LMFDB - Embedded newform 714.2.w.e.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(83,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 4, 3]))

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

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

chi := DirichletCharacter("714.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.w (of order $8$, 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	714.83
Dual form			714.2.w.e.671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.72967 + 0.0907356i) q^{3} -1.00000i q^{4} +(-1.23141 + 0.510066i) q^{5} +(-1.15890 + 1.28722i) q^{6} +(0.516019 - 2.59494i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98353 - 0.313886i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.72967 + 0.0907356i) q^{3} -1.00000i q^{4} +(-1.23141 + 0.510066i) q^{5} +(-1.15890 + 1.28722i) q^{6} +(0.516019 - 2.59494i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98353 - 0.313886i) q^{9} +(-0.510066 + 1.23141i) q^{10} +(0.931721 + 0.385932i) q^{11} +(0.0907356 + 1.72967i) q^{12} -4.76028 q^{13} +(-1.47002 - 2.19978i) q^{14} +(2.08365 - 0.993980i) q^{15} -1.00000 q^{16} +(3.30769 - 2.46154i) q^{17} +(1.88773 - 2.33163i) q^{18} +(-4.09837 + 4.09837i) q^{19} +(0.510066 + 1.23141i) q^{20} +(-0.657091 + 4.53522i) q^{21} +(0.931721 - 0.385932i) q^{22} +(-4.55721 - 1.88766i) q^{23} +(1.28722 + 1.15890i) q^{24} +(-2.27934 + 2.27934i) q^{25} +(-3.36602 + 3.36602i) q^{26} +(-5.13206 + 0.813632i) q^{27} +(-2.59494 - 0.516019i) q^{28} +(-1.86801 - 4.50977i) q^{29} +(0.770515 - 2.17621i) q^{30} +(-7.40204 + 3.06602i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.64659 - 0.582995i) q^{33} +(0.598324 - 4.07946i) q^{34} +(0.688161 + 3.45864i) q^{35} +(-0.313886 - 2.98353i) q^{36} +(-1.86713 - 4.50765i) q^{37} +5.79598i q^{38} +(8.23372 - 0.431926i) q^{39} +(1.23141 + 0.510066i) q^{40} +(7.95541 + 3.29524i) q^{41} +(2.74225 + 3.67152i) q^{42} +(-6.70448 + 6.70448i) q^{43} +(0.385932 - 0.931721i) q^{44} +(-3.51385 + 1.90832i) q^{45} +(-4.55721 + 1.88766i) q^{46} -9.15054i q^{47} +(1.72967 - 0.0907356i) q^{48} +(-6.46745 - 2.67808i) q^{49} +3.22347i q^{50} +(-5.49788 + 4.55778i) q^{51} +4.76028i q^{52} +(-9.36723 + 9.36723i) q^{53} +(-3.05359 + 4.20424i) q^{54} -1.34418 q^{55} +(-2.19978 + 1.47002i) q^{56} +(6.71698 - 7.46071i) q^{57} +(-4.50977 - 1.86801i) q^{58} +(0.517174 - 0.517174i) q^{59} +(-0.993980 - 2.08365i) q^{60} +(4.78410 - 11.5498i) q^{61} +(-3.06602 + 7.40204i) q^{62} +(0.725046 - 7.90407i) q^{63} +1.00000i q^{64} +(5.86184 - 2.42805i) q^{65} +(-1.57656 + 0.752076i) q^{66} +2.49006 q^{67} +(-2.46154 - 3.30769i) q^{68} +(8.05375 + 2.85153i) q^{69} +(2.93223 + 1.95902i) q^{70} +(7.37814 - 3.05612i) q^{71} +(-2.33163 - 1.88773i) q^{72} +(2.62613 + 6.34003i) q^{73} +(-4.50765 - 1.86713i) q^{74} +(3.73569 - 4.14932i) q^{75} +(4.09837 + 4.09837i) q^{76} +(1.48226 - 2.21861i) q^{77} +(5.51670 - 6.12754i) q^{78} +(1.01712 - 2.45554i) q^{79} +(1.23141 - 0.510066i) q^{80} +(8.80295 - 1.87298i) q^{81} +(7.95541 - 3.29524i) q^{82} +(-7.42733 - 7.42733i) q^{83} +(4.53522 + 0.657091i) q^{84} +(-2.81758 + 4.71830i) q^{85} +9.48157i q^{86} +(3.64024 + 7.63093i) q^{87} +(-0.385932 - 0.931721i) q^{88} +11.3660i q^{89} +(-1.13528 + 3.83405i) q^{90} +(-2.45639 + 12.3526i) q^{91} +(-1.88766 + 4.55721i) q^{92} +(12.5249 - 5.97484i) q^{93} +(-6.47041 - 6.47041i) q^{94} +(2.95633 - 7.13721i) q^{95} +(1.15890 - 1.28722i) q^{96} +(-1.10080 - 2.65756i) q^{97} +(-6.46687 + 2.67949i) q^{98} +(2.90096 + 0.858986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 16 q^{7}+O(q^{10}) $ 80 * q - 16 * q^7	$ 80 q - 16 q^{7} - 16 q^{14} - 16 q^{15} - 80 q^{16} + 16 q^{18} - 32 q^{21} - 16 q^{23} - 32 q^{25} + 64 q^{29} - 16 q^{30} - 48 q^{37} + 16 q^{39} - 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{49} + 104 q^{51} - 80 q^{53} - 16 q^{57} - 16 q^{58} - 48 q^{60} + 56 q^{63} + 80 q^{65} - 144 q^{67} + 8 q^{70} + 16 q^{71} - 32 q^{74} - 24 q^{77} + 32 q^{78} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} + 16 q^{92} + 48 q^{93} - 16 q^{95} - 16 q^{98} + 80 q^{99}+O(q^{100}) $ 80 * q - 16 * q^7 - 16 * q^14 - 16 * q^15 - 80 * q^16 + 16 * q^18 - 32 * q^21 - 16 * q^23 - 32 * q^25 + 64 * q^29 - 16 * q^30 - 48 * q^37 + 16 * q^39 - 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^49 + 104 * q^51 - 80 * q^53 - 16 * q^57 - 16 * q^58 - 48 * q^60 + 56 * q^63 + 80 * q^65 - 144 * q^67 + 8 * q^70 + 16 * q^71 - 32 * q^74 - 24 * q^77 + 32 * q^78 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 + 16 * q^92 + 48 * q^93 - 16 * q^95 - 16 * q^98 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.72967	+	0.0907356i	−0.998627	+	0.0523862i
$3$	−1.72967	+	0.0907356i	−0.998627	+	0.0523862i
$4$		−	1.00000i		−	0.500000i
$5$	−1.23141	+	0.510066i	−0.550702	+	0.228108i	−0.640643	−	0.767839i	$-0.721332\pi$
$5$	−1.23141	+	0.510066i	−0.550702	+	0.228108i	0.0899408	+	0.995947i	$0.471332\pi$
$6$	−1.15890	+	1.28722i	−0.473120	+	0.525507i
$7$	0.516019	−	2.59494i	0.195037	−	0.980796i
$7$	0.516019	−	2.59494i	0.195037	−	0.980796i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.98353	−	0.313886i	0.994511	−	0.104629i
$10$	−0.510066	+	1.23141i	−0.161297	+	0.389405i
$11$	0.931721	+	0.385932i	0.280925	+	0.116363i	0.518697	−	0.854958i	$-0.326417\pi$
$11$	0.931721	+	0.385932i	0.280925	+	0.116363i	−0.237772	+	0.971321i	$0.576417\pi$
$12$	0.0907356	+	1.72967i	0.0261931	+	0.499313i
$13$	−4.76028			−1.32026			−0.660131	−	0.751150i	$-0.729499\pi$
$13$	−4.76028			−1.32026			−0.660131	+	0.751150i	$0.729499\pi$
$14$	−1.47002	−	2.19978i	−0.392879	−	0.587916i
$15$	2.08365	−	0.993980i	0.537997	−	0.256644i
$16$	−1.00000			−0.250000
$17$	3.30769	−	2.46154i	0.802234	−	0.597010i
$17$	3.30769	−	2.46154i	0.802234	−	0.597010i
$18$	1.88773	−	2.33163i	0.444941	−	0.549570i
$19$	−4.09837	+	4.09837i	−0.940232	+	0.940232i	−0.998312	−	0.0580804i	$-0.981502\pi$
$19$	−4.09837	+	4.09837i	−0.940232	+	0.940232i	0.0580804	+	0.998312i	$0.481502\pi$
$20$	0.510066	+	1.23141i	0.114054	+	0.275351i
$21$	−0.657091	+	4.53522i	−0.143389	+	0.989666i
$22$	0.931721	−	0.385932i	0.198644	−	0.0822809i
$23$	−4.55721	−	1.88766i	−0.950243	−	0.393604i	−0.146921	−	0.989148i	$-0.546936\pi$
$23$	−4.55721	−	1.88766i	−0.950243	−	0.393604i	−0.803322	+	0.595545i	$0.796936\pi$
$24$	1.28722	+	1.15890i	0.262753	+	0.236560i
$25$	−2.27934	+	2.27934i	−0.455867	+	0.455867i
$26$	−3.36602	+	3.36602i	−0.660131	+	0.660131i
$27$	−5.13206	+	0.813632i	−0.987665	+	0.156584i
$28$	−2.59494	−	0.516019i	−0.490398	−	0.0975185i
$29$	−1.86801	−	4.50977i	−0.346880	−	0.837443i	−0.996985	−	0.0775981i	$-0.975275\pi$
$29$	−1.86801	−	4.50977i	−0.346880	−	0.837443i	0.650105	−	0.759845i	$-0.274725\pi$
$30$	0.770515	−	2.17621i	0.140676	−	0.397320i
$31$	−7.40204	+	3.06602i	−1.32944	+	0.550674i	−0.930497	−	0.366299i	$-0.880625\pi$
$31$	−7.40204	+	3.06602i	−1.32944	+	0.550674i	−0.398948	+	0.916974i	$0.630625\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.64659	−	0.582995i	−0.286635	−	0.101486i
$34$	0.598324	−	4.07946i	0.102612	−	0.699622i
$35$	0.688161	+	3.45864i	0.116320	+	0.584616i
$36$	−0.313886	−	2.98353i	−0.0523143	−	0.497256i
$37$	−1.86713	−	4.50765i	−0.306954	−	0.741053i	−0.999801	−	0.0199680i	$-0.993644\pi$
$37$	−1.86713	−	4.50765i	−0.306954	−	0.741053i	0.692846	−	0.721085i	$-0.256356\pi$
$38$			5.79598i			0.940232i
$39$	8.23372	−	0.431926i	1.31845	−	0.0691636i
$40$	1.23141	+	0.510066i	0.194703	+	0.0806485i
$41$	7.95541	+	3.29524i	1.24243	+	0.514630i	0.904472	−	0.426532i	$-0.140265\pi$
$41$	7.95541	+	3.29524i	1.24243	+	0.514630i	0.337955	+	0.941162i	$0.390265\pi$
$42$	2.74225	+	3.67152i	0.423139	+	0.566528i
$43$	−6.70448	+	6.70448i	−1.02242	+	1.02242i	−0.0226810	+	0.999743i	$0.507220\pi$
$43$	−6.70448	+	6.70448i	−1.02242	+	1.02242i	−0.999743	+	0.0226810i	$0.992780\pi$
$44$	0.385932	−	0.931721i	0.0581814	−	0.140462i
$45$	−3.51385	+	1.90832i	−0.523813	+	0.284476i
$46$	−4.55721	+	1.88766i	−0.671923	+	0.278320i
$47$		−	9.15054i		−	1.33474i	−0.744724	−	0.667372i	$-0.767419\pi$
$47$		−	9.15054i		−	1.33474i	0.744724	−	0.667372i	$-0.232581\pi$
$48$	1.72967	−	0.0907356i	0.249657	−	0.0130966i
$49$	−6.46745	−	2.67808i	−0.923921	−	0.382583i
$50$			3.22347i			0.455867i
$51$	−5.49788	+	4.55778i	−0.769857	+	0.638216i
$52$			4.76028i			0.660131i
$53$	−9.36723	+	9.36723i	−1.28669	+	1.28669i	−0.349901	+	0.936787i	$0.613785\pi$
$53$	−9.36723	+	9.36723i	−1.28669	+	1.28669i	−0.936787	+	0.349901i	$0.886215\pi$
$54$	−3.05359	+	4.20424i	−0.415541	+	0.572124i
$55$	−1.34418			−0.181249
$56$	−2.19978	+	1.47002i	−0.293958	+	0.196440i
$57$	6.71698	−	7.46071i	0.889685	−	0.988196i
$58$	−4.50977	−	1.86801i	−0.592162	−	0.245281i
$59$	0.517174	−	0.517174i	0.0673303	−	0.0673303i	−0.672640	−	0.739970i	$-0.734840\pi$
$59$	0.517174	−	0.517174i	0.0673303	−	0.0673303i	0.739970	+	0.672640i	$0.234840\pi$
$60$	−0.993980	−	2.08365i	−0.128322	−	0.268998i
$61$	4.78410	−	11.5498i	0.612541	−	1.47881i	−0.247658	−	0.968848i	$-0.579661\pi$
$61$	4.78410	−	11.5498i	0.612541	−	1.47881i	0.860199	−	0.509958i	$-0.170339\pi$
$62$	−3.06602	+	7.40204i	−0.389385	+	0.940060i
$63$	0.725046	−	7.90407i	0.0913473	−	0.995819i
$64$			1.00000i			0.125000i
$65$	5.86184	−	2.42805i	0.727072	−	0.301163i
$66$	−1.57656	+	0.752076i	−0.194061	+	0.0925741i
$67$	2.49006			0.304209			0.152105	−	0.988364i	$-0.451395\pi$
$67$	2.49006			0.304209			0.152105	+	0.988364i	$0.451395\pi$
$68$	−2.46154	−	3.30769i	−0.298505	−	0.401117i
$69$	8.05375	+	2.85153i	0.969558	+	0.343283i
$70$	2.93223	+	1.95902i	0.350468	+	0.234148i
$71$	7.37814	−	3.05612i	0.875624	−	0.362695i	0.100826	−	0.994904i	$-0.467852\pi$
$71$	7.37814	−	3.05612i	0.875624	−	0.362695i	0.774798	+	0.632209i	$0.217852\pi$
$72$	−2.33163	−	1.88773i	−0.274785	−	0.222471i
$73$	2.62613	+	6.34003i	0.307365	+	0.742045i	0.999789	+	0.0205537i	$0.00654290\pi$
$73$	2.62613	+	6.34003i	0.307365	+	0.742045i	−0.692424	+	0.721491i	$0.743457\pi$
$74$	−4.50765	−	1.86713i	−0.524004	−	0.217050i
$75$	3.73569	−	4.14932i	0.431360	−	0.479122i
$76$	4.09837	+	4.09837i	0.470116	+	0.470116i
$77$	1.48226	−	2.21861i	0.168919	−	0.252835i
$78$	5.51670	−	6.12754i	0.624643	−	0.693807i
$79$	1.01712	−	2.45554i	0.114434	−	0.276269i	−0.856277	−	0.516516i	$-0.827228\pi$
$79$	1.01712	−	2.45554i	0.114434	−	0.276269i	0.970712	+	0.240247i	$0.0772285\pi$
$80$	1.23141	−	0.510066i	0.137676	−	0.0570271i
$81$	8.80295	−	1.87298i	0.978106	−	0.208109i
$82$	7.95541	−	3.29524i	0.878529	−	0.363898i
$83$	−7.42733	−	7.42733i	−0.815256	−	0.815256i	0.170161	−	0.985416i	$-0.445571\pi$
$83$	−7.42733	−	7.42733i	−0.815256	−	0.815256i	−0.985416	+	0.170161i	$0.945571\pi$
$84$	4.53522	+	0.657091i	0.494833	+	0.0716945i
$85$	−2.81758	+	4.71830i	−0.305609	+	0.511771i
$86$			9.48157i			1.02242i
$87$	3.64024	+	7.63093i	0.390274	+	0.818121i
$88$	−0.385932	−	0.931721i	−0.0411405	−	0.0993218i
$89$			11.3660i			1.20480i	0.798196	+	0.602398i	$0.205788\pi$
$89$			11.3660i			1.20480i	−0.798196	+	0.602398i	$0.794212\pi$
$90$	−1.13528	+	3.83405i	−0.119669	+	0.404144i
$91$	−2.45639	+	12.3526i	−0.257500	+	1.29491i
$92$	−1.88766	+	4.55721i	−0.196802	+	0.475122i
$93$	12.5249	−	5.97484i	1.29877	−	0.619563i
$94$	−6.47041	−	6.47041i	−0.667372	−	0.667372i
$95$	2.95633	−	7.13721i	0.303313	−	0.732263i
$96$	1.15890	−	1.28722i	0.118280	−	0.131377i
$97$	−1.10080	−	2.65756i	−0.111769	−	0.269835i	0.858091	−	0.513498i	$-0.171651\pi$
$97$	−1.10080	−	2.65756i	−0.111769	−	0.269835i	−0.969860	+	0.243664i	$0.921651\pi$
$98$	−6.46687	+	2.67949i	−0.653252	+	0.270669i
$99$	2.90096	+	0.858986i	0.291558	+	0.0863314i
$100$	2.27934	+	2.27934i	0.227934	+	0.227934i
$101$	11.4442			1.13874			0.569370	−	0.822082i	$-0.307187\pi$
$101$	11.4442			1.13874			0.569370	+	0.822082i	$0.307187\pi$
$102$	−0.664752	+	7.11042i	−0.0658202	+	0.704037i
$103$		−	14.2463i		−	1.40373i	−0.712310	−	0.701865i	$-0.752351\pi$
$103$		−	14.2463i		−	1.40373i	0.712310	−	0.701865i	$-0.247649\pi$
$104$	3.36602	+	3.36602i	0.330066	+	0.330066i
$105$	−1.50411	−	5.91987i	−0.146787	−	0.577720i
$106$			13.2473i			1.28669i
$107$	−6.89968	−	16.6573i	−0.667017	−	1.61032i	−0.786576	−	0.617494i	$-0.788148\pi$
$107$	−6.89968	−	16.6573i	−0.667017	−	1.61032i	0.119559	−	0.992827i	$-0.461852\pi$
$108$	0.813632	+	5.13206i	0.0782918	+	0.493832i
$109$	11.5373	+	4.77892i	1.10508	+	0.457737i	0.859239	−	0.511574i	$-0.170938\pi$
$109$	11.5373	+	4.77892i	1.10508	+	0.457737i	0.245836	+	0.969311i	$0.420938\pi$
$110$	−0.950479	+	0.950479i	−0.0906246	+	0.0906246i
$111$	3.63853	+	7.62735i	0.345354	+	0.723956i
$112$	−0.516019	+	2.59494i	−0.0487592	+	0.245199i
$113$	15.5762	+	6.45188i	1.46529	+	0.606942i	0.965779	−	0.259367i	$-0.0835138\pi$
$113$	15.5762	+	6.45188i	1.46529	+	0.606942i	0.499509	+	0.866309i	$0.333514\pi$
$114$	−0.525901	−	10.0251i	−0.0492552	−	0.938940i
$115$	6.57461			0.613085
$116$	−4.50977	+	1.86801i	−0.418721	+	0.173440i
$117$	−14.2024	+	1.49418i	−1.31302	+	0.138137i
$118$		−	0.731394i		−	0.0673303i
$119$	−4.68071	−	9.85347i	−0.429080	−	0.903266i
$120$	−2.17621	−	0.770515i	−0.198660	−	0.0703380i
$121$	−7.05901	−	7.05901i	−0.641728	−	0.641728i
$122$	−4.78410	−	11.5498i	−0.433132	−	1.04567i
$123$	−14.0593	−	4.97785i	−1.26768	−	0.448837i
$124$	3.06602	+	7.40204i	0.275337	+	0.664722i
$125$	4.19451	−	10.1264i	0.375168	−	0.905737i
$126$	−5.07634	−	6.10171i	−0.452236	−	0.543583i
$127$	−6.12381	+	6.12381i	−0.543400	+	0.543400i	−0.924524	−	0.381124i	$-0.875537\pi$
$127$	−6.12381	+	6.12381i	−0.543400	+	0.543400i	0.381124	+	0.924524i	$0.375537\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.9882	−	12.2049i	0.967459	−	1.07458i
$130$	2.42805	−	5.86184i	0.212954	−	0.514118i
$131$	−6.73603	+	2.79016i	−0.588530	+	0.243777i	−0.657018	−	0.753875i	$-0.728182\pi$
$131$	−6.73603	+	2.79016i	−0.588530	+	0.243777i	0.0684881	+	0.997652i	$0.478182\pi$
$132$	−0.582995	+	1.64659i	−0.0507432	+	0.143317i
$133$	8.52020	+	12.7499i	0.738795	+	1.10556i
$134$	1.76074	−	1.76074i	0.152105	−	0.152105i
$135$	5.90465	−	3.61960i	0.508191	−	0.311526i
$136$	−4.07946	−	0.598324i	−0.349811	−	0.0513058i
$137$		−	3.38853i		−	0.289501i	−0.989468	−	0.144751i	$-0.953762\pi$
$137$		−	3.38853i		−	0.289501i	0.989468	−	0.144751i	$-0.0462380\pi$
$138$	7.71120	−	3.67853i	0.656421	−	0.313137i
$139$	−4.74813	+	1.96674i	−0.402731	+	0.166817i	−0.574849	−	0.818260i	$-0.694939\pi$
$139$	−4.74813	+	1.96674i	−0.402731	+	0.166817i	0.172117	+	0.985076i	$0.444939\pi$
$140$	3.45864	−	0.688161i	0.292308	−	0.0581602i
$141$	0.830280	+	15.8274i	0.0699222	+	1.33291i
$142$	3.05612	−	7.37814i	0.256464	−	0.619159i
$143$	−4.43525	−	1.83714i	−0.370894	−	0.153629i
$144$	−2.98353	+	0.313886i	−0.248628	+	0.0261571i
$145$	4.60056	+	4.60056i	0.382056	+	0.382056i
$146$	6.34003	+	2.62613i	0.524705	+	0.217340i
$147$	11.4296	+	4.04537i	0.942695	+	0.333657i
$148$	−4.50765	+	1.86713i	−0.370527	+	0.153477i
$149$	−16.7409			−1.37147			−0.685735	−	0.727851i	$-0.740519\pi$
$149$	−16.7409			−1.37147			−0.685735	+	0.727851i	$0.740519\pi$
$150$	−0.292483	−	5.57554i	−0.0238811	−	0.455241i
$151$	−10.4445	−	10.4445i	−0.849964	−	0.849964i	0.140165	−	0.990128i	$-0.455237\pi$
$151$	−10.4445	−	10.4445i	−0.849964	−	0.849964i	−0.990128	+	0.140165i	$0.955237\pi$
$152$	5.79598			0.470116
$153$	9.09598	−	8.38232i	0.735366	−	0.677670i
$154$	−0.520684	−	2.61691i	−0.0419579	−	0.210877i
$155$	7.55105	−	7.55105i	0.606515	−	0.606515i
$156$	−0.431926	−	8.23372i	−0.0345818	−	0.659225i
$157$	20.0079			1.59680			0.798401	−	0.602126i	$-0.205680\pi$
$157$	20.0079			1.59680			0.798401	+	0.602126i	$0.205680\pi$
$158$	−1.01712	−	2.45554i	−0.0809174	−	0.195352i
$159$	15.3523	−	17.0522i	1.21752	−	1.35233i
$160$	0.510066	−	1.23141i	0.0403243	−	0.0973514i
$161$	−7.24996	+	10.8516i	−0.571377	+	0.855227i
$162$	4.90023	−	7.54902i	0.384999	−	0.593107i
$163$	−7.03182	−	2.91268i	−0.550775	−	0.228138i	0.0898999	−	0.995951i	$-0.471345\pi$
$163$	−7.03182	−	2.91268i	−0.550775	−	0.228138i	−0.640675	+	0.767812i	$0.721345\pi$
$164$	3.29524	−	7.95541i	0.257315	−	0.621213i
$165$	2.32499	−	0.121965i	0.181000	−	0.00949496i
$166$	−10.5038			−0.815256
$167$	−3.72067	−	8.98248i	−0.287914	−	0.695085i	0.712061	−	0.702117i	$-0.247762\pi$
$167$	−3.72067	−	8.98248i	−0.287914	−	0.695085i	−0.999975	+	0.00703172i	$0.997762\pi$
$168$	3.67152	−	2.74225i	0.283264	−	0.211569i
$169$	9.66022			0.743094
$170$	1.34401	+	5.32867i	0.103081	+	0.408690i
$171$	−10.9412	+	13.5141i	−0.836696	+	1.03345i
$172$	6.70448	+	6.70448i	0.511212	+	0.511212i
$173$	−0.0514813	−	0.124287i	−0.00391405	−	0.00944935i	0.921910	−	0.387403i	$-0.126628\pi$
$173$	−0.0514813	−	0.124287i	−0.00391405	−	0.00944935i	−0.925824	+	0.377954i	$0.876628\pi$
$174$	7.96992	+	2.82184i	0.604198	+	0.213923i
$175$	4.73856	+	7.09092i	0.358202	+	0.536023i
$176$	−0.931721	−	0.385932i	−0.0702311	−	0.0290907i
$177$	−0.847615	+	0.941467i	−0.0637107	+	0.0707650i
$178$	8.03699	+	8.03699i	0.602398	+	0.602398i
$179$	15.7812	+	15.7812i	1.17954	+	1.17954i	0.979862	+	0.199678i	$0.0639896\pi$
$179$	15.7812	+	15.7812i	1.17954	+	1.17954i	0.199678	+	0.979862i	$0.436010\pi$
$180$	1.90832	+	3.51385i	0.142238	+	0.261907i
$181$	−13.2590	−	5.49208i	−0.985537	−	0.408223i	−0.169063	−	0.985605i	$-0.554074\pi$
$181$	−13.2590	−	5.49208i	−0.985537	−	0.408223i	−0.816474	+	0.577382i	$0.804074\pi$
$182$	6.99770	+	10.4716i	0.518704	+	0.776204i
$183$	−7.22695	+	20.4115i	−0.534231	+	1.50886i
$184$	1.88766	+	4.55721i	0.139160	+	0.335962i
$185$	4.59840	+	4.59840i	0.338081	+	0.338081i
$186$	4.63159	−	13.0813i	0.339605	−	0.959167i
$187$	4.03183	−	1.01692i	0.294837	−	0.0743647i
$188$	−9.15054			−0.667372
$189$	−0.536913	+	13.7372i	−0.0390546	+	0.999237i
$190$	−2.95633	−	7.13721i	−0.214475	−	0.517788i
$191$	9.06002			0.655560			0.327780	−	0.944754i	$-0.393700\pi$
$191$	9.06002			0.655560			0.327780	+	0.944754i	$0.393700\pi$
$192$	−0.0907356	−	1.72967i	−0.00654828	−	0.124828i
$193$	1.63185	−	3.93964i	0.117463	−	0.283582i	−0.854202	−	0.519941i	$-0.825954\pi$
$193$	1.63185	−	3.93964i	0.117463	−	0.283582i	0.971666	+	0.236359i	$0.0759541\pi$
$194$	−2.65756	−	1.10080i	−0.190802	−	0.0790327i
$195$	−9.91876	+	4.73162i	−0.710297	+	0.338838i
$196$	−2.67808	+	6.46745i	−0.191291	+	0.461961i
$197$	4.49766	−	10.8583i	0.320445	−	0.773622i	−0.678783	−	0.734339i	$-0.737492\pi$
$197$	4.49766	−	10.8583i	0.320445	−	0.773622i	0.999228	−	0.0392835i	$-0.0125075\pi$
$198$	2.65868	−	1.44389i	0.188944	−	0.102613i
$199$	−2.05133	−	4.95235i	−0.145415	−	0.351063i	0.834344	−	0.551244i	$-0.185847\pi$
$199$	−2.05133	−	4.95235i	−0.145415	−	0.351063i	−0.979759	+	0.200182i	$0.935847\pi$
$200$	3.22347			0.227934
$201$	−4.30699	+	0.225937i	−0.303792	+	0.0159364i
$202$	8.09226	−	8.09226i	0.569370	−	0.569370i
$203$	−12.6665	+	2.52024i	−0.889015	+	0.176886i
$204$	4.55778	+	5.49788i	0.319108	+	0.384928i
$205$	−11.4772			−0.801599
$206$	−10.0737	−	10.0737i	−0.701865	−	0.701865i
$207$	−14.1891	−	4.20145i	−0.986210	−	0.292021i
$208$	4.76028			0.330066
$209$	−5.40024	+	2.23685i	−0.373542	+	0.154726i
$210$	−5.24955	−	3.12241i	−0.362253	−	0.215467i
$211$	−5.70163	−	2.36169i	−0.392516	−	0.162585i	0.177691	−	0.984086i	$-0.443137\pi$
$211$	−5.70163	−	2.36169i	−0.392516	−	0.162585i	−0.570207	+	0.821501i	$0.693137\pi$
$212$	9.36723	+	9.36723i	0.643344	+	0.643344i
$213$	−12.4845	+	5.95555i	−0.855421	+	0.408068i
$214$	−16.6573	−	6.89968i	−1.13867	−	0.471652i
$215$	4.83622	−	11.6757i	0.329828	−	0.796275i
$216$	4.20424	+	3.05359i	0.286062	+	0.207770i
$217$	4.13656	+	20.7900i	0.280808	+	1.41132i
$218$	11.5373	−	4.77892i	0.781406	−	0.323669i
$219$	−5.11761	−	10.7279i	−0.345816	−	0.724924i
$220$			1.34418i			0.0906246i
$221$	−15.7455	+	11.7176i	−1.05916	+	0.788211i
$222$	7.96618	+	2.82052i	0.534655	+	0.189301i
$223$	9.16074	−	9.16074i	0.613448	−	0.613448i	−0.330395	−	0.943843i	$-0.607182\pi$
$223$	9.16074	−	9.16074i	0.613448	−	0.613448i	0.943843	+	0.330395i	$0.107182\pi$
$224$	1.47002	+	2.19978i	0.0982199	+	0.146979i
$225$	−6.08502	+	7.51592i	−0.405668	+	0.501062i
$226$	15.5762	−	6.45188i	1.03612	−	0.429173i
$227$	−0.610817	+	1.47464i	−0.0405414	+	0.0978755i	−0.942853	−	0.333208i	$-0.891869\pi$
$227$	−0.610817	+	1.47464i	−0.0405414	+	0.0978755i	0.902312	+	0.431084i	$0.141869\pi$
$228$	−7.46071	−	6.71698i	−0.494098	−	0.444843i
$229$	2.84065	+	2.84065i	0.187716	+	0.187716i	0.794708	−	0.606992i	$-0.207624\pi$
$229$	2.84065	+	2.84065i	0.187716	+	0.187716i	−0.606992	+	0.794708i	$0.707624\pi$
$230$	4.64895	−	4.64895i	0.306543	−	0.306543i
$231$	−2.36251	+	3.97197i	−0.155442	+	0.261336i
$232$	−1.86801	+	4.50977i	−0.122641	+	0.296081i
$233$	−8.32203	−	20.0912i	−0.545194	−	1.31622i	−0.921016	−	0.389524i	$-0.872640\pi$
$233$	−8.32203	−	20.0912i	−0.545194	−	1.31622i	0.375822	−	0.926692i	$-0.377360\pi$
$234$	−8.98610	+	11.0992i	−0.587440	+	0.725577i
$235$	4.66738	+	11.2681i	0.304466	+	0.735047i
$236$	−0.517174	−	0.517174i	−0.0336652	−	0.0336652i
$237$	−1.53647	+	4.33956i	−0.0998047	+	0.281885i
$238$	−10.2772	−	3.65770i	−0.666173	−	0.237093i
$239$			9.94764i			0.643460i	0.946832	+	0.321730i	$0.104264\pi$
$239$			9.94764i			0.643460i	−0.946832	+	0.321730i	$0.895736\pi$
$240$	−2.08365	+	0.993980i	−0.134499	+	0.0641611i
$241$	−10.2625	+	4.25087i	−0.661067	+	0.273823i	−0.687887	−	0.725818i	$-0.741462\pi$
$241$	−10.2625	+	4.25087i	−0.661067	+	0.273823i	0.0268207	+	0.999640i	$0.491462\pi$
$242$	−9.98295			−0.641728
$243$	−15.0563	+	4.03838i	−0.965861	+	0.259062i
$244$	−11.5498	−	4.78410i	−0.739403	−	0.306271i
$245$	9.33007	−	0.00101486i	0.596076	−	6.48367e-5i
$246$	−13.4613	+	6.42153i	−0.858259	+	0.409422i
$247$	19.5094	−	19.5094i	1.24135	−	1.24135i
$248$	7.40204	+	3.06602i	0.470030	+	0.194693i
$249$	13.5208	+	12.1729i	0.856844	+	0.771428i
$250$	−4.19451	−	10.1264i	−0.265284	−	0.640453i
$251$		−	3.83305i		−	0.241940i	−0.992656	−	0.120970i	$-0.961400\pi$
$251$		−	3.83305i		−	0.241940i	0.992656	−	0.120970i	$-0.0386005\pi$
$252$	−7.90407	−	0.725046i	−0.497910	−	0.0456736i
$253$	−3.51754	−	3.51754i	−0.221146	−	0.221146i
$254$			8.66037i			0.543400i
$255$	4.44537	−	8.41676i	0.278380	−	0.527078i
$256$	1.00000			0.0625000
$257$	13.3895	+	13.3895i	0.835213	+	0.835213i	0.988224	−	0.153011i	$-0.0488971\pi$
$257$	13.3895	+	13.3895i	0.835213	+	0.835213i	−0.153011	+	0.988224i	$0.548897\pi$
$258$	−0.860315	−	16.4000i	−0.0535609	−	1.02102i
$259$	−12.6606	+	2.51906i	−0.786690	+	0.156527i
$260$	−2.42805	−	5.86184i	−0.150582	−	0.363536i
$261$	−6.98881	−	12.8687i	−0.432597	−	0.796553i
$262$	−2.79016	+	6.73603i	−0.172376	+	0.416154i
$263$	7.66293	+	7.66293i	0.472517	+	0.472517i	0.902728	−	0.430212i	$-0.141561\pi$
$263$	7.66293	+	7.66293i	0.472517	+	0.472517i	−0.430212	+	0.902728i	$0.641561\pi$
$264$	0.752076	+	1.57656i	0.0462871	+	0.0970303i
$265$	6.75698	−	16.3128i	0.415078	−	1.00209i
$266$	15.0402	+	2.99084i	0.922175	+	0.183380i
$267$	−1.03130	−	19.6595i	−0.0631146	−	1.20314i
$268$		−	2.49006i		−	0.152105i
$269$	2.42386	+	5.85171i	0.147785	+	0.356785i	0.980386	−	0.197089i	$-0.0631488\pi$
$269$	2.42386	+	5.85171i	0.147785	+	0.356785i	−0.832600	+	0.553874i	$0.813149\pi$
$270$	1.61577	−	6.73466i	0.0983329	−	0.409858i
$271$			7.10388i			0.431530i	0.976445	+	0.215765i	$0.0692245\pi$
$271$			7.10388i			0.431530i	−0.976445	+	0.215765i	$0.930776\pi$
$272$	−3.30769	+	2.46154i	−0.200558	+	0.149253i
$273$	3.12793	−	21.5889i	0.189311	−	1.30662i
$274$	−2.39605	−	2.39605i	−0.144751	−	0.144751i
$275$	−3.00337	+	1.24404i	−0.181110	+	0.0750183i
$276$	2.85153	−	8.05375i	0.171642	−	0.484779i
$277$	−8.41062	+	3.48379i	−0.505345	+	0.209321i	−0.620766	−	0.783996i	$-0.713178\pi$
$277$	−8.41062	+	3.48379i	−0.505345	+	0.209321i	0.115421	+	0.993317i	$0.463178\pi$
$278$	−1.96674	+	4.74813i	−0.117957	+	0.284774i
$279$	−21.1218	+	11.4710i	−1.26453	+	0.686750i
$280$	1.95902	−	2.93223i	0.117074	−	0.175234i
$281$	−2.39847	−	2.39847i	−0.143081	−	0.143081i	0.631938	−	0.775019i	$-0.282260\pi$
$281$	−2.39847	−	2.39847i	−0.143081	−	0.143081i	−0.775019	+	0.631938i	$0.782260\pi$
$282$	11.7788	+	10.6046i	0.701417	+	0.631495i
$283$	3.96953	+	1.64423i	0.235964	+	0.0977394i	0.497532	−	0.867446i	$-0.334240\pi$
$283$	3.96953	+	1.64423i	0.235964	+	0.0977394i	−0.261568	+	0.965185i	$0.584240\pi$
$284$	−3.05612	−	7.37814i	−0.181348	−	0.437812i
$285$	−4.46588	+	12.6133i	−0.264536	+	0.747146i
$286$	−4.43525	+	1.83714i	−0.262262	+	0.108632i
$287$	12.6561	−	18.9434i	0.747066	−	1.11820i
$288$	−1.88773	+	2.33163i	−0.111235	+	0.137392i
$289$	4.88168	−	16.2840i	0.287157	−	0.957883i
$290$	6.50617			0.382056
$291$	2.14516	+	4.49683i	0.125751	+	0.263609i
$292$	6.34003	−	2.62613i	0.371022	−	0.153682i
$293$			7.39805i			0.432199i	0.976371	+	0.216099i	$0.0693335\pi$
$293$			7.39805i			0.432199i	−0.976371	+	0.216099i	$0.930667\pi$
$294$	10.9424	−	5.22141i	0.638176	−	0.304519i
$295$	−0.373059	+	0.900645i	−0.0217204	+	0.0524376i
$296$	−1.86713	+	4.50765i	−0.108525	+	0.262002i
$297$	−5.09565	−	1.22254i	−0.295680	−	0.0709392i
$298$	−11.8376	+	11.8376i	−0.685735	+	0.685735i
$299$	21.6936	+	8.98576i	1.25457	+	0.519660i
$300$	−4.14932	−	3.73569i	−0.239561	−	0.215680i
$301$	13.9381	+	20.8574i	0.803379	+	1.20220i
$302$	−14.7708			−0.849964
$303$	−19.7947	+	1.03839i	−1.13718	+	0.0596542i
$304$	4.09837	−	4.09837i	0.235058	−	0.235058i
$305$			16.6628i			0.954108i
$306$	0.504635	−	12.3590i	0.0288480	−	0.706518i
$307$			0.326994i			0.0186625i	0.999956	+	0.00933126i	$0.00297028\pi$
$307$			0.326994i			0.0186625i	−0.999956	+	0.00933126i	$0.997030\pi$
$308$	−2.21861	−	1.48226i	−0.126417	−	0.0844594i
$309$	1.29265	+	24.6414i	0.0735361	+	1.40180i
$310$		−	10.6788i		−	0.606515i
$311$	−15.7681	+	6.53137i	−0.894128	+	0.370360i	−0.781960	−	0.623329i	$-0.785780\pi$
$311$	−15.7681	+	6.53137i	−0.894128	+	0.370360i	−0.112169	+	0.993689i	$0.535780\pi$
$312$	−6.12754	−	5.51670i	−0.346903	−	0.312322i
$313$	−2.51545	+	6.07284i	−0.142182	+	0.343257i	−0.978889	−	0.204394i	$-0.934478\pi$
$313$	−2.51545	+	6.07284i	−0.142182	+	0.343257i	0.836707	+	0.547651i	$0.184478\pi$
$314$	14.1477	−	14.1477i	0.798401	−	0.798401i
$315$	3.13877	+	10.1030i	0.176850	+	0.569237i
$316$	−2.45554	−	1.01712i	−0.138135	−	0.0572172i
$317$	2.38547	+	0.988096i	0.133982	+	0.0554970i	0.448667	−	0.893699i	$-0.351899\pi$
$317$	2.38547	+	0.988096i	0.133982	+	0.0554970i	−0.314685	+	0.949196i	$0.601899\pi$
$318$	−1.20200	−	22.9134i	−0.0674047	−	1.28492i
$319$		−	4.92277i		−	0.275622i
$320$	−0.510066	−	1.23141i	−0.0285136	−	0.0688378i
$321$	13.4456	+	28.1856i	0.750460	+	1.57317i
$322$	2.54675	+	12.7998i	0.141925	+	0.713302i
$323$	−3.46787	+	23.6445i	−0.192957	+	1.31561i
$324$	−1.87298	−	8.80295i	−0.104054	−	0.489053i
$325$	10.8503	−	10.8503i	0.601864	−	0.601864i
$326$	−7.03182	+	2.91268i	−0.389457	+	0.161318i
$327$	−20.3894	−	7.21911i	−1.12754	−	0.399218i
$328$	−3.29524	−	7.95541i	−0.181949	−	0.439264i
$329$	−23.7451	−	4.72186i	−1.30911	−	0.260324i
$330$	1.55777	−	1.73026i	0.0857527	−	0.0952476i
$331$	1.86769	−	1.86769i	0.102658	−	0.102658i	−0.653912	−	0.756570i	$-0.726874\pi$
$331$	1.86769	−	1.86769i	0.102658	−	0.102658i	0.756570	+	0.653912i	$0.226874\pi$
$332$	−7.42733	+	7.42733i	−0.407628	+	0.407628i
$333$	−6.98553	−	12.8627i	−0.382805	−	0.704870i
$334$	−8.98248	−	3.72067i	−0.491500	−	0.203586i
$335$	−3.06628	+	1.27009i	−0.167529	+	0.0693927i
$336$	0.657091	−	4.53522i	0.0358473	−	0.247417i
$337$	−2.35557	−	5.68685i	−0.128316	−	0.309783i	0.846645	−	0.532158i	$-0.178619\pi$
$337$	−2.35557	−	5.68685i	−0.128316	−	0.309783i	−0.974961	+	0.222376i	$0.928619\pi$
$338$	6.83081	−	6.83081i	0.371547	−	0.371547i
$339$	−27.5272	−	9.74633i	−1.49507	−	0.529348i
$340$	4.71830	+	2.81758i	0.255886	+	0.152804i
$341$	−8.07991			−0.437552
$342$	1.81927	+	17.2925i	0.0983751	+	0.935071i
$343$	−10.2868	+	15.4007i	−0.555435	+	0.831560i
$344$	9.48157			0.511212
$345$	−11.3719	+	0.596551i	−0.612244	+	0.0321172i
$346$	−0.124287	−	0.0514813i	−0.00668170	−	0.00276765i
$347$	10.4570	−	25.2454i	0.561359	−	1.35524i	−0.347320	−	0.937747i	$-0.612908\pi$
$347$	10.4570	−	25.2454i	0.561359	−	1.35524i	0.908679	−	0.417495i	$-0.137092\pi$
$348$	7.63093	−	3.64024i	0.409061	−	0.195137i
$349$	3.80377	+	3.80377i	0.203611	+	0.203611i	0.801545	−	0.597934i	$-0.204012\pi$
$349$	3.80377	+	3.80377i	0.203611	+	0.203611i	−0.597934	+	0.801545i	$0.704012\pi$
$350$	8.36471	+	1.66337i	0.447113	+	0.0889109i
$351$	24.4300	−	3.87311i	1.30398	−	0.206731i
$352$	−0.931721	+	0.385932i	−0.0496609	+	0.0205702i
$353$		−	19.1118i		−	1.01722i	−0.860998	−	0.508609i	$-0.830160\pi$
$353$		−	19.1118i		−	1.01722i	0.860998	−	0.508609i	$-0.169840\pi$
$354$	0.0663635	+	1.26507i	0.00352718	+	0.0672379i
$355$	−7.52667	+	7.52667i	−0.399474	+	0.399474i
$356$	11.3660			0.602398
$357$	8.99016	+	16.6186i	0.475810	+	0.879548i
$358$	22.3179			1.17954
$359$	−12.0983	+	12.0983i	−0.638522	+	0.638522i	−0.950191	−	0.311669i	$-0.899112\pi$
$359$	−12.0983	+	12.0983i	−0.638522	+	0.638522i	0.311669	+	0.950191i	$0.399112\pi$
$360$	3.83405	+	1.13528i	0.202072	+	0.0598344i
$361$		−	14.5933i		−	0.768071i
$362$	−13.2590	+	5.49208i	−0.696880	+	0.288657i
$363$	12.8503	+	11.5693i	0.674465	+	0.607230i
$364$	12.3526	+	2.45639i	0.647454	+	0.128750i
$365$	−6.46767	−	6.46767i	−0.338533	−	0.338533i
$366$	9.32291	+	19.5434i	0.487316	+	1.02155i
$367$	−11.3419	+	27.3817i	−0.592041	+	1.42931i	0.289488	+	0.957182i	$0.406515\pi$
$367$	−11.3419	+	27.3817i	−0.592041	+	1.42931i	−0.881528	+	0.472131i	$0.843485\pi$
$368$	4.55721	+	1.88766i	0.237561	+	0.0984009i
$369$	24.7696	+	7.33437i	1.28945	+	0.381812i
$370$	6.50312			0.338081
$371$	19.4737	+	29.1411i	1.01103	+	1.51293i
$372$	−5.97484	−	12.5249i	−0.309781	−	0.649386i
$373$	22.9206			1.18678			0.593392	−	0.804914i	$-0.297788\pi$
$373$	22.9206			1.18678			0.593392	+	0.804914i	$0.297788\pi$
$374$	2.13186	−	3.57001i	0.110236	−	0.184601i
$375$	−6.33630	+	17.8960i	−0.327205	+	0.924147i
$376$	−6.47041	+	6.47041i	−0.333686	+	0.333686i
$377$	8.89223	+	21.4677i	0.457973	+	1.10564i
$378$	9.33404	+	10.0933i	0.480091	+	0.519146i
$379$	9.23469	−	3.82513i	0.474354	−	0.196484i	−0.132681	−	0.991159i	$-0.542359\pi$
$379$	9.23469	−	3.82513i	0.474354	−	0.196484i	0.607035	+	0.794675i	$0.292359\pi$
$380$	−7.13721	−	2.95633i	−0.366131	−	0.151657i
$381$	10.0365	−	11.1478i	0.514187	−	0.571121i
$382$	6.40640	−	6.40640i	0.327780	−	0.327780i
$383$	−22.7753	+	22.7753i	−1.16376	+	1.16376i	−0.180117	+	0.983645i	$0.557648\pi$
$383$	−22.7753	+	22.7753i	−1.16376	+	1.16376i	−0.983645	+	0.180117i	$0.942352\pi$
$384$	−1.28722	−	1.15890i	−0.0656883	−	0.0591400i
$385$	−0.693623	+	3.48807i	−0.0353503	+	0.177768i
$386$	−1.63185	−	3.93964i	−0.0830592	−	0.200523i
$387$	−17.8986	+	22.1075i	−0.909837	+	1.12379i
$388$	−2.65756	+	1.10080i	−0.134917	+	0.0558846i
$389$	19.1637	−	19.1637i	0.971637	−	0.971637i	−0.0279717	−	0.999609i	$-0.508905\pi$
$389$	19.1637	−	19.1637i	0.971637	−	0.971637i	0.999609	+	0.0279717i	$0.00890484\pi$
$390$	−3.66786	+	10.3594i	−0.185729	+	0.524568i
$391$	−19.7204	+	4.97394i	−0.997302	+	0.251543i
$392$	2.67949	+	6.46687i	0.135335	+	0.326626i
$393$	11.3980	−	5.43726i	0.574951	−	0.274273i
$394$	−4.49766	−	10.8583i	−0.226589	−	0.547033i
$395$			3.54256i			0.178246i
$396$	0.858986	−	2.90096i	0.0431657	−	0.145779i
$397$	−17.5510	−	7.26988i	−0.880861	−	0.364865i	−0.104030	−	0.994574i	$-0.533174\pi$
$397$	−17.5510	−	7.26988i	−0.880861	−	0.364865i	−0.776831	+	0.629710i	$0.783174\pi$
$398$	−4.95235	−	2.05133i	−0.248239	−	0.102824i
$399$	−15.8940	−	21.2800i	−0.795697	−	1.06533i
$400$	2.27934	−	2.27934i	0.113967	−	0.113967i
$401$	9.98347	−	24.1022i	0.498551	−	1.20361i	−0.451714	−	0.892163i	$-0.649187\pi$
$401$	9.98347	−	24.1022i	0.498551	−	1.20361i	0.950264	−	0.311445i	$-0.100813\pi$
$402$	−2.88574	+	3.20526i	−0.143928	+	0.159864i
$403$	35.2357	−	14.5951i	1.75522	−	0.727035i
$404$		−	11.4442i		−	0.569370i
$405$	−9.88468	+	6.79648i	−0.491174	+	0.337720i
$406$	−7.17450	+	10.7387i	−0.356064	+	0.532951i
$407$		−	4.92046i		−	0.243898i
$408$	7.11042	+	0.664752i	0.352018	+	0.0329101i
$409$		−	3.93165i		−	0.194408i	−0.995264	−	0.0972038i	$-0.969010\pi$
$409$		−	3.93165i		−	0.194408i	0.995264	−	0.0972038i	$-0.0309899\pi$
$410$	−8.11557	+	8.11557i	−0.400800	+	0.400800i
$411$	0.307460	+	5.86104i	0.0151659	+	0.289104i
$412$	−14.2463			−0.701865
$413$	−1.07516	−	1.60891i	−0.0529054	−	0.0791692i
$414$	−13.0041	+	7.06233i	−0.639115	+	0.347095i
$415$	12.9345	+	5.35765i	0.634930	+	0.262997i
$416$	3.36602	−	3.36602i	0.165033	−	0.165033i
$417$	8.03426	−	3.83264i	0.393439	−	0.187685i
$418$	−2.23685	+	5.40024i	−0.109408	+	0.264134i
$419$	2.44408	−	5.90053i	0.119401	−	0.288260i	−0.852867	−	0.522128i	$-0.825138\pi$
$419$	2.44408	−	5.90053i	0.119401	−	0.288260i	0.972268	+	0.233868i	$0.0751384\pi$
$420$	−5.91987	+	1.50411i	−0.288860	+	0.0733933i
$421$			34.7377i			1.69301i	0.532378	+	0.846507i	$0.321298\pi$
$421$			34.7377i			1.69301i	−0.532378	+	0.846507i	$0.678702\pi$
$422$	−5.70163	+	2.36169i	−0.277551	+	0.114965i
$423$	−2.87222	−	27.3010i	−0.139652	−	1.32742i
$424$	13.2473			0.643344
$425$	−1.92868	+	13.1500i	−0.0935546	+	0.637869i
$426$	−4.61663	+	13.0391i	−0.223677	+	0.631744i
$427$	−27.5025	−	18.3744i	−1.33094	−	0.889200i
$428$	−16.6573	+	6.89968i	−0.805160	+	0.333508i
$429$	7.83823	+	2.77522i	0.378433	+	0.133989i
$430$	−4.83622	−	11.6757i	−0.233223	−	0.563051i
$431$	6.25744	+	2.59192i	0.301410	+	0.124848i	0.528263	−	0.849081i	$-0.322844\pi$
$431$	6.25744	+	2.59192i	0.301410	+	0.124848i	−0.226853	+	0.973929i	$0.572844\pi$
$432$	5.13206	−	0.813632i	0.246916	−	0.0391459i
$433$	−17.9285	−	17.9285i	−0.861586	−	0.861586i	0.129936	−	0.991522i	$-0.458523\pi$
$433$	−17.9285	−	17.9285i	−0.861586	−	0.861586i	−0.991522	+	0.129936i	$0.958523\pi$
$434$	17.6257	+	11.7757i	0.846062	+	0.565254i
$435$	−8.37489	−	7.54002i	−0.401545	−	0.361517i
$436$	4.77892	−	11.5373i	0.228869	−	0.552538i
$437$	26.4135	−	10.9408i	1.26353	−	0.523370i
$438$	−11.2045	−	3.96707i	−0.535370	−	0.189554i
$439$	−1.09774	+	0.454700i	−0.0523925	+	0.0217017i	−0.408726	−	0.912657i	$-0.634027\pi$
$439$	−1.09774	+	0.454700i	−0.0523925	+	0.0217017i	0.356333	+	0.934359i	$0.384027\pi$
$440$	0.950479	+	0.950479i	0.0453123	+	0.0453123i
$441$	−20.1365	−	5.96011i	−0.958879	−	0.283815i
$442$	−2.84819	+	19.4194i	−0.135474	+	0.923685i
$443$		−	13.1081i		−	0.622785i	−0.950281	−	0.311393i	$-0.899205\pi$
$443$		−	13.1081i		−	0.622785i	0.950281	−	0.311393i	$-0.100795\pi$
$444$	7.62735	−	3.63853i	0.361978	−	0.172677i
$445$	−5.79742	−	13.9962i	−0.274824	−	0.663484i
$446$		−	12.9552i		−	0.613448i
$447$	28.9563	−	1.51900i	1.36959	−	0.0718461i
$448$	2.59494	+	0.516019i	0.122599	+	0.0243796i
$449$	−10.9594	+	26.4584i	−0.517207	+	1.24865i	0.422404	+	0.906407i	$0.361186\pi$
$449$	−10.9594	+	26.4584i	−0.517207	+	1.24865i	−0.939612	+	0.342242i	$0.888814\pi$
$450$	1.01180	+	9.61732i	0.0476967	+	0.453365i
$451$	6.14049	+	6.14049i	0.289145	+	0.289145i
$452$	6.45188	−	15.5762i	0.303471	−	0.732644i
$453$	19.0133	+	17.1179i	0.893323	+	0.804270i
$454$	0.610817	+	1.47464i	0.0286671	+	0.0692084i
$455$	−3.27584	−	16.4641i	−0.153574	−	0.771847i
$456$	−10.0251	+	0.525901i	−0.469470	+	0.0246276i
$457$	−22.8768	−	22.8768i	−1.07013	−	1.07013i	−0.997348	−	0.0727847i	$-0.976811\pi$
$457$	−22.8768	−	22.8768i	−1.07013	−	1.07013i	−0.0727847	−	0.997348i	$-0.523189\pi$
$458$	4.01729			0.187716
$459$	−14.9725	+	15.3240i	−0.698856	+	0.715263i
$460$		−	6.57461i		−	0.306543i
$461$	−23.3546	−	23.3546i	−1.08773	−	1.08773i	−0.995762	−	0.0919679i	$-0.970684\pi$
$461$	−23.3546	−	23.3546i	−1.08773	−	1.08773i	−0.0919679	−	0.995762i	$-0.529316\pi$
$462$	1.13806	+	4.47916i	0.0529473	+	0.208389i
$463$		−	10.8396i		−	0.503757i	−0.967759	−	0.251878i	$-0.918952\pi$
$463$		−	10.8396i		−	0.503757i	0.967759	−	0.251878i	$-0.0810483\pi$
$464$	1.86801	+	4.50977i	0.0867200	+	0.209361i
$465$	−12.3757	+	13.7460i	−0.573909	+	0.637455i
$466$	−20.0912	−	8.32203i	−0.930705	−	0.385511i
$467$	−13.0695	+	13.0695i	−0.604784	+	0.604784i	−0.941578	−	0.336794i	$-0.890657\pi$
$467$	−13.0695	+	13.0695i	−0.604784	+	0.604784i	0.336794	+	0.941578i	$0.390657\pi$
$468$	1.49418	+	14.2024i	0.0690686	+	0.656508i
$469$	1.28492	−	6.46156i	0.0593321	−	0.298367i
$470$	11.2681	+	4.66738i	0.519757	+	0.215290i
$471$	−34.6071	+	1.81543i	−1.59461	+	0.0836504i
$472$	−0.731394			−0.0336652
$473$	−8.83418	+	3.65924i	−0.406196	+	0.168252i
$474$	1.98208	+	4.15498i	0.0910400	+	0.190845i
$475$		−	18.6831i		−	0.857241i
$476$	−9.85347	+	4.68071i	−0.451633	+	0.214540i
$477$	−25.0072	+	30.8877i	−1.14500	+	1.41425i
$478$	7.03405	+	7.03405i	0.321730	+	0.321730i
$479$	−5.49162	−	13.2579i	−0.250919	−	0.605771i	0.747360	−	0.664419i	$-0.231321\pi$
$479$	−5.49162	−	13.2579i	−0.250919	−	0.605771i	−0.998279	+	0.0586481i	$0.981321\pi$
$480$	−0.770515	+	2.17621i	−0.0351690	+	0.0993301i
$481$	8.88806	+	21.4577i	0.405260	+	0.978385i
$482$	−4.25087	+	10.2625i	−0.193622	+	0.467445i
$483$	11.5554	−	19.4276i	0.525791	−	0.883985i
$484$	−7.05901	+	7.05901i	−0.320864	+	0.320864i
$485$	2.71106	+	2.71106i	0.123103	+	0.123103i
$486$	−7.79083	+	13.5020i	−0.353399	+	0.612461i
$487$	−1.57270	+	3.79684i	−0.0712660	+	0.172051i	−0.955499	−	0.294995i	$-0.904682\pi$
$487$	−1.57270	+	3.79684i	−0.0712660	+	0.172051i	0.884233	+	0.467047i	$0.154682\pi$
$488$	−11.5498	+	4.78410i	−0.522837	+	0.216566i
$489$	12.4270	+	4.39994i	0.561970	+	0.198972i
$490$	6.59664	−	6.59807i	0.298006	−	0.298070i
$491$	1.01753	−	1.01753i	0.0459205	−	0.0459205i	−0.683774	−	0.729694i	$-0.739662\pi$
$491$	1.01753	−	1.01753i	0.0459205	−	0.0459205i	0.729694	+	0.683774i	$0.239662\pi$
$492$	−4.97785	+	14.0593i	−0.224419	+	0.633840i
$493$	−17.2798	−	10.3188i	−0.778241	−	0.464734i
$494$		−	27.5904i		−	1.24135i
$495$	−4.01041	+	0.421919i	−0.180254	+	0.0189638i
$496$	7.40204	−	3.06602i	0.332361	−	0.137669i
$497$	−4.12320	−	20.7229i	−0.184951	−	0.929547i
$498$	18.1682	−	0.953071i	0.814136	−	0.0427082i
$499$	8.51762	−	20.5633i	0.381301	−	0.920542i	−0.610414	−	0.792083i	$-0.708997\pi$
$499$	8.51762	−	20.5633i	0.381301	−	0.920542i	0.991715	−	0.128459i	$-0.0410032\pi$
$500$	−10.1264	−	4.19451i	−0.452868	−	0.187584i
$501$	7.25056	+	15.1992i	0.323931	+	0.679048i
$502$	−2.71038	−	2.71038i	−0.120970	−	0.120970i
$503$	−5.14895	−	2.13277i	−0.229580	−	0.0950953i	0.264928	−	0.964268i	$-0.414652\pi$
$503$	−5.14895	−	2.13277i	−0.229580	−	0.0950953i	−0.494508	+	0.869173i	$0.664652\pi$
$504$	−6.10171	+	5.07634i	−0.271792	+	0.226118i
$505$	−14.0925	+	5.83729i	−0.627107	+	0.259756i
$506$	−4.97455			−0.221146
$507$	−16.7090	+	0.876526i	−0.742074	+	0.0389279i
$508$	6.12381	+	6.12381i	0.271700	+	0.271700i
$509$	14.4318			0.639680			0.319840	−	0.947472i	$-0.396371\pi$
$509$	14.4318			0.639680			0.319840	+	0.947472i	$0.396371\pi$
$510$	−2.80820	−	9.09490i	−0.124349	−	0.402729i
$511$	17.8072	−	3.54307i	0.787742	−	0.156736i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	17.6985	−	24.3677i	0.781409	−	1.07586i
$514$	18.9356			0.835213
$515$	7.26655	+	17.5430i	0.320203	+	0.773038i
$516$	−12.2049	−	10.9882i	−0.537290	−	0.483729i
$517$	3.53148	−	8.52576i	0.155315	−	0.374962i
$518$	−7.17113	+	10.7336i	−0.315081	+	0.471608i
$519$	0.100323	+	0.210304i	0.00440369	+	0.00923133i
$520$	−5.86184	−	2.42805i	−0.257059	−	0.106477i
$521$	0.900132	−	2.17311i	0.0394355	−	0.0952057i	−0.902935	−	0.429778i	$-0.858592\pi$
$521$	0.900132	−	2.17311i	0.0394355	−	0.0952057i	0.942370	+	0.334572i	$0.108592\pi$
$522$	−14.0414	−	4.15771i	−0.614575	−	0.181978i
$523$	16.8864			0.738392			0.369196	−	0.929352i	$-0.379633\pi$
$523$	16.8864			0.738392			0.369196	+	0.929352i	$0.379633\pi$
$524$	2.79016	+	6.73603i	0.121889	+	0.294265i
$525$	−8.83956	−	11.8350i	−0.385790	−	0.516523i
$526$	10.8370			0.472517
$527$	−16.9365	+	28.3618i	−0.737767	+	1.23546i
$528$	1.64659	+	0.582995i	0.0716587	+	0.0253716i
$529$	0.941420	+	0.941420i	0.0409313	+	0.0409313i
$530$	−6.75698	−	16.3128i	−0.293504	−	0.708582i
$531$	1.38067	−	1.70534i	0.0599161	−	0.0740054i
$532$	12.7499	−	8.52020i	0.552778	−	0.369398i
$533$	−37.8700	−	15.6863i	−1.64033	−	0.679447i
$534$	−14.6306	−	13.1721i	−0.633128	−	0.570013i
$535$	16.9926	+	16.9926i	0.734656	+	0.734656i
$536$	−1.76074	−	1.76074i	−0.0760523	−	0.0760523i
$537$	−28.7282	−	25.8643i	−1.23971	−	1.11613i
$538$	5.85171	+	2.42386i	0.252285	+	0.104500i
$539$	−4.99230	−	4.99122i	−0.215034	−	0.214987i
$540$	−3.61960	−	5.90465i	−0.155763	−	0.254096i
$541$	13.0001	+	31.3849i	0.558916	+	1.34934i	0.910625	+	0.413233i	$0.135601\pi$
$541$	13.0001	+	31.3849i	0.558916	+	1.34934i	−0.351709	+	0.936109i	$0.614399\pi$
$542$	5.02320	+	5.02320i	0.215765	+	0.215765i
$543$	23.4321	+	8.29643i	1.00557	+	0.356034i
$544$	−0.598324	+	4.07946i	−0.0256529	+	0.174905i
$545$	−16.6447			−0.712981
$546$	−13.0539	−	17.4774i	−0.558654	−	0.747966i
$547$	6.56949	+	15.8602i	0.280891	+	0.678131i	0.999857	−	0.0169143i	$-0.00538425\pi$
$547$	6.56949	+	15.8602i	0.280891	+	0.678131i	−0.718966	+	0.695045i	$0.755384\pi$
$548$	−3.38853			−0.144751
$549$	10.6482	−	35.9610i	0.454454	−	1.53478i
$550$	−1.24404	+	3.00337i	−0.0530460	+	0.128064i
$551$	26.1385	+	10.8269i	1.11354	+	0.461242i
$552$	−3.67853	−	7.71120i	−0.156569	−	0.328210i
$553$	−5.84712	−	3.90646i	−0.248645	−	0.166120i
$554$	−3.48379	+	8.41062i	−0.148012	+	0.357333i
$555$	−8.37096	−	7.53649i	−0.355328	−	0.319906i
$556$	1.96674	+	4.74813i	0.0834084	+	0.201366i
$557$	4.36959			0.185145			0.0925727	−	0.995706i	$-0.470491\pi$
$557$	4.36959			0.185145			0.0925727	+	0.995706i	$0.470491\pi$
$558$	−6.82419	+	23.0466i	−0.288891	+	0.975641i
$559$	31.9152	−	31.9152i	1.34987	−	1.34987i
$560$	−0.688161	−	3.45864i	−0.0290801	−	0.146154i
$561$	−6.88148	+	2.12477i	−0.290536	+	0.0897080i
$562$	−3.39195			−0.143081
$563$	−26.6806	−	26.6806i	−1.12445	−	1.12445i	−0.991064	−	0.133388i	$-0.957414\pi$
$563$	−26.6806	−	26.6806i	−1.12445	−	1.12445i	−0.133388	−	0.991064i	$-0.542586\pi$
$564$	15.8274	−	0.830280i	0.666456	−	0.0349611i
$565$	−22.4716			−0.945386
$566$	3.96953	−	1.64423i	0.166852	−	0.0691122i
$567$	−0.317773	−	23.8096i	−0.0133452	−	0.999911i
$568$	−7.37814	−	3.05612i	−0.309580	−	0.128232i
$569$	−8.09704	−	8.09704i	−0.339445	−	0.339445i	0.516713	−	0.856159i	$-0.327155\pi$
$569$	−8.09704	−	8.09704i	−0.339445	−	0.339445i	−0.856159	+	0.516713i	$0.827155\pi$
$570$	5.76108	+	12.0768i	0.241305	+	0.505841i
$571$	−14.4189	−	5.97249i	−0.603411	−	0.249941i	0.0599975	−	0.998199i	$-0.480891\pi$
$571$	−14.4189	−	5.97249i	−0.603411	−	0.249941i	−0.663408	+	0.748258i	$0.730891\pi$
$572$	−1.83714	+	4.43525i	−0.0768147	+	0.185447i
$573$	−15.6709	+	0.822066i	−0.654660	+	0.0343423i
$574$	−4.44581	−	22.3442i	−0.185565	−	0.932631i
$575$	14.6900	−	6.08480i	0.612615	−	0.253754i
$576$	0.313886	+	2.98353i	0.0130786	+	0.124314i
$577$			19.4303i			0.808893i	0.914562	+	0.404447i	$0.132536\pi$
$577$			19.4303i			0.808893i	−0.914562	+	0.404447i	$0.867464\pi$
$578$	−8.06267	−	14.9664i	−0.335363	−	0.622520i
$579$	−2.46511	+	6.96236i	−0.102446	+	0.289346i
$580$	4.60056	−	4.60056i	0.191028	−	0.191028i
$581$	−23.1061	+	15.4409i	−0.958605	+	0.640594i
$582$	4.69660	+	1.66289i	0.194680	+	0.0689288i
$583$	−12.3428	+	5.11254i	−0.511185	+	0.211740i
$584$	2.62613	−	6.34003i	0.108670	−	0.262352i
$585$	16.7269	−	9.08413i	0.691571	−	0.375583i
$586$	5.23121	+	5.23121i	0.216099	+	0.216099i
$587$	−18.6794	+	18.6794i	−0.770983	+	0.770983i	−0.978278	−	0.207296i	$-0.933534\pi$
$587$	−18.6794	+	18.6794i	−0.770983	+	0.770983i	0.207296	+	0.978278i	$0.433534\pi$
$588$	4.04537	−	11.4296i	0.166828	−	0.471347i
$589$	17.7706	−	42.9020i	0.732225	−	1.76775i
$590$	0.373059	+	0.900645i	0.0153586	+	0.0370790i
$591$	−6.79424	+	19.1894i	−0.279478	+	0.789347i
$592$	1.86713	+	4.50765i	0.0767386	+	0.185263i
$593$	−1.45576	−	1.45576i	−0.0597807	−	0.0597807i	0.676584	−	0.736365i	$-0.263459\pi$
$593$	−1.45576	−	1.45576i	−0.0597807	−	0.0597807i	−0.736365	+	0.676584i	$0.763459\pi$
$594$	−4.46764	+	2.73870i	−0.183310	+	0.112370i
$595$	10.7898	+	9.74618i	0.442338	+	0.399554i
$596$			16.7409i			0.685735i
$597$	3.99748	+	8.37982i	0.163606	+	0.342963i
$598$	21.6936	−	8.98576i	0.887115	−	0.367455i
$599$	4.25202			0.173733			0.0868664	−	0.996220i	$-0.472315\pi$
$599$	4.25202			0.173733			0.0868664	+	0.996220i	$0.472315\pi$
$600$	−5.57554	+	0.292483i	−0.227621	+	0.0119406i
$601$	−6.29865	−	2.60899i	−0.256927	−	0.106423i	0.250502	−	0.968116i	$-0.419404\pi$
$601$	−6.29865	−	2.60899i	−0.256927	−	0.106423i	−0.507430	+	0.861693i	$0.669404\pi$
$602$	24.6041	+	4.89267i	1.00279	+	0.199410i
$603$	7.42918	−	0.781594i	0.302540	−	0.0318290i
$604$	−10.4445	+	10.4445i	−0.424982	+	0.424982i
$605$	12.2931	+	5.09196i	0.499785	+	0.207018i
$606$	−13.2627	+	14.7312i	−0.538761	+	0.598415i
$607$	1.35013	+	3.25951i	0.0548003	+	0.132300i	0.948908	−	0.315551i	$-0.102189\pi$
$607$	1.35013	+	3.25951i	0.0548003	+	0.132300i	−0.894108	+	0.447851i	$0.852189\pi$
$608$		−	5.79598i		−	0.235058i
$609$	21.6802	−	5.50850i	0.878528	−	0.223216i
$610$	11.7824	+	11.7824i	0.477054	+	0.477054i
$611$			43.5591i			1.76221i
$612$	−8.38232	−	9.09598i	−0.338835	−	0.367683i
$613$	14.5712			0.588527			0.294263	−	0.955724i	$-0.404926\pi$
$613$	14.5712			0.588527			0.294263	+	0.955724i	$0.404926\pi$
$614$	0.231220	+	0.231220i	0.00933126	+	0.00933126i
$615$	19.8517	−	1.04139i	0.800498	−	0.0419927i
$616$	−2.61691	+	0.520684i	−0.105438	+	0.0209790i
$617$	8.98487	+	21.6914i	0.361717	+	0.873263i	0.995049	+	0.0993825i	$0.0316867\pi$
$617$	8.98487	+	21.6914i	0.361717	+	0.873263i	−0.633332	+	0.773880i	$0.718313\pi$
$618$	18.3382	+	16.5101i	0.737669	+	0.664133i
$619$	−11.9980	+	28.9657i	−0.482240	+	1.16423i	0.476303	+	0.879281i	$0.341976\pi$
$619$	−11.9980	+	28.9657i	−0.482240	+	1.16423i	−0.958543	+	0.284948i	$0.908024\pi$
$620$	−7.55105	−	7.55105i	−0.303258	−	0.303258i
$621$	24.9237	+	5.97967i	1.00015	+	0.239956i
$622$	−6.53137	+	15.7681i	−0.261884	+	0.632244i
$623$	29.4941	+	5.86508i	1.18166	+	0.234980i
$624$	−8.23372	+	0.431926i	−0.329613	+	0.0172909i
$625$		−	1.50807i		−	0.0603229i
$626$	2.51545	+	6.07284i	0.100538	+	0.242719i
$627$	9.13768	−	4.35901i	0.364924	−	0.174082i
$628$		−	20.0079i		−	0.798401i
$629$	−17.2716	−	10.3139i	−0.688666	−	0.411243i
$630$	9.36331	+	4.92442i	0.373043	+	0.196194i
$631$	20.2077	+	20.2077i	0.804456	+	0.804456i	0.983788	−	0.179333i	$-0.0573938\pi$
$631$	20.2077	+	20.2077i	0.804456	+	0.804456i	−0.179333	+	0.983788i	$0.557394\pi$
$632$	−2.45554	+	1.01712i	−0.0976759	+	0.0404587i
$633$	10.0762	+	3.56761i	0.400494	+	0.141800i
$634$	2.38547	−	0.988096i	0.0947393	−	0.0392423i
$635$	4.41736	−	10.6645i	0.175298	−	0.423206i
$636$	−17.0522	−	15.3523i	−0.676163	−	0.608758i
$637$	30.7868	+	12.7484i	1.21982	+	0.505110i
$638$	−3.48092	−	3.48092i	−0.137811	−	0.137811i
$639$	21.0536	−	11.4339i	0.832869	−	0.452320i
$640$	−1.23141	−	0.510066i	−0.0486757	−	0.0201621i
$641$	−14.0792	−	33.9902i	−0.556095	−	1.34253i	−0.912835	−	0.408328i	$-0.866112\pi$
$641$	−14.0792	−	33.9902i	−0.556095	−	1.34253i	0.356741	−	0.934203i	$-0.383888\pi$
$642$	29.4377	+	10.4228i	1.16181	+	0.411354i
$643$	38.8548	−	16.0942i	1.53228	−	0.634693i	0.552279	−	0.833660i	$-0.313758\pi$
$643$	38.8548	−	16.0942i	1.53228	−	0.634693i	0.980006	+	0.198966i	$0.0637585\pi$
$644$	10.8516	+	7.24996i	0.427614	+	0.285689i
$645$	−7.30569	+	20.6339i	−0.287661	+	0.812460i
$646$	14.2670	+	19.1713i	0.561328	+	0.754285i
$647$	−5.39664			−0.212164			−0.106082	−	0.994357i	$-0.533831\pi$
$647$	−5.39664			−0.212164			−0.106082	+	0.994357i	$0.533831\pi$
$648$	−7.54902	−	4.90023i	−0.296554	−	0.192499i
$649$	0.681456	−	0.282268i	0.0267495	−	0.0110800i
$650$		−	15.3446i		−	0.601864i
$651$	−9.04128	−	35.5845i	−0.354356	−	1.39467i
$652$	−2.91268	+	7.03182i	−0.114069	+	0.275387i
$653$	6.82196	−	16.4697i	0.266964	−	0.644508i	−0.732374	−	0.680903i	$-0.761588\pi$
$653$	6.82196	−	16.4697i	0.266964	−	0.644508i	0.999337	+	0.0363952i	$0.0115875\pi$
$654$	−19.5222	+	9.31280i	−0.763377	+	0.364159i
$655$	6.87164	−	6.87164i	0.268497	−	0.268497i
$656$	−7.95541	−	3.29524i	−0.310607	−	0.128658i
$657$	9.82519	+	18.0914i	0.383317	+	0.705813i
$658$	−20.1292	+	13.4515i	−0.784718	+	0.524394i
$659$	16.0624			0.625702			0.312851	−	0.949802i	$-0.398716\pi$
$659$	16.0624			0.625702			0.312851	+	0.949802i	$0.398716\pi$
$660$	−0.121965	−	2.32499i	−0.00474748	−	0.0905002i
$661$	1.76602	−	1.76602i	0.0686902	−	0.0686902i	−0.671927	−	0.740617i	$-0.734533\pi$
$661$	1.76602	−	1.76602i	0.0686902	−	0.0686902i	0.740617	+	0.671927i	$0.234533\pi$
$662$		−	2.64132i		−	0.102658i
$663$	26.1714	−	21.6963i	1.01641	−	0.842614i
$664$			10.5038i			0.407628i
$665$	−16.9951	−	11.3544i	−0.659043	−	0.440306i
$666$	−14.0348	−	4.15576i	−0.543837	−	0.161032i
$667$			24.0781i			0.932308i
$668$	−8.98248	+	3.72067i	−0.347543	+	0.143957i
$669$	−15.0139	+	16.6763i	−0.580470	+	0.644742i
$670$	−1.27009	+	3.06628i	−0.0490680	+	0.118461i
$671$	8.91490	−	8.91490i	0.344156	−	0.344156i
$672$	−2.74225	−	3.67152i	−0.105785	−	0.141632i
$673$	16.5668	+	6.86219i	0.638603	+	0.264518i	0.678403	−	0.734690i	$-0.262672\pi$
$673$	16.5668	+	6.86219i	0.638603	+	0.264518i	−0.0398005	+	0.999208i	$0.512672\pi$
$674$	−5.68685	−	2.35557i	−0.219049	−	0.0907332i
$675$	9.84314	−	13.5522i	0.378863	−	0.521625i
$676$		−	9.66022i		−	0.371547i
$677$	−5.48037	−	13.2308i	−0.210628	−	0.508501i	0.782892	−	0.622157i	$-0.213744\pi$
$677$	−5.48037	−	13.2308i	−0.210628	−	0.508501i	−0.993520	+	0.113657i	$0.963744\pi$
$678$	−26.3564	+	12.5730i	−1.01221	+	0.482862i
$679$	−7.46425	+	1.48515i	−0.286452	+	0.0569950i
$680$	5.32867	−	1.34401i	0.204345	−	0.0515406i
$681$	0.922711	−	2.60607i	0.0353584	−	0.0998649i
$682$	−5.71336	+	5.71336i	−0.218776	+	0.218776i
$683$	15.5796	−	6.45330i	0.596138	−	0.246929i	−0.0641506	−	0.997940i	$-0.520434\pi$
$683$	15.5796	−	6.45330i	0.596138	−	0.246929i	0.660289	+	0.751012i	$0.270434\pi$
$684$	13.5141	+	10.9412i	0.516723	+	0.418348i
$685$	1.72837	+	4.17266i	0.0660377	+	0.159429i
$686$	3.61609	+	18.1638i	0.138063	+	0.693497i
$687$	−5.17115	−	4.65565i	−0.197292	−	0.177624i
$688$	6.70448	−	6.70448i	0.255606	−	0.255606i
$689$	44.5906	−	44.5906i	1.69877	−	1.69877i
$690$	−7.61934	+	8.46299i	−0.290063	+	0.322180i
$691$	−3.70085	−	1.53294i	−0.140787	−	0.0583159i	0.311177	−	0.950352i	$-0.399277\pi$
$691$	−3.70085	−	1.53294i	−0.140787	−	0.0583159i	−0.451965	+	0.892036i	$0.649277\pi$
$692$	−0.124287	+	0.0514813i	−0.00472468	+	0.00195702i
$693$	3.72597	−	7.08457i	0.141538	−	0.269121i
$694$	−10.4570	−	25.2454i	−0.396941	−	0.958301i
$695$	4.84372	−	4.84372i	0.183733	−	0.183733i
$696$	2.82184	−	7.96992i	0.106962	−	0.302099i
$697$	34.4254	−	8.68290i	1.30396	−	0.328888i
$698$	5.37935			0.203611
$699$	16.2174	+	33.9960i	0.613397	+	1.28585i
$700$	7.09092	−	4.73856i	0.268012	−	0.179101i
$701$	−35.7287			−1.34946			−0.674728	−	0.738067i	$-0.735739\pi$
$701$	−35.7287			−1.34946			−0.674728	+	0.738067i	$0.735739\pi$
$702$	14.5359	−	20.0133i	0.548623	−	0.755354i
$703$	26.1262	+	10.8218i	0.985370	+	0.408154i
$704$	−0.385932	+	0.931721i	−0.0145453	+	0.0351156i
$705$	−9.09545	−	19.0665i	−0.342555	−	0.718088i
$706$	−13.5141	−	13.5141i	−0.508609	−	0.508609i
$707$	5.90542	−	29.6970i	0.222096	−	1.11687i
$708$	0.941467	+	0.847615i	0.0353825	+	0.0318553i
$709$	−29.9490	+	12.4053i	−1.12476	+	0.465890i	−0.865996	−	0.500052i	$-0.833314\pi$
$709$	−29.9490	+	12.4053i	−1.12476	+	0.465890i	−0.258761	+	0.965941i	$0.583314\pi$
$710$			10.6443i			0.399474i
$711$	2.26384	−	7.64543i	0.0849007	−	0.286726i
$712$	8.03699	−	8.03699i	0.301199	−	0.301199i
$713$	39.5202			1.48004
$714$	18.1081	+	5.39411i	0.677679	+	0.201869i
$715$	6.39867			0.239297
$716$	15.7812	−	15.7812i	0.589770	−	0.589770i
$717$	−0.902605	−	17.2062i	−0.0337084	−	0.642576i
$718$			17.1095i			0.638522i
$719$	28.8463	−	11.9485i	1.07579	−	0.445605i	0.226756	−	0.973952i	$-0.427188\pi$
$719$	28.8463	−	11.9485i	1.07579	−	0.445605i	0.849029	+	0.528347i	$0.177188\pi$
$720$	3.51385	−	1.90832i	0.130953	−	0.0711189i
$721$	−36.9683	−	7.35137i	−1.37677	−	0.273779i
$722$	−10.3191	−	10.3191i	−0.384035	−	0.384035i
$723$	17.3651	−	8.28379i	0.645814	−	0.308078i
$724$	−5.49208	+	13.2590i	−0.204111	+	0.492769i
$725$	14.5371	+	6.02146i	0.539894	+	0.223631i
$726$	17.2672	−	0.905809i	0.640847	−	0.0336177i
$727$	−25.7831			−0.956243			−0.478121	−	0.878294i	$-0.658682\pi$
$727$	−25.7831			−0.956243			−0.478121	+	0.878294i	$0.658682\pi$
$728$	10.4716	−	6.99770i	0.388102	−	0.259352i
$729$	25.6760	−	8.35121i	0.950963	−	0.309304i
$730$	−9.14667			−0.338533
$731$	−5.67305	+	38.6797i	−0.209825	+	1.43062i
$732$	20.4115	+	7.22695i	0.754432	+	0.267116i
$733$	35.1957	−	35.1957i	1.29998	−	1.29998i	0.371581	−	0.928400i	$-0.378816\pi$
$733$	35.1957	−	35.1957i	1.29998	−	1.29998i	0.928400	−	0.371581i	$-0.121184\pi$
$734$	11.3419	+	27.3817i	0.418636	+	1.01068i
$735$	−16.1379	+	0.848324i	−0.595254	+	0.0312909i
$736$	4.55721	−	1.88766i	0.167981	−	0.0695799i
$737$	2.32004	+	0.960993i	0.0854599	+	0.0353986i
$738$	22.7009	−	12.3286i	0.835632	−	0.453820i
$739$	−11.9449	+	11.9449i	−0.439402	+	0.439402i	−0.891811	−	0.452409i	$-0.850565\pi$
$739$	−11.9449	+	11.9449i	−0.439402	+	0.439402i	0.452409	+	0.891811i	$0.350565\pi$
$740$	4.59840	−	4.59840i	0.169041	−	0.169041i
$741$	−31.9747	+	35.5151i	−1.17462	+	1.30468i
$742$	34.3759	+	6.83584i	1.26198	+	0.250952i
$743$	−3.70695	−	8.94938i	−0.135995	−	0.328321i	0.841181	−	0.540754i	$-0.181861\pi$
$743$	−3.70695	−	8.94938i	−0.135995	−	0.328321i	−0.977176	+	0.212433i	$0.931861\pi$
$744$	−13.0813	−	4.63159i	−0.479584	−	0.169802i
$745$	20.6149	−	8.53897i	0.755272	−	0.312844i
$746$	16.2073	−	16.2073i	0.593392	−	0.593392i
$747$	−24.4910	−	19.8284i	−0.896080	−	0.725482i
$748$	−1.01692	−	4.03183i	−0.0371824	−	0.147418i
$749$	−46.7851	+	9.30877i	−1.70949	+	0.340135i
$750$	8.17396	+	17.1348i	0.298471	+	0.625676i
$751$	12.4357	+	30.0224i	0.453784	+	1.09553i	0.970872	+	0.239600i	$0.0770162\pi$
$751$	12.4357	+	30.0224i	0.453784	+	1.09553i	−0.517087	+	0.855933i	$0.672984\pi$
$752$			9.15054i			0.333686i
$753$	0.347794	+	6.62992i	0.0126743	+	0.241608i
$754$	21.4677	+	8.89223i	0.781809	+	0.323836i
$755$	18.1889	+	7.53408i	0.661961	+	0.274193i
$756$	13.7372	+	0.536913i	0.499619	+	0.0195273i
$757$	21.2025	−	21.2025i	0.770619	−	0.770619i	−0.207596	−	0.978215i	$-0.566564\pi$
$757$	21.2025	−	21.2025i	0.770619	−	0.770619i	0.978215	+	0.207596i	$0.0665639\pi$
$758$	3.82513	−	9.23469i	0.138935	−	0.335419i
$759$	6.40336	+	5.76503i	0.232427	+	0.209257i
$760$	−7.13721	+	2.95633i	−0.258894	+	0.107237i
$761$		−	30.9757i		−	1.12287i	−0.827522	−	0.561434i	$-0.810250\pi$
$761$		−	30.9757i		−	1.12287i	0.827522	−	0.561434i	$-0.189750\pi$
$762$	−0.785804	−	14.9796i	−0.0284667	−	0.542654i
$763$	18.3545	−	27.4727i	0.664477	−	0.994577i
$764$		−	9.06002i		−	0.327780i
$765$	−6.92533	+	14.9616i	−0.250386	+	0.540938i
$766$			32.2091i			1.16376i
$767$	−2.46189	+	2.46189i	−0.0888937	+	0.0888937i
$768$	−1.72967	+	0.0907356i	−0.0624142	+	0.00327414i
$769$	9.51746			0.343208			0.171604	−	0.985166i	$-0.445105\pi$
$769$	9.51746			0.343208			0.171604	+	0.985166i	$0.445105\pi$
$770$	1.97597	+	2.95690i	0.0712091	+	0.106559i
$771$	−24.3743	−	21.9445i	−0.877820	−	0.790313i
$772$	−3.93964	−	1.63185i	−0.141791	−	0.0587317i
$773$	9.38088	−	9.38088i	0.337407	−	0.337407i	−0.517984	−	0.855391i	$-0.673317\pi$
$773$	9.38088	−	9.38088i	0.337407	−	0.337407i	0.855391	+	0.517984i	$0.173317\pi$
$774$	2.97613	+	28.2886i	0.106975	+	1.01681i
$775$	9.88323	−	23.8602i	0.355016	−	0.857084i
$776$	−1.10080	+	2.65756i	−0.0395164	+	0.0954009i
$777$	21.6701	−	5.50591i	0.777410	−	0.197524i
$778$		−	27.1015i		−	0.971637i
$779$	−46.1094	+	19.0991i	−1.65204	+	0.684298i
$780$	4.73162	+	9.91876i	0.169419	+	0.355148i
$781$	8.05382			0.288188
$782$	−10.4273	+	17.4615i	−0.372880	+	0.624423i
$783$	13.2560	+	21.6245i	0.473731	+	0.772797i
$784$	6.46745	+	2.67808i	0.230980	+	0.0956457i
$785$	−24.6379	+	10.2053i	−0.879363	+	0.364244i
$786$	4.21486	−	11.9043i	0.150339	−	0.424612i
$787$	−1.32204	−	3.19169i	−0.0471256	−	0.113771i	0.898564	−	0.438843i	$-0.144612\pi$
$787$	−1.32204	−	3.19169i	−0.0471256	−	0.113771i	−0.945689	+	0.325072i	$0.894612\pi$
$788$	−10.8583	−	4.49766i	−0.386811	−	0.160222i
$789$	−13.9497	−	12.5591i	−0.496621	−	0.447114i
$790$	2.50497	+	2.50497i	0.0891228	+	0.0891228i
$791$	24.7799	−	37.0901i	0.881072	−	1.31877i
$792$	−1.44389	−	2.65868i	−0.0513065	−	0.0944722i
$793$	−22.7736	+	54.9804i	−0.808716	+	1.95241i
$794$	−17.5510	+	7.26988i	−0.622863	+	0.257998i
$795$	−10.2072	+	28.8289i	−0.362012	+	1.02245i
$796$	−4.95235	+	2.05133i	−0.175531	+	0.0727075i
$797$	31.8245	+	31.8245i	1.12728	+	1.12728i	0.990618	+	0.136663i	$0.0436378\pi$
$797$	31.8245	+	31.8245i	1.12728	+	1.12728i	0.136663	+	0.990618i	$0.456362\pi$
$798$	−26.2860	−	3.80848i	−0.930516	−	0.134819i
$799$	−22.5244	−	30.2672i	−0.796856	−	1.07078i
$800$		−	3.22347i		−	0.113967i
$801$	3.56763	+	33.9109i	0.126056	+	1.19818i
$802$	−9.98347	−	24.1022i	−0.352528	−	0.851079i
$803$			6.92065i			0.244224i
$804$	0.225937	+	4.30699i	0.00796818	+	0.151896i
$805$	3.39263	−	17.0607i	0.119574	−	0.601312i
$806$	14.5951	−	35.2357i	0.514091	−	1.24113i
$807$	−4.72344	−	9.90161i	−0.166273	−	0.348553i
$808$	−8.09226	−	8.09226i	−0.284685	−	0.284685i
$809$	−15.0511	+	36.3365i	−0.529168	+	1.27752i	0.402902	+	0.915243i	$0.368002\pi$
$809$	−15.0511	+	36.3365i	−0.529168	+	1.27752i	−0.932069	+	0.362280i	$0.881998\pi$
$810$	−2.18369	+	11.7954i	−0.0767269	+	0.414447i
$811$	−0.771029	−	1.86143i	−0.0270745	−	0.0653636i	0.909764	−	0.415126i	$-0.136262\pi$
$811$	−0.771029	−	1.86143i	−0.0270745	−	0.0653636i	−0.936839	+	0.349762i	$0.886262\pi$
$812$	2.52024	+	12.6665i	0.0884432	+	0.444508i
$813$	−0.644574	−	12.2874i	−0.0226062	−	0.430937i
$814$	−3.47929	−	3.47929i	−0.121949	−	0.121949i
$815$	10.1447			0.355353
$816$	5.49788	−	4.55778i	0.192464	−	0.159554i
$817$		−	54.9549i		−	1.92263i
$818$	−2.78010	−	2.78010i	−0.0972038	−	0.0972038i
$819$	−3.45142	+	37.6255i	−0.120602	+	1.31474i
$820$			11.4772i			0.400800i
$821$	12.1383	+	29.3045i	0.423630	+	1.02273i	0.981268	+	0.192649i	$0.0617078\pi$
$821$	12.1383	+	29.3045i	0.423630	+	1.02273i	−0.557638	+	0.830084i	$0.688292\pi$
$822$	4.36179	+	3.92698i	0.152135	+	0.136969i
$823$	2.74624	+	1.13753i	0.0957279	+	0.0396518i	0.430033	−	0.902813i	$-0.358502\pi$
$823$	2.74624	+	1.13753i	0.0957279	+	0.0396518i	−0.334306	+	0.942465i	$0.608502\pi$
$824$	−10.0737	+	10.0737i	−0.350933	+	0.350933i
$825$	5.08197	−	2.42429i	0.176932	−	0.0844030i
$826$	−1.89793	−	0.377414i	−0.0660373	−	0.0131319i
$827$	14.5583	+	6.03025i	0.506242	+	0.209692i	0.621162	−	0.783682i	$-0.286661\pi$
$827$	14.5583	+	6.03025i	0.506242	+	0.209692i	−0.114920	+	0.993375i	$0.536661\pi$
$828$	−4.20145	+	14.1891i	−0.146010	+	0.493105i
$829$	−52.3731			−1.81899			−0.909496	−	0.415712i	$-0.863533\pi$
$829$	−52.3731			−1.81899			−0.909496	+	0.415712i	$0.863533\pi$
$830$	12.9345	−	5.35765i	0.448963	−	0.185967i
$831$	14.2315	−	6.78896i	0.493686	−	0.235506i
$832$		−	4.76028i		−	0.165033i
$833$	−27.9845	+	7.06159i	−0.969607	+	0.244670i
$834$	2.97099	−	8.39117i	0.102877	−	0.290562i
$835$	9.16332	+	9.16332i	0.317110	+	0.317110i
$836$	2.23685	+	5.40024i	0.0773631	+	0.186771i
$837$	35.4931	−	21.7575i	1.22682	−	0.752051i
$838$	−2.44408	−	5.90053i	−0.0844293	−	0.203830i
$839$	11.1177	−	26.8404i	0.383824	−	0.926634i	−0.607394	−	0.794400i	$-0.707785\pi$
$839$	11.1177	−	26.8404i	0.383824	−	0.926634i	0.991219	−	0.132233i	$-0.0422148\pi$
$840$	−3.12241	+	5.24955i	−0.107733	+	0.181127i
$841$	3.65754	−	3.65754i	0.126122	−	0.126122i
$842$	24.5633	+	24.5633i	0.846507	+	0.846507i
$843$	4.36619	+	3.93094i	0.150380	+	0.135389i
$844$	−2.36169	+	5.70163i	−0.0812927	+	0.196258i
$845$	−11.8957	+	4.92735i	−0.409224	+	0.169506i
$846$	−21.3357	−	17.2737i	−0.733535	−	0.593883i
$847$	−21.9603	+	14.6751i	−0.754565	+	0.504244i
$848$	9.36723	−	9.36723i	0.321672	−	0.321672i
$849$	−7.01517	−	2.48380i	−0.240760	−	0.0852440i
$850$	7.93468	+	10.6622i	0.272157	+	0.365712i
$851$			24.0668i			0.824999i
$852$	5.95555	+	12.4845i	0.204034	+	0.427711i
$853$	19.7643	−	8.18664i	0.676717	−	0.280305i	−0.0177368	−	0.999843i	$-0.505646\pi$
$853$	19.7643	−	8.18664i	0.676717	−	0.280305i	0.694454	+	0.719537i	$0.255646\pi$
$854$	−32.4399	+	6.45452i	−1.11007	+	0.220869i
$855$	6.58004	−	22.2221i	0.225033	−	0.759979i
$856$	−6.89968	+	16.6573i	−0.235826	+	0.569334i
$857$	−14.6178	−	6.05490i	−0.499335	−	0.206831i	0.118778	−	0.992921i	$-0.462102\pi$
$857$	−14.6178	−	6.05490i	−0.499335	−	0.206831i	−0.618113	+	0.786090i	$0.712102\pi$
$858$	7.50484	−	3.58009i	0.256211	−	0.122222i
$859$	−21.8132	−	21.8132i	−0.744258	−	0.744258i	0.229136	−	0.973394i	$-0.426410\pi$
$859$	−21.8132	−	21.8132i	−0.744258	−	0.744258i	−0.973394	+	0.229136i	$0.926410\pi$
$860$	−11.6757	−	4.83622i	−0.398137	−	0.164914i
$861$	−20.1721	+	33.9143i	−0.687462	+	1.15580i
$862$	6.25744	−	2.59192i	0.213129	−	0.0882811i
$863$	38.1783			1.29960			0.649802	−	0.760103i	$-0.274852\pi$
$863$	38.1783			1.29960			0.649802	+	0.760103i	$0.274852\pi$
$864$	3.05359	−	4.20424i	0.103885	−	0.143031i
$865$	0.126789	+	0.126789i	0.00431095	+	0.00431095i
$866$	−25.3547			−0.861586
$867$	−6.96616	+	28.6090i	−0.236583	+	0.971611i
$868$	20.7900	−	4.13656i	0.705658	−	0.140404i
$869$	1.89534	−	1.89534i	0.0642949	−	0.0642949i
$870$	−11.2535	+	0.590341i	−0.381531	+	0.0200144i
$871$	−11.8534			−0.401636
$872$	−4.77892	−	11.5373i	−0.161834	−	0.390703i
$873$	−4.11844	−	7.58340i	−0.139388	−	0.256659i
$874$	10.9408	−	26.4135i	0.370078	−	0.893448i
$875$	−24.1131	−	16.1100i	−0.815171	−	0.544616i
$876$	−10.7279	+	5.11761i	−0.362462	+	0.172908i
$877$	−14.2119	−	5.88676i	−0.479902	−	0.198782i	0.129600	−	0.991566i	$-0.458631\pi$
$877$	−14.2119	−	5.88676i	−0.479902	−	0.198782i	−0.609502	+	0.792785i	$0.708631\pi$
$878$	−0.454700	+	1.09774i	−0.0153454	+	0.0370471i
$879$	−0.671266	−	12.7962i	−0.0226412	−	0.431605i
$880$	1.34418			0.0453123
$881$	−3.84673	−	9.28683i	−0.129600	−	0.312881i	0.845738	−	0.533598i	$-0.179160\pi$
$881$	−3.84673	−	9.28683i	−0.129600	−	0.312881i	−0.975338	+	0.220717i	$0.929160\pi$
$882$	−18.4531	+	10.0242i	−0.621347	+	0.337532i
$883$	−23.5272			−0.791752			−0.395876	−	0.918304i	$-0.629559\pi$
$883$	−23.5272			−0.791752			−0.395876	+	0.918304i	$0.629559\pi$
$884$	11.7176	+	15.7455i	0.394105	+	0.529580i
$885$	0.563550	−	1.59167i	0.0189435	−	0.0535034i
$886$	−9.26883	−	9.26883i	−0.311393	−	0.311393i
$887$	4.63670	+	11.1940i	0.155685	+	0.375858i	0.982407	−	0.186754i	$-0.0597967\pi$
$887$	4.63670	+	11.1940i	0.155685	+	0.375858i	−0.826721	+	0.562611i	$0.809797\pi$
$888$	2.82052	−	7.96618i	0.0946505	−	0.267327i
$889$	12.7309	+	19.0509i	0.426982	+	0.638948i
$890$	−13.9962	−	5.79742i	−0.469154	−	0.194330i
$891$	8.92474	+	1.65225i	0.298990	+	0.0553523i
$892$	−9.16074	−	9.16074i	−0.306724	−	0.306724i
$893$	37.5024	+	37.5024i	1.25497	+	1.25497i
$894$	19.4011	−	21.5493i	0.648870	−	0.720716i
$895$	−27.4825	−	11.3836i	−0.918638	−	0.380512i
$896$	2.19978	−	1.47002i	0.0734896	−	0.0491099i
$897$	−38.3381	−	13.5741i	−1.28007	−	0.453224i
$898$	10.9594	+	26.4584i	0.365721	+	0.882928i
$899$	27.6541	+	27.6541i	0.922316	+	0.922316i
$900$	7.51592	+	6.08502i	0.250531	+	0.202834i
$901$	−7.92615	+	54.0417i	−0.264058	+	1.80039i
$902$	8.68397			0.289145
$903$	−26.0009	−	34.8118i	−0.865254	−	1.15846i
$904$	−6.45188	−	15.5762i	−0.214586	−	0.518058i
$905$	19.1286			0.635857
$906$	25.5486	−	1.34024i	0.848797	−	0.0445264i
$907$	−21.3566	+	51.5595i	−0.709135	+	1.71200i	−0.00698393	+	0.999976i	$0.502223\pi$
$907$	−21.3566	+	51.5595i	−0.709135	+	1.71200i	−0.702151	+	0.712028i	$0.747777\pi$
$908$	1.47464	+	0.610817i	0.0489377	+	0.0202707i
$909$	34.1441	−	3.59217i	1.13249	−	0.119145i
$910$	−13.9582	−	9.32548i	−0.462710	−	0.309137i
$911$	12.3815	−	29.8915i	0.410217	−	0.990351i	−0.574862	−	0.818250i	$-0.694944\pi$
$911$	12.3815	−	29.8915i	0.410217	−	0.990351i	0.985079	−	0.172101i	$-0.0550555\pi$
$912$	−6.71698	+	7.46071i	−0.222421	+	0.247049i
$913$	−4.05376	−	9.78665i	−0.134160	−	0.323891i
$914$	−32.3527			−1.07013
$915$	−1.51191	−	28.8211i	−0.0499821	−	0.952798i
$916$	2.84065	−	2.84065i	0.0938578	−	0.0938578i
$917$	3.76437	+	18.9194i	0.124310	+	0.624773i
$918$	0.248550	+	21.4228i	0.00820336	+	0.707059i
$919$	−58.5944			−1.93285			−0.966425	−	0.256950i	$-0.917282\pi$
$919$	−58.5944			−1.93285			−0.966425	+	0.256950i	$0.917282\pi$
$920$	−4.64895	−	4.64895i	−0.153271	−	0.153271i
$921$	−0.0296700	−	0.565592i	−0.000977659	−	0.0186369i
$922$	−33.0283			−1.08773
$923$	−35.1220	+	14.5480i	−1.15605	+	0.478853i
$924$	3.97197	+	2.36251i	0.130668	+	0.0777209i
$925$	14.5303	+	6.01863i	0.477752	+	0.197891i
$926$	−7.66472	−	7.66472i	−0.251878	−	0.251878i
$927$	−4.47171	−	42.5043i	−0.146870	−	1.39603i
$928$	4.50977	+	1.86801i	0.148040	+	0.0613203i
$929$	1.12368	−	2.71280i	0.0368667	−	0.0890042i	−0.904374	−	0.426741i	$-0.859661\pi$
$929$	1.12368	−	2.71280i	0.0368667	−	0.0890042i	0.941240	+	0.337737i	$0.109661\pi$
$930$	0.968947	+	18.4708i	0.0317730	+	0.605682i
$931$	37.4818	−	15.5302i	1.22842	−	0.508983i
$932$	−20.0912	+	8.32203i	−0.658108	+	0.272597i
$933$	26.6811	−	12.7279i	0.873499	−	0.416692i
$934$			18.4831i			0.604784i
$935$	−4.44614	+	3.30875i	−0.145404	+	0.108208i
$936$	11.0992	+	8.98610i	0.362788	+	0.293720i
$937$	−18.6435	+	18.6435i	−0.609056	+	0.609056i	−0.942699	−	0.333643i	$-0.891722\pi$
$937$	−18.6435	+	18.6435i	−0.609056	+	0.609056i	0.333643	+	0.942699i	$0.391722\pi$
$938$	−3.66044	−	5.47759i	−0.119518	−	0.178850i
$939$	3.79989	−	10.7323i	0.124005	−	0.350234i
$940$	11.2681	−	4.66738i	0.367523	−	0.152233i
$941$	−17.0654	+	41.1995i	−0.556316	+	1.34307i	0.356347	+	0.934354i	$0.384022\pi$
$941$	−17.0654	+	41.1995i	−0.556316	+	1.34307i	−0.912663	+	0.408713i	$0.865978\pi$
$942$	−23.1872	+	25.7546i	−0.755479	+	0.839130i
$943$	−30.0342	−	30.0342i	−0.978047	−	0.978047i
$944$	−0.517174	+	0.517174i	−0.0168326	+	0.0168326i
$945$	−6.34574	−	17.1900i	−0.206427	−	0.559191i
$946$	−3.65924	+	8.83418i	−0.118972	+	0.287224i
$947$	−15.7427	−	38.0062i	−0.511569	−	1.23504i	−0.942970	−	0.332877i	$-0.891981\pi$
$947$	−15.7427	−	38.0062i	−0.511569	−	1.23504i	0.431401	−	0.902160i	$-0.358019\pi$
$948$	4.33956	+	1.53647i	0.140942	+	0.0499023i
$949$	−12.5011	−	30.1803i	−0.405803	−	0.979694i
$950$	−13.2110	−	13.2110i	−0.428621	−	0.428621i
$951$	−4.21575	−	1.49263i	−0.136705	−	0.0484020i
$952$	−3.65770	+	10.2772i	−0.118547	+	0.333087i
$953$			35.2415i			1.14158i	0.821095	+	0.570792i	$0.193364\pi$
$953$			35.2415i			1.14158i	−0.821095	+	0.570792i	$0.806636\pi$
$954$	4.15812	+	39.5237i	0.134624	+	1.27963i
$955$	−11.1566	+	4.62121i	−0.361019	+	0.149539i
$956$	9.94764			0.321730
$957$	0.446670	+	8.51478i	0.0144388	+	0.275244i
$958$	−13.2579	−	5.49162i	−0.428345	−	0.177426i
$959$	−8.79303	−	1.74855i	−0.283942	−	0.0564635i
$960$	0.993980	+	2.08365i	0.0320806	+	0.0672496i
$961$	23.4693	−	23.4693i	0.757075	−	0.757075i
$962$	21.4577	+	8.88806i	0.691823	+	0.286562i
$963$	−25.8139	−	47.5319i	−0.831841	−	1.53169i
$964$	4.25087	+	10.2625i	0.136911	+	0.330533i
$965$			5.68366i			0.182964i
$966$	−5.56644	−	21.9083i	−0.179097	−	0.704888i
$967$	−21.1221	−	21.1221i	−0.679239	−	0.679239i	0.280589	−	0.959828i	$-0.409470\pi$
$967$	−21.1221	−	21.1221i	−0.679239	−	0.679239i	−0.959828	+	0.280589i	$0.909470\pi$
$968$			9.98295i			0.320864i
$969$	3.85289	−	41.2118i	0.123773	−	1.32392i
$970$	3.83402			0.123103
$971$	−3.56265	−	3.56265i	−0.114331	−	0.114331i	0.647627	−	0.761958i	$-0.275762\pi$
$971$	−3.56265	−	3.56265i	−0.114331	−	0.114331i	−0.761958	+	0.647627i	$0.775762\pi$
$972$	4.03838	+	15.0563i	0.129531	+	0.482930i
$973$	2.65345	+	13.3360i	0.0850657	+	0.427533i
$974$	1.57270	+	3.79684i	0.0503927	+	0.121659i
$975$	−17.7829	+	19.7519i	−0.569509	+	0.632567i
$976$	−4.78410	+	11.5498i	−0.153135	+	0.369701i
$977$	12.9986	+	12.9986i	0.415862	+	0.415862i	0.883775	−	0.467913i	$-0.154994\pi$
$977$	12.9986	+	12.9986i	0.415862	+	0.415862i	−0.467913	+	0.883775i	$0.654994\pi$
$978$	11.8985	−	5.67601i	0.380471	−	0.181499i
$979$	−4.38650	+	10.5900i	−0.140193	+	0.338457i
$980$	−0.00101486	−	9.33007i	−3.24184e−5	−	0.298038i
$981$	35.9220	+	10.6367i	1.14690	+	0.339602i
$982$		−	1.43901i		−	0.0459205i
$983$	0.688609	+	1.66245i	0.0219632	+	0.0530239i	0.934481	−	0.356014i	$-0.115864\pi$
$983$	0.688609	+	1.66245i	0.0219632	+	0.0530239i	−0.912517	+	0.409038i	$0.865864\pi$
$984$	6.42153	+	13.4613i	0.204711	+	0.429129i
$985$			15.6651i			0.499132i
$986$	−19.5151	+	4.92216i	−0.621487	+	0.156754i
$987$	41.4997	+	6.01274i	1.32095	+	0.191388i
$988$	−19.5094	−	19.5094i	−0.620676	−	0.620676i
$989$	43.2095	−	17.8979i	1.37398	−	0.569121i
$990$	−2.53744	+	3.13413i	−0.0806453	+	0.0996091i
$991$	−34.0665	+	14.1108i	−1.08216	+	0.448244i	−0.851265	−	0.524735i	$-0.824164\pi$
$991$	−34.0665	+	14.1108i	−1.08216	+	0.448244i	−0.230892	+	0.972979i	$0.574164\pi$
$992$	3.06602	−	7.40204i	0.0973463	−	0.235015i
$993$	−3.06103	+	3.39997i	−0.0971389	+	0.107895i
$994$	−17.5688	−	11.7377i	−0.557249	−	0.372298i
$995$	5.05205	+	5.05205i	0.160161	+	0.160161i
$996$	12.1729	−	13.5208i	0.385714	−	0.428422i
$997$	−15.7482	−	6.52312i	−0.498751	−	0.206589i	0.119104	−	0.992882i	$-0.461998\pi$
$997$	−15.7482	−	6.52312i	−0.498751	−	0.206589i	−0.617854	+	0.786293i	$0.711998\pi$
$998$	−8.51762	−	20.5633i	−0.269620	−	0.650921i
$999$	13.2498	+	21.6144i	0.419205	+	0.683848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.w.e.83.1	✓	80
3.2	odd	2		714.2.w.f.83.6	yes	80
7.6	odd	2	inner	714.2.w.e.83.20	yes	80
17.8	even	8		714.2.w.f.671.15	yes	80
21.20	even	2		714.2.w.f.83.15	yes	80
51.8	odd	8	inner	714.2.w.e.671.20	yes	80
119.76	odd	8		714.2.w.f.671.6	yes	80
357.314	even	8	inner	714.2.w.e.671.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.w.e.83.1	✓	80	1.1	even	1	trivial
714.2.w.e.83.20	yes	80	7.6	odd	2	inner
714.2.w.e.671.1	yes	80	357.314	even	8	inner
714.2.w.e.671.20	yes	80	51.8	odd	8	inner
714.2.w.f.83.6	yes	80	3.2	odd	2
714.2.w.f.83.15	yes	80	21.20	even	2
714.2.w.f.671.6	yes	80	119.76	odd	8
714.2.w.f.671.15	yes	80	17.8	even	8

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.72967 + 0.0907356i) q^{3} -1.00000i q^{4} +(-1.23141 + 0.510066i) q^{5} +(-1.15890 + 1.28722i) q^{6} +(0.516019 - 2.59494i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98353 - 0.313886i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.72967 + 0.0907356i) q^{3} -1.00000i q^{4} +(-1.23141 + 0.510066i) q^{5} +(-1.15890 + 1.28722i) q^{6} +(0.516019 - 2.59494i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98353 - 0.313886i) q^{9} +(-0.510066 + 1.23141i) q^{10} +(0.931721 + 0.385932i) q^{11} +(0.0907356 + 1.72967i) q^{12} -4.76028 q^{13} +(-1.47002 - 2.19978i) q^{14} +(2.08365 - 0.993980i) q^{15} -1.00000 q^{16} +(3.30769 - 2.46154i) q^{17} +(1.88773 - 2.33163i) q^{18} +(-4.09837 + 4.09837i) q^{19} +(0.510066 + 1.23141i) q^{20} +(-0.657091 + 4.53522i) q^{21} +(0.931721 - 0.385932i) q^{22} +(-4.55721 - 1.88766i) q^{23} +(1.28722 + 1.15890i) q^{24} +(-2.27934 + 2.27934i) q^{25} +(-3.36602 + 3.36602i) q^{26} +(-5.13206 + 0.813632i) q^{27} +(-2.59494 - 0.516019i) q^{28} +(-1.86801 - 4.50977i) q^{29} +(0.770515 - 2.17621i) q^{30} +(-7.40204 + 3.06602i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.64659 - 0.582995i) q^{33} +(0.598324 - 4.07946i) q^{34} +(0.688161 + 3.45864i) q^{35} +(-0.313886 - 2.98353i) q^{36} +(-1.86713 - 4.50765i) q^{37} +5.79598i q^{38} +(8.23372 - 0.431926i) q^{39} +(1.23141 + 0.510066i) q^{40} +(7.95541 + 3.29524i) q^{41} +(2.74225 + 3.67152i) q^{42} +(-6.70448 + 6.70448i) q^{43} +(0.385932 - 0.931721i) q^{44} +(-3.51385 + 1.90832i) q^{45} +(-4.55721 + 1.88766i) q^{46} -9.15054i q^{47} +(1.72967 - 0.0907356i) q^{48} +(-6.46745 - 2.67808i) q^{49} +3.22347i q^{50} +(-5.49788 + 4.55778i) q^{51} +4.76028i q^{52} +(-9.36723 + 9.36723i) q^{53} +(-3.05359 + 4.20424i) q^{54} -1.34418 q^{55} +(-2.19978 + 1.47002i) q^{56} +(6.71698 - 7.46071i) q^{57} +(-4.50977 - 1.86801i) q^{58} +(0.517174 - 0.517174i) q^{59} +(-0.993980 - 2.08365i) q^{60} +(4.78410 - 11.5498i) q^{61} +(-3.06602 + 7.40204i) q^{62} +(0.725046 - 7.90407i) q^{63} +1.00000i q^{64} +(5.86184 - 2.42805i) q^{65} +(-1.57656 + 0.752076i) q^{66} +2.49006 q^{67} +(-2.46154 - 3.30769i) q^{68} +(8.05375 + 2.85153i) q^{69} +(2.93223 + 1.95902i) q^{70} +(7.37814 - 3.05612i) q^{71} +(-2.33163 - 1.88773i) q^{72} +(2.62613 + 6.34003i) q^{73} +(-4.50765 - 1.86713i) q^{74} +(3.73569 - 4.14932i) q^{75} +(4.09837 + 4.09837i) q^{76} +(1.48226 - 2.21861i) q^{77} +(5.51670 - 6.12754i) q^{78} +(1.01712 - 2.45554i) q^{79} +(1.23141 - 0.510066i) q^{80} +(8.80295 - 1.87298i) q^{81} +(7.95541 - 3.29524i) q^{82} +(-7.42733 - 7.42733i) q^{83} +(4.53522 + 0.657091i) q^{84} +(-2.81758 + 4.71830i) q^{85} +9.48157i q^{86} +(3.64024 + 7.63093i) q^{87} +(-0.385932 - 0.931721i) q^{88} +11.3660i q^{89} +(-1.13528 + 3.83405i) q^{90} +(-2.45639 + 12.3526i) q^{91} +(-1.88766 + 4.55721i) q^{92} +(12.5249 - 5.97484i) q^{93} +(-6.47041 - 6.47041i) q^{94} +(2.95633 - 7.13721i) q^{95} +(1.15890 - 1.28722i) q^{96} +(-1.10080 - 2.65756i) q^{97} +(-6.46687 + 2.67949i) q^{98} +(2.90096 + 0.858986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{7}+O(q^{10}) \) 80 * q - 16 * q^7	\( 80 q - 16 q^{7} - 16 q^{14} - 16 q^{15} - 80 q^{16} + 16 q^{18} - 32 q^{21} - 16 q^{23} - 32 q^{25} + 64 q^{29} - 16 q^{30} - 48 q^{37} + 16 q^{39} - 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{49} + 104 q^{51} - 80 q^{53} - 16 q^{57} - 16 q^{58} - 48 q^{60} + 56 q^{63} + 80 q^{65} - 144 q^{67} + 8 q^{70} + 16 q^{71} - 32 q^{74} - 24 q^{77} + 32 q^{78} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} + 16 q^{92} + 48 q^{93} - 16 q^{95} - 16 q^{98} + 80 q^{99}+O(q^{100}) \) 80 * q - 16 * q^7 - 16 * q^14 - 16 * q^15 - 80 * q^16 + 16 * q^18 - 32 * q^21 - 16 * q^23 - 32 * q^25 + 64 * q^29 - 16 * q^30 - 48 * q^37 + 16 * q^39 - 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^49 + 104 * q^51 - 80 * q^53 - 16 * q^57 - 16 * q^58 - 48 * q^60 + 56 * q^63 + 80 * q^65 - 144 * q^67 + 8 * q^70 + 16 * q^71 - 32 * q^74 - 24 * q^77 + 32 * q^78 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 + 16 * q^92 + 48 * q^93 - 16 * q^95 - 16 * q^98 + 80 * q^99

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