LMFDB - Embedded newform 714.2.w.f.671.15

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			671.15
Character	$\chi$	$=$	714.671
Dual form			714.2.w.f.83.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.28722 + 1.15890i) q^{3} +1.00000i q^{4} +(-1.23141 - 0.510066i) q^{5} +(-0.0907356 - 1.72967i) q^{6} +(-1.47002 - 2.19978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.313886 + 2.98353i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.28722 + 1.15890i) q^{3} +1.00000i q^{4} +(-1.23141 - 0.510066i) q^{5} +(-0.0907356 - 1.72967i) q^{6} +(-1.47002 - 2.19978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.313886 + 2.98353i) q^{9} +(0.510066 + 1.23141i) q^{10} +(-0.931721 + 0.385932i) q^{11} +(-1.15890 + 1.28722i) q^{12} +4.76028 q^{13} +(-0.516019 + 2.59494i) q^{14} +(-0.993980 - 2.08365i) 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} +(1.72967 - 0.0907356i) q^{24} +(-2.27934 - 2.27934i) q^{25} +(-3.36602 - 3.36602i) q^{26} +(-3.05359 + 4.20424i) q^{27} +(2.19978 - 1.47002i) 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} +(-2.98353 + 0.313886i) q^{36} +(-1.86713 + 4.50765i) q^{37} -5.79598i q^{38} +(6.12754 + 5.51670i) q^{39} +(-1.23141 + 0.510066i) q^{40} +(7.95541 - 3.29524i) q^{41} +(-3.67152 + 2.74225i) q^{42} +(-6.70448 - 6.70448i) q^{43} +(-0.385932 - 0.931721i) q^{44} +(1.13528 - 3.83405i) q^{45} +(-4.55721 - 1.88766i) q^{46} +9.15054i q^{47} +(-1.28722 - 1.15890i) q^{48} +(-2.67808 + 6.46745i) q^{49} +3.22347i q^{50} +(1.40506 + 7.00184i) q^{51} +4.76028i q^{52} +(9.36723 + 9.36723i) q^{53} +(5.13206 - 0.813632i) q^{54} +1.34418 q^{55} +(-2.59494 - 0.516019i) q^{56} +(0.525901 + 10.0251i) q^{57} +(-4.50977 + 1.86801i) q^{58} +(0.517174 + 0.517174i) q^{59} +(2.08365 - 0.993980i) q^{60} +(-4.78410 - 11.5498i) q^{61} +(-3.06602 - 7.40204i) q^{62} +(6.10171 - 5.07634i) q^{63} -1.00000i q^{64} +(-5.86184 - 2.42805i) q^{65} +(0.752076 + 1.57656i) q^{66} +2.49006 q^{67} +(-2.46154 + 3.30769i) q^{68} +(8.05375 + 2.85153i) q^{69} +(1.95902 - 2.93223i) 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} +(-0.292483 - 5.57554i) q^{75} +(-4.09837 + 4.09837i) q^{76} +(2.21861 + 1.48226i) q^{77} +(-0.431926 - 8.23372i) 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} +(7.63093 - 3.64024i) q^{87} +(-0.385932 + 0.931721i) q^{88} -11.3660i q^{89} +(-3.51385 + 1.90832i) q^{90} +(-6.99770 - 10.4716i) q^{91} +(1.88766 + 4.55721i) q^{92} +(5.97484 + 12.5249i) q^{93} +(6.47041 - 6.47041i) q^{94} +(-2.95633 - 7.13721i) q^{95} +(0.0907356 + 1.72967i) q^{96} +(1.10080 - 2.65756i) q^{97} +(6.46687 - 2.67949i) q^{98} +(-1.44389 - 2.65868i) 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} - 48 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} + 64 q^{39} + 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 24 q^{51} + 80 q^{53} + 48 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{63} - 80 q^{65} - 144 q^{67} + 8 q^{70} - 16 q^{71} + 32 q^{74} + 24 q^{77} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} - 16 q^{92} - 16 q^{93} + 16 q^{95} + 16 q^{98} + 48 q^{99}+O(q^{100}) $ 80 * q - 16 * q^7 + 16 * q^14 - 48 * 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 + 64 * q^39 + 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 24 * q^51 + 80 * q^53 + 48 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^63 - 80 * q^65 - 144 * q^67 + 8 * q^70 - 16 * q^71 + 32 * q^74 + 24 * q^77 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 - 16 * q^92 - 16 * q^93 + 16 * q^95 + 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$239$	$409$	$547$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

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
$3$	1.28722	+	1.15890i	0.743178	+	0.669093i
$3$	1.28722	+	1.15890i	0.743178	+	0.669093i
$4$			1.00000i			0.500000i
$5$	−1.23141	−	0.510066i	−0.550702	−	0.228108i	0.0899408	−	0.995947i	$-0.471332\pi$
$5$	−1.23141	−	0.510066i	−0.550702	−	0.228108i	−0.640643	+	0.767839i	$0.721332\pi$
$6$	−0.0907356	−	1.72967i	−0.0370426	−	0.706136i
$7$	−1.47002	−	2.19978i	−0.555615	−	0.831439i
$7$	−1.47002	−	2.19978i	−0.555615	−	0.831439i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.313886	+	2.98353i	0.104629	+	0.994511i
$10$	0.510066	+	1.23141i	0.161297	+	0.389405i
$11$	−0.931721	+	0.385932i	−0.280925	+	0.116363i	−0.518697	−	0.854958i	$-0.673583\pi$
$11$	−0.931721	+	0.385932i	−0.280925	+	0.116363i	0.237772	+	0.971321i	$0.423583\pi$
$12$	−1.15890	+	1.28722i	−0.334547	+	0.371589i
$13$	4.76028			1.32026			0.660131	−	0.751150i	$-0.270501\pi$
$13$	4.76028			1.32026			0.660131	+	0.751150i	$0.270501\pi$
$14$	−0.516019	+	2.59494i	−0.137912	+	0.693527i
$15$	−0.993980	−	2.08365i	−0.256644	−	0.537997i
$16$	−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	$-0.0184980\pi$
$19$	4.09837	+	4.09837i	0.940232	+	0.940232i	−0.0580804	+	0.998312i	$0.518498\pi$
$20$	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	$-0.453064\pi$
$23$	4.55721	−	1.88766i	0.950243	−	0.393604i	0.803322	+	0.595545i	$0.203064\pi$
$24$	1.72967	−	0.0907356i	0.353068	−	0.0185213i
$25$	−2.27934	−	2.27934i	−0.455867	−	0.455867i
$26$	−3.36602	−	3.36602i	−0.660131	−	0.660131i
$27$	−3.05359	+	4.20424i	−0.587663	+	0.809106i
$28$	2.19978	−	1.47002i	0.415720	−	0.277808i
$29$	1.86801	−	4.50977i	0.346880	−	0.837443i	−0.650105	−	0.759845i	$-0.725275\pi$
$29$	1.86801	−	4.50977i	0.346880	−	0.837443i	0.996985	−	0.0775981i	$-0.0247251\pi$
$30$	−0.770515	+	2.17621i	−0.140676	+	0.397320i
$31$	7.40204	+	3.06602i	1.32944	+	0.550674i	0.930497	−	0.366299i	$-0.119375\pi$
$31$	7.40204	+	3.06602i	1.32944	+	0.550674i	0.398948	+	0.916974i	$0.369375\pi$
$32$	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
$36$	−2.98353	+	0.313886i	−0.497256	+	0.0523143i
$37$	−1.86713	+	4.50765i	−0.306954	+	0.741053i	0.692846	+	0.721085i	$0.256356\pi$
$37$	−1.86713	+	4.50765i	−0.306954	+	0.741053i	−0.999801	+	0.0199680i	$0.993644\pi$
$38$		−	5.79598i		−	0.940232i
$39$	6.12754	+	5.51670i	0.981191	+	0.883379i
$40$	−1.23141	+	0.510066i	−0.194703	+	0.0806485i
$41$	7.95541	−	3.29524i	1.24243	−	0.514630i	0.337955	−	0.941162i	$-0.390265\pi$
$41$	7.95541	−	3.29524i	1.24243	−	0.514630i	0.904472	+	0.426532i	$0.140265\pi$
$42$	−3.67152	+	2.74225i	−0.566528	+	0.423139i
$43$	−6.70448	−	6.70448i	−1.02242	−	1.02242i	−0.999743	−	0.0226810i	$-0.992780\pi$
$43$	−6.70448	−	6.70448i	−1.02242	−	1.02242i	−0.0226810	−	0.999743i	$-0.507220\pi$
$44$	−0.385932	−	0.931721i	−0.0581814	−	0.140462i
$45$	1.13528	−	3.83405i	0.169237	−	0.571547i
$46$	−4.55721	−	1.88766i	−0.671923	−	0.278320i
$47$			9.15054i			1.33474i	0.744724	+	0.667372i	$0.232581\pi$
$47$			9.15054i			1.33474i	−0.744724	+	0.667372i	$0.767419\pi$
$48$	−1.28722	−	1.15890i	−0.185795	−	0.167273i
$49$	−2.67808	+	6.46745i	−0.382583	+	0.923921i
$50$			3.22347i			0.455867i
$51$	1.40506	+	7.00184i	0.196747	+	0.980454i
$52$			4.76028i			0.660131i
$53$	9.36723	+	9.36723i	1.28669	+	1.28669i	0.936787	+	0.349901i	$0.113785\pi$
$53$	9.36723	+	9.36723i	1.28669	+	1.28669i	0.349901	+	0.936787i	$0.386215\pi$
$54$	5.13206	−	0.813632i	0.698384	−	0.110721i
$55$	1.34418			0.181249
$56$	−2.59494	−	0.516019i	−0.346764	−	0.0689560i
$57$	0.525901	+	10.0251i	0.0696573	+	1.32786i
$58$	−4.50977	+	1.86801i	−0.592162	+	0.245281i
$59$	0.517174	+	0.517174i	0.0673303	+	0.0673303i	0.739970	−	0.672640i	$-0.234840\pi$
$59$	0.517174	+	0.517174i	0.0673303	+	0.0673303i	−0.672640	+	0.739970i	$0.734840\pi$
$60$	2.08365	−	0.993980i	0.268998	−	0.128322i
$61$	−4.78410	−	11.5498i	−0.612541	−	1.47881i	−0.860199	−	0.509958i	$-0.829661\pi$
$61$	−4.78410	−	11.5498i	−0.612541	−	1.47881i	0.247658	−	0.968848i	$-0.420339\pi$
$62$	−3.06602	−	7.40204i	−0.389385	−	0.940060i
$63$	6.10171	−	5.07634i	0.768743	−	0.639558i
$64$		−	1.00000i		−	0.125000i
$65$	−5.86184	−	2.42805i	−0.727072	−	0.301163i
$66$	0.752076	+	1.57656i	0.0925741	+	0.194061i
$67$	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
$70$	1.95902	−	2.93223i	0.234148	−	0.350468i
$71$	−7.37814	−	3.05612i	−0.875624	−	0.362695i	−0.100826	−	0.994904i	$-0.532148\pi$
$71$	−7.37814	−	3.05612i	−0.875624	−	0.362695i	−0.774798	+	0.632209i	$0.782148\pi$
$72$	2.33163	+	1.88773i	0.274785	+	0.222471i
$73$	−2.62613	+	6.34003i	−0.307365	+	0.742045i	0.692424	+	0.721491i	$0.256543\pi$
$73$	−2.62613	+	6.34003i	−0.307365	+	0.742045i	−0.999789	+	0.0205537i	$0.993457\pi$
$74$	4.50765	−	1.86713i	0.524004	−	0.217050i
$75$	−0.292483	−	5.57554i	−0.0337730	−	0.643808i
$76$	−4.09837	+	4.09837i	−0.470116	+	0.470116i
$77$	2.21861	+	1.48226i	0.252835	+	0.168919i
$78$	−0.431926	−	8.23372i	−0.0489060	−	0.932285i
$79$	1.01712	+	2.45554i	0.114434	+	0.276269i	0.970712	−	0.240247i	$-0.0772285\pi$
$79$	1.01712	+	2.45554i	0.114434	+	0.276269i	−0.856277	+	0.516516i	$0.827228\pi$
$80$	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	−0.985416	−	0.170161i	$-0.945571\pi$
$83$	−7.42733	+	7.42733i	−0.815256	+	0.815256i	0.170161	+	0.985416i	$0.445571\pi$
$84$	4.53522	+	0.657091i	0.494833	+	0.0716945i
$85$	−2.81758	−	4.71830i	−0.305609	−	0.511771i
$86$			9.48157i			1.02242i
$87$	7.63093	−	3.64024i	0.818121	−	0.390274i
$88$	−0.385932	+	0.931721i	−0.0411405	+	0.0993218i
$89$		−	11.3660i		−	1.20480i	−0.798196	−	0.602398i	$-0.794212\pi$
$89$		−	11.3660i		−	1.20480i	0.798196	−	0.602398i	$-0.205788\pi$
$90$	−3.51385	+	1.90832i	−0.370392	+	0.201155i
$91$	−6.99770	−	10.4716i	−0.733558	−	1.09772i
$92$	1.88766	+	4.55721i	0.196802	+	0.475122i
$93$	5.97484	+	12.5249i	0.619563	+	1.29877i
$94$	6.47041	−	6.47041i	0.667372	−	0.667372i
$95$	−2.95633	−	7.13721i	−0.303313	−	0.732263i
$96$	0.0907356	+	1.72967i	0.00926066	+	0.176534i
$97$	1.10080	−	2.65756i	0.111769	−	0.269835i	−0.858091	−	0.513498i	$-0.828349\pi$
$97$	1.10080	−	2.65756i	0.111769	−	0.269835i	0.969860	+	0.243664i	$0.0783493\pi$
$98$	6.46687	−	2.67949i	0.653252	−	0.270669i
$99$	−1.44389	−	2.65868i	−0.145117	−	0.267208i
$100$	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	$0.307187\pi$
$102$	3.95753	−	5.94458i	0.391854	−	0.588601i
$103$		−	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
$105$	−3.12241	+	5.24955i	−0.304716	+	0.512303i
$106$		−	13.2473i		−	1.28669i
$107$	6.89968	−	16.6573i	0.667017	−	1.61032i	−0.119559	−	0.992827i	$-0.538148\pi$
$107$	6.89968	−	16.6573i	0.667017	−	1.61032i	0.786576	−	0.617494i	$-0.211852\pi$
$108$	−4.20424	−	3.05359i	−0.404553	−	0.293832i
$109$	11.5373	−	4.77892i	1.10508	−	0.457737i	0.245836	−	0.969311i	$-0.420938\pi$
$109$	11.5373	−	4.77892i	1.10508	−	0.457737i	0.859239	+	0.511574i	$0.170938\pi$
$110$	−0.950479	−	0.950479i	−0.0906246	−	0.0906246i
$111$	−7.62735	+	3.63853i	−0.723956	+	0.345354i
$112$	1.47002	+	2.19978i	0.138904	+	0.207860i
$113$	−15.5762	+	6.45188i	−1.46529	+	0.606942i	−0.965779	−	0.259367i	$-0.916486\pi$
$113$	−15.5762	+	6.45188i	−1.46529	+	0.606942i	−0.499509	+	0.866309i	$0.666486\pi$
$114$	6.71698	−	7.46071i	0.629103	−	0.698760i
$115$	−6.57461			−0.613085
$116$	4.50977	+	1.86801i	0.418721	+	0.173440i
$117$	1.49418	+	14.2024i	0.138137	+	1.31302i
$118$		−	0.731394i		−	0.0673303i
$119$	0.552466	−	10.8947i	0.0506445	−	0.998717i
$120$	−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
$126$	−7.90407	−	0.725046i	−0.704150	−	0.0645923i
$127$	−6.12381	−	6.12381i	−0.543400	−	0.543400i	0.381124	−	0.924524i	$-0.375537\pi$
$127$	−6.12381	−	6.12381i	−0.543400	−	0.543400i	−0.924524	+	0.381124i	$0.875537\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.860315	−	16.4000i	−0.0757465	−	1.44394i
$130$	2.42805	+	5.86184i	0.212954	+	0.514118i
$131$	−6.73603	−	2.79016i	−0.588530	−	0.243777i	0.0684881	−	0.997652i	$-0.478182\pi$
$131$	−6.73603	−	2.79016i	−0.588530	−	0.243777i	−0.657018	+	0.753875i	$0.728182\pi$
$132$	0.582995	−	1.64659i	0.0507432	−	0.143317i
$133$	2.99084	−	15.0402i	0.259338	−	1.30415i
$134$	−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	$-0.0462380\pi$
$138$	−3.67853	−	7.71120i	−0.313137	−	0.656421i
$139$	4.74813	+	1.96674i	0.402731	+	0.166817i	0.574849	−	0.818260i	$-0.305061\pi$
$139$	4.74813	+	1.96674i	0.402731	+	0.166817i	−0.172117	+	0.985076i	$0.555061\pi$
$140$	−3.45864	+	0.688161i	−0.292308	+	0.0581602i
$141$	−10.6046	+	11.7788i	−0.893068	+	0.991953i
$142$	3.05612	+	7.37814i	0.256464	+	0.619159i
$143$	−4.43525	+	1.83714i	−0.370894	+	0.153629i
$144$	−0.313886	−	2.98353i	−0.0261571	−	0.248628i
$145$	−4.60056	+	4.60056i	−0.382056	+	0.382056i
$146$	6.34003	−	2.62613i	0.524705	−	0.217340i
$147$	−10.9424	+	5.22141i	−0.902517	+	0.430655i
$148$	−4.50765	−	1.86713i	−0.370527	−	0.153477i
$149$	16.7409			1.37147			0.685735	−	0.727851i	$-0.259481\pi$
$149$	16.7409			1.37147			0.685735	+	0.727851i	$0.259481\pi$
$150$	−3.73569	+	4.14932i	−0.305018	+	0.338791i
$151$	−10.4445	+	10.4445i	−0.849964	+	0.849964i	−0.990128	−	0.140165i	$-0.955237\pi$
$151$	−10.4445	+	10.4445i	−0.849964	+	0.849964i	0.140165	+	0.990128i	$0.455237\pi$
$152$	5.79598			0.470116
$153$	−6.30584	+	10.6413i	−0.509797	+	0.860295i
$154$	−0.520684	−	2.61691i	−0.0419579	−	0.210877i
$155$	−7.55105	−	7.55105i	−0.606515	−	0.606515i
$156$	−5.51670	+	6.12754i	−0.441689	+	0.490596i
$157$	−20.0079			−1.59680			−0.798401	−	0.602126i	$-0.794320\pi$
$157$	−20.0079			−1.59680			−0.798401	+	0.602126i	$0.794320\pi$
$158$	1.01712	−	2.45554i	0.0809174	−	0.195352i
$159$	1.20200	+	22.9134i	0.0953246	+	1.81715i
$160$	−0.510066	−	1.23141i	−0.0403243	−	0.0973514i
$161$	−10.8516	−	7.24996i	−0.855227	−	0.571377i
$162$	7.54902	+	4.90023i	0.593107	+	0.384999i
$163$	−7.03182	+	2.91268i	−0.550775	+	0.228138i	−0.640675	−	0.767812i	$-0.721345\pi$
$163$	−7.03182	+	2.91268i	−0.550775	+	0.228138i	0.0898999	+	0.995951i	$0.471345\pi$
$164$	3.29524	+	7.95541i	0.257315	+	0.621213i
$165$	1.73026	+	1.55777i	0.134701	+	0.121273i
$166$	10.5038			0.815256
$167$	−3.72067	+	8.98248i	−0.287914	+	0.695085i	−0.999975	−	0.00703172i	$-0.997762\pi$
$167$	−3.72067	+	8.98248i	−0.287914	+	0.695085i	0.712061	+	0.702117i	$0.247762\pi$
$168$	−2.74225	−	3.67152i	−0.211569	−	0.283264i
$169$	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	−0.925824	−	0.377954i	$-0.876628\pi$
$173$	−0.0514813	+	0.124287i	−0.00391405	+	0.00944935i	0.921910	+	0.387403i	$0.126628\pi$
$174$	−7.96992	−	2.82184i	−0.604198	−	0.213923i
$175$	−1.66337	+	8.36471i	−0.125739	+	0.632313i
$176$	0.931721	−	0.385932i	0.0702311	−	0.0290907i
$177$	0.0663635	+	1.26507i	0.00498818	+	0.0950887i
$178$	−8.03699	+	8.03699i	−0.602398	+	0.602398i
$179$	−15.7812	+	15.7812i	−1.17954	+	1.17954i	−0.199678	+	0.979862i	$0.563990\pi$
$179$	−15.7812	+	15.7812i	−1.17954	+	1.17954i	−0.979862	+	0.199678i	$0.936010\pi$
$180$	3.83405	+	1.13528i	0.285773	+	0.0846186i
$181$	13.2590	−	5.49208i	0.985537	−	0.408223i	0.169063	−	0.985605i	$-0.445926\pi$
$181$	13.2590	−	5.49208i	0.985537	−	0.408223i	0.816474	+	0.577382i	$0.195926\pi$
$182$	−2.45639	+	12.3526i	−0.182080	+	0.915639i
$183$	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
$189$	13.7372	+	0.536913i	0.999237	+	0.0390546i
$190$	−2.95633	+	7.13721i	−0.214475	+	0.517788i
$191$	−9.06002			−0.655560			−0.327780	−	0.944754i	$-0.606300\pi$
$191$	−9.06002			−0.655560			−0.327780	+	0.944754i	$0.606300\pi$
$192$	1.15890	−	1.28722i	0.0836367	−	0.0928973i
$193$	1.63185	+	3.93964i	0.117463	+	0.283582i	0.971666	−	0.236359i	$-0.0759541\pi$
$193$	1.63185	+	3.93964i	0.117463	+	0.283582i	−0.854202	+	0.519941i	$0.825954\pi$
$194$	−2.65756	+	1.10080i	−0.190802	+	0.0790327i
$195$	−4.73162	−	9.91876i	−0.338838	−	0.710297i
$196$	−6.46745	−	2.67808i	−0.461961	−	0.191291i
$197$	−4.49766	−	10.8583i	−0.320445	−	0.773622i	−0.999228	−	0.0392835i	$-0.987492\pi$
$197$	−4.49766	−	10.8583i	−0.320445	−	0.773622i	0.678783	−	0.734339i	$-0.262508\pi$
$198$	−0.858986	+	2.90096i	−0.0610455	+	0.206162i
$199$	2.05133	−	4.95235i	0.145415	−	0.351063i	−0.834344	−	0.551244i	$-0.814153\pi$
$199$	2.05133	−	4.95235i	0.145415	−	0.351063i	0.979759	+	0.200182i	$0.0641532\pi$
$200$	−3.22347			−0.227934
$201$	3.20526	+	2.88574i	0.226082	+	0.203544i
$202$	−8.09226	−	8.09226i	−0.569370	−	0.569370i
$203$	−12.6665	+	2.52024i	−0.889015	+	0.176886i
$204$	−7.00184	+	1.40506i	−0.490227	+	0.0983736i
$205$	−11.4772			−0.801599
$206$	−10.0737	+	10.0737i	−0.701865	+	0.701865i
$207$	7.06233	+	13.0041i	0.490866	+	0.903845i
$208$	−4.76028			−0.330066
$209$	−5.40024	−	2.23685i	−0.373542	−	0.154726i
$210$	5.91987	−	1.50411i	0.408510	−	0.103794i
$211$	−5.70163	+	2.36169i	−0.392516	+	0.162585i	−0.570207	−	0.821501i	$-0.693137\pi$
$211$	−5.70163	+	2.36169i	−0.392516	+	0.162585i	0.177691	+	0.984086i	$0.443137\pi$
$212$	−9.36723	+	9.36723i	−0.643344	+	0.643344i
$213$	−5.95555	−	12.4845i	−0.408068	−	0.855421i
$214$	−16.6573	+	6.89968i	−1.13867	+	0.471652i
$215$	4.83622	+	11.6757i	0.329828	+	0.796275i
$216$	0.813632	+	5.13206i	0.0553606	+	0.349192i
$217$	−4.13656	−	20.7900i	−0.280808	−	1.41132i
$218$	−11.5373	−	4.77892i	−0.781406	−	0.323669i
$219$	−10.7279	+	5.11761i	−0.724924	+	0.345816i
$220$			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	$-0.392818\pi$
$223$	−9.16074	−	9.16074i	−0.613448	−	0.613448i	−0.943843	+	0.330395i	$0.892818\pi$
$224$	0.516019	−	2.59494i	0.0344780	−	0.173382i
$225$	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	0.902312	−	0.431084i	$-0.141869\pi$
$227$	−0.610817	−	1.47464i	−0.0405414	−	0.0978755i	−0.942853	+	0.333208i	$0.891869\pi$
$228$	−10.0251	+	0.525901i	−0.663931	+	0.0348287i
$229$	−2.84065	+	2.84065i	−0.187716	+	0.187716i	−0.794708	−	0.606992i	$-0.792376\pi$
$229$	−2.84065	+	2.84065i	−0.187716	+	0.187716i	0.606992	+	0.794708i	$0.292376\pi$
$230$	4.64895	+	4.64895i	0.306543	+	0.306543i
$231$	1.13806	+	4.47916i	0.0748788	+	0.294707i
$232$	−1.86801	−	4.50977i	−0.122641	−	0.296081i
$233$	8.32203	−	20.0912i	0.545194	−	1.31622i	−0.375822	−	0.926692i	$-0.622640\pi$
$233$	8.32203	−	20.0912i	0.545194	−	1.31622i	0.921016	−	0.389524i	$-0.127360\pi$
$234$	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
$238$	−8.09438	+	7.31307i	−0.524681	+	0.474036i
$239$			9.94764i			0.643460i	0.946832	+	0.321730i	$0.104264\pi$
$239$			9.94764i			0.643460i	−0.946832	+	0.321730i	$0.895736\pi$
$240$	0.993980	+	2.08365i	0.0641611	+	0.134499i
$241$	10.2625	+	4.25087i	0.661067	+	0.273823i	0.687887	−	0.725818i	$-0.258538\pi$
$241$	10.2625	+	4.25087i	0.661067	+	0.273823i	−0.0268207	+	0.999640i	$0.508538\pi$
$242$	9.98295			0.641728
$243$	−13.5020	−	7.79083i	−0.866151	−	0.499782i
$244$	11.5498	−	4.78410i	0.739403	−	0.306271i
$245$	6.59664	−	6.59807i	0.421444	−	0.421535i
$246$	−6.42153	−	13.4613i	−0.409422	−	0.858259i
$247$	19.5094	+	19.5094i	1.24135	+	1.24135i
$248$	7.40204	−	3.06602i	0.470030	−	0.194693i
$249$	−18.1682	+	0.953071i	−1.15136	+	0.0603984i
$250$	4.19451	−	10.1264i	0.265284	−	0.640453i
$251$			3.83305i			0.241940i	0.992656	+	0.120970i	$0.0386005\pi$
$251$			3.83305i			0.241940i	−0.992656	+	0.120970i	$0.961400\pi$
$252$	5.07634	+	6.10171i	0.319779	+	0.384371i
$253$	−3.51754	+	3.51754i	−0.221146	+	0.221146i
$254$			8.66037i			0.543400i
$255$	1.84120	−	9.33880i	0.115301	−	0.584818i
$256$	1.00000			0.0625000
$257$	13.3895	−	13.3895i	0.835213	−	0.835213i	−0.153011	−	0.988224i	$-0.548897\pi$
$257$	13.3895	−	13.3895i	0.835213	−	0.835213i	0.988224	+	0.153011i	$0.0488971\pi$
$258$	−10.9882	+	12.2049i	−0.684097	+	0.759843i
$259$	12.6606	−	2.51906i	0.786690	−	0.156527i
$260$	2.42805	−	5.86184i	0.150582	−	0.363536i
$261$	14.0414	+	4.15771i	0.869140	+	0.257356i
$262$	2.79016	+	6.73603i	0.172376	+	0.416154i
$263$	−7.66293	+	7.66293i	−0.472517	+	0.472517i	−0.902728	−	0.430212i	$-0.858439\pi$
$263$	−7.66293	+	7.66293i	−0.472517	+	0.472517i	0.430212	+	0.902728i	$0.358439\pi$
$264$	−1.57656	+	0.752076i	−0.0970303	+	0.0462871i
$265$	−6.75698	−	16.3128i	−0.415078	−	1.00209i
$266$	−12.7499	+	8.52020i	−0.781746	+	0.522407i
$267$	13.1721	−	14.6306i	0.806120	−	0.895378i
$268$			2.49006i			0.152105i
$269$	2.42386	−	5.85171i	0.147785	−	0.356785i	−0.832600	−	0.553874i	$-0.813149\pi$
$269$	2.42386	−	5.85171i	0.147785	−	0.356785i	0.980386	+	0.197089i	$0.0631488\pi$
$270$	−6.73466	−	1.61577i	−0.409858	−	0.0983329i
$271$			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	0.115421	−	0.993317i	$-0.463178\pi$
$277$	−8.41062	−	3.48379i	−0.505345	−	0.209321i	−0.620766	+	0.783996i	$0.713178\pi$
$278$	−1.96674	−	4.74813i	−0.117957	−	0.284774i
$279$	−6.82419	+	23.0466i	−0.408554	+	1.37976i
$280$	2.93223	+	1.95902i	0.175234	+	0.117074i
$281$	2.39847	−	2.39847i	0.143081	−	0.143081i	−0.631938	−	0.775019i	$-0.717740\pi$
$281$	2.39847	−	2.39847i	0.143081	−	0.143081i	0.775019	+	0.631938i	$0.217740\pi$
$282$	15.8274	−	0.830280i	0.942511	−	0.0494424i
$283$	−3.96953	+	1.64423i	−0.235964	+	0.0977394i	−0.497532	−	0.867446i	$-0.665760\pi$
$283$	−3.96953	+	1.64423i	−0.235964	+	0.0977394i	0.261568	+	0.965185i	$0.415760\pi$
$284$	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
$287$	−18.9434	−	12.6561i	−1.11820	−	0.747066i
$288$	−1.88773	+	2.33163i	−0.111235	+	0.137392i
$289$	4.88168	+	16.2840i	0.287157	+	0.957883i
$290$	6.50617			0.382056
$291$	4.49683	−	2.14516i	0.263609	−	0.125751i
$292$	−6.34003	−	2.62613i	−0.371022	−	0.153682i
$293$		−	7.39805i		−	0.432199i	−0.976371	−	0.216099i	$-0.930667\pi$
$293$		−	7.39805i		−	0.432199i	0.976371	−	0.216099i	$-0.0693335\pi$
$294$	11.4296	+	4.04537i	0.666586	+	0.235931i
$295$	−0.373059	−	0.900645i	−0.0217204	−	0.0524376i
$296$	1.86713	+	4.50765i	0.108525	+	0.262002i
$297$	1.22254	−	5.09565i	0.0709392	−	0.295680i
$298$	−11.8376	−	11.8376i	−0.685735	−	0.685735i
$299$	21.6936	−	8.98576i	1.25457	−	0.519660i
$300$	5.57554	−	0.292483i	0.321904	−	0.0168865i
$301$	−4.89267	+	24.6041i	−0.282009	+	1.41816i
$302$	14.7708			0.849964
$303$	14.7312	+	13.2627i	0.846287	+	0.761923i
$304$	−4.09837	−	4.09837i	−0.235058	−	0.235058i
$305$			16.6628i			0.954108i
$306$	11.9834	−	3.06560i	0.685046	−	0.175249i
$307$			0.326994i			0.0186625i	0.999956	+	0.00933126i	$0.00297028\pi$
$307$			0.326994i			0.0186625i	−0.999956	+	0.00933126i	$0.997030\pi$
$308$	−1.48226	+	2.21861i	−0.0844594	+	0.126417i
$309$	16.5101	−	18.3382i	0.939226	−	1.04322i
$310$			10.6788i			0.606515i
$311$	−15.7681	−	6.53137i	−0.894128	−	0.370360i	−0.112169	−	0.993689i	$-0.535780\pi$
$311$	−15.7681	−	6.53137i	−0.894128	−	0.370360i	−0.781960	+	0.623329i	$0.785780\pi$
$312$	8.23372	−	0.431926i	0.466142	−	0.0244530i
$313$	2.51545	+	6.07284i	0.142182	+	0.343257i	0.978889	−	0.204394i	$-0.0655223\pi$
$313$	2.51545	+	6.07284i	0.142182	+	0.343257i	−0.836707	+	0.547651i	$0.815522\pi$
$314$	14.1477	+	14.1477i	0.798401	+	0.798401i
$315$	−10.1030	+	3.13877i	−0.569237	+	0.176850i
$316$	−2.45554	+	1.01712i	−0.138135	+	0.0572172i
$317$	−2.38547	+	0.988096i	−0.133982	+	0.0554970i	−0.448667	−	0.893699i	$-0.648101\pi$
$317$	−2.38547	+	0.988096i	−0.133982	+	0.0554970i	0.314685	+	0.949196i	$0.398101\pi$
$318$	15.3523	−	17.0522i	0.860914	−	0.956239i
$319$			4.92277i			0.275622i
$320$	−0.510066	+	1.23141i	−0.0285136	+	0.0688378i
$321$	28.1856	−	13.4456i	1.57317	−	0.750460i
$322$	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
$329$	20.1292	−	13.4515i	1.10976	−	0.741604i
$330$	−0.121965	−	2.32499i	−0.00671395	−	0.127987i
$331$	1.86769	+	1.86769i	0.102658	+	0.102658i	0.756570	−	0.653912i	$-0.226874\pi$
$331$	1.86769	+	1.86769i	0.102658	+	0.102658i	−0.653912	+	0.756570i	$0.726874\pi$
$332$	−7.42733	−	7.42733i	−0.407628	−	0.407628i
$333$	−14.0348	−	4.15576i	−0.769102	−	0.227734i
$334$	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	−0.974961	−	0.222376i	$-0.928619\pi$
$337$	−2.35557	+	5.68685i	−0.128316	+	0.309783i	0.846645	+	0.532158i	$0.178619\pi$
$338$	−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
$342$	17.2925	−	1.81927i	0.935071	−	0.0983751i
$343$	18.1638	−	3.61609i	0.980753	−	0.195250i
$344$	−9.48157			−0.511212
$345$	−8.46299	−	7.61934i	−0.455632	−	0.410211i
$346$	0.124287	−	0.0514813i	0.00668170	−	0.00276765i
$347$	−10.4570	−	25.2454i	−0.561359	−	1.35524i	−0.908679	−	0.417495i	$-0.862908\pi$
$347$	−10.4570	−	25.2454i	−0.561359	−	1.35524i	0.347320	−	0.937747i	$-0.387092\pi$
$348$	3.64024	+	7.63093i	0.195137	+	0.409061i
$349$	−3.80377	+	3.80377i	−0.203611	+	0.203611i	−0.801545	−	0.597934i	$-0.795988\pi$
$349$	−3.80377	+	3.80377i	−0.203611	+	0.203611i	0.597934	+	0.801545i	$0.295988\pi$
$350$	7.09092	−	4.73856i	0.379026	−	0.253287i
$351$	−14.5359	+	20.0133i	−0.775870	+	1.06823i
$352$	−0.931721	−	0.385932i	−0.0496609	−	0.0205702i
$353$			19.1118i			1.01722i	0.860998	+	0.508609i	$0.169840\pi$
$353$			19.1118i			1.01722i	−0.860998	+	0.508609i	$0.830160\pi$
$354$	0.847615	−	0.941467i	0.0450502	−	0.0500384i
$355$	7.52667	+	7.52667i	0.399474	+	0.399474i
$356$	11.3660			0.602398
$357$	13.3371	−	13.3837i	0.705872	−	0.708339i
$358$	22.3179			1.17954
$359$	12.0983	+	12.0983i	0.638522	+	0.638522i	0.950191	−	0.311669i	$-0.100888\pi$
$359$	12.0983	+	12.0983i	0.638522	+	0.638522i	−0.311669	+	0.950191i	$0.600888\pi$
$360$	−1.90832	−	3.51385i	−0.100577	−	0.185196i
$361$			14.5933i			0.768071i
$362$	−13.2590	−	5.49208i	−0.696880	−	0.288657i
$363$	−17.2672	+	0.905809i	−0.906295	+	0.0475426i
$364$	10.4716	−	6.99770i	0.548859	−	0.366779i
$365$	6.46767	−	6.46767i	0.338533	−	0.338533i
$366$	−19.5434	+	9.32291i	−1.02155	+	0.487316i
$367$	11.3419	+	27.3817i	0.592041	+	1.42931i	0.881528	+	0.472131i	$0.156515\pi$
$367$	11.3419	+	27.3817i	0.592041	+	1.42931i	−0.289488	+	0.957182i	$0.593485\pi$
$368$	−4.55721	+	1.88766i	−0.237561	+	0.0984009i
$369$	12.3286	+	22.7009i	0.641799	+	1.18176i
$370$	−6.50312			−0.338081
$371$	6.83584	−	34.3759i	0.354899	−	1.78471i
$372$	−12.5249	+	5.97484i	−0.649386	+	0.309781i
$373$	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	0.607035	−	0.794675i	$-0.292359\pi$
$379$	9.23469	+	3.82513i	0.474354	+	0.196484i	−0.132681	+	0.991159i	$0.542359\pi$
$380$	7.13721	−	2.95633i	0.366131	−	0.151657i
$381$	−0.785804	−	14.9796i	−0.0402580	−	0.767429i
$382$	6.40640	+	6.40640i	0.327780	+	0.327780i
$383$	−22.7753	−	22.7753i	−1.16376	−	1.16376i	−0.983645	−	0.180117i	$-0.942352\pi$
$383$	−22.7753	−	22.7753i	−1.16376	−	1.16376i	−0.180117	−	0.983645i	$-0.557648\pi$
$384$	−1.72967	+	0.0907356i	−0.0882670	+	0.00463033i
$385$	−1.97597	−	2.95690i	−0.100705	−	0.150698i
$386$	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	$-0.491095\pi$
$389$	−19.1637	−	19.1637i	−0.971637	−	0.971637i	−0.999609	+	0.0279717i	$0.991095\pi$
$390$	−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
$393$	−5.43726	−	11.3980i	−0.274273	−	0.574951i
$394$	−4.49766	+	10.8583i	−0.226589	+	0.547033i
$395$		−	3.54256i		−	0.178246i
$396$	2.65868	−	1.44389i	0.133604	−	0.0725584i
$397$	17.5510	−	7.26988i	0.880861	−	0.364865i	0.104030	−	0.994574i	$-0.466826\pi$
$397$	17.5510	−	7.26988i	0.880861	−	0.364865i	0.776831	+	0.629710i	$0.216826\pi$
$398$	−4.95235	+	2.05133i	−0.248239	+	0.102824i
$399$	21.2800	−	15.8940i	1.06533	−	0.795697i
$400$	2.27934	+	2.27934i	0.113967	+	0.113967i
$401$	−9.98347	−	24.1022i	−0.498551	−	1.20361i	−0.950264	−	0.311445i	$-0.899187\pi$
$401$	−9.98347	−	24.1022i	−0.498551	−	1.20361i	0.451714	−	0.892163i	$-0.350813\pi$
$402$	−0.225937	−	4.30699i	−0.0112687	−	0.214813i
$403$	35.2357	+	14.5951i	1.75522	+	0.727035i
$404$			11.4442i			0.569370i
$405$	11.7954	+	2.18369i	0.586117	+	0.108508i
$406$	10.7387	+	7.17450i	0.532951	+	0.356064i
$407$		−	4.92046i		−	0.243898i
$408$	5.94458	+	3.95753i	0.294300	+	0.195927i
$409$		−	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
$411$	3.92698	−	4.36179i	0.193703	−	0.215151i
$412$	14.2463			0.701865
$413$	0.377414	−	1.89793i	0.0185713	−	0.0933908i
$414$	4.20145	−	14.1891i	0.206490	−	0.697356i
$415$	12.9345	−	5.35765i	0.634930	−	0.262997i
$416$	3.36602	+	3.36602i	0.165033	+	0.165033i
$417$	3.83264	+	8.03426i	0.187685	+	0.393439i
$418$	2.23685	+	5.40024i	0.109408	+	0.264134i
$419$	2.44408	+	5.90053i	0.119401	+	0.288260i	0.972268	−	0.233868i	$-0.0751384\pi$
$419$	2.44408	+	5.90053i	0.119401	+	0.288260i	−0.852867	+	0.522128i	$0.825138\pi$
$420$	−5.24955	−	3.12241i	−0.256152	−	0.152358i
$421$		−	34.7377i		−	1.69301i	−0.532378	−	0.846507i	$-0.678702\pi$
$421$		−	34.7377i		−	1.69301i	0.532378	−	0.846507i	$-0.321298\pi$
$422$	5.70163	+	2.36169i	0.277551	+	0.114965i
$423$	−27.3010	+	2.87222i	−1.32742	+	0.139652i
$424$	13.2473			0.643344
$425$	−1.92868	−	13.1500i	−0.0935546	−	0.637869i
$426$	−4.61663	+	13.0391i	−0.223677	+	0.631744i
$427$	−18.3744	+	27.5025i	−0.889200	+	1.33094i
$428$	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	$-0.677156\pi$
$431$	−6.25744	+	2.59192i	−0.301410	+	0.124848i	0.226853	+	0.973929i	$0.427156\pi$
$432$	3.05359	−	4.20424i	0.146916	−	0.202276i
$433$	17.9285	−	17.9285i	0.861586	−	0.861586i	−0.129936	−	0.991522i	$-0.541477\pi$
$433$	17.9285	−	17.9285i	0.861586	−	0.861586i	0.991522	+	0.129936i	$0.0414772\pi$
$434$	−11.7757	+	17.6257i	−0.565254	+	0.846062i
$435$	−11.2535	+	0.590341i	−0.539566	+	0.0283047i
$436$	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	$-0.365973\pi$
$439$	1.09774	+	0.454700i	0.0523925	+	0.0217017i	−0.356333	+	0.934359i	$0.615973\pi$
$440$	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	$-0.100795\pi$
$444$	−3.63853	−	7.62735i	−0.172677	−	0.361978i
$445$	−5.79742	+	13.9962i	−0.274824	+	0.663484i
$446$			12.9552i			0.613448i
$447$	21.5493	+	19.4011i	1.01925	+	0.917641i
$448$	−2.19978	+	1.47002i	−0.103930	+	0.0694519i
$449$	10.9594	+	26.4584i	0.517207	+	1.24865i	0.939612	+	0.342242i	$0.111186\pi$
$449$	10.9594	+	26.4584i	0.517207	+	1.24865i	−0.422404	+	0.906407i	$0.638814\pi$
$450$	−9.61732	+	1.01180i	−0.453365	+	0.0476967i
$451$	−6.14049	+	6.14049i	−0.289145	+	0.289145i
$452$	−6.45188	−	15.5762i	−0.303471	−	0.732644i
$453$	−25.5486	+	1.34024i	−1.20038	+	0.0629698i
$454$	−0.610817	+	1.47464i	−0.0286671	+	0.0692084i
$455$	3.27584	+	16.4641i	0.153574	+	0.771847i
$456$	7.46071	+	6.71698i	0.349380	+	0.314551i
$457$	−22.8768	+	22.8768i	−1.07013	+	1.07013i	−0.0727847	+	0.997348i	$0.523189\pi$
$457$	−22.8768	+	22.8768i	−1.07013	+	1.07013i	−0.997348	+	0.0727847i	$0.976811\pi$
$458$	4.01729			0.187716
$459$	−20.4492	+	6.38981i	−0.954488	+	0.298251i
$460$		−	6.57461i		−	0.306543i
$461$	−23.3546	+	23.3546i	−1.08773	+	1.08773i	−0.0919679	+	0.995762i	$0.529316\pi$
$461$	−23.3546	+	23.3546i	−1.08773	+	1.08773i	−0.995762	+	0.0919679i	$0.970684\pi$
$462$	2.36251	−	3.97197i	0.109914	−	0.184793i
$463$			10.8396i			0.503757i	0.967759	+	0.251878i	$0.0810483\pi$
$463$			10.8396i			0.503757i	−0.967759	+	0.251878i	$0.918952\pi$
$464$	−1.86801	+	4.50977i	−0.0867200	+	0.209361i
$465$	−0.968947	−	18.4708i	−0.0449338	−	0.856564i
$466$	−20.0912	+	8.32203i	−0.930705	+	0.385511i
$467$	−13.0695	−	13.0695i	−0.604784	−	0.604784i	0.336794	−	0.941578i	$-0.390657\pi$
$467$	−13.0695	−	13.0695i	−0.604784	−	0.604784i	−0.941578	+	0.336794i	$0.890657\pi$
$468$	−14.2024	+	1.49418i	−0.656508	+	0.0690686i
$469$	−3.66044	−	5.47759i	−0.169023	−	0.252932i
$470$	−11.2681	+	4.66738i	−0.519757	+	0.215290i
$471$	−25.7546	−	23.1872i	−1.18671	−	1.06841i
$472$	0.731394			0.0336652
$473$	8.83418	+	3.65924i	0.406196	+	0.168252i
$474$	4.15498	−	1.98208i	0.190845	−	0.0910400i
$475$		−	18.6831i		−	0.857241i
$476$	10.8947	+	0.552466i	0.499358	+	0.0253222i
$477$	−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	−0.998279	−	0.0586481i	$-0.981321\pi$
$479$	−5.49162	+	13.2579i	−0.250919	+	0.605771i	0.747360	+	0.664419i	$0.231321\pi$
$480$	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
$483$	−5.56644	−	21.9083i	−0.253282	−	0.996862i
$484$	−7.05901	−	7.05901i	−0.320864	−	0.320864i
$485$	−2.71106	+	2.71106i	−0.123103	+	0.123103i
$486$	4.03838	+	15.0563i	0.183185	+	0.682967i
$487$	−1.57270	−	3.79684i	−0.0712660	−	0.172051i	0.884233	−	0.467047i	$-0.154682\pi$
$487$	−1.57270	−	3.79684i	−0.0712660	−	0.172051i	−0.955499	+	0.294995i	$0.904682\pi$
$488$	−11.5498	−	4.78410i	−0.522837	−	0.216566i
$489$	−12.4270	−	4.39994i	−0.561970	−	0.198972i
$490$	−9.33007	+	0.00101486i	−0.421489	+	4.58465e-5i
$491$	−1.01753	−	1.01753i	−0.0459205	−	0.0459205i	0.683774	−	0.729694i	$-0.260338\pi$
$491$	−1.01753	−	1.01753i	−0.0459205	−	0.0459205i	−0.729694	+	0.683774i	$0.760338\pi$
$492$	−4.97785	+	14.0593i	−0.224419	+	0.633840i
$493$	17.2798	−	10.3188i	0.778241	−	0.464734i
$494$		−	27.5904i		−	1.24135i
$495$	0.421919	+	4.01041i	0.0189638	+	0.180254i
$496$	−7.40204	−	3.06602i	−0.332361	−	0.137669i
$497$	4.12320	+	20.7229i	0.184951	+	0.929547i
$498$	13.5208	+	12.1729i	0.605881	+	0.545482i
$499$	8.51762	+	20.5633i	0.381301	+	0.920542i	0.991715	+	0.128459i	$0.0410032\pi$
$499$	8.51762	+	20.5633i	0.381301	+	0.920542i	−0.610414	+	0.792083i	$0.708997\pi$
$500$	−10.1264	+	4.19451i	−0.452868	+	0.187584i
$501$	−15.1992	+	7.25056i	−0.679048	+	0.323931i
$502$	2.71038	−	2.71038i	0.120970	−	0.120970i
$503$	−5.14895	+	2.13277i	−0.229580	+	0.0950953i	−0.494508	−	0.869173i	$-0.664652\pi$
$503$	−5.14895	+	2.13277i	−0.229580	+	0.0950953i	0.264928	+	0.964268i	$0.414652\pi$
$504$	0.725046	−	7.90407i	0.0322961	−	0.352075i
$505$	−14.0925	−	5.83729i	−0.627107	−	0.259756i
$506$	4.97455			0.221146
$507$	12.4349	+	11.1953i	0.552252	+	0.497199i
$508$	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	$0.396371\pi$
$510$	−7.90546	+	5.30160i	−0.350059	+	0.234759i
$511$	17.8072	−	3.54307i	0.787742	−	0.156736i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−29.7453	+	4.71579i	−1.31329	+	0.208207i
$514$	−18.9356			−0.835213
$515$	−7.26655	+	17.5430i	−0.320203	+	0.773038i
$516$	16.4000	−	0.860315i	0.721970	−	0.0378733i
$517$	−3.53148	−	8.52576i	−0.155315	−	0.374962i
$518$	−10.7336	−	7.17113i	−0.471608	−	0.315081i
$519$	−0.210304	+	0.100323i	−0.00923133	+	0.00440369i
$520$	−5.86184	+	2.42805i	−0.257059	+	0.106477i
$521$	0.900132	+	2.17311i	0.0394355	+	0.0952057i	0.942370	−	0.334572i	$-0.108592\pi$
$521$	0.900132	+	2.17311i	0.0394355	+	0.0952057i	−0.902935	+	0.429778i	$0.858592\pi$
$522$	−6.98881	−	12.8687i	−0.305892	−	0.563248i
$523$	−16.8864			−0.738392			−0.369196	−	0.929352i	$-0.620367\pi$
$523$	−16.8864			−0.738392			−0.369196	+	0.929352i	$0.620367\pi$
$524$	2.79016	−	6.73603i	0.121889	−	0.294265i
$525$	−11.8350	+	8.83956i	−0.516523	+	0.385790i
$526$	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
$532$	15.0402	+	2.99084i	0.652076	+	0.129669i
$533$	37.8700	−	15.6863i	1.64033	−	0.679447i
$534$	−19.6595	+	1.03130i	−0.850749	+	0.0446288i
$535$	−16.9926	+	16.9926i	−0.734656	+	0.734656i
$536$	1.76074	−	1.76074i	0.0760523	−	0.0760523i
$537$	−38.6027	+	2.02503i	−1.66583	+	0.0873865i
$538$	−5.85171	+	2.42386i	−0.252285	+	0.104500i
$539$	−0.000767871	−	7.05942i	−3.30745e−5	−	0.304071i
$540$	3.61960	+	5.90465i	0.155763	+	0.254096i
$541$	13.0001	−	31.3849i	0.558916	−	1.34934i	−0.351709	−	0.936109i	$-0.614399\pi$
$541$	13.0001	−	31.3849i	0.558916	−	1.34934i	0.910625	−	0.413233i	$-0.135601\pi$
$542$	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
$546$	−17.4774	+	13.0539i	−0.747966	+	0.558654i
$547$	6.56949	−	15.8602i	0.280891	−	0.678131i	−0.718966	−	0.695045i	$-0.755384\pi$
$547$	6.56949	−	15.8602i	0.280891	−	0.678131i	0.999857	+	0.0169143i	$0.00538425\pi$
$548$	3.38853			0.144751
$549$	32.9577	−	17.8989i	1.40660	−	0.763905i
$550$	−1.24404	−	3.00337i	−0.0530460	−	0.128064i
$551$	26.1385	−	10.8269i	1.11354	−	0.461242i
$552$	7.71120	−	3.67853i	0.328210	−	0.156569i
$553$	3.90646	−	5.84712i	0.166120	−	0.248645i
$554$	3.48379	+	8.41062i	0.148012	+	0.357333i
$555$	11.2483	−	0.590064i	0.477462	−	0.0250468i
$556$	−1.96674	+	4.74813i	−0.0834084	+	0.201366i
$557$	−4.36959			−0.185145			−0.0925727	−	0.995706i	$-0.529509\pi$
$557$	−4.36959			−0.185145			−0.0925727	+	0.995706i	$0.529509\pi$
$558$	21.1218	−	11.4710i	0.894159	−	0.485605i
$559$	−31.9152	−	31.9152i	−1.34987	−	1.34987i
$560$	−0.688161	−	3.45864i	−0.0290801	−	0.146154i
$561$	−4.01135	−	5.98151i	−0.169360	−	0.252540i
$562$	−3.39195			−0.143081
$563$	−26.6806	+	26.6806i	−1.12445	+	1.12445i	−0.133388	+	0.991064i	$0.542586\pi$
$563$	−26.6806	+	26.6806i	−1.12445	+	1.12445i	−0.991064	+	0.133388i	$0.957414\pi$
$564$	−11.7788	−	10.6046i	−0.495977	−	0.446534i
$565$	22.4716			0.945386
$566$	3.96953	+	1.64423i	0.166852	+	0.0691122i
$567$	17.0607	+	16.6113i	0.716480	+	0.697607i
$568$	−7.37814	+	3.05612i	−0.309580	+	0.128232i
$569$	8.09704	−	8.09704i	0.339445	−	0.339445i	−0.516713	−	0.856159i	$-0.672845\pi$
$569$	8.09704	−	8.09704i	0.339445	−	0.339445i	0.856159	+	0.516713i	$0.172845\pi$
$570$	−12.0768	+	5.76108i	−0.505841	+	0.241305i
$571$	−14.4189	+	5.97249i	−0.603411	+	0.249941i	−0.663408	−	0.748258i	$-0.730891\pi$
$571$	−14.4189	+	5.97249i	−0.603411	+	0.249941i	0.0599975	+	0.998199i	$0.480891\pi$
$572$	−1.83714	−	4.43525i	−0.0768147	−	0.185447i
$573$	−11.6623	−	10.4997i	−0.487198	−	0.438631i
$574$	4.44581	+	22.3442i	0.185565	+	0.932631i
$575$	−14.6900	−	6.08480i	−0.612615	−	0.253754i
$576$	2.98353	−	0.313886i	0.124314	−	0.0130786i
$577$			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
$581$	27.2568	+	5.42018i	1.13080	+	0.224867i
$582$	−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
$585$	5.40424	−	18.2511i	0.223438	−	0.754592i
$586$	−5.23121	+	5.23121i	−0.216099	+	0.216099i
$587$	−18.6794	−	18.6794i	−0.770983	−	0.770983i	0.207296	−	0.978278i	$-0.433534\pi$
$587$	−18.6794	−	18.6794i	−0.770983	−	0.770983i	−0.978278	+	0.207296i	$0.933534\pi$
$588$	−5.22141	−	10.9424i	−0.215327	−	0.451258i
$589$	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	−0.736365	−	0.676584i	$-0.763459\pi$
$593$	−1.45576	+	1.45576i	−0.0597807	+	0.0597807i	0.676584	+	0.736365i	$0.263459\pi$
$594$	−4.46764	+	2.73870i	−0.183310	+	0.112370i
$595$	−6.23733	+	13.1340i	−0.255706	+	0.538443i
$596$			16.7409i			0.685735i
$597$	8.37982	−	3.99748i	0.342963	−	0.163606i
$598$	−21.6936	−	8.98576i	−0.887115	−	0.367455i
$599$	−4.25202			−0.173733			−0.0868664	−	0.996220i	$-0.527685\pi$
$599$	−4.25202			−0.173733			−0.0868664	+	0.996220i	$0.527685\pi$
$600$	−4.14932	−	3.73569i	−0.169395	−	0.152509i
$601$	6.29865	−	2.60899i	0.256927	−	0.106423i	−0.250502	−	0.968116i	$-0.580596\pi$
$601$	6.29865	−	2.60899i	0.256927	−	0.106423i	0.507430	+	0.861693i	$0.330596\pi$
$602$	20.8574	−	13.9381i	0.850083	−	0.568074i
$603$	0.781594	+	7.42918i	0.0318290	+	0.302540i
$604$	−10.4445	−	10.4445i	−0.424982	−	0.424982i
$605$	12.2931	−	5.09196i	0.499785	−	0.207018i
$606$	−1.03839	−	19.7947i	−0.0421819	−	0.804105i
$607$	−1.35013	+	3.25951i	−0.0548003	+	0.132300i	−0.948908	−	0.315551i	$-0.897811\pi$
$607$	−1.35013	+	3.25951i	−0.0548003	+	0.132300i	0.894108	+	0.447851i	$0.147811\pi$
$608$			5.79598i			0.235058i
$609$	−19.2253	−	11.4352i	−0.779050	−	0.463376i
$610$	11.7824	−	11.7824i	0.477054	−	0.477054i
$611$			43.5591i			1.76221i
$612$	−10.6413	−	6.30584i	−0.430147	−	0.254898i
$613$	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
$615$	−14.7737	−	13.3009i	−0.595731	−	0.536344i
$616$	2.61691	−	0.520684i	0.105438	−	0.0209790i
$617$	−8.98487	+	21.6914i	−0.361717	+	0.873263i	0.633332	+	0.773880i	$0.281687\pi$
$617$	−8.98487	+	21.6914i	−0.361717	+	0.873263i	−0.995049	+	0.0993825i	$0.968313\pi$
$618$	−24.6414	+	1.29265i	−0.991224	+	0.0519979i
$619$	11.9980	+	28.9657i	0.482240	+	1.16423i	0.958543	+	0.284948i	$0.0919764\pi$
$619$	11.9980	+	28.9657i	0.482240	+	1.16423i	−0.476303	+	0.879281i	$0.658024\pi$
$620$	7.55105	−	7.55105i	0.303258	−	0.303258i
$621$	−5.97967	+	24.9237i	−0.239956	+	1.00015i
$622$	6.53137	+	15.7681i	0.261884	+	0.632244i
$623$	−25.0028	+	16.7083i	−1.00171	+	0.669403i
$624$	−6.12754	−	5.51670i	−0.245298	−	0.220845i
$625$			1.50807i			0.0603229i
$626$	2.51545	−	6.07284i	0.100538	−	0.242719i
$627$	−4.35901	−	9.13768i	−0.174082	−	0.364924i
$628$		−	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	−0.179333	−	0.983788i	$-0.557394\pi$
$631$	20.2077	−	20.2077i	0.804456	−	0.804456i	0.983788	+	0.179333i	$0.0573938\pi$
$632$	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
$636$	−22.9134	+	1.20200i	−0.908576	+	0.0476623i
$637$	−12.7484	+	30.7868i	−0.505110	+	1.21982i
$638$	3.48092	−	3.48092i	0.137811	−	0.137811i
$639$	6.80216	−	22.9722i	0.269089	−	0.908766i
$640$	1.23141	−	0.510066i	0.0486757	−	0.0201621i
$641$	14.0792	−	33.9902i	0.556095	−	1.34253i	−0.356741	−	0.934203i	$-0.616112\pi$
$641$	14.0792	−	33.9902i	0.556095	−	1.34253i	0.912835	−	0.408328i	$-0.133888\pi$
$642$	−29.4377	−	10.4228i	−1.16181	−	0.411354i
$643$	−38.8548	−	16.0942i	−1.53228	−	0.634693i	−0.552279	−	0.833660i	$-0.686242\pi$
$643$	−38.8548	−	16.0942i	−1.53228	−	0.634693i	−0.980006	+	0.198966i	$0.936242\pi$
$644$	7.24996	−	10.8516i	0.285689	−	0.427614i
$645$	−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	$0.533831\pi$
$648$	−4.90023	+	7.54902i	−0.192499	+	0.296554i
$649$	−0.681456	−	0.282268i	−0.0267495	−	0.0110800i
$650$			15.3446i			0.601864i
$651$	18.7689	−	31.5552i	0.735611	−	1.23675i
$652$	−2.91268	−	7.03182i	−0.114069	−	0.275387i
$653$	−6.82196	−	16.4697i	−0.266964	−	0.644508i	0.732374	−	0.680903i	$-0.238412\pi$
$653$	−6.82196	−	16.4697i	−0.266964	−	0.644508i	−0.999337	+	0.0363952i	$0.988412\pi$
$654$	−9.31280	−	19.5222i	−0.364159	−	0.763377i
$655$	6.87164	+	6.87164i	0.268497	+	0.268497i
$656$	−7.95541	+	3.29524i	−0.310607	+	0.128658i
$657$	−19.7400	−	5.84510i	−0.770131	−	0.228039i
$658$	−23.7451	−	4.72186i	−0.925682	−	0.184077i
$659$	−16.0624			−0.625702			−0.312851	−	0.949802i	$-0.601284\pi$
$659$	−16.0624			−0.625702			−0.312851	+	0.949802i	$0.601284\pi$
$660$	−1.55777	+	1.73026i	−0.0606363	+	0.0673503i
$661$	−1.76602	−	1.76602i	−0.0686902	−	0.0686902i	0.671927	−	0.740617i	$-0.265467\pi$
$661$	−1.76602	−	1.76602i	−0.0686902	−	0.0686902i	−0.740617	+	0.671927i	$0.765467\pi$
$662$		−	2.64132i		−	0.102658i
$663$	6.68846	+	33.3307i	0.259758	+	1.29446i
$664$			10.5038i			0.407628i
$665$	−11.3544	+	16.9951i	−0.440306	+	0.659043i
$666$	6.98553	+	12.8627i	0.270684	+	0.498418i
$667$		−	24.0781i		−	0.932308i
$668$	−8.98248	−	3.72067i	−0.347543	−	0.143957i
$669$	−1.17550	−	22.4083i	−0.0454475	−	0.866356i
$670$	1.27009	+	3.06628i	0.0490680	+	0.118461i
$671$	8.91490	+	8.91490i	0.344156	+	0.344156i
$672$	3.67152	−	2.74225i	0.141632	−	0.105785i
$673$	16.5668	−	6.86219i	0.638603	−	0.264518i	−0.0398005	−	0.999208i	$-0.512672\pi$
$673$	16.5668	−	6.86219i	0.638603	−	0.264518i	0.678403	+	0.734690i	$0.262672\pi$
$674$	5.68685	−	2.35557i	0.219049	−	0.0907332i
$675$	16.5430	−	2.62272i	0.636741	−	0.100948i
$676$			9.66022i			0.371547i
$677$	−5.48037	+	13.2308i	−0.210628	+	0.508501i	−0.993520	−	0.113657i	$-0.963744\pi$
$677$	−5.48037	+	13.2308i	−0.210628	+	0.508501i	0.782892	+	0.622157i	$0.213744\pi$
$678$	12.5730	+	26.3564i	0.482862	+	1.01221i
$679$	−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	$-0.479566\pi$
$683$	−15.5796	−	6.45330i	−0.596138	−	0.246929i	−0.660289	+	0.751012i	$0.729566\pi$
$684$	−13.5141	−	10.9412i	−0.516723	−	0.418348i
$685$	−1.72837	+	4.17266i	−0.0660377	+	0.159429i
$686$	−15.4007	−	10.2868i	−0.588002	−	0.392752i
$687$	−6.94860	+	0.364511i	−0.265106	+	0.0139070i
$688$	6.70448	+	6.70448i	0.255606	+	0.255606i
$689$	44.5906	+	44.5906i	1.69877	+	1.69877i
$690$	0.596551	+	11.3719i	0.0227103	+	0.432922i
$691$	3.70085	−	1.53294i	0.140787	−	0.0583159i	−0.311177	−	0.950352i	$-0.600723\pi$
$691$	3.70085	−	1.53294i	0.140787	−	0.0583159i	0.451965	+	0.892036i	$0.350723\pi$
$692$	−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
$699$	33.9960	−	16.2174i	1.28585	−	0.613397i
$700$	−8.36471	−	1.66337i	−0.316156	−	0.0628695i
$701$	35.7287			1.34946			0.674728	−	0.738067i	$-0.264261\pi$
$701$	35.7287			1.34946			0.674728	+	0.738067i	$0.264261\pi$
$702$	24.4300	−	3.87311i	0.922051	−	0.146181i
$703$	−26.1262	+	10.8218i	−0.985370	+	0.408154i
$704$	0.385932	+	0.931721i	0.0145453	+	0.0351156i
$705$	19.0665	−	9.09545i	0.718088	−	0.342555i
$706$	13.5141	−	13.5141i	0.508609	−	0.508609i
$707$	−16.8232	−	25.1747i	−0.632701	−	0.946793i
$708$	−1.26507	+	0.0663635i	−0.0475443	+	0.00249409i
$709$	−29.9490	−	12.4053i	−1.12476	−	0.465890i	−0.258761	−	0.965941i	$-0.583314\pi$
$709$	−29.9490	−	12.4053i	−1.12476	−	0.465890i	−0.865996	+	0.500052i	$0.833314\pi$
$710$		−	10.6443i		−	0.399474i
$711$	−7.00691	+	3.80536i	−0.262780	+	0.142712i
$712$	−8.03699	−	8.03699i	−0.301199	−	0.301199i
$713$	39.5202			1.48004
$714$	−18.8944	+	0.0329528i	−0.707106	+	0.00123323i
$715$	6.39867			0.239297
$716$	−15.7812	−	15.7812i	−0.589770	−	0.589770i
$717$	−11.5284	+	12.8048i	−0.430534	+	0.478205i
$718$		−	17.1095i		−	0.638522i
$719$	28.8463	+	11.9485i	1.07579	+	0.445605i	0.849029	−	0.528347i	$-0.177188\pi$
$719$	28.8463	+	11.9485i	1.07579	+	0.445605i	0.226756	+	0.973952i	$0.427188\pi$
$720$	−1.13528	+	3.83405i	−0.0423093	+	0.142887i
$721$	−31.3388	+	20.9424i	−1.16712	+	0.779934i
$722$	10.3191	−	10.3191i	0.384035	−	0.384035i
$723$	8.28379	+	17.3651i	0.308078	+	0.645814i
$724$	5.49208	+	13.2590i	0.204111	+	0.492769i
$725$	−14.5371	+	6.02146i	−0.539894	+	0.223631i
$726$	12.8503	+	11.5693i	0.476919	+	0.429376i
$727$	25.7831			0.956243			0.478121	−	0.878294i	$-0.341318\pi$
$727$	25.7831			0.956243			0.478121	+	0.878294i	$0.341318\pi$
$728$	−12.3526	−	2.45639i	−0.457819	−	0.0910400i
$729$	−8.35121	−	25.6760i	−0.309304	−	0.950963i
$730$	−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	−0.928400	−	0.371581i	$-0.878816\pi$
$733$	−35.1957	−	35.1957i	−1.29998	−	1.29998i	−0.371581	−	0.928400i	$-0.621184\pi$
$734$	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
$738$	7.33437	−	24.7696i	0.269982	−	0.911781i
$739$	−11.9449	−	11.9449i	−0.439402	−	0.439402i	0.452409	−	0.891811i	$-0.350565\pi$
$739$	−11.9449	−	11.9449i	−0.439402	−	0.439402i	−0.891811	+	0.452409i	$0.850565\pi$
$740$	4.59840	+	4.59840i	0.169041	+	0.169041i
$741$	2.50343	+	47.7224i	0.0919660	+	1.75313i
$742$	−29.1411	+	19.4737i	−1.06980	+	0.714904i
$743$	3.70695	−	8.94938i	0.135995	−	0.328321i	−0.841181	−	0.540754i	$-0.818139\pi$
$743$	3.70695	−	8.94938i	0.135995	−	0.328321i	0.977176	+	0.212433i	$0.0681389\pi$
$744$	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
$750$	17.1348	−	8.17396i	0.625676	−	0.298471i
$751$	12.4357	−	30.0224i	0.453784	−	1.09553i	−0.517087	−	0.855933i	$-0.672984\pi$
$751$	12.4357	−	30.0224i	0.453784	−	1.09553i	0.970872	−	0.239600i	$-0.0770162\pi$
$752$		−	9.15054i		−	0.333686i
$753$	−4.44213	+	4.93399i	−0.161880	+	0.179805i
$754$	−21.4677	+	8.89223i	−0.781809	+	0.323836i
$755$	18.1889	−	7.53408i	0.661961	−	0.274193i
$756$	−0.536913	+	13.7372i	−0.0195273	+	0.499619i
$757$	21.2025	+	21.2025i	0.770619	+	0.770619i	0.978215	−	0.207596i	$-0.0665639\pi$
$757$	21.2025	+	21.2025i	0.770619	+	0.770619i	−0.207596	+	0.978215i	$0.566564\pi$
$758$	−3.82513	−	9.23469i	−0.138935	−	0.335419i
$759$	−8.60435	+	0.451369i	−0.312318	+	0.0163837i
$760$	−7.13721	−	2.95633i	−0.258894	−	0.107237i
$761$			30.9757i			1.12287i	0.827522	+	0.561434i	$0.189750\pi$
$761$			30.9757i			1.12287i	−0.827522	+	0.561434i	$0.810250\pi$
$762$	−10.0365	+	11.1478i	−0.363585	+	0.403843i
$763$	−27.4727	−	18.3545i	−0.994577	−	0.664477i
$764$		−	9.06002i		−	0.327780i
$765$	13.1928	−	9.88734i	0.476987	−	0.357477i
$766$			32.2091i			1.16376i
$767$	2.46189	+	2.46189i	0.0888937	+	0.0888937i
$768$	1.28722	+	1.15890i	0.0464487	+	0.0418183i
$769$	−9.51746			−0.343208			−0.171604	−	0.985166i	$-0.554895\pi$
$769$	−9.51746			−0.343208			−0.171604	+	0.985166i	$0.554895\pi$
$770$	−0.693623	+	3.48807i	−0.0249964	+	0.125701i
$771$	32.7524	−	1.71813i	1.17955	−	0.0618770i
$772$	−3.93964	+	1.63185i	−0.141791	+	0.0587317i
$773$	9.38088	+	9.38088i	0.337407	+	0.337407i	0.855391	−	0.517984i	$-0.173317\pi$
$773$	9.38088	+	9.38088i	0.337407	+	0.337407i	−0.517984	+	0.855391i	$0.673317\pi$
$774$	−28.2886	+	2.97613i	−1.01681	+	0.106975i
$775$	−9.88323	−	23.8602i	−0.355016	−	0.857084i
$776$	−1.10080	−	2.65756i	−0.0395164	−	0.0954009i
$777$	19.2163	+	11.4298i	0.689382	+	0.410041i
$778$			27.1015i			0.971637i
$779$	46.1094	+	19.0991i	1.65204	+	0.684298i
$780$	9.91876	−	4.73162i	0.355148	−	0.169419i
$781$	8.05382			0.288188
$782$	−10.4273	−	17.4615i	−0.372880	−	0.624423i
$783$	13.2560	+	21.6245i	0.473731	+	0.772797i
$784$	2.67808	−	6.46745i	0.0956457	−	0.230980i
$785$	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	$-0.855388\pi$
$787$	1.32204	−	3.19169i	0.0471256	−	0.113771i	0.945689	+	0.325072i	$0.105388\pi$
$788$	10.8583	−	4.49766i	0.386811	−	0.160222i
$789$	−18.7445	+	0.983303i	−0.667322	+	0.0350065i
$790$	−2.50497	+	2.50497i	−0.0891228	+	0.0891228i
$791$	37.0901	+	24.7799i	1.31877	+	0.881072i
$792$	−2.90096	−	0.858986i	−0.103081	−	0.0305227i
$793$	−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	0.136663	−	0.990618i	$-0.456362\pi$
$797$	31.8245	−	31.8245i	1.12728	−	1.12728i	0.990618	−	0.136663i	$-0.0436378\pi$
$798$	−26.2860	−	3.80848i	−0.930516	−	0.134819i
$799$	−22.5244	+	30.2672i	−0.796856	+	1.07078i
$800$		−	3.22347i		−	0.113967i
$801$	33.9109	−	3.56763i	1.19818	−	0.126056i
$802$	−9.98347	+	24.1022i	−0.352528	+	0.851079i
$803$		−	6.92065i		−	0.244224i
$804$	−2.88574	+	3.20526i	−0.101772	+	0.113041i
$805$	9.66481	+	14.4627i	0.340640	+	0.509743i
$806$	−14.5951	−	35.2357i	−0.514091	−	1.24113i
$807$	9.90161	−	4.72344i	0.348553	−	0.166273i
$808$	8.09226	−	8.09226i	0.284685	−	0.284685i
$809$	15.0511	+	36.3365i	0.529168	+	1.27752i	0.932069	+	0.362280i	$0.118002\pi$
$809$	15.0511	+	36.3365i	0.529168	+	1.27752i	−0.402902	+	0.915243i	$0.631998\pi$
$810$	−6.79648	−	9.88468i	−0.238804	−	0.347312i
$811$	0.771029	−	1.86143i	0.0270745	−	0.0653636i	−0.909764	−	0.415126i	$-0.863738\pi$
$811$	0.771029	−	1.86143i	0.0270745	−	0.0653636i	0.936839	+	0.349762i	$0.113738\pi$
$812$	−2.52024	−	12.6665i	−0.0884432	−	0.444508i
$813$	−8.23271	+	9.14427i	−0.288734	+	0.320704i
$814$	−3.47929	+	3.47929i	−0.121949	+	0.121949i
$815$	10.1447			0.355353
$816$	−1.40506	−	7.00184i	−0.0491868	−	0.245114i
$817$		−	54.9549i		−	1.92263i
$818$	−2.78010	+	2.78010i	−0.0972038	+	0.0972038i
$819$	29.0458	−	24.1648i	1.01494	−	0.844385i
$820$		−	11.4772i		−	0.400800i
$821$	−12.1383	+	29.3045i	−0.423630	+	1.02273i	0.557638	+	0.830084i	$0.311708\pi$
$821$	−12.1383	+	29.3045i	−0.423630	+	1.02273i	−0.981268	+	0.192649i	$0.938292\pi$
$822$	−5.86104	+	0.307460i	−0.204427	+	0.0107239i
$823$	2.74624	−	1.13753i	0.0957279	−	0.0396518i	−0.334306	−	0.942465i	$-0.608502\pi$
$823$	2.74624	−	1.13753i	0.0957279	−	0.0396518i	0.430033	+	0.902813i	$0.358502\pi$
$824$	−10.0737	−	10.0737i	−0.350933	−	0.350933i
$825$	2.42429	+	5.08197i	0.0844030	+	0.176932i
$826$	−1.60891	+	1.07516i	−0.0559811	+	0.0374098i
$827$	−14.5583	+	6.03025i	−0.506242	+	0.209692i	−0.621162	−	0.783682i	$-0.713339\pi$
$827$	−14.5583	+	6.03025i	−0.506242	+	0.209692i	0.114920	+	0.993375i	$0.463339\pi$
$828$	−13.0041	+	7.06233i	−0.451923	+	0.245433i
$829$	52.3731			1.81899			0.909496	−	0.415712i	$-0.136467\pi$
$829$	52.3731			1.81899			0.909496	+	0.415712i	$0.136467\pi$
$830$	−12.9345	−	5.35765i	−0.448963	−	0.185967i
$831$	−6.78896	−	14.2315i	−0.235506	−	0.493686i
$832$		−	4.76028i		−	0.165033i
$833$	−24.7781	+	14.8001i	−0.858511	+	0.512795i
$834$	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	0.991219	+	0.132233i	$0.0422148\pi$
$839$	11.1177	+	26.8404i	0.383824	+	0.926634i	−0.607394	+	0.794400i	$0.707785\pi$
$840$	1.50411	+	5.91987i	0.0518969	+	0.204255i
$841$	3.65754	+	3.65754i	0.126122	+	0.126122i
$842$	−24.5633	+	24.5633i	−0.846507	+	0.846507i
$843$	5.86696	−	0.307770i	0.202069	−	0.0106002i
$844$	−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
$847$	25.9052	+	5.15140i	0.890113	+	0.177004i
$848$	−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
$852$	12.4845	−	5.95555i	0.427711	−	0.204034i
$853$	−19.7643	−	8.18664i	−0.676717	−	0.280305i	0.0177368	−	0.999843i	$-0.494354\pi$
$853$	−19.7643	−	8.18664i	−0.676717	−	0.280305i	−0.694454	+	0.719537i	$0.744354\pi$
$854$	32.4399	−	6.45452i	1.11007	−	0.220869i
$855$	20.3662	−	11.0606i	0.696508	−	0.378264i
$856$	−6.89968	−	16.6573i	−0.235826	−	0.569334i
$857$	−14.6178	+	6.05490i	−0.499335	+	0.206831i	−0.618113	−	0.786090i	$-0.712102\pi$
$857$	−14.6178	+	6.05490i	−0.499335	+	0.206831i	0.118778	+	0.992921i	$0.462102\pi$
$858$	3.58009	+	7.50484i	0.122222	+	0.256211i
$859$	21.8132	−	21.8132i	0.744258	−	0.744258i	−0.229136	−	0.973394i	$-0.573590\pi$
$859$	21.8132	−	21.8132i	0.744258	−	0.744258i	0.973394	+	0.229136i	$0.0735901\pi$
$860$	−11.6757	+	4.83622i	−0.398137	+	0.164914i
$861$	−9.71721	−	38.2448i	−0.331162	−	1.30338i
$862$	6.25744	+	2.59192i	0.213129	+	0.0882811i
$863$	−38.1783			−1.29960			−0.649802	−	0.760103i	$-0.725148\pi$
$863$	−38.1783			−1.29960			−0.649802	+	0.760103i	$0.725148\pi$
$864$	−5.13206	+	0.813632i	−0.174596	+	0.0276803i
$865$	0.126789	−	0.126789i	0.00431095	−	0.00431095i
$866$	−25.3547			−0.861586
$867$	−12.5878	+	26.6186i	−0.427504	+	0.904013i
$868$	20.7900	−	4.13656i	0.705658	−	0.140404i
$869$	−1.89534	−	1.89534i	−0.0642949	−	0.0642949i
$870$	8.37489	+	7.54002i	0.283935	+	0.255631i
$871$	11.8534			0.401636
$872$	4.77892	−	11.5373i	0.161834	−	0.390703i
$873$	8.27445	+	2.45010i	0.280048	+	0.0829233i
$874$	−10.9408	−	26.4135i	−0.370078	−	0.893448i
$875$	16.1100	−	24.1131i	0.544616	−	0.815171i
$876$	−5.11761	−	10.7279i	−0.172908	−	0.362462i
$877$	−14.2119	+	5.88676i	−0.479902	+	0.198782i	−0.609502	−	0.792785i	$-0.708631\pi$
$877$	−14.2119	+	5.88676i	−0.479902	+	0.198782i	0.129600	+	0.991566i	$0.458631\pi$
$878$	−0.454700	−	1.09774i	−0.0153454	−	0.0370471i
$879$	8.57362	−	9.52294i	0.289181	−	0.321201i
$880$	−1.34418			−0.0453123
$881$	−3.84673	+	9.28683i	−0.129600	+	0.312881i	−0.975338	−	0.220717i	$-0.929160\pi$
$881$	−3.84673	+	9.28683i	−0.129600	+	0.312881i	0.845738	+	0.533598i	$0.179160\pi$
$882$	10.0242	+	18.4531i	0.337532	+	0.621347i
$883$	−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	−0.826721	−	0.562611i	$-0.809797\pi$
$887$	4.63670	−	11.1940i	0.155685	−	0.375858i	0.982407	+	0.186754i	$0.0597967\pi$
$888$	−2.82052	+	7.96618i	−0.0946505	+	0.267327i
$889$	−4.46892	+	22.4732i	−0.149883	+	0.753726i
$890$	13.9962	−	5.79742i	0.469154	−	0.194330i
$891$	7.47906	−	5.14243i	0.250558	−	0.172278i
$892$	9.16074	−	9.16074i	0.306724	−	0.306724i
$893$	−37.5024	+	37.5024i	−1.25497	+	1.25497i
$894$	−1.51900	−	28.9563i	−0.0508029	−	0.968444i
$895$	27.4825	−	11.3836i	0.918638	−	0.380512i
$896$	2.59494	+	0.516019i	0.0866909	+	0.0172390i
$897$	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
$903$	−34.8118	+	26.0009i	−1.15846	+	0.865254i
$904$	−6.45188	+	15.5762i	−0.214586	+	0.518058i
$905$	−19.1286			−0.635857
$906$	19.0133	+	17.1179i	0.631675	+	0.568705i
$907$	−21.3566	−	51.5595i	−0.709135	−	1.71200i	−0.702151	−	0.712028i	$-0.747777\pi$
$907$	−21.3566	−	51.5595i	−0.709135	−	1.71200i	−0.00698393	−	0.999976i	$-0.502223\pi$
$908$	1.47464	−	0.610817i	0.0489377	−	0.0202707i
$909$	3.59217	+	34.1441i	0.119145	+	1.13249i
$910$	9.32548	−	13.9582i	0.309137	−	0.462710i
$911$	−12.3815	−	29.8915i	−0.410217	−	0.990351i	−0.985079	−	0.172101i	$-0.944944\pi$
$911$	−12.3815	−	29.8915i	−0.410217	−	0.990351i	0.574862	−	0.818250i	$-0.305056\pi$
$912$	−0.525901	−	10.0251i	−0.0174143	−	0.331966i
$913$	4.05376	−	9.78665i	0.134160	−	0.323891i
$914$	32.3527			1.07013
$915$	−19.3105	+	21.4487i	−0.638387	+	0.709072i
$916$	−2.84065	−	2.84065i	−0.0938578	−	0.0938578i
$917$	3.76437	+	18.9194i	0.124310	+	0.624773i
$918$	18.9781	+	9.94150i	0.626369	+	0.328118i
$919$	−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
$921$	−0.378954	+	0.420914i	−0.0124870	+	0.0138696i
$922$	33.0283			1.08773
$923$	−35.1220	−	14.5480i	−1.15605	−	0.478853i
$924$	−4.47916	+	1.13806i	−0.147353	+	0.0374394i
$925$	14.5303	−	6.01863i	0.477752	−	0.197891i
$926$	7.66472	−	7.66472i	0.251878	−	0.251878i
$927$	42.5043	−	4.47171i	1.39603	−	0.146870i
$928$	4.50977	−	1.86801i	0.148040	−	0.0613203i
$929$	1.12368	+	2.71280i	0.0368667	+	0.0890042i	0.941240	−	0.337737i	$-0.109661\pi$
$929$	1.12368	+	2.71280i	0.0368667	+	0.0890042i	−0.904374	+	0.426741i	$0.859661\pi$
$930$	−12.3757	+	13.7460i	−0.405815	+	0.450749i
$931$	−37.4818	+	15.5302i	−1.22842	+	0.508983i
$932$	20.0912	+	8.32203i	0.658108	+	0.272597i
$933$	−12.7279	−	26.6811i	−0.416692	−	0.873499i
$934$			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	$-0.108278\pi$
$937$	18.6435	+	18.6435i	0.609056	+	0.609056i	−0.333643	+	0.942699i	$0.608278\pi$
$938$	−1.28492	+	6.46156i	−0.0419541	+	0.210977i
$939$	−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	−0.912663	−	0.408713i	$-0.865978\pi$
$941$	−17.0654	−	41.1995i	−0.556316	−	1.34307i	0.356347	−	0.934354i	$-0.384022\pi$
$942$	1.81543	+	34.6071i	0.0591498	+	1.12756i
$943$	30.0342	−	30.0342i	0.978047	−	0.978047i
$944$	−0.517174	−	0.517174i	−0.0168326	−	0.0168326i
$945$	−16.6423	−	7.66806i	−0.541374	−	0.249442i
$946$	−3.65924	−	8.83418i	−0.118972	−	0.287224i
$947$	15.7427	−	38.0062i	0.511569	−	1.23504i	−0.431401	−	0.902160i	$-0.641981\pi$
$947$	15.7427	−	38.0062i	0.511569	−	1.23504i	0.942970	−	0.332877i	$-0.108019\pi$
$948$	−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
$952$	−7.31307	−	8.09438i	−0.237018	−	0.262340i
$953$			35.2415i			1.14158i	0.821095	+	0.570792i	$0.193364\pi$
$953$			35.2415i			1.14158i	−0.821095	+	0.570792i	$0.806636\pi$
$954$	39.5237	−	4.15812i	1.27963	−	0.134624i
$955$	11.1566	+	4.62121i	0.361019	+	0.149539i
$956$	−9.94764			−0.321730
$957$	−5.70502	+	6.33670i	−0.184417	+	0.204837i
$958$	13.2579	−	5.49162i	0.428345	−	0.177426i
$959$	−7.45402	+	4.98120i	−0.240703	+	0.160851i
$960$	−2.08365	+	0.993980i	−0.0672496	+	0.0320806i
$961$	23.4693	+	23.4693i	0.757075	+	0.757075i
$962$	21.4577	−	8.88806i	0.691823	−	0.286562i
$963$	51.8633	+	15.3569i	1.67127	+	0.494870i
$964$	−4.25087	+	10.2625i	−0.136911	+	0.330533i
$965$		−	5.68366i		−	0.182964i
$966$	−11.5554	+	19.4276i	−0.371790	+	0.625072i
$967$	−21.1221	+	21.1221i	−0.679239	+	0.679239i	−0.959828	−	0.280589i	$-0.909470\pi$
$967$	−21.1221	+	21.1221i	−0.679239	+	0.679239i	0.280589	+	0.959828i	$0.409470\pi$
$968$			9.98295i			0.320864i
$969$	−22.9377	+	34.4546i	−0.736866	+	1.10684i
$970$	3.83402			0.123103
$971$	−3.56265	+	3.56265i	−0.114331	+	0.114331i	−0.761958	−	0.647627i	$-0.775762\pi$
$971$	−3.56265	+	3.56265i	−0.114331	+	0.114331i	0.647627	+	0.761958i	$0.275762\pi$
$972$	7.79083	−	13.5020i	0.249891	−	0.433076i
$973$	−2.65345	−	13.3360i	−0.0850657	−	0.427533i
$974$	−1.57270	+	3.79684i	−0.0503927	+	0.121659i
$975$	−1.39230	−	26.5411i	−0.0445893	−	0.849996i
$976$	4.78410	+	11.5498i	0.153135	+	0.369701i
$977$	−12.9986	+	12.9986i	−0.415862	+	0.415862i	−0.883775	−	0.467913i	$-0.845006\pi$
$977$	−12.9986	+	12.9986i	−0.415862	+	0.415862i	0.467913	+	0.883775i	$0.345006\pi$
$978$	5.67601	+	11.8985i	0.181499	+	0.380471i
$979$	4.38650	+	10.5900i	0.140193	+	0.338457i
$980$	6.59807	+	6.59664i	0.210768	+	0.210722i
$981$	17.8795	+	32.9220i	0.570847	+	1.05112i
$982$			1.43901i			0.0459205i
$983$	0.688609	−	1.66245i	0.0219632	−	0.0530239i	−0.912517	−	0.409038i	$-0.865864\pi$
$983$	0.688609	−	1.66245i	0.0219632	−	0.0530239i	0.934481	+	0.356014i	$0.115864\pi$
$984$	13.4613	−	6.42153i	0.429129	−	0.204711i
$985$			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	−0.230892	−	0.972979i	$-0.574164\pi$
$991$	−34.0665	−	14.1108i	−1.08216	−	0.448244i	−0.851265	+	0.524735i	$0.824164\pi$
$992$	3.06602	+	7.40204i	0.0973463	+	0.235015i
$993$	0.239661	+	4.56862i	0.00760543	+	0.144981i
$994$	11.7377	−	17.5688i	0.372298	−	0.557249i
$995$	−5.05205	+	5.05205i	−0.160161	+	0.160161i
$996$	−0.953071	−	18.1682i	−0.0301992	−	0.575681i
$997$	15.7482	−	6.52312i	0.498751	−	0.206589i	−0.119104	−	0.992882i	$-0.538002\pi$
$997$	15.7482	−	6.52312i	0.498751	−	0.206589i	0.617854	+	0.786293i	$0.288002\pi$
$998$	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.f.671.15	yes	80
3.2	odd	2		714.2.w.e.671.20	yes	80
7.6	odd	2	inner	714.2.w.f.671.6	yes	80
17.15	even	8		714.2.w.e.83.1	✓	80
21.20	even	2		714.2.w.e.671.1	yes	80
51.32	odd	8	inner	714.2.w.f.83.6	yes	80
119.83	odd	8		714.2.w.e.83.20	yes	80
357.83	even	8	inner	714.2.w.f.83.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.w.e.83.1	✓	80	17.15	even	8
714.2.w.e.83.20	yes	80	119.83	odd	8
714.2.w.e.671.1	yes	80	21.20	even	2
714.2.w.e.671.20	yes	80	3.2	odd	2
714.2.w.f.83.6	yes	80	51.32	odd	8	inner
714.2.w.f.83.15	yes	80	357.83	even	8	inner
714.2.w.f.671.6	yes	80	7.6	odd	2	inner
714.2.w.f.671.15	yes	80	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.28722 + 1.15890i) q^{3} +1.00000i q^{4} +(-1.23141 - 0.510066i) q^{5} +(-0.0907356 - 1.72967i) q^{6} +(-1.47002 - 2.19978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.313886 + 2.98353i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.28722 + 1.15890i) q^{3} +1.00000i q^{4} +(-1.23141 - 0.510066i) q^{5} +(-0.0907356 - 1.72967i) q^{6} +(-1.47002 - 2.19978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.313886 + 2.98353i) q^{9} +(0.510066 + 1.23141i) q^{10} +(-0.931721 + 0.385932i) q^{11} +(-1.15890 + 1.28722i) q^{12} +4.76028 q^{13} +(-0.516019 + 2.59494i) q^{14} +(-0.993980 - 2.08365i) 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} +(1.72967 - 0.0907356i) q^{24} +(-2.27934 - 2.27934i) q^{25} +(-3.36602 - 3.36602i) q^{26} +(-3.05359 + 4.20424i) q^{27} +(2.19978 - 1.47002i) 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} +(-2.98353 + 0.313886i) q^{36} +(-1.86713 + 4.50765i) q^{37} -5.79598i q^{38} +(6.12754 + 5.51670i) q^{39} +(-1.23141 + 0.510066i) q^{40} +(7.95541 - 3.29524i) q^{41} +(-3.67152 + 2.74225i) q^{42} +(-6.70448 - 6.70448i) q^{43} +(-0.385932 - 0.931721i) q^{44} +(1.13528 - 3.83405i) q^{45} +(-4.55721 - 1.88766i) q^{46} +9.15054i q^{47} +(-1.28722 - 1.15890i) q^{48} +(-2.67808 + 6.46745i) q^{49} +3.22347i q^{50} +(1.40506 + 7.00184i) q^{51} +4.76028i q^{52} +(9.36723 + 9.36723i) q^{53} +(5.13206 - 0.813632i) q^{54} +1.34418 q^{55} +(-2.59494 - 0.516019i) q^{56} +(0.525901 + 10.0251i) q^{57} +(-4.50977 + 1.86801i) q^{58} +(0.517174 + 0.517174i) q^{59} +(2.08365 - 0.993980i) q^{60} +(-4.78410 - 11.5498i) q^{61} +(-3.06602 - 7.40204i) q^{62} +(6.10171 - 5.07634i) q^{63} -1.00000i q^{64} +(-5.86184 - 2.42805i) q^{65} +(0.752076 + 1.57656i) q^{66} +2.49006 q^{67} +(-2.46154 + 3.30769i) q^{68} +(8.05375 + 2.85153i) q^{69} +(1.95902 - 2.93223i) 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} +(-0.292483 - 5.57554i) q^{75} +(-4.09837 + 4.09837i) q^{76} +(2.21861 + 1.48226i) q^{77} +(-0.431926 - 8.23372i) 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} +(7.63093 - 3.64024i) q^{87} +(-0.385932 + 0.931721i) q^{88} -11.3660i q^{89} +(-3.51385 + 1.90832i) q^{90} +(-6.99770 - 10.4716i) q^{91} +(1.88766 + 4.55721i) q^{92} +(5.97484 + 12.5249i) q^{93} +(6.47041 - 6.47041i) q^{94} +(-2.95633 - 7.13721i) q^{95} +(0.0907356 + 1.72967i) q^{96} +(1.10080 - 2.65756i) q^{97} +(6.46687 - 2.67949i) q^{98} +(-1.44389 - 2.65868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{7}+O(q^{10}) \) 80 * q - 16 * q^7	\( 80 q - 16 q^{7} + 16 q^{14} - 48 q^{15} - 80 q^{16} + 16 q^{18} + 32 q^{21} + 16 q^{23} - 32 q^{25} - 64 q^{29} + 16 q^{30} - 48 q^{37} + 64 q^{39} + 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 24 q^{51} + 80 q^{53} + 48 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{63} - 80 q^{65} - 144 q^{67} + 8 q^{70} - 16 q^{71} + 32 q^{74} + 24 q^{77} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} - 16 q^{92} - 16 q^{93} + 16 q^{95} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) 80 * q - 16 * q^7 + 16 * q^14 - 48 * 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 + 64 * q^39 + 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 24 * q^51 + 80 * q^53 + 48 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^63 - 80 * q^65 - 144 * q^67 + 8 * q^70 - 16 * q^71 + 32 * q^74 + 24 * q^77 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 - 16 * q^92 - 16 * q^93 + 16 * q^95 + 16 * q^98 + 48 * q^99

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