LMFDB - Embedded newform 507.2.k.k.80.19

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			80.19
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.19

$q$-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} +(-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} + 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

Character values

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

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

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	−0.518156	−	0.855286i	$-0.673381\pi$
$2$	0.506604	−	1.89067i	0.358223	−	1.33691i	0.876380	−	0.481621i	$-0.159952\pi$
$3$	−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	0.433218	−	0.901289i	$-0.357378\pi$
$5$	−1.04664	−	1.04664i	−0.468071	−	0.468071i	−0.901289	+	0.433218i	$0.857378\pi$
$6$	−0.159382	+	3.38651i	−0.0650674	+	1.38254i
$7$	4.33161	−	1.16065i	1.63719	−	0.438685i	0.681206	−	0.732091i	$-0.261456\pi$
$7$	4.33161	−	1.16065i	1.63719	−	0.438685i	0.955988	+	0.293407i	$0.0947890\pi$
$8$	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	0.281059	−	0.959691i	$-0.409314\pi$
$11$	0.147979	+	0.0396510i	0.0446175	+	0.0119552i	−0.236441	+	0.971646i	$0.575981\pi$
$12$	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	−0.991642	−	0.129018i	$-0.958818\pi$
$17$	−1.58364	+	2.74294i	−0.384088	+	0.665261i	0.607554	+	0.794278i	$0.292151\pi$
$18$	−0.980382	−	5.78968i	−0.231078	−	1.36464i
$19$	−0.309737	−	1.15595i	−0.0710585	−	0.265194i	0.921252	−	0.388966i	$-0.127168\pi$
$19$	−0.309737	−	1.15595i	−0.0710585	−	0.265194i	−0.992311	+	0.123772i	$0.960501\pi$
$20$	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	−0.968881	−	0.247527i	$-0.920382\pi$
$23$	−3.35135	−	5.80471i	−0.698805	−	1.21037i	0.270076	−	0.962839i	$-0.412951\pi$
$24$	−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	−0.331815	−	0.943345i	$-0.607661\pi$
$29$	1.71915	−	0.992552i	0.319238	−	0.184312i	0.651053	+	0.759032i	$0.274328\pi$
$30$	3.71127	−	3.37764i	0.677582	−	0.616670i
$31$	−3.64859	+	3.64859i	−0.655306	+	0.655306i	−0.954266	−	0.298960i	$-0.903360\pi$
$31$	−3.64859	+	3.64859i	−0.655306	+	0.655306i	0.298960	+	0.954266i	$0.403360\pi$
$32$	−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	0.860647	+	0.509201i	$0.170059\pi$
$37$	−0.847303	+	3.16218i	−0.139296	+	0.519859i	−0.999943	+	0.0106576i	$0.996608\pi$
$38$	−2.34244			−0.379994
$39$		0			0
$40$	−0.488797			−0.0772856
$41$	2.16637	−	8.08500i	0.338330	−	1.26266i	−0.561884	−	0.827216i	$-0.689923\pi$
$41$	2.16637	−	8.08500i	0.338330	−	1.26266i	0.900214	−	0.435448i	$-0.143410\pi$
$42$	3.24018	+	14.8540i	0.499970	+	2.29203i
$43$	2.41031	+	1.39159i	0.367568	+	0.212216i	0.672396	−	0.740192i	$-0.265265\pi$
$43$	2.41031	+	1.39159i	0.367568	+	0.212216i	−0.304827	+	0.952408i	$0.598599\pi$
$44$	−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	−0.345448	−	0.938438i	$-0.612273\pi$
$47$	4.06533	−	4.06533i	0.592990	−	0.592990i	0.938438	+	0.345448i	$0.112273\pi$
$48$	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	$0.0137356\pi$
$53$			0.628103i			0.0862766i	−0.999069	+	0.0431383i	$0.986264\pi$
$54$	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	0.940511	+	0.339764i	$0.110347\pi$
$59$	2.27275	+	8.48202i	0.295887	+	1.10426i	−0.644624	+	0.764500i	$0.722986\pi$
$60$	−2.15372	−	4.17179i	−0.278045	−	0.538576i
$61$	−2.91632	+	5.05121i	−0.373396	+	0.646741i	−0.990086	−	0.140466i	$-0.955140\pi$
$61$	−2.91632	+	5.05121i	−0.373396	+	0.646741i	0.616690	+	0.787206i	$0.288473\pi$
$62$	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	0.298282	−	0.954478i	$-0.403587\pi$
$67$	0.649609	+	0.174062i	0.0793624	+	0.0212651i	−0.218919	+	0.975743i	$0.570253\pi$
$68$	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	0.465860	−	0.884859i	$-0.345745\pi$
$71$	11.0529	−	2.96161i	1.31174	−	0.351478i	0.845876	+	0.533380i	$0.179079\pi$
$72$	0.345151	−	0.928622i	0.0406764	−	0.109439i
$73$	3.92370	+	3.92370i	0.459235	+	0.459235i	0.898404	−	0.439169i	$-0.144727\pi$
$73$	3.92370	+	3.92370i	0.459235	+	0.459235i	−0.439169	+	0.898404i	$0.644727\pi$
$74$	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	0.965124	−	0.261793i	$-0.0843139\pi$
$83$	6.40765	+	6.40765i	0.703331	+	0.703331i	−0.261793	+	0.965124i	$0.584314\pi$
$84$	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	0.520193	−	0.854049i	$-0.325860\pi$
$89$	5.12896	+	1.37430i	0.543668	+	0.145676i	0.0234757	+	0.999724i	$0.492527\pi$
$90$	−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	0.881865	−	0.471502i	$-0.156288\pi$
$97$	−1.15826	−	4.32269i	−0.117604	−	0.438902i	−0.999468	+	0.0325997i	$0.989621\pi$
$98$	−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	0.821176	−	0.570676i	$-0.193319\pi$
$101$	−0.840488	−	1.45577i	−0.0836317	−	0.144854i	−0.904807	+	0.425821i	$0.859985\pi$
$102$	−9.03660	−	5.80018i	−0.894756	−	0.574304i
$103$			4.41524i			0.435046i	0.976055	+	0.217523i	$0.0697977\pi$
$103$			4.41524i			0.435046i	−0.976055	+	0.217523i	$0.930202\pi$
$104$		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	−0.979679	−	0.200574i	$-0.935719\pi$
$107$	−13.4040	+	7.73882i	−1.29582	+	0.748140i	−0.316137	+	0.948714i	$0.602386\pi$
$108$	9.44641	−	1.14587i	0.908981	−	0.110261i
$109$	8.78130	−	8.78130i	0.841096	−	0.841096i	−0.147905	−	0.989002i	$-0.547253\pi$
$109$	8.78130	−	8.78130i	0.841096	−	0.841096i	0.989002	+	0.147905i	$0.0472531\pi$
$110$	−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	0.291987	−	0.956422i	$-0.405684\pi$
$113$	−4.14900	−	2.39543i	−0.390305	−	0.225343i	−0.682292	+	0.731080i	$0.739017\pi$
$114$	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	−0.966542	−	0.256508i	$-0.917428\pi$
$127$	−13.8352	+	7.98773i	−1.22767	+	0.708796i	−0.261129	+	0.965304i	$0.584095\pi$
$128$	−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	$0.305965\pi$
$131$			18.7681i			1.63978i	−0.572524	+	0.819888i	$0.694035\pi$
$132$	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	0.999982	−	0.00598848i	$-0.00190620\pi$
$137$	1.53306	+	5.72145i	0.130978	+	0.488816i	−0.869004	+	0.494805i	$0.835240\pi$
$138$	20.1919	−	10.4242i	1.71885	−	0.887369i
$139$	7.48488	−	12.9642i	0.634859	−	1.09961i	−0.351686	−	0.936118i	$-0.614391\pi$
$139$	7.48488	−	12.9642i	0.634859	−	1.09961i	0.986545	−	0.163490i	$-0.0522753\pi$
$140$	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	0.517602	−	0.855621i	$-0.326825\pi$
$149$	17.0119	−	4.55833i	1.39367	−	0.373433i	0.876067	+	0.482189i	$0.160158\pi$
$150$	9.51303	+	0.447719i	0.776735	+	0.0365561i
$151$	7.85127	+	7.85127i	0.638928	+	0.638928i	0.950291	−	0.311363i	$-0.100786\pi$
$151$	7.85127	+	7.85127i	0.638928	+	0.638928i	−0.311363	+	0.950291i	$0.600786\pi$
$152$	−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	−0.331425	−	0.943482i	$-0.607529\pi$
$163$	−1.87301	+	0.501872i	−0.146706	+	0.0393097i	0.184719	+	0.982791i	$0.440863\pi$
$164$	−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	0.740230	−	0.672353i	$-0.234716\pi$
$167$	13.5058	+	3.61887i	1.04511	+	0.280037i	0.304882	+	0.952390i	$0.401383\pi$
$168$	−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	−0.291753	−	0.956494i	$-0.594239\pi$
$173$	8.97651	−	15.5478i	0.682471	−	1.18207i	0.974224	−	0.225581i	$-0.0724281\pi$
$174$	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	0.897156	−	0.441713i	$-0.145629\pi$
$179$	0.883597	+	1.53044i	0.0660431	+	0.114390i	−0.831113	+	0.556103i	$0.812296\pi$
$180$	5.18463	+	6.26472i	0.386440	+	0.466945i
$181$			16.9949i			1.26322i	0.775286	+	0.631611i	$0.217606\pi$
$181$			16.9949i			1.26322i	−0.775286	+	0.631611i	$0.782394\pi$
$182$		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	0.994614	−	0.103644i	$-0.0330503\pi$
$191$	19.3783	+	11.1881i	1.40216	+	0.809539i	0.407549	+	0.913183i	$0.366384\pi$
$192$	−2.43565	−	11.1658i	−0.175778	−	0.805824i
$193$	5.10117	−	19.0378i	0.367190	−	1.37037i	−0.497237	−	0.867615i	$-0.665652\pi$
$193$	5.10117	−	19.0378i	0.367190	−	1.37037i	0.864427	−	0.502758i	$-0.167681\pi$
$194$	−8.75956			−0.628900
$195$		0			0
$196$	−24.0081			−1.71486
$197$	0.385339	−	1.43810i	0.0274542	−	0.102461i	−0.950839	−	0.309685i	$-0.899776\pi$
$197$	0.385339	−	1.43810i	0.0274542	−	0.102461i	0.978293	+	0.207224i	$0.0664430\pi$
$198$	0.0844903	−	0.895628i	0.00600447	−	0.0636495i
$199$	17.0413	+	9.83880i	1.20803	+	0.697454i	0.962328	−	0.271892i	$-0.0876494\pi$
$199$	17.0413	+	9.83880i	1.20803	+	0.697454i	0.245698	+	0.969346i	$0.420983\pi$
$200$	−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	0.911484	+	0.411336i	$0.134938\pi$
$211$	11.7945	+	20.4287i	0.811969	+	1.40637i	−0.0995149	+	0.995036i	$0.531729\pi$
$212$	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	−0.173378	−	0.984855i	$-0.555468\pi$
$223$	−12.1848	−	3.26491i	−0.815955	−	0.218635i	−0.642577	+	0.766221i	$0.722135\pi$
$224$	−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	−0.887012	−	0.461746i	$-0.847223\pi$
$227$	−21.4595	+	5.75004i	−1.42431	+	0.381644i	−0.537302	+	0.843390i	$0.680556\pi$
$228$	0.178451	−	3.79169i	0.0118182	−	0.251111i
$229$	7.05247	+	7.05247i	0.466040	+	0.466040i	0.900629	−	0.434589i	$-0.143106\pi$
$229$	7.05247	+	7.05247i	0.466040	+	0.466040i	−0.434589	+	0.900629i	$0.643106\pi$
$230$	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	0.986154	−	0.165831i	$-0.0530305\pi$
$239$	12.6819	+	12.6819i	0.820323	+	0.820323i	−0.165831	+	0.986154i	$0.553031\pi$
$240$	0.519339	−	11.0348i	0.0335232	−	0.712293i
$241$	−2.72664	+	0.730600i	−0.175638	+	0.0470621i	−0.345566	−	0.938394i	$-0.612313\pi$
$241$	−2.72664	+	0.730600i	−0.175638	+	0.0470621i	0.169928	+	0.985456i	$0.445646\pi$
$242$	−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	0.456141	+	0.889907i	$0.349231\pi$
$251$	−8.59659	+	14.8897i	−0.542612	+	0.939831i	−0.998753	+	0.0499239i	$0.984102\pi$
$252$	−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	0.678797	−	0.734326i	$-0.262501\pi$
$257$	−4.75399	−	8.23416i	−0.296546	−	0.513633i	−0.975343	+	0.220693i	$0.929168\pi$
$258$	−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	−0.293786	−	0.955871i	$-0.594915\pi$
$263$	6.27819	−	3.62472i	0.387130	−	0.223510i	0.680916	+	0.732362i	$0.261582\pi$
$264$	−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	−0.418184	−	0.908362i	$-0.637333\pi$
$269$	−23.1903	−	13.3890i	−1.41394	−	0.816339i	−0.995757	+	0.0920235i	$0.970666\pi$
$270$	5.90250	−	13.8491i	0.359215	−	0.842831i
$271$	0.437592	−	1.63311i	0.0265818	−	0.0992046i	−0.951360	−	0.308080i	$-0.900314\pi$
$271$	0.437592	−	1.63311i	0.0265818	−	0.0992046i	0.977942	+	0.208875i	$0.0669803\pi$
$272$	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	−0.318656	−	0.947870i	$-0.603231\pi$
$277$	−21.6174	−	12.4808i	−1.29886	−	0.749899i	−0.980208	+	0.197971i	$0.936565\pi$
$278$	−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	−0.627587	−	0.778546i	$-0.715957\pi$
$281$	2.53054	−	2.53054i	0.150959	−	0.150959i	0.778546	+	0.627587i	$0.215957\pi$
$282$	13.1194	+	14.4152i	0.781246	+	0.858415i
$283$	4.43312	−	2.55946i	0.263522	−	0.152144i	−0.362418	−	0.932016i	$-0.618049\pi$
$283$	4.43312	−	2.55946i	0.263522	−	0.152144i	0.625940	+	0.779871i	$0.284715\pi$
$284$	−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	0.968014	−	0.250898i	$-0.0807259\pi$
$293$	0.0725803	+	0.270873i	0.00424019	+	0.0158246i	−0.963773	+	0.266723i	$0.914059\pi$
$294$	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	0.233659	−	0.972319i	$-0.424930\pi$
$307$	−12.9424	−	12.9424i	−0.738660	−	0.738660i	−0.972319	+	0.233659i	$0.924930\pi$
$308$	−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	0.847859	−	0.530222i	$-0.177892\pi$
$317$	5.65535	+	5.65535i	0.317636	+	0.317636i	−0.530222	+	0.847859i	$0.677892\pi$
$318$	−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	0.904126	+	0.427266i	$0.140523\pi$
$331$	6.09048	+	22.7300i	0.334763	+	1.24935i	−0.569363	+	0.822086i	$0.692810\pi$
$332$	−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	$0.0721567\pi$
$337$			8.25174i			0.449501i	−0.974416	+	0.224750i	$0.927843\pi$
$338$		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	0.408172	−	0.912905i	$-0.366166\pi$
$347$	−3.32212	−	1.91803i	−0.178341	−	0.102965i	−0.586513	+	0.809940i	$0.699500\pi$
$348$	6.15186	−	1.34193i	0.329774	−	0.0719352i
$349$	−2.99267	+	11.1688i	−0.160194	+	0.597853i	0.838410	+	0.545040i	$0.183485\pi$
$349$	−2.99267	+	11.1688i	−0.160194	+	0.597853i	−0.998604	+	0.0528130i	$0.983181\pi$
$350$	−24.6572			−1.31798
$351$		0			0
$352$	−1.19094			−0.0634771
$353$	2.65025	−	9.89087i	0.141059	−	0.526438i	−0.858841	−	0.512243i	$-0.828815\pi$
$353$	2.65025	−	9.89087i	0.141059	−	0.526438i	0.999899	−	0.0141951i	$-0.00451860\pi$
$354$	−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	−0.480834	−	0.876812i	$-0.659666\pi$
$359$	7.50270	−	7.50270i	0.395977	−	0.395977i	0.876812	+	0.480834i	$0.159666\pi$
$360$	−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	0.988864	−	0.148822i	$-0.0475482\pi$
$367$	7.00290	+	12.1294i	0.365548	+	0.633148i	−0.623316	+	0.781970i	$0.714215\pi$
$368$	−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	−0.482601	−	0.875841i	$-0.660308\pi$
$373$	9.98879	−	17.3011i	0.517200	−	0.895817i	0.999800	−	0.0199760i	$-0.00635897\pi$
$374$	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	0.472811	−	0.881164i	$-0.343239\pi$
$379$	8.59890	+	2.30407i	0.441696	+	0.118352i	−0.0311155	+	0.999516i	$0.509906\pi$
$380$	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	−0.786247	−	0.617912i	$-0.787979\pi$
$383$	−22.6664	+	6.07346i	−1.15820	+	0.310339i	−0.371954	+	0.928251i	$0.621312\pi$
$384$	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	0.671993	−	0.740557i	$-0.265438\pi$
$397$	32.3626	−	8.67155i	1.62423	−	0.435212i	0.952242	+	0.305345i	$0.0987718\pi$
$398$	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	−0.179158	−	0.983820i	$-0.557337\pi$
$401$	−16.5451	−	4.43325i	−0.826224	−	0.221386i	−0.647066	+	0.762434i	$0.724004\pi$
$402$	−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	0.998894	+	0.0470095i	$0.0149691\pi$
$409$	3.18183	+	11.8747i	0.157331	+	0.587168i	−0.841563	+	0.540159i	$0.818364\pi$
$410$	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	−0.830031	−	0.557717i	$-0.811678\pi$
$419$	−15.5988	+	9.00596i	−0.762050	+	0.439970i	0.0679811	+	0.997687i	$0.478344\pi$
$420$	−14.1711	−	15.5709i	−0.691478	−	0.759780i
$421$	−15.2469	+	15.2469i	−0.743088	+	0.743088i	−0.973171	−	0.230083i	$-0.926100\pi$
$421$	−15.2469	+	15.2469i	−0.743088	+	0.743088i	0.230083	+	0.973171i	$0.426100\pi$
$422$	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	0.473604	+	0.880738i	$0.342953\pi$
$431$	−7.82502	+	29.2034i	−0.376918	+	1.40668i	−0.850522	+	0.525940i	$0.823714\pi$
$432$	20.5973	+	8.77857i	0.990989	+	0.422359i
$433$	16.7054	+	9.64486i	0.802810	+	0.463503i	0.844453	−	0.535630i	$-0.179926\pi$
$433$	16.7054	+	9.64486i	0.802810	+	0.463503i	−0.0416428	+	0.999133i	$0.513259\pi$
$434$	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	−0.0956236	−	0.995418i	$-0.530485\pi$
$439$	15.0568	−	8.69304i	0.718622	−	0.414896i	0.814245	+	0.580521i	$0.197151\pi$
$440$	−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	$0.0108396\pi$
$443$			1.43321i			0.0680940i	−0.999420	+	0.0340470i	$0.989160\pi$
$444$	−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	−0.633269	−	0.773932i	$-0.718287\pi$
$449$	−9.99743	−	37.3109i	−0.471808	−	1.76081i	0.161461	−	0.986879i	$-0.448379\pi$
$450$	−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	0.362360	−	0.932038i	$-0.381971\pi$
$457$	4.49257	+	1.20378i	0.210154	+	0.0563105i	−0.152206	+	0.988349i	$0.548638\pi$
$458$	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	−0.0708141	−	0.997490i	$-0.522560\pi$
$461$	7.87132	−	2.10911i	0.366604	−	0.0982312i	0.437418	+	0.899258i	$0.355893\pi$
$462$	−0.109497	+	2.32657i	−0.00509426	+	0.108242i
$463$	4.68191	+	4.68191i	0.217587	+	0.217587i	0.807481	−	0.589894i	$-0.200830\pi$
$463$	4.68191	+	4.68191i	0.217587	+	0.217587i	−0.589894	+	0.807481i	$0.700830\pi$
$464$	−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	−0.171334	−	0.985213i	$-0.554808\pi$
$479$	−17.7785	−	4.76373i	−0.812320	−	0.217660i	−0.640986	+	0.767553i	$0.721474\pi$
$480$	−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	−0.904197	−	0.427116i	$-0.859529\pi$
$487$	−7.38613	−	27.5654i	−0.334698	−	1.24911i	0.569499	−	0.821992i	$-0.307137\pi$
$488$	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	−0.874433	−	0.485146i	$-0.838766\pi$
$491$	−18.9980	−	32.9054i	−0.857366	−	1.48500i	0.0170675	−	0.999854i	$-0.494567\pi$
$492$	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	−0.409152	−	0.912466i	$-0.634175\pi$
$499$	11.2432	−	11.2432i	0.503315	−	0.503315i	0.912466	+	0.409152i	$0.134175\pi$
$500$	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	0.577296	−	0.816535i	$-0.304108\pi$
$503$	3.56162	+	2.05630i	0.158805	+	0.0916859i	−0.418492	+	0.908221i	$0.637441\pi$
$504$	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	−0.673585	−	0.739110i	$-0.735247\pi$
$509$	6.30155	−	23.5177i	0.279311	−	1.04240i	0.952897	−	0.303295i	$-0.0980868\pi$
$510$	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	$0.103311\pi$
$521$			14.5577i			0.637784i	−0.947791	+	0.318892i	$0.896689\pi$
$522$	−7.43198	−	8.98026i	−0.325289	−	0.393055i
$523$	1.85988	+	3.22141i	0.0813270	+	0.140863i	0.903820	−	0.427912i	$-0.140751\pi$
$523$	1.85988	+	3.22141i	0.0813270	+	0.140863i	−0.822493	+	0.568775i	$0.807418\pi$
$524$	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	0.754871	−	0.655873i	$-0.227699\pi$
$541$	2.30265	+	2.30265i	0.0989985	+	0.0989985i	−0.655873	+	0.754871i	$0.727699\pi$
$542$	−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	0.0694921	−	0.997583i	$-0.477862\pi$
$557$	−8.71148	−	2.33423i	−0.369117	−	0.0989047i	−0.438609	+	0.898678i	$0.644529\pi$
$558$	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	−0.758978	−	0.651116i	$-0.774301\pi$
$563$	4.37524	−	7.57814i	0.184395	−	0.319381i	0.943372	+	0.331736i	$0.107634\pi$
$564$	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	0.980489	+	0.196572i	$0.0629810\pi$
$569$	15.7549	+	27.2883i	0.660481	+	1.14399i	−0.320008	+	0.947415i	$0.603686\pi$
$570$	−5.05391	−	3.24388i	−0.211685	−	0.135871i
$571$		−	34.4177i		−	1.44034i	−0.693799	−	0.720169i	$-0.744064\pi$
$571$		−	34.4177i		−	1.44034i	0.693799	−	0.720169i	$-0.255936\pi$
$572$		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	−0.158211	+	0.987405i	$0.550573\pi$
$577$	−27.5186	+	27.5186i	−1.14562	+	1.14562i	−0.987405	+	0.158211i	$0.949427\pi$
$578$	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	−0.941450	−	0.337151i	$-0.890537\pi$
$587$	1.02837	−	3.83792i	0.0424453	−	0.158408i	0.983896	+	0.178743i	$0.0572032\pi$
$588$	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	−0.428539	−	0.903523i	$-0.640971\pi$
$593$	11.5666	−	11.5666i	0.474985	−	0.474985i	0.903523	+	0.428539i	$0.140971\pi$
$594$	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	$0.0151595\pi$
$599$			2.33031i			0.0952139i	−0.998866	+	0.0476069i	$0.984841\pi$
$600$	1.35217	+	0.867894i	0.0552019	+	0.0354316i
$601$	1.95275	+	3.38226i	0.0796542	+	0.137965i	0.903101	−	0.429429i	$-0.141285\pi$
$601$	1.95275	+	3.38226i	0.0796542	+	0.137965i	−0.823447	+	0.567394i	$0.807952\pi$
$602$	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	0.447048	+	0.894510i	$0.352475\pi$
$607$	−13.5787	+	23.5191i	−0.551144	+	0.954609i	−0.998192	+	0.0600995i	$0.980858\pi$
$608$	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	0.135834	−	0.990732i	$-0.456629\pi$
$613$	−5.98906	−	1.60476i	−0.241896	−	0.0648158i	−0.377730	+	0.925916i	$0.623295\pi$
$614$	−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	−0.945081	−	0.326836i	$-0.894018\pi$
$617$	−39.7463	+	10.6500i	−1.60013	+	0.428753i	−0.655046	+	0.755589i	$0.727351\pi$
$618$	−14.9522	−	0.703709i	−0.601468	−	0.0283073i
$619$	−7.15152	−	7.15152i	−0.287444	−	0.287444i	0.548625	−	0.836069i	$-0.315152\pi$
$619$	−7.15152	−	7.15152i	−0.287444	−	0.287444i	−0.836069	+	0.548625i	$0.815152\pi$
$620$	−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	−0.00628685	−	0.999980i	$-0.502001\pi$
$631$	12.2649	−	3.28637i	0.488259	−	0.130829i	0.494546	+	0.869152i	$0.335335\pi$
$632$	−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	0.393894	+	0.919156i	$0.371128\pi$
$641$	−15.1671	+	26.2702i	−0.599065	+	1.03761i	−0.992959	+	0.118455i	$0.962206\pi$
$642$	−24.0712	−	46.6263i	−0.950016	−	1.84019i
$643$	−12.2478	−	45.7094i	−0.483006	−	1.80260i	−0.588878	−	0.808222i	$-0.700430\pi$
$643$	−12.2478	−	45.7094i	−0.483006	−	1.80260i	0.105872	−	0.994380i	$-0.466237\pi$
$644$	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	0.990822	−	0.135173i	$-0.0431589\pi$
$647$	9.62374	+	16.6688i	0.378348	+	0.655318i	−0.612474	+	0.790491i	$0.709826\pi$
$648$	−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	−0.657557	−	0.753405i	$-0.728410\pi$
$653$	−8.53163	+	4.92574i	−0.333868	+	0.192759i	0.323689	+	0.946164i	$0.395077\pi$
$654$	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	0.576061	−	0.817407i	$-0.304589\pi$
$659$	4.00974	+	2.31502i	0.156197	+	0.0901805i	−0.419864	+	0.907587i	$0.637922\pi$
$660$	−0.153291	−	0.702737i	−0.00596686	−	0.0273540i
$661$	−7.94714	+	29.6591i	−0.309108	+	1.15361i	0.620243	+	0.784409i	$0.287034\pi$
$661$	−7.94714	+	29.6591i	−0.309108	+	1.15361i	−0.929351	+	0.369197i	$0.879633\pi$
$662$	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	−0.961108	−	0.276173i	$-0.910934\pi$
$673$	−31.1953	+	18.0106i	−1.20249	+	0.694257i	−0.241381	+	0.970430i	$0.577600\pi$
$674$	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	$0.0343322\pi$
$677$			5.60187i			0.215297i	−0.994189	+	0.107649i	$0.965668\pi$
$678$	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	0.977533	−	0.210780i	$-0.0676004\pi$
$683$	0.668373	+	2.49440i	0.0255746	+	0.0954457i	−0.951959	+	0.306226i	$0.900934\pi$
$684$	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	−0.233641	−	0.972323i	$-0.575064\pi$
$691$	−24.2402	−	6.49515i	−0.922141	−	0.247087i	−0.688500	+	0.725236i	$0.741731\pi$
$692$	−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	0.807146	−	0.590351i	$-0.201011\pi$
$709$	47.9641	−	12.8520i	1.80133	−	0.482665i	0.994185	+	0.107686i	$0.0343441\pi$
$710$	−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	−0.881400	−	0.472371i	$-0.843398\pi$
$719$	−0.847719	+	1.46829i	−0.0316146	+	0.0547581i	0.849785	+	0.527129i	$0.176732\pi$
$720$	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	$-0.876878\pi$
$727$		−	20.3423i		−	0.754455i	0.926121	−	0.377227i	$-0.123122\pi$
$728$		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	−0.636520	−	0.771261i	$-0.719627\pi$
$733$	3.64797	−	3.64797i	0.134741	−	0.134741i	0.771261	+	0.636520i	$0.219627\pi$
$734$	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	−0.519913	−	0.854219i	$-0.674036\pi$
$739$	9.71724	−	36.2652i	0.357454	−	1.33404i	0.877367	−	0.479819i	$-0.159298\pi$
$740$	−8.87383			−0.326209
$741$		0			0
$742$	5.51326			0.202398
$743$	2.36324	−	8.81974i	0.0866989	−	0.323565i	−0.908932	−	0.416945i	$-0.863101\pi$
$743$	2.36324	−	8.81974i	0.0866989	−	0.323565i	0.995630	+	0.0933805i	$0.0297673\pi$
$744$	−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	−0.818487	−	0.574524i	$-0.805187\pi$
$751$	−20.0101	+	11.5528i	−0.730178	+	0.421569i	0.0883090	+	0.996093i	$0.471854\pi$
$752$	−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	−0.972153	−	0.234349i	$-0.924704\pi$
$757$	−18.9577	−	32.8357i	−0.689029	−	1.19343i	0.283124	−	0.959083i	$-0.408629\pi$
$758$	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	−0.731477	−	0.681866i	$-0.761169\pi$
$761$	−12.1085	−	45.1895i	−0.438932	−	1.63812i	0.292545	−	0.956252i	$-0.405498\pi$
$762$	−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	0.749619	−	0.661869i	$-0.230237\pi$
$769$	29.6131	+	7.93479i	1.06787	+	0.286136i	0.318255	+	0.948005i	$0.396903\pi$
$770$	−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	−0.305550	−	0.952176i	$-0.598840\pi$
$773$	−2.61557	+	0.700840i	−0.0940755	+	0.0252075i	0.211474	+	0.977384i

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 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

Introduction

L-functions

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