0.0220430i
$559$	4.03228	+	4.65350i	0.170547	+	0.196822i
$560$	2.14719	−	0.812119i	0.0907353	−	0.0343183i
$561$	57.6495	+	16.9274i	2.43396	+	0.714676i
$562$	−0.700706	−	5.52733i	−0.0295575	−	0.233156i
$563$	−25.3345	−	16.2815i	−1.06772	−	0.686183i	−0.116032	−	0.993245i	$-0.537018\pi$
$563$	−25.3345	−	16.2815i	−1.06772	−	0.686183i	−0.951689	+	0.307063i	$0.900654\pi$
$564$	15.6448	−	31.4347i	0.658767	−	1.32364i
$565$	1.60940	−	1.85735i	0.0677080	−	0.0781392i
$566$	−6.81655	−	11.0067i	−0.286521	−	0.462645i
$567$	0.780856	+	5.43097i	0.0327929	+	0.228079i
$568$	−2.36838	−	25.4766i	−0.0993749	−	1.06898i
$569$	−3.73314	+	1.70487i	−0.156501	+	0.0714718i	−0.492126	−	0.870524i	$-0.663780\pi$
$569$	−3.73314	+	1.70487i	−0.156501	+	0.0714718i	0.335624	+	0.941996i	$0.391053\pi$
$570$	0.0477383	+	0.0227724i	0.00199954	+	0.000953832i
$571$	7.33161	−	16.0540i	0.306818	−	0.671838i	−0.691924	−	0.721970i	$-0.743237\pi$
$571$	7.33161	−	16.0540i	0.306818	−	0.671838i	0.998743	+	0.0501317i	$0.0159641\pi$
$572$	4.79955	+	0.160375i	0.200679	+	0.00670563i
$573$	1.37802	+	2.14424i	0.0575677	+	0.0895770i
$574$	2.07469	+	1.85929i	0.0865958	+	0.0776052i
$575$	−2.78438	−	3.90477i	−0.116117	−	0.162840i
$576$	0.516154	+	1.51584i	0.0215064	+	0.0631601i
$577$	−11.5686	+	7.43466i	−0.481605	+	0.309509i	−0.758822	−	0.651299i	$-0.774225\pi$
$577$	−11.5686	+	7.43466i	−0.481605	+	0.309509i	0.277216	+	0.960808i	$0.410588\pi$
$578$	−46.6718	+	39.0960i	−1.94129	+	1.62618i
$579$	4.75195	+	2.17014i	0.197484	+	0.0901880i
$580$	−18.1256	+	7.55673i	−0.752626	+	0.313776i
$581$	1.57524	+	3.44929i	0.0653519	+	0.143101i
$582$	−0.471183	+	28.2100i	−0.0195311	+	1.16934i
$583$	−2.32533	+	0.334332i	−0.0963053	+	0.0138466i
$584$	−34.5408	+	27.0235i	−1.42931	+	1.11824i
$585$	0.0838046	+	0.0726171i	0.00346490	+	0.00300235i
$586$	−32.7506	+	9.02517i	−1.35292	+	0.372826i
$587$	−0.975840	+	1.51844i	−0.0402772	+	0.0626726i	−0.860808	−	0.508929i	$-0.830041\pi$
$587$	−0.975840	+	1.51844i	−0.0402772	+	0.0626726i	0.820531	+	0.571602i	$0.193678\pi$
$588$	13.5663	−	19.6354i	0.559466	−	0.809750i
$589$	0.0363920	−	0.123940i	0.00149951	−	0.00510685i
$590$	2.53272	−	3.79992i	0.104270	−	0.156440i
$591$	−24.4872	+	21.2183i	−1.00727	+	0.872803i
$592$	21.8575	−	16.5196i	0.898338	−	0.678951i
$593$	−27.1168	+	7.96220i	−1.11355	+	0.326968i	−0.786223	−	0.617942i	$-0.787967\pi$
$593$	−27.1168	+	7.96220i	−1.11355	+	0.326968i	−0.327328	+	0.944911i	$0.606148\pi$
$594$	12.2852	+	28.1350i	0.504068	+	1.15439i
$595$	0.632926	−	4.40210i	0.0259474	−	0.180468i
$596$	13.4259	−	10.8702i	0.549944	−	0.445261i
$597$		−	29.3524i		−	1.20131i
$598$	−2.54889	−	2.76061i	−0.104232	−	0.112890i
$599$			17.8976i			0.731276i	0.930757	+	0.365638i	$0.119149\pi$
$599$			17.8976i			0.731276i	−0.930757	+	0.365638i	$0.880851\pi$
$600$	5.05342	+	0.253406i	0.206305	+	0.0103452i
$601$	−4.63806	+	32.2584i	−0.189190	+	1.31585i	0.644920	+	0.764250i	$0.276891\pi$
$601$	−4.63806	+	32.2584i	−0.189190	+	1.31585i	−0.834110	+	0.551598i	$0.814018\pi$
$602$	−8.26725	+	3.60991i	−0.336948	+	0.147129i
$603$	−0.129686	+	0.0380793i	−0.00528123	+	0.00155071i
$604$	−2.65476	−	4.45102i	−0.108020	−	0.181109i
$605$	−5.88368	+	5.09824i	−0.239206	+	0.207273i
$606$	22.4642	+	14.9728i	0.912548	+	0.608229i
$607$	6.51480	−	22.1874i	0.264428	−	0.900558i	−0.715062	−	0.699061i	$-0.753601\pi$
$607$	6.51480	−	22.1874i	0.264428	−	0.900558i	0.979489	−	0.201496i	$-0.0645804\pi$
$608$	0.111302	−	0.0399854i	0.00451388	−	0.00162162i
$609$	5.45006	−	8.48046i	0.220847	−	0.343645i
$610$	3.23096	+	11.7246i	0.130818	+	0.474714i
$611$	−4.10895	−	3.56042i	−0.166230	−	0.144039i
$612$	3.05420	+	0.543796i	0.123459	+	0.0219816i
$613$	10.8143	−	1.55487i	0.436787	−	0.0628005i	0.0795859	−	0.996828i	$-0.474640\pi$
$613$	10.8143	−	1.55487i	0.436787	−	0.0628005i	0.357201	+	0.934028i	$0.383731\pi$
$614$	−15.9017	−	0.265601i	−0.641740	−	0.0107188i
$615$	2.55080	+	5.58548i	0.102858	+	0.225228i
$616$	−2.31773	+	6.64280i	−0.0933841	+	0.267646i
$617$	33.2984	+	15.2069i	1.34054	+	0.612206i	0.951111	−	0.308848i	$-0.0999436\pi$
$617$	33.2984	+	15.2069i	1.34054	+	0.612206i	0.389433	+	0.921055i	$0.372671\pi$
$618$	29.4829	+	35.1960i	1.18598	+	1.41579i
$619$	4.62094	−	2.96970i	0.185731	−	0.119362i	−0.444471	−	0.895793i	$-0.646608\pi$
$619$	4.62094	−	2.96970i	0.185731	−	0.119362i	0.630202	+	0.776431i	$0.282972\pi$
$620$	−1.34913	−	12.2831i	−0.0541823	−	0.493302i
$621$	8.91313	−	22.3057i	0.357672	−	0.895095i
$622$	−8.99557	+	10.0377i	−0.360689	+	0.402475i
$623$	1.84568	+	2.87193i	0.0739454	+	0.115061i
$624$	3.95272	−	0.300967i	0.158235	−	0.0120483i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	18.2987	−	38.3599i	0.731361	−	1.53317i
$627$	−0.147450	+	0.0673384i	−0.00588860	+	0.00268924i
$628$	−22.4081	−	20.7668i	−0.894181	−	0.828685i
$629$	−7.55384	−	52.5381i	−0.301191	−	2.09483i
$630$	−0.138117	+	0.0855373i	−0.00550271	+	0.00340789i
$631$	−16.8872	+	19.4889i	−0.672269	+	0.775840i	−0.984730	−	0.174091i	$-0.944301\pi$
$631$	−16.8872	+	19.4889i	−0.672269	+	0.775840i	0.312460	+	0.949931i	$0.398847\pi$
$632$	2.81792	−	1.11995i	0.112091	−	0.0445491i
$633$	2.67455	+	1.71883i	0.106304	+	0.0683173i
$634$	30.1650	−	3.82406i	1.19801	−	0.151873i
$635$	−2.34363	−	0.688153i	−0.0930043	−	0.0273085i
$636$	−1.87791	+	0.483907i	−0.0744641	+	0.0191882i
$637$	−2.42003	−	2.79286i	−0.0958850	−	0.110657i
$638$	17.9180	−	57.4555i	0.709381	−	2.27469i
$639$	0.510139	+	1.73737i	0.0201808	+	0.0687294i
$640$	8.35566	−	7.62778i	0.330286	−	0.301514i
$641$	−34.9200	−	5.02074i	−1.37926	−	0.198307i	−0.587541	−	0.809195i	$-0.699904\pi$
$641$	−34.9200	−	5.02074i	−1.37926	−	0.198307i	−0.791718	+	0.610887i	$0.790813\pi$
$642$	−4.30366	+	26.7528i	−0.169852	+	1.05585i
$643$	−10.1693			−0.401037			−0.200519	−	0.979690i	$-0.564263\pi$
$643$	−10.1693			−0.401037			−0.200519	+	0.979690i	$0.564263\pi$
$644$	4.97280	−	2.36082i	0.195956	−	0.0930295i
$645$	−19.8831			−0.782895
$646$	0.0363899	−	0.226211i	0.00143174	−	0.00890013i
$647$	−35.6832	−	5.13047i	−1.40285	−	0.201700i	−0.601012	−	0.799240i	$-0.705236\pi$
$647$	−35.6832	−	5.13047i	−1.40285	−	0.201700i	−0.801839	+	0.597540i	$0.796145\pi$
$648$	13.4618	+	23.4519i	0.528830	+	0.921279i
$649$	3.94299	+	13.4286i	0.154776	+	0.527118i
$650$	0.233251	−	0.747938i	0.00914886	−	0.0293366i
$651$	4.15395	+	4.79391i	0.162806	+	0.187888i
$652$	0.959699	+	3.72433i	0.0375847	+	0.145856i
$653$	17.9245	+	5.26312i	0.701441	+	0.205962i	0.612958	−	0.790116i	$-0.289980\pi$
$653$	17.9245	+	5.26312i	0.701441	+	0.205962i	0.0884838	+	0.996078i	$0.471798\pi$
$654$	1.17483	−	0.148935i	0.0459396	−	0.00582382i
$655$	4.21942	+	2.71166i	0.164866	+	0.105953i
$656$	12.8862	+	4.73895i	0.503121	+	0.185025i
$657$	2.03243	−	2.34555i	0.0792928	−	0.0915088i
$658$	6.77188	−	4.19390i	0.263995	−	0.163495i
$659$	1.39754	+	9.72014i	0.0544406	+	0.378643i	0.998767	+	0.0496340i	$0.0158055\pi$
$659$	1.39754	+	9.72014i	0.0544406	+	0.378643i	−0.944327	+	0.329009i	$0.893285\pi$
$660$	−10.5406	+	11.3736i	−0.410291	+	0.442719i
$661$	−15.0897	+	6.89125i	−0.586922	+	0.268039i	−0.686664	−	0.726975i	$-0.740926\pi$
$661$	−15.0897	+	6.89125i	−0.586922	+	0.268039i	0.0997416	+	0.995013i	$0.468198\pi$
$662$	−8.19513	+	17.1796i	−0.318513	+	0.667705i
$663$	3.19031	−	6.98580i	0.123901	−	0.271306i
$664$	13.4929	+	12.9301i	0.523626	+	0.501785i
$665$	0.00648692	+	0.0100938i	0.000251552	+	0.000391422i
$666$	−1.29401	+	1.44392i	−0.0501420	+	0.0559509i
$667$	−41.8411	+	21.6048i	−1.62009	+	0.836541i
$668$	−23.2714	+	2.55604i	−0.900397	+	0.0988960i
$669$	−3.33303	+	2.14201i	−0.128863	+	0.0828149i
$670$	0.613221	+	0.732048i	0.0236908	+	0.0282815i
$671$	−33.9039	−	15.4834i	−1.30884	−	0.597729i
$672$	−1.30312	+	5.65962i	−0.0502691	+	0.218325i
$673$	−8.43248	−	18.4645i	−0.325048	−	0.711756i	0.674603	−	0.738181i	$-0.264315\pi$
$673$	−8.43248	−	18.4645i	−0.325048	−	0.711756i	−0.999651	+	0.0264250i	$0.991588\pi$
$674$	30.5841	+	0.510837i	1.17806	+	0.0196767i
$675$	4.95765	−	0.712802i	0.190820	−	0.0274358i
$676$	−4.44998	+	24.9931i	−0.171153	+	0.961274i
$677$	−9.62466	−	8.33982i	−0.369906	−	0.320525i	0.449995	−	0.893031i	$-0.351426\pi$
$677$	−9.62466	−	8.33982i	−0.369906	−	0.320525i	−0.819901	+	0.572506i	$0.805971\pi$
$678$	1.65180	+	5.99408i	0.0634371	+	0.230201i
$679$	−3.46031	+	5.38435i	−0.132794	+	0.206632i
$680$	−5.11407	−	21.3132i	−0.196115	−	0.817324i
$681$	2.29768	−	7.82517i	0.0880472	−	0.299861i
$682$	31.5127	+	21.0038i	1.20668	+	0.804276i
$683$	13.9183	−	12.0603i	0.532568	−	0.461473i	−0.346581	−	0.938020i	$-0.612657\pi$
$683$	13.9183	−	12.0603i	0.532568	−	0.461473i	0.879149	+	0.476547i	$0.158112\pi$
$684$	−0.00718809	+	0.00428725i	−0.000274844	+	0.000163927i
$685$	−4.96556	+	1.45802i	−0.189724	+	0.0557081i
$686$	10.1684	−	4.44004i	0.388231	−	0.169522i
$687$	3.94537	−	27.4407i	0.150525	−	1.04693i
$688$	−31.2923	+	31.5812i	−1.19301	+	1.20402i
$689$			0.300279i			0.0114397i
$690$	12.1269	−	0.382662i	0.461662	−	0.0145677i
$691$			9.69686i			0.368886i	0.982843	+	0.184443i	$0.0590481\pi$
$691$			9.69686i			0.368886i	−0.982843	+	0.184443i	$0.940952\pi$
$692$	22.0297	+	27.2090i	0.837445	+	1.03433i
$693$	0.0708577	−	0.492826i	0.00269166	−	0.0187209i
$694$	−10.1233	−	23.1839i	−0.384275	−	0.880050i
$695$	−13.9402	+	4.09323i	−0.528784	+	0.155265i
$696$	9.52437	−	48.7599i	0.361020	−	1.84824i
$697$	20.1023	−	17.4188i	0.761429	−	0.659782i
$698$	14.1374	−	21.2108i	0.535109	−	0.802842i
$699$	−0.288012	+	0.980878i	−0.0108936	+	0.0371002i
$700$	0.944344	+	0.652459i	0.0356928	+	0.0246606i
$701$	20.9075	−	32.5327i	0.789664	−	1.22874i	−0.179847	−	0.983695i	$-0.557560\pi$
$701$	20.9075	−	32.5327i	0.789664	−	1.22874i	0.969511	−	0.245047i	$-0.0788035\pi$
$702$	3.78307	−	1.04251i	0.142783	−	0.0393470i
$703$	0.108224	+	0.0937763i	0.00408173	+	0.00353684i
$704$	1.47640	+	34.6421i	0.0556440	+	1.30562i
$705$	17.3776	−	2.49853i	0.654479	−	0.0940999i
$706$	−0.400537	+	23.9804i	−0.0150744	+	0.902516i
$707$	2.54412	+	5.57084i	0.0956813	+	0.209513i
$708$	4.44567	+	10.6634i	0.167079	+	0.400757i
$709$	26.6642	+	12.1771i	1.00139	+	0.457322i	0.847517	−	0.530768i	$-0.178097\pi$
$709$	26.6642	+	12.1771i	1.00139	+	0.457322i	0.153878	+	0.988090i	$0.450824\pi$
$710$	9.80705	−	8.21516i	0.368052	−	0.308309i
$711$	−0.180527	+	0.116017i	−0.00677028	+	0.00435100i
$712$	13.6805	+	9.79358i	0.512700	+	0.367030i
$713$	−5.62649	−	29.0919i	−0.210714	−	1.08950i
$714$	8.37896	+	7.50904i	0.313575	+	0.281019i
$715$	1.29814	+	2.01995i	0.0485477	+	0.0755417i
$716$	1.05347	−	31.5271i	0.0393699	−	1.17822i
$717$	−4.85598	+	10.6331i	−0.181350	+	0.397101i
$718$	0.489117	+	0.233322i	0.0182537	+	0.00870749i
$719$	11.4008	−	5.20655i	0.425176	−	0.194172i	−0.191323	−	0.981527i	$-0.561278\pi$
$719$	11.4008	−	5.20655i	0.425176	−	0.194172i	0.616499	+	0.787356i	$0.288550\pi$
$720$	−0.476864	+	0.643155i	−0.0177717	+	0.0239690i
$721$	1.48227	+	10.3094i	0.0552026	+	0.383943i
$722$	−14.1472	−	22.8435i	−0.526504	−	0.850146i
$723$	18.1954	−	20.9986i	0.676695	−	0.780947i
$724$	−14.1852	−	7.05988i	−0.527188	−	0.262378i
$725$	−8.26018	−	5.30850i	−0.306775	−	0.197153i
$726$	−2.47703	−	19.5393i	−0.0919311	−	0.725173i
$727$	12.1601	+	3.57053i	0.450994	+	0.132424i	0.499339	−	0.866407i	$-0.333576\pi$
$727$	12.1601	+	3.57053i	0.450994	+	0.132424i	−0.0483446	+	0.998831i	$0.515395\pi$
$728$	0.798275	+	0.414072i	0.0295860	+	0.0153465i
$729$	16.3494	+	18.8682i	0.605532	+	0.698821i
$730$	−20.9336	−	6.52832i	−0.774786	−	0.241624i
$731$	24.2658	+	82.6416i	0.897502	+	3.05661i
$732$	−29.2152	−	9.64925i	−1.07983	−	0.356647i
$733$	−17.2996	−	2.48731i	−0.638975	−	0.0918708i	−0.184790	−	0.982778i	$-0.559160\pi$
$733$	−17.2996	−	2.48731i	−0.638975	−	0.0918708i	−0.454185	+	0.890907i	$0.650070\pi$
$734$	22.5636	+	3.62974i	0.832836	+	0.133976i
$735$	11.9331			0.440159
$736$	18.4777	−	19.8639i	0.681096	−	0.732194i
$737$	−2.92668			−0.107806
$738$	−0.959314	−	0.154322i	−0.0353128	−	0.00568068i
$739$	−41.9735	−	6.03488i	−1.54402	−	0.221997i	−0.682944	−	0.730471i	$-0.739301\pi$
$739$	−41.9735	−	6.03488i	−1.54402	−	0.221997i	−0.861077	+	0.508474i	$0.830210\pi$
$740$	13.0079	+	4.29625i	0.478178	+	0.157933i
$741$	0.00583733	+	0.0198801i	0.000214440	+	0.000730314i
$742$	−0.419976	−	0.130973i	−0.0154178	−	0.00480817i
$743$	−6.92891	−	7.99639i	−0.254197	−	0.293359i	0.614280	−	0.789088i	$-0.289446\pi$
$743$	−6.92891	−	7.99639i	−0.254197	−	0.293359i	−0.868477	+	0.495729i	$0.834901\pi$
$744$	27.7506	+	14.3945i	1.01739	+	0.527728i
$745$	8.28747	+	2.43342i	0.303630	+	0.0891537i
$746$	1.84606	+	14.5621i	0.0675890	+	0.533157i
$747$	−1.11258	−	0.715014i	−0.0407073	−	0.0261610i
$748$	60.1371	+	29.9299i	2.19883	+	1.09435i
$749$	−4.02540	+	4.64556i	−0.147085	+	0.169745i
$750$	1.33203	+	2.15082i	0.0486387	+	0.0785369i
$751$	−1.03643	−	7.20853i	−0.0378199	−	0.263043i	0.962135	−	0.272574i	$-0.0878751\pi$
$751$	−1.03643	−	7.20853i	−0.0378199	−	0.263043i	−0.999955	+	0.00953141i	$0.996966\pi$
$752$	23.3807	−	31.5339i	0.852605	−	1.14992i
$753$	−7.78415	+	3.55490i	−0.283670	+	0.129548i
$754$	−6.94324	−	3.31211i	−0.252858	−	0.120620i
$755$	1.07646	−	2.35713i	0.0391765	−	0.0857846i
$756$	−0.191994	+	5.74579i	−0.00698274	+	0.208972i
$757$	−7.32492	−	11.3978i	−0.266229	−	0.414260i	0.682241	−	0.731127i	$-0.261005\pi$
$757$	−7.32492	−	11.3978i	−0.266229	−	0.414260i	−0.948470	+	0.316867i	$0.897369\pi$
$758$	29.8320	+	26.7348i	1.08355	+	0.971052i
$759$	−22.9669	+	29.2436i	−0.833644	+	1.06147i
$760$	0.0480824	+	0.0344211i	0.00174413	+	0.00124858i
$761$	−41.4465	+	26.6360i	−1.50243	+	0.965556i	−0.507870	+	0.861434i	$0.669567\pi$
$761$	−41.4465	+	26.6360i	−1.50243	+	0.965556i	−0.994565	+	0.104122i	$0.966797\pi$
$762$	4.73704	−	3.96812i	0.171605	−	0.143750i
$763$	0.244369	+	0.111600i	0.00884675	+	0.00404017i
$764$	1.09656	+	2.63022i	0.0396721	+	0.0951579i
$765$	0.644358	+	1.41095i	0.0232968	+	0.0510129i
$766$	−0.0386783	+	2.31570i	−0.00139751	+	0.0836696i
$767$	1.77069	−	0.254587i	0.0639359	−	0.00919259i
$768$	4.33360	+	28.2924i	0.156375	+	1.02092i
$769$	−1.40103	−	1.21400i	−0.0505223	−	0.0437779i	0.629234	−	0.777216i	$-0.283369\pi$
$769$	−1.40103	−	1.21400i	−0.0505223	−	0.0437779i	−0.679756	+	0.733438i	$0.737914\pi$
$770$	−3.39135	+	0.934562i	−0.122216	+	0.0336793i
$771$	−15.3514	+	23.8872i	−0.552866	+	0.860276i
$772$	4.80515	+	3.31994i	0.172941	+	0.119487i
$773$	−1.14453	+	3.89793i	−0.0411660	+	0.140199i	−0.977512	−	0.210880i	$-0.932367\pi$
$773$	−1.14453	+	3.89793i	−0.0411660	+	0.140199i	0.936346	+	0.351079i	$0.114185\pi$
$774$	1.74497	−	2.61804i	0.0627218	−	0.0941037i
$775$	4.66939	−	4.04605i	0.167730	−	0.145339i
$776$	−6.04714	+	30.9583i	−0.217080	+	1.11134i
$777$	−6.74729	+	1.98118i	−0.242058	+	0.0710746i
$778$	−11.2839	−	25.8420i	−0.404549	−	0.926481i
$779$	−0.0102128	+	0.0710316i	−0.000365912	+	0.00254497i
$780$	1.24724	+	1.54047i	0.0446582	+	0.0551576i
$781$			39.2079i			1.40297i
$782$	−16.3904	−	49.9369i	−0.586120	−	1.78574i
$783$		−	49.1792i		−	1.75752i
$784$	18.7805	−	18.9539i	0.670732	−	0.676925i
$785$	2.17395	−	15.1202i	0.0775917	−	0.539662i
$786$	−11.6287	+	5.07770i	−0.414783	+	0.181116i
$787$	1.88887	−	0.554621i	0.0673308	−	0.0197701i	−0.247894	−	0.968787i	$-0.579738\pi$
$787$	1.88887	−	0.554621i	0.0673308	−	0.0197701i	0.315224	+	0.949017i	$0.397920\pi$
$788$	−31.1112	+	18.5559i	−1.10829	+	0.661027i
$789$	−37.8431	+	32.7912i	−1.34725	+	1.16740i
$790$	1.26161	+	0.840883i	0.0448859	+	0.0299173i
$791$	−0.397371	+	1.35332i	−0.0141289	+	0.0481185i
$792$	−0.572533	−	2.38607i	−0.0203441	−	0.0847852i
$793$	−2.57566	+	4.00781i	−0.0914645	+	0.142322i
$794$	−0.129190	−	0.468805i	−0.00458477	−	0.0166373i
$795$	−0.732797	−	0.634972i	−0.0259896	−	0.0225201i
$796$	5.75239	−	32.3080i	0.203888	−	1.14513i
$797$	7.11419	−	1.02287i	0.251997	−	0.0362318i	−0.0151584	−	0.999885i	$-0.504825\pi$
$797$	7.11419	−	1.02287i	0.251997	−	0.0362318i	0.267156	+	0.963653i	$0.413916\pi$
$798$	−0.0303508		0.000506939i	−0.00107441		1.79455e-5i
$799$	−31.5929	−	69.1788i	−1.11768	−	2.44737i
$800$	5.51262	+	1.26928i	0.194900	+	0.0448757i
$801$	−1.08306	−	0.494619i	−0.0382682	−	0.0174765i
$802$	−15.4852	−	18.4858i	−0.546801	−	0.652758i
$803$	56.5350	−	36.3328i	1.99508	−	1.28216i
$804$	−2.40148	+	0.263769i	−0.0846936	+	0.00930240i
$805$	2.38451	+	1.37465i	0.0840430	+	0.0484500i
$806$	3.23060	−	3.60486i	0.113793	−	0.126976i
$807$	2.92198	+	4.54669i	0.102859	+	0.160051i
$808$	21.7919	+	20.8830i	0.766638	+	0.734661i
$809$	−3.98034	+	8.71572i	−0.139941	+	0.306428i	−0.966606	−	0.256266i	$-0.917508\pi$
$809$	−3.98034	+	8.71572i	−0.139941	+	0.306428i	0.826665	+	0.562694i	$0.190235\pi$
$810$	−5.82122	+	12.2031i	−0.204537	+	0.428775i
$811$	3.87437	−	1.76937i	0.136048	−	0.0621309i	−0.346228	−	0.938150i	$-0.612538\pi$
$811$	3.87437	−	1.76937i	0.136048	−	0.0621309i	0.482276	+	0.876020i	$0.339810\pi$
$812$	7.66082	−	8.26631i	0.268842	−	0.290091i
$813$	−1.74766	−	12.1552i	−0.0612930	−	0.426302i
$814$	−35.6931	+	22.1051i	−1.25104	+	0.774784i
$815$	−1.25930	+	1.45330i	−0.0441112	+	0.0509070i
$816$	52.0428	+	19.1390i	1.82186	+	0.670000i
$817$	−0.195484	−	0.125630i	−0.00683911	−	0.00439523i
$818$	−29.2412	+	3.70694i	−1.02240	+	0.129610i
$819$	−0.0610626	−	0.0179296i	−0.00213370	−	0.000626511i
$820$	1.71303	+	6.64780i	0.0598216	+	0.232151i
$821$	17.2140	+	19.8660i	0.600773	+	0.693329i	0.971938	−	0.235238i	$-0.0755871\pi$
$821$	17.2140	+	19.8660i	0.600773	+	0.693329i	−0.371165	+	0.928567i	$0.621042\pi$
$822$	3.89791	−	12.4990i	0.135955	−	0.435951i
$823$	−9.96757	−	33.9464i	−0.347448	−	1.18330i	−0.929090	−	0.369854i	$-0.879408\pi$
$823$	−9.96757	−	33.9464i	−0.347448	−	1.18330i	0.581642	−	0.813445i	$-0.302410\pi$
$824$	25.5541	+	44.5180i	0.890219	+	1.55086i
$825$	−7.67452	−	1.10343i	−0.267192	−	0.0384165i
$826$	−0.416254	+	2.58756i	−0.0144833	+	0.0900328i
$827$	−55.5501			−1.93166			−0.965832	−	0.259167i	$-0.916552\pi$
$827$	−55.5501			−1.93166			−0.965832	+	0.259167i	$0.916552\pi$
$828$	−1.01389	+	1.63035i	−0.0352351	+	0.0566587i
$829$	36.3139			1.26123			0.630617	−	0.776094i	$-0.282802\pi$
$829$	36.3139			1.26123			0.630617	+	0.776094i	$0.282802\pi$
$830$	−1.48407	+	9.22545i	−0.0515129	+	0.320220i
$831$	52.9409	+	7.61176i	1.83650	+	0.264049i
$832$	4.40972	+	0.443368i	0.152879	+	0.0153710i
$833$	−14.5634	−	49.5984i	−0.504592	−	1.71848i
$834$	10.9429	−	35.0894i	0.378923	−	1.21505i
$835$	−7.66559	−	8.84656i	−0.265279	−	0.306148i
$836$	−0.175495	+	0.0452221i	−0.00606961	+	0.00156404i
$837$	29.6923	+	8.71843i	1.02631	+	0.301353i
$838$	−44.4376	+	5.63341i	−1.53507	+	0.194603i
$839$	−3.92872	−	2.52483i	−0.135634	−	0.0871669i	0.471064	−	0.882099i	$-0.343870\pi$
$839$	−3.92872	−	2.52483i	−0.135634	−	0.0871669i	−0.606698	+	0.794932i	$0.707506\pi$
$840$	−2.69854	+	1.07250i	−0.0931084	+	0.0370048i
$841$	−44.1447	+	50.9457i	−1.52223	+	1.75675i
$842$	−9.19564	+	5.69496i	−0.316903	+	0.196261i
$843$	1.00299	+	6.97598i	0.0345450	+	0.240265i
$844$	2.60701	+	2.41606i	0.0897370	+	0.0831640i
$845$	−11.5460	+	5.27290i	−0.397196	+	0.181393i
$846$	−1.19611	+	2.50742i	−0.0411230	+	0.0862070i
$847$	1.85608	−	4.06425i	0.0637756	−	0.139649i
$848$	−2.16184	+	0.164607i	−0.0742380	+	0.00565262i
$849$	8.85386	+	13.7769i	0.303864	+	0.472821i
$850$	7.31400	−	8.16132i	0.250868	−	0.279931i
$851$	31.9280	+	7.72383i	1.09448	+	0.264769i
$852$	3.53364	+	32.1720i	0.121061	+	1.10219i
$853$	−22.0342	+	14.1605i	−0.754436	+	0.484846i	−0.860461	−	0.509517i	$-0.829824\pi$
$853$	−22.0342	+	14.1605i	−0.754436	+	0.484846i	0.106025	+	0.994363i	$0.466188\pi$
$854$	−4.48197	−	5.35047i	−0.153370	−	0.183089i
$855$	−0.00380660	−	0.00173842i	−0.000130183	−	5.94526e-5i
$856$	−9.97995	+	28.6033i	−0.341108	+	0.977640i
$857$	16.0478	+	35.1397i	0.548182	+	1.20035i	0.957626	+	0.288016i	$0.0929955\pi$
$857$	16.0478	+	35.1397i	0.548182	+	1.20035i	−0.409444	+	0.912335i	$0.634277\pi$
$858$	−6.07370	−	0.101447i	−0.207353	−	0.00346335i
$859$	−26.4125	+	3.79755i	−0.901183	+	0.129571i	−0.577305	−	0.816528i	$-0.695896\pi$
$859$	−26.4125	+	3.79755i	−0.901183	+	0.129571i	−0.323878	+	0.946099i	$0.604987\pi$
$860$	−21.8852	−	3.89662i	−0.746279	−	0.132874i
$861$	−2.66327	−	2.30774i	−0.0907641	−	0.0786476i
$862$	10.2612	+	37.2360i	0.349498	+	1.26826i
$863$	20.6373	−	32.1123i	0.702503	−	1.09312i	−0.288265	−	0.957551i	$-0.593078\pi$
$863$	20.6373	−	32.1123i	0.702503	−	1.09312i	0.990768	−	0.135566i	$-0.0432852\pi$
$864$	9.57931	+	26.6646i	0.325895	+	0.907148i
$865$	−4.93161	+	16.7955i	−0.167680	+	0.571065i
$866$	19.8041	+	13.1998i	0.672972	+	0.448548i
$867$	58.2030	−	50.4332i	1.97668	−	1.71280i
$868$	3.63273	+	6.09071i	0.123303	+	0.206732i
$869$	−4.45840	+	1.30910i	−0.151241	+	0.0444083i
$870$	22.7651	−	9.94040i	0.771808	−	0.337011i
$871$	−0.0532380	+	0.370278i	−0.00180390	+	0.0125464i
$872$	1.32232	+	0.0663082i	0.0447794	+	0.00224548i
$873$		−	2.23228i		−	0.0755511i
$874$	0.121645	+	0.0728606i	0.00411471	+	0.00246455i
$875$			0.573909i			0.0194017i
$876$	43.1152	−	34.9081i	1.45673	−	1.17944i
$877$	5.02330	−	34.9378i	0.169625	−	1.17977i	−0.710037	−	0.704165i	$-0.751322\pi$
$877$	5.02330	−	34.9378i	0.169625	−	1.17977i	0.879661	−	0.475601i	$-0.157769\pi$
$878$	−23.3111	−	53.3861i	−0.786712	−	1.80169i
$879$	41.2313	−	12.1066i	1.39070	−	0.408345i
$880$	−13.8309	+	10.4532i	−0.466240	+	0.352378i
$881$	10.4303	−	9.03788i	0.351405	−	0.304494i	−0.461215	−	0.887289i	$-0.652586\pi$
$881$	10.4303	−	9.03788i	0.351405	−	0.304494i	0.812620	+	0.582795i	$0.198041\pi$
$882$	−1.04727	+	1.57125i	−0.0352634	+	0.0529069i
$883$	−9.27922	+	31.6021i	−0.312271	+	1.06350i	0.642533	+	0.766258i	$0.277884\pi$
$883$	−9.27922	+	31.6021i	−0.312271	+	1.06350i	−0.954804	+	0.297238i	$0.903935\pi$
$884$	4.88061	−	7.06401i	0.164153	−	0.237588i
$885$	−3.12302	+	4.85952i	−0.104979	+	0.163351i
$886$	−24.7251	+	6.81356i	−0.830657	+	0.228906i
$887$	9.44456	+	8.18376i	0.317117	+	0.274784i	0.798845	−	0.601538i	$-0.205445\pi$
$887$	9.44456	+	8.18376i	0.317117	+	0.274784i	−0.481727	+	0.876321i	$0.659990\pi$
$888$	−27.2957	+	21.3552i	−0.915983	+	0.716633i
$889$	1.38755	−	0.199499i	0.0465369	−	0.00669099i
$890$	−0.140489	+	8.41119i	−0.00470921	+	0.281944i
$891$	−17.2134	−	37.6922i	−0.576672	−	1.26274i
$892$	−4.08844	+	1.70450i	−0.136891	+	0.0570710i
$893$	0.186638	+	0.0852346i	0.00624559	+	0.00285227i
$894$	−16.7509	+	14.0319i	−0.560235	+	0.469297i
$895$	13.2685	−	8.52717i	0.443518	−	0.285032i
$896$	−2.54350	+	5.97413i	−0.0849723	+	0.199582i
$897$	3.28207	+	3.43769i	0.109585	+	0.114781i
$898$	21.5603	+	19.3218i	0.719476	+	0.644778i
$899$	−32.7985	−	51.0355i	−1.09389	−	1.70213i
$900$	−0.400104	−	0.0133693i	−0.0133368	−	0.000445645i
$901$	−1.74486	+	3.82072i	−0.0581298	+	0.127287i
$902$	−18.9894	−	9.05844i	−0.632278	−	0.301613i
$903$	10.3799	−	4.74034i	0.345421	−	0.157748i
$904$	0.643429	+	6.92137i	0.0214001	+	0.230201i
$905$	−1.12748	−	7.84181i	−0.0374788	−	0.260671i
$906$	3.45168	+	5.57342i	0.114674	+	0.185164i
$907$	1.85337	−	2.13890i	0.0615401	−	0.0710211i	−0.724145	−	0.689648i	$-0.757765\pi$
$907$	1.85337	−	2.13890i	0.0615401	−	0.0710211i	0.785685	+	0.618627i	$0.212311\pi$
$908$	4.06260	−	8.16284i	0.134822	−	0.270893i
$909$	−1.79690	−	1.15480i	−0.0595994	−	0.0383022i
$910$	0.0565486	+	0.446068i	0.00187457	+	0.0147870i
$911$	41.8756	+	12.2958i	1.38740	+	0.407378i	0.888339	−	0.459188i	$-0.151860\pi$
$911$	41.8756	+	12.2958i	1.38740	+	0.407378i	0.499062	+	0.866566i	$0.333678\pi$
$912$	−0.139926	+	0.0529235i	−0.00463342	+	0.00175247i
$913$	−18.7533	−	21.6425i	−0.620643	−	0.716261i
$914$	−34.2221	−	10.6725i	−1.13197	−	0.353014i
$915$	−4.33410	−	14.7606i	−0.143281	−	0.487970i
$916$	9.72039	−	29.4306i	0.321171	−	0.972414i
$917$	−2.84922	−	0.409656i	−0.0940896	−	0.0135280i
$918$	54.1933	+	8.71792i	1.78864	+	0.287734i
$919$	56.4519			1.86218			0.931088	−	0.364794i	$-0.118860\pi$
$919$	56.4519			1.86218			0.931088	+	0.364794i	$0.118860\pi$
$920$	13.4230	+	1.95539i	0.442543	+	0.0644674i
$921$	20.1176			0.662896
$922$	−11.6732	−	1.87783i	−0.384435	−	0.0618430i
$923$	4.96052	+	0.713215i	0.163278	+	0.0234758i
$924$	2.79106	−	8.45055i	0.0918192	−	0.278003i
$925$	1.92972	+	6.57204i	0.0634489	+	0.216087i
$926$	−38.8612	−	12.1192i	−1.27706	−	0.398261i
$927$	−2.37886	−	2.74535i	−0.0781319	−	0.0901690i
$928$	20.0392	−	51.8032i	0.657820	−	1.70052i
$929$	17.9714	+	5.27689i	0.589623	+	0.173129i	0.562916	−	0.826514i	$-0.309680\pi$
$929$	17.9714	+	5.27689i	0.589623	+	0.173129i	0.0267075	+	0.999643i	$0.491498\pi$
$930$	1.96581	+	15.5068i	0.0644616	+	0.508488i
$931$	0.117322	+	0.0753983i	0.00384508	+	0.00247108i
$932$	−0.509243	+	1.02320i	−0.0166808	+	0.0335162i
$933$	11.1652	−	12.8854i	0.365534	−	0.421849i
$934$	−25.5368	−	41.2342i	−0.835589	−	1.34923i
$935$	4.77989	+	33.2449i	0.156319	+	1.08722i
$936$	−0.312296	+	0.0290319i	−0.0102077	+	0.000948937i
$937$	−4.05463	+	1.85169i	−0.132459	+	0.0604920i	−0.480542	−	0.876972i	$-0.659560\pi$
$937$	−4.05463	+	1.85169i	−0.132459	+	0.0604920i	0.348083	+	0.937464i	$0.386833\pi$
$938$	−0.494658	−	0.235965i	−0.0161511	−	0.00770452i
$939$	−22.3332	+	48.9028i	−0.728816	+	1.59588i
$940$	19.6171	+	0.655500i	0.639840	+	0.0213800i
$941$	−9.37776	−	14.5921i	−0.305706	−	0.475688i	0.654078	−	0.756427i	$-0.273057\pi$
$941$	−9.37776	−	14.5921i	−0.305706	−	0.475688i	−0.959784	+	0.280739i	$0.909420\pi$
$942$	28.7797	+	25.7918i	0.937694	+	0.840341i
$943$	5.39411	+	15.5528i	0.175656	+	0.506468i
$944$	2.80354	+	12.6084i	0.0912475	+	0.410370i
$945$	−2.41818	+	1.55407i	−0.0786635	+	0.0505539i
$946$	52.2250	−	43.7478i	1.69798	−	1.42236i
$947$	−39.3504	−	17.9707i	−1.27872	−	0.583970i	−0.343868	−	0.939018i	$-0.611737\pi$
$947$	−39.3504	−	17.9707i	−1.27872	−	0.583970i	−0.934848	+	0.355048i	$0.884465\pi$
$948$	−3.54035	+	1.47600i	−0.114985	+	0.0479382i
$949$	−3.56837	−	7.81363i	−0.115834	−	0.253641i
$950$	−0.000493772		0.0295625i	−1.60201e−5		0.000959133i
$951$	−38.0710	+	5.47378i	−1.23454	+	0.177499i
$952$	7.75108	+	9.90724i	0.251214	+	0.321095i
$953$	−17.0877	−	14.8066i	−0.553525	−	0.479632i	0.332607	−	0.943066i	$-0.392072\pi$
$953$	−17.0877	−	14.8066i	−0.553525	−	0.479632i	−0.886132	+	0.463433i	$0.846617\pi$
$954$	0.147920	−	0.0407626i	0.00478908	−	0.00131974i
$955$	−0.770318	+	1.19864i	−0.0249269	+	0.0387870i
$956$	−7.42880	+	10.7522i	−0.240264	+	0.347749i
$957$	−21.4484	+	73.0464i	−0.693327	+	2.36125i
$958$	−7.08312	+	10.6271i	−0.228845	+	0.343345i
$959$	2.24465	−	1.94500i	0.0724834	−	0.0628072i
$960$	−10.4068	+	9.82388i	−0.335879	+	0.317064i
$961$	6.88321	−	2.02109i	0.222039	−	0.0651965i
$962$	2.14743	+	4.91794i	0.0692358	+	0.158561i
$963$	0.305107	−	2.12207i	0.00983193	−	0.0683826i
$964$	24.1428	−	19.5472i	0.777588	−	0.629573i
$965$			2.92025i			0.0940061i
$966$	−6.23956	+	3.09094i	−0.200755	+	0.0994495i
$967$			1.07960i			0.0347177i	0.999849	+	0.0173589i	$0.00552578\pi$
$967$			1.07960i			0.0347177i	−0.999849	+	0.0173589i	$0.994474\pi$
$968$	1.10281	−	21.9923i	0.0354457	−	0.706859i
$969$	−0.0412460	+	0.286872i	−0.00132501	+	0.00921567i
$970$	−14.4538	+	6.31129i	−0.464085	+	0.202643i
$971$	−41.3137	+	12.1308i	−1.32582	+	0.389296i	−0.866590	−	0.499021i	$-0.833693\pi$
$971$	−41.3137	+	12.1308i	−1.32582	+	0.389296i	−0.459231	+	0.888317i	$0.651875\pi$
$972$	−2.12762	−	3.56721i	−0.0682435	−	0.114418i
$973$	6.30159	−	5.46036i	0.202020	−	0.175051i
$974$	2.51730	+	1.67782i	0.0806594	+	0.0537610i
$975$	−0.279208	+	0.950895i	−0.00894181	+	0.0304530i
$976$	−30.2660	−	16.3464i	−0.968791	−	0.523235i
$977$	−17.5985	+	27.3839i	−0.563027	+	0.876087i	−0.999723	−	0.0235220i	$-0.992512\pi$
$977$	−17.5985	+	27.3839i	−0.563027	+	0.876087i	0.436696	+	0.899609i	$0.356148\pi$
$978$	−1.29247	−	4.69014i	−0.0413287	−	0.149974i
$979$	−19.4845	−	16.8834i	−0.622727	−	0.539596i
$980$	13.1347	+	2.33861i	0.419572	+	0.0747041i
$981$	−0.0927425	+	0.0133344i	−0.00296104	+	0.000425734i
$982$	−30.4571	−	0.508716i	−0.971926	−	0.0162338i
$983$	−13.7324	−	30.0697i	−0.437994	−	0.959073i	−0.991962	−	0.126535i	$-0.959614\pi$
$983$	−13.7324	−	30.0697i	−0.437994	−	0.959073i	0.553968	−	0.832538i	$-0.313113\pi$
$984$	−16.3981	−	5.72145i	−0.522753	−	0.182393i
$985$	−16.4756	−	7.52414i	−0.524955	−	0.239739i
$986$	−69.0991	−	82.4888i	−2.20056	−	2.62698i
$987$	−8.47626	+	5.44736i	−0.269802	+	0.173391i
$988$	0.00252907	+	0.0230259i	8.04606e−5	+	0.000732552i
$989$	−53.0661	−	5.03262i	−1.68740	−	0.160028i
$990$	0.818820	−	0.913681i	0.0260238	−	0.0290387i
$991$	0.490392	+	0.763065i	0.0155778	+	0.0242396i	0.848955	−	0.528465i	$-0.177232\pi$
$991$	0.490392	+	0.763065i	0.0155778	+	0.0242396i	−0.833377	+	0.552704i	$0.813596\pi$
$992$	27.7240	+	21.2824i	0.880238	+	0.675718i
$993$	10.0020	−	21.9014i	0.317404	−	0.695019i
$994$	−3.16116	+	6.62680i	−0.100266	+	0.210189i
$995$	14.9253	−	6.81616i	0.473164	−	0.216087i
$996$	−17.3385	−	16.0685i	−0.549392	−	0.509150i
$997$	−4.37072	−	30.3990i	−0.138422	−	0.962747i	−0.934096	−	0.357022i	$-0.883792\pi$
$997$	−4.37072	−	30.3990i	−0.138422	−	0.962747i	0.795674	−	0.605725i	$-0.207117\pi$
$998$	−21.9857	+	13.6160i	−0.695946	+	0.431007i
$999$	−22.4660	+	25.9272i	−0.710793	+	0.820299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.q.a.11.3	✓	480
4.3	odd	2	inner	460.2.q.a.11.20	yes	480
23.21	odd	22	inner	460.2.q.a.251.20	yes	480
92.67	even	22	inner	460.2.q.a.251.3	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.q.a.11.3	✓	480	1.1	even	1	trivial
460.2.q.a.11.20	yes	480	4.3	odd	2	inner
460.2.q.a.251.3	yes	480	92.67	even	22	inner
460.2.q.a.251.20	yes	480	23.21	odd	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39626 - 0.224613i) q^{2} +(1.77069 + 0.254587i) q^{3} +(1.89910 + 0.627237i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-2.41517 - 0.753191i) q^{6} +(-0.375831 - 0.433732i) q^{7} +(-2.51075 - 1.30235i) q^{8} +(0.192056 + 0.0563926i) q^{9} +O(q^{10})\)	\(q+(-1.39626 - 0.224613i) q^{2} +(1.77069 + 0.254587i) q^{3} +(1.89910 + 0.627237i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-2.41517 - 0.753191i) q^{6} +(-0.375831 - 0.433732i) q^{7} +(-2.51075 - 1.30235i) q^{8} +(0.192056 + 0.0563926i) q^{9} +(-0.177858 - 1.40298i) q^{10} +(3.64615 + 2.34324i) q^{11} +(3.20303 + 1.59413i) q^{12} +(0.362789 - 0.418681i) q^{13} +(0.427337 + 0.690020i) q^{14} +(0.254587 + 1.77069i) q^{15} +(3.21315 + 2.38237i) q^{16} +(7.04896 - 3.21915i) q^{17} +(-0.255494 - 0.121877i) q^{18} +(-0.00868497 + 0.0190174i) q^{19} +(-0.0667921 + 1.99888i) q^{20} +(-0.555058 - 0.863687i) q^{21} +(-4.56467 - 4.09075i) q^{22} +(0.231288 + 4.79025i) q^{23} +(-4.11421 - 2.94527i) q^{24} +(-0.841254 + 0.540641i) q^{25} +(-0.600589 + 0.503101i) q^{26} +(-4.55601 - 2.08066i) q^{27} +(-0.441687 - 1.05943i) q^{28} +(4.07892 + 8.93158i) q^{29} +(0.0422500 - 2.52953i) q^{30} +(-6.11561 + 0.879291i) q^{31} +(-3.95129 - 4.04813i) q^{32} +(5.85966 + 5.07742i) q^{33} +(-10.5653 + 2.91150i) q^{34} +(0.310279 - 0.482803i) q^{35} +(0.329361 + 0.227560i) q^{36} +(1.92972 - 6.57204i) q^{37} +(0.0163981 - 0.0246026i) q^{38} +(0.748978 - 0.648993i) q^{39} +(0.542235 - 2.77596i) q^{40} +(3.29344 - 0.967042i) q^{41} +(0.581011 + 1.33061i) q^{42} +(-1.58179 + 11.0016i) q^{43} +(5.45464 + 6.73705i) q^{44} +0.200164i q^{45} +(0.753014 - 6.74040i) q^{46} -9.81404i q^{47} +(5.08297 + 5.03647i) q^{48} +(0.949329 - 6.60273i) q^{49} +(1.29605 - 0.565920i) q^{50} +(13.3011 - 3.90555i) q^{51} +(0.951583 - 0.567561i) q^{52} +(-0.409635 + 0.354951i) q^{53} +(5.89404 + 3.92848i) q^{54} +(-1.22108 + 4.15863i) q^{55} +(0.378748 + 1.57846i) q^{56} +(-0.0202200 + 0.0314629i) q^{57} +(-3.68909 - 13.3870i) q^{58} +(2.44039 + 2.11461i) q^{59} +(-0.627158 + 3.52240i) q^{60} +(-8.51202 + 1.22384i) q^{61} +(8.73649 + 0.145923i) q^{62} +(-0.0477212 - 0.104495i) q^{63} +(4.60777 + 6.53976i) q^{64} +(0.503930 + 0.230137i) q^{65} +(-7.04116 - 8.40557i) q^{66} +(-0.568059 + 0.365069i) q^{67} +(15.4058 - 1.69212i) q^{68} +(-0.809996 + 8.54094i) q^{69} +(-0.541675 + 0.604428i) q^{70} +(4.89074 + 7.61014i) q^{71} +(-0.408762 - 0.391712i) q^{72} +(6.44117 - 14.1042i) q^{73} +(-4.17057 + 8.74285i) q^{74} +(-1.62724 + 0.743136i) q^{75} +(-0.0284221 + 0.0306684i) q^{76} +(-0.353999 - 2.46212i) q^{77} +(-1.19154 + 0.737934i) q^{78} +(-0.702066 + 0.810228i) q^{79} +(-1.38062 + 3.75418i) q^{80} +(-8.04274 - 5.16876i) q^{81} +(-4.81572 + 0.610495i) q^{82} +(-6.33961 - 1.86148i) q^{83} +(-0.512373 - 1.98838i) q^{84} +(5.07468 + 5.85649i) q^{85} +(4.67968 - 15.0058i) q^{86} +(4.94864 + 16.8535i) q^{87} +(-6.10288 - 10.6319i) q^{88} +(-5.88789 - 0.846551i) q^{89} +(0.0449594 - 0.279481i) q^{90} -0.317942 q^{91} +(-2.56539 + 9.24223i) q^{92} -11.0527 q^{93} +(-2.20436 + 13.7030i) q^{94} +(-0.0206939 - 0.00297534i) q^{95} +(-5.96591 - 8.17393i) q^{96} +(-3.14195 - 10.7005i) q^{97} +(-2.80857 + 9.00591i) q^{98} +(0.568123 + 0.655649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q - 4 * q^2 + 2 * q^6 + 2 * q^8 + 48 * q^9	\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9} + 6 q^{12} - 24 q^{16} + 26 q^{18} + 4 q^{24} + 48 q^{25} - 14 q^{26} + 40 q^{29} + 16 q^{32} - 22 q^{34} - 152 q^{36} - 110 q^{38} - 88 q^{40} - 8 q^{41} - 22 q^{44} - 132 q^{46} - 190 q^{48} - 56 q^{49} - 18 q^{50} - 50 q^{52} - 90 q^{54} - 110 q^{56} - 136 q^{58} - 22 q^{60} + 30 q^{62} - 30 q^{64} + 4 q^{69} + 110 q^{72} + 22 q^{74} - 176 q^{77} + 66 q^{78} - 8 q^{81} + 154 q^{82} + 308 q^{84} + 32 q^{85} + 176 q^{88} - 88 q^{89} + 134 q^{92} - 448 q^{93} + 204 q^{94} + 6 q^{96} - 88 q^{97} + 132 q^{98}+O(q^{100}) \) 480 * q - 4 * q^2 + 2 * q^6 + 2 * q^8 + 48 * q^9 + 6 * q^12 - 24 * q^16 + 26 * q^18 + 4 * q^24 + 48 * q^25 - 14 * q^26 + 40 * q^29 + 16 * q^32 - 22 * q^34 - 152 * q^36 - 110 * q^38 - 88 * q^40 - 8 * q^41 - 22 * q^44 - 132 * q^46 - 190 * q^48 - 56 * q^49 - 18 * q^50 - 50 * q^52 - 90 * q^54 - 110 * q^56 - 136 * q^58 - 22 * q^60 + 30 * q^62 - 30 * q^64 + 4 * q^69 + 110 * q^72 + 22 * q^74 - 176 * q^77 + 66 * q^78 - 8 * q^81 + 154 * q^82 + 308 * q^84 + 32 * q^85 + 176 * q^88 - 88 * q^89 + 134 * q^92 - 448 * q^93 + 204 * q^94 + 6 * q^96 - 88 * q^97 + 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more