LMFDB - Embedded newform 507.2.k.k.80.20

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			80.20
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.20

$q$-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} +(1.16581 - 1.28097i) q^{3} +(-1.58594 - 0.915644i) q^{4} +(-1.04664 - 1.04664i) q^{5} +(-1.83128 - 2.85311i) q^{6} +(-4.33161 + 1.16065i) q^{7} +(0.233508 - 0.233508i) q^{8} +(-0.281758 - 2.98674i) q^{9} +(-2.50908 + 1.44862i) q^{10} +(0.147979 + 0.0396510i) q^{11} +(-3.02182 + 0.964071i) q^{12} +8.77764i q^{14} +(-2.56090 + 0.120525i) q^{15} +(-2.15448 - 3.73167i) q^{16} +(1.58364 - 2.74294i) q^{17} +(-5.78968 - 0.980382i) q^{18} +(0.309737 + 1.15595i) q^{19} +(0.701560 + 2.61826i) q^{20} +(-3.56309 + 6.90175i) q^{21} +(0.149934 - 0.259693i) q^{22} +(3.35135 + 5.80471i) q^{23} +(-0.0268896 - 0.571343i) q^{24} -2.80909i q^{25} +(-4.15440 - 3.12106i) q^{27} +(7.93243 + 2.12549i) q^{28} +(-1.71915 + 0.992552i) q^{29} +(-1.06949 + 4.90288i) q^{30} +(3.64859 - 3.64859i) q^{31} +(-7.50887 + 2.01200i) q^{32} +(0.223308 - 0.143331i) q^{33} +(-4.38372 - 4.38372i) q^{34} +(5.74841 + 3.31885i) q^{35} +(-2.28794 + 4.99479i) q^{36} +(0.847303 - 3.16218i) q^{37} +2.34244 q^{38} -0.488797 q^{40} +(2.16637 - 8.08500i) q^{41} +(11.2439 + 10.2331i) q^{42} +(2.41031 + 1.39159i) q^{43} +(-0.198381 - 0.198381i) q^{44} +(-2.83114 + 3.42094i) q^{45} +(12.6726 - 3.39562i) q^{46} +(4.06533 - 4.06533i) q^{47} +(-7.29187 - 1.59061i) q^{48} +(11.3535 - 6.55497i) q^{49} +(-5.31107 - 1.42310i) q^{50} +(-1.66739 - 5.22634i) q^{51} -0.628103i q^{53} +(-8.00553 + 6.27346i) q^{54} +(-0.113381 - 0.196381i) q^{55} +(-0.740444 + 1.28249i) q^{56} +(1.84183 + 0.950863i) q^{57} +(1.00566 + 3.75318i) q^{58} +(2.27275 + 8.48202i) q^{59} +(4.17179 + 2.15372i) q^{60} +(-2.91632 + 5.05121i) q^{61} +(-5.04989 - 8.74667i) q^{62} +(4.68703 + 12.6104i) q^{63} +6.59818i q^{64} +(-0.157864 - 0.494815i) q^{66} +(-0.649609 - 0.174062i) q^{67} +(-5.02311 + 2.90010i) q^{68} +(11.3427 + 2.47424i) q^{69} +(9.18702 - 9.18702i) q^{70} +(11.0529 - 2.96161i) q^{71} +(-0.763221 - 0.631635i) q^{72} +(-3.92370 - 3.92370i) q^{73} +(-5.54940 - 3.20395i) q^{74} +(-3.59836 - 3.27488i) q^{75} +(0.567217 - 2.11688i) q^{76} -0.687010 q^{77} -5.46386 q^{79} +(-1.65075 + 6.16067i) q^{80} +(-8.84122 + 1.68308i) q^{81} +(-14.1886 - 8.19178i) q^{82} +(6.40765 + 6.40765i) q^{83} +(11.9704 - 7.68326i) q^{84} +(-4.52836 + 1.21337i) q^{85} +(3.85212 - 3.85212i) q^{86} +(-0.732781 + 3.35931i) q^{87} +(0.0438132 - 0.0252956i) q^{88} +(5.12896 + 1.37430i) q^{89} +(5.03360 + 7.08582i) q^{90} -12.2746i q^{92} +(-0.420152 - 8.92730i) q^{93} +(-5.62670 - 9.74572i) q^{94} +(0.885683 - 1.53405i) q^{95} +(-6.17664 + 11.9642i) q^{96} +(1.15826 + 4.32269i) q^{97} +(-6.64155 - 24.7866i) q^{98} +(0.0767327 - 0.453148i) 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	$-0.159952\pi$
$3$	1.16581	−	1.28097i	0.673083	−	0.739567i
$3$	1.16581	−	1.28097i	0.673083	−	0.739567i
$4$	−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	$0.857378\pi$
$6$	−1.83128	−	2.85311i	−0.747619	−	1.16478i
$7$	−4.33161	+	1.16065i	−1.63719	+	0.438685i	−0.955988	−	0.293407i	$-0.905211\pi$
$7$	−4.33161	+	1.16065i	−1.63719	+	0.438685i	−0.681206	+	0.732091i	$0.738544\pi$
$8$	0.233508	−	0.233508i	0.0825576	−	0.0825576i
$9$	−0.281758	−	2.98674i	−0.0939195	−	0.995580i
$10$	−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
$15$	−2.56090	+	0.120525i	−0.661221	+	0.0311195i
$16$	−2.15448	−	3.73167i	−0.538620	−	0.932917i
$17$	1.58364	−	2.74294i	0.384088	−	0.665261i	−0.607554	−	0.794278i	$-0.707849\pi$
$17$	1.58364	−	2.74294i	0.384088	−	0.665261i	0.991642	+	0.129018i	$0.0411824\pi$
$18$	−5.78968	−	0.980382i	−1.36464	−	0.231078i
$19$	0.309737	+	1.15595i	0.0710585	+	0.265194i	0.992311	−	0.123772i	$-0.0394991\pi$
$19$	0.309737	+	1.15595i	0.0710585	+	0.265194i	−0.921252	+	0.388966i	$0.872832\pi$
$20$	0.701560	+	2.61826i	0.156874	+	0.585460i
$21$	−3.56309	+	6.90175i	−0.777530	+	1.50609i
$22$	0.149934	−	0.259693i	0.0319660	−	0.0553668i
$23$	3.35135	+	5.80471i	0.698805	+	1.21037i	0.968881	+	0.247527i	$0.0796180\pi$
$23$	3.35135	+	5.80471i	0.698805	+	1.21037i	−0.270076	+	0.962839i	$0.587049\pi$
$24$	−0.0268896	−	0.571343i	−0.00548881	−	0.116625i
$25$		−	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	$-0.725672\pi$
$29$	−1.71915	+	0.992552i	−0.319238	+	0.184312i	0.331815	+	0.943345i	$0.392339\pi$
$30$	−1.06949	+	4.90288i	−0.195261	+	0.895138i
$31$	3.64859	−	3.64859i	0.655306	−	0.655306i	−0.298960	−	0.954266i	$-0.596640\pi$
$31$	3.64859	−	3.64859i	0.655306	−	0.655306i	0.954266	+	0.298960i	$0.0966397\pi$
$32$	−7.50887	+	2.01200i	−1.32739	+	0.355674i
$33$	0.223308	−	0.143331i	0.0388729	−	0.0249508i
$34$	−4.38372	−	4.38372i	−0.751802	−	0.751802i
$35$	5.74841	+	3.31885i	0.971659	+	0.560988i
$36$	−2.28794	+	4.99479i	−0.381323	+	0.832465i
$37$	0.847303	−	3.16218i	0.139296	−	0.519859i	−0.860647	−	0.509201i	$-0.829941\pi$
$37$	0.847303	−	3.16218i	0.139296	−	0.519859i	0.999943	−	0.0106576i	$-0.00339249\pi$
$38$	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	$-0.143410\pi$
$42$	11.2439	+	10.2331i	1.73497	+	1.57900i
$43$	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
$45$	−2.83114	+	3.42094i	−0.422041	+	0.509963i
$46$	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	$0.112273\pi$
$48$	−7.29187	−	1.59061i	−1.05249	−	0.229585i
$49$	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	$-0.0137356\pi$
$54$	−8.00553	+	6.27346i	−1.08941	+	0.853710i
$55$	−0.113381	−	0.196381i	−0.0152883	−	0.0264801i
$56$	−0.740444	+	1.28249i	−0.0989460	+	0.171380i
$57$	1.84183	+	0.950863i	0.243957	+	0.125945i
$58$	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	$0.722986\pi$
$60$	4.17179	+	2.15372i	0.538576	+	0.278045i
$61$	−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
$63$	4.68703	+	12.6104i	0.590510	+	1.58876i
$64$			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	$-0.429747\pi$
$67$	−0.649609	−	0.174062i	−0.0793624	−	0.0212651i	−0.298282	+	0.954478i	$0.596413\pi$
$68$	−5.02311	+	2.90010i	−0.609142	+	0.351688i
$69$	11.3427	+	2.47424i	1.36550	+	0.297863i
$70$	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	$0.179079\pi$
$72$	−0.763221	−	0.631635i	−0.0899464	−	0.0744389i
$73$	−3.92370	−	3.92370i	−0.459235	−	0.459235i	0.439169	−	0.898404i	$-0.355273\pi$
$73$	−3.92370	−	3.92370i	−0.459235	−	0.459235i	−0.898404	+	0.439169i	$0.855273\pi$
$74$	−5.54940	−	3.20395i	−0.645104	−	0.372451i
$75$	−3.59836	−	3.27488i	−0.415503	−	0.378150i
$76$	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
$81$	−8.84122	+	1.68308i	−0.982358	+	0.187009i
$82$	−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	$0.584314\pi$
$84$	11.9704	−	7.68326i	1.30608	−	0.838313i
$85$	−4.52836	+	1.21337i	−0.491170	+	0.131609i
$86$	3.85212	−	3.85212i	0.415384	−	0.415384i
$87$	−0.732781	+	3.35931i	−0.0785624	+	0.360155i
$88$	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
$93$	−0.420152	−	8.92730i	−0.0435677	−	0.925717i
$94$	−5.62670	−	9.74572i	−0.580349	−	1.00519i
$95$	0.885683	−	1.53405i	0.0908692	−	0.157390i
$96$	−6.17664	+	11.9642i	−0.630401	+	1.22110i
$97$	1.15826	+	4.32269i	0.117604	+	0.438902i	0.999468	−	0.0325997i	$-0.0103786\pi$
$97$	1.15826	+	4.32269i	0.117604	+	0.438902i	−0.881865	+	0.471502i	$0.843712\pi$
$98$	−6.64155	−	24.7866i	−0.670898	−	2.50382i
$99$	0.0767327	−	0.453148i	0.00771193	−	0.0455431i
$100$	−2.57213	+	4.45506i	−0.257213	+	0.445506i
$101$	0.840488	+	1.45577i	0.0836317	+	0.144854i	0.904807	−	0.425821i	$-0.140015\pi$
$101$	0.840488	+	1.45577i	0.0836317	+	0.144854i	−0.821176	+	0.570676i	$0.806681\pi$
$102$	−10.7260	+	0.504806i	−1.06203	+	0.0499833i
$103$			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	0.316137	−	0.948714i	$-0.397614\pi$
$107$	13.4040	−	7.73882i	1.29582	−	0.748140i	0.979679	+	0.200574i	$0.0642807\pi$
$108$	3.73085	+	8.75377i	0.359002	+	0.842331i
$109$	−8.78130	+	8.78130i	−0.841096	+	0.841096i	−0.989002	−	0.147905i	$-0.952747\pi$
$109$	−8.78130	+	8.78130i	−0.841096	+	0.841096i	0.147905	+	0.989002i	$0.452747\pi$
$110$	−0.428732	+	0.114878i	−0.0408780	+	0.0109532i
$111$	−3.06285	−	4.77188i	−0.290713	−	0.452927i
$112$	13.6635	+	13.6635i	1.29108	+	1.29108i
$113$	4.14900	+	2.39543i	0.390305	+	0.225343i	0.682292	−	0.731080i	$-0.260983\pi$
$113$	4.14900	+	2.39543i	0.390305	+	0.225343i	−0.291987	+	0.956422i	$0.594316\pi$
$114$	2.73085	−	3.00059i	0.255768	−	0.281031i
$115$	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
$120$	−0.569847	+	0.626134i	−0.0520196	+	0.0571579i
$121$	−9.50595	−	5.48826i	−0.864178	−	0.498933i
$122$	8.07276	+	8.07276i	0.730873	+	0.730873i
$123$	−7.83104	−	12.2006i	−0.706101	−	1.10010i
$124$	−9.12726	+	2.44564i	−0.819652	+	0.219625i
$125$	−8.17330	+	8.17330i	−0.731042	+	0.731042i
$126$	26.2165	−	2.47317i	2.33555	−	0.220328i
$127$	−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	$-0.694035\pi$
$131$		−	18.7681i		−	1.63978i	0.572524	−	0.819888i	$-0.305965\pi$
$132$	−0.485394	+	0.0228445i	−0.0422481	+	0.00198836i
$133$	−2.68332	−	4.64764i	−0.232673	−	0.403001i
$134$	−0.658189	+	1.14002i	−0.0568589	+	0.0984825i
$135$	1.08153	+	7.61477i	0.0930835	+	0.655375i
$136$	−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	$0.835240\pi$
$138$	10.4242	−	20.1919i	0.887369	−	1.71885i
$139$	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
$141$	−0.468142	−	9.94698i	−0.0394247	−	0.837687i
$142$		−	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
$147$	4.83940	−	22.1854i	0.399147	−	1.82982i
$148$	−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	$0.160158\pi$
$150$	−8.01466	+	5.14425i	−0.654395	+	0.420026i
$151$	−7.85127	−	7.85127i	−0.638928	−	0.638928i	0.311363	−	0.950291i	$-0.399214\pi$
$151$	−7.85127	−	7.85127i	−0.638928	−	0.638928i	−0.950291	+	0.311363i	$0.899214\pi$
$152$	0.342250	+	0.197598i	0.0277602	+	0.0160273i
$153$	−8.63865	−	3.95707i	−0.698393	−	0.319910i
$154$	−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
$159$	−0.804580	−	0.732251i	−0.0638073	−	0.0580713i
$160$	9.96491	+	5.75325i	0.787796	+	0.454834i
$161$	−21.2540	−	21.2540i	−1.67505	−	1.67505i
$162$	−1.29685	+	17.5685i	−0.101890	+	1.38031i
$163$	1.87301	−	0.501872i	0.146706	−	0.0393097i	−0.184719	−	0.982791i	$-0.559137\pi$
$163$	1.87301	−	0.501872i	0.146706	−	0.0393097i	0.331425	+	0.943482i	$0.392471\pi$
$164$	−10.8387	+	10.8387i	−0.846362	+	0.846362i
$165$	−0.383739	−	0.0837068i	−0.0298741	−	0.00651656i
$166$	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
$171$	3.36526	−	1.25080i	0.257348	−	0.0956512i
$172$	−2.54841	−	4.41397i	−0.194314	−	0.336562i
$173$	−8.97651	+	15.5478i	−0.682471	+	1.18207i	0.291753	+	0.956494i	$0.405761\pi$
$173$	−8.97651	+	15.5478i	−0.682471	+	1.18207i	−0.974224	+	0.225581i	$0.927572\pi$
$174$	5.98012	+	3.08729i	0.453351	+	0.234047i
$175$	3.26038	+	12.1679i	0.246461	+	0.919806i
$176$	−0.170854	−	0.637638i	−0.0128786	−	0.0480637i
$177$	13.5148	+	6.97713i	1.01583	+	0.524433i
$178$	5.19670	−	9.00095i	0.389509	−	0.674650i
$179$	−0.883597	−	1.53044i	−0.0660431	−	0.114390i	0.831113	−	0.556103i	$-0.187704\pi$
$179$	−0.883597	−	1.53044i	−0.0660431	−	0.114390i	−0.897156	+	0.441713i	$0.854371\pi$
$180$	7.62239	−	2.83309i	0.568139	−	0.211166i
$181$			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
$186$	−17.0914	−	3.72823i	−1.25321	−	0.273367i
$187$	0.343106	−	0.343106i	0.0250904	−	0.0250904i
$188$	−10.1698	+	2.72498i	−0.741707	+	0.198740i
$189$	21.6177	+	8.69739i	1.57245	+	0.632642i
$190$	−2.45169	−	2.45169i	−0.177864	−	0.177864i
$191$	−19.3783	−	11.1881i	−1.40216	−	0.809539i	−0.407549	−	0.913183i	$-0.633616\pi$
$191$	−19.3783	−	11.1881i	−1.40216	−	0.809539i	−0.994614	+	0.103644i	$0.966950\pi$
$192$	8.45206	+	7.69225i	0.609975	+	0.555140i
$193$	−5.10117	+	19.0378i	−0.367190	+	1.37037i	0.497237	+	0.867615i	$0.334348\pi$
$193$	−5.10117	+	19.0378i	−0.367190	+	1.37037i	−0.864427	+	0.502758i	$0.832319\pi$
$194$	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	$0.0664430\pi$
$198$	−0.817881	−	0.374643i	−0.0581243	−	0.0266247i
$199$	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
$201$	−0.980291	+	0.629204i	−0.0691444	+	0.0443806i
$202$	3.17818	−	0.851590i	0.223616	−	0.0599176i
$203$	6.29468	−	6.29468i	0.441800	−	0.441800i
$204$	−2.14108	+	9.81542i	−0.149906	+	0.687217i
$205$	−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
$210$	−1.05793	−	22.4786i	−0.0730040	−	1.55117i
$211$	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
$213$	9.09186	−	17.6111i	0.622964	−	1.20669i
$214$	−7.84103	−	29.2631i	−0.536002	−	2.00039i
$215$	−1.06623	−	3.97922i	−0.0727161	−	0.271380i
$216$	−1.69888	+	0.241293i	−0.115594	+	0.0164179i
$217$	−11.5695	+	20.0390i	−0.785390	+	1.36034i
$218$	12.1539	+	21.0512i	0.823167	+	1.42577i
$219$	−9.60045	+	0.451833i	−0.648738	+	0.0305320i
$220$			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	$-0.277865\pi$
$223$	12.1848	+	3.26491i	0.815955	+	0.218635i	0.173378	+	0.984855i	$0.444532\pi$
$224$	30.1903	−	17.4304i	2.01717	−	1.16462i
$225$	−8.39003	+	0.791486i	−0.559335	+	0.0527657i
$226$	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	$0.680556\pi$
$228$	−2.05039	−	3.19448i	−0.135790	−	0.211559i
$229$	−7.05247	−	7.05247i	−0.466040	−	0.466040i	0.434589	−	0.900629i	$-0.356894\pi$
$229$	−7.05247	−	7.05247i	−0.466040	−	0.466040i	−0.900629	+	0.434589i	$0.856894\pi$
$230$	−16.8176	−	9.70967i	−1.10892	−	0.640237i
$231$	−0.800926	+	0.880038i	−0.0526970	+	0.0579022i
$232$	−0.169667	+	0.633204i	−0.0111392	+	0.0415719i
$233$	−22.9574			−1.50399			−0.751996	−	0.659168i	$-0.770909\pi$
$233$	−22.9574			−1.50399			−0.751996	+	0.659168i	$0.770909\pi$
$234$		0			0
$235$	−8.50987			−0.555123
$236$	4.16206	−	15.5330i	0.270927	−	1.01111i
$237$	−6.36985	+	6.99903i	−0.413766	+	0.454636i
$238$	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	$0.553031\pi$
$240$	5.96716	+	9.29675i	0.385179	+	0.600103i
$241$	2.72664	−	0.730600i	0.175638	−	0.0470621i	−0.169928	−	0.985456i	$-0.554354\pi$
$241$	2.72664	−	0.730600i	0.175638	−	0.0470621i	0.345566	+	0.938394i	$0.387687\pi$
$242$	−15.1923	+	15.1923i	−0.976596	+	0.976596i
$243$	−8.15125	+	13.2875i	−0.522903	+	0.852392i
$244$	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
$249$	15.6781	−	0.737871i	0.993560	−	0.0467606i
$250$	11.3124	+	19.5937i	0.715459	+	1.23921i
$251$	8.59659	−	14.8897i	0.542612	−	0.939831i	−0.456141	−	0.889907i	$-0.650769\pi$
$251$	8.59659	−	14.8897i	0.542612	−	0.939831i	0.998753	−	0.0499239i	$-0.0158979\pi$
$252$	4.11325	−	24.2910i	0.259110	−	1.53019i
$253$	0.265769	+	0.991863i	0.0167087	+	0.0623579i
$254$	8.09323	+	30.2044i	0.507815	+	1.89519i
$255$	−3.72494	+	7.21526i	−0.233265	+	0.451837i
$256$	−9.17451	+	15.8907i	−0.573407	+	0.993170i
$257$	4.75399	+	8.23416i	0.296546	+	0.513633i	0.975343	−	0.220693i	$-0.0708318\pi$
$257$	4.75399	+	8.23416i	0.296546	+	0.513633i	−0.678797	+	0.734326i	$0.737499\pi$
$258$	−0.443589	−	9.42528i	−0.0276167	−	0.586793i
$259$			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	$-0.738418\pi$
$263$	−6.27819	+	3.62472i	−0.387130	+	0.223510i	0.293786	+	0.955871i	$0.405085\pi$
$264$	0.0186752	−	0.0856133i	0.00114938	−	0.00526913i
$265$	−0.657397	+	0.657397i	−0.0403836	+	0.0403836i
$266$	−10.1465	+	2.71876i	−0.622124	+	0.166698i
$267$	7.73984	−	4.96785i	0.473671	−	0.304028i
$268$	0.870863	+	0.870863i	0.0531964	+	0.0531964i
$269$	23.1903	+	13.3890i	1.41394	+	0.816339i	0.995757	−	0.0920235i	$-0.0293335\pi$
$269$	23.1903	+	13.3890i	1.41394	+	0.816339i	0.418184	+	0.908362i	$0.362667\pi$
$270$	14.9449	+	1.81285i	0.909521	+	0.110327i
$271$	−0.437592	+	1.63311i	−0.0265818	+	0.0992046i	−0.977942	−	0.208875i	$-0.933020\pi$
$271$	−0.437592	+	1.63311i	−0.0265818	+	0.0992046i	0.951360	+	0.308080i	$0.0996864\pi$
$272$	−13.6477			−0.827511
$273$		0			0
$274$	11.5940			0.700421
$275$	0.111383	−	0.415688i	0.00671667	−	0.0250669i
$276$	−15.7234	−	14.3099i	−0.946435	−	0.861353i
$277$	−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
$279$	−11.9254	−	9.86936i	−0.713955	−	0.590863i
$280$	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	$0.215957\pi$
$282$	−19.0436	−	4.15408i	−1.13403	−	0.247372i
$283$	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
$288$	8.12500	+	21.8602i	0.478770	+	1.28812i
$289$	3.48419	+	6.03479i	0.204952	+	0.354988i
$290$	2.87566	−	4.98079i	0.168865	−	0.292482i
$291$	6.88754	+	3.55575i	0.403755	+	0.208442i
$292$	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	$0.914059\pi$
$294$	−39.4937	−	20.3889i	−2.30332	−	1.18911i
$295$	6.49886	−	11.2564i	0.378378	−	0.655370i
$296$	−0.540542	−	0.936246i	−0.0314184	−	0.0544182i
$297$	−0.491012	−	0.626578i	−0.0284914	−	0.0363578i
$298$		−	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
$303$	2.84465	+	0.620516i	0.163421	+	0.0356477i
$304$	3.64631	−	3.64631i	0.209130	−	0.209130i
$305$	8.33912	−	2.23446i	0.477497	−	0.127945i
$306$	−11.8579	+	14.3282i	−0.677870	+	0.819088i
$307$	12.9424	+	12.9424i	0.738660	+	0.738660i	0.972319	−	0.233659i	$-0.0750699\pi$
$307$	12.9424	+	12.9424i	0.738660	+	0.738660i	−0.233659	+	0.972319i	$0.575070\pi$
$308$	1.08956	+	0.629057i	0.0620834	+	0.0358438i
$309$	5.65578	+	5.14734i	0.321746	+	0.292822i
$310$	−3.86919	+	14.4400i	−0.219755	+	0.820138i
$311$	6.76425			0.383565			0.191783	−	0.981437i	$-0.438573\pi$
$311$	6.76425			0.383565			0.191783	+	0.981437i	$0.438573\pi$
$312$		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
$315$	8.29287	−	18.1041i	0.467250	−	1.02005i
$316$	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	$0.677892\pi$
$318$	−1.79205	+	1.15024i	−0.100493	+	0.0645020i
$319$	−0.293755	+	0.0787113i	−0.0164471	+	0.00440699i
$320$	6.90592	−	6.90592i	0.386052	−	0.386052i
$321$	5.71341	−	26.1921i	0.318892	−	1.46190i
$322$	−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
$327$	1.01121	+	21.4859i	0.0559199	+	1.18817i
$328$	−1.38205	−	2.39378i	−0.0763108	−	0.132174i
$329$	−12.8910	+	22.3279i	−0.710703	+	1.23097i
$330$	−0.352666	+	0.683119i	−0.0194136	+	0.0376044i
$331$	−6.09048	−	22.7300i	−0.334763	−	1.24935i	−0.904126	−	0.427266i	$-0.859477\pi$
$331$	−6.09048	−	22.7300i	−0.334763	−	1.24935i	0.569363	−	0.822086i	$-0.307190\pi$
$332$	−4.29503	−	16.0293i	−0.235721	−	0.879721i
$333$	−9.68334	−	1.63970i	−0.530644	−	0.0898552i
$334$	13.6842	−	23.7017i	0.748767	−	1.29690i
$335$	0.497726	+	0.862086i	0.0271937	+	0.0471008i
$336$	33.4317	−	1.57342i	1.82385	−	0.0858371i
$337$			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
$342$	−0.660002	−	6.99626i	−0.0356888	−	0.378315i
$343$	−19.3744	+	19.3744i	−1.04612	+	1.04612i
$344$	0.887774	−	0.237878i	0.0478656	−	0.0128255i
$345$	−9.28208	−	14.4613i	−0.499731	−	0.778573i
$346$	24.8482	+	24.8482i	1.33585	+	1.33585i
$347$	3.32212	+	1.91803i	0.178341	+	0.102965i	0.586513	−	0.809940i	$-0.300500\pi$
$347$	3.32212	+	1.91803i	0.178341	+	0.102965i	−0.408172	+	0.912905i	$0.633834\pi$
$348$	4.23808	−	4.65670i	0.227185	−	0.249625i
$349$	2.99267	−	11.1688i	0.160194	−	0.597853i	−0.838410	−	0.545040i	$-0.816515\pi$
$349$	2.99267	−	11.1688i	0.160194	−	0.597853i	0.998604	−	0.0528130i	$-0.0168187\pi$
$350$	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	$-0.00451860\pi$
$354$	20.0381	−	22.0174i	1.06501	−	1.17021i
$355$	−14.6681	−	8.46864i	−0.778502	−	0.449469i
$356$	−6.87586	−	6.87586i	−0.364420	−	0.364420i
$357$	13.2885	+	20.7032i	0.703300	+	1.09573i
$358$	−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	$0.159666\pi$
$360$	0.137723	+	1.45991i	0.00725863	+	0.0769440i
$361$	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
$366$	19.7523	−	0.929616i	1.03247	−	0.0485918i
$367$	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
$369$	−24.7582	−	4.19236i	−1.28886	−	0.218246i
$370$	2.45484	+	9.16159i	0.127621	+	0.476288i
$371$	0.729008	+	2.72070i	0.0378482	+	0.141251i
$372$	−7.50789	+	14.5429i	−0.389266	+	0.754014i
$373$	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
$375$	0.941194	+	19.9983i	0.0486031	+	1.03271i
$376$		−	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	$-0.490094\pi$
$379$	−8.59890	−	2.30407i	−0.441696	−	0.118352i	−0.472811	+	0.881164i	$0.656761\pi$
$380$	−2.80928	+	1.62194i	−0.144113	+	0.0832038i
$381$	−5.89718	+	27.0346i	−0.302122	+	1.38502i
$382$	−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	$0.621312\pi$
$384$	−3.83712	+	2.46288i	−0.195812	+	0.125683i
$385$	0.719052	+	0.719052i	0.0366463	+	0.0366463i
$386$	33.4100	+	19.2893i	1.70053	+	0.981799i
$387$	3.47720	−	7.59105i	0.176756	−	0.385875i
$388$	2.12111	−	7.91609i	0.107683	−	0.401878i
$389$	33.0750			1.67697			0.838484	−	0.544926i	$-0.183442\pi$
$389$	33.0750			1.67697			0.838484	+	0.544926i	$0.183442\pi$
$390$		0			0
$391$	21.2293			1.07361
$392$	1.12051	−	4.18178i	0.0565941	−	0.211212i
$393$	−24.0413	−	21.8801i	−1.21273	−	1.10371i
$394$	−2.52377	−	1.45710i	−0.127146	−	0.0734076i
$395$	5.71869	+	5.71869i	0.287739	+	0.287739i
$396$	−0.536616	+	0.648407i	−0.0269660	+	0.0325837i
$397$	−32.3626	+	8.67155i	−1.62423	+	0.435212i	−0.952242	−	0.305345i	$-0.901228\pi$
$397$	−32.3626	+	8.67155i	−1.62423	+	0.435212i	−0.671993	+	0.740557i	$0.734562\pi$
$398$	27.2351	−	27.2351i	1.36517	−	1.36517i
$399$	−9.08172	−	1.98104i	−0.454655	−	0.0991759i
$400$	−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
$405$	11.0151	+	7.49200i	0.547347	+	0.372280i
$406$	−8.71226	−	15.0901i	−0.432382	−	0.748908i
$407$	0.250767	−	0.434341i	0.0124301	−	0.0215295i
$408$	−1.60974	−	0.831044i	−0.0796942	−	0.0411428i
$409$	−3.18183	−	11.8747i	−0.157331	−	0.587168i	−0.998894	−	0.0470095i	$-0.985031\pi$
$409$	−3.18183	−	11.8747i	−0.157331	−	0.587168i	0.841563	−	0.540159i	$-0.181636\pi$
$410$	6.27649	+	23.4242i	0.309974	+	1.15684i
$411$	9.11625	+	4.70634i	0.449672	+	0.232147i
$412$	4.04279	−	7.00231i	0.199174	−	0.344979i
$413$	−19.6893	−	34.1029i	−0.968848	−	1.67809i
$414$	−13.7124	−	36.8931i	−0.673930	−	1.81320i
$415$		−	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	$-0.521656\pi$
$419$	15.5988	−	9.00596i	0.762050	−	0.439970i	0.830031	+	0.557717i	$0.188322\pi$
$420$	−20.5703	−	4.48709i	−1.00373	−	0.218948i
$421$	15.2469	−	15.2469i	0.743088	−	0.743088i	−0.230083	−	0.973171i	$-0.573900\pi$
$421$	15.2469	−	15.2469i	0.743088	−	0.743088i	0.973171	+	0.230083i	$0.0738996\pi$
$422$	44.5992	−	11.9503i	2.17105	−	0.581732i
$423$	−13.2875	−	10.9966i	−0.646062	−	0.534675i
$424$	−0.146667	−	0.146667i	−0.00712278	−	0.00712278i
$425$	−7.70517	−	4.44858i	−0.373756	−	0.215788i
$426$	−28.6908	−	26.1116i	−1.39007	−	1.26511i
$427$	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	$0.823714\pi$
$432$	−2.69619	+	22.2271i	−0.129720	+	1.06940i
$433$	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
$435$	4.28294	−	2.74902i	0.205351	−	0.131806i
$436$	21.9672	−	5.88609i	1.05204	−	0.281893i
$437$	−5.67194	+	5.67194i	−0.271326	+	0.271326i
$438$	−4.00936	+	18.3802i	−0.191574	+	0.878240i
$439$	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	$-0.989160\pi$
$443$		−	1.43321i		−	0.0680940i	0.999420	−	0.0340470i	$-0.0108396\pi$
$444$	0.488164	+	10.3724i	0.0231673	+	0.492253i
$445$	−3.92977	−	6.80656i	−0.186289	−	0.322662i
$446$	12.3457	−	21.3835i	0.584588	−	1.01254i
$447$	13.9936	−	27.1059i	0.661876	−	1.28206i
$448$	−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	$-0.448379\pi$
$450$	−2.75398	+	16.2638i	−0.129824	+	0.766681i
$451$	0.641156	−	1.11051i	0.0301909	−	0.0522921i
$452$	−4.38672	−	7.59801i	−0.206334	−	0.357381i
$453$	−19.2104	+	0.904111i	−0.902581	+	0.0424788i
$454$			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	$-0.451362\pi$
$457$	−4.49257	−	1.20378i	−0.210154	−	0.0563105i	−0.362360	+	0.932038i	$0.618029\pi$
$458$	−16.9067	+	9.76110i	−0.789999	+	0.456106i
$459$	−15.1399	+	6.45264i	−0.706671	+	0.301183i
$460$	−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	$0.355893\pi$
$462$	1.25811	+	1.96012i	0.0585326	+	0.0911930i
$463$	−4.68191	−	4.68191i	−0.217587	−	0.217587i	0.589894	−	0.807481i	$-0.299170\pi$
$463$	−4.68191	−	4.68191i	−0.217587	−	0.217587i	−0.807481	+	0.589894i	$0.799170\pi$
$464$	7.40775	+	4.27686i	0.343896	+	0.198548i
$465$	−8.90391	+	9.78340i	−0.412909	+	0.453694i
$466$	−11.6303	+	43.4050i	−0.538765	+	2.01070i
$467$	15.0964			0.698578			0.349289	−	0.937015i	$-0.386423\pi$
$467$	15.0964			0.698578			0.349289	+	0.937015i	$0.386423\pi$
$468$		0			0
$469$	3.01588			0.139260
$470$	−4.31113	+	16.0894i	−0.198858	+	0.742147i
$471$	12.2007	−	13.4058i	0.562177	−	0.617707i
$472$	2.51132	+	1.44991i	0.115593	+	0.0667377i
$473$	0.301498	+	0.301498i	0.0138629	+	0.0138629i
$474$	10.0059	+	15.5890i	0.459586	+	0.716028i
$475$	3.24718	−	0.870079i	0.148991	−	0.0399220i
$476$	18.3922	−	18.3922i	0.843004	−	0.843004i
$477$	−1.87598	+	0.176973i	−0.0858952	+	0.00810305i
$478$	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
$483$	−52.0039	+	2.44750i	−2.36626	+	0.111365i
$484$	10.0506	+	17.4081i	0.456845	+	0.791279i
$485$	3.31201	−	5.73657i	0.150391	−	0.260484i
$486$	20.9928	+	22.1428i	0.952253	+	1.00442i
$487$	7.38613	+	27.5654i	0.334698	+	1.24911i	0.904197	+	0.427116i	$0.140471\pi$
$487$	7.38613	+	27.5654i	0.334698	+	1.24911i	−0.569499	+	0.821992i	$0.692863\pi$
$488$	0.498514	+	1.86048i	0.0225667	+	0.0842200i
$489$	1.54070	−	2.98436i	0.0696729	−	0.134957i
$490$	−18.9913	+	32.8939i	−0.857940	+	1.48600i
$491$	18.9980	+	32.9054i	0.857366	+	1.48500i	0.874433	+	0.485146i	$0.161234\pi$
$491$	18.9980	+	32.9054i	0.857366	+	1.48500i	−0.0170675	+	0.999854i	$0.505433\pi$
$492$	1.24813	+	26.5200i	0.0562700	+	1.19561i
$493$			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
$498$	6.54752	−	30.0160i	0.293402	−	1.34505i
$499$	−11.2432	+	11.2432i	−0.503315	+	0.503315i	−0.912466	−	0.409152i	$-0.865825\pi$
$499$	−11.2432	+	11.2432i	−0.503315	+	0.503315i	0.409152	+	0.912466i	$0.365825\pi$
$500$	20.4462	−	5.47855i	0.914383	−	0.245008i
$501$	20.3809	−	13.0816i	0.910553	−	0.584443i
$502$	−23.7965	−	23.7965i	−1.06209	−	1.06209i
$503$	−3.56162	−	2.05630i	−0.158805	−	0.0916859i	0.418492	−	0.908221i	$-0.362559\pi$
$503$	−3.56162	−	2.05630i	−0.158805	−	0.0916859i	−0.577296	+	0.816535i	$0.695892\pi$
$504$	4.03908	+	1.85016i	0.179915	+	0.0824128i
$505$	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	$-0.0980868\pi$
$510$	11.7546	+	10.6979i	0.520503	+	0.473712i
$511$	21.5500	+	12.4419i	0.953316	+	0.550397i
$512$	21.6735	+	21.6735i	0.957841	+	0.957841i
$513$	2.32103	−	5.76899i	0.102476	−	0.254707i
$514$	17.9765	−	4.81679i	0.792909	−	0.212459i
$515$	4.62116	−	4.62116i	0.203633	−	0.203633i
$516$	−8.62512	−	1.88144i	−0.379700	−	0.0828257i
$517$	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	$-0.103311\pi$
$522$	10.9264	−	4.06114i	0.478236	−	0.177751i
$523$	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
$525$	19.3877	+	10.0091i	0.846147	+	0.436831i
$526$	3.67259	+	13.7063i	0.160133	+	0.597623i
$527$	−4.22982	−	15.7859i	−0.184254	−	0.687644i
$528$	−1.01598	−	0.524507i	−0.0442148	−	0.0228262i
$529$	−10.9631	+	18.9887i	−0.476658	+	0.825596i
$530$	0.909882	+	1.57596i	0.0395228	+	0.0684554i
$531$	24.6932	−	9.17799i	1.07159	−	0.398291i
$532$			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
$537$	−2.99055	−	0.652342i	−0.129052	−	0.0281506i
$538$	37.0624	−	37.0624i	1.59788	−	1.59788i
$539$	1.94000	−	0.519822i	0.0835618	−	0.0223903i
$540$	5.25718	−	13.0669i	0.226233	−	0.562309i
$541$	−2.30265	−	2.30265i	−0.0989985	−	0.0989985i	0.655873	−	0.754871i	$-0.272301\pi$
$541$	−2.30265	−	2.30265i	−0.0989985	−	0.0989985i	−0.754871	+	0.655873i	$0.772301\pi$
$542$	2.86600	+	1.65468i	0.123105	+	0.0710748i
$543$	21.7699	+	19.8129i	0.934237	+	0.850252i
$544$	−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
$549$	15.9083	+	7.28705i	0.678951	+	0.311004i
$550$	−0.729503	−	0.421179i	−0.0311061	−	0.0179591i
$551$	−1.67983	−	1.67983i	−0.0715630	−	0.0715630i
$552$	3.22637	−	2.07086i	0.137323	−	0.0881416i
$553$	23.6673	−	6.34164i	1.00644	−	0.269674i
$554$	−34.5486	+	34.5486i	−1.46783	+	1.46783i
$555$	−1.78873	+	8.20014i	−0.0759275	+	0.348076i
$556$	−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
$561$	−0.0395103	−	0.839506i	−0.00166812	−	0.0354440i
$562$	−3.50244	−	6.06641i	−0.147742	−	0.255896i
$563$	−4.37524	+	7.57814i	−0.184395	+	0.319381i	−0.943372	−	0.331736i	$-0.892366\pi$
$563$	−4.37524	+	7.57814i	−0.184395	+	0.319381i	0.758978	+	0.651116i	$0.225699\pi$
$564$	−8.36545	+	16.2040i	−0.352249	+	0.682311i
$565$	−1.83536	−	6.84965i	−0.0772141	−	0.288167i
$566$	−2.59327	−	9.67821i	−0.109003	−	0.406806i
$567$	36.3433	−	17.5520i	1.52627	−	0.737115i
$568$	1.88938	−	3.27250i	0.0792765	−	0.137311i
$569$	−15.7549	−	27.2883i	−0.660481	−	1.14399i	−0.980489	−	0.196572i	$-0.937019\pi$
$569$	−15.7549	−	27.2883i	−0.660481	−	1.14399i	0.320008	−	0.947415i	$-0.396314\pi$
$570$	−5.99875	+	0.282324i	−0.251260	+	0.0118252i
$571$		−	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
$576$	19.7071	−	1.85909i	0.821127	−	0.0774622i
$577$	27.5186	−	27.5186i	1.14562	−	1.14562i	0.158211	−	0.987405i	$-0.449427\pi$
$577$	27.5186	−	27.5186i	1.14562	−	1.14562i	0.987405	−	0.158211i	$-0.0505726\pi$
$578$	13.1749	−	3.53021i	0.548004	−	0.146837i
$579$	18.4398	+	28.7290i	0.766334	+	1.19394i
$580$	−3.80484	−	3.80484i	−0.157988	−	0.157988i
$581$	−35.1925	−	20.3184i	−1.46003	−	0.842948i
$582$	10.2120	−	11.2207i	0.423302	−	0.465114i
$583$	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	$0.0572032\pi$
$588$	−27.9889	+	30.7536i	−1.15424	+	1.26826i
$589$	5.34770	+	3.08749i	0.220348	+	0.127218i
$590$	−17.9897	−	17.9897i	−0.740625	−	0.740625i
$591$	−1.39293	−	2.17017i	−0.0572976	−	0.0892688i
$592$	−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	$0.140971\pi$
$594$	−1.43340	+	0.610916i	−0.0588132	+	0.0250662i
$595$	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	$-0.0151595\pi$
$600$	−1.60496	+	0.0755353i	−0.0655221	+	0.00308371i
$601$	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
$603$	−0.336846	+	1.98926i	−0.0137174	+	0.0810088i
$604$	5.26269	+	19.6406i	0.214136	+	0.799166i
$605$	4.20507	+	15.6935i	0.170960	+	0.638033i
$606$	2.61430	−	5.06394i	0.106199	−	0.205708i
$607$	−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
$609$	−0.724862	−	15.4017i	−0.0293729	−	0.624108i
$610$		−	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	$-0.376705\pi$
$613$	5.98906	+	1.60476i	0.241896	+	0.0648158i	−0.135834	+	0.990732i	$0.543371\pi$
$614$	31.0264	−	17.9131i	1.25212	−	0.722914i
$615$	−4.57340	+	20.9659i	−0.184417	+	0.845429i
$616$	−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	$0.727351\pi$
$618$	12.5972	−	8.08555i	0.506733	−	0.325249i
$619$	7.15152	+	7.15152i	0.287444	+	0.287444i	0.836069	−	0.548625i	$-0.184848\pi$
$619$	7.15152	+	7.15152i	0.287444	+	0.287444i	−0.548625	+	0.836069i	$0.684848\pi$
$620$	12.1126	+	6.99324i	0.486456	+	0.280855i
$621$	4.19400	−	34.5748i	0.168299	−	1.38744i
$622$	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
$627$	0.234851	+	0.213739i	0.00937904	+	0.00853590i
$628$	−16.5975	−	9.58256i	−0.662311	−	0.382386i
$629$	−7.33185	−	7.33185i	−0.292340	−	0.292340i
$630$	−30.0278	−	24.8507i	−1.19633	−	0.990076i
$631$	−12.2649	+	3.28637i	−0.488259	+	0.130829i	−0.494546	−	0.869152i	$-0.664665\pi$
$631$	−12.2649	+	3.28637i	−0.488259	+	0.130829i	0.00628685	+	0.999980i	$0.497999\pi$
$632$	−1.27586	+	1.27586i	−0.0507508	+	0.0507508i
$633$	39.9188	+	8.70767i	1.58663	+	0.346099i
$634$	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
$639$	−11.9598	−	32.1776i	−0.473122	−	1.27293i
$640$	1.94823	+	3.37444i	0.0770107	+	0.133386i
$641$	15.1671	−	26.2702i	0.599065	−	1.03761i	−0.393894	−	0.919156i	$-0.628872\pi$
$641$	15.1671	−	26.2702i	0.599065	−	1.03761i	0.992959	−	0.118455i	$-0.0377943\pi$
$642$	−46.6263	−	24.0712i	−1.84019	−	0.950016i
$643$	12.2478	+	45.7094i	0.483006	+	1.80260i	0.588878	+	0.808222i	$0.299570\pi$
$643$	12.2478	+	45.7094i	0.483006	+	1.80260i	−0.105872	+	0.994380i	$0.533763\pi$
$644$	14.2465	+	53.1687i	0.561391	+	2.09514i
$645$	−6.34027	−	3.27322i	−0.249648	−	0.128883i
$646$	3.70958	−	6.42518i	0.145951	−	0.252795i
$647$	−9.62374	−	16.6688i	−0.378348	−	0.655318i	0.612474	−	0.790491i	$-0.290174\pi$
$647$	−9.62374	−	16.6688i	−0.378348	−	0.655318i	−0.990822	+	0.135173i	$0.956841\pi$
$648$	−1.67149	+	2.45751i	−0.0656621	+	0.0965401i
$649$			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	$-0.604923\pi$
$653$	8.53163	−	4.92574i	0.333868	−	0.192759i	0.657557	+	0.753405i	$0.271590\pi$
$654$	41.1351	+	8.97300i	1.60851	+	0.350872i
$655$	−19.6434	+	19.6434i	−0.767532	+	0.767532i
$656$	−34.8379	+	9.33479i	−1.36019	+	0.364462i
$657$	−10.6135	+	12.8246i	−0.414074	+	0.500336i
$658$	35.6840	+	35.6840i	1.39111	+	1.39111i
$659$	−4.00974	−	2.31502i	−0.156197	−	0.0901805i	0.419864	−	0.907587i	$-0.362078\pi$
$659$	−4.00974	−	2.31502i	−0.156197	−	0.0901805i	−0.576061	+	0.817407i	$0.695411\pi$
$660$	0.531943	+	0.484123i	0.0207058	+	0.0188445i
$661$	7.94714	−	29.6591i	0.309108	−	1.15361i	−0.620243	−	0.784409i	$-0.712966\pi$
$661$	7.94714	−	29.6591i	0.309108	−	1.15361i	0.929351	−	0.369197i	$-0.120367\pi$
$662$	−46.0604			−1.79019
$663$		0			0
$664$	2.99247			0.116131
$665$	−2.05594	+	7.67286i	−0.0797258	+	0.297541i
$666$	−8.00576	+	17.4773i	−0.310217	+	0.677233i
$667$	−11.5230	−	6.65278i	−0.446171	−	0.257597i
$668$	−18.1059	−	18.1059i	−0.700537	−	0.700537i
$669$	18.3875	−	11.8021i	0.710900	−	0.456295i
$670$	1.88207	−	0.504300i	0.0727108	−	0.0194828i
$671$	−0.631840	+	0.631840i	−0.0243919	+	0.0243919i
$672$	12.8685	−	58.9933i	0.496413	−	2.27572i
$673$	−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	$-0.965668\pi$
$677$		−	5.60187i		−	0.215297i	0.994189	−	0.107649i	$-0.0343322\pi$
$678$	−0.763575	−	16.2243i	−0.0293249	−	0.623090i
$679$	−10.0343	−	17.3799i	−0.385080	−	0.666977i
$680$	−0.774078	+	1.34074i	−0.0296845	+	0.0514151i
$681$	−17.6521	+	34.1924i	−0.676430	+	1.31025i
$682$	−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	$0.900934\pi$
$684$	−6.48240	−	1.09768i	−0.247861	−	0.0419709i
$685$	4.38373	−	7.59285i	0.167494	−	0.290108i
$686$	26.8154	+	46.4457i	1.02382	+	1.77331i
$687$	−17.2558	+	0.812125i	−0.658352	+	0.0309845i
$688$		−	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	$-0.258269\pi$
$691$	24.2402	+	6.49515i	0.922141	+	0.247087i	0.233641	+	0.972323i	$0.424936\pi$
$692$	28.4724	−	16.4386i	1.08236	−	0.624901i
$693$	0.193571	+	2.05192i	0.00735315	+	0.0779460i
$694$	5.30936	−	5.30936i	0.201541	−	0.201541i
$695$	−21.4028	+	5.73486i	−0.811854	+	0.217536i
$696$	0.613315	+	0.955535i	0.0232476	+	0.0362195i
$697$	−18.7459	−	18.7459i	−0.710052	−	0.710052i
$698$	−19.6005	−	11.3163i	−0.741888	−	0.428329i
$699$	−26.7641	+	29.4077i	−1.01231	+	1.11230i
$700$	5.97069	−	22.2829i	0.225671	−	0.842215i
$701$	0.474084			0.0179059			0.00895296	−	0.999960i	$-0.497150\pi$
$701$	0.474084			0.0179059			0.00895296	+	0.999960i	$0.497150\pi$
$702$		0			0
$703$	3.91777			0.147761
$704$	−0.261624	+	0.976396i	−0.00986034	+	0.0367993i
$705$	−9.92092	+	10.9009i	−0.373643	+	0.410551i
$706$	−17.3578	−	10.0215i	−0.653268	−	0.377165i
$707$	−5.33031	−	5.33031i	−0.200467	−	0.200467i
$708$	−15.0451	−	23.4401i	−0.565430	−	0.880932i
$709$	−47.9641	+	12.8520i	−1.80133	+	0.482665i	−0.994185	−	0.107686i	$-0.965656\pi$
$709$	−47.9641	+	12.8520i	−1.80133	+	0.482665i	−0.807146	+	0.590351i	$0.798989\pi$
$710$	−23.4423	+	23.4423i	−0.879775	+	0.879775i
$711$	1.53949	+	16.3191i	0.0577354	+	0.612015i
$712$	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
$717$	31.0298	−	1.46038i	1.15883	−	0.0545389i
$718$	−10.3843	−	17.9860i	−0.387537	−	0.671233i
$719$	0.847719	−	1.46829i	0.0316146	−	0.0547581i	−0.849785	−	0.527129i	$-0.823268\pi$
$719$	0.847719	−	1.46829i	0.0316146	−	0.0547581i	0.881400	+	0.472371i	$0.156602\pi$
$720$	18.8654	+	3.19453i	0.703073	+	0.119053i
$721$	−5.12455	−	19.1251i	−0.190848	−	0.712255i
$722$	−8.89994	−	33.2150i	−0.331221	−	1.23613i
$723$	2.24287	−	4.34448i	0.0834134	−	0.161573i
$724$	15.5613	−	26.9529i	0.578331	−	1.00170i
$725$	2.78817	+	4.82925i	0.103550	+	0.179354i
$726$	1.74946	+	37.1721i	0.0649286	+	1.37959i
$727$		−	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
$732$	3.94287	−	18.0754i	0.145733	−	0.668086i
$733$	−3.64797	+	3.64797i	−0.134741	+	0.134741i	−0.771261	−	0.636520i	$-0.780373\pi$
$733$	−3.64797	+	3.64797i	−0.134741	+	0.134741i	0.636520	+	0.771261i	$0.280373\pi$
$734$	26.4804	−	7.09539i	0.977408	−	0.261896i
$735$	−28.2852	+	18.1550i	−1.04332	+	0.669657i
$736$	−36.8439	−	36.8439i	−1.35809	−	1.35809i
$737$	−0.0892271	−	0.0515153i	−0.00328672	−	0.00189759i
$738$	−20.4690	+	44.6857i	−0.753473	+	1.64490i
$739$	−9.71724	+	36.2652i	−0.357454	+	1.33404i	0.519913	+	0.854219i	$0.325964\pi$
$739$	−9.71724	+	36.2652i	−0.357454	+	1.33404i	−0.877367	+	0.479819i	$0.840702\pi$
$740$	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	$0.0297673\pi$
$744$	−2.18270	−	1.98649i	−0.0800218	−	0.0728281i
$745$	−22.5762	−	13.0344i	−0.827130	−	0.477544i
$746$	−27.6503	−	27.6503i	−1.01235	−	1.01235i
$747$	17.3326	−	20.9434i	0.634165	−	0.766278i
$748$	−0.858310	+	0.229983i	−0.0313829	+	0.00840902i
$749$	−49.0789	+	49.0789i	−1.79330	+	1.79330i
$750$	38.2870	+	8.35172i	1.39804	+	0.304962i
$751$	−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
$756$	−26.3207	−	33.5877i	−0.957273	−	1.22157i
$757$	−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
$759$	1.58038	+	0.815886i	0.0573642	+	0.0296148i
$760$	−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	$-0.405498\pi$
$762$	48.1260	+	24.8455i	1.74342	+	0.900056i
$763$	27.8451	−	48.2292i	1.00806	−	1.74601i
$764$	20.4886	+	35.4872i	0.741250	+	1.28388i
$765$	4.89993	+	13.1832i	0.177157	+	0.476638i
$766$			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	$-0.603097\pi$
$769$	−29.6131	−	7.93479i	−1.06787	−	0.286136i	−0.749619	+	0.661869i	$0.769763\pi$
$770$	1.72377	−	0.995216i	0.0621202	−	0.0358651i
$771$	16.0900	+	3.50978i	0.579466	+	0.126402i
$772$	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

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} +(1.16581 - 1.28097i) q^{3} +(-1.58594 - 0.915644i) q^{4} +(-1.04664 - 1.04664i) q^{5} +(-1.83128 - 2.85311i) q^{6} +(-4.33161 + 1.16065i) q^{7} +(0.233508 - 0.233508i) q^{8} +(-0.281758 - 2.98674i) q^{9} +(-2.50908 + 1.44862i) q^{10} +(0.147979 + 0.0396510i) q^{11} +(-3.02182 + 0.964071i) q^{12} +8.77764i q^{14} +(-2.56090 + 0.120525i) q^{15} +(-2.15448 - 3.73167i) q^{16} +(1.58364 - 2.74294i) q^{17} +(-5.78968 - 0.980382i) q^{18} +(0.309737 + 1.15595i) q^{19} +(0.701560 + 2.61826i) q^{20} +(-3.56309 + 6.90175i) q^{21} +(0.149934 - 0.259693i) q^{22} +(3.35135 + 5.80471i) q^{23} +(-0.0268896 - 0.571343i) q^{24} -2.80909i q^{25} +(-4.15440 - 3.12106i) q^{27} +(7.93243 + 2.12549i) q^{28} +(-1.71915 + 0.992552i) q^{29} +(-1.06949 + 4.90288i) q^{30} +(3.64859 - 3.64859i) q^{31} +(-7.50887 + 2.01200i) q^{32} +(0.223308 - 0.143331i) q^{33} +(-4.38372 - 4.38372i) q^{34} +(5.74841 + 3.31885i) q^{35} +(-2.28794 + 4.99479i) q^{36} +(0.847303 - 3.16218i) q^{37} +2.34244 q^{38} -0.488797 q^{40} +(2.16637 - 8.08500i) q^{41} +(11.2439 + 10.2331i) q^{42} +(2.41031 + 1.39159i) q^{43} +(-0.198381 - 0.198381i) q^{44} +(-2.83114 + 3.42094i) q^{45} +(12.6726 - 3.39562i) q^{46} +(4.06533 - 4.06533i) q^{47} +(-7.29187 - 1.59061i) q^{48} +(11.3535 - 6.55497i) q^{49} +(-5.31107 - 1.42310i) q^{50} +(-1.66739 - 5.22634i) q^{51} -0.628103i q^{53} +(-8.00553 + 6.27346i) q^{54} +(-0.113381 - 0.196381i) q^{55} +(-0.740444 + 1.28249i) q^{56} +(1.84183 + 0.950863i) q^{57} +(1.00566 + 3.75318i) q^{58} +(2.27275 + 8.48202i) q^{59} +(4.17179 + 2.15372i) q^{60} +(-2.91632 + 5.05121i) q^{61} +(-5.04989 - 8.74667i) q^{62} +(4.68703 + 12.6104i) q^{63} +6.59818i q^{64} +(-0.157864 - 0.494815i) q^{66} +(-0.649609 - 0.174062i) q^{67} +(-5.02311 + 2.90010i) q^{68} +(11.3427 + 2.47424i) q^{69} +(9.18702 - 9.18702i) q^{70} +(11.0529 - 2.96161i) q^{71} +(-0.763221 - 0.631635i) q^{72} +(-3.92370 - 3.92370i) q^{73} +(-5.54940 - 3.20395i) q^{74} +(-3.59836 - 3.27488i) q^{75} +(0.567217 - 2.11688i) q^{76} -0.687010 q^{77} -5.46386 q^{79} +(-1.65075 + 6.16067i) q^{80} +(-8.84122 + 1.68308i) q^{81} +(-14.1886 - 8.19178i) q^{82} +(6.40765 + 6.40765i) q^{83} +(11.9704 - 7.68326i) q^{84} +(-4.52836 + 1.21337i) q^{85} +(3.85212 - 3.85212i) q^{86} +(-0.732781 + 3.35931i) q^{87} +(0.0438132 - 0.0252956i) q^{88} +(5.12896 + 1.37430i) q^{89} +(5.03360 + 7.08582i) q^{90} -12.2746i q^{92} +(-0.420152 - 8.92730i) q^{93} +(-5.62670 - 9.74572i) q^{94} +(0.885683 - 1.53405i) q^{95} +(-6.17664 + 11.9642i) q^{96} +(1.15826 + 4.32269i) q^{97} +(-6.64155 - 24.7866i) q^{98} +(0.0767327 - 0.453148i) 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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