LMFDB - Embedded newform 462.2.w.b.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(29,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("462.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.w (of order $10$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	462.29
Dual form			462.2.w.b.239.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(1.39186 - 1.03088i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.54008 + 2.11973i) q^{5} +(1.73198 - 0.0158825i) q^{6} +(-0.951057 + 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.874572 - 2.86969i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(1.39186 - 1.03088i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.54008 + 2.11973i) q^{5} +(1.73198 - 0.0158825i) q^{6} +(-0.951057 + 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.874572 - 2.86969i) q^{9} +2.62013i q^{10} +(-0.567824 + 3.26766i) q^{11} +(1.41054 + 1.00518i) q^{12} +(-0.538590 + 0.741305i) q^{13} +(-0.951057 - 0.309017i) q^{14} +(4.32877 + 1.36275i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.44431 - 2.50244i) q^{17} +(2.39431 - 1.80757i) q^{18} +(-1.49341 - 0.485240i) q^{19} +(-1.54008 + 2.11973i) q^{20} +(-1.00518 + 1.41054i) q^{21} +(-2.38006 + 2.30983i) q^{22} -2.00120i q^{23} +(0.550316 + 1.64230i) q^{24} +(-0.576349 + 1.77382i) q^{25} +(-0.871457 + 0.283154i) q^{26} +(-1.74102 - 4.89580i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-2.38864 - 7.35147i) q^{29} +(2.70105 + 3.64687i) q^{30} +(-1.41610 - 1.02886i) q^{31} -1.00000 q^{32} +(2.57823 + 5.13349i) q^{33} +4.25740 q^{34} +(-2.11973 - 1.54008i) q^{35} +(2.99950 - 0.0550161i) q^{36} +(-2.04896 - 6.30605i) q^{37} +(-0.922980 - 1.27037i) q^{38} +(0.0145532 + 1.58702i) q^{39} +(-2.49190 + 0.809666i) q^{40} +(-1.42723 + 4.39257i) q^{41} +(-1.64230 + 0.550316i) q^{42} +11.8699i q^{43} +(-3.28319 + 0.469729i) q^{44} +(7.42989 - 2.56568i) q^{45} +(1.17627 - 1.61900i) q^{46} +(5.43953 + 1.76741i) q^{47} +(-0.520106 + 1.65212i) q^{48} +(0.809017 - 0.587785i) q^{49} +(-1.50890 + 1.09628i) q^{50} +(2.21430 - 7.03373i) q^{51} +(-0.871457 - 0.283154i) q^{52} +(6.38961 - 8.79454i) q^{53} +(1.46916 - 4.98413i) q^{54} +(-7.80105 + 3.82880i) q^{55} -1.00000i q^{56} +(-2.57885 + 0.864143i) q^{57} +(2.38864 - 7.35147i) q^{58} +(-0.219835 + 0.0714286i) q^{59} +(0.0416142 + 4.53802i) q^{60} +(-7.88564 - 10.8537i) q^{61} +(-0.540903 - 1.66473i) q^{62} +(0.0550161 + 2.99950i) q^{63} +(-0.809017 - 0.587785i) q^{64} -2.40084 q^{65} +(-0.931560 + 5.66853i) q^{66} +5.86420 q^{67} +(3.44431 + 2.50244i) q^{68} +(-2.06299 - 2.78539i) q^{69} +(-0.809666 - 2.49190i) q^{70} +(4.47311 + 6.15671i) q^{71} +(2.45898 + 1.71855i) q^{72} +(-13.6086 + 4.42169i) q^{73} +(2.04896 - 6.30605i) q^{74} +(1.02640 + 3.06306i) q^{75} -1.57027i q^{76} +(-0.469729 - 3.28319i) q^{77} +(-0.921052 + 1.29248i) q^{78} +(-1.66335 + 2.28940i) q^{79} +(-2.49190 - 0.809666i) q^{80} +(-7.47025 - 5.01950i) q^{81} +(-3.73654 + 2.71476i) q^{82} +(-11.4756 + 8.33754i) q^{83} +(-1.65212 - 0.520106i) q^{84} +(10.6090 + 3.44708i) q^{85} +(-6.97698 + 9.60299i) q^{86} +(-10.9032 - 7.76985i) q^{87} +(-2.93226 - 1.54979i) q^{88} +8.91639i q^{89} +(7.51898 + 2.29150i) q^{90} +(0.283154 - 0.871457i) q^{91} +(1.90325 - 0.618404i) q^{92} +(-3.03165 + 0.0278006i) q^{93} +(3.36182 + 4.62714i) q^{94} +(-1.27139 - 3.91295i) q^{95} +(-1.39186 + 1.03088i) q^{96} +(-13.7768 - 10.0095i) q^{97} +1.00000 q^{98} +(8.88056 + 4.48728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 6 * q^12 - 24 * q^15 - 12 * q^16 + 24 * q^17 + 10 * q^18 + 30 * q^19 - 8 * q^22 - 6 * q^24 + 18 * q^25 + 20 * q^26 + 38 * q^27 - 8 * q^29 - 36 * q^30 - 32 * q^31 - 48 * q^32 + 24 * q^33 - 4 * q^34 - 6 * q^35 - 20 * q^37 - 20 * q^38 - 34 * q^39 - 22 * q^44 + 12 * q^45 + 20 * q^46 - 20 * q^47 - 4 * q^48 + 12 * q^49 - 28 * q^50 + 2 * q^51 + 20 * q^52 - 20 * q^53 - 18 * q^54 + 16 * q^55 + 12 * q^57 + 8 * q^58 - 30 * q^59 - 4 * q^60 - 20 * q^61 - 8 * q^62 - 4 * q^63 - 12 * q^64 + 46 * q^66 + 36 * q^67 + 24 * q^68 + 30 * q^69 - 4 * q^70 - 10 * q^72 - 20 * q^73 + 20 * q^74 + 40 * q^75 + 16 * q^77 - 16 * q^78 - 20 * q^79 - 54 * q^81 - 10 * q^82 + 46 * q^83 - 10 * q^84 + 10 * q^85 + 30 * q^86 - 8 * q^87 - 8 * q^88 - 62 * q^90 - 36 * q^91 - 10 * q^92 + 44 * q^93 - 50 * q^95 + 4 * q^96 - 2 * q^97 + 48 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	1.39186	−	1.03088i	0.803593	−	0.595179i
$3$	1.39186	−	1.03088i	0.803593	−	0.595179i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.54008	+	2.11973i	0.688743	+	0.947974i	0.999997	−	0.00235312i	$-0.000749022\pi$
$5$	1.54008	+	2.11973i	0.688743	+	0.947974i	−0.311254	+	0.950327i	$0.600749\pi$
$6$	1.73198	−	0.0158825i	0.707077	−	0.00648399i
$7$	−0.951057	+	0.309017i	−0.359466	+	0.116797i
$7$	−0.951057	+	0.309017i	−0.359466	+	0.116797i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.874572	−	2.86969i	0.291524	−	0.956564i
$10$			2.62013i			0.828559i
$11$	−0.567824	+	3.26766i	−0.171205	+	0.985235i
$11$	−0.567824	+	3.26766i	−0.171205	+	0.985235i
$12$	1.41054	+	1.00518i	0.407186	+	0.290171i
$13$	−0.538590	+	0.741305i	−0.149378	+	0.205601i	−0.877148	−	0.480220i	$-0.840557\pi$
$13$	−0.538590	+	0.741305i	−0.149378	+	0.205601i	0.727770	+	0.685821i	$0.240557\pi$
$14$	−0.951057	−	0.309017i	−0.254181	−	0.0825883i
$15$	4.32877	+	1.36275i	1.11768	+	0.351860i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.44431	−	2.50244i	0.835368	−	0.606931i	−0.0857046	−	0.996321i	$-0.527314\pi$
$17$	3.44431	−	2.50244i	0.835368	−	0.606931i	0.921073	+	0.389390i	$0.127314\pi$
$18$	2.39431	−	1.80757i	0.564343	−	0.426048i
$19$	−1.49341	−	0.485240i	−0.342613	−	0.111322i	0.132656	−	0.991162i	$-0.457649\pi$
$19$	−1.49341	−	0.485240i	−0.342613	−	0.111322i	−0.475269	+	0.879840i	$0.657649\pi$
$20$	−1.54008	+	2.11973i	−0.344372	+	0.473987i
$21$	−1.00518	+	1.41054i	−0.219349	+	0.307804i
$22$	−2.38006	+	2.30983i	−0.507430	+	0.492458i
$23$		−	2.00120i		−	0.417278i	−0.977993	−	0.208639i	$-0.933097\pi$
$23$		−	2.00120i		−	0.417278i	0.977993	−	0.208639i	$-0.0669034\pi$
$24$	0.550316	+	1.64230i	0.112333	+	0.335233i
$25$	−0.576349	+	1.77382i	−0.115270	+	0.354764i
$26$	−0.871457	+	0.283154i	−0.170907	+	0.0555310i
$27$	−1.74102	−	4.89580i	−0.335060	−	0.942197i
$28$	−0.587785	−	0.809017i	−0.111081	−	0.152890i
$29$	−2.38864	−	7.35147i	−0.443559	−	1.36513i	−0.884056	−	0.467380i	$-0.845198\pi$
$29$	−2.38864	−	7.35147i	−0.443559	−	1.36513i	0.440497	−	0.897754i	$-0.354802\pi$
$30$	2.70105	+	3.64687i	0.493141	+	0.665825i
$31$	−1.41610	−	1.02886i	−0.254340	−	0.184788i	0.453308	−	0.891354i	$-0.350244\pi$
$31$	−1.41610	−	1.02886i	−0.254340	−	0.184788i	−0.707648	+	0.706565i	$0.750244\pi$
$32$	−1.00000			−0.176777
$33$	2.57823	+	5.13349i	0.448812	+	0.893626i
$34$	4.25740			0.730139
$35$	−2.11973	−	1.54008i	−0.358300	−	0.260320i
$36$	2.99950	−	0.0550161i	0.499916	−	0.00916936i
$37$	−2.04896	−	6.30605i	−0.336847	−	1.03671i	−0.965805	−	0.259269i	$-0.916518\pi$
$37$	−2.04896	−	6.30605i	−0.336847	−	1.03671i	0.628958	−	0.777439i	$-0.283482\pi$
$38$	−0.922980	−	1.27037i	−0.149727	−	0.206082i
$39$	0.0145532	+	1.58702i	0.00233037	+	0.254126i
$40$	−2.49190	+	0.809666i	−0.394003	+	0.128019i
$41$	−1.42723	+	4.39257i	−0.222896	+	0.686004i	0.775602	+	0.631222i	$0.217446\pi$
$41$	−1.42723	+	4.39257i	−0.222896	+	0.686004i	−0.998498	+	0.0547820i	$0.982554\pi$
$42$	−1.64230	+	0.550316i	−0.253413	+	0.0849156i
$43$			11.8699i			1.81015i	0.425252	+	0.905075i	$0.360185\pi$
$43$			11.8699i			1.81015i	−0.425252	+	0.905075i	$0.639815\pi$
$44$	−3.28319	+	0.469729i	−0.494960	+	0.0708143i
$45$	7.42989	−	2.56568i	1.10758	−	0.382470i
$46$	1.17627	−	1.61900i	0.173432	−	0.238709i
$47$	5.43953	+	1.76741i	0.793438	+	0.257804i	0.677567	−	0.735461i	$-0.263034\pi$
$47$	5.43953	+	1.76741i	0.793438	+	0.257804i	0.115870	+	0.993264i	$0.463034\pi$
$48$	−0.520106	+	1.65212i	−0.0750708	+	0.238463i
$49$	0.809017	−	0.587785i	0.115574	−	0.0839693i
$50$	−1.50890	+	1.09628i	−0.213391	+	0.155038i
$51$	2.21430	−	7.03373i	0.310064	−	0.984919i
$52$	−0.871457	−	0.283154i	−0.120849	−	0.0392663i
$53$	6.38961	−	8.79454i	0.877680	−	1.20802i	−0.0993783	−	0.995050i	$-0.531685\pi$
$53$	6.38961	−	8.79454i	0.877680	−	1.20802i	0.977058	−	0.212973i	$-0.0683146\pi$
$54$	1.46916	−	4.98413i	0.199927	−	0.678254i
$55$	−7.80105	+	3.82880i	−1.05189	+	0.516276i
$56$		−	1.00000i		−	0.133631i
$57$	−2.57885	+	0.864143i	−0.341577	+	0.114459i
$58$	2.38864	−	7.35147i	0.313644	−	0.965296i
$59$	−0.219835	+	0.0714286i	−0.0286200	+	0.00929922i	−0.323292	−	0.946299i	$-0.604790\pi$
$59$	−0.219835	+	0.0714286i	−0.0286200	+	0.00929922i	0.294672	+	0.955598i	$0.404790\pi$
$60$	0.0416142	+	4.53802i	0.00537237	+	0.585855i
$61$	−7.88564	−	10.8537i	−1.00965	−	1.38967i	−0.919211	−	0.393766i	$-0.871172\pi$
$61$	−7.88564	−	10.8537i	−1.00965	−	1.38967i	−0.0904424	−	0.995902i	$-0.528828\pi$
$62$	−0.540903	−	1.66473i	−0.0686948	−	0.211421i
$63$	0.0550161	+	2.99950i	0.00693138	+	0.377901i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.40084			−0.297788
$66$	−0.931560	+	5.66853i	−0.114667	+	0.697747i
$67$	5.86420			0.716426			0.358213	−	0.933640i	$-0.383386\pi$
$67$	5.86420			0.716426			0.358213	+	0.933640i	$0.383386\pi$
$68$	3.44431	+	2.50244i	0.417684	+	0.303465i
$69$	−2.06299	−	2.78539i	−0.248355	−	0.335322i
$70$	−0.809666	−	2.49190i	−0.0967736	−	0.297839i
$71$	4.47311	+	6.15671i	0.530861	+	0.730667i	0.987261	−	0.159107i	$-0.0508615\pi$
$71$	4.47311	+	6.15671i	0.530861	+	0.730667i	−0.456400	+	0.889775i	$0.650862\pi$
$72$	2.45898	+	1.71855i	0.289794	+	0.202533i
$73$	−13.6086	+	4.42169i	−1.59276	+	0.517520i	−0.965304	−	0.261129i	$-0.915905\pi$
$73$	−13.6086	+	4.42169i	−1.59276	+	0.517520i	−0.627460	+	0.778649i	$0.715905\pi$
$74$	2.04896	−	6.30605i	0.238187	−	0.733063i
$75$	1.02640	+	3.06306i	0.118518	+	0.353692i
$76$		−	1.57027i		−	0.180122i
$77$	−0.469729	−	3.28319i	−0.0535305	−	0.374155i
$78$	−0.921052	+	1.29248i	−0.104289	+	0.146344i
$79$	−1.66335	+	2.28940i	−0.187141	+	0.257578i	−0.892271	−	0.451501i	$-0.850889\pi$
$79$	−1.66335	+	2.28940i	−0.187141	+	0.257578i	0.705129	+	0.709079i	$0.250889\pi$
$80$	−2.49190	−	0.809666i	−0.278602	−	0.0905234i
$81$	−7.47025	−	5.01950i	−0.830028	−	0.557722i
$82$	−3.73654	+	2.71476i	−0.412632	+	0.299795i
$83$	−11.4756	+	8.33754i	−1.25961	+	0.915164i	−0.998739	−	0.0502085i	$-0.984011\pi$
$83$	−11.4756	+	8.33754i	−1.25961	+	0.915164i	−0.260876	+	0.965372i	$0.584011\pi$
$84$	−1.65212	−	0.520106i	−0.180261	−	0.0567482i
$85$	10.6090	+	3.44708i	1.15071	+	0.373888i
$86$	−6.97698	+	9.60299i	−0.752347	+	1.03552i
$87$	−10.9032	−	7.76985i	−1.16894	−	0.833016i
$88$	−2.93226	−	1.54979i	−0.312580	−	0.165209i
$89$			8.91639i			0.945136i	0.881294	+	0.472568i	$0.156673\pi$
$89$			8.91639i			0.945136i	−0.881294	+	0.472568i	$0.843327\pi$
$90$	7.51898	+	2.29150i	0.792570	+	0.241545i
$91$	0.283154	−	0.871457i	0.0296826	−	0.0913535i
$92$	1.90325	−	0.618404i	0.198428	−	0.0644731i
$93$	−3.03165	+	0.0278006i	−0.314368	+	0.00288279i
$94$	3.36182	+	4.62714i	0.346745	+	0.477254i
$95$	−1.27139	−	3.91295i	−0.130442	−	0.401460i
$96$	−1.39186	+	1.03088i	−0.142057	+	0.105214i
$97$	−13.7768	−	10.0095i	−1.39883	−	1.01631i	−0.994831	−	0.101545i	$-0.967621\pi$
$97$	−13.7768	−	10.0095i	−1.39883	−	1.01631i	−0.403995	−	0.914761i	$-0.632379\pi$
$98$	1.00000			0.101015
$99$	8.88056	+	4.48728i	0.892530	+	0.450988i
$100$	−1.86511			−0.186511
$101$	3.86048	+	2.80480i	0.384132	+	0.279088i	0.763047	−	0.646344i	$-0.223703\pi$
$101$	3.86048	+	2.80480i	0.384132	+	0.279088i	−0.378915	+	0.925432i	$0.623703\pi$
$102$	5.92573	−	4.38887i	0.586734	−	0.434563i
$103$	−1.58362	−	4.87388i	−0.156039	−	0.480237i	0.842226	−	0.539124i	$-0.181245\pi$
$103$	−1.58362	−	4.87388i	−0.156039	−	0.480237i	−0.998265	+	0.0588872i	$0.981245\pi$
$104$	−0.538590	−	0.741305i	−0.0528131	−	0.0726910i
$105$	−4.53802	+	0.0416142i	−0.442865	+	0.00406113i
$106$	10.3386	−	3.35921i	1.00417	−	0.326276i
$107$	−0.102228	+	0.314626i	−0.00988278	+	0.0304161i	−0.955876	−	0.293769i	$-0.905090\pi$
$107$	−0.102228	+	0.314626i	−0.00988278	+	0.0304161i	0.945994	+	0.324186i	$0.105090\pi$
$108$	4.11818	−	3.16870i	0.396272	−	0.304908i
$109$		−	13.0104i		−	1.24617i	−0.782155	−	0.623084i	$-0.785880\pi$
$109$		−	13.0104i		−	1.24617i	0.782155	−	0.623084i	$-0.214120\pi$
$110$	−8.56170	−	1.48778i	−0.816326	−	0.141854i
$111$	−9.35265	−	6.66493i	−0.887715	−	0.632607i
$112$	0.587785	−	0.809017i	0.0555405	−	0.0764449i
$113$	9.76666	+	3.17338i	0.918771	+	0.298527i	0.729962	−	0.683487i	$-0.239538\pi$
$113$	9.76666	+	3.17338i	0.918771	+	0.298527i	0.188808	+	0.982014i	$0.439538\pi$
$114$	−2.59427	−	0.816705i	−0.242975	−	0.0764914i
$115$	4.24200	−	3.08200i	0.395569	−	0.287398i
$116$	6.25354	−	4.54346i	0.580626	−	0.421850i
$117$	1.65628	+	2.19391i	0.153123	+	0.202827i
$118$	−0.219835	−	0.0714286i	−0.0202374	−	0.00657554i
$119$	−2.50244	+	3.44431i	−0.229398	+	0.315740i
$120$	−2.63371	+	3.69579i	−0.240424	+	0.337378i
$121$	−10.3552	−	3.71091i	−0.941377	−	0.337355i
$122$		−	13.4159i		−	1.21461i
$123$	2.54170	+	7.58517i	0.229177	+	0.683931i
$124$	0.540903	−	1.66473i	0.0485745	−	0.149497i
$125$	7.81183	−	2.53822i	0.698711	−	0.227025i
$126$	−1.71855	+	2.45898i	−0.153101	+	0.219063i
$127$	−2.42944	−	3.34384i	−0.215578	−	0.296718i	0.687508	−	0.726176i	$-0.258704\pi$
$127$	−2.42944	−	3.34384i	−0.215578	−	0.296718i	−0.903087	+	0.429458i	$0.858704\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	12.2365	+	16.5214i	1.07736	+	1.45462i
$130$	−1.94232	−	1.41118i	−0.170353	−	0.123769i
$131$	−17.1298			−1.49664			−0.748318	−	0.663340i	$-0.769138\pi$
$131$	−17.1298			−1.49664			−0.748318	+	0.663340i	$0.769138\pi$
$132$	−4.08552	+	4.03838i	−0.355599	+	0.351496i
$133$	1.57027			0.136160
$134$	4.74424	+	3.44689i	0.409840	+	0.297766i
$135$	7.69648	−	11.2304i	0.662407	−	0.966560i
$136$	1.31561	+	4.04903i	0.112813	+	0.347202i
$137$	9.00623	+	12.3960i	0.769454	+	1.05906i	0.996368	+	0.0851478i	$0.0271363\pi$
$137$	9.00623	+	12.3960i	0.769454	+	1.05906i	−0.226914	+	0.973915i	$0.572864\pi$
$138$	−0.0317839	−	3.46603i	−0.00270563	−	0.295048i
$139$	7.74206	−	2.51555i	0.656673	−	0.213366i	0.0383188	−	0.999266i	$-0.487800\pi$
$139$	7.74206	−	2.51555i	0.656673	−	0.213366i	0.618354	+	0.785900i	$0.287800\pi$
$140$	0.809666	−	2.49190i	0.0684293	−	0.210604i
$141$	9.39308	−	3.14751i	0.791040	−	0.265068i
$142$			7.61012i			0.638627i
$143$	−2.11651	−	2.18086i	−0.176991	−	0.182372i
$144$	0.979219	+	2.83569i	0.0816015	+	0.236307i
$145$	11.9045	−	16.3851i	0.988613	−	1.36071i
$146$	−13.6086	−	4.42169i	−1.12625	−	0.365942i
$147$	0.520106	−	1.65212i	0.0428976	−	0.136264i
$148$	5.36424	−	3.89735i	0.440938	−	0.320360i
$149$	4.64528	−	3.37499i	0.380556	−	0.276490i	−0.381019	−	0.924567i	$-0.624427\pi$
$149$	4.64528	−	3.37499i	0.380556	−	0.276490i	0.761575	+	0.648077i	$0.224427\pi$
$150$	−0.970052	+	3.08137i	−0.0792044	+	0.251593i
$151$	15.0143	+	4.87845i	1.22185	+	0.397003i	0.847755	−	0.530388i	$-0.177954\pi$
$151$	15.0143	+	4.87845i	1.22185	+	0.397003i	0.374094	+	0.927391i	$0.377954\pi$
$152$	0.922980	−	1.27037i	0.0748636	−	0.103041i
$153$	−4.16893	−	12.0727i	−0.337038	−	0.976018i
$154$	1.54979	−	2.93226i	0.124886	−	0.236288i
$155$		−	4.58628i		−	0.368379i
$156$	−1.50485	+	0.504257i	−0.120484	+	0.0403728i
$157$	−6.37547	+	19.6217i	−0.508818	+	1.56598i	0.285439	+	0.958397i	$0.407861\pi$
$157$	−6.37547	+	19.6217i	−0.508818	+	1.56598i	−0.794256	+	0.607583i	$0.792139\pi$
$158$	−2.69135	+	0.874474i	−0.214113	+	0.0695694i
$159$	−0.172653	−	18.8277i	−0.0136922	−	1.49314i
$160$	−1.54008	−	2.11973i	−0.121754	−	0.167580i
$161$	0.618404	+	1.90325i	0.0487371	+	0.149997i
$162$	−3.09317	−	8.45176i	−0.243022	−	0.664033i
$163$	−8.98326	−	6.52672i	−0.703623	−	0.511212i	0.177487	−	0.984123i	$-0.443203\pi$
$163$	−8.98326	−	6.52672i	−0.703623	−	0.511212i	−0.881110	+	0.472911i	$0.843203\pi$
$164$	−4.61862			−0.360654
$165$	−6.91097	+	13.3711i	−0.538018	+	1.04094i
$166$	−14.1847			−1.10094
$167$	−0.223384	−	0.162298i	−0.0172860	−	0.0125590i	0.579109	−	0.815250i	$-0.303401\pi$
$167$	−0.223384	−	0.162298i	−0.0172860	−	0.0125590i	−0.596395	+	0.802691i	$0.703401\pi$
$168$	−1.03088	−	1.39186i	−0.0795341	−	0.107385i
$169$	3.75777	+	11.5652i	0.289059	+	0.889632i
$170$	6.55673	+	9.02456i	0.502878	+	0.692152i
$171$	−2.69858	+	3.86126i	−0.206366	+	0.295278i
$172$	−11.2890	+	3.66802i	−0.860777	+	0.279684i
$173$	0.543756	−	1.67351i	0.0413410	−	0.127234i	−0.928256	−	0.371942i	$-0.878692\pi$
$173$	0.543756	−	1.67351i	0.0413410	−	0.127234i	0.969597	+	0.244708i	$0.0786920\pi$
$174$	−4.25383	−	12.6947i	−0.322482	−	0.962379i
$175$		−	1.86511i		−	0.140989i
$176$	−1.46130	−	2.97735i	−0.110150	−	0.224426i
$177$	−0.232346	+	0.326042i	−0.0174642	+	0.0245068i
$178$	−5.24092	+	7.21351i	−0.392824	+	0.540676i
$179$	11.9449	+	3.88113i	0.892803	+	0.290089i	0.719263	−	0.694737i	$-0.244479\pi$
$179$	11.9449	+	3.88113i	0.892803	+	0.290089i	0.173540	+	0.984827i	$0.444479\pi$
$180$	4.73607	+	6.27340i	0.353006	+	0.467592i
$181$	3.77538	−	2.74297i	0.280621	−	0.203883i	−0.438567	−	0.898699i	$-0.644514\pi$
$181$	3.77538	−	2.74297i	0.280621	−	0.203883i	0.719188	+	0.694815i	$0.244514\pi$
$182$	0.741305	−	0.538590i	0.0549492	−	0.0399229i
$183$	−22.1646	−	6.97766i	−1.63845	−	0.515803i
$184$	1.90325	+	0.618404i	0.140310	+	0.0455893i
$185$	10.2116	−	14.0550i	0.750771	−	1.03335i
$186$	−2.46900	−	1.75947i	−0.181036	−	0.129011i
$187$	6.22135	+	12.6758i	0.454950	+	0.926944i
$188$			5.71947i			0.417135i
$189$	3.16870	+	4.11818i	0.230489	+	0.299553i
$190$	1.27139	−	3.91295i	0.0922365	−	0.283875i
$191$	−7.65015	+	2.48568i	−0.553545	+	0.179858i	−0.572415	−	0.819964i	$-0.693993\pi$
$191$	−7.65015	+	2.48568i	−0.553545	+	0.179858i	0.0188696	+	0.999822i	$0.493993\pi$
$192$	−1.73198	+	0.0158825i	−0.124995	+	0.00114622i
$193$	9.89609	+	13.6208i	0.712336	+	0.980446i	0.999744	+	0.0226379i	$0.00720648\pi$
$193$	9.89609	+	13.6208i	0.712336	+	0.980446i	−0.287408	+	0.957808i	$0.592794\pi$
$194$	−5.26228	−	16.1956i	−0.377810	−	1.16278i
$195$	−3.34164	+	2.47498i	−0.239300	+	0.177237i
$196$	0.809017	+	0.587785i	0.0577869	+	0.0419847i
$197$	3.14379			0.223986			0.111993	−	0.993709i	$-0.464277\pi$
$197$	3.14379			0.223986			0.111993	+	0.993709i	$0.464277\pi$
$198$	4.54697	+	8.85015i	0.323139	+	0.628952i
$199$	6.14540			0.435636			0.217818	−	0.975989i	$-0.430106\pi$
$199$	6.14540			0.435636			0.217818	+	0.975989i	$0.430106\pi$
$200$	−1.50890	−	1.09628i	−0.106695	−	0.0775188i
$201$	8.16217	−	6.04529i	0.575715	−	0.426402i
$202$	1.47457	+	4.53826i	0.103750	+	0.319311i
$203$	4.54346	+	6.25354i	0.318888	+	0.438912i
$204$	7.37373	−	0.0676180i	0.516264	−	0.00473421i
$205$	−11.5091	+	3.73954i	−0.803832	+	0.261181i
$206$	1.58362	−	4.87388i	0.110336	−	0.339579i
$207$	−5.74282	−	1.75019i	−0.399153	−	0.121647i
$208$		−	0.916304i		−	0.0635342i
$209$	2.43359	−	4.60443i	0.168335	−	0.318495i
$210$	−3.69579	−	2.63371i	−0.255034	−	0.181743i
$211$	1.13878	−	1.56739i	0.0783965	−	0.107904i	−0.768018	−	0.640429i	$-0.778757\pi$
$211$	1.13878	−	1.56739i	0.0783965	−	0.107904i	0.846414	+	0.532525i	$0.178757\pi$
$212$	10.3386	+	3.35921i	0.710058	+	0.230712i
$213$	12.5728	+	3.95806i	0.861474	+	0.271202i
$214$	−0.267637	+	0.194450i	−0.0182953	+	0.0132923i
$215$	−25.1611	+	18.2806i	−1.71597	+	1.24673i
$216$	5.19419	−	0.142926i	0.353420	−	0.00972489i
$217$	1.66473	+	0.540903i	0.113009	+	0.0367189i
$218$	7.64730	−	10.5256i	0.517941	−	0.712884i
$219$	−14.3831	+	20.1832i	−0.971917	+	1.36386i
$220$	−6.05207	−	6.23608i	−0.408030	−	0.420436i
$221$			3.90108i			0.262415i
$222$	−3.64891	−	10.8894i	−0.244899	−	0.730848i
$223$	−7.22741	+	22.2437i	−0.483983	+	1.48955i	0.349466	+	0.936949i	$0.386363\pi$
$223$	−7.22741	+	22.2437i	−0.483983	+	1.48955i	−0.833449	+	0.552597i	$0.813637\pi$
$224$	0.951057	−	0.309017i	0.0635451	−	0.0206471i
$225$	4.58626	+	3.20528i	0.305751	+	0.213685i
$226$	6.03613	+	8.30802i	0.401517	+	0.552641i
$227$	2.55715	+	7.87011i	0.169724	+	0.522358i	0.999353	−	0.0359573i	$-0.0114480\pi$
$227$	2.55715	+	7.87011i	0.169724	+	0.522358i	−0.829629	+	0.558315i	$0.811448\pi$
$228$	−1.61876	−	2.18560i	−0.107205	−	0.144745i
$229$	9.83193	+	7.14331i	0.649712	+	0.472043i	0.863173	−	0.504908i	$-0.168474\pi$
$229$	9.83193	+	7.14331i	0.649712	+	0.472043i	−0.213461	+	0.976952i	$0.568474\pi$
$230$	5.24341			0.345740
$231$	−4.03838	−	4.08552i	−0.265706	−	0.268808i
$232$	7.72980			0.507486
$233$	7.26813	+	5.28061i	0.476151	+	0.345944i	0.799834	−	0.600222i	$-0.204921\pi$
$233$	7.26813	+	5.28061i	0.476151	+	0.345944i	−0.323682	+	0.946166i	$0.604921\pi$
$234$	0.0504115	+	2.74845i	0.00329550	+	0.179672i
$235$	4.63086	+	14.2523i	0.302084	+	0.929718i
$236$	−0.135865	−	0.187003i	−0.00884408	−	0.0121728i
$237$	0.0449451	+	4.90125i	0.00291950	+	0.318370i
$238$	−4.04903	+	1.31561i	−0.262460	+	0.0852783i
$239$	2.96566	−	9.12736i	0.191833	−	0.590400i	−0.808166	−	0.588954i	$-0.799540\pi$
$239$	2.96566	−	9.12736i	0.191833	−	0.590400i	0.999999	−	0.00144564i	$-0.000460162\pi$
$240$	−4.30305	+	1.44190i	−0.277761	+	0.0930743i
$241$			1.16681i			0.0751610i	0.999294	+	0.0375805i	$0.0119651\pi$
$241$			1.16681i			0.0751610i	−0.999294	+	0.0375805i	$0.988035\pi$
$242$	−6.19628	−	9.08879i	−0.398312	−	0.584250i
$243$	−15.5721	+	0.714470i	−0.998949	+	0.0458333i
$244$	7.88564	−	10.8537i	0.504826	−	0.694834i
$245$	2.49190	+	0.809666i	0.159201	+	0.0517277i
$246$	−2.40217	+	7.63050i	−0.153157	+	0.486503i
$247$	1.16405	−	0.845731i	0.0740666	−	0.0538126i
$248$	1.41610	−	1.02886i	0.0899226	−	0.0653326i
$249$	−7.37752	+	23.4347i	−0.467532	+	1.48512i
$250$	7.81183	+	2.53822i	0.494064	+	0.160531i
$251$	5.54672	−	7.63441i	0.350106	−	0.481879i	−0.597253	−	0.802053i	$-0.703741\pi$
$251$	5.54672	−	7.63441i	0.350106	−	0.481879i	0.947359	+	0.320173i	$0.103741\pi$
$252$	−2.83569	+	0.979219i	−0.178632	+	0.0616850i
$253$	6.53922	+	1.13633i	0.411117	+	0.0714403i
$254$		−	4.13322i		−	0.259341i
$255$	18.3198	−	6.13876i	1.14723	−	0.384424i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.68958	+	0.548979i	−0.105393	+	0.0342444i	−0.361239	−	0.932473i	$-0.617646\pi$
$257$	−1.68958	+	0.548979i	−0.105393	+	0.0342444i	0.255846	+	0.966718i	$0.417646\pi$
$258$	0.188524	+	20.5585i	0.0117370	+	1.27992i
$259$	3.89735	+	5.36424i	0.242170	+	0.333318i
$260$	−0.741900	−	2.28333i	−0.0460107	−	0.141606i
$261$	−23.1855	+	0.425264i	−1.43515	+	0.0263232i
$262$	−13.8583	−	10.0686i	−0.856167	−	0.622042i
$263$	11.1451			0.687236			0.343618	−	0.939109i	$-0.388347\pi$
$263$	11.1451			0.687236			0.343618	+	0.939109i	$0.388347\pi$
$264$	−5.67896	+	0.865705i	−0.349516	+	0.0532804i
$265$	28.4826			1.74967
$266$	1.27037	+	0.922980i	0.0778916	+	0.0565916i
$267$	9.19173	+	12.4104i	0.562525	+	0.759505i
$268$	1.81214	+	5.57718i	0.110694	+	0.340681i
$269$	9.51258	+	13.0929i	0.579992	+	0.798291i	0.993694	−	0.112122i	$-0.0357646\pi$
$269$	9.51258	+	13.0929i	0.579992	+	0.798291i	−0.413702	+	0.910412i	$0.635765\pi$
$270$	12.8277	−	4.56171i	0.780666	−	0.277617i
$271$	−23.3334	+	7.58148i	−1.41740	+	0.460542i	−0.914776	−	0.403961i	$-0.867633\pi$
$271$	−23.3334	+	7.58148i	−1.41740	+	0.460542i	−0.502627	+	0.864503i	$0.667633\pi$
$272$	−1.31561	+	4.04903i	−0.0797706	+	0.245509i
$273$	−0.504257	−	1.50485i	−0.0305190	−	0.0910775i
$274$			15.3223i			0.925655i
$275$	−5.46897	−	2.89053i	−0.329791	−	0.174305i
$276$	2.01157	−	2.82276i	0.121082	−	0.169910i
$277$	7.77226	−	10.6976i	0.466990	−	0.642757i	−0.508950	−	0.860796i	$-0.669966\pi$
$277$	7.77226	−	10.6976i	0.466990	−	0.642757i	0.975940	+	0.218039i	$0.0699662\pi$
$278$	7.74206	+	2.51555i	0.464338	+	0.150873i
$279$	−4.19099	+	3.16397i	−0.250908	+	0.189422i
$280$	2.11973	−	1.54008i	0.126678	−	0.0920372i
$281$	−15.7077	+	11.4123i	−0.937043	+	0.680802i	−0.947707	−	0.319141i	$-0.896606\pi$
$281$	−15.7077	+	11.4123i	−0.937043	+	0.680802i	0.0106637	+	0.999943i	$0.496606\pi$
$282$	9.44922	+	2.97473i	0.562693	+	0.177142i
$283$	2.14218	+	0.696036i	0.127339	+	0.0413750i	0.371993	−	0.928235i	$-0.378674\pi$
$283$	2.14218	+	0.696036i	0.127339	+	0.0413750i	−0.244654	+	0.969610i	$0.578674\pi$
$284$	−4.47311	+	6.15671i	−0.265430	+	0.365334i
$285$	−5.80338	−	4.13563i	−0.343763	−	0.244974i
$286$	−0.430414	−	3.00840i	−0.0254509	−	0.177891i
$287$		−	4.61862i		−	0.272629i
$288$	−0.874572	+	2.86969i	−0.0515346	+	0.169098i
$289$	0.347795	−	1.07040i	0.0204585	−	0.0629649i
$290$	19.2619	−	6.25856i	1.13109	−	0.367515i
$291$	−29.4940	+	0.270464i	−1.72897	+	0.0158549i
$292$	−8.41056	−	11.5761i	−0.492191	−	0.677443i
$293$	−2.53614	−	7.80544i	−0.148163	−	0.455998i	0.849241	−	0.528005i	$-0.177060\pi$
$293$	−2.53614	−	7.80544i	−0.148163	−	0.455998i	−0.997404	+	0.0720065i	$0.977060\pi$
$294$	1.39186	−	1.03088i	0.0811752	−	0.0601222i
$295$	−0.489972	−	0.355986i	−0.0285273	−	0.0207263i
$296$	6.63057			0.385394
$297$	16.9864	−	2.90911i	0.985650	−	0.168804i
$298$	5.74188			0.332618
$299$	1.48350	+	1.07782i	0.0857929	+	0.0623322i
$300$	−2.59597	+	1.92270i	−0.149879	+	0.111007i
$301$	−3.66802	−	11.2890i	−0.211421	−	0.650687i
$302$	9.27936	+	12.7719i	0.533967	+	0.734943i
$303$	8.26467	−	0.0757881i	0.474793	−	0.00435391i
$304$	1.49341	−	0.485240i	0.0856532	−	0.0278304i
$305$	10.8624	−	33.4309i	0.621977	−	1.91425i
$306$	3.72340	−	12.2174i	0.212853	−	0.698424i
$307$		−	11.2413i		−	0.641576i	−0.947151	−	0.320788i	$-0.896052\pi$
$307$		−	11.2413i		−	0.641576i	0.947151	−	0.320788i	$-0.103948\pi$
$308$	2.97735	−	1.46130i	0.169650	−	0.0832653i
$309$	−7.22856	−	5.15125i	−0.411219	−	0.293044i
$310$	2.69575	−	3.71038i	0.153108	−	0.210735i
$311$	3.27459	+	1.06398i	0.185685	+	0.0603328i	0.400384	−	0.916348i	$-0.368877\pi$
$311$	3.27459	+	1.06398i	0.185685	+	0.0603328i	−0.214698	+	0.976680i	$0.568877\pi$
$312$	−1.51384	−	0.476575i	−0.0857044	−	0.0269807i
$313$	21.2415	−	15.4329i	1.20064	−	0.872317i	0.206293	−	0.978490i	$-0.433860\pi$
$313$	21.2415	−	15.4329i	1.20064	−	0.872317i	0.994348	+	0.106174i	$0.0338599\pi$
$314$	−16.6912	+	12.1269i	−0.941938	+	0.684358i
$315$	−6.27340	+	4.73607i	−0.353466	+	0.266847i
$316$	−2.69135	−	0.874474i	−0.151401	−	0.0491930i
$317$	15.2396	−	20.9755i	0.855943	−	1.17810i	−0.126579	−	0.991957i	$-0.540400\pi$
$317$	15.2396	−	20.9755i	0.855943	−	1.17810i	0.982522	−	0.186148i	$-0.0596003\pi$
$318$	10.9270	−	15.3334i	0.612754	−	0.859856i
$319$	25.3784	−	3.63091i	1.42092	−	0.203292i
$320$		−	2.62013i		−	0.146470i
$321$	0.182054	+	0.543302i	0.0101613	+	0.0303242i
$322$	−0.618404	+	1.90325i	−0.0344623	+	0.106064i
$323$	−6.35807	+	2.06586i	−0.353772	+	0.114948i
$324$	2.46539	−	8.65574i	0.136966	−	0.480874i
$325$	−1.00453	−	1.38261i	−0.0557211	−	0.0766936i
$326$	−3.43130	−	10.5605i	−0.190042	−	0.584890i
$327$	−13.4121	−	18.1087i	−0.741693	−	1.00141i
$328$	−3.73654	−	2.71476i	−0.206316	−	0.149897i
$329$	−5.71947			−0.315324
$330$	−13.4504	+	6.75531i	−0.740422	+	0.371867i
$331$	−1.23655			−0.0679668			−0.0339834	−	0.999422i	$-0.510819\pi$
$331$	−1.23655			−0.0679668			−0.0339834	+	0.999422i	$0.510819\pi$
$332$	−11.4756	−	8.33754i	−0.629807	−	0.457582i
$333$	−19.8884	+	0.364788i	−1.08988	+	0.0199903i
$334$	−0.0853251	−	0.262604i	−0.00466878	−	0.0143690i
$335$	9.03132	+	12.4305i	0.493433	+	0.679153i
$336$	−0.0158825	−	1.73198i	−0.000866459	−	0.0944871i
$337$	24.2797	−	7.88897i	1.32260	−	0.429739i	0.439214	−	0.898382i	$-0.355257\pi$
$337$	24.2797	−	7.88897i	1.32260	−	0.429739i	0.883388	+	0.468643i	$0.155257\pi$
$338$	−3.75777	+	11.5652i	−0.204396	+	0.629065i
$339$	16.8652	−	5.65135i	0.915994	−	0.306939i
$340$			11.1550i			0.604963i
$341$	4.16605	−	4.04313i	0.225604	−	0.218948i
$342$	−4.45279	+	1.53764i	−0.240779	+	0.0831458i
$343$	−0.587785	+	0.809017i	−0.0317374	+	0.0436828i
$344$	−11.2890	−	3.66802i	−0.608662	−	0.197766i
$345$	2.72712	−	8.66272i	0.146823	−	0.466385i
$346$	1.42357	−	1.03429i	0.0765317	−	0.0556035i
$347$	−29.1943	+	21.2109i	−1.56723	+	1.13866i	−0.637485	+	0.770462i	$0.720025\pi$
$347$	−29.1943	+	21.2109i	−1.56723	+	1.13866i	−0.929747	+	0.368199i	$0.879975\pi$
$348$	4.02031	−	12.7705i	0.215511	−	0.684572i
$349$	14.9151	+	4.84621i	0.798387	+	0.259412i	0.679671	−	0.733517i	$-0.262122\pi$
$349$	14.9151	+	4.84621i	0.798387	+	0.259412i	0.118715	+	0.992928i	$0.462122\pi$
$350$	1.09628	−	1.50890i	0.0585987	−	0.0806542i
$351$	4.56698	+	1.34620i	0.243767	+	0.0718547i
$352$	0.567824	−	3.26766i	0.0302651	−	0.174167i
$353$			32.5879i			1.73448i	0.497893	+	0.867239i	$0.334107\pi$
$353$			32.5879i			1.73448i	−0.497893	+	0.867239i	$0.665893\pi$
$354$	−0.379615	+	0.127204i	−0.0201763	+	0.00676084i
$355$	−6.16165	+	18.9636i	−0.327027	+	1.00648i
$356$	−8.47999	+	2.75532i	−0.449439	+	0.146032i
$357$	0.0676180	+	7.37373i	0.00357873	+	0.390259i
$358$	7.38235	+	10.1609i	0.390169	+	0.537022i
$359$	−9.71329	−	29.8944i	−0.512648	−	1.57777i	−0.787521	−	0.616288i	$-0.788636\pi$
$359$	−9.71329	−	29.8944i	−0.512648	−	1.57777i	0.274873	−	0.961480i	$-0.411364\pi$
$360$	0.144150	+	7.85908i	0.00759736	+	0.414210i
$361$	−13.3765	−	9.71859i	−0.704026	−	0.511505i
$362$	4.66662			0.245272
$363$	−18.2385	+	5.50984i	−0.957271	+	0.289192i
$364$	0.916304			0.0480274
$365$	−30.3311	−	22.0368i	−1.58760	−	1.15346i
$366$	−13.8301	−	18.6730i	−0.722913	−	0.976056i
$367$	0.789783	+	2.43070i	0.0412263	+	0.126882i	0.969551	−	0.244888i	$-0.0787512\pi$
$367$	0.789783	+	2.43070i	0.0412263	+	0.126882i	−0.928325	+	0.371770i	$0.878751\pi$
$368$	1.17627	+	1.61900i	0.0613175	+	0.0843963i
$369$	11.3571	+	7.93733i	0.591227	+	0.413201i
$370$	16.5227	−	5.36855i	0.858974	−	0.279098i
$371$	−3.35921	+	10.3386i	−0.174402	+	0.536753i
$372$	−0.963272	−	2.87468i	−0.0499433	−	0.149045i
$373$			3.66251i			0.189638i	0.995495	+	0.0948189i	$0.0302272\pi$
$373$			3.66251i			0.189638i	−0.995495	+	0.0948189i	$0.969773\pi$
$374$	−2.41746	+	13.9117i	−0.125004	+	0.719359i
$375$	8.25641	−	11.5859i	0.426359	−	0.598294i
$376$	−3.36182	+	4.62714i	−0.173372	+	0.238627i
$377$	6.73619	+	2.18872i	0.346931	+	0.112725i
$378$	0.142926	+	5.19419i	0.00735133	+	0.267160i
$379$	20.5604	−	14.9380i	1.05612	−	0.767315i	0.0827525	−	0.996570i	$-0.473629\pi$
$379$	20.5604	−	14.9380i	1.05612	−	0.767315i	0.973366	+	0.229255i	$0.0736289\pi$
$380$	3.32855	−	2.41833i	0.170751	−	0.124058i
$381$	−6.82856	−	2.14971i	−0.349838	−	0.110133i
$382$	−7.65015	−	2.48568i	−0.391416	−	0.127179i
$383$	−14.4748	+	19.9229i	−0.739630	+	1.01801i	0.259010	+	0.965875i	$0.416604\pi$
$383$	−14.4748	+	19.9229i	−0.739630	+	1.01801i	−0.998640	+	0.0521386i	$0.983396\pi$
$384$	−1.41054	−	1.00518i	−0.0719811	−	0.0512955i
$385$	6.23608	−	6.05207i	0.317820	−	0.308442i
$386$			16.8362i			0.856941i
$387$	34.0631	+	10.3811i	1.73152	+	0.527702i
$388$	5.26228	−	16.1956i	0.267152	−	0.822209i
$389$	−30.7452	+	9.98973i	−1.55884	+	0.506499i	−0.956499	−	0.291736i	$-0.905767\pi$
$389$	−30.7452	+	9.98973i	−1.55884	+	0.506499i	−0.602346	+	0.798235i	$0.705767\pi$
$390$	−4.15820	+	0.0381312i	−0.210559	+	0.00193085i
$391$	−5.00787	−	6.89275i	−0.253259	−	0.348581i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	−23.8423	+	17.6588i	−1.20269	+	0.890766i
$394$	2.54338	+	1.84787i	0.128134	+	0.0930946i
$395$	−7.41461			−0.373069
$396$	−1.52341	+	9.83256i	−0.0765543	+	0.494105i
$397$	−22.0709			−1.10770			−0.553852	−	0.832615i	$-0.686843\pi$
$397$	−22.0709			−1.10770			−0.553852	+	0.832615i	$0.686843\pi$
$398$	4.97173	+	3.61217i	0.249210	+	0.181062i
$399$	2.18560	−	1.61876i	0.109417	−	0.0810393i
$400$	−0.576349	−	1.77382i	−0.0288175	−	0.0886910i
$401$	−2.19603	−	3.02257i	−0.109664	−	0.150940i	0.750657	−	0.660692i	$-0.229737\pi$
$401$	−2.19603	−	3.02257i	−0.109664	−	0.150940i	−0.860321	+	0.509752i	$0.829737\pi$
$402$	10.1567	−	0.0931379i	0.506568	−	0.00464530i
$403$	1.52540	−	0.495632i	0.0759855	−	0.0246892i
$404$	−1.47457	+	4.53826i	−0.0733626	+	0.225787i
$405$	−0.864753	−	23.5654i	−0.0429699	−	1.17097i
$406$			7.72980i			0.383623i
$407$	21.7694	−	3.11457i	1.07907	−	0.154383i
$408$	6.00522	+	4.27947i	0.297303	+	0.211865i
$409$	−5.96852	+	8.21496i	−0.295124	+	0.406203i	−0.930670	−	0.365860i	$-0.880775\pi$
$409$	−5.96852	+	8.21496i	−0.295124	+	0.406203i	0.635546	+	0.772063i	$0.280775\pi$
$410$	−11.5091	−	3.73954i	−0.568395	−	0.184683i
$411$	25.3142	+	7.96922i	1.24866	+	0.393093i
$412$	4.14597	−	3.01222i	0.204257	−	0.148401i
$413$	0.187003	−	0.135865i	0.00920180	−	0.00668550i
$414$	−3.61730	−	4.79148i	−0.177781	−	0.235488i
$415$	−35.3467	−	11.4848i	−1.73510	−	0.563769i
$416$	0.538590	−	0.741305i	0.0264065	−	0.0363455i
$417$	8.18267	−	11.4824i	0.400707	−	0.562297i
$418$	4.67523	−	2.29463i	0.228673	−	0.112234i
$419$		−	7.37033i		−	0.360064i	−0.983661	−	0.180032i	$-0.942380\pi$
$419$		−	7.37033i		−	0.360064i	0.983661	−	0.180032i	$-0.0576202\pi$
$420$	−1.44190	−	4.30305i	−0.0703576	−	0.209967i
$421$	6.16436	−	18.9720i	0.300433	−	0.924637i	−0.680910	−	0.732367i	$-0.738415\pi$
$421$	6.16436	−	18.9720i	0.300433	−	0.924637i	0.981342	−	0.192269i	$-0.0615847\pi$
$422$	1.84258	−	0.598690i	0.0896952	−	0.0291437i
$423$	9.82919	−	14.0641i	0.477911	−	0.683818i
$424$	6.38961	+	8.79454i	0.310307	+	0.427100i
$425$	2.45375	+	7.55187i	0.119024	+	0.366320i
$426$	7.84512	+	10.5922i	0.380097	+	0.513196i
$427$	10.8537	+	7.88564i	0.525245	+	0.381613i
$428$	−0.330818			−0.0159907
$429$	−5.19409	−	0.853592i	−0.250773	−	0.0412118i
$430$	−31.1009			−1.49982
$431$	29.3657	+	21.3354i	1.41450	+	1.02769i	0.992650	+	0.121024i	$0.0386177\pi$
$431$	29.3657	+	21.3354i	1.41450	+	1.02769i	0.421846	+	0.906668i	$0.361382\pi$
$432$	4.28619	+	2.93744i	0.206220	+	0.141327i
$433$	−11.6849	−	35.9624i	−0.561540	−	1.72824i	−0.678014	−	0.735049i	$-0.737159\pi$
$433$	−11.6849	−	35.9624i	−0.561540	−	1.72824i	0.116474	−	0.993194i	$-0.462841\pi$
$434$	1.02886	+	1.41610i	0.0493868	+	0.0679751i
$435$	−0.321669	−	35.0779i	−0.0154229	−	1.68186i
$436$	12.3736	−	4.02043i	0.592588	−	0.192543i
$437$	−0.971060	+	2.98862i	−0.0464521	+	0.142965i
$438$	−23.4995	+	7.87442i	−1.12285	+	0.376254i
$439$		−	0.693175i		−	0.0330835i	−0.999863	−	0.0165417i	$-0.994734\pi$
$439$		−	0.693175i		−	0.0330835i	0.999863	−	0.0165417i	$-0.00526564\pi$
$440$	−1.23075	−	8.60241i	−0.0586738	−	0.410104i
$441$	−0.979219	−	2.83569i	−0.0466295	−	0.135033i
$442$	−2.29300	+	3.15604i	−0.109067	+	0.150117i
$443$	−13.1784	−	4.28191i	−0.626124	−	0.203440i	−0.0212664	−	0.999774i	$-0.506770\pi$
$443$	−13.1784	−	4.28191i	−0.626124	−	0.203440i	−0.604857	+	0.796334i	$0.706770\pi$
$444$	3.44860	−	10.9545i	0.163663	−	0.519877i
$445$	−18.9004	+	13.7319i	−0.895964	+	0.650956i
$446$	−18.9216	+	13.7473i	−0.895964	+	0.650956i
$447$	2.98638	−	9.48626i	0.141251	−	0.448684i
$448$	0.951057	+	0.309017i	0.0449332	+	0.0145997i
$449$	−4.91467	+	6.76447i	−0.231938	+	0.319235i	−0.909083	−	0.416614i	$-0.863217\pi$
$449$	−4.91467	+	6.76447i	−0.231938	+	0.319235i	0.677146	+	0.735849i	$0.263217\pi$
$450$	1.82635	+	5.28886i	0.0860948	+	0.249319i
$451$	−13.5430	−	7.15791i	−0.637714	−	0.337053i
$452$			10.2693i			0.483026i
$453$	25.9270	−	8.68783i	1.21816	−	0.408190i
$454$	−2.55715	+	7.87011i	−0.120013	+	0.369363i
$455$	2.28333	−	0.741900i	0.107044	−	0.0347808i
$456$	−0.0249397	−	2.71967i	−0.00116791	−	0.127360i
$457$	22.9450	+	31.5811i	1.07332	+	1.47730i	0.866665	+	0.498890i	$0.166259\pi$
$457$	22.9450	+	31.5811i	1.07332	+	1.47730i	0.206659	+	0.978413i	$0.433741\pi$
$458$	3.75546	+	11.5581i	0.175481	+	0.540076i
$459$	−18.2481	−	12.5059i	−0.851747	−	0.583723i
$460$	4.24200	+	3.08200i	0.197784	+	0.143699i
$461$	37.0739			1.72670			0.863352	−	0.504601i	$-0.168361\pi$
$461$	37.0739			1.72670			0.863352	+	0.504601i	$0.168361\pi$
$462$	−0.865705	−	5.67896i	−0.0402762	−	0.264209i
$463$	−39.8489			−1.85194			−0.925968	−	0.377601i	$-0.876749\pi$
$463$	−39.8489			−1.85194			−0.925968	+	0.377601i	$0.876749\pi$
$464$	6.25354	+	4.54346i	0.290313	+	0.210925i
$465$	−4.72791	−	6.38348i	−0.219251	−	0.296027i
$466$	2.77618	+	8.54420i	0.128604	+	0.395803i
$467$	−15.5026	−	21.3375i	−0.717373	−	0.987379i	−0.999607	−	0.0280338i	$-0.991075\pi$
$467$	−15.5026	−	21.3375i	−0.717373	−	0.987379i	0.282234	−	0.959346i	$-0.408925\pi$
$468$	−1.57471	+	2.25317i	−0.0727912	+	0.104153i
$469$	−5.57718	+	1.81214i	−0.257530	+	0.0836767i
$470$	−4.63086	+	14.2523i	−0.213606	+	0.657410i
$471$	11.3538	+	33.8830i	0.523156	+	1.56125i
$472$		−	0.231148i		−	0.0106394i
$473$	−38.7869	−	6.74004i	−1.78342	−	0.309907i
$474$	−2.84452	+	3.99161i	−0.130653	+	0.183341i
$475$	1.72146	−	2.36938i	0.0789858	−	0.108715i
$476$	−4.04903	−	1.31561i	−0.185587	−	0.0603009i
$477$	−19.6494	−	26.0276i	−0.899686	−	1.19172i
$478$	7.76420	−	5.64102i	0.355126	−	0.258014i
$479$	18.5194	−	13.4551i	0.846174	−	0.614781i	−0.0779148	−	0.996960i	$-0.524826\pi$
$479$	18.5194	−	13.4551i	0.846174	−	0.614781i	0.924088	+	0.382179i	$0.124826\pi$
$480$	−4.32877	−	1.36275i	−0.197580	−	0.0622006i
$481$	5.77826	+	1.87747i	0.263466	+	0.0856052i
$482$	−0.685835	+	0.943971i	−0.0312389	+	0.0429967i
$483$	2.82276	+	2.01157i	0.128440	+	0.0915295i
$484$	0.329364	−	10.9951i	0.0149711	−	0.499776i
$485$		−	44.6185i		−	2.02602i
$486$	−13.0180	−	8.57502i	−0.590510	−	0.388971i
$487$	5.43080	−	16.7143i	0.246093	−	0.757396i	−0.749362	−	0.662161i	$-0.769640\pi$
$487$	5.43080	−	16.7143i	0.246093	−	0.757396i	0.995455	−	0.0952356i	$-0.0303604\pi$
$488$	12.7592	−	4.14573i	0.577583	−	0.187668i
$489$	−19.2317	+	0.176358i	−0.869690	+	0.00797517i
$490$	1.54008	+	2.11973i	0.0695736	+	0.0957598i
$491$	2.36230	+	7.27043i	0.106609	+	0.328110i	0.990105	−	0.140330i	$-0.0448163\pi$
$491$	2.36230	+	7.27043i	0.106609	+	0.328110i	−0.883495	+	0.468440i	$0.844816\pi$
$492$	−6.42849	+	4.76125i	−0.289819	+	0.214654i
$493$	−26.6238	−	19.3433i	−1.19908	−	0.871181i
$494$	1.43884			0.0647366
$495$	4.16491	+	25.7352i	0.187199	+	1.15671i
$496$	1.75040			0.0785952
$497$	−6.15671	−	4.47311i	−0.276166	−	0.200647i
$498$	−19.7431	+	14.6227i	−0.884711	+	0.655259i
$499$	−12.1296	−	37.3310i	−0.542995	−	1.67117i	−0.725711	−	0.688000i	$-0.758489\pi$
$499$	−12.1296	−	37.3310i	−0.542995	−	1.67117i	0.182716	−	0.983166i	$-0.441511\pi$
$500$	4.82798	+	6.64514i	0.215914	+	0.297180i
$501$	−0.478230	+	0.00438543i	−0.0213657	+	0.000195927i
$502$	8.97478	−	2.91608i	0.400564	−	0.130151i
$503$	−5.73151	+	17.6398i	−0.255556	+	0.786519i	0.738164	+	0.674621i	$0.235693\pi$
$503$	−5.73151	+	17.6398i	−0.255556	+	0.786519i	−0.993720	+	0.111898i	$0.964307\pi$
$504$	−2.86969	−	0.874572i	−0.127826	−	0.0389565i
$505$			12.5028i			0.556367i
$506$	4.62243	+	4.76297i	0.205492	+	0.211740i
$507$	17.1527	+	12.2234i	0.761776	+	0.542860i
$508$	2.42944	−	3.34384i	0.107789	−	0.148359i
$509$	−1.94210	−	0.631026i	−0.0860821	−	0.0279698i	0.265659	−	0.964067i	$-0.414410\pi$
$509$	−1.94210	−	0.631026i	−0.0860821	−	0.0279698i	−0.351741	+	0.936097i	$0.614410\pi$
$510$	18.4293	+	5.80176i	0.816064	+	0.256906i
$511$	11.5761	−	8.41056i	0.512099	−	0.372061i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.224432	+	8.15627i	0.00990893	+	0.360108i
$514$	−1.68958	−	0.548979i	−0.0745244	−	0.0242144i
$515$	7.89242	−	10.8630i	0.347782	−	0.478681i
$516$	−11.9315	+	16.7430i	−0.525253	+	0.737068i
$517$	−8.86399	+	16.7709i	−0.389838	+	0.737586i
$518$			6.63057i			0.291331i
$519$	−0.968353	−	2.88984i	−0.0425060	−	0.126850i
$520$	0.741900	−	2.28333i	0.0325345	−	0.100131i
$521$	−39.2643	+	12.7577i	−1.72020	+	0.558927i	−0.991978	−	0.126413i	$-0.959653\pi$
$521$	−39.2643	+	12.7577i	−1.72020	+	0.558927i	−0.728223	+	0.685340i	$0.759653\pi$
$522$	−19.0074	−	13.2840i	−0.831932	−	0.581427i
$523$	2.41673	+	3.32635i	0.105676	+	0.145451i	0.858580	−	0.512680i	$-0.171347\pi$
$523$	2.41673	+	3.32635i	0.105676	+	0.145451i	−0.752903	+	0.658131i	$0.771347\pi$
$524$	−5.29339	−	16.2914i	−0.231243	−	0.711693i
$525$	−1.92270	−	2.59597i	−0.0839135	−	0.113298i
$526$	9.01658	+	6.55093i	0.393141	+	0.285634i
$527$	−7.45216			−0.324621
$528$	−5.10322	−	2.63764i	−0.222089	−	0.114788i
$529$	18.9952			0.825879
$530$	23.0429	+	16.7416i	1.00092	+	0.727210i
$531$	0.0127169	+	0.693327i	0.000551865	+	0.0300878i
$532$	0.485240	+	1.49341i	0.0210378	+	0.0647477i
$533$	−2.48754	−	3.42381i	−0.107747	−	0.148302i
$534$	0.141614	+	15.4430i	0.00612825	+	0.668284i
$535$	−0.824363	+	0.267852i	−0.0356403	+	0.0115802i
$536$	−1.81214	+	5.57718i	−0.0782724	+	0.240898i
$537$	20.6267	−	6.91175i	0.890106	−	0.298264i
$538$			16.1838i			0.697732i
$539$	1.46130	+	2.97735i	0.0629427	+	0.128243i
$540$	13.0591	+	3.84940i	0.561974	+	0.165652i
$541$	−20.1344	+	27.7126i	−0.865646	+	1.19146i	0.114548	+	0.993418i	$0.463458\pi$
$541$	−20.1344	+	27.7126i	−0.865646	+	1.19146i	−0.980194	+	0.198041i	$0.936542\pi$
$542$	−23.3334	−	7.58148i	−1.00226	−	0.325652i
$543$	2.42714	−	7.70980i	0.104158	−	0.330859i
$544$	−3.44431	+	2.50244i	−0.147674	+	0.107291i
$545$	27.5785	−	20.0370i	1.18133	−	0.858289i
$546$	0.476575	−	1.51384i	0.0203955	−	0.0647864i
$547$	−3.52316	−	1.14474i	−0.150639	−	0.0489457i	0.232727	−	0.972542i	$-0.425235\pi$
$547$	−3.52316	−	1.14474i	−0.150639	−	0.0489457i	−0.383366	+	0.923596i	$0.625235\pi$
$548$	−9.00623	+	12.3960i	−0.384727	+	0.529531i
$549$	−38.0432	+	13.1371i	−1.62364	+	0.560676i
$550$	−2.72548	−	5.55307i	−0.116215	−	0.236784i
$551$			12.1379i			0.517090i
$552$	3.28657	−	1.10129i	0.139886	−	0.0468740i
$553$	0.874474	−	2.69135i	0.0371864	−	0.114448i
$554$	12.5758	−	4.08612i	0.534294	−	0.173603i
$555$	−0.275926	−	30.0896i	−0.0117124	−	1.27723i
$556$	4.78486	+	6.58579i	0.202923	+	0.279300i
$557$	−4.72903	−	14.5545i	−0.200375	−	0.616692i	−0.999872	−	0.0160210i	$-0.994900\pi$
$557$	−4.72903	−	14.5545i	−0.200375	−	0.616692i	0.799496	−	0.600671i	$-0.205100\pi$
$558$	−5.25031	+	0.0963002i	−0.222264	+	0.00407671i
$559$	−8.79926	−	6.39303i	−0.372169	−	0.270397i
$560$	2.62013			0.110721
$561$	21.7265	+	11.2295i	0.917292	+	0.474109i
$562$	−19.4158			−0.819006
$563$	−13.6236	−	9.89816i	−0.574168	−	0.417158i	0.262449	−	0.964946i	$-0.415470\pi$
$563$	−13.6236	−	9.89816i	−0.574168	−	0.417158i	−0.836617	+	0.547788i	$0.815470\pi$
$564$	5.89608	+	7.96072i	0.248270	+	0.335207i
$565$	8.31469	+	25.5900i	0.349802	+	1.07658i
$566$	1.32394	+	1.82225i	0.0556493	+	0.0765947i
$567$	8.65574	+	2.46539i	0.363507	+	0.103537i
$568$	−7.23765	+	2.35165i	−0.303685	+	0.0986733i
$569$	8.73073	−	26.8704i	0.366011	−	1.12647i	−0.583334	−	0.812232i	$-0.698252\pi$
$569$	8.73073	−	26.8704i	0.366011	−	1.12647i	0.949346	−	0.314234i	$-0.101748\pi$
$570$	−2.26417	−	6.75694i	−0.0948357	−	0.283017i
$571$		−	29.7432i		−	1.24472i	−0.782733	−	0.622358i	$-0.786175\pi$
$571$		−	29.7432i		−	1.24472i	0.782733	−	0.622358i	$-0.213825\pi$
$572$	1.42008	−	2.68684i	0.0593766	−	0.112342i
$573$	−8.08552	+	11.3461i	−0.337778	+	0.473991i
$574$	2.71476	−	3.73654i	0.113312	−	0.155960i
$575$	3.54976	+	1.15339i	0.148035	+	0.0480996i
$576$	−2.39431	+	1.80757i	−0.0997627	+	0.0753153i
$577$	−34.3606	+	24.9645i	−1.43045	+	1.03928i	−0.440520	+	0.897743i	$0.645206\pi$
$577$	−34.3606	+	24.9645i	−1.43045	+	1.03928i	−0.989932	+	0.141542i	$0.954794\pi$
$578$	0.910539	−	0.661546i	0.0378734	−	0.0275167i
$579$	27.8154	+	8.75661i	1.15597	+	0.363912i
$580$	19.2619	+	6.25856i	0.799805	+	0.259872i
$581$	8.33754	−	11.4756i	0.345899	−	0.476090i
$582$	−24.0202	−	17.1173i	−0.995667	−	0.709537i
$583$	25.1094	+	25.8728i	1.03992	+	1.07154i
$584$		−	14.3089i		−	0.592107i
$585$	−2.09971	+	6.88967i	−0.0868122	+	0.284853i
$586$	2.53614	−	7.80544i	0.104767	−	0.322440i
$587$	−8.77320	+	2.85058i	−0.362109	+	0.117656i	−0.484420	−	0.874836i	$-0.660969\pi$
$587$	−8.77320	+	2.85058i	−0.362109	+	0.117656i	0.122311	+	0.992492i	$0.460969\pi$
$588$	1.73198	−	0.0158825i	0.0714256	−	0.000654982i
$589$	1.61558	+	2.22366i	0.0665690	+	0.0916243i
$590$	−0.187153	−	0.575997i	−0.00770495	−	0.0237134i
$591$	4.37573	−	3.24087i	0.179993	−	0.133312i
$592$	5.36424	+	3.89735i	0.220469	+	0.160180i
$593$	30.1833			1.23948			0.619739	−	0.784808i	$-0.287238\pi$
$593$	30.1833			1.23948			0.619739	+	0.784808i	$0.287238\pi$
$594$	15.4522	+	7.63082i	0.634012	+	0.313096i
$595$	−11.1550			−0.457309
$596$	4.64528	+	3.37499i	0.190278	+	0.138245i
$597$	8.55356	−	6.33517i	0.350074	−	0.259281i
$598$	0.566646	+	1.74396i	0.0231719	+	0.0713157i
$599$	−3.23859	−	4.45754i	−0.132325	−	0.182130i	0.737713	−	0.675115i	$-0.235906\pi$
$599$	−3.23859	−	4.45754i	−0.132325	−	0.182130i	−0.870038	+	0.492985i	$0.835906\pi$
$600$	−3.23032	+	0.0296225i	−0.131877	+	0.00120933i
$601$	−7.29963	+	2.37179i	−0.297758	+	0.0967474i	−0.454086	−	0.890958i	$-0.650034\pi$
$601$	−7.29963	+	2.37179i	−0.297758	+	0.0967474i	0.156328	+	0.987705i	$0.450034\pi$
$602$	3.66802	−	11.2890i	0.149497	−	0.460105i
$603$	5.12866	−	16.8284i	0.208855	−	0.685307i
$604$			15.7870i			0.642364i
$605$	−8.08159	−	27.6652i	−0.328564	−	1.12475i
$606$	6.73081	+	4.79654i	0.273420	+	0.194846i
$607$	−14.6867	+	20.2145i	−0.596113	+	0.820479i	−0.995346	−	0.0963704i	$-0.969277\pi$
$607$	−14.6867	+	20.2145i	−0.596113	+	0.820479i	0.399232	+	0.916850i	$0.369277\pi$
$608$	1.49341	+	0.485240i	0.0605659	+	0.0196791i
$609$	12.7705	+	4.02031i	0.517488	+	0.162911i
$610$	28.4380	−	20.6614i	1.15142	−	0.836557i
$611$	−4.23987	+	3.08045i	−0.171527	+	0.124622i
$612$	10.1935	−	7.69555i	0.412049	−	0.311074i
$613$	−9.75352	−	3.16911i	−0.393941	−	0.127999i	0.105346	−	0.994436i	$-0.466405\pi$
$613$	−9.75352	−	3.16911i	−0.393941	−	0.127999i	−0.499288	+	0.866436i	$0.666405\pi$
$614$	6.60748	−	9.09442i	0.266656	−	0.367021i
$615$	−12.1641	+	17.0695i	−0.490505	+	0.688307i
$616$	3.26766	+	0.567824i	0.131658	+	0.0228783i
$617$		−	12.7883i		−	0.514836i	−0.966300	−	0.257418i	$-0.917128\pi$
$617$		−	12.7883i		−	0.514836i	0.966300	−	0.257418i	$-0.0828718\pi$
$618$	−2.82020	−	8.41629i	−0.113445	−	0.338553i
$619$	−1.70064	+	5.23402i	−0.0683544	+	0.210373i	−0.979399	−	0.201935i	$-0.935277\pi$
$619$	−1.70064	+	5.23402i	−0.0683544	+	0.210373i	0.911045	+	0.412308i	$0.135277\pi$
$620$	4.36181	−	1.41724i	0.175175	−	0.0569177i
$621$	−9.79746	+	3.48413i	−0.393158	+	0.139813i
$622$	2.02381	+	2.78554i	0.0811474	+	0.111690i
$623$	−2.75532	−	8.47999i	−0.110389	−	0.339744i
$624$	−0.944600	−	1.27537i	−0.0378143	−	0.0510557i
$625$	24.9557	+	18.1314i	0.998227	+	0.725254i
$626$	26.2559			1.04940
$627$	−1.35939	−	8.91749i	−0.0542888	−	0.356130i
$628$	−20.6314			−0.823284
$629$	−22.8378	−	16.5926i	−0.910601	−	0.661590i
$630$	−7.85908	+	0.144150i	−0.313113	+	0.00574306i
$631$	−11.1976	−	34.4626i	−0.445768	−	1.37193i	−0.881639	−	0.471924i	$-0.843560\pi$
$631$	−11.1976	−	34.4626i	−0.445768	−	1.37193i	0.435872	−	0.900009i	$-0.356440\pi$
$632$	−1.66335	−	2.28940i	−0.0661645	−	0.0910676i
$633$	−0.0307707	−	3.35553i	−0.00122302	−	0.133371i
$634$	24.6582	−	8.01195i	0.979304	−	0.318195i
$635$	3.34653	−	10.2995i	0.132803	−	0.408725i
$636$	17.8529	−	5.98229i	0.707912	−	0.237213i
$637$			0.916304i			0.0363053i
$638$	22.6658	+	11.9796i	0.897346	+	0.474277i
$639$	21.5799	−	7.45197i	0.853688	−	0.294795i
$640$	1.54008	−	2.11973i	0.0608769	−	0.0837898i
$641$	45.1319	+	14.6642i	1.78260	+	0.579203i	0.999109	−	0.0421975i	$-0.0134359\pi$
$641$	45.1319	+	14.6642i	1.78260	+	0.579203i	0.783493	+	0.621400i	$0.213436\pi$
$642$	−0.172060	+	0.546549i	−0.00679067	+	0.0215706i
$643$	18.5666	−	13.4894i	0.732196	−	0.531971i	−0.158062	−	0.987429i	$-0.550524\pi$
$643$	18.5666	−	13.4894i	0.732196	−	0.531971i	0.890257	+	0.455458i	$0.150524\pi$
$644$	−1.61900	+	1.17627i	−0.0637976	+	0.0463517i
$645$	−16.1757	+	51.3823i	−0.636919	+	2.02317i
$646$	−6.35807	−	2.06586i	−0.250155	−	0.0812802i
$647$	−9.49447	+	13.0680i	−0.373266	+	0.513757i	−0.953785	−	0.300490i	$-0.902850\pi$
$647$	−9.49447	+	13.0680i	−0.373266	+	0.513757i	0.580519	+	0.814247i	$0.302850\pi$
$648$	7.08226	−	5.55352i	0.278218	−	0.218163i
$649$	−0.108577	−	0.758903i	−0.00426201	−	0.0297896i
$650$		−	1.70900i		−	0.0670326i
$651$	2.87468	−	0.963272i	0.112668	−	0.0377536i
$652$	3.43130	−	10.5605i	0.134380	−	0.413579i
$653$	−43.4043	+	14.1029i	−1.69854	+	0.551890i	−0.988361	−	0.152129i	$-0.951387\pi$
$653$	−43.4043	+	14.1029i	−1.69854	+	0.551890i	−0.710181	+	0.704019i	$0.751387\pi$
$654$	−0.206637	−	22.5337i	−0.00808014	−	0.881137i
$655$	−26.3812	−	36.3106i	−1.03080	−	1.41877i
$656$	−1.42723	−	4.39257i	−0.0557241	−	0.171501i
$657$	0.787221	+	42.9195i	0.0307124	+	1.67445i
$658$	−4.62714	−	3.36182i	−0.180385	−	0.131057i
$659$	19.5568			0.761827			0.380913	−	0.924611i	$-0.375610\pi$
$659$	19.5568			0.761827			0.380913	+	0.924611i	$0.375610\pi$
$660$	−14.8523	−	2.44081i	−0.578125	−	0.0950085i
$661$	7.08687			0.275647			0.137824	−	0.990457i	$-0.455989\pi$
$661$	7.08687			0.275647			0.137824	+	0.990457i	$0.455989\pi$
$662$	−1.00039	−	0.726824i	−0.0388812	−	0.0282488i
$663$	4.02154	+	5.42977i	0.156184	+	0.210875i
$664$	−4.38330	−	13.4904i	−0.170105	−	0.523530i
$665$	2.41833	+	3.32855i	0.0937789	+	0.129076i
$666$	−16.3044	−	11.3950i	−0.631784	−	0.441546i
$667$	−14.7117	+	4.78014i	−0.569641	+	0.185088i
$668$	0.0853251	−	0.262604i	0.00330133	−	0.0101604i
$669$	12.8710	+	38.4108i	0.497621	+	1.48505i
$670$			15.3650i			0.593601i
$671$	39.9437	−	19.6046i	1.54201	−	0.756827i
$672$	1.00518	−	1.41054i	0.0387757	−	0.0544126i
$673$	−9.51228	+	13.0925i	−0.366671	+	0.504680i	−0.951992	−	0.306122i	$-0.900968\pi$
$673$	−9.51228	+	13.0925i	−0.366671	+	0.504680i	0.585321	+	0.810802i	$0.300968\pi$
$674$	24.2797	+	7.88897i	0.935221	+	0.303872i
$675$	9.68771	−	0.266572i	0.372880	−	0.0102604i
$676$	−9.83796	+	7.14770i	−0.378383	+	0.274911i
$677$	19.7900	−	14.3783i	0.760590	−	0.552601i	−0.138501	−	0.990362i	$-0.544228\pi$
$677$	19.7900	−	14.3783i	0.760590	−	0.552601i	0.899091	+	0.437761i	$0.144228\pi$
$678$	16.9660	+	5.34111i	0.651577	+	0.205124i
$679$	16.1956	+	5.26228i	0.621532	+	0.201948i
$680$	−6.55673	+	9.02456i	−0.251439	+	0.346076i
$681$	11.6724	+	8.31801i	0.447286	+	0.318747i
$682$	5.74690	−	0.822213i	0.220060	−	0.0314841i
$683$			2.32409i			0.0889288i	0.999011	+	0.0444644i	$0.0141581\pi$
$683$			2.32409i			0.0889288i	−0.999011	+	0.0444644i	$0.985842\pi$
$684$	−4.50618	−	1.37331i	−0.172298	−	0.0525099i
$685$	−12.4060	+	38.1816i	−0.474007	+	1.45884i
$686$	−0.951057	+	0.309017i	−0.0363115	+	0.0117983i
$687$	21.0486	−	0.193018i	0.803054	−	0.00736411i
$688$	−6.97698	−	9.60299i	−0.265995	−	0.366110i
$689$	3.07806	+	9.47330i	0.117265	+	0.360904i
$690$	7.29811	−	5.40532i	0.277834	−	0.205777i
$691$	23.1283	+	16.8037i	0.879844	+	0.639244i	0.933210	−	0.359331i	$-0.116995\pi$
$691$	23.1283	+	16.8037i	0.879844	+	0.639244i	−0.0533663	+	0.998575i	$0.516995\pi$
$692$	1.75963			0.0668911
$693$	−9.83256	−	1.52341i	−0.373508	−	0.0578696i
$694$	−36.0861			−1.36981
$695$	17.2557	+	12.5370i	0.654544	+	0.475554i
$696$	10.7588	−	7.96850i	0.407812	−	0.302045i
$697$	6.07630	+	18.7009i	0.230156	+	0.708349i
$698$	9.21803	+	12.6875i	0.348908	+	0.480230i
$699$	15.5599	−	0.142687i	0.588531	−	0.00539690i
$700$	1.77382	−	0.576349i	0.0670441	−	0.0217840i
$701$	1.72514	−	5.30943i	0.0651575	−	0.200534i	−0.913178	−	0.407562i	$-0.866379\pi$
$701$	1.72514	−	5.30943i	0.0651575	−	0.200534i	0.978335	+	0.207028i	$0.0663790\pi$
$702$	2.90349	+	3.77350i	0.109585	+	0.142422i
$703$			10.4118i			0.392688i
$704$	2.38006	−	2.30983i	0.0897019	−	0.0870550i
$705$	21.1380	+	15.0634i	0.796101	+	0.567321i
$706$	−19.1547	+	26.3641i	−0.720896	+	0.992228i
$707$	−4.53826	−	1.47457i	−0.170679	−	0.0554569i
$708$	−0.381883	−	0.120221i	−0.0143521	−	0.00451819i
$709$	0.965624	−	0.701567i	0.0362648	−	0.0263479i	−0.569505	−	0.821988i	$-0.692865\pi$
$709$	0.965624	−	0.701567i	0.0362648	−	0.0263479i	0.605770	+	0.795640i	$0.292865\pi$
$710$	−16.1314	+	11.7202i	−0.605401	+	0.439850i
$711$	5.11516	+	6.77554i	0.191834	+	0.254103i
$712$	−8.47999	−	2.75532i	−0.317801	−	0.103260i
$713$	−2.05895	+	2.83390i	−0.0771083	+	0.106130i
$714$	−4.27947	+	6.00522i	−0.160155	+	0.224740i
$715$	1.36325	−	7.84512i	0.0509828	−	0.293391i
$716$			12.5596i			0.469374i
$717$	−5.28142	−	15.7613i	−0.197238	−	0.588616i
$718$	9.71329	−	29.8944i	0.362497	−	1.11565i
$719$	37.6422	−	12.2307i	1.40382	−	0.456127i	0.493393	−	0.869806i	$-0.335756\pi$
$719$	37.6422	−	12.2307i	1.40382	−	0.456127i	0.910423	+	0.413679i	$0.135756\pi$
$720$	−4.50283	+	6.44286i	−0.167811	+	0.240111i
$721$	3.01222	+	4.14597i	0.112181	+	0.154404i
$722$	−5.10937	−	15.7250i	−0.190151	−	0.585224i
$723$	1.20284	+	1.62404i	0.0447343	+	0.0603989i
$724$	3.77538	+	2.74297i	0.140311	+	0.101942i
$725$	14.4169			0.535430
$726$	−17.9938	−	6.26274i	−0.667814	−	0.232432i
$727$	28.9835			1.07494			0.537469	−	0.843283i	$-0.319380\pi$
$727$	28.9835			1.07494			0.537469	+	0.843283i	$0.319380\pi$
$728$	0.741305	+	0.538590i	0.0274746	+	0.0199615i
$729$	−20.9377	+	17.0474i	−0.775470	+	0.631385i
$730$	−11.5854	−	35.6563i	−0.428796	−	1.31970i
$731$	29.7038	+	40.8838i	1.09864	+	1.51214i
$732$	−0.213077	−	23.2360i	−0.00787554	−	0.858826i
$733$	−34.1311	+	11.0899i	−1.26066	+	0.409613i	−0.861730	−	0.507368i	$-0.830619\pi$
$733$	−34.1311	+	11.0899i	−1.26066	+	0.409613i	−0.398931	+	0.916981i	$0.630619\pi$
$734$	−0.789783	+	2.43070i	−0.0291514	+	0.0897188i
$735$	4.30305	−	1.44190i	0.158720	−	0.0531853i
$736$			2.00120i			0.0737651i
$737$	−3.32983	+	19.1622i	−0.122656	+	0.705848i
$738$	4.52264	+	13.0970i	0.166481	+	0.482106i
$739$	8.63485	−	11.8849i	0.317638	−	0.437191i	−0.620106	−	0.784518i	$-0.712910\pi$
$739$	8.63485	−	11.8849i	0.317638	−	0.437191i	0.937744	+	0.347327i	$0.112910\pi$
$740$	16.5227	+	5.36855i	0.607386	+	0.197352i
$741$	0.748350	−	2.37714i	0.0274913	−	0.0873263i
$742$	−8.79454	+	6.38961i	−0.322858	+	0.234570i
$743$	−25.1042	+	18.2392i	−0.920982	+	0.669133i	−0.943768	−	0.330608i	$-0.892746\pi$
$743$	−25.1042	+	18.2392i	−0.920982	+	0.669133i	0.0227861	+	0.999740i	$0.492746\pi$
$744$	0.910392	−	2.89186i	0.0333766	−	0.106021i
$745$	14.3082	+	4.64900i	0.524211	+	0.170326i
$746$	−2.15277	+	2.96304i	−0.0788186	+	0.108484i
$747$	13.8899	+	40.2233i	0.508205	+	1.47169i
$748$	−10.1329	+	9.83388i	−0.370495	+	0.359562i
$749$		−	0.330818i		−	0.0120878i
$750$	13.4896	−	4.52021i	0.492571	−	0.165055i
$751$	−9.91813	+	30.5249i	−0.361918	+	1.11387i	0.589971	+	0.807424i	$0.299139\pi$
$751$	−9.91813	+	30.5249i	−0.361918	+	1.11387i	−0.951889	+	0.306444i	$0.900861\pi$
$752$	−5.43953	+	1.76741i	−0.198359	+	0.0644509i
$753$	−0.149877	−	16.3441i	−0.00546183	−	0.595611i
$754$	4.16319	+	5.73014i	0.151614	+	0.208679i
$755$	12.7822	+	39.3395i	0.465192	+	1.43171i
$756$	−2.93744	+	4.28619i	−0.106834	+	0.155887i
$757$	−24.8663	−	18.0664i	−0.903781	−	0.656635i	0.0356534	−	0.999364i	$-0.488649\pi$
$757$	−24.8663	−	18.0664i	−0.903781	−	0.656635i	−0.939434	+	0.342729i	$0.888649\pi$
$758$	25.4141			0.923082
$759$	10.2731	−	5.15954i	0.372891	−	0.187280i
$760$	4.11431			0.149242
$761$	13.2586	+	9.63293i	0.480624	+	0.349193i	0.801567	−	0.597905i	$-0.204000\pi$
$761$	13.2586	+	9.63293i	0.480624	+	0.349193i	−0.320943	+	0.947098i	$0.604000\pi$
$762$	−4.26085	−	5.75288i	−0.154354	−	0.208405i
$763$	4.02043	+	12.3736i	0.145549	+	0.447954i
$764$	−4.72805	−	6.50760i	−0.171055	−	0.235437i
$765$	19.1704	−	27.4299i	0.693107	−	0.991729i
$766$	−23.4208	+	7.60988i	−0.846228	+	0.274956i
$767$	0.0654504	−	0.201435i	0.00236328	−	0.00727341i
$768$	−0.550316	−	1.64230i	−0.0198578	−	0.0592614i
$769$		−	33.5084i		−	1.20834i	−0.796854	−	0.604172i	$-0.793504\pi$
$769$		−	33.5084i		−	1.20834i	0.796854	−	0.604172i	$-0.206496\pi$
$770$	8.60241	−	1.23075i	0.310009	−	0.0443532i
$771$	−1.78574	+	2.50586i	−0.0643119	+	0.0902465i
$772$	−9.89609	+	13.6208i	−0.356168	+	0.490223i
$773$	−32.4733	−	10.5512i	−1.16798	−	0.379501i	−0.340094	−	0.940391i	$-0.610459\pi$
$773$	−32.4733	−	10.5512i	−1.16798	−	0.379501i	−0.827890	+	0.560890i	$0.810459\pi$
$774$	21.4557	+	28.4203i	0.771211	+	1.02155i
$775$	2.64118	−	1.91893i	0.0948740	−	0.0689300i
$776$	13.7768	−	10.0095i	0.494560	−	0.359319i
$777$	10.9545	+	3.44860i	0.392990	+	0.123718i
$778$	−30.7452	−	9.98973i	−1.10227	−	0.358149i
$779$	4.26290	−	5.86737i	0.152734	−	0.210220i
$780$	−3.38647	−	2.41328i	−0.121255	−	0.0864093i
$781$	−22.6580	+	11.1207i	−0.810766	+	0.397929i
$782$		−	8.51990i		−	0.304671i
$783$	−31.8327	+	24.4934i	−1.13761	+	0.875322i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	−51.4114	+	16.7046i	−1.83495	+	0.596212i
$786$	−29.6684	+	0.272063i	−1.05824	+	0.00970417i
$787$	−19.2718	−	26.5254i	−0.686967	−	0.945529i	0.313024	−	0.949745i	$-0.398658\pi$
$787$	−19.2718	−	26.5254i	−0.686967	−	0.945529i	−0.999991	+	0.00421634i	$0.998658\pi$
$788$	0.971485	+	2.98992i	0.0346077	+	0.106512i
$789$	15.5125	−	11.4893i	0.552258	−	0.409029i
$790$	−5.99854	−	4.35820i	−0.213419	−	0.155058i
$791$	−10.2693			−0.365134
$792$	−7.01190	+	7.05927i	−0.249157	+	0.250840i
$793$	12.2930			0.436537
$794$	−17.8557	−	12.9729i	−0.633675	−	0.460392i
$795$	39.6438	−	29.3621i	1.40602	−	1.04137i
$796$	1.89903	+	5.84462i	0.0673094	+	0.207157i
$797$	3.38186	+	4.65473i	0.119792	+	0.164879i	0.864701	−	0.502286i	$-0.167508\pi$
$797$	3.38186	+	4.65473i	0.119792	+	0.164879i	−0.744910	+	0.667165i	$0.767508\pi$
$798$	2.71967	−	0.0249397i	0.0962753	−	0.000882857i
$799$	23.1583	−	7.52459i	0.819282	−	0.266201i
$800$	0.576349	−	1.77382i	0.0203770	−	0.0627140i
$801$	25.5873	+	7.79802i	0.904083	+	0.275530i
$802$		−	3.73610i		−	0.131926i
$803$	−6.72130	−	46.9789i	−0.237190	−	1.65785i
$804$	8.27166	+	5.89459i	0.291719	+	0.207886i
$805$	−3.08200	+	4.24200i	−0.108626	+	0.149511i
$806$	1.52540	+	0.495632i	0.0537298	+	0.0174579i
$807$	26.7375	+	8.41726i	0.941203	+	0.296302i
$808$	−3.86048	+	2.80480i	−0.135811	+	0.0986725i
$809$	15.6956	−	11.4035i	0.551828	−	0.400927i	−0.276631	−	0.960976i	$-0.589218\pi$
$809$	15.6956	−	11.4035i	0.551828	−	0.400927i	0.828459	+	0.560050i	$0.189218\pi$
$810$	13.1518	−	19.5731i	0.462106	−	0.687727i
$811$	47.5016	+	15.4342i	1.66801	+	0.541968i	0.982526	−	0.186124i	$-0.0595926\pi$
$811$	47.5016	+	15.4342i	1.66801	+	0.541968i	0.685480	+	0.728092i	$0.259593\pi$
$812$	−4.54346	+	6.25354i	−0.159444	+	0.219456i
$813$	−24.6613	+	34.6063i	−0.864910	+	1.21370i
$814$	19.4425	+	10.2760i	0.681461	+	0.360174i
$815$		−	29.0938i		−	1.01911i
$816$	2.34292	+	6.99194i	0.0820185	+	0.244767i
$817$	5.75977	−	17.7267i	0.201509	−	0.620180i
$818$	−9.65726	+	3.13783i	−0.337658	+	0.109712i
$819$	−2.25317	−	1.57471i	−0.0787323	−	0.0550250i
$820$	−7.11303	−	9.79025i	−0.248398	−	0.341890i
$821$	10.3637	+	31.8960i	0.361694	+	1.11318i	0.952025	+	0.306019i	$0.0989970\pi$
$821$	10.3637	+	31.8960i	0.361694	+	1.11318i	−0.590332	+	0.807161i	$0.701003\pi$
$822$	15.7955	+	21.3266i	0.550930	+	0.743850i
$823$	20.7324	+	15.0629i	0.722685	+	0.525061i	0.887241	−	0.461306i	$-0.152619\pi$
$823$	20.7324	+	15.0629i	0.722685	+	0.525061i	−0.164556	+	0.986368i	$0.552619\pi$
$824$	5.12470			0.178527
$825$	−10.5919	+	1.61463i	−0.368761	+	0.0562142i
$826$	0.231148			0.00804267
$827$	−18.8660	−	13.7069i	−0.656034	−	0.476636i	0.209287	−	0.977854i	$-0.432886\pi$
$827$	−18.8660	−	13.7069i	−0.656034	−	0.476636i	−0.865321	+	0.501218i	$0.832886\pi$
$828$	−0.110098	−	6.00258i	−0.00382618	−	0.208604i
$829$	−1.49661	−	4.60610i	−0.0519795	−	0.159976i	0.921697	−	0.387910i	$-0.126803\pi$
$829$	−1.49661	−	4.60610i	−0.0519795	−	0.159976i	−0.973677	+	0.227934i	$0.926803\pi$
$830$	−21.8455	−	30.0677i	−0.758267	−	1.04367i
$831$	−0.210013	−	22.9019i	−0.00728528	−	0.794458i
$832$	0.871457	−	0.283154i	0.0302123	−	0.00981658i
$833$	1.31561	−	4.04903i	0.0455832	−	0.140291i
$834$	13.3691	−	4.47984i	0.462935	−	0.155124i
$835$		−	0.723466i		−	0.0250366i
$836$	5.13110	+	0.891636i	0.177463	+	0.0308379i
$837$	−2.57162	+	8.72422i	−0.0888881	+	0.301553i
$838$	4.33217	−	5.96272i	0.149652	−	0.205979i
$839$	−39.5176	−	12.8400i	−1.36430	−	0.443287i	−0.466822	−	0.884351i	$-0.654601\pi$
$839$	−39.5176	−	12.8400i	−1.36430	−	0.443287i	−0.897476	+	0.441064i	$0.854601\pi$
$840$	1.36275	−	4.32877i	0.0470192	−	0.149357i
$841$	−24.8771	+	18.0743i	−0.857831	+	0.623250i
$842$	16.1385	−	11.7253i	0.556170	−	0.404081i
$843$	−10.0983	+	32.0772i	−0.347803	+	1.10480i
$844$	1.84258	+	0.598690i	0.0634241	+	0.0206077i
$845$	−18.7279	+	25.7768i	−0.644260	+	0.886748i
$846$	16.2186	−	5.60061i	0.557608	−	0.192553i
$847$	10.9951	+	0.329364i	0.377795	+	0.0113171i
$848$			10.8706i			0.373300i
$849$	3.69915	−	1.23954i	0.126955	−	0.0425410i
$850$	−2.45375	+	7.55187i	−0.0841630	+	0.259027i
$851$	−12.6196	+	4.10037i	−0.432596	+	0.140559i
$852$	0.120867	+	13.1806i	0.00414085	+	0.451558i
$853$	−3.62573	−	4.99038i	−0.124143	−	0.170867i	0.742422	−	0.669932i	$-0.233677\pi$
$853$	−3.62573	−	4.99038i	−0.124143	−	0.170867i	−0.866565	+	0.499065i	$0.833677\pi$
$854$	4.14573	+	12.7592i	0.141864	+	0.436612i
$855$	−12.3409	+	0.226354i	−0.422049	+	0.00774113i
$856$	−0.267637	−	0.194450i	−0.00914765	−	0.00664615i
$857$	−26.8084			−0.915758			−0.457879	−	0.889015i	$-0.651391\pi$
$857$	−26.8084			−0.915758			−0.457879	+	0.889015i	$0.651391\pi$
$858$	−3.70038	−	3.74358i	−0.126329	−	0.127804i
$859$	14.4684			0.493655			0.246828	−	0.969059i	$-0.420612\pi$
$859$	14.4684			0.493655			0.246828	+	0.969059i	$0.420612\pi$
$860$	−25.1611	−	18.2806i	−0.857987	−	0.623364i
$861$	−4.76125	−	6.42849i	−0.162263	−	0.219082i
$862$	11.2167	+	34.5214i	0.382042	+	1.17580i
$863$	12.8304	+	17.6595i	0.436750	+	0.601135i	0.969486	−	0.245146i	$-0.0788360\pi$
$863$	12.8304	+	17.6595i	0.436750	+	0.601135i	−0.532736	+	0.846282i	$0.678836\pi$
$864$	1.74102	+	4.89580i	0.0592308	+	0.166558i
$865$	4.38482	−	1.42471i	0.149088	−	0.0484417i
$866$	11.6849	−	35.9624i	0.397069	−	1.22205i
$867$	−0.619374	−	1.84839i	−0.0210350	−	0.0627746i
$868$			1.75040i			0.0594124i
$869$	−6.53649	−	6.73523i	−0.221735	−	0.228477i
$870$	20.3581	−	28.5677i	0.690203	−	0.968536i
$871$	−3.15840	+	4.34716i	−0.107018	+	0.147298i
$872$	12.3736	+	4.02043i	0.419023	+	0.136149i
$873$	−40.7729	+	30.7813i	−1.37995	+	1.04179i
$874$	−2.54227	+	1.84707i	−0.0859935	+	0.0624779i
$875$	−6.64514	+	4.82798i	−0.224647	+	0.163215i
$876$	−23.6400	−	7.44214i	−0.798721	−	0.251447i
$877$	−28.5577	−	9.27896i	−0.964325	−	0.313328i	−0.215802	−	0.976437i	$-0.569237\pi$
$877$	−28.5577	−	9.27896i	−0.964325	−	0.313328i	−0.748523	+	0.663109i	$0.769237\pi$
$878$	0.407438	−	0.560791i	0.0137504	−	0.0189258i
$879$	−11.5764	−	8.24965i	−0.390463	−	0.278254i
$880$	4.06067	−	7.68291i	0.136885	−	0.258991i
$881$		−	13.6297i		−	0.459196i	−0.973286	−	0.229598i	$-0.926259\pi$
$881$		−	13.6297i		−	0.459196i	0.973286	−	0.229598i	$-0.0737411\pi$
$882$	0.874572	−	2.86969i	0.0294484	−	0.0966275i
$883$	11.8546	−	36.4848i	0.398940	−	1.22781i	−0.526911	−	0.849920i	$-0.676650\pi$
$883$	11.8546	−	36.4848i	0.398940	−	1.22781i	0.925851	−	0.377889i	$-0.123350\pi$
$884$	−3.71014	+	1.20550i	−0.124786	+	0.0405453i
$885$	−1.04895	+	0.00961903i	−0.0352602	+	0.000323340i
$886$	−8.14469	−	11.2102i	−0.273626	−	0.376614i
$887$	5.47025	+	16.8357i	0.183673	+	0.565288i	0.999923	−	0.0124113i	$-0.00395075\pi$
$887$	5.47025	+	16.8357i	0.183673	+	0.565288i	−0.816250	+	0.577699i	$0.803951\pi$
$888$	9.22885	−	6.83533i	0.309700	−	0.229378i
$889$	3.34384	+	2.42944i	0.112149	+	0.0814809i
$890$	−23.3622			−0.783101
$891$	20.6438	−	21.5600i	0.691593	−	0.722288i
$892$	−23.3884			−0.783101
$893$	−7.26586	−	5.27895i	−0.243143	−	0.176653i
$894$	7.99192	−	5.91919i	0.267290	−	0.197967i
$895$	10.1691	+	31.2972i	0.339915	+	1.04615i
$896$	0.587785	+	0.809017i	0.0196365	+	0.0270274i
$897$	3.17594	−	0.0291237i	0.106041	−	0.000972414i
$898$	−7.95211	+	2.58380i	−0.265365	+	0.0862224i
$899$	−4.18107	+	12.8680i	−0.139447	+	0.429172i
$900$	−1.63117	+	5.35228i	−0.0543723	+	0.178409i
$901$		−	46.2807i		−	1.54183i
$902$	−6.74919	−	13.7512i	−0.224724	−	0.457866i
$903$	−16.7430	−	11.9315i	−0.557171	−	0.397054i
$904$	−6.03613	+	8.30802i	−0.200759	+	0.276321i
$905$	11.6287	+	3.77841i	0.386552	+	0.125598i
$906$	26.0820	+	8.21090i	0.866515	+	0.272789i
$907$	−44.1679	+	32.0899i	−1.46657	+	1.06553i	−0.484982	+	0.874524i	$0.661174\pi$
$907$	−44.1679	+	32.0899i	−1.46657	+	1.06553i	−0.981590	+	0.191002i	$0.938826\pi$
$908$	−6.69472	+	4.86400i	−0.222172	+	0.161417i
$909$	11.4252	−	8.62537i	0.378949	−	0.286086i
$910$	2.28333	+	0.741900i	0.0756918	+	0.0245938i
$911$	−19.3486	+	26.6311i	−0.641048	+	0.882327i	−0.998671	−	0.0515390i	$-0.983587\pi$
$911$	−19.3486	+	26.6311i	−0.641048	+	0.882327i	0.357623	+	0.933866i	$0.383587\pi$
$912$	1.57841	−	2.21492i	0.0522662	−	0.0733433i
$913$	−20.7281	−	42.2327i	−0.685999	−	1.39770i
$914$			39.0364i			1.29121i
$915$	−19.3443	−	57.7291i	−0.639504	−	1.90846i
$916$	−3.75546	+	11.5581i	−0.124084	+	0.381891i
$917$	16.2914	−	5.29339i	0.537989	−	0.174803i
$918$	−7.41224	−	20.8434i	−0.244640	−	0.687934i
$919$	−22.6716	−	31.2048i	−0.747867	−	1.02935i	−0.998127	−	0.0611717i	$-0.980516\pi$
$919$	−22.6716	−	31.2048i	−0.747867	−	1.02935i	0.250261	−	0.968179i	$-0.419484\pi$
$920$	1.62030	+	4.98678i	0.0534198	+	0.164409i
$921$	−11.5885	−	15.6464i	−0.381853	−	0.515566i
$922$	29.9934	+	21.7915i	0.987781	+	0.717665i
$923$	−6.97318			−0.229525
$924$	2.63764	−	5.10322i	0.0867719	−	0.167884i
$925$	12.3667			0.406615
$926$	−32.2385	−	23.4226i	−1.05942	−	0.769715i
$927$	−15.3715	+	0.281941i	−0.504866	+	0.00926016i
$928$	2.38864	+	7.35147i	0.0784109	+	0.241324i
$929$	−16.0430	−	22.0813i	−0.526353	−	0.724463i	0.460216	−	0.887807i	$-0.347772\pi$
$929$	−16.0430	−	22.0813i	−0.526353	−	0.724463i	−0.986569	+	0.163344i	$0.947772\pi$
$930$	−0.0728414	−	7.94334i	−0.00238856	−	0.260472i
$931$	−1.49341	+	0.485240i	−0.0489447	+	0.0159031i
$932$	−2.77618	+	8.54420i	−0.0909368	+	0.279875i
$933$	5.65462	−	1.89480i	0.185124	−	0.0620329i
$934$		−	26.3745i		−	0.863001i
$935$	−17.2879	+	32.7093i	−0.565375	+	1.06971i
$936$	−2.59835	+	0.897262i	−0.0849298	+	0.0293279i
$937$	−5.87081	+	8.08048i	−0.191791	+	0.263978i	−0.894073	−	0.447921i	$-0.852165\pi$
$937$	−5.87081	+	8.08048i	−0.191791	+	0.263978i	0.702282	+	0.711899i	$0.252165\pi$
$938$	−5.57718	−	1.81214i	−0.182102	−	0.0591684i
$939$	13.6559	−	43.3779i	0.445642	−	1.41558i
$940$	−12.1237	+	8.80841i	−0.395433	+	0.287299i
$941$	6.17279	−	4.48479i	0.201227	−	0.146200i	−0.482608	−	0.875836i	$-0.660311\pi$
$941$	6.17279	−	4.48479i	0.201227	−	0.146200i	0.683836	+	0.729636i	$0.260311\pi$
$942$	−10.7305	+	34.0856i	−0.349619	+	1.11057i
$943$	8.79040	+	2.85617i	0.286255	+	0.0930098i
$944$	0.135865	−	0.187003i	0.00442204	−	0.00608642i
$945$	−3.84940	+	13.0591i	−0.125221	+	0.424812i
$946$	−27.4176	−	28.2512i	−0.891422	−	0.918525i
$947$			38.5374i			1.25230i	0.779704	+	0.626148i	$0.215369\pi$
$947$			38.5374i			1.25230i	−0.779704	+	0.626148i	$0.784631\pi$
$948$	−4.64748	+	1.55732i	−0.150943	+	0.0505793i
$949$	4.05162	−	12.4696i	0.131521	−	0.404780i
$950$	2.78537	−	0.905023i	0.0903695	−	0.0293628i
$951$	−0.411788	−	44.9053i	−0.0133531	−	1.45616i
$952$	−2.50244	−	3.44431i	−0.0811045	−	0.111631i
$953$	−5.14328	−	15.8294i	−0.166607	−	0.512764i	0.832544	−	0.553959i	$-0.186884\pi$
$953$	−5.14328	−	15.8294i	−0.166607	−	0.512764i	−0.999151	+	0.0411948i	$0.986884\pi$
$954$	−0.598061	−	32.6065i	−0.0193629	−	1.05567i
$955$	−17.0508	−	12.3881i	−0.551751	−	0.400870i
$956$	9.59707			0.310392
$957$	31.5803	−	31.2158i	1.02085	−	1.00906i
$958$	22.8913			0.739583
$959$	−12.3960	−	9.00623i	−0.400288	−	0.290826i
$960$	−2.70105	−	3.64687i	−0.0871759	−	0.117702i
$961$	−8.63273	−	26.5688i	−0.278475	−	0.857058i
$962$	3.57116	+	4.91528i	0.115139	+	0.158475i
$963$	0.813474	+	0.568527i	0.0262138	+	0.0183205i
$964$	−1.10970	+	0.360565i	−0.0357412	+	0.0116130i
$965$	−13.6317	+	41.9541i	−0.438821	+	1.35055i
$966$	1.10129	+	3.28657i	0.0354334	+	0.105744i
$967$		−	22.9812i		−	0.739026i	−0.929226	−	0.369513i	$-0.879525\pi$
$967$		−	22.9812i		−	0.739026i	0.929226	−	0.369513i	$-0.120475\pi$
$968$	6.72920	−	8.70160i	0.216285	−	0.279680i
$969$	−6.71991	+	9.42980i	−0.215875	+	0.302929i
$970$	26.2261	−	36.0972i	0.842070	−	1.15901i
$971$	−18.3182	−	5.95193i	−0.587857	−	0.191006i	−3.98952e−5	−	1.00000i	$-0.500013\pi$
$971$	−18.3182	−	5.95193i	−0.587857	−	0.191006i	−0.587818	+	0.808994i	$0.700013\pi$
$972$	−5.49154	−	14.5891i	−0.176141	−	0.467947i
$973$	−6.58579	+	4.78486i	−0.211131	+	0.153395i
$974$	14.2180	−	10.3300i	0.455575	−	0.330994i
$975$	−2.82347	−	0.888862i	−0.0904235	−	0.0284664i
$976$	12.7592	+	4.14573i	0.408413	+	0.132701i
$977$	−27.9940	+	38.5305i	−0.895608	+	1.23270i	0.0762392	+	0.997090i	$0.475709\pi$
$977$	−27.9940	+	38.5305i	−0.895608	+	1.23270i	−0.971848	+	0.235610i	$0.924291\pi$
$978$	−15.6625	−	11.1615i	−0.500831	−	0.356904i
$979$	−29.1357	−	5.06294i	−0.931181	−	0.161812i
$980$			2.62013i			0.0836971i
$981$	−37.3357	−	11.3785i	−1.19204	−	0.363288i
$982$	−2.36230	+	7.27043i	−0.0753842	+	0.232009i
$983$	45.0741	−	14.6455i	1.43764	−	0.467118i	0.516479	−	0.856300i	$-0.327242\pi$
$983$	45.0741	−	14.6455i	1.43764	−	0.467118i	0.921161	+	0.389182i	$0.127242\pi$
$984$	−7.99935	+	0.0733551i	−0.255010	+	0.00233847i
$985$	4.84168	+	6.66400i	0.154269	+	0.212333i
$986$	−10.1694	−	31.2982i	−0.323860	−	0.996738i
$987$	−7.96072	+	5.89608i	−0.253392	+	0.187674i
$988$	1.16405	+	0.845731i	0.0370333	+	0.0269063i
$989$	23.7541			0.755337
$990$	−11.7573	+	23.2683i	−0.373671	+	0.739514i
$991$	2.58100			0.0819882			0.0409941	−	0.999159i	$-0.486948\pi$
$991$	2.58100			0.0819882			0.0409941	+	0.999159i	$0.486948\pi$
$992$	1.41610	+	1.02886i	0.0449613	+	0.0326663i
$993$	−1.72111	+	1.27473i	−0.0546176	+	0.0404524i
$994$	−2.35165	−	7.23765i	−0.0745900	−	0.229564i
$995$	9.46438	+	13.0266i	0.300041	+	0.412971i
$996$	−24.5675	+	0.225287i	−0.778452	+	0.00713851i
$997$	40.3948	−	13.1251i	1.27932	−	0.415675i	0.410977	−	0.911646i	$-0.365188\pi$
$997$	40.3948	−	13.1251i	1.27932	−	0.415675i	0.868339	+	0.495970i	$0.165188\pi$
$998$	12.1296	−	37.3310i	0.383955	−	1.18169i
$999$	−27.3059	+	21.0103i	−0.863919	+	0.664735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.w.b.29.9	yes	48
3.2	odd	2		462.2.w.a.29.6	✓	48
11.8	odd	10		462.2.w.a.239.6	yes	48
33.8	even	10	inner	462.2.w.b.239.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.w.a.29.6	✓	48	3.2	odd	2
462.2.w.a.239.6	yes	48	11.8	odd	10
462.2.w.b.29.9	yes	48	1.1	even	1	trivial
462.2.w.b.239.9	yes	48	33.8	even	10	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(1.39186 - 1.03088i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.54008 + 2.11973i) q^{5} +(1.73198 - 0.0158825i) q^{6} +(-0.951057 + 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.874572 - 2.86969i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(1.39186 - 1.03088i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.54008 + 2.11973i) q^{5} +(1.73198 - 0.0158825i) q^{6} +(-0.951057 + 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.874572 - 2.86969i) q^{9} +2.62013i q^{10} +(-0.567824 + 3.26766i) q^{11} +(1.41054 + 1.00518i) q^{12} +(-0.538590 + 0.741305i) q^{13} +(-0.951057 - 0.309017i) q^{14} +(4.32877 + 1.36275i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.44431 - 2.50244i) q^{17} +(2.39431 - 1.80757i) q^{18} +(-1.49341 - 0.485240i) q^{19} +(-1.54008 + 2.11973i) q^{20} +(-1.00518 + 1.41054i) q^{21} +(-2.38006 + 2.30983i) q^{22} -2.00120i q^{23} +(0.550316 + 1.64230i) q^{24} +(-0.576349 + 1.77382i) q^{25} +(-0.871457 + 0.283154i) q^{26} +(-1.74102 - 4.89580i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-2.38864 - 7.35147i) q^{29} +(2.70105 + 3.64687i) q^{30} +(-1.41610 - 1.02886i) q^{31} -1.00000 q^{32} +(2.57823 + 5.13349i) q^{33} +4.25740 q^{34} +(-2.11973 - 1.54008i) q^{35} +(2.99950 - 0.0550161i) q^{36} +(-2.04896 - 6.30605i) q^{37} +(-0.922980 - 1.27037i) q^{38} +(0.0145532 + 1.58702i) q^{39} +(-2.49190 + 0.809666i) q^{40} +(-1.42723 + 4.39257i) q^{41} +(-1.64230 + 0.550316i) q^{42} +11.8699i q^{43} +(-3.28319 + 0.469729i) q^{44} +(7.42989 - 2.56568i) q^{45} +(1.17627 - 1.61900i) q^{46} +(5.43953 + 1.76741i) q^{47} +(-0.520106 + 1.65212i) q^{48} +(0.809017 - 0.587785i) q^{49} +(-1.50890 + 1.09628i) q^{50} +(2.21430 - 7.03373i) q^{51} +(-0.871457 - 0.283154i) q^{52} +(6.38961 - 8.79454i) q^{53} +(1.46916 - 4.98413i) q^{54} +(-7.80105 + 3.82880i) q^{55} -1.00000i q^{56} +(-2.57885 + 0.864143i) q^{57} +(2.38864 - 7.35147i) q^{58} +(-0.219835 + 0.0714286i) q^{59} +(0.0416142 + 4.53802i) q^{60} +(-7.88564 - 10.8537i) q^{61} +(-0.540903 - 1.66473i) q^{62} +(0.0550161 + 2.99950i) q^{63} +(-0.809017 - 0.587785i) q^{64} -2.40084 q^{65} +(-0.931560 + 5.66853i) q^{66} +5.86420 q^{67} +(3.44431 + 2.50244i) q^{68} +(-2.06299 - 2.78539i) q^{69} +(-0.809666 - 2.49190i) q^{70} +(4.47311 + 6.15671i) q^{71} +(2.45898 + 1.71855i) q^{72} +(-13.6086 + 4.42169i) q^{73} +(2.04896 - 6.30605i) q^{74} +(1.02640 + 3.06306i) q^{75} -1.57027i q^{76} +(-0.469729 - 3.28319i) q^{77} +(-0.921052 + 1.29248i) q^{78} +(-1.66335 + 2.28940i) q^{79} +(-2.49190 - 0.809666i) q^{80} +(-7.47025 - 5.01950i) q^{81} +(-3.73654 + 2.71476i) q^{82} +(-11.4756 + 8.33754i) q^{83} +(-1.65212 - 0.520106i) q^{84} +(10.6090 + 3.44708i) q^{85} +(-6.97698 + 9.60299i) q^{86} +(-10.9032 - 7.76985i) q^{87} +(-2.93226 - 1.54979i) q^{88} +8.91639i q^{89} +(7.51898 + 2.29150i) q^{90} +(0.283154 - 0.871457i) q^{91} +(1.90325 - 0.618404i) q^{92} +(-3.03165 + 0.0278006i) q^{93} +(3.36182 + 4.62714i) q^{94} +(-1.27139 - 3.91295i) q^{95} +(-1.39186 + 1.03088i) q^{96} +(-13.7768 - 10.0095i) q^{97} +1.00000 q^{98} +(8.88056 + 4.48728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 6 * q^12 - 24 * q^15 - 12 * q^16 + 24 * q^17 + 10 * q^18 + 30 * q^19 - 8 * q^22 - 6 * q^24 + 18 * q^25 + 20 * q^26 + 38 * q^27 - 8 * q^29 - 36 * q^30 - 32 * q^31 - 48 * q^32 + 24 * q^33 - 4 * q^34 - 6 * q^35 - 20 * q^37 - 20 * q^38 - 34 * q^39 - 22 * q^44 + 12 * q^45 + 20 * q^46 - 20 * q^47 - 4 * q^48 + 12 * q^49 - 28 * q^50 + 2 * q^51 + 20 * q^52 - 20 * q^53 - 18 * q^54 + 16 * q^55 + 12 * q^57 + 8 * q^58 - 30 * q^59 - 4 * q^60 - 20 * q^61 - 8 * q^62 - 4 * q^63 - 12 * q^64 + 46 * q^66 + 36 * q^67 + 24 * q^68 + 30 * q^69 - 4 * q^70 - 10 * q^72 - 20 * q^73 + 20 * q^74 + 40 * q^75 + 16 * q^77 - 16 * q^78 - 20 * q^79 - 54 * q^81 - 10 * q^82 + 46 * q^83 - 10 * q^84 + 10 * q^85 + 30 * q^86 - 8 * q^87 - 8 * q^88 - 62 * q^90 - 36 * q^91 - 10 * q^92 + 44 * q^93 - 50 * q^95 + 4 * q^96 - 2 * q^97 + 48 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more