LMFDB - Embedded newform 572.2.bb.b.51.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(51,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("572.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.17
Character	$\chi$	$=$	572.51
Dual form			572.2.bb.b.415.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16754 + 0.798029i) q^{2} +(-2.45868 - 0.798874i) q^{3} +(0.726298 - 1.86346i) q^{4} +(-0.870035 - 1.19750i) q^{5} +(3.50813 - 1.02938i) q^{6} +(-3.66344 + 1.19032i) q^{7} +(0.639116 + 2.75527i) q^{8} +(2.97986 + 2.16500i) q^{9} +O(q^{10})$	\(q+(-1.16754 + 0.798029i) q^{2} +(-2.45868 - 0.798874i) q^{3} +(0.726298 - 1.86346i) q^{4} +(-0.870035 - 1.19750i) q^{5} +(3.50813 - 1.02938i) q^{6} +(-3.66344 + 1.19032i) q^{7} +(0.639116 + 2.75527i) q^{8} +(2.97986 + 2.16500i) q^{9} +(1.97144 + 0.703816i) q^{10} +(-3.06807 + 1.25974i) q^{11} +(-3.27441 + 4.00144i) q^{12} +(-3.30652 + 1.43767i) q^{13} +(3.32730 - 4.31328i) q^{14} +(1.18249 + 3.63932i) q^{15} +(-2.94498 - 2.70686i) q^{16} +(-0.395960 - 0.544992i) q^{17} +(-5.20684 - 0.149702i) q^{18} +(0.804357 + 0.261351i) q^{19} +(-2.86340 + 0.751535i) q^{20} +9.95814 q^{21} +(2.57678 - 3.91921i) q^{22} -5.85290i q^{23} +(0.629734 - 7.28491i) q^{24} +(0.868038 - 2.67155i) q^{25} +(2.71320 - 4.31724i) q^{26} +(-1.03832 - 1.42913i) q^{27} +(-0.442626 + 7.69121i) q^{28} +(0.920517 - 0.299094i) q^{29} +(-4.28488 - 3.30539i) q^{30} +(6.64648 + 4.82895i) q^{31} +(5.59854 + 0.810182i) q^{32} +(8.54978 - 0.646298i) q^{33} +(0.897219 + 0.320312i) q^{34} +(4.61273 + 3.35135i) q^{35} +(6.19865 - 3.98043i) q^{36} +(-4.09470 + 1.33045i) q^{37} +(-1.14768 + 0.336762i) q^{38} +(9.27821 - 0.893274i) q^{39} +(2.74339 - 3.16253i) q^{40} +(0.428667 - 1.31930i) q^{41} +(-11.6265 + 7.94689i) q^{42} -5.46982 q^{43} +(0.119145 + 6.63218i) q^{44} -5.45201i q^{45} +(4.67079 + 6.83350i) q^{46} +(1.64463 - 5.06164i) q^{47} +(5.07833 + 9.00797i) q^{48} +(6.34079 - 4.60686i) q^{49} +(1.11850 + 3.81186i) q^{50} +(0.538159 + 1.65628i) q^{51} +(0.277520 + 7.20576i) q^{52} +(6.86444 + 4.98731i) q^{53} +(2.35277 + 0.839952i) q^{54} +(4.17787 + 2.57800i) q^{55} +(-5.62103 - 9.33302i) q^{56} +(-1.76887 - 1.28516i) q^{57} +(-0.836054 + 1.08380i) q^{58} +(-2.07065 - 6.37280i) q^{59} +(7.64057 + 0.439712i) q^{60} +(4.10632 + 5.65186i) q^{61} +(-11.6137 - 0.333905i) q^{62} +(-13.4936 - 4.38433i) q^{63} +(-7.18306 + 3.52188i) q^{64} +(4.59840 + 2.70874i) q^{65} +(-9.46644 + 7.57755i) q^{66} -2.53992 q^{67} +(-1.30316 + 0.342030i) q^{68} +(-4.67573 + 14.3904i) q^{69} +(-8.06002 - 0.231734i) q^{70} +(10.3705 - 7.53463i) q^{71} +(-4.06068 + 9.59401i) q^{72} +(3.37053 + 10.3734i) q^{73} +(3.71899 - 4.82105i) q^{74} +(-4.26846 + 5.87503i) q^{75} +(1.07122 - 1.30907i) q^{76} +(9.74019 - 8.26698i) q^{77} +(-10.1198 + 8.44721i) q^{78} +(11.3490 + 8.24553i) q^{79} +(-0.679226 + 5.88168i) q^{80} +(-2.00341 - 6.16585i) q^{81} +(0.552355 + 1.88242i) q^{82} +(-1.36133 - 1.87371i) q^{83} +(7.23258 - 18.5566i) q^{84} +(-0.308129 + 0.948325i) q^{85} +(6.38623 - 4.36508i) q^{86} -2.50220 q^{87} +(-5.43178 - 7.64825i) q^{88} -1.90925i q^{89} +(4.35086 + 6.36543i) q^{90} +(10.4020 - 9.20265i) q^{91} +(-10.9067 - 4.25095i) q^{92} +(-12.4838 - 17.1825i) q^{93} +(2.11917 + 7.22212i) q^{94} +(-0.386850 - 1.19060i) q^{95} +(-13.1178 - 6.46450i) q^{96} +(-3.47624 + 4.78464i) q^{97} +(-3.72672 + 10.4388i) q^{98} +(-11.8698 - 2.88851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) $ 304 * q - 14 * q^4 + 72 * q^9	$ 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) $ 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−1.16754	+	0.798029i	−0.825575	+	0.564292i
$2$	−1.16754	+	0.798029i	−0.825575	+	0.564292i
$3$	−2.45868	−	0.798874i	−1.41952	−	0.461230i	−0.504070	−	0.863663i	$-0.668165\pi$
$3$	−2.45868	−	0.798874i	−1.41952	−	0.461230i	−0.915450	+	0.402433i	$0.868165\pi$
$4$	0.726298	−	1.86346i	0.363149	−	0.931731i
$5$	−0.870035	−	1.19750i	−0.389092	−	0.535539i	0.568873	−	0.822425i	$-0.307380\pi$
$5$	−0.870035	−	1.19750i	−0.389092	−	0.535539i	−0.957964	+	0.286887i	$0.907380\pi$
$6$	3.50813	−	1.02938i	1.43219	−	0.420244i
$7$	−3.66344	+	1.19032i	−1.38465	+	0.449900i	−0.904195	−	0.427120i	$-0.859528\pi$
$7$	−3.66344	+	1.19032i	−1.38465	+	0.449900i	−0.480455	+	0.877020i	$0.659528\pi$
$8$	0.639116	+	2.75527i	0.225962	+	0.974136i
$9$	2.97986	+	2.16500i	0.993287	+	0.721665i
$10$	1.97144	+	0.703816i	0.623424	+	0.222566i
$11$	−3.06807	+	1.25974i	−0.925058	+	0.379826i
$11$	−3.06807	+	1.25974i	−0.925058	+	0.379826i
$12$	−3.27441	+	4.00144i	−0.945240	+	1.15512i
$13$	−3.30652	+	1.43767i	−0.917065	+	0.398738i
$13$	−3.30652	+	1.43767i	−0.917065	+	0.398738i
$14$	3.32730	−	4.31328i	0.889258	−	1.15277i
$15$	1.18249	+	3.63932i	0.305317	+	0.939668i
$16$	−2.94498	−	2.70686i	−0.736246	−	0.676714i
$17$	−0.395960	−	0.544992i	−0.0960344	−	0.132180i	0.758296	−	0.651911i	$-0.226032\pi$
$17$	−0.395960	−	0.544992i	−0.0960344	−	0.132180i	−0.854330	+	0.519731i	$0.826032\pi$
$18$	−5.20684	−	0.149702i	−1.22726	−	0.0352850i
$19$	0.804357	+	0.261351i	0.184532	+	0.0599581i	0.399825	−	0.916591i	$-0.369071\pi$
$19$	0.804357	+	0.261351i	0.184532	+	0.0599581i	−0.215293	+	0.976549i	$0.569071\pi$
$20$	−2.86340	+	0.751535i	−0.640276	+	0.168048i
$21$	9.95814			2.17305
$22$	2.57678	−	3.91921i	0.549372	−	0.835578i
$23$		−	5.85290i		−	1.22041i	−0.792242	−	0.610207i	$-0.791086\pi$
$23$		−	5.85290i		−	1.22041i	0.792242	−	0.610207i	$-0.208914\pi$
$24$	0.629734	−	7.28491i	0.128544	−	1.48703i
$25$	0.868038	−	2.67155i	0.173608	−	0.534310i
$26$	2.71320	−	4.31724i	0.532102	−	0.846680i
$27$	−1.03832	−	1.42913i	−0.199825	−	0.275036i
$28$	−0.442626	+	7.69121i	−0.0836484	+	1.45350i
$29$	0.920517	−	0.299094i	0.170936	−	0.0555404i	−0.222299	−	0.974979i	$-0.571356\pi$
$29$	0.920517	−	0.299094i	0.170936	−	0.0555404i	0.393235	+	0.919438i	$0.371356\pi$
$30$	−4.28488	−	3.30539i	−0.782309	−	0.603479i
$31$	6.64648	+	4.82895i	1.19374	+	0.867305i	0.993655	−	0.112473i	$-0.0358772\pi$
$31$	6.64648	+	4.82895i	1.19374	+	0.867305i	0.200088	+	0.979778i	$0.435877\pi$
$32$	5.59854	+	0.810182i	0.989691	+	0.143221i
$33$	8.54978	−	0.646298i	1.48833	−	0.112506i
$34$	0.897219	+	0.320312i	0.153872	+	0.0549331i
$35$	4.61273	+	3.35135i	0.779694	+	0.566481i
$36$	6.19865	−	3.98043i	1.03311	−	0.663404i
$37$	−4.09470	+	1.33045i	−0.673165	+	0.218725i	−0.625600	−	0.780144i	$-0.715146\pi$
$37$	−4.09470	+	1.33045i	−0.673165	+	0.218725i	−0.0475644	+	0.998868i	$0.515146\pi$
$38$	−1.14768	+	0.336762i	−0.186179	+	0.0546301i
$39$	9.27821	−	0.893274i	1.48570	−	0.143038i
$40$	2.74339	−	3.16253i	0.433768	−	0.500039i
$41$	0.428667	−	1.31930i	0.0669465	−	0.206040i	−0.911987	−	0.410219i	$-0.865452\pi$
$41$	0.428667	−	1.31930i	0.0669465	−	0.206040i	0.978934	+	0.204179i	$0.0654523\pi$
$42$	−11.6265	+	7.94689i	−1.79401	+	1.22623i
$43$	−5.46982			−0.834140			−0.417070	−	0.908874i	$-0.636943\pi$
$43$	−5.46982			−0.834140			−0.417070	+	0.908874i	$0.636943\pi$
$44$	0.119145	+	6.63218i	0.0179617	+	0.999839i
$45$		−	5.45201i		−	0.812737i
$46$	4.67079	+	6.83350i	0.688670	+	1.00754i
$47$	1.64463	−	5.06164i	0.239893	−	0.738315i	−0.756541	−	0.653946i	$-0.773112\pi$
$47$	1.64463	−	5.06164i	0.239893	−	0.738315i	0.996435	−	0.0843696i	$-0.0268876\pi$
$48$	5.07833	+	9.00797i	0.732994	+	1.30019i
$49$	6.34079	−	4.60686i	0.905828	−	0.658122i
$50$	1.11850	+	3.81186i	0.158180	+	0.539078i
$51$	0.538159	+	1.65628i	0.0753574	+	0.231926i
$52$	0.277520	+	7.20576i	0.0384851	+	0.999259i
$53$	6.86444	+	4.98731i	0.942904	+	0.685059i	0.949118	−	0.314921i	$-0.101978\pi$
$53$	6.86444	+	4.98731i	0.942904	+	0.685059i	−0.00621432	+	0.999981i	$0.501978\pi$
$54$	2.35277	+	0.839952i	0.320171	+	0.114303i
$55$	4.17787	+	2.57800i	0.563344	+	0.347617i
$56$	−5.62103	−	9.33302i	−0.751141	−	1.24718i
$57$	−1.76887	−	1.28516i	−0.234292	−	0.170223i
$58$	−0.836054	+	1.08380i	−0.109779	+	0.142310i
$59$	−2.07065	−	6.37280i	−0.269575	−	0.829668i	−0.990604	−	0.136762i	$-0.956330\pi$
$59$	−2.07065	−	6.37280i	−0.269575	−	0.829668i	0.721029	−	0.692905i	$-0.243670\pi$
$60$	7.64057	+	0.439712i	0.986394	+	0.0567666i
$61$	4.10632	+	5.65186i	0.525760	+	0.723647i	0.986477	−	0.163900i	$-0.0524076\pi$
$61$	4.10632	+	5.65186i	0.525760	+	0.723647i	−0.460717	+	0.887547i	$0.652408\pi$
$62$	−11.6137	−	0.333905i	−1.47494	−	0.0424059i
$63$	−13.4936	−	4.38433i	−1.70003	−	0.552374i
$64$	−7.18306	+	3.52188i	−0.897883	+	0.440235i
$65$	4.59840	+	2.70874i	0.570362	+	0.335978i
$66$	−9.46644	+	7.57755i	−1.16524	+	0.932732i
$67$	−2.53992			−0.310300			−0.155150	−	0.987891i	$-0.549586\pi$
$67$	−2.53992			−0.310300			−0.155150	+	0.987891i	$0.549586\pi$
$68$	−1.30316	+	0.342030i	−0.158031	+	0.0414772i
$69$	−4.67573	+	14.3904i	−0.562892	+	1.73240i
$70$	−8.06002	−	0.231734i	−0.963357	−	0.0276975i
$71$	10.3705	−	7.53463i	1.23076	−	0.894197i	0.233809	−	0.972282i	$-0.424881\pi$
$71$	10.3705	−	7.53463i	1.23076	−	0.894197i	0.996947	+	0.0780859i	$0.0248809\pi$
$72$	−4.06068	+	9.59401i	−0.478556	+	1.13067i
$73$	3.37053	+	10.3734i	0.394490	+	1.21412i	0.929358	+	0.369180i	$0.120361\pi$
$73$	3.37053	+	10.3734i	0.394490	+	1.21412i	−0.534868	+	0.844936i	$0.679639\pi$
$74$	3.71899	−	4.82105i	0.432324	−	0.560435i
$75$	−4.26846	+	5.87503i	−0.492879	+	0.678390i
$76$	1.07122	−	1.30907i	0.122877	−	0.150161i
$77$	9.74019	−	8.26698i	1.11000	−	0.942109i
$78$	−10.1198	+	8.44721i	−1.14584	+	0.956459i
$79$	11.3490	+	8.24553i	1.27686	+	0.927695i	0.999453	−	0.0330574i	$-0.0105244\pi$
$79$	11.3490	+	8.24553i	1.27686	+	0.927695i	0.277409	+	0.960752i	$0.410524\pi$
$80$	−0.679226	+	5.88168i	−0.0759398	+	0.657592i
$81$	−2.00341	−	6.16585i	−0.222601	−	0.685094i
$82$	0.552355	+	1.88242i	0.0609974	+	0.207879i
$83$	−1.36133	−	1.87371i	−0.149425	−	0.205666i	0.727742	−	0.685851i	$-0.240570\pi$
$83$	−1.36133	−	1.87371i	−0.149425	−	0.205666i	−0.877167	+	0.480185i	$0.840570\pi$
$84$	7.23258	−	18.5566i	0.789139	−	2.02469i
$85$	−0.308129	+	0.948325i	−0.0334213	+	0.102860i
$86$	6.38623	−	4.36508i	0.688645	−	0.470698i
$87$	−2.50220			−0.268264
$88$	−5.43178	−	7.64825i	−0.579030	−	0.815306i
$89$		−	1.90925i		−	0.202380i	−0.994867	−	0.101190i	$-0.967735\pi$
$89$		−	1.90925i		−	0.202380i	0.994867	−	0.101190i	$-0.0322650\pi$
$90$	4.35086	+	6.36543i	0.458621	+	0.670976i
$91$	10.4020	−	9.20265i	1.09042	−	0.964700i
$92$	−10.9067	−	4.25095i	−1.13710	−	0.443192i
$93$	−12.4838	−	17.1825i	−1.29451	−	1.78175i
$94$	2.11917	+	7.22212i	0.218576	+	0.744905i
$95$	−0.386850	−	1.19060i	−0.0396900	−	0.122153i
$96$	−13.1178	−	6.46450i	−1.33883	−	0.659780i
$97$	−3.47624	+	4.78464i	−0.352959	+	0.485806i	−0.948170	−	0.317763i	$-0.897068\pi$
$97$	−3.47624	+	4.78464i	−0.352959	+	0.485806i	0.595211	+	0.803569i	$0.297068\pi$
$98$	−3.72672	+	10.4388i	−0.376456	+	1.05448i
$99$	−11.8698	−	2.88851i	−1.19296	−	0.290306i
$100$	−4.34787	−	3.55790i	−0.434787	−	0.355790i
$101$	−4.27202	+	5.87993i	−0.425082	+	0.585075i	−0.966816	−	0.255475i	$-0.917768\pi$
$101$	−4.27202	+	5.87993i	−0.425082	+	0.585075i	0.541734	+	0.840550i	$0.317768\pi$
$102$	−1.95009	−	1.50431i	−0.193087	−	0.148949i
$103$	16.1843	−	5.25860i	1.59469	−	0.518145i	0.628902	−	0.777485i	$-0.283505\pi$
$103$	16.1843	−	5.25860i	1.59469	−	0.518145i	0.965786	+	0.259339i	$0.0835048\pi$
$104$	−6.07442	−	8.19154i	−0.595646	−	0.803247i
$105$	−8.66393	−	11.9249i	−0.845513	−	1.16375i
$106$	−11.9945	−	0.344855i	−1.16501	−	0.0334953i
$107$	3.61403	−	11.1228i	0.349381	−	1.07529i	−0.609815	−	0.792544i	$-0.708756\pi$
$107$	3.61403	−	11.1228i	0.349381	−	1.07529i	0.959196	−	0.282741i	$-0.0912438\pi$
$108$	−3.41726	+	0.896902i	−0.328826	+	0.0863044i
$109$	−7.41547			−0.710274			−0.355137	−	0.934814i	$-0.615566\pi$
$109$	−7.41547			−0.710274			−0.355137	+	0.934814i	$0.615566\pi$
$110$	−6.93515	+	0.324147i	−0.661240	+	0.0309062i
$111$	11.1304			1.05645
$112$	14.0108	+	6.41093i	1.32390	+	0.605776i
$113$	−4.30080	+	13.2365i	−0.404585	+	1.24518i	0.516657	+	0.856193i	$0.327176\pi$
$113$	−4.30080	+	13.2365i	−0.404585	+	1.24518i	−0.921241	+	0.388991i	$0.872824\pi$
$114$	3.09082	+	0.0888642i	0.289482	+	0.00832290i
$115$	−7.00885	+	5.09223i	−0.653579	+	0.474853i
$116$	0.111219	−	1.93258i	0.0103264	−	0.179436i
$117$	−12.9655	−	2.87456i	−1.19866	−	0.265753i
$118$	7.50324	+	5.78806i	0.690729	+	0.532834i
$119$	2.09929	+	1.52523i	0.192442	+	0.139817i
$120$	−9.27157	+	5.58402i	−0.846375	+	0.509749i
$121$	7.82611	−	7.72994i	0.711465	−	0.702722i
$122$	−9.30464	−	3.32181i	−0.842403	−	0.300743i
$123$	−2.10791	+	2.90129i	−0.190064	+	0.261600i
$124$	13.8259	−	8.87820i	1.24160	−	0.797286i
$125$	−10.9931	+	3.57189i	−0.983256	+	0.319479i
$126$	19.2531	−	5.64939i	1.71520	−	0.503288i
$127$	−17.2174	+	12.5092i	−1.52779	+	1.11001i	−0.570346	+	0.821405i	$0.693191\pi$
$127$	−17.2174	+	12.5092i	−1.52779	+	1.11001i	−0.957449	+	0.288603i	$0.906809\pi$
$128$	5.57595	−	9.84423i	0.492849	−	0.870115i
$129$	13.4485	+	4.36970i	1.18408	+	0.384730i
$130$	−7.53047	+	0.507096i	−0.660466	+	0.0444753i
$131$	−19.0907			−1.66797			−0.833983	−	0.551790i	$-0.813945\pi$
$131$	−19.0907			−1.66797			−0.833983	+	0.551790i	$0.813945\pi$
$132$	5.00534	−	16.4016i	0.435659	−	1.42758i
$133$	−3.25780			−0.282487
$134$	2.96545	−	2.02693i	0.256176	−	0.175100i
$135$	−0.808005	+	2.48678i	−0.0695420	+	0.214028i
$136$	1.24854	−	1.43929i	0.107061	−	0.123418i
$137$	−9.00896	−	12.3998i	−0.769688	−	1.05938i	−0.996346	−	0.0854098i	$-0.972780\pi$
$137$	−9.00896	−	12.3998i	−0.769688	−	1.05938i	0.226658	−	0.973974i	$-0.427220\pi$
$138$	−6.02488	−	20.5328i	−0.512872	−	1.74786i
$139$	0.340157	+	1.04689i	0.0288517	+	0.0887965i	0.964445	−	0.264282i	$-0.0851349\pi$
$139$	0.340157	+	1.04689i	0.0288517	+	0.0887965i	−0.935594	+	0.353078i	$0.885135\pi$
$140$	9.59533	−	6.16158i	0.810953	−	0.520748i
$141$	−8.08722	+	11.1311i	−0.681066	+	0.937408i
$142$	−6.09515	+	17.0730i	−0.511494	+	1.43273i
$143$	8.33356	−	8.57623i	0.696887	−	0.717181i
$144$	−2.91530	−	14.4419i	−0.242942	−	1.20349i
$145$	−1.15905	−	0.842097i	−0.0962536	−	0.0699324i
$146$	−12.2135	−	9.42159i	−1.01080	−	0.779736i
$147$	−19.2703	+	6.26129i	−1.58939	+	0.516423i
$148$	−0.494732	+	8.59663i	−0.0406667	+	0.706638i
$149$	16.3802	−	11.9009i	1.34192	−	0.974959i	0.342544	−	0.939502i	$-0.388711\pi$
$149$	16.3802	−	11.9009i	1.34192	−	0.974959i	0.999371	−	0.0354572i	$-0.0112887\pi$
$150$	0.295149	−	10.2657i	0.0240988	−	0.838190i
$151$	1.50926	+	0.490389i	0.122822	+	0.0399073i	0.369783	−	0.929118i	$-0.379432\pi$
$151$	1.50926	+	0.490389i	0.122822	+	0.0399073i	−0.246961	+	0.969025i	$0.579432\pi$
$152$	−0.206017	+	2.38326i	−0.0167102	+	0.193308i
$153$		−	2.48125i		−	0.200597i
$154$	−4.77477	+	17.4250i	−0.384762	+	1.40414i
$155$		−	12.1605i		−	0.976756i
$156$	5.07416	−	17.9384i	0.406258	−	1.43622i
$157$	1.09616	−	3.37362i	0.0874829	−	0.269245i	−0.897739	−	0.440528i	$-0.854791\pi$
$157$	1.09616	−	3.37362i	0.0874829	−	0.269245i	0.985222	+	0.171283i	$0.0547913\pi$
$158$	−19.8306	−	0.570149i	−1.57764	−	0.0453586i
$159$	−12.8932	−	17.7460i	−1.02250	−	1.40735i
$160$	−3.90073	−	7.40914i	−0.308380	−	0.585744i
$161$	6.96685	+	21.4418i	0.549064	+	1.68985i
$162$	7.25958	+	5.60010i	0.570367	+	0.439985i
$163$	13.1364	+	9.54418i	1.02892	+	0.747558i	0.968093	−	0.250590i	$-0.0806247\pi$
$163$	13.1364	+	9.54418i	1.02892	+	0.747558i	0.0608318	+	0.998148i	$0.480625\pi$
$164$	−2.14713	−	1.75701i	−0.167662	−	0.137199i
$165$	−8.21255	−	9.67606i	−0.639346	−	0.753280i
$166$	3.08467	+	1.10125i	0.239417	+	0.0854733i
$167$	−3.74781	+	5.15841i	−0.290014	+	0.399170i	−0.929019	−	0.370033i	$-0.879346\pi$
$167$	−3.74781	+	5.15841i	−0.290014	+	0.399170i	0.639005	+	0.769203i	$0.279346\pi$
$168$	6.36441	+	27.4374i	0.491025	+	2.11684i
$169$	8.86621	−	9.50738i	0.682016	−	0.731337i
$170$	−0.397038	−	1.35310i	−0.0304514	−	0.103778i
$171$	1.83105	+	2.52022i	0.140024	+	0.192726i
$172$	−3.97272	+	10.1928i	−0.302917	+	0.777194i
$173$	18.0085	+	5.85132i	1.36916	+	0.444868i	0.899091	−	0.437761i	$-0.144229\pi$
$173$	18.0085	+	5.85132i	1.36916	+	0.444868i	0.470070	+	0.882629i	$0.344229\pi$
$174$	2.92141	−	1.99683i	0.221472	−	0.151379i
$175$			10.8203i			0.817938i
$176$	12.4453	+	4.59492i	0.938104	+	0.346355i
$177$			17.3229i			1.30207i
$178$	1.52364	+	2.22913i	0.114201	+	0.167080i
$179$	12.4748	+	4.05330i	0.932408	+	0.302958i	0.735547	−	0.677474i	$-0.236925\pi$
$179$	12.4748	+	4.05330i	0.932408	+	0.302958i	0.196861	+	0.980431i	$0.436925\pi$
$180$	−10.1596	−	3.95978i	−0.757252	−	0.295145i
$181$	−12.8634	+	9.34581i	−0.956129	+	0.694669i	−0.952249	−	0.305324i	$-0.901235\pi$
$181$	−12.8634	+	9.34581i	−0.956129	+	0.694669i	−0.00388078	+	0.999992i	$0.501235\pi$
$182$	−4.80072	+	19.0455i	−0.355853	+	1.41175i
$183$	−5.58100	−	17.1766i	−0.412560	−	1.26973i
$184$	16.1263	−	3.74068i	1.18885	−	0.275767i
$185$	5.15575	+	3.74587i	0.379058	+	0.275402i
$186$	28.2876	+	10.0988i	2.07414	+	0.740482i
$187$	1.90138	+	1.17327i	0.139043	+	0.0857978i
$188$	−8.23768	−	6.74095i	−0.600794	−	0.491635i
$189$	5.50496	+	3.99959i	0.400427	+	0.290927i
$190$	1.40180	+	1.08136i	0.101697	+	0.0784499i
$191$	−11.3117	+	3.67541i	−0.818489	+	0.265943i	−0.688189	−	0.725532i	$-0.741594\pi$
$191$	−11.3117	+	3.67541i	−0.818489	+	0.265943i	−0.130300	+	0.991475i	$0.541594\pi$
$192$	20.4744	−	2.92081i	1.47761	−	0.210791i
$193$	0.0643693	−	0.0467670i	0.00463340	−	0.00336636i	−0.585466	−	0.810697i	$-0.699088\pi$
$193$	0.0643693	−	0.0467670i	0.00463340	−	0.00336636i	0.590100	+	0.807330i	$0.299088\pi$
$194$	0.240370	−	8.36039i	0.0172575	−	0.600241i
$195$	−9.14206	−	10.3335i	−0.654677	−	0.739996i
$196$	−3.97940	−	15.1618i	−0.284243	−	1.08298i
$197$	9.01750			0.642470			0.321235	−	0.946999i	$-0.395902\pi$
$197$	9.01750			0.642470			0.321235	+	0.946999i	$0.395902\pi$
$198$	16.1635	−	6.09996i	1.14869	−	0.433506i
$199$			14.9291i			1.05830i	0.848528	+	0.529150i	$0.177489\pi$
$199$			14.9291i			1.05830i	−0.848528	+	0.529150i	$0.822511\pi$
$200$	7.91562	+	0.684255i	0.559719	+	0.0483841i
$201$	6.24484	+	2.02907i	0.440477	+	0.143120i
$202$	0.295395	−	10.2742i	0.0207839	−	0.722894i
$203$	−3.01624	+	2.19143i	−0.211698	+	0.153808i
$204$	3.47729	+	0.200116i	0.243459	+	0.0140110i
$205$	−1.95282	+	0.634509i	−0.136391	+	0.0443160i
$206$	−14.6993	+	19.0552i	−1.02415	+	1.32764i
$207$	12.6715	−	17.4408i	0.880731	−	1.21222i
$208$	13.6292	+	4.71638i	0.945017	+	0.327022i
$209$	−2.79706	+	0.211436i	−0.193477	+	0.0146253i
$210$	19.6319	+	7.00870i	1.35473	+	0.483646i
$211$	2.04073	+	1.48268i	0.140490	+	0.102072i	0.655810	−	0.754926i	$-0.272327\pi$
$211$	2.04073	+	1.48268i	0.140490	+	0.102072i	−0.515320	+	0.856998i	$0.672327\pi$
$212$	14.2793	−	9.16935i	0.980706	−	0.629754i
$213$	−31.5171	+	10.2405i	−2.15951	+	0.701668i
$214$	4.65683	+	15.8705i	0.318334	+	1.08488i
$215$	4.75894	+	6.55011i	0.324557	+	0.446714i
$216$	3.27403	−	3.77424i	0.222770	−	0.256805i
$217$	−30.0970	−	9.77910i	−2.04312	−	0.663849i
$218$	8.65786	−	5.91777i	0.586384	−	0.400802i
$219$		−	28.1975i		−	1.90541i
$220$	7.83838	−	5.91290i	0.528463	−	0.398648i
$221$	2.09277	+	1.23277i	0.140775	+	0.0829251i
$222$	−12.9952	+	8.88241i	−0.872182	+	0.596148i
$223$	−8.22198	+	25.3047i	−0.550585	+	1.69452i	0.156743	+	0.987639i	$0.449900\pi$
$223$	−8.22198	+	25.3047i	−0.550585	+	1.69452i	−0.707328	+	0.706886i	$0.750100\pi$
$224$	−21.4743	+	3.69602i	−1.43481	+	0.246951i
$225$	8.37052	−	6.08154i	0.558035	−	0.405436i
$226$	−5.54176	−	18.8863i	−0.368632	−	1.25630i
$227$	23.4170	−	7.60863i	1.55424	−	0.505003i	0.598978	−	0.800766i	$-0.295574\pi$
$227$	23.4170	−	7.60863i	1.55424	−	0.505003i	0.955261	+	0.295763i	$0.0955739\pi$
$228$	−3.67957	+	2.36281i	−0.243686	+	0.156481i
$229$	6.13912	−	8.44978i	0.405685	−	0.558377i	−0.556475	−	0.830865i	$-0.687846\pi$
$229$	6.13912	−	8.44978i	0.405685	−	0.558377i	0.962159	+	0.272487i	$0.0878463\pi$
$230$	4.11937	−	11.5387i	0.271623	−	0.760836i
$231$	−30.5523	+	12.5447i	−2.01019	+	0.825379i
$232$	1.41240	+	2.34512i	0.0927288	+	0.153965i
$233$	−1.53093	+	2.10715i	−0.100295	+	0.138044i	−0.856215	−	0.516620i	$-0.827190\pi$
$233$	−1.53093	+	2.10715i	−0.100295	+	0.138044i	0.755920	+	0.654664i	$0.227190\pi$
$234$	17.4318	−	6.99072i	1.13955	−	0.456997i
$235$	−7.49219	+	2.43436i	−0.488737	+	0.158800i
$236$	−13.3794	−	0.769977i	−0.870923	−	0.0501213i
$237$	−21.3164	−	29.3395i	−1.38465	−	1.90581i
$238$	−3.66818	−	0.105464i	−0.237773	−	0.00683621i
$239$	−21.4218	−	6.96036i	−1.38566	−	0.450229i	−0.481135	−	0.876647i	$-0.659775\pi$
$239$	−21.4218	−	6.96036i	−1.38566	−	0.450229i	−0.904526	+	0.426418i	$0.859775\pi$
$240$	6.36872	−	13.9186i	0.411099	−	0.898439i
$241$	1.72267			0.110967			0.0554835	−	0.998460i	$-0.482330\pi$
$241$	1.72267			0.110967			0.0554835	+	0.998460i	$0.482330\pi$
$242$	−2.96857	+	15.2705i	−0.190827	+	0.981624i
$243$			22.0598i			1.41514i
$244$	13.5144	−	3.54703i	0.865174	−	0.227075i
$245$	−11.0334	−	3.58498i	−0.704900	−	0.229036i
$246$	0.145755	−	5.06954i	0.00929297	−	0.323222i
$247$	−3.03536	+	0.292234i	−0.193135	+	0.0185944i
$248$	−9.05721	+	21.3991i	−0.575133	+	1.35885i
$249$	1.85021	+	5.69437i	0.117252	+	0.360866i
$250$	9.98445	−	12.9432i	0.631472	−	0.818598i
$251$	−15.7605	+	21.6925i	−0.994795	+	1.36922i	−0.0663307	+	0.997798i	$0.521129\pi$
$251$	−15.7605	+	21.6925i	−0.994795	+	1.36922i	−0.928465	+	0.371421i	$0.878871\pi$
$252$	−17.9704	+	21.9604i	−1.13203	+	1.38338i
$253$	7.37314	+	17.9571i	0.463545	+	1.12895i
$254$	10.1193	−	28.3449i	0.634941	−	1.77852i
$255$	1.51518	−	2.08547i	0.0948845	−	0.130597i
$256$	1.34584	+	15.9433i	0.0841150	+	0.996456i
$257$	3.50429	+	10.7851i	0.218591	+	0.672755i	0.998879	+	0.0473343i	$0.0150726\pi$
$257$	3.50429	+	10.7851i	0.218591	+	0.672755i	−0.780288	+	0.625421i	$0.784927\pi$
$258$	−19.1889	+	5.63054i	−1.19465	+	0.350542i
$259$	13.4170	−	9.74804i	0.833693	−	0.605714i
$260$	8.38745	−	6.60159i	0.520168	−	0.409414i
$261$	3.39055	+	1.10166i	0.209870	+	0.0681908i
$262$	22.2892	−	15.2350i	1.37703	−	0.941220i
$263$	19.8646			1.22491			0.612453	−	0.790507i	$-0.290183\pi$
$263$	19.8646			1.22491			0.612453	+	0.790507i	$0.290183\pi$
$264$	7.24503	+	23.1439i	0.445900	+	1.42441i
$265$		−	12.5593i		−	0.771512i
$266$	3.80362	−	2.59982i	0.233215	−	0.159405i
$267$	−1.52525	+	4.69424i	−0.0933438	+	0.287283i
$268$	−1.84474	+	4.73304i	−0.112685	+	0.289116i
$269$	−8.19165	+	5.95158i	−0.499453	+	0.362874i	−0.808808	−	0.588073i	$-0.799887\pi$
$269$	−8.19165	+	5.95158i	−0.499453	+	0.362874i	0.309355	+	0.950947i	$0.399887\pi$
$270$	−1.04115	−	3.54823i	−0.0633623	−	0.215938i
$271$	−0.694195	+	0.225558i	−0.0421694	+	0.0137017i	−0.330026	−	0.943972i	$-0.607057\pi$
$271$	−0.694195	+	0.225558i	−0.0421694	+	0.0137017i	0.287856	+	0.957674i	$0.407057\pi$
$272$	−0.309121	+	2.67680i	−0.0187432	+	0.162305i
$273$	−32.9269	+	14.3165i	−1.99282	+	0.866475i
$274$	20.4137	+	7.28781i	1.23324	+	0.440273i
$275$	0.702253	+	9.29000i	0.0423474	+	0.560208i
$276$	23.4200	+	19.1648i	1.40972	+	1.15358i
$277$	8.77085	−	12.0720i	0.526990	−	0.725339i	−0.459678	−	0.888085i	$-0.652035\pi$
$277$	8.77085	−	12.0720i	0.526990	−	0.725339i	0.986668	+	0.162747i	$0.0520353\pi$
$278$	−1.23260	−	0.950836i	−0.0739264	−	0.0570274i
$279$	9.35093	+	28.7792i	0.559825	+	1.72297i
$280$	−6.28581	+	14.8512i	−0.375649	+	0.887531i
$281$	15.7681	−	11.4562i	0.940646	−	0.683419i	−0.00793012	−	0.999969i	$-0.502524\pi$
$281$	15.7681	−	11.4562i	0.940646	−	0.683419i	0.948576	+	0.316549i	$0.102524\pi$
$282$	0.559202	−	19.4498i	0.0333000	−	1.15822i
$283$	−3.95268	+	12.1651i	−0.234963	+	0.723140i	0.762164	+	0.647384i	$0.224137\pi$
$283$	−3.95268	+	12.1651i	−0.234963	+	0.723140i	−0.997126	+	0.0757561i	$0.975863\pi$
$284$	−6.50841	−	24.7975i	−0.386203	−	1.47146i
$285$			3.23636i			0.191705i
$286$	−2.88568	+	16.6635i	−0.170634	+	0.985335i
$287$			5.34343i			0.315413i
$288$	14.9288	+	14.5350i	0.879689	+	0.856485i
$289$	5.11306	−	15.7364i	0.300768	−	0.925669i
$290$	2.02525	+	0.0582280i	0.118927	+	0.00341927i
$291$	12.3693	−	8.98681i	0.725100	−	0.526816i
$292$	21.7785	+	1.25334i	1.27449	+	0.0733463i
$293$	−5.02542	−	15.4667i	−0.293588	−	0.903572i	−0.983692	−	0.179861i	$-0.942435\pi$
$293$	−5.02542	−	15.4667i	−0.293588	−	0.903572i	0.690104	−	0.723711i	$-0.257565\pi$
$294$	17.5021	−	22.6886i	1.02074	−	1.32322i
$295$	−5.82989	+	8.02416i	−0.339429	+	0.467185i
$296$	−6.28274	−	10.4317i	−0.365177	−	0.606331i
$297$	4.98598	+	3.07665i	0.289316	+	0.178525i
$298$	−9.62724	+	26.9666i	−0.557691	+	1.56213i
$299$	8.41454	+	19.3528i	0.486625	+	1.11920i
$300$	7.84772	+	12.2211i	0.453088	+	0.705587i
$301$	20.0384	−	6.51086i	1.15499	−	0.375279i
$302$	−2.15347	+	0.631886i	−0.123918	+	0.0363610i
$303$	15.2009	−	11.0441i	0.873266	−	0.634465i
$304$	−1.66138	−	2.94695i	−0.0952864	−	0.169019i
$305$	3.19547	−	9.83464i	0.182972	−	0.563130i
$306$	1.98011	+	2.89696i	0.113195	+	0.165608i
$307$		−	13.7808i		−	0.786513i	−0.919429	−	0.393257i	$-0.871348\pi$
$307$		−	13.7808i		−	0.786513i	0.919429	−	0.393257i	$-0.128652\pi$
$308$	−8.33092	−	24.1548i	−0.474698	−	1.37635i
$309$	−43.9930			−2.50268
$310$	9.70445	+	14.1979i	0.551176	+	0.806386i
$311$	25.6395	+	8.33078i	1.45388	+	0.472395i	0.926195	−	0.377044i	$-0.123059\pi$
$311$	25.6395	+	8.33078i	1.45388	+	0.472395i	0.527687	+	0.849439i	$0.323059\pi$
$312$	8.39106	+	24.9931i	0.475050	+	1.41495i
$313$	3.25138	−	2.36226i	0.183779	−	0.133523i	−0.492092	−	0.870543i	$-0.663768\pi$
$313$	3.25138	−	2.36226i	0.183779	−	0.133523i	0.675871	+	0.737020i	$0.263768\pi$
$314$	1.41244	+	4.81361i	0.0797089	+	0.271648i
$315$	6.48965	+	19.9731i	0.365650	+	1.12536i
$316$	23.6080	−	15.1597i	1.32805	−	0.852801i
$317$	−2.99771	+	4.12600i	−0.168368	+	0.231739i	−0.884861	−	0.465856i	$-0.845747\pi$
$317$	−2.99771	+	4.12600i	−0.168368	+	0.231739i	0.716492	+	0.697595i	$0.245747\pi$
$318$	29.2152	+	10.4300i	1.63831	+	0.584885i
$319$	−2.44743	+	2.07725i	−0.137030	+	0.116304i
$320$	10.4670	+	5.53756i	0.585121	+	0.309559i
$321$	−17.7715	+	24.4604i	−0.991908	+	1.36524i
$322$	−25.2452	−	19.4743i	−1.40686	−	1.08526i
$323$	−0.176059	−	0.541853i	−0.00979617	−	0.0301495i
$324$	−12.9449	−	0.744973i	−0.719161	−	0.0413874i
$325$	0.970612	+	10.0815i	0.0538399	+	0.559220i
$326$	−22.9538	−	0.659946i	−1.27130	−	0.0365510i
$327$	18.2323	+	5.92403i	1.00825	+	0.327599i
$328$	3.90900	+	0.337908i	0.215839	+	0.0186579i
$329$			20.5006i			1.13024i
$330$	17.3103	+	4.74333i	0.952898	+	0.261112i
$331$	−23.6265			−1.29863			−0.649315	−	0.760520i	$-0.724944\pi$
$331$	−23.6265			−1.29863			−0.649315	+	0.760520i	$0.724944\pi$
$332$	−4.48031	+	1.17591i	−0.245889	+	0.0645365i
$333$	−15.0821	−	4.90046i	−0.826492	−	0.268543i
$334$	0.259148	−	9.01351i	0.0141799	−	0.493197i
$335$	2.20982	+	3.04155i	0.120735	+	0.166178i
$336$	−29.3266	−	26.9553i	−1.59989	−	1.47053i
$337$	24.9920	−	8.12040i	1.36140	−	0.442346i	0.464891	−	0.885368i	$-0.346093\pi$
$337$	24.9920	−	8.12040i	1.36140	−	0.442346i	0.896511	+	0.443022i	$0.146093\pi$
$338$	−2.76449	+	18.1757i	−0.150368	+	0.988630i
$339$	21.1486	−	29.1085i	1.14863	−	1.58096i
$340$	1.54337	+	1.26295i	0.0837012	+	0.0684933i
$341$	−26.4751	−	6.44272i	−1.43371	−	0.348893i
$342$	−4.14903	−	1.48123i	−0.224354	−	0.0800956i
$343$	−1.89655	+	2.61038i	−0.102404	+	0.140947i
$344$	−3.49585	−	15.0709i	−0.188484	−	0.812566i
$345$	21.3006	−	6.92098i	1.14678	−	0.372613i
$346$	−25.6952	+	7.53967i	−1.38138	+	0.405335i
$347$	26.4107	−	19.1885i	1.41780	−	1.03009i	0.425671	−	0.904878i	$-0.360038\pi$
$347$	26.4107	−	19.1885i	1.41780	−	1.03009i	0.992130	−	0.125214i	$-0.0399617\pi$
$348$	−1.81734	+	4.66275i	−0.0974196	+	0.249949i
$349$	−6.05593	+	18.6382i	−0.324166	+	0.997682i	0.647649	+	0.761939i	$0.275752\pi$
$349$	−6.05593	+	18.6382i	−0.324166	+	0.997682i	−0.971815	+	0.235743i	$0.924248\pi$
$350$	−8.63492	−	12.6331i	−0.461556	−	0.675269i
$351$	5.48785	+	3.23268i	0.292920	+	0.172548i
$352$	−18.1973	+	4.56701i	−0.969920	+	0.243422i
$353$		−	1.95937i		−	0.104287i	−0.998640	−	0.0521433i	$-0.983395\pi$
$353$		−	1.95937i		−	0.104287i	0.998640	−	0.0521433i	$-0.0166052\pi$
$354$	−13.8242	−	20.2251i	−0.734745	−	1.07495i
$355$	−18.0455	−	5.86332i	−0.957753	−	0.311193i
$356$	−3.55782	−	1.38668i	−0.188564	−	0.0734942i
$357$	−3.94303	−	5.42711i	−0.208687	−	0.287233i
$358$	−17.7994	+	5.22284i	−0.940729	+	0.276036i
$359$	11.2327	−	3.64971i	0.592837	−	0.192625i	0.00279395	−	0.999996i	$-0.499111\pi$
$359$	11.2327	−	3.64971i	0.592837	−	0.192625i	0.590043	+	0.807372i	$0.299111\pi$
$360$	15.0218	−	3.48446i	0.791717	−	0.183647i
$361$	−14.7926	−	10.7475i	−0.778560	−	0.565657i
$362$	7.56030	−	21.1770i	0.397361	−	1.11304i
$363$	−25.4172	+	12.7534i	−1.33405	+	0.669379i
$364$	−9.59386	−	26.0675i	−0.502855	−	1.36631i
$365$	9.48969	−	13.0614i	0.496713	−	0.683667i
$366$	20.2234	+	15.6005i	1.05710	+	0.815452i
$367$	26.0672	−	8.46975i	1.36070	−	0.442117i	0.464421	−	0.885614i	$-0.346262\pi$
$367$	26.0672	−	8.46975i	1.36070	−	0.442117i	0.896276	+	0.443497i	$0.146262\pi$
$368$	−15.8430	+	17.2367i	−0.825872	+	0.898525i
$369$	4.13365	−	3.00327i	0.215189	−	0.156344i
$370$	−9.00886	−	0.259014i	−0.468348	−	0.0134655i
$371$	−31.0840	−	10.0998i	−1.61380	−	0.524355i
$372$	−41.0860	+	10.7835i	−2.13021	+	0.559100i
$373$		−	26.4489i		−	1.36947i	−0.728790	−	0.684737i	$-0.759917\pi$
$373$		−	26.4489i		−	1.36947i	0.728790	−	0.684737i	$-0.240083\pi$
$374$	−3.15624	+	0.147522i	−0.163205	+	0.00762818i
$375$	29.8821			1.54310
$376$	14.9973	+	1.29642i	0.773427	+	0.0668578i
$377$	−2.61371	+	2.31236i	−0.134613	+	0.119093i
$378$	−9.61904	−	0.276557i	−0.494750	−	0.0142246i
$379$	24.4402	−	17.7568i	1.25541	−	0.912107i	0.256885	−	0.966442i	$-0.417304\pi$
$379$	24.4402	−	17.7568i	1.25541	−	0.912107i	0.998523	+	0.0543345i	$0.0173037\pi$
$380$	−2.49961	−	0.143852i	−0.128227	−	0.00737943i
$381$	52.3252	−	17.0015i	2.68070	−	0.871013i
$382$	10.2738	−	13.3183i	0.525654	−	0.681423i
$383$	22.7137	+	16.5025i	1.16062	+	0.843237i	0.989856	−	0.142075i	$-0.0453775\pi$
$383$	22.7137	+	16.5025i	1.16062	+	0.843237i	0.170761	+	0.985313i	$0.445377\pi$
$384$	−21.5738	+	19.7493i	−1.10093	+	1.00783i
$385$	−18.3740	−	4.47132i	−0.936426	−	0.227880i
$386$	−0.0378322	+	0.105971i	−0.00192561	+	0.00539378i
$387$	−16.2993	−	11.8421i	−0.828540	−	0.601970i
$388$	6.39120	+	9.95291i	0.324464	+	0.505283i
$389$	−6.07937	−	18.7104i	−0.308236	−	0.948654i	−0.978450	−	0.206486i	$-0.933797\pi$
$389$	−6.07937	−	18.7104i	−0.308236	−	0.948654i	0.670213	−	0.742169i	$-0.266203\pi$
$390$	18.9201	+	4.76911i	0.958058	+	0.241493i
$391$	−3.18979	+	2.31752i	−0.161314	+	0.117202i
$392$	16.7456	+	14.5263i	0.845783	+	0.733689i
$393$	46.9380	+	15.2511i	2.36771	+	0.769316i
$394$	−10.5283	+	7.19623i	−0.530408	+	0.362541i
$395$		−	20.7643i		−	1.04477i
$396$	−14.0036	+	20.0209i	−0.703708	+	1.00609i
$397$			11.2807i			0.566161i	0.959096	+	0.283081i	$0.0913564\pi$
$397$			11.2807i			0.566161i	−0.959096	+	0.283081i	$0.908644\pi$
$398$	−11.9139	−	17.4304i	−0.597190	−	0.873706i
$399$	8.00990	+	2.60257i	0.400997	+	0.130292i
$400$	−9.78786	+	5.51800i	−0.489393	+	0.275900i
$401$	4.39065	+	6.04322i	0.219259	+	0.301784i	0.904450	−	0.426579i	$-0.140281\pi$
$401$	4.39065	+	6.04322i	0.219259	+	0.301784i	−0.685191	+	0.728363i	$0.740281\pi$
$402$	−8.91036	+	2.61454i	−0.444408	+	0.130402i
$403$	−28.9192	−	6.41160i	−1.44057	−	0.319385i
$404$	7.85427	+	12.2313i	0.390764	+	0.608531i
$405$	−5.64057	+	7.76358i	−0.280282	+	0.385776i
$406$	1.77276	−	4.96562i	0.0879804	−	0.246440i
$407$	10.8868	−	9.24017i	0.539639	−	0.458018i
$408$	−4.21957	+	2.54133i	−0.208900	+	0.125815i
$409$	−17.8204	−	12.9473i	−0.881165	−	0.640204i	0.0523948	−	0.998626i	$-0.483315\pi$
$409$	−17.8204	−	12.9473i	−0.881165	−	0.640204i	−0.933559	+	0.358423i	$0.883315\pi$
$410$	1.77364	−	2.29922i	0.0875937	−	0.113550i
$411$	12.2443	+	37.6841i	0.603967	+	1.85882i
$412$	1.95543	−	33.9782i	0.0963371	−	1.67398i
$413$	15.1714	+	20.8816i	0.746535	+	1.02752i
$414$	−0.876190	+	30.4751i	−0.0430624	+	1.49777i
$415$	−1.05936	+	3.26038i	−0.0520020	+	0.160046i
$416$	−19.6765	+	5.36996i	−0.964718	+	0.263284i
$417$		−	2.84572i		−	0.139356i
$418$	3.09694	−	2.47899i	0.151476	−	0.121252i
$419$		−	10.2684i		−	0.501643i	−0.968033	−	0.250821i	$-0.919299\pi$
$419$		−	10.2684i		−	0.501643i	0.968033	−	0.250821i	$-0.0807007\pi$
$420$	−28.5142	+	7.48389i	−1.39135	+	0.365177i
$421$	33.8164	+	10.9876i	1.64811	+	0.535503i	0.978329	−	0.207056i	$-0.0663883\pi$
$421$	33.8164	+	10.9876i	1.64811	+	0.535503i	0.669780	+	0.742559i	$0.266388\pi$
$422$	−3.56586	−	0.102522i	−0.173583	−	0.00499069i
$423$	15.8592	−	11.5224i	0.771099	−	0.560236i
$424$	−9.35423	+	22.1009i	−0.454281	+	1.07331i
$425$	−1.79968	+	0.584752i	−0.0872974	+	0.0283646i
$426$	28.6252	−	37.1077i	1.38689	−	1.79788i
$427$	−21.7708	−	15.8174i	−1.05356	−	0.765458i
$428$	−18.1021	−	14.8131i	−0.874999	−	0.716018i
$429$	−27.3409	+	14.4288i	−1.32003	+	0.696627i
$430$	−10.7834	−	3.84975i	−0.520023	−	0.185651i
$431$	1.51443	−	2.08443i	0.0729473	−	0.100403i	−0.770984	−	0.636854i	$-0.780235\pi$
$431$	1.51443	−	2.08443i	0.0729473	−	0.100403i	0.843932	+	0.536451i	$0.180235\pi$
$432$	−0.810606	+	7.01935i	−0.0390003	+	0.337719i
$433$	−6.01918	−	18.5251i	−0.289263	−	0.890261i	−0.985088	−	0.172050i	$-0.944961\pi$
$433$	−6.01918	−	18.5251i	−0.289263	−	0.890261i	0.695825	−	0.718212i	$-0.255039\pi$
$434$	42.9434	−	12.6008i	2.06135	−	0.604857i
$435$	2.17700	+	2.99638i	0.104379	+	0.143665i
$436$	−5.38584	+	13.8185i	−0.257935	+	0.661784i
$437$	1.52966	−	4.70782i	0.0731738	−	0.225206i
$438$	22.5025	+	32.9217i	1.07521	+	1.57306i
$439$	2.57138			0.122725			0.0613626	−	0.998116i	$-0.480455\pi$
$439$	2.57138			0.122725			0.0613626	+	0.998116i	$0.480455\pi$
$440$	−4.43295	+	13.1588i	−0.211332	+	0.627322i
$441$	28.8685			1.37469
$442$	−3.42718	+	0.230784i	−0.163014	+	0.0109773i
$443$	−23.0483	−	7.48883i	−1.09506	−	0.355805i	−0.294858	−	0.955541i	$-0.595272\pi$
$443$	−23.0483	−	7.48883i	−1.09506	−	0.355805i	−0.800198	+	0.599736i	$0.795272\pi$
$444$	8.08401	−	20.7411i	0.383650	−	0.984330i
$445$	−2.28633	+	1.66111i	−0.108382	+	0.0787444i
$446$	−10.5944	−	36.1056i	−0.501658	−	1.70965i
$447$	−49.7809	+	16.1748i	−2.35456	+	0.765042i
$448$	22.1225	−	21.4523i	1.04519	−	1.01353i
$449$	−6.93095	+	9.53963i	−0.327092	+	0.450203i	−0.940616	−	0.339473i	$-0.889751\pi$
$449$	−6.93095	+	9.53963i	−0.327092	+	0.450203i	0.613524	+	0.789676i	$0.289751\pi$
$450$	−4.91967	+	13.7804i	−0.231915	+	0.649613i
$451$	0.346796	+	4.58772i	0.0163300	+	0.216027i
$452$	21.5420	+	17.6280i	1.01325	+	0.829152i
$453$	−3.31903	−	2.41142i	−0.155942	−	0.113298i
$454$	−21.2683	+	27.5708i	−0.998172	+	1.29396i
$455$	−20.0702	−	4.44973i	−0.940908	−	0.208606i
$456$	2.41045	−	5.69508i	0.112880	−	0.266697i
$457$	−4.35306	+	3.16268i	−0.203628	+	0.147944i	−0.684926	−	0.728613i	$-0.740165\pi$
$457$	−4.35306	+	3.16268i	−0.203628	+	0.147944i	0.481298	+	0.876557i	$0.340165\pi$
$458$	−0.424499	+	14.7647i	−0.0198355	+	0.689907i
$459$	−0.367730	+	1.13176i	−0.0171642	+	0.0528258i
$460$	4.39866	+	16.7592i	0.205089	+	0.781402i
$461$	−9.86777			−0.459588			−0.229794	−	0.973239i	$-0.573805\pi$
$461$	−9.86777			−0.459588			−0.229794	+	0.973239i	$0.573805\pi$
$462$	25.6600	−	39.0280i	1.19381	−	1.81575i
$463$	12.6570			0.588221			0.294111	−	0.955771i	$-0.404977\pi$
$463$	12.6570			0.588221			0.294111	+	0.955771i	$0.404977\pi$
$464$	−3.52051	−	1.61088i	−0.163436	−	0.0747833i
$465$	−9.71472	+	29.8988i	−0.450509	+	1.38652i
$466$	0.105858	−	3.68190i	0.00490380	−	0.170561i
$467$	−6.58912	−	9.06914i	−0.304908	−	0.419670i	0.628877	−	0.777505i	$-0.283515\pi$
$467$	−6.58912	−	9.06914i	−0.304908	−	0.419670i	−0.933785	+	0.357835i	$0.883515\pi$
$468$	−14.7735	+	22.0730i	−0.682904	+	1.02032i
$469$	9.30482	−	3.02332i	0.429657	−	0.139604i
$470$	6.80474	−	8.82120i	0.313879	−	0.406892i
$471$	−5.39020	+	7.41897i	−0.248367	+	0.341848i
$472$	16.2354	−	9.77815i	0.747296	−	0.450076i
$473$	16.7818	−	6.89055i	0.771628	−	0.316828i
$474$	48.3016	+	17.2439i	2.21857	+	0.792041i
$475$	1.39643	−	1.92201i	0.0640724	−	0.0881881i
$476$	4.36691	−	2.80418i	0.200157	−	0.128530i
$477$	9.65758	+	29.7230i	0.442190	+	1.36092i
$478$	30.5654	−	8.96872i	1.39803	−	0.410220i
$479$	21.8039	+	30.0105i	0.996247	+	1.37122i	0.927600	+	0.373576i	$0.121868\pi$
$479$	21.8039	+	30.0105i	0.996247	+	1.37122i	0.0686477	+	0.997641i	$0.478132\pi$
$480$	3.67168	+	21.3329i	0.167589	+	0.973709i
$481$	11.6265	−	10.2860i	0.530122	−	0.469001i
$482$	−2.01129	+	1.37474i	−0.0916116	+	0.0626178i
$483$		−	58.2841i		−	2.65202i
$484$	−8.72037	−	20.1979i	−0.396380	−	0.918086i
$485$	8.75405			0.397501
$486$	−17.6044	−	25.7557i	−0.798551	−	1.16830i
$487$	8.25598	−	25.4093i	0.374114	−	1.15141i	−0.569960	−	0.821672i	$-0.693041\pi$
$487$	8.25598	−	25.4093i	0.374114	−	1.15141i	0.944074	−	0.329733i	$-0.106959\pi$
$488$	−12.9480	+	14.9262i	−0.586129	+	0.675678i
$489$	−24.6737	−	33.9604i	−1.11578	−	1.53574i
$490$	15.7429	−	4.61939i	0.711191	−	0.208683i
$491$	9.48370	+	29.1878i	0.427993	+	1.31723i	0.900099	+	0.435686i	$0.143494\pi$
$491$	9.48370	+	29.1878i	0.427993	+	1.31723i	−0.472105	+	0.881542i	$0.656506\pi$
$492$	3.87547	+	6.03521i	0.174720	+	0.272088i
$493$	−0.527492	−	0.383245i	−0.0237570	−	0.0172605i
$494$	3.31069	−	2.76350i	0.148955	−	0.124336i
$495$	6.86811	+	16.7271i	0.308699	+	0.751829i
$496$	−6.50248	−	32.2122i	−0.291970	−	1.44637i
$497$	−29.0232	+	39.9470i	−1.30187	+	1.79187i
$498$	−6.70447	−	5.17188i	−0.300435	−	0.231757i
$499$	−5.01288	−	15.4280i	−0.224407	−	0.690654i	−0.998351	−	0.0574002i	$-0.981719\pi$
$499$	−5.01288	−	15.4280i	−0.224407	−	0.690654i	0.773944	−	0.633254i	$-0.218281\pi$
$500$	−1.32822	+	23.0795i	−0.0593997	+	1.03215i
$501$	13.3356	−	9.68887i	0.595790	−	0.432867i
$502$	1.08978	−	37.9042i	0.0486395	−	1.69175i
$503$	−4.76560	+	14.6670i	−0.212487	+	0.653969i	0.786835	+	0.617163i	$0.211718\pi$
$503$	−4.76560	+	14.6670i	−0.212487	+	0.653969i	−0.999322	+	0.0368057i	$0.988282\pi$
$504$	3.45607	−	39.9806i	0.153946	−	1.78088i
$505$	10.7580			0.478726
$506$	−22.9387	−	15.0817i	−1.01975	−	0.670462i
$507$	−29.3944	+	16.2926i	−1.30545	+	0.723581i
$508$	10.8054	+	41.1693i	0.479412	+	1.82659i
$509$	29.5966	+	9.61653i	1.31185	+	0.426245i	0.879688	−	0.475552i	$-0.157751\pi$
$509$	29.5966	+	9.61653i	1.31185	+	0.426245i	0.432160	+	0.901797i	$0.357751\pi$
$510$	−0.104770	+	3.64403i	−0.00463928	+	0.161360i
$511$	−24.6954	−	33.9903i	−1.09246	−	1.50364i
$512$	−14.2945	−	17.5404i	−0.631735	−	0.775184i
$513$	−0.461677	−	1.42090i	−0.0203835	−	0.0627341i
$514$	−12.6982	−	9.79549i	−0.560094	−	0.432060i
$515$	−20.3781	−	14.8056i	−0.897966	−	0.652411i
$516$	17.9104	−	21.8871i	0.788462	−	0.963528i
$517$	1.33052	+	17.6013i	0.0585162	+	0.774102i
$518$	−7.88569	+	22.0884i	−0.346477	+	0.970509i
$519$	−39.6027	−	28.7730i	−1.73837	−	1.26300i
$520$	−4.52441	+	14.4011i	−0.198409	+	0.631528i
$521$	1.60553	+	4.94131i	0.0703395	+	0.216483i	0.980047	−	0.198768i	$-0.0636940\pi$
$521$	1.60553	+	4.94131i	0.0703395	+	0.216483i	−0.909707	+	0.415250i	$0.863694\pi$
$522$	−4.83775	+	1.41953i	−0.211743	+	0.0621312i
$523$	−14.2139	+	10.3270i	−0.621530	+	0.451568i	−0.853456	−	0.521165i	$-0.825497\pi$
$523$	−14.2139	+	10.3270i	−0.621530	+	0.451568i	0.231926	+	0.972734i	$0.425497\pi$
$524$	−13.8656	+	35.5749i	−0.605720	+	1.55410i
$525$	8.64405	−	26.6037i	0.377257	−	1.16108i
$526$	−23.1928	+	15.8526i	−1.01125	+	0.691205i
$527$		−	5.53435i		−	0.241080i
$528$	−26.9284	−	21.2397i	−1.17191	−	0.924339i
$529$	−11.2565			−0.489412
$530$	10.0227	+	14.6635i	0.435358	+	0.636941i
$531$	7.62684	−	23.4730i	0.330976	−	1.01864i
$532$	−2.36614	+	6.07079i	−0.102585	+	0.263202i
$533$	0.479321	+	4.97858i	0.0207617	+	0.215646i
$534$	−1.96535	−	6.69790i	−0.0850490	−	0.289847i
$535$	−16.4639	+	5.34946i	−0.711798	+	0.231277i
$536$	−1.62330	−	6.99816i	−0.0701159	−	0.302275i
$537$	−27.4334	−	19.9315i	−1.18384	−	0.860109i
$538$	4.81454	−	13.4859i	0.207569	−	0.581418i
$539$	−13.6506	+	22.1219i	−0.587971	+	0.952858i
$540$	4.04718	+	3.31183i	0.174163	+	0.142519i
$541$	−4.40614	−	3.20125i	−0.189435	−	0.137632i	0.489026	−	0.872269i	$-0.337352\pi$
$541$	−4.40614	−	3.20125i	−0.189435	−	0.137632i	−0.678460	+	0.734637i	$0.737352\pi$
$542$	0.630499	−	0.817336i	0.0270822	−	0.0351076i
$543$	39.0931	−	12.7021i	1.67765	−	0.545100i
$544$	−1.77525	−	3.37196i	−0.0761134	−	0.144572i
$545$	6.45172	+	8.88003i	0.276361	+	0.380379i
$546$	27.0184	−	42.9917i	1.15628	−	1.83987i
$547$	−5.78435	+	17.8024i	−0.247321	+	0.761176i	0.747925	+	0.663783i	$0.231050\pi$
$547$	−5.78435	+	17.8024i	−0.247321	+	0.761176i	−0.995246	+	0.0973926i	$0.968950\pi$
$548$	−29.6497	+	7.78193i	−1.26657	+	0.332428i
$549$			25.7319i			1.09821i
$550$	−8.23360	−	10.2860i	−0.351082	−	0.438598i
$551$	0.818593			0.0348732
$552$	−42.6379	−	3.68577i	−1.81479	−	0.156877i
$553$	−51.3912	−	16.6980i	−2.18538	−	0.710072i
$554$	−0.606474	+	21.0940i	−0.0257666	+	0.896198i
$555$	−9.68386	−	13.3287i	−0.411057	−	0.565771i
$556$	2.19790	+	0.126488i	0.0932119	+	0.00536431i
$557$	4.84154	+	14.9007i	0.205142	+	0.631364i	0.999708	+	0.0241846i	$0.00769893\pi$
$557$	4.84154	+	14.9007i	0.205142	+	0.631364i	−0.794565	+	0.607179i	$0.792301\pi$
$558$	−33.8842	−	26.1385i	−1.43443	−	1.10653i
$559$	18.0861	−	7.86379i	0.764960	−	0.332603i
$560$	−4.51280	−	22.3557i	−0.190700	−	0.944699i
$561$	−3.73760	−	4.40365i	−0.157801	−	0.185922i
$562$	−9.26750	+	25.9590i	−0.390926	+	1.09501i
$563$	2.41111	+	1.75177i	0.101616	+	0.0738285i	0.637433	−	0.770506i	$-0.279996\pi$
$563$	2.41111	+	1.75177i	0.101616	+	0.0738285i	−0.535817	+	0.844334i	$0.679996\pi$
$564$	14.8687	+	23.1547i	0.626083	+	0.974989i
$565$	19.5925	−	6.36600i	0.824265	−	0.267820i
$566$	−5.09320	−	17.3576i	−0.214083	−	0.729594i
$567$	14.6787	+	20.2035i	0.616448	+	0.848468i
$568$	27.3879	+	23.7582i	1.14917	+	0.996870i
$569$	6.48237	+	2.10625i	0.271755	+	0.0882985i	0.441724	−	0.897151i	$-0.354367\pi$
$569$	6.48237	+	2.10625i	0.271755	+	0.0882985i	−0.169969	+	0.985449i	$0.554367\pi$
$570$	−2.58271	−	3.77857i	−0.108178	−	0.158267i
$571$	−4.35895			−0.182416			−0.0912082	−	0.995832i	$-0.529073\pi$
$571$	−4.35895			−0.182416			−0.0912082	+	0.995832i	$0.529073\pi$
$572$	−9.92884	−	21.7582i	−0.415145	−	0.909755i
$573$	30.7481			1.28452
$574$	−4.26421	−	6.23867i	−0.177985	−	0.260397i
$575$	−15.6363	−	5.08054i	−0.652079	−	0.211873i
$576$	−29.0294	−	5.05659i	−1.20956	−	0.210691i
$577$	9.58727	+	13.1958i	0.399123	+	0.549346i	0.960524	−	0.278198i	$-0.0897372\pi$
$577$	9.58727	+	13.1958i	0.399123	+	0.549346i	−0.561400	+	0.827544i	$0.689737\pi$
$578$	6.58839	+	22.4532i	0.274041	+	0.933930i
$579$	−0.195624	+	0.0635622i	−0.00812987	+	0.00264156i
$580$	−2.41103	+	1.54823i	−0.100113	+	0.0642866i
$581$	7.21745	+	5.24378i	0.299430	+	0.217549i
$582$	−7.26989	+	20.3635i	−0.301347	+	0.844095i
$583$	−27.3433	−	6.65400i	−1.13244	−	0.275581i
$584$	−26.4274	+	15.9165i	−1.09357	+	0.658631i
$585$	7.83818	+	18.0272i	0.324069	+	0.745333i
$586$	18.2102	+	14.0475i	0.752258	+	0.580297i
$587$	0.295079	+	0.908159i	0.0121792	+	0.0374837i	0.956961	−	0.290215i	$-0.0937269\pi$
$587$	0.295079	+	0.908159i	0.0121792	+	0.0374837i	−0.944782	+	0.327699i	$0.893727\pi$
$588$	−2.32828	+	40.4570i	−0.0960168	+	1.66842i
$589$	4.08409	+	5.62126i	0.168282	+	0.231620i
$590$	0.403116	−	14.0209i	0.0165960	−	0.577233i
$591$	−22.1712	−	7.20384i	−0.911999	−	0.296327i
$592$	15.6602	+	7.16563i	0.643629	+	0.294505i
$593$	−1.24304			−0.0510453			−0.0255227	−	0.999674i	$-0.508125\pi$
$593$	−1.24304			−0.0510453			−0.0255227	+	0.999674i	$0.508125\pi$
$594$	−8.27658	+	0.386846i	−0.339592	+	0.0158725i
$595$		−	3.84090i		−	0.157462i
$596$	−10.2800	−	39.1674i	−0.421084	−	1.60436i
$597$	11.9265	−	36.7060i	0.488119	−	1.50228i
$598$	−25.2684	−	15.8801i	−1.03330	−	0.649385i
$599$	−18.5006	−	25.4639i	−0.755915	−	1.04043i	−0.997543	−	0.0700584i	$-0.977681\pi$
$599$	−18.5006	−	25.4639i	−0.755915	−	1.04043i	0.241628	−	0.970369i	$-0.422319\pi$
$600$	−18.9154	−	8.00595i	−0.772216	−	0.326841i
$601$	−15.4909	+	5.03331i	−0.631888	+	0.205313i	−0.607411	−	0.794387i	$-0.707792\pi$
$601$	−15.4909	+	5.03331i	−0.631888	+	0.205313i	−0.0244769	+	0.999700i	$0.507792\pi$
$602$	−18.1997	+	23.5929i	−0.741765	+	0.961574i
$603$	−7.56859	−	5.49890i	−0.308217	−	0.223933i
$604$	2.00999	−	2.45628i	0.0817855	−	0.0999447i
$605$	−16.0656	−	2.64645i	−0.653160	−	0.107593i
$606$	−8.93411	+	25.0251i	−0.362923	+	1.01658i
$607$	−21.0249	−	15.2755i	−0.853374	−	0.620012i	0.0727006	−	0.997354i	$-0.476838\pi$
$607$	−21.0249	−	15.2755i	−0.853374	−	0.620012i	−0.926074	+	0.377342i	$0.876838\pi$
$608$	4.29148	+	2.11486i	0.174042	+	0.0857689i
$609$	9.16664	−	2.97842i	0.371451	−	0.120692i
$610$	4.11750	+	14.0324i	0.166713	+	0.568156i
$611$	1.83897	+	19.1009i	0.0743966	+	0.772738i
$612$	−4.62372	−	1.80213i	−0.186903	−	0.0728467i
$613$	12.7059	−	39.1049i	0.513188	−	1.57943i	−0.273367	−	0.961910i	$-0.588137\pi$
$613$	12.7059	−	39.1049i	0.513188	−	1.57943i	0.786555	−	0.617520i	$-0.211863\pi$
$614$	10.9975	+	16.0897i	0.443823	+	0.649326i
$615$	5.30825			0.214049
$616$	29.0029	+	21.5533i	1.16856	+	0.868408i
$617$		−	12.0622i		−	0.485607i	−0.970076	−	0.242803i	$-0.921933\pi$
$617$		−	12.0622i		−	0.485607i	0.970076	−	0.242803i	$-0.0780670\pi$
$618$	51.3636	−	35.1077i	2.06615	−	1.41224i
$619$	−2.28347	+	7.02778i	−0.0917802	+	0.282470i	−0.986401	−	0.164355i	$-0.947446\pi$
$619$	−2.28347	+	7.02778i	−0.0917802	+	0.282470i	0.894621	+	0.446826i	$0.147446\pi$
$620$	−22.6607	−	8.83216i	−0.910074	−	0.354708i
$621$	−8.36455	+	6.07720i	−0.335658	+	0.243870i
$622$	−36.5833	+	10.7346i	−1.46686	+	0.430417i
$623$	2.27263	+	6.99442i	0.0910508	+	0.280226i
$624$	−29.7421	−	22.4841i	−1.19064	−	0.900085i
$625$	2.47898	+	1.80108i	0.0991591	+	0.0720433i
$626$	−1.91096	+	5.35273i	−0.0763772	+	0.213938i
$627$	7.04598	+	1.71464i	0.281389	+	0.0684762i
$628$	−5.49048	−	4.49290i	−0.219094	−	0.179286i
$629$	2.34642	+	1.70478i	0.0935580	+	0.0679739i
$630$	−23.5160	−	18.1404i	−0.936901	−	0.722733i
$631$	13.7991	+	42.4694i	0.549335	+	1.69068i	0.710452	+	0.703745i	$0.248490\pi$
$631$	13.7991	+	42.4694i	0.549335	+	1.69068i	−0.161117	+	0.986935i	$0.551510\pi$
$632$	−15.4654	+	36.5394i	−0.615179	+	1.45346i
$633$	−3.83304	−	5.27572i	−0.152350	−	0.209691i
$634$	0.207281	−	7.20953i	0.00823219	−	0.286327i
$635$	29.9594	+	9.73441i	1.18890	+	0.386298i
$636$	−42.4334	+	11.1372i	−1.68259	+	0.441617i
$637$	−14.3429	+	24.3486i	−0.568285	+	0.964729i
$638$	1.19976	−	4.37840i	0.0474990	−	0.173342i
$639$	47.2152			1.86780
$640$	−16.6397	+	1.88762i	−0.657743	+	0.0746147i
$641$	−13.3627	+	41.1260i	−0.527793	+	1.62438i	0.230933	+	0.972970i	$0.425822\pi$
$641$	−13.3627	+	41.1260i	−0.527793	+	1.62438i	−0.758726	+	0.651410i	$0.774178\pi$
$642$	1.22884	−	42.7406i	0.0484983	−	1.68684i
$643$	11.9380	−	8.67345i	0.470788	−	0.342048i	−0.326960	−	0.945038i	$-0.606024\pi$
$643$	11.9380	−	8.67345i	0.470788	−	0.342048i	0.797748	+	0.602991i	$0.206024\pi$
$644$	45.0159	+	2.59065i	1.77387	+	0.102086i
$645$	−6.46799	−	19.9064i	−0.254677	−	0.783815i
$646$	0.637970	+	0.492135i	0.0251006	+	0.0193628i
$647$	22.5512	−	31.0391i	0.886579	−	1.22027i	−0.0879759	−	0.996123i	$-0.528040\pi$
$647$	22.5512	−	31.0391i	0.886579	−	1.22027i	0.974555	−	0.224149i	$-0.0719602\pi$
$648$	15.7082	−	9.46062i	0.617076	−	0.371648i
$649$	14.3810	+	16.9437i	0.564502	+	0.665099i
$650$	−9.17855	−	10.9960i	−0.360013	−	0.431297i
$651$	66.1866	+	48.0874i	2.59406	+	1.88469i
$652$	27.3262	−	17.5473i	1.07018	−	0.687206i
$653$	−6.68218	−	20.5656i	−0.261494	−	0.804795i	−0.992480	−	0.122404i	$-0.960940\pi$
$653$	−6.68218	−	20.5656i	−0.261494	−	0.804795i	0.730987	−	0.682392i	$-0.239060\pi$
$654$	−26.0145	+	7.63336i	−1.01725	+	0.298488i
$655$	16.6096	+	22.8612i	0.648991	+	0.893260i
$656$	−4.83358	+	2.72498i	−0.188719	+	0.106392i
$657$	−12.4147	+	38.2085i	−0.484343	+	1.49066i
$658$	−16.3601	−	23.9353i	−0.637783	−	0.933095i
$659$	−9.27264			−0.361211			−0.180605	−	0.983556i	$-0.557806\pi$
$659$	−9.27264			−0.361211			−0.180605	+	0.983556i	$0.557806\pi$
$660$	−23.9957	+	8.27607i	−0.934033	+	0.322146i
$661$			3.08954i			0.120169i	0.998193	+	0.0600846i	$0.0191370\pi$
$661$			3.08954i			0.120169i	−0.998193	+	0.0600846i	$0.980863\pi$
$662$	27.5849	−	18.8546i	1.07212	−	0.732806i
$663$	−4.16063	−	4.70285i	−0.161585	−	0.182644i
$664$	4.29252	−	4.94834i	0.166582	−	0.192033i
$665$	2.83440	+	3.90122i	0.109913	+	0.151283i
$666$	21.5196	−	6.31445i	0.833868	−	0.244680i
$667$	−1.75057	−	5.38770i	−0.0677823	−	0.208612i
$668$	6.89048	+	10.7304i	0.266601	+	0.415173i
$669$	40.4304	−	55.6477i	1.56313	−	2.15147i
$670$	−5.00729	−	1.78763i	−0.193449	−	0.0690623i
$671$	−19.7184	−	12.1674i	−0.761219	−	0.469718i
$672$	55.7510	+	8.06791i	2.15064	+	0.311226i
$673$	26.6395	−	36.6662i	1.02688	−	1.41338i	0.119612	−	0.992821i	$-0.461835\pi$
$673$	26.6395	−	36.6662i	1.02688	−	1.41338i	0.907266	−	0.420556i	$-0.138165\pi$
$674$	−22.6989	+	29.4253i	−0.874327	+	1.13342i
$675$	−4.71929	+	1.53339i	−0.181646	+	0.0590202i
$676$	−11.2771	−	23.4270i	−0.433736	−	0.901040i
$677$	19.5694	+	26.9349i	0.752112	+	1.03519i	0.997829	+	0.0658514i	$0.0209763\pi$
$677$	19.5694	+	26.9349i	0.752112	+	1.03519i	−0.245718	+	0.969341i	$0.579024\pi$
$678$	−1.46235	+	50.8625i	−0.0561612	+	1.95336i
$679$	7.03973	−	21.6661i	0.270160	−	0.831467i
$680$	−2.80982	−	0.242891i	−0.107752	−	0.00931446i
$681$	−63.6532			−2.43920
$682$	36.0522	−	13.6058i	1.38051	−	0.520992i
$683$	−40.9762			−1.56791			−0.783956	−	0.620817i	$-0.786801\pi$
$683$	−40.9762			−1.56791			−0.783956	+	0.620817i	$0.786801\pi$
$684$	6.02622	−	1.58166i	0.230418	−	0.0604761i
$685$	−7.01062	+	21.5765i	−0.267862	+	0.824395i
$686$	0.131140	−	4.56123i	0.00500694	−	0.174148i
$687$	−21.8445	+	15.8709i	−0.833418	+	0.605514i
$688$	16.1085	+	14.8060i	0.614132	+	0.564474i
$689$	−29.8675	−	6.62186i	−1.13786	−	0.252273i
$690$	−19.3461	+	25.0790i	−0.736495	+	0.954742i
$691$	22.6792	+	16.4774i	0.862758	+	0.626830i	0.928634	−	0.370997i	$-0.120984\pi$
$691$	22.6792	+	16.4774i	0.862758	+	0.626830i	−0.0658758	+	0.997828i	$0.520984\pi$
$692$	23.9833	−	29.3084i	0.911707	−	1.11414i
$693$	46.9224	−	3.54697i	1.78243	−	0.134738i
$694$	−15.5226	+	43.4798i	−0.589228	+	1.65047i
$695$	0.957709	−	1.31817i	0.0363280	−	0.0500012i
$696$	−1.59919	−	6.89423i	−0.0606172	−	0.261325i
$697$	−0.888744	+	0.288770i	−0.0336636	+	0.0109380i
$698$	−7.80332	−	26.5937i	−0.295360	−	1.00659i
$699$	5.44741	−	3.95778i	0.206040	−	0.149697i
$700$	20.1632	+	7.85876i	0.762098	+	0.297033i
$701$	23.3479	+	7.58618i	0.881836	+	0.286526i	0.714720	−	0.699411i	$-0.246554\pi$
$701$	23.3479	+	7.58618i	0.881836	+	0.286526i	0.167117	+	0.985937i	$0.446554\pi$
$702$	−8.98707	+	0.605182i	−0.339195	+	0.0228411i
$703$	−3.64132			−0.137335
$704$	17.6015	−	19.8542i	0.663381	−	0.748282i
$705$	20.3657			0.767015
$706$	1.56363	+	2.28764i	0.0588481	+	0.0860964i
$707$	8.65126	−	26.6258i	0.325364	−	1.00137i
$708$	32.2805	+	12.5816i	1.21318	+	0.472844i
$709$	29.0125	+	39.9323i	1.08959	+	1.49969i	0.848506	+	0.529185i	$0.177502\pi$
$709$	29.0125	+	39.9323i	1.08959	+	1.49969i	0.241082	+	0.970505i	$0.422498\pi$
$710$	25.7479	−	7.55514i	0.966301	−	0.283539i
$711$	15.9669	+	49.1411i	0.598805	+	1.84293i
$712$	5.26051	−	1.22023i	0.197146	−	0.0457301i
$713$	28.2634	−	38.9012i	1.05847	−	1.45686i
$714$	8.93463	+	3.18972i	0.334370	+	0.119372i
$715$	−17.5205	−	2.51782i	−0.655231	−	0.0941611i
$716$	16.6136	−	20.3024i	0.620878	−	0.758734i
$717$	47.1089	+	34.2266i	1.75931	+	1.27822i
$718$	−10.2020	+	13.2252i	−0.380735	+	0.493559i
$719$	−0.419543	+	0.136318i	−0.0156463	+	0.00508380i	−0.316830	−	0.948482i	$-0.602618\pi$
$719$	−0.419543	+	0.136318i	−0.0156463	+	0.00508380i	0.301183	+	0.953566i	$0.402618\pi$
$720$	−14.7578	+	16.0561i	−0.549991	+	0.598374i
$721$	−53.0308	+	38.5291i	−1.97497	+	1.43490i
$722$	25.8478	+	0.743150i	0.961955	+	0.0276572i
$723$	−4.23550	−	1.37620i	−0.157520	−	0.0511813i
$724$	8.07290	+	30.7583i	0.300027	+	1.14312i
$725$		−	2.71883i		−	0.100975i
$726$	19.4980	−	35.1737i	0.723637	−	1.30542i
$727$			12.9889i			0.481733i	0.970558	+	0.240866i	$0.0774316\pi$
$727$			12.9889i			0.481733i	−0.970558	+	0.240866i	$0.922568\pi$
$728$	32.0039	+	22.7787i	1.18614	+	0.844234i
$729$	11.6128	−	35.7405i	0.430104	−	1.32372i
$730$	−0.656178	+	22.8228i	−0.0242863	+	0.844710i
$731$	2.16583	+	2.98101i	0.0801061	+	0.110257i
$732$	−36.0613	−	2.07531i	−1.33287	−	0.0767058i
$733$	11.7550	+	36.1783i	0.434182	+	1.33627i	0.893923	+	0.448221i	$0.147942\pi$
$733$	11.7550	+	36.1783i	0.434182	+	1.33627i	−0.459741	+	0.888053i	$0.652058\pi$
$734$	−23.6754	+	30.6912i	−0.873875	+	1.13283i
$735$	24.2637	+	17.6286i	0.894981	+	0.650242i
$736$	4.74192	−	32.7677i	0.174789	−	1.20783i
$737$	7.79264	−	3.19963i	0.287046	−	0.117860i
$738$	−2.42950	+	6.80521i	−0.0894311	+	0.250503i
$739$	−5.35239	+	7.36693i	−0.196891	+	0.270997i	−0.896035	−	0.443984i	$-0.853565\pi$
$739$	−5.35239	+	7.36693i	−0.196891	+	0.270997i	0.699144	+	0.714981i	$0.253565\pi$
$740$	10.7249	−	6.88692i	0.394255	−	0.253168i
$741$	7.69644	+	1.70636i	0.282736	+	0.0626847i
$742$	44.3517	−	13.0140i	1.62820	−	0.477759i
$743$	−17.4556	−	24.0255i	−0.640382	−	0.881411i	0.358254	−	0.933624i	$-0.383372\pi$
$743$	−17.4556	−	24.0255i	−0.640382	−	0.881411i	−0.998636	+	0.0522137i	$0.983372\pi$
$744$	39.3640	−	45.3780i	1.44315	−	1.66364i
$745$	−28.5026	−	9.26107i	−1.04426	−	0.339299i
$746$	21.1070	+	30.8802i	0.772783	+	1.13060i
$747$		−	8.53065i		−	0.312120i
$748$	3.56731	−	2.69101i	0.130434	−	0.0983931i
$749$			45.0497i			1.64608i
$750$	−34.8885	+	23.8468i	−1.27395	+	0.870762i
$751$	27.4039	+	8.90407i	0.999983	+	0.324914i	0.762859	−	0.646565i	$-0.223795\pi$
$751$	27.4039	+	8.90407i	0.999983	+	0.324914i	0.237124	+	0.971479i	$0.423795\pi$
$752$	−18.5445	+	10.4547i	−0.676249	+	0.381242i
$753$	56.0797	−	40.7443i	2.04366	−	1.48480i
$754$	1.20628	−	4.78559i	0.0439302	−	0.174281i
$755$	−0.725869	−	2.23400i	−0.0264171	−	0.0813034i
$756$	11.4513	−	7.35339i	0.416480	−	0.267440i
$757$	32.7330	+	23.7819i	1.18970	+	0.864367i	0.993232	−	0.116143i	$-0.0370532\pi$
$757$	32.7330	+	23.7819i	1.18970	+	0.864367i	0.196467	+	0.980510i	$0.437053\pi$
$758$	−14.3644	+	40.2358i	−0.521739	+	1.46143i
$759$	−3.78272	−	50.0410i	−0.137304	−	1.81637i
$760$	3.03319	−	1.82681i	0.110025	−	0.0662654i
$761$	9.11644	+	6.62348i	0.330471	+	0.240101i	0.740630	−	0.671913i	$-0.234527\pi$
$761$	9.11644	+	6.62348i	0.330471	+	0.240101i	−0.410160	+	0.912014i	$0.634527\pi$
$762$	−47.5241	+	61.6070i	−1.72162	+	2.23179i
$763$	27.1661	−	8.82681i	0.983480	−	0.319552i
$764$	−1.36671	+	23.7484i	−0.0494459	+	0.859188i
$765$	−2.97130	+	2.15878i	−0.107428	+	0.0780507i
$766$	−39.6886	−	1.14109i	−1.43401	−	0.0412292i
$767$	16.0086	+	18.0949i	0.578038	+	0.653369i
$768$	9.42769	−	40.2746i	0.340192	−	1.45329i
$769$	−25.5409			−0.921029			−0.460514	−	0.887652i	$-0.652335\pi$
$769$	−25.5409			−0.921029			−0.460514	+	0.887652i	$0.652335\pi$
$770$	25.0206	−	9.44256i	0.901681	−	0.340286i
$771$		−	29.3166i		−	1.05581i
$772$	−0.0403973	−	0.153916i	−0.00145393	−	0.00553957i
$773$	38.9727	+	12.6630i	1.40175	+	0.455456i	0.909756	−	0.415143i	$-0.136269\pi$
$773$	38.9727	+	12.6630i	1.40175	+	0.455456i	0.491993	+	0.870599i	$0.336269\pi$
$774$	28.4805	+	0.818842i	1.02371	+	0.0294327i
$775$	18.6702	−	13.5647i	0.670652	−	0.487257i
$776$	−15.4047	−	6.52006i	−0.552996	−	0.234056i
$777$	−40.7756	+	13.2488i	−1.46282	+	0.475298i
$778$	22.0293	+	16.9936i	0.789790	+	0.609250i
$779$	0.689602	−	0.949156i	0.0247076	−	0.0340070i
$780$	−25.8959	+	9.53070i	−0.927222	+	0.341254i
$781$	−22.3258	+	36.1810i	−0.798882	+	1.29466i
$782$	1.87476	−	5.25134i	0.0670412	−	0.187787i
$783$	−1.38324	−	1.00498i	−0.0494329	−	0.0359151i
$784$	−31.1436	−	3.59652i	−1.11227	−	0.128447i
$785$	−4.99361	+	1.62252i	−0.178230	+	0.0579103i
$786$	−66.9728	+	19.6517i	−2.38884	+	0.700952i
$787$	−16.5698	−	22.8064i	−0.590651	−	0.812961i	0.404161	−	0.914688i	$-0.367563\pi$
$787$	−16.5698	−	22.8064i	−0.590651	−	0.812961i	−0.994812	+	0.101726i	$0.967563\pi$
$788$	6.54939	−	16.8038i	0.233312	−	0.598610i
$789$	−48.8408	−	15.8693i	−1.73878	−	0.564964i
$790$	16.5705	+	24.2432i	0.589554	+	0.862534i
$791$		−	53.6104i		−	1.90617i
$792$	0.372483	−	34.5505i	0.0132356	−	1.22770i
$793$	−21.7032	−	12.7845i	−0.770702	−	0.453991i
$794$	−9.00232	−	13.1706i	−0.319480	−	0.467409i
$795$	−10.0333	+	30.8793i	−0.355844	+	1.09518i
$796$	27.8199	+	10.8430i	0.986050	+	0.384320i
$797$	−4.48047	+	3.25525i	−0.158706	+	0.115307i	−0.664304	−	0.747462i	$-0.731272\pi$
$797$	−4.48047	+	3.25525i	−0.158706	+	0.115307i	0.505598	+	0.862769i	$0.331272\pi$
$798$	−11.4288	+	3.35353i	−0.404575	+	0.118714i
$799$	−3.40976	+	1.10790i	−0.120629	+	0.0391946i
$800$	7.02418	−	14.2535i	0.248342	−	0.503937i
$801$	4.13352	−	5.68930i	0.146051	−	0.201022i
$802$	−9.94893	−	3.55182i	−0.351309	−	0.125419i
$803$	−23.4088	−	27.5804i	−0.826079	−	0.973290i
$804$	8.31671	−	10.1633i	0.293308	−	0.358432i
$805$	19.6151	−	26.9979i	0.691342	−	0.951550i
$806$	38.8809	−	15.5926i	1.36952	−	0.549224i
$807$	24.8952	−	8.08894i	0.876353	−	0.284744i
$808$	−18.9311	−	8.01262i	−0.665995	−	0.281883i
$809$	−2.02511	−	2.78732i	−0.0711990	−	0.0979970i	0.771932	−	0.635705i	$-0.219290\pi$
$809$	−2.02511	−	2.78732i	−0.0711990	−	0.0979970i	−0.843131	+	0.537708i	$0.819290\pi$
$810$	0.390026	−	13.5656i	0.0137041	−	0.476648i
$811$	16.8949	+	5.48950i	0.593262	+	0.192762i	0.590233	−	0.807233i	$-0.299036\pi$
$811$	16.8949	+	5.48950i	0.593262	+	0.192762i	0.00302877	+	0.999995i	$0.499036\pi$
$812$	1.89295	+	7.21227i	0.0664295	+	0.253101i
$813$	1.88700			0.0661799
$814$	−5.33686	+	19.4763i	−0.187057	+	0.682643i
$815$		−	24.0347i		−	0.841897i
$816$	2.89846	−	6.33445i	0.101466	−	0.221750i
$817$	−4.39969	−	1.42954i	−0.153926	−	0.0500134i
$818$	31.1384	+	0.895261i	1.08873	+	0.0313021i
$819$	50.9201	−	4.90241i	1.77929	−	0.171304i
$820$	−0.235944	+	4.09985i	−0.00823954	+	0.143173i
$821$	−7.36162	−	22.6567i	−0.256922	−	0.790725i	−0.993445	−	0.114312i	$-0.963533\pi$
$821$	−7.36162	−	22.6567i	−0.256922	−	0.790725i	0.736523	−	0.676413i	$-0.236467\pi$
$822$	−44.3687	−	34.2264i	−1.54754	−	1.19378i
$823$	2.57581	−	3.54529i	0.0897869	−	0.123581i	−0.761760	−	0.647859i	$-0.775665\pi$
$823$	2.57581	−	3.54529i	0.0897869	−	0.123581i	0.851547	+	0.524278i	$0.175665\pi$
$824$	24.8325	+	41.2314i	0.865082	+	1.43636i
$825$	5.69492	−	23.4022i	0.198272	−	0.814758i
$826$	−34.3773	−	12.2729i	−1.19614	−	0.427029i
$827$	−5.33688	+	7.34558i	−0.185581	+	0.255431i	−0.891663	−	0.452699i	$-0.850461\pi$
$827$	−5.33688	+	7.34558i	−0.185581	+	0.255431i	0.706082	+	0.708130i	$0.250461\pi$
$828$	−23.2970	−	36.2801i	−0.809628	−	1.26082i
$829$	−9.25443	−	28.4822i	−0.321420	−	0.989228i	−0.973031	−	0.230675i	$-0.925907\pi$
$829$	−9.25443	−	28.4822i	−0.321420	−	0.989228i	0.651611	−	0.758553i	$-0.274093\pi$
$830$	−1.36503	−	4.65202i	−0.0473809	−	0.161474i
$831$	−31.2088	+	22.6745i	−1.08262	+	0.786570i
$832$	18.6877	−	21.9720i	0.647879	−	0.761744i
$833$	−5.02140	−	1.63155i	−0.173981	−	0.0565299i
$834$	2.27097	+	3.32249i	0.0786373	+	0.115049i
$835$	9.43792			0.326613
$836$	−1.63749	+	5.36578i	−0.0566339	+	0.185579i
$837$		−	14.5127i		−	0.501632i
$838$	8.19446	+	11.9887i	0.283073	+	0.414144i
$839$	4.04826	−	12.4593i	0.139761	−	0.430141i	−0.856539	−	0.516083i	$-0.827390\pi$
$839$	4.04826	−	12.4593i	0.139761	−	0.430141i	0.996300	+	0.0859413i	$0.0273898\pi$
$840$	27.3191	−	31.4929i	0.942597	−	1.08661i
$841$	−22.7036	+	16.4951i	−0.782883	+	0.568798i
$842$	−48.2504	+	14.1580i	−1.66282	+	0.487917i
$843$	−47.9208	+	15.5704i	−1.65048	+	0.536273i
$844$	4.24510	−	2.72596i	0.146122	−	0.0938315i
$845$	−19.0990	−	2.34554i	−0.657026	−	0.0806891i
$846$	−9.32103	+	26.1089i	−0.320464	+	0.897643i
$847$	−19.4693	+	37.6338i	−0.668974	+	1.29311i
$848$	−6.71572	−	33.2686i	−0.230619	−	1.14245i
$849$	19.4368	−	26.7524i	0.667068	−	0.918140i
$850$	1.63455	−	2.11892i	0.0560646	−	0.0726783i
$851$	7.78699	+	23.9659i	0.266935	+	0.821540i
$852$	−3.80797	+	66.1685i	−0.130459	+	2.26690i
$853$	−12.7410	+	9.25690i	−0.436245	+	0.316950i	−0.784141	−	0.620583i	$-0.786896\pi$
$853$	−12.7410	+	9.25690i	−0.436245	+	0.316950i	0.347896	+	0.937533i	$0.386896\pi$
$854$	38.0410	+	1.09372i	1.30174	+	0.0374262i
$855$	1.42489	−	4.38536i	0.0487302	−	0.149976i
$856$	32.9562	+	2.84886i	1.12642	+	0.0973719i
$857$		−	26.2280i		−	0.895931i	−0.894051	−	0.447965i	$-0.852149\pi$
$857$		−	26.2280i		−	0.895931i	0.894051	−	0.447965i	$-0.147851\pi$
$858$	20.4070	−	38.6650i	0.696684	−	1.32000i
$859$		−	41.9630i		−	1.43176i	−0.698223	−	0.715880i	$-0.746026\pi$
$859$		−	41.9630i		−	1.43176i	0.698223	−	0.715880i	$-0.253974\pi$
$860$	15.6623	−	4.11076i	0.534080	−	0.140176i
$861$	4.26873	−	13.1378i	0.145478	−	0.447735i
$862$	−0.104717	+	3.64221i	−0.00356668	+	0.124054i
$863$	−15.3321	+	11.1394i	−0.521912	+	0.379191i	−0.817324	−	0.576179i	$-0.804543\pi$
$863$	−15.3321	+	11.1394i	−0.521912	+	0.379191i	0.295412	+	0.955370i	$0.404543\pi$
$864$	−4.65523	−	8.84226i	−0.158374	−	0.300820i
$865$	−8.66108	−	26.6561i	−0.294485	−	0.906333i
$866$	21.8112	+	16.8254i	0.741176	+	0.571749i
$867$	−25.1427	+	34.6060i	−0.853892	+	1.17528i
$868$	−40.0824	+	48.9820i	−1.36048	+	1.66256i
$869$	−45.2067	−	11.0011i	−1.53353	−	0.373186i
$870$	−4.93293	−	1.76108i	−0.167242	−	0.0597064i
$871$	8.39829	−	3.65156i	0.284565	−	0.123728i
$872$	−4.73935	−	20.4317i	−0.160495	−	0.691903i
$873$	−20.7174	+	6.73150i	−0.701179	+	0.227827i
$874$	1.97104	+	6.71729i	0.0666713	+	0.227216i
$875$	36.0210	−	26.1708i	1.21773	−	0.884734i
$876$	−52.5450	−	20.4798i	−1.77533	−	0.691949i
$877$	−5.25375	+	16.1694i	−0.177407	+	0.546002i	−0.999735	−	0.0230114i	$-0.992675\pi$
$877$	−5.25375	+	16.1694i	−0.177407	+	0.546002i	0.822329	+	0.569013i	$0.192675\pi$
$878$	−3.00219	+	2.05203i	−0.101319	+	0.0692528i
$879$			42.0423i			1.41805i
$880$	−5.32547	−	18.9011i	−0.179522	−	0.637154i
$881$	17.6560			0.594846			0.297423	−	0.954746i	$-0.403873\pi$
$881$	17.6560			0.594846			0.297423	+	0.954746i	$0.403873\pi$
$882$	−33.7051	+	23.0379i	−1.13491	+	0.775727i
$883$	−43.2132	−	14.0408i	−1.45424	−	0.472512i	−0.527935	−	0.849285i	$-0.677034\pi$
$883$	−43.2132	−	14.0408i	−1.45424	−	0.472512i	−0.926306	+	0.376773i	$0.877034\pi$
$884$	3.81720	−	3.00444i	0.128386	−	0.101050i
$885$	20.7441	−	15.0715i	0.697306	−	0.506623i
$886$	32.8861	−	9.64968i	1.10483	−	0.324187i
$887$	12.3391	+	37.9758i	0.414305	+	1.27510i	0.912871	+	0.408249i	$0.133860\pi$
$887$	12.3391	+	37.9758i	0.414305	+	1.27510i	−0.498565	+	0.866852i	$0.666140\pi$
$888$	7.11363	+	30.6674i	0.238718	+	1.02913i
$889$	48.1848	−	66.3207i	1.61607	−	2.22433i
$890$	1.34376	−	3.76398i	0.0450430	−	0.126169i
$891$	13.9140	+	16.3935i	0.466135	+	0.549202i
$892$	41.1827	+	33.7001i	1.37890	+	1.12836i
$893$	2.64573	−	3.64154i	0.0885360	−	0.121859i
$894$	45.2132	−	58.6114i	1.51216	−	1.96026i
$895$	−5.99966	−	18.4650i	−0.200546	−	0.617219i
$896$	−8.70933	+	42.7009i	−0.290958	+	1.42654i
$897$	−5.22825	−	54.3044i	−0.174566	−	1.81317i
$898$	0.479251	−	16.6690i	0.0159928	−	0.556252i
$899$	7.56251	+	2.45721i	0.252224	+	0.0819524i
$900$	−5.25323	−	20.0152i	−0.175108	−	0.667172i
$901$		−	5.71584i		−	0.190422i
$902$	−4.06603	−	5.07959i	−0.135384	−	0.169132i
$903$	−54.4693			−1.81262
$904$	−39.2188	−	3.39022i	−1.30440	−	0.112757i
$905$	22.3832	+	7.27275i	0.744044	+	0.241754i
$906$	5.79948	+	0.166741i	0.192675	+	0.00553960i
$907$	22.6764	+	31.2114i	0.752958	+	1.03636i	0.997767	+	0.0667862i	$0.0212745\pi$
$907$	22.6764	+	31.2114i	0.752958	+	1.03636i	−0.244810	+	0.969571i	$0.578725\pi$
$908$	2.82930	−	49.1628i	0.0938935	−	1.63152i
$909$	−25.4600	+	8.27247i	−0.844456	+	0.274380i
$910$	26.9838	−	10.8214i	0.894505	−	0.358726i
$911$	−14.0615	+	19.3540i	−0.465877	+	0.641225i	−0.975715	−	0.219046i	$-0.929706\pi$
$911$	−14.0615	+	19.3540i	−0.465877	+	0.641225i	0.509837	+	0.860271i	$0.329706\pi$
$912$	1.73055	+	8.57285i	0.0573041	+	0.283875i
$913$	6.53703	+	4.03374i	0.216344	+	0.133497i
$914$	2.55846	−	7.16643i	0.0846262	−	0.237044i
$915$	−15.7133	+	21.6275i	−0.519465	+	0.714982i
$916$	−11.2870	−	17.5771i	−0.372933	−	0.580763i
$917$	69.9378	−	22.7242i	2.30955	−	0.750418i
$918$	−0.473835	−	1.61483i	−0.0156389	−	0.0532973i
$919$	2.76138	−	2.00626i	0.0910897	−	0.0661805i	−0.541308	−	0.840824i	$-0.682071\pi$
$919$	2.76138	−	2.00626i	0.0910897	−	0.0661805i	0.632398	+	0.774644i	$0.282071\pi$
$920$	−18.5100	−	16.0568i	−0.610255	−	0.529377i
$921$	−11.0091	+	33.8826i	−0.362763	+	1.11647i
$922$	11.5210	−	7.87477i	0.379424	−	0.259342i
$923$	−23.4581	+	39.8229i	−0.772133	+	1.31079i
$924$	1.18646	+	66.0442i	0.0390316	+	2.17269i
$925$			12.0941i			0.397651i
$926$	−14.7776	+	10.1007i	−0.485621	+	0.331928i
$927$	59.6118	+	19.3691i	1.95791	+	0.636164i
$928$	5.39587	−	0.928703i	0.177128	−	0.0304862i
$929$	−2.90068	−	3.99245i	−0.0951683	−	0.130988i	0.758777	−	0.651350i	$-0.225797\pi$
$929$	−2.90068	−	3.99245i	−0.0951683	−	0.130988i	−0.853946	+	0.520362i	$0.825797\pi$
$930$	−12.5178	−	42.6607i	−0.410476	−	1.39890i
$931$	6.30427	−	2.04838i	0.206614	−	0.0671330i
$932$	2.81467	+	4.38325i	0.0921977	+	0.143578i
$933$	−56.3841	−	40.9654i	−1.84593	−	1.34115i
$934$	14.9305	+	5.33028i	0.488541	+	0.174412i
$935$	−0.249280	−	3.29769i	−0.00815233	−	0.107846i
$936$	−0.366286	−	37.5608i	−0.0119724	−	1.22771i
$937$	3.06604	−	4.22005i	0.100163	−	0.137863i	−0.755993	−	0.654579i	$-0.772846\pi$
$937$	3.06604	−	4.22005i	0.100163	−	0.137863i	0.856157	+	0.516716i	$0.172846\pi$
$938$	−8.45105	+	10.9554i	−0.275937	+	0.357706i
$939$	−9.88125	+	3.21061i	−0.322462	+	0.104774i
$940$	−0.905226	+	15.7295i	−0.0295252	+	0.513039i
$941$	−21.9652	+	15.9587i	−0.716045	+	0.520237i	−0.885118	−	0.465366i	$-0.845923\pi$
$941$	−21.9652	+	15.9587i	−0.716045	+	0.520237i	0.169073	+	0.985604i	$0.445923\pi$
$942$	0.372713	−	12.9635i	0.0121437	−	0.422373i
$943$	−7.72174	−	2.50895i	−0.251454	−	0.0817025i
$944$	−11.1522	+	24.3727i	−0.362974	+	0.793265i
$945$		−	10.0720i		−	0.327641i
$946$	−14.0945	+	21.4374i	−0.458253	+	0.696989i
$947$	16.9142			0.549637			0.274819	−	0.961496i	$-0.411382\pi$
$947$	16.9142			0.549637			0.274819	+	0.961496i	$0.411382\pi$
$948$	−70.1552	+	18.4131i	−2.27854	+	0.598030i
$949$	−26.0583	−	29.4542i	−0.845887	−	0.956125i
$950$	−0.0965579	+	3.35842i	−0.00313275	+	0.108961i
$951$	10.6666	−	7.74972i	0.345887	−	0.251302i
$952$	−2.86072	+	6.75892i	−0.0927165	+	0.219058i
$953$	31.0283	−	10.0817i	1.00511	−	0.326579i	0.240202	−	0.970723i	$-0.422786\pi$
$953$	31.0283	−	10.0817i	1.00511	−	0.326579i	0.764904	+	0.644144i	$0.222786\pi$
$954$	−34.9954	−	26.9957i	−1.13302	−	0.874019i
$955$	14.2429	+	10.3481i	0.460890	+	0.334856i
$956$	−28.5290	+	34.8634i	−0.922693	+	1.12756i
$957$	7.67691	−	3.15212i	0.248159	−	0.101893i
$958$	−49.4063	−	17.6383i	−1.59624	−	0.569868i
$959$	47.7635	+	34.7022i	1.54236	+	1.12059i
$960$	−21.3111	−	21.9769i	−0.687813	−	0.709301i
$961$	11.2774	+	34.7083i	0.363787	+	1.11962i
$962$	−5.36586	+	21.2876i	−0.173002	+	0.686339i
$963$	34.8502	−	25.3202i	1.12303	−	0.815930i
$964$	1.25117	−	3.21013i	0.0402975	−	0.103391i
$965$	−0.112007	−	0.0363933i	−0.00360563	−	0.00117154i
$966$	46.5124	+	68.0489i	1.49651	+	2.18944i
$967$			48.9423i			1.57388i	0.617030	+	0.786939i	$0.288336\pi$
$967$			48.9423i			1.57388i	−0.617030	+	0.786939i	$0.711664\pi$
$968$	26.2999	+	16.6227i	0.845311	+	0.534275i
$969$			1.47289i			0.0473161i
$970$	−10.2207	+	6.98599i	−0.328167	+	0.224307i
$971$	−21.7513	−	7.06743i	−0.698033	−	0.226805i	−0.0615598	−	0.998103i	$-0.519607\pi$
$971$	−21.7513	−	7.06743i	−0.698033	−	0.226805i	−0.636473	+	0.771299i	$0.719607\pi$
$972$	41.1076	+	16.0220i	1.31853	+	0.513906i
$973$	−2.49229	−	3.43034i	−0.0798990	−	0.109972i
$974$	10.6382	+	36.2549i	0.340869	+	1.16168i
$975$	5.66741	−	25.5626i	0.181503	−	0.818657i
$976$	3.20575	−	27.7599i	0.102614	−	0.888571i
$977$	−6.87040	+	9.45629i	−0.219804	+	0.302534i	−0.904651	−	0.426153i	$-0.859869\pi$
$977$	−6.87040	+	9.45629i	−0.219804	+	0.302534i	0.684848	+	0.728686i	$0.259869\pi$
$978$	55.9090	+	19.9598i	1.78777	+	0.638245i
$979$	2.40516	+	5.85771i	0.0768692	+	0.187213i
$980$	−14.6940	+	17.9566i	−0.469383	+	0.573603i
$981$	−22.0971	−	16.0545i	−0.705505	−	0.512580i
$982$	−34.3653	−	26.5097i	−1.09664	−	0.845958i
$983$	−3.04797	−	9.38069i	−0.0972151	−	0.299197i	0.890610	−	0.454769i	$-0.150278\pi$
$983$	−3.04797	−	9.38069i	−0.0972151	−	0.299197i	−0.987825	+	0.155571i	$0.950278\pi$
$984$	−9.34104	−	3.95361i	−0.297782	−	0.126036i
$985$	−7.84554	−	10.7985i	−0.249980	−	0.344068i
$986$	0.921709	+	0.0265001i	0.0293532	+	0.000843934i
$987$	16.3774	−	50.4045i	0.521299	−	1.60439i
$988$	−1.66001	+	5.86853i	−0.0528120	+	0.186703i
$989$			32.0143i			1.01800i
$990$	−21.3675	−	14.0486i	−0.679105	−	0.446495i
$991$		−	3.29505i		−	0.104671i	−0.998630	−	0.0523354i	$-0.983334\pi$
$991$		−	3.29505i		−	0.104671i	0.998630	−	0.0523354i	$-0.0166665\pi$
$992$	33.2982	+	32.4199i	1.05722	+	1.02933i
$993$	58.0900	+	18.8746i	1.84343	+	0.598967i
$994$	2.00685	−	69.8010i	0.0636534	−	2.21395i
$995$	17.8777	−	12.9889i	0.566760	−	0.411775i
$996$	11.9551	+	0.688008i	0.378810	+	0.0218004i
$997$	3.34420	−	1.08659i	0.105912	−	0.0344128i	−0.255582	−	0.966787i	$-0.582267\pi$
$997$	3.34420	−	1.08659i	0.105912	−	0.0344128i	0.361493	+	0.932375i	$0.382267\pi$
$998$	18.1648	+	14.0124i	0.574996	+	0.443556i
$999$	6.15301	+	4.47042i	0.194672	+	0.141438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.b.51.17	✓	304
4.3	odd	2	inner	572.2.bb.b.51.46	yes	304
11.8	odd	10	inner	572.2.bb.b.415.31	yes	304
13.12	even	2	inner	572.2.bb.b.51.60	yes	304
44.19	even	10	inner	572.2.bb.b.415.60	yes	304
52.51	odd	2	inner	572.2.bb.b.51.31	yes	304
143.129	odd	10	inner	572.2.bb.b.415.46	yes	304
572.415	even	10	inner	572.2.bb.b.415.17	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.b.51.17	✓	304	1.1	even	1	trivial
572.2.bb.b.51.31	yes	304	52.51	odd	2	inner
572.2.bb.b.51.46	yes	304	4.3	odd	2	inner
572.2.bb.b.51.60	yes	304	13.12	even	2	inner
572.2.bb.b.415.17	yes	304	572.415	even	10	inner
572.2.bb.b.415.31	yes	304	11.8	odd	10	inner
572.2.bb.b.415.46	yes	304	143.129	odd	10	inner
572.2.bb.b.415.60	yes	304	44.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16754 + 0.798029i) q^{2} +(-2.45868 - 0.798874i) q^{3} +(0.726298 - 1.86346i) q^{4} +(-0.870035 - 1.19750i) q^{5} +(3.50813 - 1.02938i) q^{6} +(-3.66344 + 1.19032i) q^{7} +(0.639116 + 2.75527i) q^{8} +(2.97986 + 2.16500i) q^{9} +O(q^{10})\)	\(q+(-1.16754 + 0.798029i) q^{2} +(-2.45868 - 0.798874i) q^{3} +(0.726298 - 1.86346i) q^{4} +(-0.870035 - 1.19750i) q^{5} +(3.50813 - 1.02938i) q^{6} +(-3.66344 + 1.19032i) q^{7} +(0.639116 + 2.75527i) q^{8} +(2.97986 + 2.16500i) q^{9} +(1.97144 + 0.703816i) q^{10} +(-3.06807 + 1.25974i) q^{11} +(-3.27441 + 4.00144i) q^{12} +(-3.30652 + 1.43767i) q^{13} +(3.32730 - 4.31328i) q^{14} +(1.18249 + 3.63932i) q^{15} +(-2.94498 - 2.70686i) q^{16} +(-0.395960 - 0.544992i) q^{17} +(-5.20684 - 0.149702i) q^{18} +(0.804357 + 0.261351i) q^{19} +(-2.86340 + 0.751535i) q^{20} +9.95814 q^{21} +(2.57678 - 3.91921i) q^{22} -5.85290i q^{23} +(0.629734 - 7.28491i) q^{24} +(0.868038 - 2.67155i) q^{25} +(2.71320 - 4.31724i) q^{26} +(-1.03832 - 1.42913i) q^{27} +(-0.442626 + 7.69121i) q^{28} +(0.920517 - 0.299094i) q^{29} +(-4.28488 - 3.30539i) q^{30} +(6.64648 + 4.82895i) q^{31} +(5.59854 + 0.810182i) q^{32} +(8.54978 - 0.646298i) q^{33} +(0.897219 + 0.320312i) q^{34} +(4.61273 + 3.35135i) q^{35} +(6.19865 - 3.98043i) q^{36} +(-4.09470 + 1.33045i) q^{37} +(-1.14768 + 0.336762i) q^{38} +(9.27821 - 0.893274i) q^{39} +(2.74339 - 3.16253i) q^{40} +(0.428667 - 1.31930i) q^{41} +(-11.6265 + 7.94689i) q^{42} -5.46982 q^{43} +(0.119145 + 6.63218i) q^{44} -5.45201i q^{45} +(4.67079 + 6.83350i) q^{46} +(1.64463 - 5.06164i) q^{47} +(5.07833 + 9.00797i) q^{48} +(6.34079 - 4.60686i) q^{49} +(1.11850 + 3.81186i) q^{50} +(0.538159 + 1.65628i) q^{51} +(0.277520 + 7.20576i) q^{52} +(6.86444 + 4.98731i) q^{53} +(2.35277 + 0.839952i) q^{54} +(4.17787 + 2.57800i) q^{55} +(-5.62103 - 9.33302i) q^{56} +(-1.76887 - 1.28516i) q^{57} +(-0.836054 + 1.08380i) q^{58} +(-2.07065 - 6.37280i) q^{59} +(7.64057 + 0.439712i) q^{60} +(4.10632 + 5.65186i) q^{61} +(-11.6137 - 0.333905i) q^{62} +(-13.4936 - 4.38433i) q^{63} +(-7.18306 + 3.52188i) q^{64} +(4.59840 + 2.70874i) q^{65} +(-9.46644 + 7.57755i) q^{66} -2.53992 q^{67} +(-1.30316 + 0.342030i) q^{68} +(-4.67573 + 14.3904i) q^{69} +(-8.06002 - 0.231734i) q^{70} +(10.3705 - 7.53463i) q^{71} +(-4.06068 + 9.59401i) q^{72} +(3.37053 + 10.3734i) q^{73} +(3.71899 - 4.82105i) q^{74} +(-4.26846 + 5.87503i) q^{75} +(1.07122 - 1.30907i) q^{76} +(9.74019 - 8.26698i) q^{77} +(-10.1198 + 8.44721i) q^{78} +(11.3490 + 8.24553i) q^{79} +(-0.679226 + 5.88168i) q^{80} +(-2.00341 - 6.16585i) q^{81} +(0.552355 + 1.88242i) q^{82} +(-1.36133 - 1.87371i) q^{83} +(7.23258 - 18.5566i) q^{84} +(-0.308129 + 0.948325i) q^{85} +(6.38623 - 4.36508i) q^{86} -2.50220 q^{87} +(-5.43178 - 7.64825i) q^{88} -1.90925i q^{89} +(4.35086 + 6.36543i) q^{90} +(10.4020 - 9.20265i) q^{91} +(-10.9067 - 4.25095i) q^{92} +(-12.4838 - 17.1825i) q^{93} +(2.11917 + 7.22212i) q^{94} +(-0.386850 - 1.19060i) q^{95} +(-13.1178 - 6.46450i) q^{96} +(-3.47624 + 4.78464i) q^{97} +(-3.72672 + 10.4388i) q^{98} +(-11.8698 - 2.88851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) \) 304 * q - 14 * q^4 + 72 * q^9	\( 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) \) 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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