LMFDB - Embedded newform 714.2.bh.a.457.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(25,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,8,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.3
Character	$\chi$	$=$	714.457
Dual form			714.2.bh.a.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.0350384 + 0.266143i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(-2.10959 - 1.59676i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.0350384 + 0.266143i) q^{10} +(3.88714 - 0.511752i) q^{11} +(-0.130526 + 0.991445i) q^{12} -4.16020i q^{13} +(-2.45098 - 0.996347i) q^{14} +(-0.189816 - 0.189816i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.80255 - 1.59393i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.93202 - 0.517682i) q^{19} +(0.102727 + 0.248006i) q^{20} +(2.55103 - 0.701606i) q^{21} +(3.62224 - 1.50038i) q^{22} +(0.991281 + 1.29186i) q^{23} +(0.130526 + 0.991445i) q^{24} +(4.76002 + 1.27544i) q^{25} +(-1.07674 - 4.01844i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-2.62534 - 0.328037i) q^{28} +(2.84175 - 1.17709i) q^{29} +(-0.232476 - 0.134220i) q^{30} +(-2.90010 + 3.77949i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.96034 + 3.39541i) q^{33} +(3.26044 - 2.52379i) q^{34} +(0.498882 - 0.505505i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.873250 + 0.114966i) q^{37} +(1.73220 - 1.00009i) q^{38} +(3.30051 + 2.53257i) q^{39} +(0.163416 + 0.212967i) q^{40} +(-7.90751 - 3.27540i) q^{41} +(2.28252 - 1.33795i) q^{42} +(1.85233 - 1.85233i) q^{43} +(3.11049 - 2.38676i) q^{44} +(0.266143 - 0.0350384i) q^{45} +(1.29186 + 0.991281i) q^{46} +(-0.614829 - 0.354972i) q^{47} +(0.382683 + 0.923880i) q^{48} +(1.90074 + 6.73700i) q^{49} +4.92794 q^{50} +(-1.05030 + 3.98709i) q^{51} +(-2.08010 - 3.60284i) q^{52} +(2.69941 - 10.0743i) q^{53} +(0.991445 + 0.130526i) q^{54} +1.05247i q^{55} +(-2.62078 + 0.362628i) q^{56} +(-0.765432 + 1.84792i) q^{57} +(2.44027 - 1.87248i) q^{58} +(-7.53745 - 2.01965i) q^{59} +(-0.259293 - 0.0694773i) q^{60} +(-8.75586 + 6.71861i) q^{61} +(-1.82308 + 4.40131i) q^{62} +(-0.996347 + 2.45098i) q^{63} -1.00000i q^{64} +(1.10721 + 0.145767i) q^{65} +(-1.01475 + 3.78709i) q^{66} +(2.88126 + 4.99050i) q^{67} +(2.49614 - 3.28166i) q^{68} -1.62836 q^{69} +(0.351049 - 0.617401i) q^{70} +(0.146170 + 0.352885i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(2.16611 + 1.66211i) q^{73} +(0.873250 - 0.114966i) q^{74} +(-3.90960 + 2.99994i) q^{75} +(1.41433 - 1.41433i) q^{76} +(-9.01742 - 5.12723i) q^{77} +(3.84352 + 1.59204i) q^{78} +(-2.70474 - 3.52489i) q^{79} +(0.212967 + 0.163416i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-8.48580 - 1.11718i) q^{82} +(4.08001 + 4.08001i) q^{83} +(1.85845 - 1.88312i) q^{84} +(0.290977 + 1.06787i) q^{85} +(1.30980 - 2.26863i) q^{86} +(-0.796099 + 2.97108i) q^{87} +(2.38676 - 3.11049i) q^{88} +(-0.709748 - 0.409773i) q^{89} +(0.248006 - 0.102727i) q^{90} +(-6.64282 + 8.77631i) q^{91} +(1.50441 + 0.623145i) q^{92} +(-1.23300 - 4.60161i) q^{93} +(-0.685753 - 0.183747i) q^{94} +(0.0700828 + 0.532332i) q^{95} +(0.608761 + 0.793353i) q^{96} +(9.49217 - 3.93179i) q^{97} +(3.57963 + 6.01550i) q^{98} +(-1.50038 - 3.62224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} - 8 q^{10} - 16 q^{11} - 16 q^{15} + 48 q^{16} + 8 q^{17} - 48 q^{18} + 8 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{29} + 48 q^{33} + 32 q^{35} + 16 q^{37} + 16 q^{39} + 16 q^{42} - 16 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) $ 96 * q + 8 * q^5 - 8 * q^10 - 16 * q^11 - 16 * q^15 + 48 * q^16 + 8 * q^17 - 48 * q^18 + 8 * q^19 + 16 * q^22 - 40 * q^25 + 32 * q^29 + 48 * q^33 + 32 * q^35 + 16 * q^37 + 16 * q^39 + 16 * q^42 - 16 * q^43 + 8 * q^44 + 8 * q^46 + 16 * q^49 - 128 * q^50 - 16 * q^52 - 24 * q^53 - 16 * q^57 + 16 * q^58 + 56 * q^59 - 8 * q^60 - 64 * q^65 + 32 * q^67 + 128 * q^69 + 24 * q^70 + 64 * q^71 - 40 * q^73 + 16 * q^74 + 16 * q^76 - 16 * q^77 + 32 * q^78 + 56 * q^79 - 8 * q^80 + 16 * q^83 - 48 * q^85 - 16 * q^86 - 24 * q^87 + 16 * q^88 - 16 * q^90 + 8 * q^91 + 16 * q^92 - 8 * q^93 - 24 * q^94 + 64 * q^95 + 32 * q^97 + 32 * q^99

Character values

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

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

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.0350384	+	0.266143i	−0.0156697	+	0.119023i	−0.997492	−	0.0707794i	$-0.977451\pi$
$5$	−0.0350384	+	0.266143i	−0.0156697	+	0.119023i	0.981822	+	0.189802i	$0.0607847\pi$
$6$	−0.382683	+	0.923880i	−0.156230	+	0.377172i
$7$	−2.10959	−	1.59676i	−0.797350	−	0.603517i
$7$	−2.10959	−	1.59676i	−0.797350	−	0.603517i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	0.0350384	+	0.266143i	0.0110801	+	0.0841618i
$11$	3.88714	−	0.511752i	1.17202	−	0.154299i	0.480723	−	0.876872i	$-0.340374\pi$
$11$	3.88714	−	0.511752i	1.17202	−	0.154299i	0.691294	+	0.722573i	$0.257041\pi$
$12$	−0.130526	+	0.991445i	−0.0376797	+	0.286205i
$13$		−	4.16020i		−	1.15383i	−0.816804	−	0.576916i	$-0.804256\pi$
$13$		−	4.16020i		−	1.15383i	0.816804	−	0.576916i	$-0.195744\pi$
$14$	−2.45098	−	0.996347i	−0.655051	−	0.266285i
$15$	−0.189816	−	0.189816i	−0.0490102	−	0.0490102i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.80255	−	1.59393i	0.922254	−	0.386584i
$17$	3.80255	−	1.59393i	0.922254	−	0.386584i
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.93202	−	0.517682i	0.443235	−	0.118764i	−0.0302972	−	0.999541i	$-0.509645\pi$
$19$	1.93202	−	0.517682i	0.443235	−	0.118764i	0.473532	+	0.880776i	$0.342979\pi$
$20$	0.102727	+	0.248006i	0.0229705	+	0.0554558i
$21$	2.55103	−	0.701606i	0.556680	−	0.153103i
$22$	3.62224	−	1.50038i	0.772264	−	0.319882i
$23$	0.991281	+	1.29186i	0.206696	+	0.269372i	0.885185	−	0.465239i	$-0.154032\pi$
$23$	0.991281	+	1.29186i	0.206696	+	0.269372i	−0.678489	+	0.734611i	$0.737365\pi$
$24$	0.130526	+	0.991445i	0.0266435	+	0.202378i
$25$	4.76002	+	1.27544i	0.952005	+	0.255089i
$26$	−1.07674	−	4.01844i	−0.211166	−	0.788081i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	−2.62534	−	0.328037i	−0.496142	−	0.0619932i
$29$	2.84175	−	1.17709i	0.527700	−	0.218580i	−0.102896	−	0.994692i	$-0.532811\pi$
$29$	2.84175	−	1.17709i	0.527700	−	0.218580i	0.630595	+	0.776112i	$0.282811\pi$
$30$	−0.232476	−	0.134220i	−0.0424440	−	0.0245051i
$31$	−2.90010	+	3.77949i	−0.520874	+	0.678816i	−0.977523	−	0.210831i	$-0.932383\pi$
$31$	−2.90010	+	3.77949i	−0.520874	+	0.678816i	0.456648	+	0.889647i	$0.349050\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−1.96034	+	3.39541i	−0.341252	+	0.591065i
$34$	3.26044	−	2.52379i	0.559162	−	0.432826i
$35$	0.498882	−	0.505505i	0.0843265	−	0.0854459i
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	0.873250	+	0.114966i	0.143561	+	0.0189002i	0.201964	−	0.979393i	$-0.435267\pi$
$37$	0.873250	+	0.114966i	0.143561	+	0.0189002i	−0.0584029	+	0.998293i	$0.518601\pi$
$38$	1.73220	−	1.00009i	0.281000	−	0.162235i
$39$	3.30051	+	2.53257i	0.528504	+	0.405535i
$40$	0.163416	+	0.212967i	0.0258383	+	0.0336731i
$41$	−7.90751	−	3.27540i	−1.23495	−	0.511531i	−0.332814	−	0.942992i	$-0.607998\pi$
$41$	−7.90751	−	3.27540i	−1.23495	−	0.511531i	−0.902131	+	0.431461i	$0.857998\pi$
$42$	2.28252	−	1.33795i	0.352200	−	0.206451i
$43$	1.85233	−	1.85233i	0.282478	−	0.282478i	−0.551619	−	0.834096i	$-0.685990\pi$
$43$	1.85233	−	1.85233i	0.282478	−	0.282478i	0.834096	+	0.551619i	$0.185990\pi$
$44$	3.11049	−	2.38676i	0.468924	−	0.359818i
$45$	0.266143	−	0.0350384i	0.0396743	−	0.00522322i
$46$	1.29186	+	0.991281i	0.190475	+	0.146156i
$47$	−0.614829	−	0.354972i	−0.0896821	−	0.0517780i	0.454488	−	0.890753i	$-0.349822\pi$
$47$	−0.614829	−	0.354972i	−0.0896821	−	0.0517780i	−0.544170	+	0.838975i	$0.683155\pi$
$48$	0.382683	+	0.923880i	0.0552356	+	0.133351i
$49$	1.90074	+	6.73700i	0.271534	+	0.962429i
$50$	4.92794			0.696916
$51$	−1.05030	+	3.98709i	−0.147071	+	0.558304i
$52$	−2.08010	−	3.60284i	−0.288458	−	0.499624i
$53$	2.69941	−	10.0743i	0.370793	−	1.38382i	−0.488603	−	0.872506i	$-0.662493\pi$
$53$	2.69941	−	10.0743i	0.370793	−	1.38382i	0.859396	−	0.511311i	$-0.170840\pi$
$54$	0.991445	+	0.130526i	0.134919	+	0.0177624i
$55$			1.05247i			0.141915i
$56$	−2.62078	+	0.362628i	−0.350217	+	0.0484582i
$57$	−0.765432	+	1.84792i	−0.101384	+	0.244763i
$58$	2.44027	−	1.87248i	0.320423	−	0.245869i
$59$	−7.53745	−	2.01965i	−0.981293	−	0.262937i	−0.267704	−	0.963501i	$-0.586265\pi$
$59$	−7.53745	−	2.01965i	−0.981293	−	0.262937i	−0.713589	+	0.700565i	$0.752932\pi$
$60$	−0.259293	−	0.0694773i	−0.0334746	−	0.00896948i
$61$	−8.75586	+	6.71861i	−1.12107	+	0.860229i	−0.991340	−	0.131320i	$-0.958079\pi$
$61$	−8.75586	+	6.71861i	−1.12107	+	0.860229i	−0.129733	+	0.991549i	$0.541412\pi$
$62$	−1.82308	+	4.40131i	−0.231532	+	0.558967i
$63$	−0.996347	+	2.45098i	−0.125528	+	0.308794i
$64$		−	1.00000i		−	0.125000i
$65$	1.10721	+	0.145767i	0.137332	+	0.0180801i
$66$	−1.01475	+	3.78709i	−0.124907	+	0.466159i
$67$	2.88126	+	4.99050i	0.352002	+	0.609686i	0.986600	−	0.163156i	$-0.0521675\pi$
$67$	2.88126	+	4.99050i	0.352002	+	0.609686i	−0.634598	+	0.772843i	$0.718834\pi$
$68$	2.49614	−	3.28166i	0.302702	−	0.397959i
$69$	−1.62836			−0.196031
$70$	0.351049	−	0.617401i	0.0419584	−	0.0737935i
$71$	0.146170	+	0.352885i	0.0173471	+	0.0418797i	0.932316	−	0.361645i	$-0.117785\pi$
$71$	0.146170	+	0.352885i	0.0173471	+	0.0418797i	−0.914969	+	0.403525i	$0.867785\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	2.16611	+	1.66211i	0.253524	+	0.194536i	0.727702	−	0.685893i	$-0.240588\pi$
$73$	2.16611	+	1.66211i	0.253524	+	0.194536i	−0.474178	+	0.880429i	$0.657255\pi$
$74$	0.873250	−	0.114966i	0.101513	−	0.0133645i
$75$	−3.90960	+	2.99994i	−0.451441	+	0.346403i
$76$	1.41433	−	1.41433i	0.162235	−	0.162235i
$77$	−9.01742	−	5.12723i	−1.02763	−	0.584302i
$78$	3.84352	+	1.59204i	0.435193	+	0.180263i
$79$	−2.70474	−	3.52489i	−0.304307	−	0.396581i	0.616020	−	0.787731i	$-0.288744\pi$
$79$	−2.70474	−	3.52489i	−0.304307	−	0.396581i	−0.920327	+	0.391150i	$0.872077\pi$
$80$	0.212967	+	0.163416i	0.0238105	+	0.0182704i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−8.48580	−	1.11718i	−0.937100	−	0.123372i
$83$	4.08001	+	4.08001i	0.447839	+	0.447839i	0.894636	−	0.446796i	$-0.147435\pi$
$83$	4.08001	+	4.08001i	0.447839	+	0.447839i	−0.446796	+	0.894636i	$0.647435\pi$
$84$	1.85845	−	1.88312i	0.202774	−	0.205466i
$85$	0.290977	+	1.06787i	0.0315609	+	0.115827i
$86$	1.30980	−	2.26863i	0.141239	−	0.244633i
$87$	−0.796099	+	2.97108i	−0.0853507	+	0.318533i
$88$	2.38676	−	3.11049i	0.254430	−	0.331579i
$89$	−0.709748	−	0.409773i	−0.0752331	−	0.0434359i	0.461912	−	0.886926i	$-0.347164\pi$
$89$	−0.709748	−	0.409773i	−0.0752331	−	0.0434359i	−0.537145	+	0.843490i	$0.680497\pi$
$90$	0.248006	−	0.102727i	0.0261421	−	0.0108284i
$91$	−6.64282	+	8.77631i	−0.696357	+	0.920007i
$92$	1.50441	+	0.623145i	0.156845	+	0.0649674i
$93$	−1.23300	−	4.60161i	−0.127856	−	0.477165i
$94$	−0.685753	−	0.183747i	−0.0707300	−	0.0189521i
$95$	0.0700828	+	0.532332i	0.00719034	+	0.0546161i
$96$	0.608761	+	0.793353i	0.0621315	+	0.0809713i
$97$	9.49217	−	3.93179i	0.963784	−	0.399212i	0.155389	−	0.987853i	$-0.450337\pi$
$97$	9.49217	−	3.93179i	0.963784	−	0.399212i	0.808395	+	0.588641i	$0.200337\pi$
$98$	3.57963	+	6.01550i	0.361598	+	0.607657i
$99$	−1.50038	−	3.62224i	−0.150794	−	0.364049i
$100$	4.76002	−	1.27544i	0.476002	−	0.127544i
$101$	−7.64455	−	13.2407i	−0.760661	−	1.31750i	−0.942510	−	0.334177i	$-0.891542\pi$
$101$	−7.64455	−	13.2407i	−0.760661	−	1.31750i	0.181850	−	0.983326i	$-0.441792\pi$
$102$	0.0174222	+	4.12307i	0.00172505	+	0.408245i
$103$	1.66076	−	2.87653i	0.163640	−	0.283433i	−0.772531	−	0.634976i	$-0.781010\pi$
$103$	1.66076	−	2.87653i	0.163640	−	0.283433i	0.936171	+	0.351544i	$0.114343\pi$
$104$	−2.94170	−	2.94170i	−0.288458	−	0.288458i
$105$	0.0973436	+	0.703522i	0.00949977	+	0.0686567i
$106$		−	10.4297i		−	1.01302i
$107$	−0.889606	+	6.75723i	−0.0860015	+	0.653246i	0.893098	+	0.449863i	$0.148527\pi$
$107$	−0.889606	+	6.75723i	−0.0860015	+	0.653246i	−0.979099	+	0.203383i	$0.934806\pi$
$108$	0.991445	−	0.130526i	0.0954018	−	0.0125599i
$109$	0.223885	+	1.70057i	0.0214443	+	0.162885i	0.998816	−	0.0486423i	$-0.0154894\pi$
$109$	0.223885	+	1.70057i	0.0214443	+	0.162885i	−0.977372	+	0.211528i	$0.932156\pi$
$110$	0.272398	+	1.01661i	0.0259722	+	0.0969295i
$111$	−0.622809	+	0.622809i	−0.0591145	+	0.0591145i
$112$	−2.43763	+	1.02858i	−0.230334	+	0.0971917i
$113$	1.42656	−	3.44403i	0.134200	−	0.323987i	−0.842467	−	0.538748i	$-0.818897\pi$
$113$	1.42656	−	3.44403i	0.134200	−	0.323987i	0.976667	+	0.214761i	$0.0688974\pi$
$114$	−0.261075	+	1.98306i	−0.0244519	+	0.185731i
$115$	−0.378553	+	0.218558i	−0.0353003	+	0.0203806i
$116$	1.87248	−	2.44027i	0.173856	−	0.226573i
$117$	−4.01844	+	1.07674i	−0.371505	+	0.0995445i
$118$	−7.80335			−0.718356
$119$	−10.5669	−	2.70922i	−0.968669	−	0.248354i
$120$	−0.268440			−0.0245051
$121$	4.22280	−	1.13149i	0.383891	−	0.102863i
$122$	−6.71861	+	8.75586i	−0.608274	+	0.792718i
$123$	7.41233	−	4.27951i	0.668348	−	0.385871i
$124$	−0.621819	+	4.72319i	−0.0558410	+	0.424155i
$125$	−1.01987	+	2.46219i	−0.0912201	+	0.220225i
$126$	−0.328037	+	2.62534i	−0.0292239	+	0.233884i
$127$	−9.80959	+	9.80959i	−0.870461	+	0.870461i	−0.992523	−	0.122062i	$-0.961049\pi$
$127$	−9.80959	+	9.80959i	−0.870461	+	0.870461i	0.122062	+	0.992523i	$0.461049\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.341925	+	2.59718i	0.0301048	+	0.228669i
$130$	1.10721	−	0.145767i	0.0971086	−	0.0127846i
$131$	−2.88670	+	21.9267i	−0.252212	+	1.91574i	0.129720	+	0.991551i	$0.458592\pi$
$131$	−2.88670	+	21.9267i	−0.252212	+	1.91574i	−0.381932	+	0.924190i	$0.624741\pi$
$132$			3.92068i			0.341252i
$133$	−4.90238	−	1.99286i	−0.425090	−	0.172803i
$134$	4.07472	+	4.07472i	0.352002	+	0.352002i
$135$	−0.134220	+	0.232476i	−0.0115518	+	0.0200083i
$136$	1.56173	−	3.81589i	0.133918	−	0.327210i
$137$	−1.55078	−	2.68602i	−0.132492	−	0.229483i	0.792145	−	0.610333i	$-0.208964\pi$
$137$	−1.55078	−	2.68602i	−0.132492	−	0.229483i	−0.924637	+	0.380851i	$0.875631\pi$
$138$	−1.57287	+	0.421450i	−0.133892	+	0.0358762i
$139$	6.61687	+	15.9745i	0.561235	+	1.35494i	0.908779	+	0.417278i	$0.137016\pi$
$139$	6.61687	+	15.9745i	0.561235	+	1.35494i	−0.347544	+	0.937664i	$0.612984\pi$
$140$	0.179292	−	0.687221i	0.0151530	−	0.0580808i
$141$	0.655903	−	0.271684i	0.0552370	−	0.0228799i
$142$	0.232522	+	0.303029i	0.0195128	+	0.0254296i
$143$	−2.12899	−	16.1713i	−0.178035	−	1.35231i
$144$	−0.965926	−	0.258819i	−0.0804938	−	0.0215683i
$145$	0.213704	+	0.797556i	0.0177472	+	0.0662334i
$146$	2.52249	+	1.04485i	0.208763	+	0.0864723i
$147$	−6.50192	−	2.59327i	−0.536269	−	0.213889i
$148$	0.813740	−	0.337062i	0.0668890	−	0.0277063i
$149$	−6.80392	−	3.92824i	−0.557398	−	0.321814i	0.194702	−	0.980862i	$-0.437626\pi$
$149$	−6.80392	−	3.92824i	−0.557398	−	0.321814i	−0.752101	+	0.659048i	$0.770959\pi$
$150$	−2.99994	+	3.90960i	−0.244944	+	0.319217i
$151$	−3.81718	+	14.2459i	−0.310637	+	1.15931i	0.617346	+	0.786692i	$0.288208\pi$
$151$	−3.81718	+	14.2459i	−0.310637	+	1.15931i	−0.927983	+	0.372623i	$0.878459\pi$
$152$	1.00009	−	1.73220i	0.0811177	−	0.140500i
$153$	−2.52379	−	3.26044i	−0.204036	−	0.263591i
$154$	−10.0372	−	2.61865i	−0.808819	−	0.211017i
$155$	−0.904270	−	0.904270i	−0.0726327	−	0.0726327i
$156$	4.12461	+	0.543015i	0.330233	+	0.0434760i
$157$	1.50009	−	0.866078i	0.119720	−	0.0691205i	−0.438944	−	0.898514i	$-0.644647\pi$
$157$	1.50009	−	0.866078i	0.119720	−	0.0691205i	0.558664	+	0.829394i	$0.311314\pi$
$158$	−3.52489	−	2.70474i	−0.280425	−	0.215178i
$159$	6.34922	+	8.27446i	0.503526	+	0.656207i
$160$	0.248006	+	0.102727i	0.0196066	+	0.00812131i
$161$	−0.0284059	−	4.30813i	−0.00223870	−	0.339529i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−18.2875	+	14.0325i	−1.43239	+	1.09911i	−0.454313	+	0.890842i	$0.650115\pi$
$163$	−18.2875	+	14.0325i	−1.43239	+	1.09911i	−0.978072	+	0.208266i	$0.933218\pi$
$164$	−8.48580	+	1.11718i	−0.662630	+	0.0872369i
$165$	−0.834978	−	0.640701i	−0.0650030	−	0.0498785i
$166$	4.99697	+	2.88500i	0.387840	+	0.223920i
$167$	2.76955	+	6.68630i	0.214315	+	0.517401i	0.994077	−	0.108674i	$-0.0346604\pi$
$167$	2.76955	+	6.68630i	0.214315	+	0.517401i	−0.779763	+	0.626075i	$0.784660\pi$
$168$	1.30774	−	2.29996i	0.100894	−	0.177446i
$169$	−4.30724			−0.331326
$170$	0.557448	+	0.956174i	0.0427543	+	0.0733352i
$171$	−1.00009	−	1.73220i	−0.0764785	−	0.132465i
$172$	0.678000	−	2.53033i	0.0516970	−	0.192936i
$173$	8.68584	+	1.14351i	0.660372	+	0.0869396i	0.453261	−	0.891378i	$-0.350261\pi$
$173$	8.68584	+	1.14351i	0.660372	+	0.0869396i	0.207111	+	0.978317i	$0.433594\pi$
$174$			3.07589i			0.233183i
$175$	−8.00512	−	10.2913i	−0.605130	−	0.777947i
$176$	1.50038	−	3.62224i	0.113095	−	0.273037i
$177$	6.19081	−	4.75038i	0.465330	−	0.357060i
$178$	−0.791621	−	0.212114i	−0.0593345	−	0.0158986i
$179$	−0.496285	−	0.132979i	−0.0370941	−	0.00993933i	0.240224	−	0.970717i	$-0.422779\pi$
$179$	−0.496285	−	0.132979i	−0.0370941	−	0.00993933i	−0.277318	+	0.960778i	$0.589446\pi$
$180$	0.212967	−	0.163416i	0.0158737	−	0.0121803i
$181$	−9.32223	+	22.5059i	−0.692916	+	1.67285i	0.0459059	+	0.998946i	$0.485383\pi$
$181$	−9.32223	+	22.5059i	−0.692916	+	1.67285i	−0.738822	+	0.673901i	$0.764617\pi$
$182$	−4.14500	+	10.1966i	−0.307248	+	0.755819i
$183$		−	11.0365i		−	0.815843i
$184$	1.61443	+	0.212543i	0.119017	+	0.0156689i
$185$	−0.0611946	+	0.228381i	−0.00449912	+	0.0167909i
$186$	−2.38197	−	4.12569i	−0.174655	−	0.302511i
$187$	13.9654	−	8.14178i	1.02125	−	0.595386i
$188$	−0.709944			−0.0517780
$189$	−1.33795	−	2.28252i	−0.0973219	−	0.166029i
$190$	0.205472	+	0.496054i	0.0149065	+	0.0359876i
$191$	0.915058	+	0.528309i	0.0662113	+	0.0382271i	0.532740	−	0.846279i	$-0.321162\pi$
$191$	0.915058	+	0.528309i	0.0662113	+	0.0382271i	−0.466529	+	0.884506i	$0.654496\pi$
$192$	0.793353	+	0.608761i	0.0572553	+	0.0439336i
$193$	23.5510	−	3.10055i	1.69524	−	0.223182i	0.779910	−	0.625892i	$-0.215265\pi$
$193$	23.5510	−	3.10055i	1.69524	−	0.223182i	0.915328	+	0.402710i	$0.131932\pi$
$194$	8.15111	−	6.25457i	0.585216	−	0.449052i
$195$	−0.789670	+	0.789670i	−0.0565494	+	0.0565494i
$196$	5.01459	+	4.88405i	0.358185	+	0.348861i
$197$	9.76463	+	4.04464i	0.695701	+	0.288169i	0.702373	−	0.711809i	$-0.252124\pi$
$197$	9.76463	+	4.04464i	0.695701	+	0.288169i	−0.00667200	+	0.999978i	$0.502124\pi$
$198$	−2.38676	−	3.11049i	−0.169620	−	0.221053i
$199$	−11.8163	−	9.06699i	−0.837638	−	0.642742i	0.0982025	−	0.995166i	$-0.468691\pi$
$199$	−11.8163	−	9.06699i	−0.837638	−	0.642742i	−0.935840	+	0.352424i	$0.885357\pi$
$200$	4.26772	−	2.46397i	0.301773	−	0.174229i
$201$	−5.71323	−	0.752161i	−0.402980	−	0.0530533i
$202$	−10.8110	−	10.8110i	−0.760661	−	0.760661i
$203$	−7.87446	−	2.05440i	−0.552678	−	0.144191i
$204$	1.08396	+	3.97807i	0.0758922	+	0.278521i
$205$	1.14879	−	1.98976i	0.0802350	−	0.138971i
$206$	0.859675	−	3.20835i	0.0598964	−	0.223536i
$207$	0.991281	−	1.29186i	0.0688988	−	0.0897906i
$208$	−3.60284	−	2.08010i	−0.249812	−	0.144229i
$209$	7.24510	−	3.00102i	0.501154	−	0.207585i
$210$	0.276112	+	0.654356i	0.0190535	+	0.0451548i
$211$	−1.54691	−	0.640752i	−0.106494	−	0.0441112i	0.328800	−	0.944399i	$-0.393356\pi$
$211$	−1.54691	−	0.640752i	−0.106494	−	0.0441112i	−0.435294	+	0.900288i	$0.643356\pi$
$212$	−2.69941	−	10.0743i	−0.185396	−	0.691909i
$213$	−0.368945	−	0.0988584i	−0.0252797	−	0.00677367i
$214$	0.889606	+	6.75723i	0.0608122	+	0.461915i
$215$	0.428082	+	0.557888i	0.0291950	+	0.0380476i
$216$	0.923880	−	0.382683i	0.0628620	−	0.0260383i
$217$	12.1530	−	3.34241i	0.824996	−	0.226898i
$218$	0.656397	+	1.58468i	0.0444568	+	0.107328i
$219$	−2.63729	+	0.706659i	−0.178211	+	0.0477516i
$220$	0.526233	+	0.911463i	0.0354787	+	0.0614508i
$221$	−6.63105	−	15.8194i	−0.446053	−	1.06413i
$222$	−0.440393	+	0.762783i	−0.0295572	+	0.0511946i
$223$	10.9237	+	10.9237i	0.731505	+	0.731505i	0.970918	−	0.239413i	$-0.0769550\pi$
$223$	10.9237	+	10.9237i	0.731505	+	0.731505i	−0.239413	+	0.970918i	$0.576955\pi$
$224$	−2.08835	+	1.62444i	−0.139534	+	0.108537i
$225$		−	4.92794i		−	0.328529i
$226$	0.486574	−	3.69590i	0.0323664	−	0.245847i
$227$	14.2701	−	1.87870i	0.947143	−	0.124694i	0.358898	−	0.933377i	$-0.383153\pi$
$227$	14.2701	−	1.87870i	0.947143	−	0.124694i	0.588245	+	0.808683i	$0.299819\pi$
$228$	0.261075	+	1.98306i	0.0172901	+	0.131331i
$229$	3.13297	+	11.6924i	0.207033	+	0.772657i	0.988820	+	0.149112i	$0.0476415\pi$
$229$	3.13297	+	11.6924i	0.207033	+	0.772657i	−0.781788	+	0.623545i	$0.785692\pi$
$230$	−0.309087	+	0.309087i	−0.0203806	+	0.0203806i
$231$	9.55716	−	4.03274i	0.628815	−	0.265335i
$232$	1.17709	−	2.84175i	0.0772798	−	0.186570i
$233$	−1.79505	+	13.6348i	−0.117598	+	0.893245i	0.826351	+	0.563155i	$0.190412\pi$
$233$	−1.79505	+	13.6348i	−0.117598	+	0.893245i	−0.943949	+	0.330090i	$0.892921\pi$
$234$	−3.60284	+	2.08010i	−0.235525	+	0.135980i
$235$	0.116016	−	0.151195i	0.00756805	−	0.00986287i
$236$	−7.53745	+	2.01965i	−0.490646	+	0.131468i
$237$	4.44302			0.288605
$238$	−10.9081	+	0.118019i	−0.707065	+	0.00765002i
$239$	22.2633			1.44009			0.720046	−	0.693927i	$-0.244121\pi$
$239$	22.2633			1.44009			0.720046	+	0.693927i	$0.244121\pi$
$240$	−0.259293	+	0.0694773i	−0.0167373	+	0.00448474i
$241$	−3.43712	+	4.47934i	−0.221404	+	0.288540i	−0.890828	−	0.454341i	$-0.849875\pi$
$241$	−3.43712	+	4.47934i	−0.221404	+	0.288540i	0.669423	+	0.742881i	$0.266541\pi$
$242$	3.78606	−	2.18588i	0.243377	−	0.140514i
$243$	0.130526	−	0.991445i	0.00837326	−	0.0636012i
$244$	−4.22349	+	10.1964i	−0.270381	+	0.652758i
$245$	−1.85961	+	0.269814i	−0.118806	+	0.0172378i
$246$	6.05215	−	6.05215i	0.385871	−	0.385871i
$247$	−2.15366	−	8.03757i	−0.137034	−	0.511418i
$248$	0.621819	+	4.72319i	0.0394856	+	0.299923i
$249$	−5.72064	+	0.753137i	−0.362531	+	0.0477281i
$250$	−0.347859	+	2.64225i	−0.0220005	+	0.167111i
$251$		−	20.4299i		−	1.28952i	−0.764384	−	0.644761i	$-0.776957\pi$
$251$		−	20.4299i		−	1.28952i	0.764384	−	0.644761i	$-0.223043\pi$
$252$	0.362628	+	2.62078i	0.0228434	+	0.165094i
$253$	4.51436	+	4.51436i	0.283816	+	0.283816i
$254$	−6.93643	+	12.0142i	−0.435230	+	0.753841i
$255$	−1.02434	−	0.419231i	−0.0641464	−	0.0262533i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.87598	+	1.30652i	−0.304156	+	0.0814982i	−0.407669	−	0.913130i	$-0.633658\pi$
$257$	−4.87598	+	1.30652i	−0.304156	+	0.0814982i	0.103513	+	0.994628i	$0.466992\pi$
$258$	1.00247	+	2.42019i	0.0624113	+	0.150674i
$259$	−1.65863	−	1.63690i	−0.103062	−	0.101712i
$260$	1.03175	−	0.427366i	0.0639866	−	0.0265041i
$261$	−1.87248	−	2.44027i	−0.115904	−	0.151049i
$262$	2.88670	+	21.9267i	0.178341	+	1.35463i
$263$	−13.6928	−	3.66898i	−0.844336	−	0.226239i	−0.189378	−	0.981904i	$-0.560647\pi$
$263$	−13.6928	−	3.66898i	−0.844336	−	0.226239i	−0.654958	+	0.755665i	$0.727314\pi$
$264$	1.01475	+	3.78709i	0.0624534	+	0.233079i
$265$	2.58663	+	1.07142i	0.158896	+	0.0658167i
$266$	−5.25112	−	0.656130i	−0.321967	−	0.0402299i
$267$	0.757162	−	0.313627i	0.0463376	−	0.0191936i
$268$	4.99050	+	2.88126i	0.304843	+	0.176001i
$269$	5.89481	−	7.68226i	0.359413	−	0.468396i	−0.578292	−	0.815830i	$-0.696280\pi$
$269$	5.89481	−	7.68226i	0.359413	−	0.468396i	0.937704	+	0.347434i	$0.112947\pi$
$270$	−0.0694773	+	0.259293i	−0.00422825	+	0.0157801i
$271$	−7.06680	+	12.2401i	−0.429278	+	0.743531i	−0.996809	−	0.0798208i	$-0.974565\pi$
$271$	−7.06680	+	12.2401i	−0.429278	+	0.743531i	0.567531	+	0.823352i	$0.307899\pi$
$272$	0.520895	−	4.09007i	0.0315839	−	0.247997i
$273$	−2.91882	−	10.6128i	−0.176655	−	0.642315i
$274$	−2.19313	−	2.19313i	−0.132492	−	0.132492i
$275$	19.1556	+	2.52188i	1.15513	+	0.152075i
$276$	−1.41020	+	0.814178i	−0.0848840	+	0.0490078i
$277$	24.6372	+	18.9048i	1.48031	+	1.13588i	0.959323	+	0.282311i	$0.0911010\pi$
$277$	24.6372	+	18.9048i	1.48031	+	1.13588i	0.520983	+	0.853567i	$0.325566\pi$
$278$	10.5259	+	13.7176i	0.631302	+	0.822729i
$279$	4.40131	+	1.82308i	0.263499	+	0.109145i
$280$	−0.00468281	−	0.710209i	−0.000279851	−	0.0424431i
$281$	16.7277	−	16.7277i	0.997889	−	0.997889i	−0.00210923	−	0.999998i	$-0.500671\pi$
$281$	16.7277	−	16.7277i	0.997889	−	0.997889i	0.999998	+	0.00210923i	$0.000671389\pi$
$282$	0.563236	−	0.432186i	0.0335402	−	0.0257363i
$283$	−28.5042	+	3.75265i	−1.69440	+	0.223072i	−0.914999	−	0.403457i	$-0.867809\pi$
$283$	−28.5042	+	3.75265i	−1.69440	+	0.223072i	−0.779399	+	0.626528i	$0.784475\pi$
$284$	0.303029	+	0.232522i	0.0179815	+	0.0137977i
$285$	−0.464991	−	0.268463i	−0.0275437	−	0.0159024i
$286$	−6.24188	−	15.0692i	−0.369090	−	0.891062i
$287$	11.4516	+	19.5361i	0.675966	+	1.15318i
$288$	−1.00000			−0.0589256
$289$	11.9188	−	12.1220i	0.701106	−	0.713057i
$290$	0.412845	+	0.715069i	0.0242431	+	0.0419903i
$291$	−2.65917	+	9.92416i	−0.155883	+	0.581765i
$292$	2.70696	+	0.356378i	0.158413	+	0.0208555i
$293$		−	15.3873i		−	0.898934i	−0.893297	−	0.449467i	$-0.851614\pi$
$293$		−	15.3873i		−	0.898934i	0.893297	−	0.449467i	$-0.148386\pi$
$294$	−6.95156	−	0.822088i	−0.405423	−	0.0479451i
$295$	0.801618	−	1.93528i	0.0466720	−	0.112676i
$296$	0.698774	−	0.536188i	0.0406154	−	0.0311653i
$297$	3.78709	+	1.01475i	0.219749	+	0.0588816i
$298$	−7.58878	−	2.03341i	−0.439606	−	0.117792i
$299$	5.37440	−	4.12392i	0.310810	−	0.238493i
$300$	−1.88584	+	4.55282i	−0.108879	+	0.262857i
$301$	−6.86538	+	0.949936i	−0.395714	+	0.0547534i
$302$			14.7484i			0.848677i
$303$	15.1583	+	1.99563i	0.870821	+	0.114646i
$304$	0.517682	−	1.93202i	0.0296911	−	0.110809i
$305$	−1.48132	−	2.56572i	−0.0848201	−	0.146913i
$306$	−3.28166	−	2.49614i	−0.187600	−	0.142695i
$307$	23.8664			1.36212			0.681062	−	0.732225i	$-0.261518\pi$
$307$	23.8664			1.36212			0.681062	+	0.732225i	$0.261518\pi$
$308$	−10.3729	+	0.0683945i	−0.591052	+	0.00389714i
$309$	1.27109	+	3.06869i	0.0723100	+	0.174572i
$310$	−1.10750	−	0.639415i	−0.0629018	−	0.0363164i
$311$	−20.1618	−	15.4707i	−1.14327	−	0.877265i	−0.149509	−	0.988760i	$-0.547769\pi$
$311$	−20.1618	−	15.4707i	−1.14327	−	0.877265i	−0.993765	+	0.111496i	$0.964436\pi$
$312$	4.12461	−	0.543015i	0.233510	−	0.0307422i
$313$	−8.43804	+	6.47473i	−0.476946	+	0.365974i	−0.819082	−	0.573677i	$-0.805516\pi$
$313$	−8.43804	+	6.47473i	−0.476946	+	0.365974i	0.342136	+	0.939651i	$0.388850\pi$
$314$	1.22482	−	1.22482i	0.0691205	−	0.0691205i
$315$	−0.617401	−	0.351049i	−0.0347866	−	0.0197794i
$316$	−4.10482	−	1.70027i	−0.230914	−	0.0956477i
$317$	−18.5875	−	24.2236i	−1.04398	−	1.36054i	−0.930210	−	0.367028i	$-0.880375\pi$
$317$	−18.5875	−	24.2236i	−1.04398	−	1.36054i	−0.113766	−	0.993508i	$-0.536291\pi$
$318$	8.27446	+	6.34922i	0.464009	+	0.356046i
$319$	10.4439	−	6.02979i	0.584747	−	0.337604i
$320$	0.266143	+	0.0350384i	0.0148779	+	0.00195871i
$321$	−4.81931	−	4.81931i	−0.268988	−	0.268988i
$322$	−1.14247	−	4.15399i	−0.0636671	−	0.231493i
$323$	6.52145	−	5.04801i	0.362863	−	0.280879i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.30610	−	19.8026i	0.294330	−	1.09845i
$326$	−14.0325	+	18.2875i	−0.777187	+	1.01285i
$327$	−1.48545	−	0.857624i	−0.0821455	−	0.0474267i
$328$	−7.90751	+	3.27540i	−0.436619	+	0.180854i
$329$	0.730234	+	1.73058i	0.0402591	+	0.0954099i
$330$	−0.972353	−	0.402762i	−0.0535263	−	0.0221713i
$331$	−8.65323	−	32.2943i	−0.475625	−	1.77506i	−0.619005	−	0.785387i	$-0.712464\pi$
$331$	−8.65323	−	32.2943i	−0.475625	−	1.77506i	0.143380	−	0.989668i	$-0.454203\pi$
$332$	5.57340	+	1.49339i	0.305880	+	0.0819603i
$333$	−0.114966	−	0.873250i	−0.00630008	−	0.0478538i
$334$	4.40573	+	5.74165i	0.241071	+	0.314169i
$335$	−1.42914	+	0.591970i	−0.0780823	+	0.0323428i
$336$	0.667906	−	2.56006i	0.0364372	−	0.139663i
$337$	−12.7832	−	30.8615i	−0.696348	−	1.68113i	−0.731583	−	0.681753i	$-0.761218\pi$
$337$	−12.7832	−	30.8615i	−0.696348	−	1.68113i	0.0352352	−	0.999379i	$-0.488782\pi$
$338$	−4.16048	+	1.11480i	−0.226300	+	0.0606370i
$339$	1.86389	+	3.22836i	0.101233	+	0.175340i
$340$	0.785929	+	0.779315i	0.0426230	+	0.0422643i
$341$	−9.33895	+	16.1755i	−0.505733	+	0.875955i
$342$	−1.41433	−	1.41433i	−0.0764785	−	0.0764785i
$343$	6.74758	−	17.2473i	0.364335	−	0.931268i
$344$		−	2.61959i		−	0.141239i
$345$	0.0570550	−	0.433376i	0.00307174	−	0.0233322i
$346$	8.68584	−	1.14351i	0.466953	−	0.0614756i
$347$	4.64489	+	35.2814i	0.249351	+	1.89401i	0.418187	+	0.908361i	$0.362666\pi$
$347$	4.64489	+	35.2814i	0.249351	+	1.89401i	−0.168836	+	0.985644i	$0.554001\pi$
$348$	0.796099	+	2.97108i	0.0426754	+	0.159267i
$349$	5.97980	−	5.97980i	0.320091	−	0.320091i	−0.528711	−	0.848802i	$-0.677324\pi$
$349$	5.97980	−	5.97980i	0.320091	−	0.320091i	0.848802	+	0.528711i	$0.177324\pi$
$350$	−10.3959	−	7.86872i	−0.555686	−	0.420601i
$351$	1.59204	−	3.84352i	0.0849767	−	0.205152i
$352$	0.511752	−	3.88714i	0.0272765	−	0.207185i
$353$	18.7023	−	10.7978i	0.995421	−	0.574707i	0.0885308	−	0.996073i	$-0.471783\pi$
$353$	18.7023	−	10.7978i	0.995421	−	0.574707i	0.906890	+	0.421367i	$0.138450\pi$
$354$	4.75038	−	6.19081i	0.252480	−	0.329038i
$355$	−0.0990394	+	0.0265375i	−0.00525647	+	0.00140847i
$356$	−0.819546			−0.0434359
$357$	8.58211	−	6.73405i	0.454214	−	0.356403i
$358$	−0.513792			−0.0271548
$359$	−10.0205	+	2.68498i	−0.528860	+	0.141708i	−0.513362	−	0.858172i	$-0.671600\pi$
$359$	−10.0205	+	2.68498i	−0.528860	+	0.141708i	−0.0154983	+	0.999880i	$0.504933\pi$
$360$	0.163416	−	0.212967i	0.00861276	−	0.0112244i
$361$	−12.9898	+	7.49966i	−0.683673	+	0.394719i
$362$	−3.17964	+	24.1518i	−0.167118	+	1.26939i
$363$	−1.67300	+	4.03898i	−0.0878097	+	0.211991i
$364$	−1.36470	+	10.9219i	−0.0715297	+	0.572464i
$365$	−0.518257	+	0.518257i	−0.0271268	+	0.0271268i
$366$	−2.85646	−	10.6605i	−0.149310	−	0.557231i
$367$	1.45760	+	11.0715i	0.0760859	+	0.577929i	0.986443	+	0.164106i	$0.0524738\pi$
$367$	1.45760	+	11.0715i	0.0760859	+	0.577929i	−0.910357	+	0.413824i	$0.864193\pi$
$368$	1.61443	−	0.212543i	0.0841578	−	0.0110796i
$369$	−1.11718	+	8.48580i	−0.0581579	+	0.441753i
$370$			0.236438i			0.0122918i
$371$	−21.7809	+	16.9424i	−1.13081	+	0.879607i
$372$	−3.36862	−	3.36862i	−0.174655	−	0.174655i
$373$	−4.97634	+	8.61928i	−0.257665	+	0.446289i	−0.965616	−	0.259972i	$-0.916287\pi$
$373$	−4.97634	+	8.61928i	−0.257665	+	0.446289i	0.707951	+	0.706262i	$0.249620\pi$
$374$	11.3823	−	11.4789i	0.588562	−	0.593558i
$375$	−1.33253	−	2.30800i	−0.0688114	−	0.119185i
$376$	−0.685753	+	0.183747i	−0.0353650	+	0.00947603i
$377$	−4.89693	−	11.8222i	−0.252205	−	0.608877i
$378$	−1.88312	−	1.85845i	−0.0968574	−	0.0955885i
$379$	−3.37666	+	1.39866i	−0.173447	+	0.0718442i	−0.467717	−	0.883878i	$-0.654923\pi$
$379$	−3.37666	+	1.39866i	−0.173447	+	0.0718442i	0.294270	+	0.955722i	$0.404923\pi$
$380$	0.326859	+	0.425971i	0.0167675	+	0.0218519i
$381$	−1.81077	−	13.7542i	−0.0927686	−	0.704648i
$382$	1.02061	+	0.273473i	0.0522192	+	0.0139921i
$383$	−3.35997	−	12.5396i	−0.171686	−	0.640742i	−0.997092	−	0.0762024i	$-0.975720\pi$
$383$	−3.35997	−	12.5396i	−0.171686	−	0.640742i	0.825406	−	0.564539i	$-0.190946\pi$
$384$	0.923880	+	0.382683i	0.0471465	+	0.0195287i
$385$	1.68053	−	2.22027i	0.0856479	−	0.113156i
$386$	21.9460	−	9.09034i	1.11702	−	0.462686i
$387$	−2.26863	−	1.30980i	−0.115321	−	0.0665807i
$388$	6.25457	−	8.15111i	0.317528	−	0.413810i
$389$	−9.31478	+	34.7632i	−0.472278	+	1.76257i	0.159276	+	0.987234i	$0.449084\pi$
$389$	−9.31478	+	34.7632i	−0.472278	+	1.76257i	−0.631554	+	0.775332i	$0.717583\pi$
$390$	−0.558381	+	0.967144i	−0.0282747	+	0.0489733i
$391$	5.82853	+	3.33235i	0.294761	+	0.168524i
$392$	6.10780	+	3.41976i	0.308491	+	0.172724i
$393$	−15.6383	−	15.6383i	−0.788847	−	0.788847i
$394$	10.4787	+	1.37955i	0.527911	+	0.0695008i
$395$	1.03289	−	0.596342i	0.0519705	−	0.0300052i
$396$	−3.11049	−	2.38676i	−0.156308	−	0.119939i
$397$	−9.74022	−	12.6937i	−0.488848	−	0.637079i	0.482172	−	0.876076i	$-0.339848\pi$
$397$	−9.74022	−	12.6937i	−0.488848	−	0.637079i	−0.971020	+	0.238998i	$0.923181\pi$
$398$	−13.7604	−	5.69975i	−0.689747	−	0.285703i
$399$	4.56542	−	2.67614i	0.228557	−	0.133974i
$400$	3.48458	−	3.48458i	0.174229	−	0.174229i
$401$	−27.7102	+	21.2628i	−1.38378	+	1.06181i	−0.394018	+	0.919103i	$0.628915\pi$
$401$	−27.7102	+	21.2628i	−1.38378	+	1.06181i	−0.989764	+	0.142711i	$0.954418\pi$
$402$	−5.71323	+	0.752161i	−0.284950	+	0.0375144i
$403$	15.7234	+	12.0650i	0.783239	+	0.601001i
$404$	−13.2407	−	7.64455i	−0.658752	−	0.380330i
$405$	−0.102727	−	0.248006i	−0.00510457	−	0.0123235i
$406$	−8.13786	+	0.0536575i	−0.403875	+	0.00266298i
$407$	3.45328			0.171173
$408$	2.07662	+	3.56197i	0.102808	+	0.176344i
$409$	−6.79435	−	11.7682i	−0.335959	−	0.581898i	0.647709	−	0.761887i	$-0.275727\pi$
$409$	−6.79435	−	11.7682i	−0.335959	−	0.581898i	−0.983669	+	0.179989i	$0.942394\pi$
$410$	0.594658	−	2.21929i	0.0293681	−	0.109603i
$411$	3.07502	+	0.404834i	0.151680	+	0.0199690i
$412$		−	3.32153i		−	0.163640i
$413$	12.6760	+	16.2961i	0.623747	+	0.801880i
$414$	0.623145	−	1.50441i	0.0306259	−	0.0739375i
$415$	−1.22882	+	0.942910i	−0.0603206	+	0.0462856i
$416$	−4.01844	−	1.07674i	−0.197020	−	0.0527914i
$417$	−16.7015	−	4.47516i	−0.817878	−	0.219150i
$418$	6.22151	−	4.77393i	0.304304	−	0.233501i
$419$	8.72651	−	21.0677i	0.426318	−	1.02922i	−0.554127	−	0.832432i	$-0.686948\pi$
$419$	8.72651	−	21.0677i	0.426318	−	1.02922i	0.980445	−	0.196791i	$-0.0630520\pi$
$420$	0.436063	+	0.560596i	0.0212777	+	0.0273543i
$421$		−	2.76062i		−	0.134544i	−0.997735	−	0.0672722i	$-0.978570\pi$
$421$		−	2.76062i		−	0.134544i	0.997735	−	0.0672722i	$-0.0214296\pi$
$422$	−1.66004	−	0.218549i	−0.0808095	−	0.0106388i
$423$	−0.183747	+	0.685753i	−0.00893408	+	0.0333425i
$424$	−5.21486	−	9.03241i	−0.253256	−	0.438653i
$425$	20.1332	−	2.73718i	0.976604	−	0.132773i
$426$	−0.381960			−0.0185060
$427$	29.1992	−	0.192527i	1.41305	−	0.00931704i
$428$	2.60819	+	6.29674i	0.126072	+	0.304364i
$429$	14.1256	+	8.15541i	0.681990	+	0.393747i
$430$	0.557888	+	0.428082i	0.0269037	+	0.0206440i
$431$	16.1261	−	2.12304i	0.776766	−	0.102263i	0.268289	−	0.963339i	$-0.413542\pi$
$431$	16.1261	−	2.12304i	0.776766	−	0.102263i	0.508477	+	0.861075i	$0.330209\pi$
$432$	0.793353	−	0.608761i	0.0381702	−	0.0292890i
$433$	13.4089	−	13.4089i	0.644391	−	0.644391i	−0.307241	−	0.951632i	$-0.599406\pi$
$433$	13.4089	−	13.4089i	0.644391	−	0.644391i	0.951632	+	0.307241i	$0.0994058\pi$
$434$	10.8738	−	6.37394i	0.521958	−	0.305959i
$435$	−0.762839	−	0.315978i	−0.0365753	−	0.0151500i
$436$	1.04418	+	1.36080i	0.0500070	+	0.0651704i
$437$	2.58395	+	1.98273i	0.123607	+	0.0948469i
$438$	−2.36453	+	1.36516i	−0.112981	+	0.0652299i
$439$	21.8588	+	2.87777i	1.04326	+	0.137348i	0.632632	−	0.774453i	$-0.281975\pi$
$439$	21.8588	+	2.87777i	1.04326	+	0.137348i	0.410632	+	0.911801i	$0.365308\pi$
$440$	0.744207	+	0.744207i	0.0354787	+	0.0354787i
$441$	6.01550	−	3.57963i	0.286452	−	0.170459i
$442$	−10.4995	−	13.5641i	−0.499408	−	0.645178i
$443$	−6.16712	+	10.6818i	−0.293009	+	0.507506i	−0.974520	−	0.224302i	$-0.927990\pi$
$443$	−6.16712	+	10.6818i	−0.293009	+	0.507506i	0.681511	+	0.731808i	$0.261323\pi$
$444$	−0.227964	+	0.850774i	−0.0108187	+	0.0403759i
$445$	0.133927	−	0.174537i	0.00634873	−	0.00827383i
$446$	13.3787	+	7.72422i	0.633502	+	0.365752i
$447$	7.25845	−	3.00655i	0.343313	−	0.142205i
$448$	−1.59676	+	2.10959i	−0.0754397	+	0.0996687i
$449$	10.8534	+	4.49563i	0.512204	+	0.212162i	0.623789	−	0.781593i	$-0.285593\pi$
$449$	10.8534	+	4.49563i	0.512204	+	0.212162i	−0.111584	+	0.993755i	$0.535593\pi$
$450$	−1.27544	−	4.76002i	−0.0601250	−	0.224390i
$451$	−32.4138	−	8.68525i	−1.52631	−	0.408973i
$452$	−0.486574	−	3.69590i	−0.0228865	−	0.173840i
$453$	−8.97828	−	11.7007i	−0.421836	−	0.549748i
$454$	13.2977	−	5.50807i	0.624090	−	0.258507i
$455$	−2.10300	−	2.07545i	−0.0985902	−	0.0972986i
$456$	0.765432	+	1.84792i	0.0358447	+	0.0865366i
$457$	1.24024	−	0.332322i	0.0580161	−	0.0155454i	−0.229694	−	0.973263i	$-0.573773\pi$
$457$	1.24024	−	0.332322i	0.0580161	−	0.0155454i	0.287710	+	0.957717i	$0.407106\pi$
$458$	6.05244	+	10.4831i	0.282812	+	0.489845i
$459$	4.12307	−	0.0174222i	0.192448	−	0.000813197i
$460$	−0.218558	+	0.378553i	−0.0101903	+	0.0176501i
$461$	13.5866	+	13.5866i	0.632793	+	0.632793i	0.948768	−	0.315975i	$-0.102331\pi$
$461$	13.5866	+	13.5866i	0.632793	+	0.632793i	−0.315975	+	0.948768i	$0.602331\pi$
$462$	8.18776	−	6.36890i	0.380929	−	0.296308i
$463$			4.53617i			0.210814i	0.994429	+	0.105407i	$0.0336145\pi$
$463$			4.53617i			0.210814i	−0.994429	+	0.105407i	$0.966385\pi$
$464$	0.401484	−	3.04957i	0.0186384	−	0.141573i
$465$	1.26789	−	0.166921i	0.0587970	−	0.00774077i
$466$	1.79505	+	13.6348i	0.0831543	+	0.631620i
$467$	8.99878	+	33.5839i	0.416414	+	1.55408i	0.781987	+	0.623295i	$0.214206\pi$
$467$	8.99878	+	33.5839i	0.416414	+	1.55408i	−0.365573	+	0.930783i	$0.619127\pi$
$468$	−2.94170	+	2.94170i	−0.135980	+	0.135980i
$469$	1.89032	−	15.1286i	0.0872870	−	0.698573i
$470$	0.0729307	−	0.176070i	0.00336404	−	0.00812152i
$471$	−0.226092	+	1.71734i	−0.0104178	+	0.0791307i
$472$	−6.75790	+	3.90167i	−0.311057	+	0.179589i
$473$	6.25234	−	8.14821i	0.287483	−	0.374655i
$474$	4.29163	−	1.14994i	0.197121	−	0.0528184i
$475$	9.85672			0.452257
$476$	−10.5058	+	2.93721i	−0.481535	+	0.134627i
$477$	−10.4297			−0.477544
$478$	21.5047	−	5.76216i	0.983601	−	0.263555i
$479$	23.4370	−	30.5437i	1.07086	−	1.39558i	0.157938	−	0.987449i	$-0.449516\pi$
$479$	23.4370	−	30.5437i	1.07086	−	1.39558i	0.912925	−	0.408127i	$-0.133818\pi$
$480$	−0.232476	+	0.134220i	−0.0106110	+	0.00612627i
$481$	0.478280	−	3.63289i	0.0218077	−	0.165646i
$482$	−2.16067	+	5.21631i	−0.0984156	+	0.237596i
$483$	3.43516	+	2.60009i	0.156305	+	0.118308i
$484$	3.09130	−	3.09130i	0.140514	−	0.140514i
$485$	0.713827	+	2.66404i	0.0324132	+	0.120968i
$486$	−0.130526	−	0.991445i	−0.00592079	−	0.0449729i
$487$	−41.6098	+	5.47803i	−1.88552	+	0.248233i	−0.983159	−	0.182751i	$-0.941500\pi$
$487$	−41.6098	+	5.47803i	−1.88552	+	0.248233i	−0.902359	+	0.430985i	$0.858166\pi$
$488$	−1.44055	+	10.9421i	−0.0652108	+	0.495326i
$489$		−	23.0509i		−	1.04240i
$490$	−1.72641	+	0.741922i	−0.0779912	+	0.0335166i
$491$	14.6959	+	14.6959i	0.663216	+	0.663216i	0.956137	−	0.292921i	$-0.0946271\pi$
$491$	14.6959	+	14.6959i	0.663216	+	0.663216i	−0.292921	+	0.956137i	$0.594627\pi$
$492$	4.27951	−	7.41233i	0.192935	−	0.334174i
$493$	8.92971	−	9.00549i	0.402174	−	0.405587i
$494$	−4.16055	−	7.20629i	−0.187192	−	0.324226i
$495$	1.01661	−	0.272398i	0.0456930	−	0.0122434i
$496$	1.82308	+	4.40131i	0.0818588	+	0.197625i
$497$	0.255113	−	0.977839i	0.0114434	−	0.0438621i
$498$	−5.33079	+	2.20809i	−0.238879	+	0.0989467i
$499$	6.46257	+	8.42218i	0.289304	+	0.377029i	0.915283	−	0.402812i	$-0.131967\pi$
$499$	6.46257	+	8.42218i	0.289304	+	0.377029i	−0.625979	+	0.779840i	$0.715300\pi$
$500$	0.347859	+	2.64225i	0.0155567	+	0.118165i
$501$	−6.99059	−	1.87312i	−0.312317	−	0.0836850i
$502$	−5.28764	−	19.7337i	−0.235999	−	0.880760i
$503$	−5.46689	−	2.26446i	−0.243757	−	0.100967i	0.257461	−	0.966289i	$-0.417114\pi$
$503$	−5.46689	−	2.26446i	−0.243757	−	0.100967i	−0.501217	+	0.865322i	$0.667114\pi$
$504$	1.02858	+	2.43763i	0.0458166	+	0.108581i
$505$	3.79179	−	1.57061i	0.168732	−	0.0698912i
$506$	5.52894	+	3.19214i	0.245791	+	0.141908i
$507$	2.62208	−	3.41717i	0.116451	−	0.151762i
$508$	−3.59056	+	13.4002i	−0.159305	+	0.594536i
$509$	7.51081	−	13.0091i	0.332911	−	0.576618i	−0.650171	−	0.759788i	$-0.725303\pi$
$509$	7.51081	−	13.0091i	0.332911	−	0.576618i	0.983081	+	0.183170i	$0.0586359\pi$
$510$	−1.09794	−	0.139829i	−0.0486175	−	0.00619173i
$511$	−1.91561	−	6.96513i	−0.0847416	−	0.308119i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.98306	+	0.261075i	0.0875542	+	0.0115267i
$514$	−4.37169	+	2.52400i	−0.192827	+	0.111329i
$515$	0.707378	+	0.542790i	0.0311708	+	0.0239182i
$516$	1.59471	+	2.07826i	0.0702030	+	0.0914904i
$517$	−2.57159	−	1.06519i	−0.113098	−	0.0468468i
$518$	−2.02577	−	1.15184i	−0.0890073	−	0.0506089i
$519$	−6.19481	+	6.19481i	−0.271922	+	0.271922i
$520$	0.885987	−	0.679842i	0.0388531	−	0.0298130i
$521$	−21.2709	+	2.80036i	−0.931894	+	0.122686i	−0.581160	−	0.813789i	$-0.697401\pi$
$521$	−21.2709	+	2.80036i	−0.931894	+	0.122686i	−0.350734	+	0.936475i	$0.614068\pi$
$522$	−2.44027	−	1.87248i	−0.106808	−	0.0819563i
$523$	36.8791	+	21.2922i	1.61261	+	0.931042i	0.988762	+	0.149497i	$0.0477655\pi$
$523$	36.8791	+	21.2922i	1.61261	+	0.931042i	0.623849	+	0.781545i	$0.285568\pi$
$524$	8.46337	+	20.4324i	0.369724	+	0.892593i
$525$	13.0378	−	0.0859657i	0.569017	−	0.00375185i
$526$	−14.1759			−0.618097
$527$	−5.00357	+	18.9943i	−0.217959	+	0.827403i
$528$	1.96034	+	3.39541i	0.0853129	+	0.147766i
$529$	5.26657	−	19.6551i	0.228981	−	0.854569i
$530$	2.77580	+	0.365441i	0.120573	+	0.0158737i
$531$			7.80335i			0.338636i
$532$	−5.24201	+	0.725317i	−0.227270	+	0.0314465i
$533$	−13.6263	+	32.8968i	−0.590221	+	1.42492i
$534$	0.650190	−	0.498908i	0.0281365	−	0.0215899i
$535$	−1.76722	−	0.473525i	−0.0764036	−	0.0204723i
$536$	5.56617	+	1.49145i	0.240422	+	0.0644209i
$537$	0.407619	−	0.312777i	0.0175901	−	0.0134973i
$538$	3.70563	−	8.94619i	0.159761	−	0.385697i
$539$	10.8361	+	25.2150i	0.466744	+	1.08609i
$540$			0.268440i			0.0115518i
$541$	−25.2558	−	3.32499i	−1.08583	−	0.142952i	−0.433699	−	0.901058i	$-0.642792\pi$
$541$	−25.2558	−	3.32499i	−1.08583	−	0.142952i	−0.652132	+	0.758106i	$0.726125\pi$
$542$	−3.65805	+	13.6520i	−0.157127	+	0.586404i
$543$	−12.1801	−	21.0965i	−0.522697	−	0.905338i
$544$	−0.555442	−	4.08552i	−0.0238144	−	0.175165i
$545$	−0.460441			−0.0197231
$546$	−5.56615	−	9.49572i	−0.238209	−	0.406379i
$547$	−11.4164	−	27.5616i	−0.488130	−	1.17845i	−0.955660	−	0.294472i	$-0.904856\pi$
$547$	−11.4164	−	27.5616i	−0.488130	−	1.17845i	0.467530	−	0.883977i	$-0.345144\pi$
$548$	−2.68602	−	1.55078i	−0.114741	−	0.0662459i
$549$	8.75586	+	6.71861i	0.373691	+	0.286743i
$550$	19.1556	−	2.52188i	0.816798	−	0.107533i
$551$	4.88095	−	3.74528i	0.207935	−	0.159555i
$552$	−1.15142	+	1.15142i	−0.0490078	+	0.0490078i
$553$	0.0775065	+	11.7549i	0.00329591	+	0.499868i
$554$	28.6906	+	11.8840i	1.21895	+	0.504905i
$555$	−0.143934	−	0.187579i	−0.00610967	−	0.00796227i
$556$	13.7176	+	10.5259i	0.581757	+	0.446398i
$557$	7.41888	−	4.28329i	0.314348	−	0.181489i	−0.334522	−	0.942388i	$-0.608575\pi$
$557$	7.41888	−	4.28329i	0.314348	−	0.181489i	0.648871	+	0.760899i	$0.275242\pi$
$558$	4.72319	+	0.621819i	0.199948	+	0.0263237i
$559$	−7.70606	−	7.70606i	−0.325932	−	0.325932i
$560$	−0.188339	−	0.684797i	−0.00795877	−	0.0289380i
$561$	−2.04227	+	16.0359i	−0.0862245	+	0.677035i
$562$	11.8282	−	20.4871i	0.498944	−	0.864197i
$563$	−9.49907	+	35.4510i	−0.400338	+	1.49408i	0.412156	+	0.911113i	$0.364776\pi$
$563$	−9.49907	+	35.4510i	−0.400338	+	1.49408i	−0.812494	+	0.582969i	$0.801891\pi$
$564$	0.432186	−	0.563236i	0.0181983	−	0.0237165i
$565$	0.866620	+	0.500343i	0.0364590	+	0.0210496i
$566$	−26.5617	+	11.0022i	−1.11647	+	0.462457i
$567$	2.62534	+	0.328037i	0.110254	+	0.0137763i
$568$	0.352885	+	0.146170i	0.0148067	+	0.00613314i
$569$	−1.98863	−	7.42166i	−0.0833676	−	0.311132i	0.911632	−	0.411006i	$-0.134823\pi$
$569$	−1.98863	−	7.42166i	−0.0833676	−	0.311132i	−0.995000	+	0.0998742i	$0.968156\pi$
$570$	−0.518630	−	0.138966i	−0.0217230	−	0.00582067i
$571$	0.144063	+	1.09427i	0.00602885	+	0.0457937i	0.994195	−	0.107595i	$-0.0343148\pi$
$571$	0.144063	+	1.09427i	0.00602885	+	0.0457937i	−0.988166	+	0.153388i	$0.950981\pi$
$572$	−9.92940	−	12.9402i	−0.415169	−	0.541059i
$573$	−0.976188	+	0.404350i	−0.0407808	+	0.0168920i
$574$	16.1177	+	15.9065i	0.672740	+	0.663926i
$575$	3.07082	+	7.41362i	0.128062	+	0.309169i
$576$	−0.965926	+	0.258819i	−0.0402469	+	0.0107841i
$577$	3.53566	+	6.12395i	0.147192	+	0.254943i	0.930188	−	0.367082i	$-0.119643\pi$
$577$	3.53566	+	6.12395i	0.147192	+	0.254943i	−0.782997	+	0.622026i	$0.786310\pi$
$578$	8.37528	−	14.7937i	0.348366	−	0.615338i
$579$	−11.8771	+	20.5718i	−0.493596	+	0.854933i
$580$	0.583851	+	0.583851i	0.0242431	+	0.0242431i
$581$	−2.09236	−	15.1219i	−0.0868059	−	0.627364i
$582$			10.2743i			0.425881i
$583$	5.33743	−	40.5418i	0.221054	−	1.67907i
$584$	2.70696	−	0.356378i	0.112015	−	0.0147470i
$585$	−0.145767	−	1.10721i	−0.00602671	−	0.0457774i
$586$	−3.98252	−	14.8630i	−0.164516	−	0.613983i
$587$	−24.6750	+	24.6750i	−1.01845	+	1.01845i	−0.0186191	+	0.999827i	$0.505927\pi$
$587$	−24.6750	+	24.6750i	−1.01845	+	1.01845i	−0.999827	+	0.0186191i	$0.994073\pi$
$588$	−6.92746	+	1.00512i	−0.285684	+	0.0414505i
$589$	−3.64648	+	8.80337i	−0.150250	+	0.362737i
$590$	0.273417	−	2.07681i	0.0112564	−	0.0855008i
$591$	−9.15316	+	5.28458i	−0.376511	+	0.217379i
$592$	0.536188	−	0.698774i	0.0220372	−	0.0287194i
$593$	−11.5942	+	3.10667i	−0.476119	+	0.127576i	−0.488895	−	0.872343i	$-0.662600\pi$
$593$	−11.5942	+	3.10667i	−0.476119	+	0.127576i	0.0127761	+	0.999918i	$0.495933\pi$
$594$	3.92068			0.160868
$595$	1.09129	−	2.71739i	0.0447385	−	0.111402i
$596$	−7.85648			−0.321814
$597$	14.3867	−	3.85489i	0.588807	−	0.157770i
$598$	4.12392	−	5.37440i	0.168640	−	0.219776i
$599$	−14.1022	+	8.14188i	−0.576198	+	0.332668i	−0.759621	−	0.650366i	$-0.774616\pi$
$599$	−14.1022	+	8.14188i	−0.576198	+	0.332668i	0.183423	+	0.983034i	$0.441282\pi$
$600$	−0.643225	+	4.88578i	−0.0262596	+	0.199461i
$601$	1.18737	−	2.86656i	0.0484337	−	0.116929i	−0.897811	−	0.440381i	$-0.854843\pi$
$601$	1.18737	−	2.86656i	0.0484337	−	0.116929i	0.946245	+	0.323452i	$0.104843\pi$
$602$	−6.38559	+	2.69446i	−0.260257	+	0.109818i
$603$	4.07472	−	4.07472i	0.165936	−	0.165936i
$604$	3.81718	+	14.2459i	0.155319	+	0.579657i
$605$	0.153180	+	1.16351i	0.00622763	+	0.0473036i
$606$	15.1583	−	1.99563i	0.615764	−	0.0810668i
$607$	1.33749	−	10.1593i	0.0542872	−	0.412352i	−0.942627	−	0.333849i	$-0.891653\pi$
$607$	1.33749	−	10.1593i	0.0542872	−	0.412352i	0.996914	−	0.0785034i	$-0.0250141\pi$
$608$		−	2.00017i		−	0.0811177i
$609$	6.42353	−	4.99658i	0.260295	−	0.202472i
$610$	−2.09490	−	2.09490i	−0.0848201	−	0.0848201i
$611$	−1.47675	+	2.55781i	−0.0597430	+	0.103478i
$612$	−3.81589	−	1.56173i	−0.154248	−	0.0631294i
$613$	−1.39801	−	2.42143i	−0.0564651	−	0.0978005i	0.836411	−	0.548103i	$-0.184650\pi$
$613$	−1.39801	−	2.42143i	−0.0564651	−	0.0978005i	−0.892876	+	0.450302i	$0.851316\pi$
$614$	23.0531	−	6.17707i	0.930349	−	0.249286i
$615$	0.879247	+	2.12269i	0.0354546	+	0.0855951i
$616$	−10.0018	+	2.75078i	−0.402983	+	0.110832i
$617$	−16.3208	+	6.76031i	−0.657052	+	0.272160i	−0.686197	−	0.727415i	$-0.740721\pi$
$617$	−16.3208	+	6.76031i	−0.657052	+	0.272160i	0.0291455	+	0.999575i	$0.490721\pi$
$618$	2.02202	+	2.63515i	0.0813375	+	0.106001i
$619$	1.00120	+	7.60488i	0.0402417	+	0.305666i	0.999715	+	0.0238669i	$0.00759780\pi$
$619$	1.00120	+	7.60488i	0.0402417	+	0.305666i	−0.959473	+	0.281799i	$0.909069\pi$
$620$	−1.23526	−	0.330986i	−0.0496091	−	0.0132927i
$621$	0.421450	+	1.57287i	0.0169122	+	0.0631172i
$622$	−23.4790	−	9.72531i	−0.941421	−	0.389949i
$623$	0.842969	+	1.99775i	0.0337728	+	0.0800381i
$624$	3.84352	−	1.59204i	0.153864	−	0.0637326i
$625$	20.7190	+	11.9621i	0.828762	+	0.478486i
$626$	−6.47473	+	8.43804i	−0.258782	+	0.337252i
$627$	−2.02967	+	7.57483i	−0.0810572	+	0.302509i
$628$	0.866078	−	1.50009i	0.0345603	−	0.0598601i
$629$	3.50383	−	0.954734i	0.139707	−	0.0380677i
$630$	−0.687221	−	0.179292i	−0.0273796	−	0.00714318i
$631$	−12.7089	−	12.7089i	−0.505934	−	0.505934i	0.407342	−	0.913276i	$-0.366456\pi$
$631$	−12.7089	−	12.7089i	−0.505934	−	0.505934i	−0.913276	+	0.407342i	$0.866456\pi$
$632$	−4.40501	−	0.579931i	−0.175222	−	0.0230684i
$633$	1.45004	−	0.837183i	0.0576340	−	0.0332750i
$634$	−24.2236	−	18.5875i	−0.962044	−	0.738202i
$635$	−2.26704	−	2.95447i	−0.0899649	−	0.117245i
$636$	9.63581	+	3.99128i	0.382085	+	0.158265i
$637$	28.0273	−	7.90744i	1.11048	−	0.313304i
$638$	8.52741	−	8.52741i	0.337604	−	0.337604i
$639$	0.303029	−	0.232522i	0.0119876	−	0.00919844i
$640$	0.266143	−	0.0350384i	0.0105202	−	0.00138501i
$641$	−5.97498	−	4.58477i	−0.235998	−	0.181087i	0.483991	−	0.875073i	$-0.339187\pi$
$641$	−5.97498	−	4.58477i	−0.235998	−	0.181087i	−0.719989	+	0.693985i	$0.755853\pi$
$642$	−5.90243	−	3.40777i	−0.232950	−	0.134494i
$643$	−8.86165	−	21.3939i	−0.349469	−	0.843694i	−0.996683	−	0.0813847i	$-0.974066\pi$
$643$	−8.86165	−	21.3939i	−0.349469	−	0.843694i	0.647213	−	0.762309i	$-0.275934\pi$
$644$	−2.17867	−	3.71675i	−0.0858515	−	0.146460i
$645$	−0.703202			−0.0276886
$646$	4.99271	−	6.56387i	0.196436	−	0.258252i
$647$	−7.78047	−	13.4762i	−0.305882	−	0.529803i	0.671575	−	0.740936i	$-0.265618\pi$
$647$	−7.78047	−	13.4762i	−0.305882	−	0.529803i	−0.977457	+	0.211133i	$0.932285\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−30.3327	−	3.99338i	−1.19066	−	0.156754i
$650$		−	20.5012i		−	0.804123i
$651$	−4.74654	+	11.6763i	−0.186031	+	0.457631i
$652$	−8.82118	+	21.2962i	−0.345464	+	0.834024i
$653$	−22.6813	+	17.4039i	−0.887586	+	0.681069i	−0.948399	−	0.317081i	$-0.897297\pi$
$653$	−22.6813	+	17.4039i	−0.887586	+	0.681069i	0.0608127	+	0.998149i	$0.480631\pi$
$654$	−1.65680	−	0.443939i	−0.0647861	−	0.0173594i
$655$	−5.73448	−	1.53655i	−0.224065	−	0.0600380i
$656$	−6.79033	+	5.21041i	−0.265118	+	0.203432i
$657$	1.04485	−	2.52249i	0.0407634	−	0.0984116i
$658$	1.15326	+	1.48261i	0.0449587	+	0.0577982i
$659$		−	18.2809i		−	0.712124i	−0.934462	−	0.356062i	$-0.884119\pi$
$659$		−	18.2809i		−	0.712124i	0.934462	−	0.356062i	$-0.115881\pi$
$660$	−1.04346	−	0.137375i	−0.0406167	−	0.00534730i
$661$	−8.89445	+	33.1946i	−0.345954	+	1.29112i	0.545539	+	0.838085i	$0.316325\pi$
$661$	−8.89445	+	33.1946i	−0.345954	+	1.29112i	−0.891494	+	0.453033i	$0.850342\pi$
$662$	−16.7168	−	28.9543i	−0.649715	−	1.12534i
$663$	16.5871	+	4.36946i	0.644189	+	0.169696i
$664$	5.77001			0.223920
$665$	0.702158	−	1.23491i	0.0272285	−	0.0478876i
$666$	−0.337062	−	0.813740i	−0.0130609	−	0.0315318i
$667$	4.33761	+	2.50432i	0.167953	+	0.0969677i
$668$	5.74165	+	4.40573i	0.222151	+	0.170463i
$669$	−15.3163	+	2.01643i	−0.592161	+	0.0779595i
$670$	−1.22723	+	0.941688i	−0.0474121	+	0.0363806i
$671$	−30.5970	+	30.5970i	−1.18118	+	1.18118i
$672$	−0.0174445	−	2.64569i	−0.000672938	−	0.102060i
$673$	20.2568	+	8.39064i	0.780842	+	0.323436i	0.737255	−	0.675614i	$-0.236121\pi$
$673$	20.2568	+	8.39064i	0.780842	+	0.323436i	0.0435870	+	0.999050i	$0.486121\pi$
$674$	−20.3352	−	26.5014i	−0.783283	−	1.02079i
$675$	3.90960	+	2.99994i	0.150480	+	0.115468i
$676$	−3.73018	+	2.15362i	−0.143469	+	0.0828316i
$677$	7.00370	+	0.922054i	0.269174	+	0.0354374i	0.263905	−	0.964549i	$-0.414989\pi$
$677$	7.00370	+	0.922054i	0.269174	+	0.0354374i	0.00526898	+	0.999986i	$0.498323\pi$
$678$	2.63594	+	2.63594i	0.101233	+	0.101233i
$679$	−26.3027	−	6.86223i	−1.00940	−	0.263348i
$680$	0.960851	+	0.549347i	0.0368470	+	0.0210665i
$681$	−7.19664	+	12.4649i	−0.275776	+	0.477658i
$682$	−4.83420	+	18.0415i	−0.185111	+	0.690844i
$683$	19.5125	−	25.4292i	0.746627	−	0.973023i	−0.253357	−	0.967373i	$-0.581535\pi$
$683$	19.5125	−	25.4292i	0.746627	−	0.973023i	0.999984	−	0.00565006i	$-0.00179848\pi$
$684$	−1.73220	−	1.00009i	−0.0662323	−	0.0382392i
$685$	0.769204	−	0.318615i	0.0293898	−	0.0121736i
$686$	2.05373	−	18.4060i	0.0784116	−	0.702746i
$687$	−11.1835	−	4.63234i	−0.426675	−	0.176735i
$688$	−0.678000	−	2.53033i	−0.0258485	−	0.0964680i
$689$	−41.9113	−	11.2301i	−1.59669	−	0.427832i
$690$	−0.0570550	−	0.433376i	−0.00217205	−	0.0164983i
$691$	5.25367	+	6.84671i	0.199859	+	0.260461i	0.882521	−	0.470273i	$-0.155845\pi$
$691$	5.25367	+	6.84671i	0.199859	+	0.260461i	−0.682662	+	0.730734i	$0.739178\pi$
$692$	8.09391	−	3.35261i	0.307684	−	0.127447i
$693$	−2.61865	+	10.0372i	−0.0994742	+	0.381281i
$694$	13.6181	+	32.8770i	0.516937	+	1.24800i
$695$	−4.48336	+	1.20131i	−0.170063	+	0.0455683i
$696$	1.53794	+	2.66380i	0.0582956	+	0.100971i
$697$	−35.2895	+	0.149117i	−1.33668	+	0.00564820i
$698$	4.22836	−	7.32373i	0.160046	−	0.277207i
$699$	−9.72445	−	9.72445i	−0.367812	−	0.367812i
$700$	−12.0783	−	4.90994i	−0.456516	−	0.185578i
$701$			51.7692i			1.95530i	0.210249	+	0.977648i	$0.432572\pi$
$701$			51.7692i			1.95530i	−0.210249	+	0.977648i	$0.567428\pi$
$702$	0.543015	−	4.12461i	0.0204948	−	0.155673i
$703$	1.74665	−	0.229951i	0.0658762	−	0.00867276i
$704$	−0.511752	−	3.88714i	−0.0192874	−	0.146502i
$705$	0.0493250	+	0.184083i	0.00185769	+	0.00693298i
$706$	15.2703	−	15.2703i	0.574707	−	0.574707i
$707$	−5.01539	+	40.1390i	−0.188623	+	1.50958i
$708$	2.98621	−	7.20935i	0.112229	−	0.270944i
$709$	−5.89334	+	44.7644i	−0.221329	+	1.68116i	0.415060	+	0.909794i	$0.363761\pi$
$709$	−5.89334	+	44.7644i	−0.221329	+	1.68116i	−0.636389	+	0.771368i	$0.719573\pi$
$710$	−0.0887963	+	0.0512666i	−0.00333247	+	0.00192400i
$711$	−2.70474	+	3.52489i	−0.101436	+	0.132194i
$712$	−0.791621	+	0.212114i	−0.0296672	+	0.00794931i
$713$	−7.75740			−0.290517
$714$	6.54678	−	8.72580i	0.245007	−	0.326555i
$715$	4.37847			0.163746
$716$	−0.496285	+	0.132979i	−0.0185471	+	0.00496967i
$717$	−13.5530	+	17.6626i	−0.506147	+	0.659623i
$718$	−8.98411	+	5.18698i	−0.335284	+	0.193576i
$719$	4.39612	−	33.3918i	0.163948	−	1.24531i	−0.689562	−	0.724227i	$-0.742197\pi$
$719$	4.39612	−	33.3918i	0.163948	−	1.24531i	0.853509	−	0.521078i	$-0.174470\pi$
$720$	0.102727	−	0.248006i	0.00382842	−	0.00924263i
$721$	−8.09665	+	3.41646i	−0.301535	+	0.127236i
$722$	−10.6061	+	10.6061i	−0.394719	+	0.394719i
$723$	−1.46132	−	5.45370i	−0.0543469	−	0.202825i
$724$	3.17964	+	24.1518i	0.118170	+	0.897593i
$725$	15.0281	−	1.97849i	0.558130	−	0.0734792i
$726$	−0.570629	+	4.33436i	−0.0211780	+	0.160863i
$727$		−	22.4754i		−	0.833568i	−0.909006	−	0.416784i	$-0.863157\pi$
$727$		−	22.4754i		−	0.833568i	0.909006	−	0.416784i	$-0.136843\pi$
$728$	1.50860	+	10.9030i	0.0559125	+	0.404091i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−0.366463	+	0.634733i	−0.0135634	+	0.0234925i
$731$	4.09110	−	9.99606i	0.151315	−	0.369718i
$732$	−5.51826	−	9.55791i	−0.203961	−	0.353270i
$733$	−2.54004	+	0.680601i	−0.0938184	+	0.0251386i	−0.305423	−	0.952217i	$-0.598798\pi$
$733$	−2.54004	+	0.680601i	−0.0938184	+	0.0251386i	0.211604	+	0.977355i	$0.432131\pi$
$734$	4.27345	+	10.3170i	0.157736	+	0.380809i
$735$	0.917998	−	1.63958i	0.0338609	−	0.0604767i
$736$	1.50441	−	0.623145i	0.0554531	−	0.0229694i
$737$	13.7538	+	17.9243i	0.506627	+	0.660249i
$738$	1.11718	+	8.48580i	0.0411239	+	0.312367i
$739$	−3.01035	−	0.806621i	−0.110738	−	0.0296720i	0.203025	−	0.979174i	$-0.434923\pi$
$739$	−3.01035	−	0.806621i	−0.110738	−	0.0296720i	−0.313762	+	0.949502i	$0.601589\pi$
$740$	0.0611946	+	0.228381i	0.00224956	+	0.00839547i
$741$	7.68770	+	3.18435i	0.282415	+	0.116980i
$742$	−16.6537	+	22.0024i	−0.611378	+	0.807735i
$743$	−20.3430	+	8.42636i	−0.746314	+	0.309133i	−0.723236	−	0.690600i	$-0.757346\pi$
$743$	−20.3430	+	8.42636i	−0.746314	+	0.309133i	−0.0230771	+	0.999734i	$0.507346\pi$
$744$	−4.12569	−	2.38197i	−0.151255	−	0.0873273i
$745$	1.28387	−	1.67318i	0.0470375	−	0.0613004i
$746$	−2.57594	+	9.61356i	−0.0943120	+	0.351977i
$747$	2.88500	−	4.99697i	0.105557	−	0.182830i
$748$	8.02347	−	14.0337i	0.293367	−	0.513122i
$749$	12.6664	−	12.8345i	0.462819	−	0.468962i
$750$	−1.88448	−	1.88448i	−0.0688114	−	0.0688114i
$751$	−15.9548	−	2.10049i	−0.582199	−	0.0766480i	−0.166326	−	0.986071i	$-0.553191\pi$
$751$	−15.9548	−	2.10049i	−0.582199	−	0.0766480i	−0.415873	+	0.909423i	$0.636524\pi$
$752$	−0.614829	+	0.354972i	−0.0224205	+	0.0129445i
$753$	16.2081	+	12.4369i	0.590656	+	0.453226i
$754$	−7.78990	−	10.1520i	−0.283691	−	0.369714i
$755$	−3.65770	−	1.51507i	−0.133117	−	0.0551390i
$756$	−2.29996	−	1.30774i	−0.0836487	−	0.0475620i
$757$	−27.3526	+	27.3526i	−0.994146	+	0.994146i	−0.999983	−	0.00583725i	$-0.998142\pi$
$757$	−27.3526	+	27.3526i	−0.994146	+	0.994146i	0.00583725	+	0.999983i	$0.498142\pi$
$758$	−2.89960	+	2.22494i	−0.105318	+	0.0808136i
$759$	−6.32965	+	0.833315i	−0.229752	+	0.0302474i
$760$	0.425971	+	0.326859i	0.0154516	+	0.0118564i
$761$	−30.5661	−	17.6473i	−1.10802	−	0.639715i	−0.169704	−	0.985495i	$-0.554281\pi$
$761$	−30.5661	−	17.6473i	−1.10802	−	0.639715i	−0.938316	+	0.345780i	$0.887614\pi$
$762$	−5.30891	−	12.8169i	−0.192322	−	0.464306i
$763$	2.24310	−	3.94500i	0.0812056	−	0.142819i
$764$	1.05662			0.0382271
$765$	0.956174	−	0.557448i	0.0345706	−	0.0201546i
$766$	−6.49096	−	11.2427i	−0.234528	−	0.406214i
$767$	−8.40216	+	31.3573i	−0.303385	+	1.13225i
$768$	0.991445	+	0.130526i	0.0357757	+	0.00470996i
$769$			47.1854i			1.70155i	0.525530	+	0.850775i	$0.323867\pi$
$769$			47.1854i			1.70155i	−0.525530	+	0.850775i	$0.676133\pi$
$770$	1.04862	−	2.57957i	0.0377897	−	0.0929614i
$771$	1.93178	−	4.66374i	0.0695714	−	0.167960i
$772$	18.8455	−	14.4606i	0.678264	−	0.520450i
$773$	20.9822	+	5.62217i	0.754679	+	0.202216i	0.615592	−	0.788065i	$-0.288917\pi$
$773$	20.9822	+	5.62217i	0.754679	+	0.202216i	0.139086	+	0.990280i	$0.455583\pi$
$774$	−2.53033	−	0.678000i	−0.0909509	−	0.0243702i
$775$	−18.6251	+	14.2915i	−0.669033	+	0.513367i
$776$	3.93179	−	9.49217i	0.141143	−	0.340749i
$777$	2.30835	−	0.319397i	0.0828115	−	0.0114583i
$778$			35.9895i			1.29029i
$779$	−16.9731	−	2.23455i	−0.608123	−	0.0800609i
$780$	−0.289039	+	1.07871i	−0.0103493	+	0.0386240i
$781$	0.748772	+	1.29691i	0.0267932	+	0.0464071i
$782$	6.49240	+	1.71026i	0.232168	+	0.0611589i
$783$	3.07589			0.109923
$784$	6.78478	+	1.72242i	0.242314	+	0.0615148i
$785$	0.177940	+	0.429585i	0.00635095	+	0.0153325i
$786$	−19.1529	−	11.0579i	−0.683161	−	0.394423i
$787$	2.04357	+	1.56809i	0.0728454	+	0.0558962i	0.644542	−	0.764569i	$-0.277048\pi$
$787$	2.04357	+	1.56809i	0.0728454	+	0.0558962i	−0.571697	+	0.820465i	$0.693715\pi$
$788$	10.4787	−	1.37955i	0.373290	−	0.0491445i
$789$	11.2465	−	8.62972i	0.400385	−	0.307226i
$790$	0.843354	−	0.843354i	0.0300052	−	0.0300052i
$791$	−8.50873	+	4.98761i	−0.302536	+	0.177339i
$792$	−3.62224	−	1.50038i	−0.128711	−	0.0533137i
$793$	27.9507	+	36.4261i	0.992560	+	1.29353i
$794$	−12.6937	−	9.74022i	−0.450483	−	0.345668i
$795$	−2.42466	+	1.39988i	−0.0859937	+	0.0496485i
$796$	−14.7667	−	1.94408i	−0.523393	−	0.0689060i
$797$	−9.77145	−	9.77145i	−0.346123	−	0.346123i	0.512540	−	0.858663i	$-0.328704\pi$
$797$	−9.77145	−	9.77145i	−0.346123	−	0.346123i	−0.858663	+	0.512540i	$0.828704\pi$
$798$	3.71722	−	3.76657i	0.131588	−	0.133335i
$799$	−2.90372	−	0.369806i	−0.102726	−	0.0130828i
$800$	2.46397	−	4.26772i	0.0871145	−	0.150887i
$801$	−0.212114	+	0.791621i	−0.00749468	+	0.0279705i
$802$	−21.2628	+	27.7102i	−0.750816	+	0.978482i
$803$	9.27056	+	5.35236i	0.327151	+	0.188881i
$804$	−5.32388	+	2.20522i	−0.187759	+	0.0777723i
$805$	1.14758	+	0.143390i	0.0404467	+	0.00505384i
$806$	18.3103	+	7.58438i	0.644953	+	0.267148i
$807$	2.50622	+	9.35333i	0.0882230	+	0.329253i
$808$	−14.7681	−	3.95711i	−0.519541	−	0.139211i
$809$	−1.24775	−	9.47762i	−0.0438686	−	0.333215i	−0.999280	−	0.0379377i	$-0.987921\pi$
$809$	−1.24775	−	9.47762i	−0.0438686	−	0.333215i	0.955411	−	0.295278i	$-0.0954122\pi$
$810$	−0.163416	−	0.212967i	−0.00574184	−	0.00748292i
$811$	−22.5062	+	9.32238i	−0.790300	+	0.327353i	−0.741064	−	0.671434i	$-0.765679\pi$
$811$	−22.5062	+	9.32238i	−0.790300	+	0.327353i	−0.0492358	+	0.998787i	$0.515679\pi$
$812$	−7.84668	+	2.15806i	−0.275365	+	0.0757331i
$813$	−5.40870	−	13.0578i	−0.189691	−	0.457955i
$814$	3.33561	−	0.893775i	0.116913	−	0.0313268i
$815$	−3.09388	−	5.35876i	−0.108374	−	0.187709i
$816$	2.92777	+	2.90313i	0.102492	+	0.101630i
$817$	2.61982	−	4.53765i	0.0916557	−	0.158752i
$818$	−9.60867	−	9.60867i	−0.335959	−	0.335959i
$819$	10.1966	+	4.14500i	0.356296	+	0.144838i
$820$		−	2.29758i		−	0.0802350i
$821$	−1.10536	+	8.39603i	−0.0385772	+	0.293023i	0.961271	+	0.275605i	$0.0888781\pi$
$821$	−1.10536	+	8.39603i	−0.0385772	+	0.293023i	−0.999848	+	0.0174185i	$0.994455\pi$
$822$	3.07502	−	0.404834i	0.107254	−	0.0141202i
$823$	−5.05405	−	38.3893i	−0.176173	−	1.33817i	−0.819721	−	0.572763i	$-0.805872\pi$
$823$	−5.05405	−	38.3893i	−0.176173	−	1.33817i	0.643548	−	0.765406i	$-0.277462\pi$
$824$	−0.859675	−	3.20835i	−0.0299482	−	0.111768i
$825$	−13.6619	+	13.6619i	−0.475648	+	0.475648i
$826$	16.4619	+	12.4600i	0.572781	+	0.433540i
$827$	8.81856	−	21.2899i	0.306651	−	0.740322i	−0.693158	−	0.720786i	$-0.743781\pi$
$827$	8.81856	−	21.2899i	0.306651	−	0.740322i	0.999809	−	0.0195360i	$-0.00621889\pi$
$828$	0.212543	−	1.61443i	0.00738639	−	0.0561052i
$829$	3.89811	−	2.25058i	0.135387	−	0.0781657i	−0.430777	−	0.902459i	$-0.641760\pi$
$829$	3.89811	−	2.25058i	0.135387	−	0.0781657i	0.566164	+	0.824293i	$0.308427\pi$
$830$	−0.942910	+	1.22882i	−0.0327289	+	0.0426531i
$831$	−29.9963	+	8.03750i	−1.04056	+	0.278818i
$832$	−4.16020			−0.144229
$833$	17.9659	+	22.5882i	0.622483	+	0.782634i
$834$	−17.2907			−0.598728
$835$	−1.87655	+	0.502821i	−0.0649408	+	0.0174008i
$836$	4.77393	−	6.22151i	0.165110	−	0.215175i
$837$	−4.12569	+	2.38197i	−0.142605	+	0.0823330i
$838$	2.97645	−	22.6084i	0.102820	−	0.780994i
$839$	19.7261	−	47.6229i	0.681020	−	1.64413i	−0.0811125	−	0.996705i	$-0.525847\pi$
$839$	19.7261	−	47.6229i	0.681020	−	1.64413i	0.762132	−	0.647422i	$-0.224153\pi$
$840$	0.566297	+	0.428633i	0.0195391	+	0.0147892i
$841$	−13.8161	+	13.8161i	−0.476417	+	0.476417i
$842$	−0.714501	−	2.66655i	−0.0246233	−	0.0918955i
$843$	3.08779	+	23.4541i	0.106349	+	0.807802i
$844$	−1.66004	+	0.218549i	−0.0571410	+	0.00752275i
$845$	0.150919	−	1.14634i	0.00519177	−	0.0394354i
$846$			0.709944i			0.0244084i
$847$	−10.7151	−	4.35579i	−0.368175	−	0.149667i
$848$	−7.37493	−	7.37493i	−0.253256	−	0.253256i
$849$	14.3751	−	24.8984i	0.493351	−	0.854509i
$850$	18.7387	−	7.85477i	0.642734	−	0.269416i
$851$	0.717117	+	1.24208i	0.0245824	+	0.0425780i
$852$	−0.368945	+	0.0988584i	−0.0126398	+	0.00338683i
$853$	−0.729333	−	1.76076i	−0.0249719	−	0.0602874i	0.910902	−	0.412623i	$-0.135387\pi$
$853$	−0.729333	−	1.76076i	−0.0249719	−	0.0602874i	−0.935874	+	0.352336i	$0.885387\pi$
$854$	28.1545	−	7.74329i	0.963426	−	0.264970i
$855$	0.496054	−	0.205472i	0.0169647	−	0.00702701i
$856$	4.14904	+	5.40713i	0.141811	+	0.184812i
$857$	−4.33652	−	32.9392i	−0.148133	−	1.12518i	−0.890434	−	0.455113i	$-0.849599\pi$
$857$	−4.33652	−	32.9392i	−0.148133	−	1.12518i	0.742301	−	0.670067i	$-0.233735\pi$
$858$	15.7550	+	4.22155i	0.537868	+	0.144121i
$859$	−3.92341	−	14.6424i	−0.133865	−	0.499591i	0.866135	−	0.499810i	$-0.166597\pi$
$859$	−3.92341	−	14.6424i	−0.133865	−	0.499591i	−1.00000		0.000219100i	$0.999930\pi$
$860$	0.649674	+	0.269104i	0.0221537	+	0.00917636i
$861$	−22.4703	−	2.80768i	−0.765787	−	0.0956854i
$862$	15.0271	−	6.22443i	0.511825	−	0.212005i
$863$	18.9307	+	10.9297i	0.644409	+	0.372050i	0.786311	−	0.617831i	$-0.211988\pi$
$863$	18.9307	+	10.9297i	0.644409	+	0.372050i	−0.141902	+	0.989881i	$0.545322\pi$
$864$	0.608761	−	0.793353i	0.0207105	−	0.0269904i
$865$	−0.608676	+	2.27161i	−0.0206956	+	0.0772370i
$866$	9.48152	−	16.4225i	0.322195	−	0.558059i
$867$	2.36130	+	16.8352i	0.0801940	+	0.571754i
$868$	8.85356	−	8.97109i	0.300509	−	0.304499i
$869$	−12.3176	−	12.3176i	−0.417845	−	0.417845i
$870$	−0.818627	−	0.107774i	−0.0277540	−	0.00365389i
$871$	20.7614	−	11.9866i	0.703475	−	0.406151i
$872$	1.36080	+	1.04418i	0.0460824	+	0.0353603i
$873$	−6.25457	−	8.15111i	−0.211685	−	0.275873i
$874$	3.00907	+	1.24640i	0.101783	+	0.0421600i
$875$	6.08303	−	3.56572i	0.205644	−	0.120543i
$876$	−1.93063	+	1.93063i	−0.0652299	+	0.0652299i
$877$	−39.8613	+	30.5866i	−1.34602	+	1.03284i	−0.350671	+	0.936499i	$0.614046\pi$
$877$	−39.8613	+	30.5866i	−1.34602	+	1.03284i	−0.995349	+	0.0963385i	$0.969287\pi$
$878$	21.8588	−	2.87777i	0.737699	−	0.0971199i
$879$	12.2075	+	9.36717i	0.411750	+	0.315947i
$880$	0.911463	+	0.526233i	0.0307254	+	0.0177393i
$881$	12.3016	+	29.6986i	0.414450	+	1.00057i	0.983928	+	0.178565i	$0.0571454\pi$
$881$	12.3016	+	29.6986i	0.414450	+	1.00057i	−0.569478	+	0.822007i	$0.692855\pi$
$882$	4.88405	−	5.01459i	0.164454	−	0.168850i
$883$	−47.3351			−1.59295			−0.796476	−	0.604670i	$-0.793305\pi$
$883$	−47.3351			−1.59295			−0.796476	+	0.604670i	$0.793305\pi$
$884$	−13.6523	−	10.3844i	−0.459178	−	0.349267i
$885$	1.04736	+	1.81409i	0.0352068	+	0.0609799i
$886$	−3.19234	+	11.9140i	−0.107249	+	0.400257i
$887$	−7.04345	−	0.927288i	−0.236496	−	0.0311353i	0.0113465	−	0.999936i	$-0.496388\pi$
$887$	−7.04345	−	0.927288i	−0.236496	−	0.0311353i	−0.247843	+	0.968800i	$0.579722\pi$
$888$			0.880786i			0.0295572i
$889$	36.3578	−	5.03068i	1.21940	−	0.168724i
$890$	0.0841898	−	0.203252i	0.00282205	−	0.00681303i
$891$	−3.11049	+	2.38676i	−0.104205	+	0.0799595i
$892$	14.9220	+	3.99835i	0.499627	+	0.133875i
$893$	−1.37162	−	0.367525i	−0.0458996	−	0.0122988i
$894$	6.23297	−	4.78272i	0.208462	−	0.159958i
$895$	0.0527806	−	0.127424i	0.00176426	−	0.00425930i
$896$	−0.996347	+	2.45098i	−0.0332856	+	0.0818814i
$897$			6.77429i			0.226187i
$898$	11.6472	+	1.53338i	0.388670	+	0.0511694i
$899$	−3.79257	+	14.1541i	−0.126489	+	0.472064i
$900$	−2.46397	−	4.26772i	−0.0821323	−	0.142257i
$901$	−5.79310	−	42.6109i	−0.192996	−	1.41957i
$902$	−33.5572			−1.11733
$903$	3.42574	−	6.02496i	0.114002	−	0.200498i
$904$	−1.42656	−	3.44403i	−0.0474468	−	0.114547i
$905$	−5.66314	−	3.26962i	−0.188249	−	0.108686i
$906$	−11.7007	−	8.97828i	−0.388730	−	0.298283i
$907$	48.4683	−	6.38097i	1.60936	−	0.211877i	0.728431	−	0.685119i	$-0.240250\pi$
$907$	48.4683	−	6.38097i	1.60936	−	0.211877i	0.880932	+	0.473242i	$0.156916\pi$
$908$	11.4190	−	8.76208i	0.378951	−	0.290780i
$909$	−10.8110	+	10.8110i	−0.358579	+	0.358579i
$910$	−2.56851	−	1.46043i	−0.0851452	−	0.0484129i
$911$	37.5253	+	15.5435i	1.24327	+	0.514979i	0.904735	−	0.425975i	$-0.140069\pi$
$911$	37.5253	+	15.5435i	1.24327	+	0.514979i	0.338535	+	0.940954i	$0.390069\pi$
$912$	1.21763	+	1.58684i	0.0403197	+	0.0525456i
$913$	17.9475	+	13.7716i	0.593977	+	0.455774i
$914$	1.11197	−	0.641997i	0.0367808	−	0.0212354i
$915$	2.93729	+	0.386702i	0.0971039	+	0.0127840i
$916$	8.55945	+	8.55945i	0.282812	+	0.282812i
$917$	41.1013	−	41.6469i	1.35728	−	1.37530i
$918$	3.97807	−	1.08396i	0.131296	−	0.0357759i
$919$	17.2800	−	29.9299i	0.570015	−	0.987296i	−0.426548	−	0.904465i	$-0.640271\pi$
$919$	17.2800	−	29.9299i	0.570015	−	0.987296i	0.996564	−	0.0828309i	$-0.0263961\pi$
$920$	−0.113134	+	0.422221i	−0.00372991	+	0.0139202i
$921$	−14.5289	+	18.9345i	−0.478744	+	0.623911i
$922$	16.6402	+	9.60721i	0.548015	+	0.316397i
$923$	1.46807	−	0.608095i	0.0483221	−	0.0200157i
$924$	6.26038	−	8.27103i	0.205951	−	0.272097i
$925$	4.01006	+	1.66102i	0.131850	+	0.0546141i
$926$	1.17405	+	4.38161i	0.0385816	+	0.143989i
$927$	−3.20835	−	0.859675i	−0.105376	−	0.0282354i
$928$	−0.401484	−	3.04957i	−0.0131794	−	0.100107i
$929$	−5.26889	−	6.86655i	−0.172867	−	0.225284i	0.698883	−	0.715236i	$-0.253681\pi$
$929$	−5.26889	−	6.86655i	−0.172867	−	0.225284i	−0.871749	+	0.489952i	$0.837014\pi$
$930$	1.18149	−	0.489387i	0.0387424	−	0.0160476i
$931$	7.15988	+	12.0320i	0.234656	+	0.394334i
$932$	5.26283	+	12.7056i	0.172390	+	0.416186i
$933$	24.5475	−	6.57749i	0.803649	−	0.215337i
$934$	17.3843	+	30.1105i	0.568832	+	0.985245i
$935$	1.67755	+	4.00206i	0.0548619	+	0.130881i
$936$	−2.08010	+	3.60284i	−0.0679902	+	0.117762i
$937$	17.5765	+	17.5765i	0.574198	+	0.574198i	0.933299	−	0.359101i	$-0.116917\pi$
$937$	17.5765	+	17.5765i	0.574198	+	0.574198i	−0.359101	+	0.933299i	$0.616917\pi$
$938$	−2.08965	−	15.1023i	−0.0682296	−	0.493109i
$939$		−	10.6359i		−	0.347090i
$940$	0.0248753	−	0.188947i	0.000811343	−	0.00616276i
$941$	34.8078	−	4.58253i	1.13470	−	0.149386i	0.460308	−	0.887759i	$-0.347739\pi$
$941$	34.8078	−	4.58253i	1.13470	−	0.149386i	0.674393	+	0.738373i	$0.264406\pi$
$942$	0.226092	+	1.71734i	0.00736647	+	0.0559539i
$943$	−3.60720	−	13.4623i	−0.117467	−	0.438391i
$944$	−5.51780	+	5.51780i	−0.179589	+	0.179589i
$945$	0.654356	−	0.276112i	0.0212862	−	0.00898191i
$946$	3.93038	−	9.48879i	0.127788	−	0.308507i
$947$	4.93456	−	37.4817i	0.160352	−	1.21799i	−0.702184	−	0.711996i	$-0.747792\pi$
$947$	4.93456	−	37.4817i	0.160352	−	1.21799i	0.862536	−	0.505996i	$-0.168875\pi$
$948$	3.84777	−	2.22151i	0.124970	−	0.0721513i
$949$	6.91472	−	9.01144i	0.224461	−	0.292524i
$950$	9.52086	−	2.55111i	0.308898	−	0.0827689i
$951$	30.5332			0.990108
$952$	−9.38766	+	5.55624i	−0.304256	+	0.180079i
$953$	31.6029			1.02372			0.511859	−	0.859069i	$-0.328957\pi$
$953$	31.6029			1.02372			0.511859	+	0.859069i	$0.328957\pi$
$954$	−10.0743	+	2.69941i	−0.326169	+	0.0873967i
$955$	−0.172668	+	0.225025i	−0.00558741	+	0.00728165i
$956$	19.2806	−	11.1316i	0.623578	−	0.360023i
$957$	−1.57409	+	11.9564i	−0.0508832	+	0.386496i
$958$	14.7331	−	35.5689i	0.476005	−	1.14918i
$959$	−1.01742	+	8.14262i	−0.0328544	+	0.262939i
$960$	−0.189816	+	0.189816i	−0.00612627	+	0.00612627i
$961$	2.14945	+	8.02187i	0.0693372	+	0.258770i
$962$	−0.478280	−	3.63289i	−0.0154204	−	0.117129i
$963$	6.75723	−	0.889606i	0.217749	−	0.0286672i
$964$	−0.736963	+	5.59779i	−0.0237360	+	0.180293i
$965$			6.37657i			0.205269i
$966$	3.99107	+	1.62241i	0.128410	+	0.0522001i
$967$	−41.8177	−	41.8177i	−1.34477	−	1.34477i	−0.891245	−	0.453522i	$-0.850168\pi$
$967$	−41.8177	−	41.8177i	−1.34477	−	1.34477i	−0.453522	−	0.891245i	$-0.649832\pi$
$968$	2.18588	−	3.78606i	0.0702568	−	0.121688i
$969$	0.0348473	+	8.24684i	0.00111946	+	0.264927i
$970$	1.37901	+	2.38851i	0.0442773	+	0.0766905i
$971$	24.0611	−	6.44716i	0.772159	−	0.206899i	0.148834	−	0.988862i	$-0.452448\pi$
$971$	24.0611	−	6.44716i	0.772159	−	0.206899i	0.623325	+	0.781963i	$0.285781\pi$
$972$	−0.382683	−	0.923880i	−0.0122746	−	0.0296334i
$973$	11.5486	−	44.2652i	0.370230	−	1.41908i
$974$	−38.7741	+	16.0608i	−1.24240	+	0.514620i
$975$	12.4803	+	16.2647i	0.399691	+	0.520887i
$976$	1.44055	+	10.9421i	0.0461110	+	0.350248i
$977$	−49.6958	−	13.3160i	−1.58991	−	0.426015i	−0.647935	−	0.761696i	$-0.724367\pi$
$977$	−49.6958	−	13.3160i	−1.58991	−	0.426015i	−0.941976	+	0.335680i	$0.891034\pi$
$978$	−5.96600	−	22.2654i	−0.190772	−	0.711969i
$979$	−2.96859	−	1.22963i	−0.0948766	−	0.0392992i
$980$	−1.47556	+	1.16347i	−0.0471350	+	0.0371656i
$981$	1.58468	−	0.656397i	0.0505950	−	0.0209571i
$982$	17.9987	+	10.3916i	0.574362	+	0.331608i
$983$	8.55102	−	11.1439i	0.272735	−	0.355435i	−0.636824	−	0.771009i	$-0.719752\pi$
$983$	8.55102	−	11.1439i	0.272735	−	0.355435i	0.909560	+	0.415573i	$0.136419\pi$
$984$	2.21524	−	8.26738i	0.0706192	−	0.263555i
$985$	−1.41859	+	2.45707i	−0.0452001	+	0.0782888i
$986$	6.29464	−	11.0098i	0.200462	−	0.350624i
$987$	−1.81750	−	0.474176i	−0.0578516	−	0.0150932i
$988$	−5.88391	−	5.88391i	−0.187192	−	0.187192i
$989$	4.22914	+	0.556776i	0.134479	+	0.0177045i
$990$	0.911463	−	0.526233i	0.0289682	−	0.0167248i
$991$	1.70040	+	1.30476i	0.0540149	+	0.0414471i	0.635416	−	0.772170i	$-0.280829\pi$
$991$	1.70040	+	1.30476i	0.0540149	+	0.0414471i	−0.581401	+	0.813617i	$0.697495\pi$
$992$	2.90010	+	3.77949i	0.0920784	+	0.119999i
$993$	30.8885	+	12.7945i	0.980218	+	0.406020i
$994$	−0.00666311	−	1.01055i	−0.000211341	−	0.0320526i
$995$	2.82714	−	2.82714i	0.0896265	−	0.0896265i
$996$	−4.57765	+	3.51256i	−0.145049	+	0.111300i
$997$	29.7422	−	3.91563i	0.941945	−	0.124009i	0.356114	−	0.934443i	$-0.384102\pi$
$997$	29.7422	−	3.91563i	0.941945	−	0.124009i	0.585831	+	0.810433i	$0.300768\pi$
$998$	8.42218	+	6.46257i	0.266600	+	0.204569i
$999$	0.762783	+	0.440393i	0.0241334	+	0.0139334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bh.a.457.3	yes	96
7.4	even	3	inner	714.2.bh.a.151.9	yes	96
17.8	even	8	inner	714.2.bh.a.331.9	yes	96
119.25	even	24	inner	714.2.bh.a.25.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.a.25.3	✓	96	119.25	even	24	inner
714.2.bh.a.151.9	yes	96	7.4	even	3	inner
714.2.bh.a.331.9	yes	96	17.8	even	8	inner
714.2.bh.a.457.3	yes	96	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.0350384 + 0.266143i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(-2.10959 - 1.59676i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.0350384 + 0.266143i) q^{10} +(3.88714 - 0.511752i) q^{11} +(-0.130526 + 0.991445i) q^{12} -4.16020i q^{13} +(-2.45098 - 0.996347i) q^{14} +(-0.189816 - 0.189816i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.80255 - 1.59393i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.93202 - 0.517682i) q^{19} +(0.102727 + 0.248006i) q^{20} +(2.55103 - 0.701606i) q^{21} +(3.62224 - 1.50038i) q^{22} +(0.991281 + 1.29186i) q^{23} +(0.130526 + 0.991445i) q^{24} +(4.76002 + 1.27544i) q^{25} +(-1.07674 - 4.01844i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-2.62534 - 0.328037i) q^{28} +(2.84175 - 1.17709i) q^{29} +(-0.232476 - 0.134220i) q^{30} +(-2.90010 + 3.77949i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.96034 + 3.39541i) q^{33} +(3.26044 - 2.52379i) q^{34} +(0.498882 - 0.505505i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.873250 + 0.114966i) q^{37} +(1.73220 - 1.00009i) q^{38} +(3.30051 + 2.53257i) q^{39} +(0.163416 + 0.212967i) q^{40} +(-7.90751 - 3.27540i) q^{41} +(2.28252 - 1.33795i) q^{42} +(1.85233 - 1.85233i) q^{43} +(3.11049 - 2.38676i) q^{44} +(0.266143 - 0.0350384i) q^{45} +(1.29186 + 0.991281i) q^{46} +(-0.614829 - 0.354972i) q^{47} +(0.382683 + 0.923880i) q^{48} +(1.90074 + 6.73700i) q^{49} +4.92794 q^{50} +(-1.05030 + 3.98709i) q^{51} +(-2.08010 - 3.60284i) q^{52} +(2.69941 - 10.0743i) q^{53} +(0.991445 + 0.130526i) q^{54} +1.05247i q^{55} +(-2.62078 + 0.362628i) q^{56} +(-0.765432 + 1.84792i) q^{57} +(2.44027 - 1.87248i) q^{58} +(-7.53745 - 2.01965i) q^{59} +(-0.259293 - 0.0694773i) q^{60} +(-8.75586 + 6.71861i) q^{61} +(-1.82308 + 4.40131i) q^{62} +(-0.996347 + 2.45098i) q^{63} -1.00000i q^{64} +(1.10721 + 0.145767i) q^{65} +(-1.01475 + 3.78709i) q^{66} +(2.88126 + 4.99050i) q^{67} +(2.49614 - 3.28166i) q^{68} -1.62836 q^{69} +(0.351049 - 0.617401i) q^{70} +(0.146170 + 0.352885i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(2.16611 + 1.66211i) q^{73} +(0.873250 - 0.114966i) q^{74} +(-3.90960 + 2.99994i) q^{75} +(1.41433 - 1.41433i) q^{76} +(-9.01742 - 5.12723i) q^{77} +(3.84352 + 1.59204i) q^{78} +(-2.70474 - 3.52489i) q^{79} +(0.212967 + 0.163416i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-8.48580 - 1.11718i) q^{82} +(4.08001 + 4.08001i) q^{83} +(1.85845 - 1.88312i) q^{84} +(0.290977 + 1.06787i) q^{85} +(1.30980 - 2.26863i) q^{86} +(-0.796099 + 2.97108i) q^{87} +(2.38676 - 3.11049i) q^{88} +(-0.709748 - 0.409773i) q^{89} +(0.248006 - 0.102727i) q^{90} +(-6.64282 + 8.77631i) q^{91} +(1.50441 + 0.623145i) q^{92} +(-1.23300 - 4.60161i) q^{93} +(-0.685753 - 0.183747i) q^{94} +(0.0700828 + 0.532332i) q^{95} +(0.608761 + 0.793353i) q^{96} +(9.49217 - 3.93179i) q^{97} +(3.57963 + 6.01550i) q^{98} +(-1.50038 - 3.62224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} - 8 q^{10} - 16 q^{11} - 16 q^{15} + 48 q^{16} + 8 q^{17} - 48 q^{18} + 8 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{29} + 48 q^{33} + 32 q^{35} + 16 q^{37} + 16 q^{39} + 16 q^{42} - 16 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) \) 96 * q + 8 * q^5 - 8 * q^10 - 16 * q^11 - 16 * q^15 + 48 * q^16 + 8 * q^17 - 48 * q^18 + 8 * q^19 + 16 * q^22 - 40 * q^25 + 32 * q^29 + 48 * q^33 + 32 * q^35 + 16 * q^37 + 16 * q^39 + 16 * q^42 - 16 * q^43 + 8 * q^44 + 8 * q^46 + 16 * q^49 - 128 * q^50 - 16 * q^52 - 24 * q^53 - 16 * q^57 + 16 * q^58 + 56 * q^59 - 8 * q^60 - 64 * q^65 + 32 * q^67 + 128 * q^69 + 24 * q^70 + 64 * q^71 - 40 * q^73 + 16 * q^74 + 16 * q^76 - 16 * q^77 + 32 * q^78 + 56 * q^79 - 8 * q^80 + 16 * q^83 - 48 * q^85 - 16 * q^86 - 24 * q^87 + 16 * q^88 - 16 * q^90 + 8 * q^91 + 16 * q^92 - 8 * q^93 - 24 * q^94 + 64 * q^95 + 32 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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