LMFDB - Embedded newform 507.2.k.k.488.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.19
Character	$\chi$	$=$	507.488
Dual form			507.2.k.k.80.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.506604 + 1.89067i) q^{2} +(-1.69226 - 0.369140i) q^{3} +(-1.58594 + 0.915644i) q^{4} +(-1.04664 + 1.04664i) q^{5} +(-0.159382 - 3.38651i) q^{6} +(4.33161 + 1.16065i) q^{7} +(0.233508 + 0.233508i) q^{8} +(2.72747 + 1.24936i) q^{9} +O(q^{10})$	\(q+(0.506604 + 1.89067i) q^{2} +(-1.69226 - 0.369140i) q^{3} +(-1.58594 + 0.915644i) q^{4} +(-1.04664 + 1.04664i) q^{5} +(-0.159382 - 3.38651i) q^{6} +(4.33161 + 1.16065i) q^{7} +(0.233508 + 0.233508i) q^{8} +(2.72747 + 1.24936i) q^{9} +(-2.50908 - 1.44862i) q^{10} +(0.147979 - 0.0396510i) q^{11} +(3.02182 - 0.964071i) q^{12} +8.77764i q^{14} +(2.15754 - 1.38483i) q^{15} +(-2.15448 + 3.73167i) q^{16} +(-1.58364 - 2.74294i) q^{17} +(-0.980382 + 5.78968i) q^{18} +(-0.309737 + 1.15595i) q^{19} +(0.701560 - 2.61826i) q^{20} +(-6.90175 - 3.56309i) q^{21} +(0.149934 + 0.259693i) q^{22} +(-3.35135 + 5.80471i) q^{23} +(-0.308959 - 0.481353i) q^{24} +2.80909i q^{25} +(-4.15440 - 3.12106i) q^{27} +(-7.93243 + 2.12549i) q^{28} +(1.71915 + 0.992552i) q^{29} +(3.71127 + 3.37764i) q^{30} +(-3.64859 - 3.64859i) q^{31} +(-7.50887 - 2.01200i) q^{32} +(-0.265056 + 0.0124745i) q^{33} +(4.38372 - 4.38372i) q^{34} +(-5.74841 + 3.31885i) q^{35} +(-5.46958 + 0.515981i) q^{36} +(-0.847303 - 3.16218i) q^{37} -2.34244 q^{38} -0.488797 q^{40} +(2.16637 + 8.08500i) q^{41} +(3.24018 - 14.8540i) q^{42} +(2.41031 - 1.39159i) q^{43} +(-0.198381 + 0.198381i) q^{44} +(-4.16231 + 1.54705i) q^{45} +(-12.6726 - 3.39562i) q^{46} +(4.06533 + 4.06533i) q^{47} +(5.02344 - 5.51964i) q^{48} +(11.3535 + 6.55497i) q^{49} +(-5.31107 + 1.42310i) q^{50} +(1.66739 + 5.22634i) q^{51} -0.628103i q^{53} +(3.79626 - 9.43574i) q^{54} +(-0.113381 + 0.196381i) q^{55} +(0.740444 + 1.28249i) q^{56} +(0.950863 - 1.84183i) q^{57} +(-1.00566 + 3.75318i) q^{58} +(2.27275 - 8.48202i) q^{59} +(-2.15372 + 4.17179i) q^{60} +(-2.91632 - 5.05121i) q^{61} +(5.04989 - 8.74667i) q^{62} +(10.3643 + 8.57738i) q^{63} -6.59818i q^{64} +(-0.157864 - 0.494815i) q^{66} +(0.649609 - 0.174062i) q^{67} +(5.02311 + 2.90010i) q^{68} +(7.81410 - 8.58595i) q^{69} +(-9.18702 - 9.18702i) q^{70} +(11.0529 + 2.96161i) q^{71} +(0.345151 + 0.928622i) q^{72} +(3.92370 - 3.92370i) q^{73} +(5.54940 - 3.20395i) q^{74} +(1.03695 - 4.75371i) q^{75} +(-0.567217 - 2.11688i) q^{76} +0.687010 q^{77} -5.46386 q^{79} +(-1.65075 - 6.16067i) q^{80} +(5.87820 + 6.81519i) q^{81} +(-14.1886 + 8.19178i) q^{82} +(6.40765 - 6.40765i) q^{83} +(14.2083 - 0.668696i) q^{84} +(4.52836 + 1.21337i) q^{85} +(3.85212 + 3.85212i) q^{86} +(-2.54285 - 2.31426i) q^{87} +(0.0438132 + 0.0252956i) q^{88} +(5.12896 - 1.37430i) q^{89} +(-5.03360 - 7.08582i) q^{90} -12.2746i q^{92} +(4.82751 + 7.52119i) q^{93} +(-5.62670 + 9.74572i) q^{94} +(-0.885683 - 1.53405i) q^{95} +(11.9642 + 6.17664i) q^{96} +(-1.15826 + 4.32269i) q^{97} +(-6.64155 + 24.7866i) q^{98} +(0.453148 + 0.0767327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9}+O(q^{10}) $ 96 * q + 24 * q^9	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.506604	+	1.89067i	0.358223	+	1.33691i	0.876380	+	0.481621i	$0.159952\pi$
$2$	0.506604	+	1.89067i	0.358223	+	1.33691i	−0.518156	+	0.855286i	$0.673381\pi$
$3$	−1.69226	−	0.369140i	−0.977025	−	0.213123i
$3$	−1.69226	−	0.369140i	−0.977025	−	0.213123i
$4$	−1.58594	+	0.915644i	−0.792971	+	0.457822i
$5$	−1.04664	+	1.04664i	−0.468071	+	0.468071i	−0.901289	−	0.433218i	$-0.857378\pi$
$5$	−1.04664	+	1.04664i	−0.468071	+	0.468071i	0.433218	+	0.901289i	$0.357378\pi$
$6$	−0.159382	−	3.38651i	−0.0650674	−	1.38254i
$7$	4.33161	+	1.16065i	1.63719	+	0.438685i	0.955988	−	0.293407i	$-0.0947890\pi$
$7$	4.33161	+	1.16065i	1.63719	+	0.438685i	0.681206	+	0.732091i	$0.261456\pi$
$8$	0.233508	+	0.233508i	0.0825576	+	0.0825576i
$9$	2.72747	+	1.24936i	0.909157	+	0.416453i
$10$	−2.50908	−	1.44862i	−0.793442	−	0.458094i
$11$	0.147979	−	0.0396510i	0.0446175	−	0.0119552i	−0.236441	−	0.971646i	$-0.575981\pi$
$11$	0.147979	−	0.0396510i	0.0446175	−	0.0119552i	0.281059	+	0.959691i	$0.409314\pi$
$12$	3.02182	−	0.964071i	0.872325	−	0.278303i
$13$		0			0
$13$		0			0
$14$			8.77764i			2.34592i
$15$	2.15754	−	1.38483i	0.557074	−	0.357561i
$16$	−2.15448	+	3.73167i	−0.538620	+	0.932917i
$17$	−1.58364	−	2.74294i	−0.384088	−	0.665261i	0.607554	−	0.794278i	$-0.292151\pi$
$17$	−1.58364	−	2.74294i	−0.384088	−	0.665261i	−0.991642	+	0.129018i	$0.958818\pi$
$18$	−0.980382	+	5.78968i	−0.231078	+	1.36464i
$19$	−0.309737	+	1.15595i	−0.0710585	+	0.265194i	−0.992311	−	0.123772i	$-0.960501\pi$
$19$	−0.309737	+	1.15595i	−0.0710585	+	0.265194i	0.921252	+	0.388966i	$0.127168\pi$
$20$	0.701560	−	2.61826i	0.156874	−	0.585460i
$21$	−6.90175	−	3.56309i	−1.50609	−	0.777530i
$22$	0.149934	+	0.259693i	0.0319660	+	0.0553668i
$23$	−3.35135	+	5.80471i	−0.698805	+	1.21037i	0.270076	+	0.962839i	$0.412951\pi$
$23$	−3.35135	+	5.80471i	−0.698805	+	1.21037i	−0.968881	+	0.247527i	$0.920382\pi$
$24$	−0.308959	−	0.481353i	−0.0630659	−	0.0982558i
$25$			2.80909i			0.561819i
$26$		0			0
$27$	−4.15440	−	3.12106i	−0.799514	−	0.600648i
$28$	−7.93243	+	2.12549i	−1.49909	+	0.401679i
$29$	1.71915	+	0.992552i	0.319238	+	0.184312i	0.651053	−	0.759032i	$-0.274328\pi$
$29$	1.71915	+	0.992552i	0.319238	+	0.184312i	−0.331815	+	0.943345i	$0.607661\pi$
$30$	3.71127	+	3.37764i	0.677582	+	0.616670i
$31$	−3.64859	−	3.64859i	−0.655306	−	0.655306i	0.298960	−	0.954266i	$-0.403360\pi$
$31$	−3.64859	−	3.64859i	−0.655306	−	0.655306i	−0.954266	+	0.298960i	$0.903360\pi$
$32$	−7.50887	−	2.01200i	−1.32739	−	0.355674i
$33$	−0.265056	+	0.0124745i	−0.0461404	+	0.00217154i
$34$	4.38372	−	4.38372i	0.751802	−	0.751802i
$35$	−5.74841	+	3.31885i	−0.971659	+	0.560988i
$36$	−5.46958	+	0.515981i	−0.911597	+	0.0859968i
$37$	−0.847303	−	3.16218i	−0.139296	−	0.519859i	−0.999943	−	0.0106576i	$-0.996608\pi$
$37$	−0.847303	−	3.16218i	−0.139296	−	0.519859i	0.860647	−	0.509201i	$-0.170059\pi$
$38$	−2.34244			−0.379994
$39$		0			0
$40$	−0.488797			−0.0772856
$41$	2.16637	+	8.08500i	0.338330	+	1.26266i	0.900214	+	0.435448i	$0.143410\pi$
$41$	2.16637	+	8.08500i	0.338330	+	1.26266i	−0.561884	+	0.827216i	$0.689923\pi$
$42$	3.24018	−	14.8540i	0.499970	−	2.29203i
$43$	2.41031	−	1.39159i	0.367568	−	0.212216i	−0.304827	−	0.952408i	$-0.598599\pi$
$43$	2.41031	−	1.39159i	0.367568	−	0.212216i	0.672396	+	0.740192i	$0.265265\pi$
$44$	−0.198381	+	0.198381i	−0.0299070	+	0.0299070i
$45$	−4.16231	+	1.54705i	−0.620480	+	0.230620i
$46$	−12.6726	−	3.39562i	−1.86848	−	0.500657i
$47$	4.06533	+	4.06533i	0.592990	+	0.592990i	0.938438	−	0.345448i	$-0.112273\pi$
$47$	4.06533	+	4.06533i	0.592990	+	0.592990i	−0.345448	+	0.938438i	$0.612273\pi$
$48$	5.02344	−	5.51964i	0.725071	−	0.796691i
$49$	11.3535	+	6.55497i	1.62193	+	0.936424i
$50$	−5.31107	+	1.42310i	−0.751099	+	0.201256i
$51$	1.66739	+	5.22634i	0.233482	+	0.731835i
$52$		0			0
$53$		−	0.628103i		−	0.0862766i	−0.999069	−	0.0431383i	$-0.986264\pi$
$53$		−	0.628103i		−	0.0862766i	0.999069	−	0.0431383i	$-0.0137356\pi$
$54$	3.79626	−	9.43574i	0.516606	−	1.28404i
$55$	−0.113381	+	0.196381i	−0.0152883	+	0.0264801i
$56$	0.740444	+	1.28249i	0.0989460	+	0.171380i
$57$	0.950863	−	1.84183i	0.125945	−	0.243957i
$58$	−1.00566	+	3.75318i	−0.132050	+	0.492817i
$59$	2.27275	−	8.48202i	0.295887	−	1.10426i	−0.644624	−	0.764500i	$-0.722986\pi$
$59$	2.27275	−	8.48202i	0.295887	−	1.10426i	0.940511	−	0.339764i	$-0.110347\pi$
$60$	−2.15372	+	4.17179i	−0.278045	+	0.538576i
$61$	−2.91632	−	5.05121i	−0.373396	−	0.646741i	0.616690	−	0.787206i	$-0.288473\pi$
$61$	−2.91632	−	5.05121i	−0.373396	−	0.646741i	−0.990086	+	0.140466i	$0.955140\pi$
$62$	5.04989	−	8.74667i	0.641337	−	1.11083i
$63$	10.3643	+	8.57738i	1.30577	+	1.08065i
$64$		−	6.59818i		−	0.824773i
$65$		0			0
$66$	−0.157864	−	0.494815i	−0.0194317	−	0.0609075i
$67$	0.649609	−	0.174062i	0.0793624	−	0.0212651i	−0.218919	−	0.975743i	$-0.570253\pi$
$67$	0.649609	−	0.174062i	0.0793624	−	0.0212651i	0.298282	+	0.954478i	$0.403587\pi$
$68$	5.02311	+	2.90010i	0.609142	+	0.351688i
$69$	7.81410	−	8.58595i	0.940708	−	1.03363i
$70$	−9.18702	−	9.18702i	−1.09806	−	1.09806i
$71$	11.0529	+	2.96161i	1.31174	+	0.351478i	0.845876	−	0.533380i	$-0.179079\pi$
$71$	11.0529	+	2.96161i	1.31174	+	0.351478i	0.465860	+	0.884859i	$0.345745\pi$
$72$	0.345151	+	0.928622i	0.0406764	+	0.109439i
$73$	3.92370	−	3.92370i	0.459235	−	0.459235i	−0.439169	−	0.898404i	$-0.644727\pi$
$73$	3.92370	−	3.92370i	0.459235	−	0.459235i	0.898404	+	0.439169i	$0.144727\pi$
$74$	5.54940	−	3.20395i	0.645104	−	0.372451i
$75$	1.03695	−	4.75371i	0.119737	−	0.548911i
$76$	−0.567217	−	2.11688i	−0.0650643	−	0.242823i
$77$	0.687010			0.0782921
$78$		0			0
$79$	−5.46386			−0.614733			−0.307366	−	0.951591i	$-0.599448\pi$
$79$	−5.46386			−0.614733			−0.307366	+	0.951591i	$0.599448\pi$
$80$	−1.65075	−	6.16067i	−0.184559	−	0.688784i
$81$	5.87820	+	6.81519i	0.653133	+	0.757243i
$82$	−14.1886	+	8.19178i	−1.56687	+	0.904631i
$83$	6.40765	−	6.40765i	0.703331	−	0.703331i	−0.261793	−	0.965124i	$-0.584314\pi$
$83$	6.40765	−	6.40765i	0.703331	−	0.703331i	0.965124	+	0.261793i	$0.0843139\pi$
$84$	14.2083	−	0.668696i	1.55025	−	0.0729607i
$85$	4.52836	+	1.21337i	0.491170	+	0.131609i
$86$	3.85212	+	3.85212i	0.415384	+	0.415384i
$87$	−2.54285	−	2.31426i	−0.272623	−	0.248115i
$88$	0.0438132	+	0.0252956i	0.00467051	+	0.00269652i
$89$	5.12896	−	1.37430i	0.543668	−	0.145676i	0.0234757	−	0.999724i	$-0.492527\pi$
$89$	5.12896	−	1.37430i	0.543668	−	0.145676i	0.520193	+	0.854049i	$0.325860\pi$
$90$	−5.03360	−	7.08582i	−0.530588	−	0.746911i
$91$		0			0
$92$		−	12.2746i		−	1.27971i
$93$	4.82751	+	7.52119i	0.500589	+	0.779911i
$94$	−5.62670	+	9.74572i	−0.580349	+	1.00519i
$95$	−0.885683	−	1.53405i	−0.0908692	−	0.157390i
$96$	11.9642	+	6.17664i	1.22110	+	0.630401i
$97$	−1.15826	+	4.32269i	−0.117604	+	0.438902i	−0.999468	−	0.0325997i	$-0.989621\pi$
$97$	−1.15826	+	4.32269i	−0.117604	+	0.438902i	0.881865	+	0.471502i	$0.156288\pi$
$98$	−6.64155	+	24.7866i	−0.670898	+	2.50382i
$99$	0.453148	+	0.0767327i	0.0455431	+	0.00771193i
$100$	−2.57213	−	4.45506i	−0.257213	−	0.445506i
$101$	−0.840488	+	1.45577i	−0.0836317	+	0.144854i	−0.904807	−	0.425821i	$-0.859985\pi$
$101$	−0.840488	+	1.45577i	−0.0836317	+	0.144854i	0.821176	+	0.570676i	$0.193319\pi$
$102$	−9.03660	+	5.80018i	−0.894756	+	0.574304i
$103$		−	4.41524i		−	0.435046i	−0.976055	−	0.217523i	$-0.930202\pi$
$103$		−	4.41524i		−	0.435046i	0.976055	−	0.217523i	$-0.0697977\pi$
$104$		0			0
$105$	10.9529	−	3.49438i	1.06890	−	0.341016i
$106$	1.18754	−	0.318199i	0.115344	−	0.0309063i
$107$	−13.4040	−	7.73882i	−1.29582	−	0.748140i	−0.316137	−	0.948714i	$-0.602386\pi$
$107$	−13.4040	−	7.73882i	−1.29582	−	0.748140i	−0.979679	+	0.200574i	$0.935719\pi$
$108$	9.44641	+	1.14587i	0.908981	+	0.110261i
$109$	8.78130	+	8.78130i	0.841096	+	0.841096i	0.989002	−	0.147905i	$-0.0472531\pi$
$109$	8.78130	+	8.78130i	0.841096	+	0.841096i	−0.147905	+	0.989002i	$0.547253\pi$
$110$	−0.428732	−	0.114878i	−0.0408780	−	0.0109532i
$111$	0.266569	+	5.66399i	0.0253016	+	0.537603i
$112$	−13.6635	+	13.6635i	−1.29108	+	1.29108i
$113$	−4.14900	+	2.39543i	−0.390305	+	0.225343i	−0.682292	−	0.731080i	$-0.739017\pi$
$113$	−4.14900	+	2.39543i	−0.390305	+	0.225343i	0.291987	+	0.956422i	$0.405684\pi$
$114$	3.96401	+	0.864689i	0.371264	+	0.0809855i
$115$	−2.56778	−	9.58310i	−0.239447	−	0.893628i
$116$	−3.63530			−0.337529
$117$		0			0
$118$	17.1881			1.58229
$119$	−3.67610	−	13.7194i	−0.336988	−	1.25765i
$120$	0.827171	+	0.180435i	0.0755100	+	0.0164714i
$121$	−9.50595	+	5.48826i	−0.864178	+	0.498933i
$122$	8.07276	−	8.07276i	0.730873	−	0.730873i
$123$	−0.681558	−	14.4816i	−0.0614540	−	1.30576i
$124$	9.12726	+	2.44564i	0.819652	+	0.219625i
$125$	−8.17330	−	8.17330i	−0.731042	−	0.731042i
$126$	−10.9664	+	23.9408i	−0.976967	+	2.13281i
$127$	−13.8352	−	7.98773i	−1.22767	−	0.708796i	−0.261129	−	0.965304i	$-0.584095\pi$
$127$	−13.8352	−	7.98773i	−1.22767	−	0.708796i	−0.966542	+	0.256508i	$0.917428\pi$
$128$	−2.54274	+	0.681326i	−0.224749	+	0.0602213i
$129$	−4.59255	+	1.46519i	−0.404352	+	0.129003i
$130$		0			0
$131$		−	18.7681i		−	1.63978i	−0.572524	−	0.819888i	$-0.694035\pi$
$131$		−	18.7681i		−	1.63978i	0.572524	−	0.819888i	$-0.305965\pi$
$132$	0.408942	−	0.262481i	0.0355938	−	0.0228460i
$133$	−2.68332	+	4.64764i	−0.232673	+	0.403001i
$134$	0.658189	+	1.14002i	0.0568589	+	0.0984825i
$135$	7.61477	−	1.08153i	0.655375	−	0.0930835i
$136$	0.270707	−	1.01029i	0.0232129	−	0.0866317i
$137$	1.53306	−	5.72145i	0.130978	−	0.488816i	−0.869004	−	0.494805i	$-0.835240\pi$
$137$	1.53306	−	5.72145i	0.130978	−	0.488816i	0.999982	+	0.00598848i	$0.00190620\pi$
$138$	20.1919	+	10.4242i	1.71885	+	0.887369i
$139$	7.48488	+	12.9642i	0.634859	+	1.09961i	0.986545	+	0.163490i	$0.0522753\pi$
$139$	7.48488	+	12.9642i	0.634859	+	1.09961i	−0.351686	+	0.936118i	$0.614391\pi$
$140$	6.07777	−	10.5270i	0.513665	−	0.889694i
$141$	−5.37891	−	8.38026i	−0.452986	−	0.705746i
$142$			22.3977i			1.87958i
$143$		0			0
$144$	−10.5385	+	7.48630i	−0.878206	+	0.623858i
$145$	−2.83817	+	0.760486i	−0.235697	+	0.0631549i
$146$	9.40620	+	5.43067i	0.778463	+	0.449446i
$147$	−16.7934	−	15.2837i	−1.38510	−	1.26058i
$148$	4.23920	+	4.23920i	0.348460	+	0.348460i
$149$	17.0119	+	4.55833i	1.39367	+	0.373433i	0.876067	−	0.482189i	$-0.160158\pi$
$149$	17.0119	+	4.55833i	1.39367	+	0.373433i	0.517602	+	0.855621i	$0.326825\pi$
$150$	9.51303	−	0.447719i	0.776735	−	0.0365561i
$151$	7.85127	−	7.85127i	0.638928	−	0.638928i	−0.311363	−	0.950291i	$-0.600786\pi$
$151$	7.85127	−	7.85127i	0.638928	−	0.638928i	0.950291	+	0.311363i	$0.100786\pi$
$152$	−0.342250	+	0.197598i	−0.0277602	+	0.0160273i
$153$	−0.892406	−	9.45982i	−0.0721468	−	0.764781i
$154$	0.348042	+	1.29891i	0.0280460	+	0.104669i
$155$	7.63751			0.613459
$156$		0			0
$157$	10.4654			0.835227			0.417614	−	0.908625i	$-0.362867\pi$
$157$	10.4654			0.835227			0.417614	+	0.908625i	$0.362867\pi$
$158$	−2.76802	−	10.3304i	−0.220211	−	0.821840i
$159$	−0.231858	+	1.06291i	−0.0183875	+	0.0842944i
$160$	9.96491	−	5.75325i	0.787796	−	0.454834i
$161$	−21.2540	+	21.2540i	−1.67505	+	1.67505i
$162$	−9.90736	+	14.5663i	−0.778396	+	1.14444i
$163$	−1.87301	−	0.501872i	−0.146706	−	0.0393097i	0.184719	−	0.982791i	$-0.440863\pi$
$163$	−1.87301	−	0.501872i	−0.146706	−	0.0393097i	−0.331425	+	0.943482i	$0.607529\pi$
$164$	−10.8387	−	10.8387i	−0.846362	−	0.846362i
$165$	0.264362	−	0.290474i	0.0205805	−	0.0226134i
$166$	15.3609	+	8.86862i	1.19224	+	0.688338i
$167$	13.5058	−	3.61887i	1.04511	−	0.280037i	0.304882	−	0.952390i	$-0.401383\pi$
$167$	13.5058	−	3.61887i	1.04511	−	0.280037i	0.740230	+	0.672353i	$0.234716\pi$
$168$	−0.779605	−	2.44363i	−0.0601478	−	0.188530i
$169$		0			0
$170$			9.17635i			0.703794i
$171$	−2.28900	+	2.76586i	−0.175044	+	0.211510i
$172$	−2.54841	+	4.41397i	−0.194314	+	0.336562i
$173$	8.97651	+	15.5478i	0.682471	+	1.18207i	0.974224	+	0.225581i	$0.0724281\pi$
$173$	8.97651	+	15.5478i	0.682471	+	1.18207i	−0.291753	+	0.956494i	$0.594239\pi$
$174$	3.08729	−	5.98012i	0.234047	−	0.453351i
$175$	−3.26038	+	12.1679i	−0.246461	+	0.919806i
$176$	−0.170854	+	0.637638i	−0.0128786	+	0.0480637i
$177$	−6.97713	+	13.5148i	−0.524433	+	1.01583i
$178$	5.19670	+	9.00095i	0.389509	+	0.674650i
$179$	0.883597	−	1.53044i	0.0660431	−	0.114390i	−0.831113	−	0.556103i	$-0.812296\pi$
$179$	0.883597	−	1.53044i	0.0660431	−	0.114390i	0.897156	+	0.441713i	$0.145629\pi$
$180$	5.18463	−	6.26472i	0.386440	−	0.466945i
$181$		−	16.9949i		−	1.26322i	−0.775286	−	0.631611i	$-0.782394\pi$
$181$		−	16.9949i		−	1.26322i	0.775286	−	0.631611i	$-0.217606\pi$
$182$		0			0
$183$	3.07055	+	9.62447i	0.226982	+	0.711461i
$184$	−2.13802	+	0.572879i	−0.157617	+	0.0422332i
$185$	4.19648	+	2.42284i	0.308531	+	0.178131i
$186$	−11.7745	+	12.9375i	−0.863346	+	0.948624i
$187$	−0.343106	−	0.343106i	−0.0250904	−	0.0250904i
$188$	−10.1698	−	2.72498i	−0.741707	−	0.198740i
$189$	−14.3728	−	18.3410i	−1.04546	−	1.33411i
$190$	2.45169	−	2.45169i	0.177864	−	0.177864i
$191$	19.3783	−	11.1881i	1.40216	−	0.809539i	0.407549	−	0.913183i	$-0.366384\pi$
$191$	19.3783	−	11.1881i	1.40216	−	0.809539i	0.994614	+	0.103644i	$0.0330503\pi$
$192$	−2.43565	+	11.1658i	−0.175778	+	0.805824i
$193$	5.10117	+	19.0378i	0.367190	+	1.37037i	0.864427	+	0.502758i	$0.167681\pi$
$193$	5.10117	+	19.0378i	0.367190	+	1.37037i	−0.497237	+	0.867615i	$0.665652\pi$
$194$	−8.75956			−0.628900
$195$		0			0
$196$	−24.0081			−1.71486
$197$	0.385339	+	1.43810i	0.0274542	+	0.102461i	0.978293	−	0.207224i	$-0.0664430\pi$
$197$	0.385339	+	1.43810i	0.0274542	+	0.102461i	−0.950839	+	0.309685i	$0.899776\pi$
$198$	0.0844903	+	0.895628i	0.00600447	+	0.0636495i
$199$	17.0413	−	9.83880i	1.20803	−	0.697454i	0.245698	−	0.969346i	$-0.420983\pi$
$199$	17.0413	−	9.83880i	1.20803	−	0.697454i	0.962328	+	0.271892i	$0.0876494\pi$
$200$	−0.655946	+	0.655946i	−0.0463824	+	0.0463824i
$201$	−1.16356	+	0.0547614i	−0.0820711	+	0.00386257i
$202$	−3.17818	−	0.851590i	−0.223616	−	0.0599176i
$203$	6.29468	+	6.29468i	0.441800	+	0.441800i
$204$	−7.42986	−	6.76194i	−0.520194	−	0.473431i
$205$	−10.7295	−	6.19467i	−0.749379	−	0.432654i
$206$	8.34776	−	2.23678i	0.581616	−	0.155844i
$207$	−16.3929	+	11.6451i	−1.13938	+	0.809393i
$208$		0			0
$209$			0.183339i			0.0126818i
$210$	12.1555	+	18.9381i	0.838810	+	1.30685i
$211$	11.7945	−	20.4287i	0.811969	−	1.40637i	−0.0995149	−	0.995036i	$-0.531729\pi$
$211$	11.7945	−	20.4287i	0.811969	−	1.40637i	0.911484	−	0.411336i	$-0.134938\pi$
$212$	0.575119	+	0.996135i	0.0394993	+	0.0684148i
$213$	−17.6111	−	9.09186i	−1.20669	−	0.622964i
$214$	7.84103	−	29.2631i	0.536002	−	2.00039i
$215$	−1.06623	+	3.97922i	−0.0727161	+	0.271380i
$216$	−0.241293	−	1.69888i	−0.0164179	−	0.115594i
$217$	−11.5695	−	20.0390i	−0.785390	−	1.36034i
$218$	−12.1539	+	21.0512i	−0.823167	+	1.42577i
$219$	−8.08831	+	5.19152i	−0.546558	+	0.350811i
$220$		−	0.415266i		−	0.0279972i
$221$		0			0
$222$	−10.5737	+	3.37340i	−0.709661	+	0.226408i
$223$	−12.1848	+	3.26491i	−0.815955	+	0.218635i	−0.642577	−	0.766221i	$-0.722135\pi$
$223$	−12.1848	+	3.26491i	−0.815955	+	0.218635i	−0.173378	+	0.984855i	$0.555468\pi$
$224$	−30.1903	−	17.4304i	−2.01717	−	1.16462i
$225$	−3.50957	+	7.66172i	−0.233971	+	0.510781i
$226$	−6.63086	−	6.63086i	−0.441079	−	0.441079i
$227$	−21.4595	−	5.75004i	−1.42431	−	0.381644i	−0.537302	−	0.843390i	$-0.680556\pi$
$227$	−21.4595	−	5.75004i	−1.42431	−	0.381644i	−0.887012	+	0.461746i	$0.847223\pi$
$228$	0.178451	+	3.79169i	0.0118182	+	0.251111i
$229$	7.05247	−	7.05247i	0.466040	−	0.466040i	−0.434589	−	0.900629i	$-0.643106\pi$
$229$	7.05247	−	7.05247i	0.466040	−	0.466040i	0.900629	+	0.434589i	$0.143106\pi$
$230$	16.8176	−	9.70967i	1.10892	−	0.640237i
$231$	−1.16260	−	0.253603i	−0.0764933	−	0.0166858i
$232$	0.169667	+	0.633204i	0.0111392	+	0.0415719i
$233$	22.9574			1.50399			0.751996	−	0.659168i	$-0.229091\pi$
$233$	22.9574			1.50399			0.751996	+	0.659168i	$0.229091\pi$
$234$		0			0
$235$	−8.50987			−0.555123
$236$	4.16206	+	15.5330i	0.270927	+	1.01111i
$237$	9.24626	+	2.01693i	0.600609	+	0.131014i
$238$	24.0765	−	13.9006i	1.56065	−	0.901042i
$239$	12.6819	−	12.6819i	0.820323	−	0.820323i	−0.165831	−	0.986154i	$-0.553031\pi$
$239$	12.6819	−	12.6819i	0.820323	−	0.820323i	0.986154	+	0.165831i	$0.0530305\pi$
$240$	0.519339	+	11.0348i	0.0335232	+	0.712293i
$241$	−2.72664	−	0.730600i	−0.175638	−	0.0470621i	0.169928	−	0.985456i	$-0.445646\pi$
$241$	−2.72664	−	0.730600i	−0.175638	−	0.0470621i	−0.345566	+	0.938394i	$0.612313\pi$
$242$	−15.1923	−	15.1923i	−0.976596	−	0.976596i
$243$	−7.43167	−	13.7029i	−0.476742	−	0.879043i
$244$	9.25022	+	5.34062i	0.592184	+	0.341898i
$245$	−18.7438	+	5.02237i	−1.19749	+	0.320868i
$246$	27.0347	−	8.62503i	1.72367	−	0.549912i
$247$		0			0
$248$		−	1.70395i		−	0.108201i
$249$	−13.2087	+	8.47807i	−0.837068	+	0.537276i
$250$	11.3124	−	19.5937i	0.715459	−	1.23921i
$251$	−8.59659	−	14.8897i	−0.542612	−	0.939831i	−0.998753	−	0.0499239i	$-0.984102\pi$
$251$	−8.59659	−	14.8897i	−0.542612	−	0.939831i	0.456141	−	0.889907i	$-0.349231\pi$
$252$	−24.2910	−	4.11325i	−1.53019	−	0.259110i
$253$	−0.265769	+	0.991863i	−0.0167087	+	0.0623579i
$254$	8.09323	−	30.2044i	0.507815	−	1.89519i
$255$	−7.21526	−	3.72494i	−0.451837	−	0.233265i
$256$	−9.17451	−	15.8907i	−0.573407	−	0.993170i
$257$	−4.75399	+	8.23416i	−0.296546	+	0.513633i	−0.975343	−	0.220693i	$-0.929168\pi$
$257$	−4.75399	+	8.23416i	−0.296546	+	0.513633i	0.678797	+	0.734326i	$0.262501\pi$
$258$	−5.09680	−	7.94074i	−0.317313	−	0.494369i
$259$		−	14.6807i		−	0.912217i
$260$		0			0
$261$	3.44888	+	4.85499i	0.213480	+	0.300517i
$262$	35.4843	−	9.50800i	2.19223	−	0.587406i
$263$	6.27819	+	3.62472i	0.387130	+	0.223510i	0.680916	−	0.732362i	$-0.261582\pi$
$263$	6.27819	+	3.62472i	0.387130	+	0.223510i	−0.293786	+	0.955871i	$0.594915\pi$
$264$	−0.0648057	−	0.0589798i	−0.00398851	−	0.00362996i
$265$	0.657397	+	0.657397i	0.0403836	+	0.0403836i
$266$	−10.1465	−	2.71876i	−0.622124	−	0.166698i
$267$	−9.18683	+	0.432366i	−0.562225	+	0.0264604i
$268$	−0.870863	+	0.870863i	−0.0531964	+	0.0531964i
$269$	−23.1903	+	13.3890i	−1.41394	+	0.816339i	−0.995757	−	0.0920235i	$-0.970666\pi$
$269$	−23.1903	+	13.3890i	−1.41394	+	0.816339i	−0.418184	+	0.908362i	$0.637333\pi$
$270$	5.90250	+	13.8491i	0.359215	+	0.842831i
$271$	0.437592	+	1.63311i	0.0265818	+	0.0992046i	0.977942	−	0.208875i	$-0.0669803\pi$
$271$	0.437592	+	1.63311i	0.0265818	+	0.0992046i	−0.951360	+	0.308080i	$0.900314\pi$
$272$	13.6477			0.827511
$273$		0			0
$274$	11.5940			0.700421
$275$	0.111383	+	0.415688i	0.00671667	+	0.0250669i
$276$	−4.53104	+	20.7718i	−0.272737	+	1.25031i
$277$	−21.6174	+	12.4808i	−1.29886	+	0.749899i	−0.980208	−	0.197971i	$-0.936565\pi$
$277$	−21.6174	+	12.4808i	−1.29886	+	0.749899i	−0.318656	+	0.947870i	$0.603231\pi$
$278$	−20.7192	+	20.7192i	−1.24265	+	1.24265i
$279$	−5.39302	−	14.5098i	−0.322872	−	0.868680i
$280$	−2.11728	−	0.567323i	−0.126532	−	0.0339040i
$281$	2.53054	+	2.53054i	0.150959	+	0.150959i	0.778546	−	0.627587i	$-0.215957\pi$
$281$	2.53054	+	2.53054i	0.150959	+	0.150959i	−0.627587	+	0.778546i	$0.715957\pi$
$282$	13.1194	−	14.4152i	0.781246	−	0.858415i
$283$	4.43312	+	2.55946i	0.263522	+	0.152144i	0.625940	−	0.779871i	$-0.284715\pi$
$283$	4.43312	+	2.55946i	0.263522	+	0.152144i	−0.362418	+	0.932016i	$0.618049\pi$
$284$	−20.2410	+	5.42356i	−1.20108	+	0.321829i
$285$	0.932525	+	2.92295i	0.0552380	+	0.173140i
$286$		0			0
$287$			37.5354i			2.21565i
$288$	−17.9665	−	14.8689i	−1.05869	−	0.876161i
$289$	3.48419	−	6.03479i	0.204952	−	0.354988i
$290$	−2.87566	−	4.98079i	−0.168865	−	0.292482i
$291$	3.55575	−	6.88754i	0.208442	−	0.403755i
$292$	−2.63005	+	9.81548i	−0.153912	+	0.574408i
$293$	0.0725803	−	0.270873i	0.00424019	−	0.0158246i	−0.963773	−	0.266723i	$-0.914059\pi$
$293$	0.0725803	−	0.270873i	0.00424019	−	0.0158246i	0.968014	+	0.250898i	$0.0807259\pi$
$294$	20.3889	−	39.4937i	1.18911	−	2.30332i
$295$	6.49886	+	11.2564i	0.378378	+	0.655370i
$296$	0.540542	−	0.936246i	0.0314184	−	0.0544182i
$297$	−0.738518	−	0.297127i	−0.0428532	−	0.0172410i
$298$			34.4732i			1.99698i
$299$		0			0
$300$	2.70817	+	8.48859i	0.156356	+	0.490089i
$301$	12.0557	−	3.23030i	0.694877	−	0.186192i
$302$	18.8217	+	10.8667i	1.08307	+	0.625308i
$303$	1.95971	−	2.15328i	0.112582	−	0.123703i
$304$	−3.64631	−	3.64631i	−0.209130	−	0.209130i
$305$	8.33912	+	2.23446i	0.477497	+	0.127945i
$306$	17.4333	−	6.47963i	0.996597	−	0.370416i
$307$	−12.9424	+	12.9424i	−0.738660	+	0.738660i	−0.972319	−	0.233659i	$-0.924930\pi$
$307$	−12.9424	+	12.9424i	−0.738660	+	0.738660i	0.233659	+	0.972319i	$0.424930\pi$
$308$	−1.08956	+	0.629057i	−0.0620834	+	0.0358438i
$309$	−1.62984	+	7.47172i	−0.0927184	+	0.425051i
$310$	3.86919	+	14.4400i	0.219755	+	0.820138i
$311$	−6.76425			−0.383565			−0.191783	−	0.981437i	$-0.561427\pi$
$311$	−6.76425			−0.383565			−0.191783	+	0.981437i	$0.561427\pi$
$312$		0			0
$313$	−25.3673			−1.43385			−0.716923	−	0.697153i	$-0.754450\pi$
$313$	−25.3673			−1.43385			−0.716923	+	0.697153i	$0.754450\pi$
$314$	5.30180	+	19.7866i	0.299198	+	1.11662i
$315$	−19.8251	+	1.87023i	−1.11702	+	0.105375i
$316$	8.66537	−	5.00296i	0.487465	−	0.281438i
$317$	5.65535	−	5.65535i	0.317636	−	0.317636i	−0.530222	−	0.847859i	$-0.677892\pi$
$317$	5.65535	−	5.65535i	0.317636	−	0.317636i	0.847859	+	0.530222i	$0.177892\pi$
$318$	−2.12708	+	0.100108i	−0.119281	+	0.00561379i
$319$	0.293755	+	0.0787113i	0.0164471	+	0.00440699i
$320$	6.90592	+	6.90592i	0.386052	+	0.386052i
$321$	19.8264	+	18.0440i	1.10660	+	1.00712i
$322$	−50.9517	−	29.4170i	−2.83943	−	1.63934i
$323$	3.66122	−	0.981021i	0.203716	−	0.0545855i
$324$	−15.5628	−	5.42615i	−0.864599	−	0.301453i
$325$		0			0
$326$		−	3.79550i		−	0.210214i
$327$	−11.6187	−	18.1018i	−0.642515	−	1.00103i
$328$	−1.38205	+	2.39378i	−0.0763108	+	0.132174i
$329$	12.8910	+	22.3279i	0.710703	+	1.23097i
$330$	0.683119	+	0.352666i	0.0376044	+	0.0194136i
$331$	6.09048	−	22.7300i	0.334763	−	1.24935i	−0.569363	−	0.822086i	$-0.692810\pi$
$331$	6.09048	−	22.7300i	0.334763	−	1.24935i	0.904126	−	0.427266i	$-0.140523\pi$
$332$	−4.29503	+	16.0293i	−0.235721	+	0.879721i
$333$	1.63970	−	9.68334i	0.0898552	−	0.530644i
$334$	13.6842	+	23.7017i	0.748767	+	1.29690i
$335$	−0.497726	+	0.862086i	−0.0271937	+	0.0471008i
$336$	28.1660	−	18.0785i	1.53658	−	0.986260i
$337$		−	8.25174i		−	0.449501i	−0.974416	−	0.224750i	$-0.927843\pi$
$337$		−	8.25174i		−	0.449501i	0.974416	−	0.224750i	$-0.0721567\pi$
$338$		0			0
$339$	7.90542	−	2.52212i	0.429364	−	0.136983i
$340$	−8.29274	+	2.22203i	−0.449737	+	0.120507i
$341$	−0.684586	−	0.395246i	−0.0370724	−	0.0214038i
$342$	−6.38894	−	2.92655i	−0.345474	−	0.158250i
$343$	19.3744	+	19.3744i	1.04612	+	1.04612i
$344$	0.887774	+	0.237878i	0.0478656	+	0.0128255i
$345$	0.807846	+	17.1649i	0.0434930	+	0.924129i
$346$	−24.8482	+	24.8482i	−1.33585	+	1.33585i
$347$	−3.32212	+	1.91803i	−0.178341	+	0.102965i	−0.586513	−	0.809940i	$-0.699500\pi$
$347$	−3.32212	+	1.91803i	−0.178341	+	0.102965i	0.408172	+	0.912905i	$0.366166\pi$
$348$	6.15186	+	1.34193i	0.329774	+	0.0719352i
$349$	−2.99267	−	11.1688i	−0.160194	−	0.597853i	−0.998604	−	0.0528130i	$-0.983181\pi$
$349$	−2.99267	−	11.1688i	−0.160194	−	0.597853i	0.838410	−	0.545040i	$-0.183485\pi$
$350$	−24.6572			−1.31798
$351$		0			0
$352$	−1.19094			−0.0634771
$353$	2.65025	+	9.89087i	0.141059	+	0.526438i	0.999899	+	0.0141951i	$0.00451860\pi$
$353$	2.65025	+	9.89087i	0.141059	+	0.526438i	−0.858841	+	0.512243i	$0.828815\pi$
$354$	−29.0867	−	6.34481i	−1.54594	−	0.337223i
$355$	−14.6681	+	8.46864i	−0.778502	+	0.449469i
$356$	−6.87586	+	6.87586i	−0.364420	+	0.364420i
$357$	1.15653	+	24.5737i	0.0612102	+	1.30058i
$358$	3.34118	+	0.895268i	0.176587	+	0.0473164i
$359$	7.50270	+	7.50270i	0.395977	+	0.395977i	0.876812	−	0.480834i	$-0.159666\pi$
$359$	7.50270	+	7.50270i	0.395977	+	0.395977i	−0.480834	+	0.876812i	$0.659666\pi$
$360$	−1.33318	−	0.610684i	−0.0702648	−	0.0321859i
$361$	15.2142	+	8.78392i	0.800747	+	0.462311i
$362$	32.1318	−	8.60969i	1.68881	−	0.452515i
$363$	18.1125	−	5.77853i	0.950658	−	0.303294i
$364$		0			0
$365$			8.21340i			0.429909i
$366$	−16.6412	+	10.6812i	−0.869848	+	0.558316i
$367$	7.00290	−	12.1294i	0.365548	−	0.633148i	−0.623316	−	0.781970i	$-0.714215\pi$
$367$	7.00290	−	12.1294i	0.365548	−	0.633148i	0.988864	+	0.148822i	$0.0475482\pi$
$368$	−14.4408	−	25.0123i	−0.752781	−	1.30385i
$369$	−4.19236	+	24.7582i	−0.218246	+	1.28886i
$370$	−2.45484	+	9.16159i	−0.127621	+	0.476288i
$371$	0.729008	−	2.72070i	0.0378482	−	0.141251i
$372$	−14.5429	−	7.50789i	−0.754014	−	0.389266i
$373$	9.98879	+	17.3011i	0.517200	+	0.895817i	0.999800	+	0.0199760i	$0.00635897\pi$
$373$	9.98879	+	17.3011i	0.517200	+	0.895817i	−0.482601	+	0.875841i	$0.660308\pi$
$374$	0.474882	−	0.822520i	0.0245556	−	0.0425315i
$375$	10.8142	+	16.8484i	0.558445	+	0.870049i
$376$			1.89858i			0.0979116i
$377$		0			0
$378$	27.3955	−	36.4658i	1.40907	−	1.87560i
$379$	8.59890	−	2.30407i	0.441696	−	0.118352i	−0.0311155	−	0.999516i	$-0.509906\pi$
$379$	8.59890	−	2.30407i	0.441696	−	0.118352i	0.472811	+	0.881164i	$0.343239\pi$
$380$	2.80928	+	1.62194i	0.144113	+	0.0832038i
$381$	20.4641	+	18.6244i	1.04841	+	0.954157i
$382$	30.9701	+	30.9701i	1.58457	+	1.58457i
$383$	−22.6664	−	6.07346i	−1.15820	−	0.310339i	−0.371954	−	0.928251i	$-0.621312\pi$
$383$	−22.6664	−	6.07346i	−1.15820	−	0.310339i	−0.786247	+	0.617912i	$0.787979\pi$
$384$	4.55448	−	0.214351i	0.232420	−	0.0109386i
$385$	−0.719052	+	0.719052i	−0.0366463	+	0.0366463i
$386$	−33.4100	+	19.2893i	−1.70053	+	0.981799i
$387$	8.31264	−	0.784185i	0.422555	−	0.0398624i
$388$	−2.12111	−	7.91609i	−0.107683	−	0.401878i
$389$	−33.0750			−1.67697			−0.838484	−	0.544926i	$-0.816558\pi$
$389$	−33.0750			−1.67697			−0.838484	+	0.544926i	$0.816558\pi$
$390$		0			0
$391$	21.2293			1.07361
$392$	1.12051	+	4.18178i	0.0565941	+	0.211212i
$393$	−6.92806	+	31.7605i	−0.349474	+	1.60210i
$394$	−2.52377	+	1.45710i	−0.127146	+	0.0734076i
$395$	5.71869	−	5.71869i	0.287739	−	0.287739i
$396$	−0.788927	+	0.293229i	−0.0396451	+	0.0147353i
$397$	32.3626	+	8.67155i	1.62423	+	0.435212i	0.952242	−	0.305345i	$-0.0987718\pi$
$397$	32.3626	+	8.67155i	1.62423	+	0.435212i	0.671993	+	0.740557i	$0.265438\pi$
$398$	27.2351	+	27.2351i	1.36517	+	1.36517i
$399$	6.25649	−	6.87448i	0.313216	−	0.344155i
$400$	−10.4826	−	6.05213i	−0.524130	−	0.302607i
$401$	−16.5451	+	4.43325i	−0.826224	+	0.221386i	−0.647066	−	0.762434i	$-0.724004\pi$
$401$	−16.5451	+	4.43325i	−0.826224	+	0.221386i	−0.179158	+	0.983820i	$0.557337\pi$
$402$	−0.693000	−	2.17217i	−0.0345637	−	0.108338i
$403$		0			0
$404$		−	3.07835i		−	0.153154i
$405$	−13.2854	−	0.980686i	−0.660157	−	0.0487307i
$406$	−8.71226	+	15.0901i	−0.432382	+	0.748908i
$407$	−0.250767	−	0.434341i	−0.0124301	−	0.0215295i
$408$	−0.831044	+	1.60974i	−0.0411428	+	0.0796942i
$409$	3.18183	−	11.8747i	0.157331	−	0.587168i	−0.841563	−	0.540159i	$-0.818364\pi$
$409$	3.18183	−	11.8747i	0.157331	−	0.587168i	0.998894	−	0.0470095i	$-0.0149691\pi$
$410$	6.27649	−	23.4242i	0.309974	−	1.15684i
$411$	−4.70634	+	9.11625i	−0.232147	+	0.449672i
$412$	4.04279	+	7.00231i	0.199174	+	0.344979i
$413$	19.6893	−	34.1029i	0.968848	−	1.67809i
$414$	−30.3219	−	25.0941i	−1.49024	−	1.23331i
$415$			13.4130i			0.658418i
$416$		0			0
$417$	−7.88074	−	24.7017i	−0.385922	−	1.20965i
$418$	−0.346633	+	0.0928801i	−0.0169544	+	0.00454291i
$419$	−15.5988	−	9.00596i	−0.762050	−	0.439970i	0.0679811	−	0.997687i	$-0.478344\pi$
$419$	−15.5988	−	9.00596i	−0.762050	−	0.439970i	−0.830031	+	0.557717i	$0.811678\pi$
$420$	−14.1711	+	15.5709i	−0.691478	+	0.759780i
$421$	−15.2469	−	15.2469i	−0.743088	−	0.743088i	0.230083	−	0.973171i	$-0.426100\pi$
$421$	−15.2469	−	15.2469i	−0.743088	−	0.743088i	−0.973171	+	0.230083i	$0.926100\pi$
$422$	44.5992	+	11.9503i	2.17105	+	0.581732i
$423$	6.00901	+	16.1671i	0.292168	+	0.786073i
$424$	0.146667	−	0.146667i	0.00712278	−	0.00712278i
$425$	7.70517	−	4.44858i	0.373756	−	0.215788i
$426$	8.26790	−	37.9027i	0.400581	−	1.83639i
$427$	−6.76965	−	25.2647i	−0.327606	−	1.22264i
$428$	28.3440			1.37006
$429$		0			0
$430$	−8.06355			−0.388859
$431$	−7.82502	−	29.2034i	−0.376918	−	1.40668i	−0.850522	−	0.525940i	$-0.823714\pi$
$431$	−7.82502	−	29.2034i	−0.376918	−	1.40668i	0.473604	−	0.880738i	$-0.342953\pi$
$432$	20.5973	−	8.77857i	0.990989	−	0.422359i
$433$	16.7054	−	9.64486i	0.802810	−	0.463503i	−0.0416428	−	0.999133i	$-0.513259\pi$
$433$	16.7054	−	9.64486i	0.802810	−	0.463503i	0.844453	+	0.535630i	$0.179926\pi$
$434$	32.0260	−	32.0260i	1.53730	−	1.53730i
$435$	5.08364	−	0.239255i	0.243742	−	0.0114714i
$436$	−21.9672	−	5.88609i	−1.05204	−	0.281893i
$437$	−5.67194	−	5.67194i	−0.271326	−	0.271326i
$438$	−13.9130	−	12.6623i	−0.664791	−	0.605028i
$439$	15.0568	+	8.69304i	0.718622	+	0.414896i	0.814245	−	0.580521i	$-0.197151\pi$
$439$	15.0568	+	8.69304i	0.718622	+	0.414896i	−0.0956236	+	0.995418i	$0.530485\pi$
$440$	−0.0723320	+	0.0193813i	−0.00344829	+	0.000923967i
$441$	22.7769	+	32.0632i	1.08462	+	1.52682i
$442$		0			0
$443$		−	1.43321i		−	0.0680940i	−0.999420	−	0.0340470i	$-0.989160\pi$
$443$		−	1.43321i		−	0.0680940i	0.999420	−	0.0340470i	$-0.0108396\pi$
$444$	−5.60897	−	8.73869i	−0.266190	−	0.414720i
$445$	−3.92977	+	6.80656i	−0.186289	+	0.322662i
$446$	−12.3457	−	21.3835i	−0.584588	−	1.01254i
$447$	−27.1059	−	13.9936i	−1.28206	−	0.661876i
$448$	7.65819	−	28.5807i	0.361815	−	1.35031i
$449$	−9.99743	+	37.3109i	−0.471808	+	1.76081i	0.161461	+	0.986879i	$0.448379\pi$
$449$	−9.99743	+	37.3109i	−0.471808	+	1.76081i	−0.633269	+	0.773932i	$0.718287\pi$
$450$	−16.2638	−	2.75398i	−0.766681	−	0.129824i
$451$	0.641156	+	1.11051i	0.0301909	+	0.0522921i
$452$	4.38672	−	7.59801i	0.206334	−	0.357381i
$453$	−16.1846	+	10.3882i	−0.760419	+	0.488078i
$454$		−	43.4858i		−	2.04089i
$455$		0			0
$456$	0.652117	−	0.208049i	0.0305382	−	0.00974279i
$457$	4.49257	−	1.20378i	0.210154	−	0.0563105i	−0.152206	−	0.988349i	$-0.548638\pi$
$457$	4.49257	−	1.20378i	0.210154	−	0.0563105i	0.362360	+	0.932038i	$0.381971\pi$
$458$	16.9067	+	9.76110i	0.789999	+	0.456106i
$459$	−1.98182	+	16.3379i	−0.0925033	+	0.762587i
$460$	12.8471	+	12.8471i	0.598997	+	0.598997i
$461$	7.87132	+	2.10911i	0.366604	+	0.0982312i	0.437418	−	0.899258i	$-0.355893\pi$
$461$	7.87132	+	2.10911i	0.366604	+	0.0982312i	−0.0708141	+	0.997490i	$0.522560\pi$
$462$	−0.109497	−	2.32657i	−0.00509426	−	0.108242i
$463$	4.68191	−	4.68191i	0.217587	−	0.217587i	−0.589894	−	0.807481i	$-0.700830\pi$
$463$	4.68191	−	4.68191i	0.217587	−	0.217587i	0.807481	+	0.589894i	$0.200830\pi$
$464$	−7.40775	+	4.27686i	−0.343896	+	0.198548i
$465$	−12.9246	−	2.81931i	−0.599365	−	0.130742i
$466$	11.6303	+	43.4050i	0.538765	+	2.01070i
$467$	−15.0964			−0.698578			−0.349289	−	0.937015i	$-0.613577\pi$
$467$	−15.0964			−0.698578			−0.349289	+	0.937015i	$0.613577\pi$
$468$		0			0
$469$	3.01588			0.139260
$470$	−4.31113	−	16.0894i	−0.198858	−	0.742147i
$471$	−17.7101	−	3.86319i	−0.816038	−	0.178006i
$472$	2.51132	−	1.44991i	0.115593	−	0.0667377i
$473$	0.301498	−	0.301498i	0.0138629	−	0.0138629i
$474$	0.870841	+	18.5034i	0.0399991	+	0.849891i
$475$	−3.24718	−	0.870079i	−0.148991	−	0.0399220i
$476$	18.3922	+	18.3922i	0.843004	+	0.843004i
$477$	0.784726	−	1.71313i	0.0359302	−	0.0784389i
$478$	30.4020	+	17.5526i	1.39056	+	0.802837i
$479$	−17.7785	+	4.76373i	−0.812320	+	0.217660i	−0.640986	−	0.767553i	$-0.721474\pi$
$479$	−17.7785	+	4.76373i	−0.812320	+	0.217660i	−0.171334	+	0.985213i	$0.554808\pi$
$480$	−18.9870	+	6.05753i	−0.866632	+	0.276487i
$481$		0			0
$482$		−	5.52530i		−	0.251671i
$483$	43.8129	−	28.1215i	1.99356	−	1.27957i
$484$	10.0506	−	17.4081i	0.456845	−	0.791279i
$485$	−3.31201	−	5.73657i	−0.150391	−	0.260484i
$486$	22.1428	−	20.9928i	1.00442	−	0.952253i
$487$	−7.38613	+	27.5654i	−0.334698	+	1.24911i	0.569499	+	0.821992i	$0.307137\pi$
$487$	−7.38613	+	27.5654i	−0.334698	+	1.24911i	−0.904197	+	0.427116i	$0.859529\pi$
$488$	0.498514	−	1.86048i	0.0225667	−	0.0842200i
$489$	2.98436	+	1.54070i	0.134957	+	0.0696729i
$490$	−18.9913	−	32.8939i	−0.857940	−	1.48600i
$491$	−18.9980	+	32.9054i	−0.857366	+	1.48500i	0.0170675	+	0.999854i	$0.494567\pi$
$491$	−18.9980	+	32.9054i	−0.857366	+	1.48500i	−0.874433	+	0.485146i	$0.838766\pi$
$492$	14.3409	+	22.3429i	0.646538	+	1.00730i
$493$		−	6.28737i		−	0.283169i
$494$		0			0
$495$	−0.554594	+	0.393971i	−0.0249271	+	0.0177077i
$496$	21.4761	−	5.75451i	0.964306	−	0.258385i
$497$	44.4393	+	25.6571i	1.99338	+	1.15088i
$498$	−22.7208	−	20.6783i	−1.01815	−	0.926617i
$499$	11.2432	+	11.2432i	0.503315	+	0.503315i	0.912466	−	0.409152i	$-0.134175\pi$
$499$	11.2432	+	11.2432i	0.503315	+	0.503315i	−0.409152	+	0.912466i	$0.634175\pi$
$500$	20.4462	+	5.47855i	0.914383	+	0.245008i
$501$	−24.1912	+	1.13853i	−1.08078	+	0.0508657i
$502$	23.7965	−	23.7965i	1.06209	−	1.06209i
$503$	3.56162	−	2.05630i	0.158805	−	0.0916859i	−0.418492	−	0.908221i	$-0.637441\pi$
$503$	3.56162	−	2.05630i	0.158805	−	0.0916859i	0.577296	+	0.816535i	$0.304108\pi$
$504$	0.417253	+	4.42303i	0.0185859	+	0.197017i
$505$	−0.643976	−	2.40335i	−0.0286566	−	0.106948i
$506$	−2.00993			−0.0893521
$507$		0			0
$508$	29.2557			1.29801
$509$	6.30155	+	23.5177i	0.279311	+	1.04240i	0.952897	+	0.303295i	$0.0980868\pi$
$509$	6.30155	+	23.5177i	0.279311	+	1.04240i	−0.673585	+	0.739110i	$0.735247\pi$
$510$	3.38736	−	15.5288i	0.149995	−	0.687625i
$511$	21.5500	−	12.4419i	0.953316	−	0.550397i
$512$	21.6735	−	21.6735i	0.957841	−	0.957841i
$513$	4.89456	−	3.83558i	0.216100	−	0.169345i
$514$	−17.9765	−	4.81679i	−0.792909	−	0.212459i
$515$	4.62116	+	4.62116i	0.203633	+	0.203633i
$516$	5.94193	−	6.52885i	0.261579	−	0.287417i
$517$	0.762780	+	0.440391i	0.0335470	+	0.0193684i
$518$	27.7565	−	7.43732i	1.21955	−	0.326777i
$519$	−9.45126	−	29.6244i	−0.414864	−	1.30037i
$520$		0			0
$521$		−	14.5577i		−	0.637784i	−0.947791	−	0.318892i	$-0.896689\pi$
$521$		−	14.5577i		−	0.637784i	0.947791	−	0.318892i	$-0.103311\pi$
$522$	−7.43198	+	8.98026i	−0.325289	+	0.393055i
$523$	1.85988	−	3.22141i	0.0813270	−	0.140863i	−0.822493	−	0.568775i	$-0.807418\pi$
$523$	1.85988	−	3.22141i	0.0813270	−	0.140863i	0.903820	+	0.427912i	$0.140751\pi$
$524$	17.1849	+	29.7651i	0.750726	+	1.30030i
$525$	10.0091	−	19.3877i	0.436831	−	0.846147i
$526$	−3.67259	+	13.7063i	−0.160133	+	0.597623i
$527$	−4.22982	+	15.7859i	−0.184254	+	0.687644i
$528$	0.524507	−	1.01598i	0.0228262	−	0.0442148i
$529$	−10.9631	−	18.9887i	−0.476658	−	0.825596i
$530$	−0.909882	+	1.57596i	−0.0395228	+	0.0684554i
$531$	16.7959	−	20.2950i	0.728882	−	0.880727i
$532$		−	9.82785i		−	0.426091i
$533$		0			0
$534$	−5.47155	−	17.1502i	−0.236777	−	0.742163i
$535$	22.1289	−	5.92943i	0.956717	−	0.256351i
$536$	0.192334	+	0.111044i	0.00830756	+	0.00479637i
$537$	−2.06022	+	2.26372i	−0.0889050	+	0.0976867i
$538$	−37.0624	−	37.0624i	−1.59788	−	1.59788i
$539$	1.94000	+	0.519822i	0.0835618	+	0.0223903i
$540$	−11.0863	+	8.68767i	−0.477078	+	0.373858i
$541$	2.30265	−	2.30265i	0.0989985	−	0.0989985i	−0.655873	−	0.754871i	$-0.727699\pi$
$541$	2.30265	−	2.30265i	0.0989985	−	0.0989985i	0.754871	+	0.655873i	$0.227699\pi$
$542$	−2.86600	+	1.65468i	−0.123105	+	0.0710748i
$543$	−6.27350	+	28.7598i	−0.269222	+	1.23420i
$544$	6.37254	+	23.7827i	0.273221	+	1.01967i
$545$	−18.3817			−0.787386
$546$		0			0
$547$	−25.9324			−1.10879			−0.554395	−	0.832253i	$-0.687050\pi$
$547$	−25.9324			−1.10879			−0.554395	+	0.832253i	$0.687050\pi$
$548$	2.80747	+	10.4776i	0.119929	+	0.447582i
$549$	−1.64339	−	17.4205i	−0.0701383	−	0.743491i
$550$	−0.729503	+	0.421179i	−0.0311061	+	0.0179591i
$551$	−1.67983	+	1.67983i	−0.0715630	+	0.0715630i
$552$	3.82955	−	0.180233i	0.162996	−	0.00767121i
$553$	−23.6673	−	6.34164i	−1.00644	−	0.269674i
$554$	−34.5486	−	34.5486i	−1.46783	−	1.46783i
$555$	−6.20716	−	5.64916i	−0.263479	−	0.239793i
$556$	−23.7412	−	13.7070i	−1.00685	−	0.581305i
$557$	−8.71148	+	2.33423i	−0.369117	+	0.0989047i	−0.438609	−	0.898678i	$-0.644529\pi$
$557$	−8.71148	+	2.33423i	−0.369117	+	0.0989047i	0.0694921	+	0.997583i	$0.477862\pi$
$558$	24.7012	−	17.5472i	1.04568	−	0.742831i
$559$		0			0
$560$		−	28.6016i		−	1.20864i
$561$	0.453970	+	0.707278i	0.0191666	+	0.0298613i
$562$	−3.50244	+	6.06641i	−0.147742	+	0.255896i
$563$	4.37524	+	7.57814i	0.184395	+	0.319381i	0.943372	−	0.331736i	$-0.107634\pi$
$563$	4.37524	+	7.57814i	0.184395	+	0.319381i	−0.758978	+	0.651116i	$0.774301\pi$
$564$	16.2040	+	8.36545i	0.682311	+	0.352249i
$565$	1.83536	−	6.84965i	0.0772141	−	0.288167i
$566$	−2.59327	+	9.67821i	−0.109003	+	0.406806i
$567$	17.5520	+	36.3433i	0.737115	+	1.52627i
$568$	1.88938	+	3.27250i	0.0792765	+	0.137311i
$569$	15.7549	−	27.2883i	0.660481	−	1.14399i	−0.320008	−	0.947415i	$-0.603686\pi$
$569$	15.7549	−	27.2883i	0.660481	−	1.14399i	0.980489	−	0.196572i	$-0.0629810\pi$
$570$	−5.05391	+	3.24388i	−0.211685	+	0.135871i
$571$			34.4177i			1.44034i	0.693799	+	0.720169i	$0.255936\pi$
$571$			34.4177i			1.44034i	−0.693799	+	0.720169i	$0.744064\pi$
$572$		0			0
$573$	−36.9230	+	11.7798i	−1.54248	+	0.492107i
$574$	−70.9672	+	19.0156i	−2.96211	+	0.793696i
$575$	−16.3060	−	9.41426i	−0.680006	−	0.392602i
$576$	8.24351	−	17.9964i	0.343479	−	0.749848i
$577$	−27.5186	−	27.5186i	−1.14562	−	1.14562i	−0.987405	−	0.158211i	$-0.949427\pi$
$577$	−27.5186	−	27.5186i	−1.14562	−	1.14562i	−0.158211	−	0.987405i	$-0.550573\pi$
$578$	13.1749	+	3.53021i	0.548004	+	0.146837i
$579$	−1.60487	−	34.1000i	−0.0666962	−	1.41715i
$580$	3.80484	−	3.80484i	0.157988	−	0.157988i
$581$	35.1925	−	20.3184i	1.46003	−	0.842948i
$582$	14.8234	+	3.23350i	0.614451	+	0.134033i
$583$	−0.0249049	−	0.0929463i	−0.00103146	−	0.00384944i
$584$	1.83243			0.0758266
$585$		0			0
$586$	0.548902			0.0226749
$587$	1.02837	+	3.83792i	0.0424453	+	0.158408i	0.983896	−	0.178743i	$-0.0572032\pi$
$587$	1.02837	+	3.83792i	0.0424453	+	0.158408i	−0.941450	+	0.337151i	$0.890537\pi$
$588$	40.6279	+	8.86234i	1.67547	+	0.365477i
$589$	5.34770	−	3.08749i	0.220348	−	0.127218i
$590$	−17.9897	+	17.9897i	−0.740625	+	0.740625i
$591$	−0.121231	−	2.57589i	−0.00498677	−	0.105958i
$592$	13.6257	+	3.65100i	0.560013	+	0.150055i
$593$	11.5666	+	11.5666i	0.474985	+	0.474985i	0.903523	−	0.428539i	$-0.140971\pi$
$593$	11.5666	+	11.5666i	0.474985	+	0.474985i	−0.428539	+	0.903523i	$0.640971\pi$
$594$	0.187633	−	1.54682i	0.00769866	−	0.0634668i
$595$	18.2068	+	10.5117i	0.746406	+	0.430938i
$596$	−31.1537	+	8.34761i	−1.27611	+	0.341931i
$597$	−32.4702	+	10.3592i	−1.32892	+	0.423972i
$598$		0			0
$599$		−	2.33031i		−	0.0952139i	−0.998866	−	0.0476069i	$-0.984841\pi$
$599$		−	2.33031i		−	0.0952139i	0.998866	−	0.0476069i	$-0.0151595\pi$
$600$	1.35217	−	0.867894i	0.0552019	−	0.0354316i
$601$	1.95275	−	3.38226i	0.0796542	−	0.137965i	−0.823447	−	0.567394i	$-0.807952\pi$
$601$	1.95275	−	3.38226i	0.0796542	−	0.137965i	0.903101	+	0.429429i	$0.141285\pi$
$602$	12.2149	+	21.1568i	0.497842	+	0.862287i
$603$	1.98926	+	0.336846i	0.0810088	+	0.0137174i
$604$	−5.26269	+	19.6406i	−0.214136	+	0.799166i
$605$	4.20507	−	15.6935i	0.170960	−	0.638033i
$606$	5.06394	+	2.61430i	0.205708	+	0.106199i
$607$	−13.5787	−	23.5191i	−0.551144	−	0.954609i	−0.998192	−	0.0600995i	$-0.980858\pi$
$607$	−13.5787	−	23.5191i	−0.551144	−	0.954609i	0.447048	−	0.894510i	$-0.352475\pi$
$608$	4.65155	−	8.05671i	0.188645	−	0.326743i
$609$	−8.32860	−	12.9758i	−0.337492	−	0.525807i
$610$			16.8985i			0.684201i
$611$		0			0
$612$	10.0771	+	14.1856i	0.407344	+	0.573419i
$613$	−5.98906	+	1.60476i	−0.241896	+	0.0648158i	−0.377730	−	0.925916i	$-0.623295\pi$
$613$	−5.98906	+	1.60476i	−0.241896	+	0.0648158i	0.135834	+	0.990732i	$0.456629\pi$
$614$	−31.0264	−	17.9131i	−1.25212	−	0.722914i
$615$	15.8703	+	14.4437i	0.639954	+	0.582424i
$616$	0.160422	+	0.160422i	0.00646360	+	0.00646360i
$617$	−39.7463	−	10.6500i	−1.60013	−	0.428753i	−0.655046	−	0.755589i	$-0.727351\pi$
$617$	−39.7463	−	10.6500i	−1.60013	−	0.428753i	−0.945081	+	0.326836i	$0.894018\pi$
$618$	−14.9522	+	0.703709i	−0.601468	+	0.0283073i
$619$	−7.15152	+	7.15152i	−0.287444	+	0.287444i	−0.836069	−	0.548625i	$-0.815152\pi$
$619$	−7.15152	+	7.15152i	−0.287444	+	0.287444i	0.548625	+	0.836069i	$0.315152\pi$
$620$	−12.1126	+	6.99324i	−0.486456	+	0.280855i
$621$	32.0397	−	13.6553i	1.28571	−	0.547969i
$622$	−3.42680	−	12.7890i	−0.137402	−	0.512791i
$623$	23.8117			0.953996
$624$		0			0
$625$	3.06353			0.122541
$626$	−12.8512	−	47.9613i	−0.513637	−	1.91692i
$627$	0.0676776	−	0.310256i	0.00270278	−	0.0123904i
$628$	−16.5975	+	9.58256i	−0.662311	+	0.382386i
$629$	−7.33185	+	7.33185i	−0.292340	+	0.292340i
$630$	−13.5794	−	36.5352i	−0.541018	−	1.45560i
$631$	12.2649	+	3.28637i	0.488259	+	0.130829i	0.494546	−	0.869152i	$-0.335335\pi$
$631$	12.2649	+	3.28637i	0.488259	+	0.130829i	−0.00628685	+	0.999980i	$0.502001\pi$
$632$	−1.27586	−	1.27586i	−0.0507508	−	0.0507508i
$633$	−27.5004	+	30.2168i	−1.09304	+	1.20101i
$634$	13.5574	+	7.82740i	0.538435	+	0.310866i
$635$	22.8407	−	6.12014i	0.906405	−	0.242870i
$636$	−0.605536	−	1.89802i	−0.0240111	−	0.0752612i
$637$		0			0
$638$			0.595269i			0.0235669i
$639$	26.4463	+	21.8867i	1.04620	+	0.865825i
$640$	1.94823	−	3.37444i	0.0770107	−	0.133386i
$641$	−15.1671	−	26.2702i	−0.599065	−	1.03761i	−0.992959	−	0.118455i	$-0.962206\pi$
$641$	−15.1671	−	26.2702i	−0.599065	−	1.03761i	0.393894	−	0.919156i	$-0.371128\pi$
$642$	−24.0712	+	46.6263i	−0.950016	+	1.84019i
$643$	−12.2478	+	45.7094i	−0.483006	+	1.80260i	0.105872	+	0.994380i	$0.466237\pi$
$643$	−12.2478	+	45.7094i	−0.483006	+	1.80260i	−0.588878	+	0.808222i	$0.700430\pi$
$644$	14.2465	−	53.1687i	0.561391	−	2.09514i
$645$	3.27322	−	6.34027i	0.128883	−	0.249648i
$646$	3.70958	+	6.42518i	0.145951	+	0.252795i
$647$	9.62374	−	16.6688i	0.378348	−	0.655318i	−0.612474	−	0.790491i	$-0.709826\pi$
$647$	9.62374	−	16.6688i	0.378348	−	0.655318i	0.990822	+	0.135173i	$0.0431589\pi$
$648$	−0.218794	+	2.96401i	−0.00859503	+	0.116437i
$649$		−	1.34528i		−	0.0528069i
$650$		0			0
$651$	12.1814	+	38.1819i	0.477427	+	1.49647i
$652$	3.43003	−	0.919073i	0.134330	−	0.0359937i
$653$	−8.53163	−	4.92574i	−0.333868	−	0.192759i	0.323689	−	0.946164i	$-0.395077\pi$
$653$	−8.53163	−	4.92574i	−0.333868	−	0.192759i	−0.657557	+	0.753405i	$0.728410\pi$
$654$	28.3384	−	31.1376i	1.10812	−	1.21758i
$655$	19.6434	+	19.6434i	0.767532	+	0.767532i
$656$	−34.8379	−	9.33479i	−1.36019	−	0.364462i
$657$	15.6039	−	5.79967i	0.608766	−	0.226267i
$658$	−35.6840	+	35.6840i	−1.39111	+	1.39111i
$659$	4.00974	−	2.31502i	0.156197	−	0.0901805i	−0.419864	−	0.907587i	$-0.637922\pi$
$659$	4.00974	−	2.31502i	0.156197	−	0.0901805i	0.576061	+	0.817407i	$0.304589\pi$
$660$	−0.153291	+	0.702737i	−0.00596686	+	0.0273540i
$661$	−7.94714	−	29.6591i	−0.309108	−	1.15361i	−0.929351	−	0.369197i	$-0.879633\pi$
$661$	−7.94714	−	29.6591i	−0.309108	−	1.15361i	0.620243	−	0.784409i	$-0.287034\pi$
$662$	46.0604			1.79019
$663$		0			0
$664$	2.99247			0.116131
$665$	−2.05594	−	7.67286i	−0.0797258	−	0.297541i
$666$	19.1387	−	1.80548i	0.741609	−	0.0699608i
$667$	−11.5230	+	6.65278i	−0.446171	+	0.257597i
$668$	−18.1059	+	18.1059i	−0.700537	+	0.700537i
$669$	21.8250	−	1.02717i	0.843805	−	0.0397126i
$670$	−1.88207	−	0.504300i	−0.0727108	−	0.0194828i
$671$	−0.631840	−	0.631840i	−0.0243919	−	0.0243919i
$672$	44.6555	+	40.6411i	1.72262	+	1.56776i
$673$	−31.1953	−	18.0106i	−1.20249	−	0.694257i	−0.241381	−	0.970430i	$-0.577600\pi$
$673$	−31.1953	−	18.0106i	−1.20249	−	0.694257i	−0.961108	+	0.276173i	$0.910934\pi$
$674$	15.6013	−	4.18036i	0.600941	−	0.161022i
$675$	8.76734	−	11.6701i	0.337455	−	0.449182i
$676$		0			0
$677$		−	5.60187i		−	0.215297i	−0.994189	−	0.107649i	$-0.965668\pi$
$677$		−	5.60187i		−	0.215297i	0.994189	−	0.107649i	$-0.0343322\pi$
$678$	8.77341	+	13.6688i	0.336941	+	0.524949i
$679$	−10.0343	+	17.3799i	−0.385080	+	0.666977i
$680$	0.774078	+	1.34074i	0.0296845	+	0.0514151i
$681$	34.1924	+	17.6521i	1.31025	+	0.676430i
$682$	0.400466	−	1.49456i	0.0153347	−	0.0572297i
$683$	0.668373	−	2.49440i	0.0255746	−	0.0954457i	−0.951959	−	0.306226i	$-0.900934\pi$
$683$	0.668373	−	2.49440i	0.0255746	−	0.0954457i	0.977533	+	0.210780i	$0.0676004\pi$
$684$	1.09768	−	6.48240i	0.0419709	−	0.247861i
$685$	4.38373	+	7.59285i	0.167494	+	0.290108i
$686$	−26.8154	+	46.4457i	−1.02382	+	1.77331i
$687$	−14.5379	+	9.33125i	−0.554657	+	0.356009i
$688$			11.9926i			0.457215i
$689$		0			0
$690$	−32.0440	+	10.2232i	−1.21989	+	0.389191i
$691$	−24.2402	+	6.49515i	−0.922141	+	0.247087i	−0.688500	−	0.725236i	$-0.741731\pi$
$691$	−24.2402	+	6.49515i	−0.922141	+	0.247087i	−0.233641	+	0.972323i	$0.575064\pi$
$692$	−28.4724	−	16.4386i	−1.08236	−	0.624901i
$693$	1.87380	+	0.858323i	0.0711798	+	0.0326050i
$694$	−5.30936	−	5.30936i	−0.201541	−	0.201541i
$695$	−21.4028	−	5.73486i	−0.811854	−	0.217536i
$696$	−0.0533785	−	1.13418i	−0.00202331	−	0.0429908i
$697$	18.7459	−	18.7459i	0.710052	−	0.710052i
$698$	19.6005	−	11.3163i	0.741888	−	0.428329i
$699$	−38.8499	−	8.47451i	−1.46944	−	0.320535i
$700$	−5.97069	−	22.2829i	−0.225671	−	0.842215i
$701$	−0.474084			−0.0179059			−0.00895296	−	0.999960i	$-0.502850\pi$
$701$	−0.474084			−0.0179059			−0.00895296	+	0.999960i	$0.502850\pi$
$702$		0			0
$703$	3.91777			0.147761
$704$	−0.261624	−	0.976396i	−0.00986034	−	0.0367993i
$705$	14.4009	+	3.14133i	0.542369	+	0.118309i
$706$	−17.3578	+	10.0215i	−0.653268	+	0.377165i
$707$	−5.33031	+	5.33031i	−0.200467	+	0.200467i
$708$	−1.30942	−	27.8222i	−0.0492110	−	1.04562i
$709$	47.9641	+	12.8520i	1.80133	+	0.482665i	0.994185	−	0.107686i	$-0.0343441\pi$
$709$	47.9641	+	12.8520i	1.80133	+	0.482665i	0.807146	+	0.590351i	$0.201011\pi$
$710$	−23.4423	−	23.4423i	−0.879775	−	0.879775i
$711$	−14.9025	−	6.82633i	−0.558889	−	0.256007i
$712$	1.51856	+	0.876743i	0.0569106	+	0.0328573i
$713$	33.4067	−	8.95130i	1.25109	−	0.335229i
$714$	−45.8750	+	14.6358i	−1.71683	+	0.547730i
$715$		0			0
$716$			3.23624i			0.120944i
$717$	−26.1424	+	16.7796i	−0.976307	+	0.626647i
$718$	−10.3843	+	17.9860i	−0.387537	+	0.671233i
$719$	−0.847719	−	1.46829i	−0.0316146	−	0.0547581i	0.849785	−	0.527129i	$-0.176732\pi$
$719$	−0.847719	−	1.46829i	−0.0316146	−	0.0547581i	−0.881400	+	0.472371i	$0.843398\pi$
$720$	3.19453	−	18.8654i	0.119053	−	0.703073i
$721$	5.12455	−	19.1251i	0.190848	−	0.712255i
$722$	−8.89994	+	33.2150i	−0.331221	+	1.23613i
$723$	4.34448	+	2.24287i	0.161573	+	0.0834134i
$724$	15.5613	+	26.9529i	0.578331	+	1.00170i
$725$	−2.78817	+	4.82925i	−0.103550	+	0.179354i
$726$	20.1012	+	31.3173i	0.746024	+	1.16229i
$727$			20.3423i			0.754455i	0.926121	+	0.377227i	$0.123122\pi$
$727$			20.3423i			0.754455i	−0.926121	+	0.377227i	$0.876878\pi$
$728$		0			0
$729$	7.51800	+	25.9322i	0.278445	+	0.960452i
$730$	−15.5289	+	4.16094i	−0.574749	+	0.154003i
$731$	−7.63411	−	4.40755i	−0.282358	−	0.163019i
$732$	−13.6823	−	12.4523i	−0.505713	−	0.460251i
$733$	3.64797	+	3.64797i	0.134741	+	0.134741i	0.771261	−	0.636520i	$-0.219627\pi$
$733$	3.64797	+	3.64797i	0.134741	+	0.134741i	−0.636520	+	0.771261i	$0.719627\pi$
$734$	26.4804	+	7.09539i	0.977408	+	0.261896i
$735$	33.5732	−	1.58008i	1.23837	−	0.0582822i
$736$	36.8439	−	36.8439i	1.35809	−	1.35809i
$737$	0.0892271	−	0.0515153i	0.00328672	−	0.00189759i
$738$	−48.9335	+	4.61621i	−1.80127	+	0.169925i
$739$	9.71724	+	36.2652i	0.357454	+	1.33404i	0.877367	+	0.479819i	$0.159298\pi$
$739$	9.71724	+	36.2652i	0.357454	+	1.33404i	−0.519913	+	0.854219i	$0.674036\pi$
$740$	−8.87383			−0.326209
$741$		0			0
$742$	5.51326			0.202398
$743$	2.36324	+	8.81974i	0.0866989	+	0.323565i	0.995630	−	0.0933805i	$-0.0297673\pi$
$743$	2.36324	+	8.81974i	0.0866989	+	0.323565i	−0.908932	+	0.416945i	$0.863101\pi$
$744$	−0.628996	+	2.88352i	−0.0230601	+	0.105715i
$745$	−22.5762	+	13.0344i	−0.827130	+	0.477544i
$746$	−27.6503	+	27.6503i	−1.01235	+	1.01235i
$747$	25.4821	−	9.47122i	0.932342	−	0.346534i
$748$	0.858310	+	0.229983i	0.0313829	+	0.00840902i
$749$	−49.0789	−	49.0789i	−1.79330	−	1.79330i
$750$	−26.3763	+	28.9817i	−0.963127	+	1.05826i
$751$	−20.0101	−	11.5528i	−0.730178	−	0.421569i	0.0883090	−	0.996093i	$-0.471854\pi$
$751$	−20.0101	−	11.5528i	−0.730178	−	0.421569i	−0.818487	+	0.574524i	$0.805187\pi$
$752$	−23.9291	+	6.41179i	−0.872606	+	0.233814i
$753$	9.05125	+	28.3706i	0.329846	+	1.03388i
$754$		0			0
$755$			16.4349i			0.598127i
$756$	39.5882	+	15.9274i	1.43981	+	0.579275i
$757$	−18.9577	+	32.8357i	−0.689029	+	1.19343i	0.283124	+	0.959083i	$0.408629\pi$
$757$	−18.9577	+	32.8357i	−0.689029	+	1.19343i	−0.972153	+	0.234349i	$0.924704\pi$
$758$	8.71247	+	15.0904i	0.316451	+	0.548110i
$759$	0.815886	−	1.58038i	0.0296148	−	0.0573642i
$760$	0.151398	−	0.565027i	0.00549180	−	0.0204957i
$761$	−12.1085	+	45.1895i	−0.438932	+	1.63812i	0.292545	+	0.956252i	$0.405498\pi$
$761$	−12.1085	+	45.1895i	−0.438932	+	1.63812i	−0.731477	+	0.681866i	$0.761169\pi$
$762$	−24.8455	+	48.1260i	−0.900056	+	1.74342i
$763$	27.8451	+	48.2292i	1.00806	+	1.74601i
$764$	−20.4886	+	35.4872i	−0.741250	+	1.28388i
$765$	10.8350	+	8.96699i	0.391742	+	0.324202i
$766$		−	45.9317i		−	1.65958i
$767$		0			0
$768$	9.65974	+	30.2779i	0.348566	+	1.09256i
$769$	29.6131	−	7.93479i	1.06787	−	0.286136i	0.318255	−	0.948005i	$-0.396903\pi$
$769$	29.6131	−	7.93479i	1.06787	−	0.286136i	0.749619	+	0.661869i	$0.230237\pi$
$770$	−1.72377	−	0.995216i	−0.0621202	−	0.0358651i
$771$	11.0845	−	12.1794i	0.399200	−	0.438631i
$772$	−25.5221	−	25.5221i	−0.918559	−	0.918559i
$773$	−2.61557	−	0.700840i	−0.0940755	−	0.0252075i	0.211474	−	0.977384i	$-0.432174\pi$
$773$	−2.61557	−	0.700840i	−0.0940755	−	0.0252075i	−0.305550	+	0.952176i	$0.598840\pi$
$774$	5.69386	+	15.3192i	0.204661	+	0.550638i
$775$	10.2492	−	10.2492i	0.368163	−	0.368163i
$776$	−1.27985	+	0.738919i	−0.0459438	+	0.0265257i
$777$	−5.41925	+	24.8436i	−0.194414	+	0.891259i
$778$	−16.7559	−	62.5339i	−0.600729	−	2.24195i
$779$	−10.0169			−0.358892
$780$		0			0
$781$	1.75303			0.0627283
$782$	10.7549	+	40.1377i	0.384593	+	1.43532i
$783$	−4.04422	−	9.48902i	−0.144529	−	0.339110i
$784$	−48.9220	+	28.2451i	−1.74721	+	1.00875i
$785$	−10.9535	+	10.9535i	−0.390946	+	0.390946i
$786$	−63.5584	+	2.99130i	−2.26705	+	0.106696i
$787$	−51.6469	−	13.8387i	−1.84101	−	0.493298i	−0.842075	−	0.539361i	$-0.818666\pi$
$787$	−51.6469	−	13.8387i	−1.84101	−	0.493298i	−0.998939	+	0.0460627i	$0.985333\pi$
$788$	−1.92792	−	1.92792i	−0.0686792	−	0.0686792i
$789$	−9.28629	−	8.45149i	−0.330601	−	0.300881i
$790$	13.7093	+	7.91506i	0.487755	+	0.281605i
$791$	−20.7521	+	5.56051i	−0.737859	+	0.197709i
$792$	0.0878960	+	0.123731i	0.00312325	+	0.00439661i
$793$		0			0
$794$			65.5802i			2.32735i
$795$	−0.869813	−	1.35516i	−0.0308491	−	0.0480624i
$796$	−18.0177	+	31.2075i	−0.638620	+	1.10612i
$797$	18.2143	+	31.5481i	0.645183	+	1.11749i	0.984259	+	0.176730i	$0.0565521\pi$
$797$	18.2143	+	31.5481i	0.645183	+	1.11749i	−0.339077	+	0.940759i	$0.610115\pi$
$798$	16.1670	+	8.34633i	0.572304	+	0.295457i
$799$	4.71295	−	17.5890i	0.166732	−	0.622253i
$800$	5.65189	−	21.0931i	0.199824	−	0.745755i
$801$	15.7061	+	2.65955i	0.554947	+	0.0939706i
$802$	−16.7636	−	29.0355i	−0.591945	−	1.02528i
$803$	0.425049	−	0.736206i	0.0149996	−	0.0259802i
$804$	1.79520	−	1.15225i	0.0633117	−	0.0406369i
$805$		−	44.4905i		−	1.56808i
$806$		0			0
$807$	44.1864	−	14.0971i	1.55544	−	0.496241i
$808$	−0.536195	+	0.143673i	−0.0188633	+	0.00505440i
$809$	24.1681	+	13.9534i	0.849704	+	0.490577i	0.860551	−	0.509364i	$-0.170119\pi$
$809$	24.1681	+	13.9534i	0.849704	+	0.490577i	−0.0108468	+	0.999941i	$0.503453\pi$
$810$	−4.87628	−	25.6151i	−0.171335	−	0.900024i
$811$	9.41030	+	9.41030i	0.330440	+	0.330440i	0.852754	−	0.522313i	$-0.174931\pi$
$811$	9.41030	+	9.41030i	0.330440	+	0.330440i	−0.522313	+	0.852754i	$0.674931\pi$
$812$	−15.7467	−	4.21931i	−0.552600	−	0.148069i
$813$	−0.137670	−	2.92518i	−0.00482830	−	0.102591i
$814$	0.694157	−	0.694157i	0.0243302	−	0.0243302i
$815$	2.48565	−	1.43509i	0.0870685	−	0.0502690i
$816$	−23.0954	−	5.03790i	−0.808499	−	0.176362i
$817$	0.862054	+	3.21723i	0.0301594	+	0.112557i
$818$	24.0632			0.841349
$819$		0			0
$820$	22.6884			0.792315
$821$	−3.31670	−	12.3781i	−0.115754	−	0.431999i	0.883588	−	0.468264i	$-0.155120\pi$
$821$	−3.31670	−	12.3781i	−0.115754	−	0.431999i	−0.999342	+	0.0362655i	$0.988454\pi$
$822$	−19.6201	−	4.27982i	−0.684329	−	0.149276i
$823$	−17.9530	+	10.3652i	−0.625803	+	0.361308i	−0.779125	−	0.626869i	$-0.784336\pi$
$823$	−17.9530	+	10.3652i	−0.625803	+	0.361308i	0.153322	+	0.988176i	$0.451003\pi$
$824$	1.03099	−	1.03099i	0.0359164	−	0.0359164i
$825$	−0.0350421	−	0.744567i	−0.00122001	−	0.0259225i
$826$	74.4521	+	19.9494i	2.59052	+	0.694128i
$827$	−30.0036	−	30.0036i	−1.04333	−	1.04333i	−0.999018	−	0.0443105i	$-0.985891\pi$
$827$	−30.0036	−	30.0036i	−1.04333	−	1.04333i	−0.0443105	−	0.999018i	$-0.514109\pi$
$828$	15.3354	−	33.4786i	0.532941	−	1.16346i
$829$	1.61557	+	0.932749i	0.0561110	+	0.0323957i	0.527793	−	0.849373i	$-0.323020\pi$
$829$	1.61557	+	0.932749i	0.0561110	+	0.0323957i	−0.471682	+	0.881769i	$0.656353\pi$
$830$	−25.3596	+	6.79507i	−0.880243	+	0.235860i
$831$	41.1894	−	13.1409i	1.42884	−	0.455853i
$832$		0			0
$833$		−	41.5228i		−	1.43868i
$834$	42.7104	−	27.4139i	1.47894	−	0.949266i
$835$	−10.3481	+	17.9234i	−0.358110	+	0.620264i
$836$	−0.167873	−	0.290765i	−0.00580601	−	0.0100563i
$837$	3.77022	+	26.5451i	0.130318	+	0.917534i
$838$	9.12491	−	34.0546i	0.315215	−	1.17640i
$839$	6.87949	−	25.6746i	0.237506	−	0.886386i	−0.739497	−	0.673160i	$-0.764936\pi$
$839$	6.87949	−	25.6746i	0.237506	−	0.886386i	0.977003	−	0.213226i	$-0.0683970\pi$
$840$	3.37356	+	1.74163i	0.116399	+	0.0600919i
$841$	−12.5297	−	21.7020i	−0.432058	−	0.748346i
$842$	21.1027	−	36.5510i	0.727249	−	1.25963i
$843$	−3.34820	−	5.21645i	−0.115318	−	0.179664i
$844$			43.1984i			1.48695i
$845$		0			0
$846$	−27.5226	+	19.5514i	−0.946245	+	0.672191i
$847$	−47.5460	+	12.7399i	−1.63370	+	0.437749i
$848$	2.34387	+	1.35323i	0.0804889	+	0.0464703i
$849$	−6.55718	−	5.96771i	−0.225042	−	0.204811i
$850$	12.3143	+	12.3143i	0.422377	+	0.422377i
$851$	21.1952	+	5.67922i	0.726560	+	0.194681i
$852$	36.2551	−	1.70630i	1.24208	−	0.0584568i
$853$	−15.8825	+	15.8825i	−0.543806	+	0.543806i	−0.924642	−	0.380837i	$-0.875636\pi$
$853$	−15.8825	+	15.8825i	−0.543806	+	0.543806i	0.380837	+	0.924642i	$0.375636\pi$
$854$	44.3377	−	25.5984i	1.51720	−	0.875958i
$855$	−0.499097	−	5.29061i	−0.0170688	−	0.180935i
$856$	−1.32287	−	4.93702i	−0.0452148	−	0.168744i
$857$	48.2304			1.64752			0.823759	−	0.566941i	$-0.191873\pi$
$857$	48.2304			1.64752			0.823759	+	0.566941i	$0.191873\pi$
$858$		0			0
$859$	−20.5416			−0.700870			−0.350435	−	0.936587i	$-0.613966\pi$
$859$	−20.5416			−0.700870			−0.350435	+	0.936587i	$0.613966\pi$
$860$	−1.95257	−	7.28709i	−0.0665821	−	0.248488i
$861$	13.8558	−	63.5196i	0.472205	−	2.16474i
$862$	51.2498	−	29.5891i	1.74558	−	1.00781i
$863$	−3.75723	+	3.75723i	−0.127898	+	0.127898i	−0.768158	−	0.640260i	$-0.778826\pi$
$863$	−3.75723	+	3.75723i	−0.127898	+	0.127898i	0.640260	+	0.768158i	$0.278826\pi$
$864$	24.9153	+	31.7943i	0.847635	+	1.08166i
$865$	−25.6681	−	6.87774i	−0.872740	−	0.233850i
$866$	26.6983	+	26.6983i	0.907245	+	0.907245i
$867$	−8.12382	+	8.92626i	−0.275899	+	0.303152i
$868$	36.6972	+	21.1871i	1.24558	+	0.719138i
$869$	−0.808540	+	0.216648i	−0.0274278	+	0.00734926i
$870$	3.02775	+	9.49030i	0.102650	+	0.321751i
$871$		0			0
$872$			4.10101i			0.138878i
$873$	−8.55971	+	10.3429i	−0.289702	+	0.350055i
$874$	7.85035	−	13.5972i	0.265542	−	0.459932i
$875$	−25.9172	−	44.8899i	−0.876161	−	1.51756i
$876$	8.07401	−	15.6395i	0.272796	−	0.528409i
$877$	12.3544	−	46.1072i	0.417178	−	1.55693i	−0.363255	−	0.931690i	$-0.618334\pi$
$877$	12.3544	−	46.1072i	0.417178	−	1.55693i	0.780433	−	0.625240i	$-0.214999\pi$
$878$	−8.80786	+	32.8714i	−0.297251	+	1.10936i
$879$	−0.222815	+	0.431595i	−0.00751535	+	0.0145573i
$880$	−0.488553	−	0.846199i	−0.0164691	−	0.0285254i
$881$	−11.2113	+	19.4186i	−0.377718	+	0.654228i	−0.990730	−	0.135846i	$-0.956625\pi$
$881$	−11.2113	+	19.4186i	−0.377718	+	0.654228i	0.613011	+	0.790074i	$0.289958\pi$
$882$	−49.0820	+	59.3071i	−1.65268	+	1.99697i
$883$		−	21.7280i		−	0.731205i	−0.930771	−	0.365602i	$-0.880863\pi$
$883$		−	21.7280i		−	0.731205i	0.930771	−	0.365602i	$-0.119137\pi$
$884$		0			0
$885$	−6.84257	−	21.4476i	−0.230011	−	0.720955i
$886$	2.70974	−	0.726071i	0.0910353	−	0.0243928i
$887$	−20.9061	−	12.0702i	−0.701959	−	0.405276i	0.106117	−	0.994354i	$-0.466158\pi$
$887$	−20.9061	−	12.0702i	−0.701959	−	0.405276i	−0.808077	+	0.589077i	$0.799491\pi$
$888$	−1.26034	+	1.38483i	−0.0422943	+	0.0464720i
$889$	−50.6575	−	50.6575i	−1.69900	−	1.69900i
$890$	−14.8598	−	3.98168i	−0.498102	−	0.133466i
$891$	1.14008	+	0.775431i	0.0381942	+	0.0259779i
$892$	16.3349	−	16.3349i	0.546933	−	0.546933i
$893$	−5.95851	+	3.44015i	−0.199394	+	0.115120i
$894$	12.7254	−	58.3375i	0.425602	−	1.95110i
$895$	0.677006	+	2.52662i	0.0226298	+	0.0844556i
$896$	−11.8050			−0.394376
$897$		0			0
$898$	−75.6075			−2.52305
$899$	−2.65106	−	9.89388i	−0.0884177	−	0.329979i
$900$	−1.44944	−	15.3646i	−0.0483146	−	0.512152i
$901$	−1.72285	+	0.994687i	−0.0573964	+	0.0331378i
$902$	−1.77481	+	1.77481i	−0.0590946	+	0.0590946i
$903$	−21.5937	+	1.01628i	−0.718594	+	0.0338197i
$904$	−1.52818	−	0.409474i	−0.0508264	−	0.0136189i
$905$	17.7875	+	17.7875i	0.591277	+	0.591277i
$906$	−27.8398	−	25.3371i	−0.924915	−	0.841768i
$907$	20.0171	+	11.5569i	0.664658	+	0.383741i	0.794050	−	0.607853i	$-0.207969\pi$
$907$	20.0171	+	11.5569i	0.664658	+	0.383741i	−0.129391	+	0.991594i	$0.541302\pi$
$908$	39.2985	−	10.5300i	1.30417	−	0.349450i
$909$	−4.11119	+	2.92050i	−0.136359	+	0.0968667i
$910$		0			0
$911$		−	8.77371i		−	0.290686i	−0.989381	−	0.145343i	$-0.953571\pi$
$911$		−	8.77371i		−	0.290686i	0.989381	−	0.145343i	$-0.0464286\pi$
$912$	4.82450	+	7.51650i	0.159755	+	0.248896i
$913$	0.694131	−	1.20227i	0.0229724	−	0.0397893i
$914$	4.55191	+	7.88414i	0.150564	+	0.260784i
$915$	−13.2871	−	6.85958i	−0.439258	−	0.226771i
$916$	−4.72726	+	17.6424i	−0.156193	+	0.582920i
$917$	21.7832	−	81.2961i	0.719345	−	2.68463i
$918$	−31.8936	+	4.52987i	−1.05264	+	0.149508i
$919$	0.139907	+	0.242326i	0.00461510	+	0.00799358i	0.868324	−	0.495998i	$-0.165198\pi$
$919$	0.139907	+	0.242326i	0.00461510	+	0.00799358i	−0.863709	+	0.503991i	$0.831864\pi$
$920$	1.63813	−	2.83733i	0.0540076	−	0.0935439i
$921$	26.6794	−	17.1243i	0.879115	−	0.564264i
$922$			15.9506i			0.525304i
$923$		0			0
$924$	2.07602	−	0.662327i	0.0682962	−	0.0217889i
$925$	8.88285	−	2.38015i	0.292066	−	0.0782590i
$926$	11.2238	+	6.48009i	0.368838	+	0.212949i
$927$	5.51622	−	12.0424i	0.181176	−	0.395525i
$928$	−10.9119	−	10.9119i	−0.358200	−	0.358200i
$929$	17.7942	+	4.76794i	0.583809	+	0.156431i	0.538622	−	0.842548i	$-0.318945\pi$
$929$	17.7942	+	4.76794i	0.583809	+	0.156431i	0.0451866	+	0.998979i	$0.485612\pi$
$930$	−1.21728	−	25.8645i	−0.0399162	−	0.848131i
$931$	−11.0938	+	11.0938i	−0.363586	+	0.363586i
$932$	−36.4092	+	21.0208i	−1.19262	+	0.688561i
$933$	11.4469	+	2.49695i	0.374753	+	0.0817466i
$934$	−7.64790	−	28.5423i	−0.250247	−	0.933934i
$935$	0.718216			0.0234882
$936$		0			0
$937$	58.7234			1.91841			0.959205	−	0.282712i	$-0.0912341\pi$
$937$	58.7234			1.91841			0.959205	+	0.282712i	$0.0912341\pi$
$938$	1.52786	+	5.70203i	0.0498863	+	0.186178i
$939$	42.9280	+	9.36409i	1.40090	+	0.305585i
$940$	13.4962	−	7.79201i	0.440196	−	0.254147i
$941$	21.2364	−	21.2364i	0.692286	−	0.692286i	−0.270448	−	0.962734i	$-0.587172\pi$
$941$	21.2364	−	21.2364i	0.692286	−	0.692286i	0.962734	+	0.270448i	$0.0871720\pi$
$942$	−1.66799	−	35.4411i	−0.0543461	−	1.15473i
$943$	−54.1914	−	14.5205i	−1.76471	−	0.472853i
$944$	26.7555	+	26.7555i	0.870817	+	0.870817i
$945$	34.2395	+	4.15332i	1.11381	+	0.135108i
$946$	0.722774	+	0.417294i	0.0234994	+	0.0135674i
$947$	34.5192	−	9.24940i	1.12172	−	0.300565i	0.350143	−	0.936696i	$-0.386133\pi$
$947$	34.5192	−	9.24940i	1.12172	−	0.300565i	0.771581	+	0.636131i	$0.219466\pi$
$948$	−16.5108	+	5.26755i	−0.536247	+	0.171082i
$949$		0			0
$950$		−	6.58014i		−	0.213488i
$951$	−11.6579	+	7.48270i	−0.378034	+	0.242643i
$952$	2.34519	−	4.06199i	0.0760080	−	0.131650i
$953$	−10.0506	−	17.4081i	−0.325570	−	0.563903i	0.656058	−	0.754711i	$-0.272223\pi$
$953$	−10.0506	−	17.4081i	−0.325570	−	0.563903i	−0.981628	+	0.190807i	$0.938889\pi$
$954$	3.63652	+	0.615780i	0.117737	+	0.0199366i
$955$	−8.57221	+	31.9919i	−0.277390	+	1.03523i
$956$	−8.50065	+	31.7249i	−0.274931	+	1.02606i
$957$	−0.468053	−	0.241636i	−0.0151300	−	0.00781099i
$958$	−18.0133	−	31.2000i	−0.581984	−	1.00803i
$959$	13.2812	−	23.0037i	0.428873	−	0.742829i
$960$	−9.13734	−	14.2358i	−0.294906	−	0.459460i
$961$		−	4.37562i		−	0.141149i
$962$		0			0
$963$	−26.8905	−	37.8538i	−0.866535	−	1.21982i
$964$	4.99326	−	1.33794i	0.160822	−	0.0430921i
$965$	−25.2648	−	14.5867i	−0.813304	−	0.469561i
$966$	75.3644	+	68.5894i	2.42481	+	2.20683i
$967$	4.09441	+	4.09441i	0.131667	+	0.131667i	0.769869	−	0.638202i	$-0.220321\pi$
$967$	4.09441	+	4.09441i	0.131667	+	0.131667i	−0.638202	+	0.769869i	$0.720321\pi$
$968$	−3.50127	−	0.938163i	−0.112535	−	0.0301537i
$969$	−6.55786	+	0.308637i	−0.210669	+	0.00991486i
$970$	9.16810	−	9.16810i	0.294370	−	0.294370i
$971$	31.6496	−	18.2729i	1.01568	−	0.586405i	0.102833	−	0.994699i	$-0.467209\pi$
$971$	31.6496	−	18.2729i	1.01568	−	0.586405i	0.912851	+	0.408293i	$0.133876\pi$
$972$	24.3332	+	14.9273i	0.780488	+	0.478793i
$973$	17.3747	+	64.8431i	0.557006	+	2.07878i
$974$	−55.8590			−1.78984
$975$		0			0
$976$	25.1326			0.804474
$977$	−0.678110	−	2.53074i	−0.0216947	−	0.0809656i	0.954230	−	0.299074i	$-0.0966779\pi$
$977$	−0.678110	−	2.53074i	−0.0216947	−	0.0809656i	−0.975924	+	0.218109i	$0.930011\pi$
$978$	−1.40107	+	6.42297i	−0.0448014	+	0.205384i
$979$	0.704488	−	0.406736i	0.0225155	−	0.0129994i
$980$	25.1278	−	25.1278i	0.802678	−	0.802678i
$981$	12.9797	+	34.9218i	0.414411	+	1.11497i
$982$	−71.8378	−	19.2489i	−2.29244	−	0.614256i
$983$	−6.87065	−	6.87065i	−0.219140	−	0.219140i	0.588996	−	0.808136i	$-0.299523\pi$
$983$	−6.87065	−	6.87065i	−0.219140	−	0.219140i	−0.808136	+	0.588996i	$0.799523\pi$
$984$	3.22242	−	3.54072i	0.102727	−	0.112874i
$985$	−1.90849	−	1.10186i	−0.0608094	−	0.0351083i
$986$	11.8873	−	3.18521i	0.378570	−	0.101438i
$987$	−13.5728	−	42.5431i	−0.432026	−	1.35416i
$988$		0			0
$989$			18.6549i			0.593190i
$990$	−1.02583	−	0.848968i	−0.0326030	−	0.0269820i
$991$	14.5303	−	25.1672i	0.461570	−	0.799463i	−0.537469	−	0.843283i	$-0.680620\pi$
$991$	14.5303	−	25.1672i	0.461570	−	0.799463i	0.999039	+	0.0438203i	$0.0139529\pi$
$992$	20.0558	+	34.7377i	0.636773	+	1.10292i
$993$	−18.6972	+	36.2167i	−0.593337	+	1.14930i
$994$	−25.9959	+	97.0182i	−0.824541	+	3.07723i
$995$	−7.53842	+	28.1338i	−0.238984	+	0.891901i
$996$	13.1854	−	25.5402i	0.417794	−	0.809273i
$997$	−11.7210	−	20.3014i	−0.371209	−	0.642953i	0.618543	−	0.785751i	$-0.287723\pi$
$997$	−11.7210	−	20.3014i	−0.371209	−	0.642953i	−0.989752	+	0.142798i	$0.954390\pi$
$998$	−15.5613	+	26.9530i	−0.492586	+	0.853184i
$999$	−6.34931	+	15.7814i	−0.200883	+	0.499302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.488.19		96
3.2	odd	2	inner	507.2.k.k.488.6		96
13.2	odd	12	inner	507.2.k.k.80.6		96
13.3	even	3	inner	507.2.k.k.89.6		96
13.4	even	6		507.2.f.g.437.6	yes	48
13.5	odd	4	inner	507.2.k.k.188.19		96
13.6	odd	12		507.2.f.g.239.6	yes	48
13.7	odd	12		507.2.f.g.239.20	yes	48
13.8	odd	4	inner	507.2.k.k.188.5		96
13.9	even	3		507.2.f.g.437.20	yes	48
13.10	even	6	inner	507.2.k.k.89.20		96
13.11	odd	12	inner	507.2.k.k.80.20		96
13.12	even	2	inner	507.2.k.k.488.5		96
39.2	even	12	inner	507.2.k.k.80.19		96
39.5	even	4	inner	507.2.k.k.188.6		96
39.8	even	4	inner	507.2.k.k.188.20		96
39.11	even	12	inner	507.2.k.k.80.5		96
39.17	odd	6		507.2.f.g.437.19	yes	48
39.20	even	12		507.2.f.g.239.5	✓	48
39.23	odd	6	inner	507.2.k.k.89.5		96
39.29	odd	6	inner	507.2.k.k.89.19		96
39.32	even	12		507.2.f.g.239.19	yes	48
39.35	odd	6		507.2.f.g.437.5	yes	48
39.38	odd	2	inner	507.2.k.k.488.20		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.5	✓	48	39.20	even	12
507.2.f.g.239.6	yes	48	13.6	odd	12
507.2.f.g.239.19	yes	48	39.32	even	12
507.2.f.g.239.20	yes	48	13.7	odd	12
507.2.f.g.437.5	yes	48	39.35	odd	6
507.2.f.g.437.6	yes	48	13.4	even	6
507.2.f.g.437.19	yes	48	39.17	odd	6
507.2.f.g.437.20	yes	48	13.9	even	3
507.2.k.k.80.5		96	39.11	even	12	inner
507.2.k.k.80.6		96	13.2	odd	12	inner
507.2.k.k.80.19		96	39.2	even	12	inner
507.2.k.k.80.20		96	13.11	odd	12	inner
507.2.k.k.89.5		96	39.23	odd	6	inner
507.2.k.k.89.6		96	13.3	even	3	inner
507.2.k.k.89.19		96	39.29	odd	6	inner
507.2.k.k.89.20		96	13.10	even	6	inner
507.2.k.k.188.5		96	13.8	odd	4	inner
507.2.k.k.188.6		96	39.5	even	4	inner
507.2.k.k.188.19		96	13.5	odd	4	inner
507.2.k.k.188.20		96	39.8	even	4	inner
507.2.k.k.488.5		96	13.12	even	2	inner
507.2.k.k.488.6		96	3.2	odd	2	inner
507.2.k.k.488.19		96	1.1	even	1	trivial
507.2.k.k.488.20		96	39.38	odd	2	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.506604 + 1.89067i) q^{2} +(-1.69226 - 0.369140i) q^{3} +(-1.58594 + 0.915644i) q^{4} +(-1.04664 + 1.04664i) q^{5} +(-0.159382 - 3.38651i) q^{6} +(4.33161 + 1.16065i) q^{7} +(0.233508 + 0.233508i) q^{8} +(2.72747 + 1.24936i) q^{9} +O(q^{10})\)	\(q+(0.506604 + 1.89067i) q^{2} +(-1.69226 - 0.369140i) q^{3} +(-1.58594 + 0.915644i) q^{4} +(-1.04664 + 1.04664i) q^{5} +(-0.159382 - 3.38651i) q^{6} +(4.33161 + 1.16065i) q^{7} +(0.233508 + 0.233508i) q^{8} +(2.72747 + 1.24936i) q^{9} +(-2.50908 - 1.44862i) q^{10} +(0.147979 - 0.0396510i) q^{11} +(3.02182 - 0.964071i) q^{12} +8.77764i q^{14} +(2.15754 - 1.38483i) q^{15} +(-2.15448 + 3.73167i) q^{16} +(-1.58364 - 2.74294i) q^{17} +(-0.980382 + 5.78968i) q^{18} +(-0.309737 + 1.15595i) q^{19} +(0.701560 - 2.61826i) q^{20} +(-6.90175 - 3.56309i) q^{21} +(0.149934 + 0.259693i) q^{22} +(-3.35135 + 5.80471i) q^{23} +(-0.308959 - 0.481353i) q^{24} +2.80909i q^{25} +(-4.15440 - 3.12106i) q^{27} +(-7.93243 + 2.12549i) q^{28} +(1.71915 + 0.992552i) q^{29} +(3.71127 + 3.37764i) q^{30} +(-3.64859 - 3.64859i) q^{31} +(-7.50887 - 2.01200i) q^{32} +(-0.265056 + 0.0124745i) q^{33} +(4.38372 - 4.38372i) q^{34} +(-5.74841 + 3.31885i) q^{35} +(-5.46958 + 0.515981i) q^{36} +(-0.847303 - 3.16218i) q^{37} -2.34244 q^{38} -0.488797 q^{40} +(2.16637 + 8.08500i) q^{41} +(3.24018 - 14.8540i) q^{42} +(2.41031 - 1.39159i) q^{43} +(-0.198381 + 0.198381i) q^{44} +(-4.16231 + 1.54705i) q^{45} +(-12.6726 - 3.39562i) q^{46} +(4.06533 + 4.06533i) q^{47} +(5.02344 - 5.51964i) q^{48} +(11.3535 + 6.55497i) q^{49} +(-5.31107 + 1.42310i) q^{50} +(1.66739 + 5.22634i) q^{51} -0.628103i q^{53} +(3.79626 - 9.43574i) q^{54} +(-0.113381 + 0.196381i) q^{55} +(0.740444 + 1.28249i) q^{56} +(0.950863 - 1.84183i) q^{57} +(-1.00566 + 3.75318i) q^{58} +(2.27275 - 8.48202i) q^{59} +(-2.15372 + 4.17179i) q^{60} +(-2.91632 - 5.05121i) q^{61} +(5.04989 - 8.74667i) q^{62} +(10.3643 + 8.57738i) q^{63} -6.59818i q^{64} +(-0.157864 - 0.494815i) q^{66} +(0.649609 - 0.174062i) q^{67} +(5.02311 + 2.90010i) q^{68} +(7.81410 - 8.58595i) q^{69} +(-9.18702 - 9.18702i) q^{70} +(11.0529 + 2.96161i) q^{71} +(0.345151 + 0.928622i) q^{72} +(3.92370 - 3.92370i) q^{73} +(5.54940 - 3.20395i) q^{74} +(1.03695 - 4.75371i) q^{75} +(-0.567217 - 2.11688i) q^{76} +0.687010 q^{77} -5.46386 q^{79} +(-1.65075 - 6.16067i) q^{80} +(5.87820 + 6.81519i) q^{81} +(-14.1886 + 8.19178i) q^{82} +(6.40765 - 6.40765i) q^{83} +(14.2083 - 0.668696i) q^{84} +(4.52836 + 1.21337i) q^{85} +(3.85212 + 3.85212i) q^{86} +(-2.54285 - 2.31426i) q^{87} +(0.0438132 + 0.0252956i) q^{88} +(5.12896 - 1.37430i) q^{89} +(-5.03360 - 7.08582i) q^{90} -12.2746i q^{92} +(4.82751 + 7.52119i) q^{93} +(-5.62670 + 9.74572i) q^{94} +(-0.885683 - 1.53405i) q^{95} +(11.9642 + 6.17664i) q^{96} +(-1.15826 + 4.32269i) q^{97} +(-6.64155 + 24.7866i) q^{98} +(0.453148 + 0.0767327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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