LMFDB - Embedded newform 546.2.ch.a.137.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.19
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.72220 - 0.184470i) q^{3} -1.00000i q^{4} +(-3.71876 - 0.996438i) q^{5} +(-1.08734 + 1.34822i) q^{6} +(-0.403232 + 2.61484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.93194 - 0.635390i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.72220 - 0.184470i) q^{3} -1.00000i q^{4} +(-3.71876 - 0.996438i) q^{5} +(-1.08734 + 1.34822i) q^{6} +(-0.403232 + 2.61484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.93194 - 0.635390i) q^{9} +(3.33415 - 1.92497i) q^{10} +(1.04048 - 3.88311i) q^{11} +(-0.184470 - 1.72220i) q^{12} +(3.45190 - 1.04134i) q^{13} +(-1.56385 - 2.13410i) q^{14} +(-6.58826 - 1.03006i) q^{15} -1.00000 q^{16} +4.76887 q^{17} +(-1.62391 + 2.52248i) q^{18} +(1.65728 - 0.444067i) q^{19} +(-0.996438 + 3.71876i) q^{20} +(-0.212084 + 4.57767i) q^{21} +(2.01004 + 3.48150i) q^{22} +6.31097 q^{23} +(1.34822 + 1.08734i) q^{24} +(8.50614 + 4.91102i) q^{25} +(-1.70452 + 3.17720i) q^{26} +(4.93218 - 1.63512i) q^{27} +(2.61484 + 0.403232i) q^{28} +(-7.51497 - 4.33877i) q^{29} +(5.38697 - 3.93023i) q^{30} +(0.714216 - 0.191374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.07559 - 6.87942i) q^{33} +(-3.37210 + 3.37210i) q^{34} +(4.10505 - 9.32217i) q^{35} +(-0.635390 - 2.93194i) q^{36} +(2.45903 - 2.45903i) q^{37} +(-0.857872 + 1.48588i) q^{38} +(5.75276 - 2.43017i) q^{39} +(-1.92497 - 3.33415i) q^{40} +(0.359724 + 1.34251i) q^{41} +(-3.08693 - 3.38686i) q^{42} +(3.59149 - 2.07355i) q^{43} +(-3.88311 - 1.04048i) q^{44} +(-11.5363 - 0.558637i) q^{45} +(-4.46253 + 4.46253i) q^{46} +(-1.87226 + 6.98738i) q^{47} +(-1.72220 + 0.184470i) q^{48} +(-6.67481 - 2.10878i) q^{49} +(-9.48737 + 2.54213i) q^{50} +(8.21295 - 0.879717i) q^{51} +(-1.04134 - 3.45190i) q^{52} +(-4.91024 - 2.83493i) q^{53} +(-2.33137 + 4.64378i) q^{54} +(-7.73855 + 13.4036i) q^{55} +(-2.13410 + 1.56385i) q^{56} +(2.77225 - 1.07049i) q^{57} +(8.38186 - 2.24591i) q^{58} +(-3.58381 - 3.58381i) q^{59} +(-1.03006 + 6.58826i) q^{60} +(-3.35385 + 5.80903i) q^{61} +(-0.369706 + 0.640349i) q^{62} +(0.479193 + 7.92278i) q^{63} +1.00000i q^{64} +(-13.8744 + 0.432891i) q^{65} +(4.10393 + 5.62504i) q^{66} +(2.50976 - 9.36655i) q^{67} -4.76887i q^{68} +(10.8687 - 1.16419i) q^{69} +(3.68906 + 9.49448i) q^{70} +(9.32653 + 2.49904i) q^{71} +(2.52248 + 1.62391i) q^{72} +(-2.56673 - 9.57915i) q^{73} +3.47759i q^{74} +(15.5552 + 6.88863i) q^{75} +(-0.444067 - 1.65728i) q^{76} +(9.73417 + 4.28647i) q^{77} +(-2.34943 + 5.78621i) q^{78} +(1.97302 + 3.41737i) q^{79} +(3.71876 + 0.996438i) q^{80} +(8.19256 - 3.72585i) q^{81} +(-1.20366 - 0.694934i) q^{82} +(-7.55428 + 7.55428i) q^{83} +(4.57767 + 0.212084i) q^{84} +(-17.7343 - 4.75189i) q^{85} +(-1.07335 + 4.00578i) q^{86} +(-13.7427 - 6.08594i) q^{87} +(3.48150 - 2.01004i) q^{88} +(7.87927 + 7.87927i) q^{89} +(8.55242 - 7.76238i) q^{90} +(1.33103 + 9.44608i) q^{91} -6.31097i q^{92} +(1.19472 - 0.461335i) q^{93} +(-3.61694 - 6.26472i) q^{94} -6.60552 q^{95} +(1.08734 - 1.34822i) q^{96} +(-1.13852 + 4.24901i) q^{97} +(6.21093 - 3.22867i) q^{98} +(0.583326 - 12.0462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.72220	−	0.184470i	0.994312	−	0.106504i
$3$	1.72220	−	0.184470i	0.994312	−	0.106504i
$4$		−	1.00000i		−	0.500000i
$5$	−3.71876	−	0.996438i	−1.66308	−	0.445621i	−0.699847	−	0.714293i	$-0.746749\pi$
$5$	−3.71876	−	0.996438i	−1.66308	−	0.445621i	−0.963232	+	0.268672i	$0.913415\pi$
$6$	−1.08734	+	1.34822i	−0.443904	+	0.550408i
$7$	−0.403232	+	2.61484i	−0.152407	+	0.988318i
$7$	−0.403232	+	2.61484i	−0.152407	+	0.988318i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.93194	−	0.635390i	0.977314	−	0.211797i
$10$	3.33415	−	1.92497i	1.05435	−	0.608729i
$11$	1.04048	−	3.88311i	0.313715	−	1.17080i	−0.611464	−	0.791272i	$-0.709419\pi$
$11$	1.04048	−	3.88311i	0.313715	−	1.17080i	0.925180	−	0.379529i	$-0.123914\pi$
$12$	−0.184470	−	1.72220i	−0.0532520	−	0.497156i
$13$	3.45190	−	1.04134i	0.957385	−	0.288816i
$13$	3.45190	−	1.04134i	0.957385	−	0.288816i
$14$	−1.56385	−	2.13410i	−0.417955	−	0.570363i
$15$	−6.58826	−	1.03006i	−1.70108	−	0.265961i
$16$	−1.00000			−0.250000
$17$	4.76887			1.15662			0.578311	−	0.815816i	$-0.303712\pi$
$17$	4.76887			1.15662			0.578311	+	0.815816i	$0.303712\pi$
$18$	−1.62391	+	2.52248i	−0.382759	+	0.594555i
$19$	1.65728	−	0.444067i	0.380207	−	0.101876i	−0.0636537	−	0.997972i	$-0.520275\pi$
$19$	1.65728	−	0.444067i	0.380207	−	0.101876i	0.443860	+	0.896096i	$0.353609\pi$
$20$	−0.996438	+	3.71876i	−0.222810	+	0.831539i
$21$	−0.212084	+	4.57767i	−0.0462806	+	0.998928i
$22$	2.01004	+	3.48150i	0.428543	+	0.742258i
$23$	6.31097			1.31593			0.657964	−	0.753050i	$-0.271418\pi$
$23$	6.31097			1.31593			0.657964	+	0.753050i	$0.271418\pi$
$24$	1.34822	+	1.08734i	0.275204	+	0.221952i
$25$	8.50614	+	4.91102i	1.70123	+	0.982205i
$26$	−1.70452	+	3.17720i	−0.334284	+	0.623100i
$27$	4.93218	−	1.63512i	0.949198	−	0.314680i
$28$	2.61484	+	0.403232i	0.494159	+	0.0762036i
$29$	−7.51497	−	4.33877i	−1.39550	−	0.805689i	−0.401578	−	0.915825i	$-0.631538\pi$
$29$	−7.51497	−	4.33877i	−1.39550	−	0.805689i	−0.993917	+	0.110135i	$0.964872\pi$
$30$	5.38697	−	3.93023i	0.983521	−	0.717559i
$31$	0.714216	−	0.191374i	0.128277	−	0.0343717i	−0.194109	−	0.980980i	$-0.562182\pi$
$31$	0.714216	−	0.191374i	0.128277	−	0.0343717i	0.322386	+	0.946608i	$0.395515\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.07559	−	6.87942i	0.187236	−	1.19755i
$34$	−3.37210	+	3.37210i	−0.578311	+	0.578311i
$35$	4.10505	−	9.32217i	0.693880	−	1.57573i
$36$	−0.635390	−	2.93194i	−0.105898	−	0.488657i
$37$	2.45903	−	2.45903i	0.404262	−	0.404262i	−0.475470	−	0.879732i	$-0.657722\pi$
$37$	2.45903	−	2.45903i	0.404262	−	0.404262i	0.879732	+	0.475470i	$0.157722\pi$
$38$	−0.857872	+	1.48588i	−0.139165	+	0.241041i
$39$	5.75276	−	2.43017i	0.921179	−	0.389139i
$40$	−1.92497	−	3.33415i	−0.304365	−	0.527175i
$41$	0.359724	+	1.34251i	0.0561795	+	0.209665i	0.988310	−	0.152458i	$-0.0487188\pi$
$41$	0.359724	+	1.34251i	0.0561795	+	0.209665i	−0.932130	+	0.362123i	$0.882052\pi$
$42$	−3.08693	−	3.38686i	−0.476324	−	0.522605i
$43$	3.59149	−	2.07355i	0.547696	−	0.316213i	−0.200496	−	0.979695i	$-0.564255\pi$
$43$	3.59149	−	2.07355i	0.547696	−	0.316213i	0.748192	+	0.663482i	$0.230922\pi$
$44$	−3.88311	−	1.04048i	−0.585401	−	0.156858i
$45$	−11.5363	−	0.558637i	−1.71973	−	0.0832767i
$46$	−4.46253	+	4.46253i	−0.657964	+	0.657964i
$47$	−1.87226	+	6.98738i	−0.273098	+	1.01921i	0.684008	+	0.729475i	$0.260235\pi$
$47$	−1.87226	+	6.98738i	−0.273098	+	1.01921i	−0.957105	+	0.289740i	$0.906431\pi$
$48$	−1.72220	+	0.184470i	−0.248578	+	0.0266260i
$49$	−6.67481	−	2.10878i	−0.953544	−	0.301254i
$50$	−9.48737	+	2.54213i	−1.34172	+	0.359512i
$51$	8.21295	−	0.879717i	1.15004	−	0.123185i
$52$	−1.04134	−	3.45190i	−0.144408	−	0.478692i
$53$	−4.91024	−	2.83493i	−0.674473	−	0.389407i	0.123296	−	0.992370i	$-0.460653\pi$
$53$	−4.91024	−	2.83493i	−0.674473	−	0.389407i	−0.797769	+	0.602963i	$0.793987\pi$
$54$	−2.33137	+	4.64378i	−0.317259	+	0.631939i
$55$	−7.73855	+	13.4036i	−1.04347	+	1.80734i
$56$	−2.13410	+	1.56385i	−0.285181	+	0.208978i
$57$	2.77225	−	1.07049i	0.367194	−	0.141790i
$58$	8.38186	−	2.24591i	1.10059	−	0.294903i
$59$	−3.58381	−	3.58381i	−0.466572	−	0.466572i	0.434230	−	0.900802i	$-0.357021\pi$
$59$	−3.58381	−	3.58381i	−0.466572	−	0.466572i	−0.900802	+	0.434230i	$0.857021\pi$
$60$	−1.03006	+	6.58826i	−0.132981	+	0.850540i
$61$	−3.35385	+	5.80903i	−0.429416	+	0.743770i	−0.996821	−	0.0796683i	$-0.974614\pi$
$61$	−3.35385	+	5.80903i	−0.429416	+	0.743770i	0.567406	+	0.823439i	$0.307947\pi$
$62$	−0.369706	+	0.640349i	−0.0469526	+	0.0813244i
$63$	0.479193	+	7.92278i	0.0603726	+	0.998176i
$64$			1.00000i			0.125000i
$65$	−13.8744	+	0.432891i	−1.72091	+	0.0536936i
$66$	4.10393	+	5.62504i	0.505159	+	0.692395i
$67$	2.50976	−	9.36655i	0.306616	−	1.14431i	−0.624930	−	0.780681i	$-0.714872\pi$
$67$	2.50976	−	9.36655i	0.306616	−	1.14431i	0.931545	−	0.363625i	$-0.118461\pi$
$68$		−	4.76887i		−	0.578311i
$69$	10.8687	−	1.16419i	1.30844	−	0.140152i
$70$	3.68906	+	9.49448i	0.440927	+	1.13481i
$71$	9.32653	+	2.49904i	1.10686	+	0.296581i	0.765553	−	0.643373i	$-0.222465\pi$
$71$	9.32653	+	2.49904i	1.10686	+	0.296581i	0.341302	+	0.939954i	$0.389132\pi$
$72$	2.52248	+	1.62391i	0.297278	+	0.191379i
$73$	−2.56673	−	9.57915i	−0.300413	−	1.12115i	−0.936823	−	0.349804i	$-0.886248\pi$
$73$	−2.56673	−	9.57915i	−0.300413	−	1.12115i	0.636410	−	0.771351i	$-0.280419\pi$
$74$			3.47759i			0.404262i
$75$	15.5552	+	6.88863i	1.79616	+	0.795430i
$76$	−0.444067	−	1.65728i	−0.0509380	−	0.190103i
$77$	9.73417	+	4.28647i	1.10931	+	0.488489i
$78$	−2.34943	+	5.78621i	−0.266020	+	0.655159i
$79$	1.97302	+	3.41737i	0.221982	+	0.384485i	0.955410	−	0.295283i	$-0.0954140\pi$
$79$	1.97302	+	3.41737i	0.221982	+	0.384485i	−0.733428	+	0.679768i	$0.762081\pi$
$80$	3.71876	+	0.996438i	0.415770	+	0.111405i
$81$	8.19256	−	3.72585i	0.910284	−	0.413984i
$82$	−1.20366	−	0.694934i	−0.132922	−	0.0767426i
$83$	−7.55428	+	7.55428i	−0.829190	+	0.829190i	−0.987405	−	0.158215i	$-0.949426\pi$
$83$	−7.55428	+	7.55428i	−0.829190	+	0.829190i	0.158215	+	0.987405i	$0.449426\pi$
$84$	4.57767	+	0.212084i	0.499464	+	0.0231403i
$85$	−17.7343	−	4.75189i	−1.92355	−	0.515415i
$86$	−1.07335	+	4.00578i	−0.115742	+	0.431955i
$87$	−13.7427	−	6.08594i	−1.47337	−	0.652481i
$88$	3.48150	−	2.01004i	0.371129	−	0.214272i
$89$	7.87927	+	7.87927i	0.835201	+	0.835201i	0.988223	−	0.153022i	$-0.0489005\pi$
$89$	7.87927	+	7.87927i	0.835201	+	0.835201i	−0.153022	+	0.988223i	$0.548900\pi$
$90$	8.55242	−	7.76238i	0.901504	−	0.818227i
$91$	1.33103	+	9.44608i	0.139530	+	0.990218i
$92$		−	6.31097i		−	0.657964i
$93$	1.19472	−	0.461335i	0.123887	−	0.0478383i
$94$	−3.61694	−	6.26472i	−0.373058	−	0.646156i
$95$	−6.60552			−0.677712
$96$	1.08734	−	1.34822i	0.110976	−	0.137602i
$97$	−1.13852	+	4.24901i	−0.115599	+	0.431422i	−0.999331	−	0.0365717i	$-0.988356\pi$
$97$	−1.13852	+	4.24901i	−0.115599	+	0.431422i	0.883732	+	0.467993i	$0.155023\pi$
$98$	6.21093	−	3.22867i	0.627399	−	0.326145i
$99$	0.583326	−	12.0462i	0.0586265	−	1.21068i
$100$	4.91102	−	8.50614i	0.491102	−	0.850614i
$101$	9.08453	+	15.7349i	0.903944	+	1.56568i	0.822328	+	0.569014i	$0.192675\pi$
$101$	9.08453	+	15.7349i	0.903944	+	1.56568i	0.0816163	+	0.996664i	$0.473992\pi$
$102$	−5.18538	+	6.42949i	−0.513429	+	0.636614i
$103$	5.23236	−	3.02090i	0.515559	−	0.297658i	−0.219556	−	0.975600i	$-0.570461\pi$
$103$	5.23236	−	3.02090i	0.515559	−	0.297658i	0.735116	+	0.677941i	$0.237128\pi$
$104$	3.17720	+	1.70452i	0.311550	+	0.167142i
$105$	5.35005	−	16.8119i	0.522111	−	1.64067i
$106$	5.47666	−	1.46747i	0.531940	−	0.142533i
$107$			3.01756i			0.291719i	0.989305	+	0.145859i	$0.0465947\pi$
$107$			3.01756i			0.291719i	−0.989305	+	0.145859i	$0.953405\pi$
$108$	−1.63512	−	4.93218i	−0.157340	−	0.474599i
$109$	−14.4992	+	3.88505i	−1.38877	+	0.372120i	−0.874300	−	0.485386i	$-0.838679\pi$
$109$	−14.4992	+	3.88505i	−1.38877	+	0.372120i	−0.514473	+	0.857507i	$0.672012\pi$
$110$	−4.00577	−	14.9497i	−0.381935	−	1.42540i
$111$	3.78132	−	4.68856i	0.358907	−	0.445018i
$112$	0.403232	−	2.61484i	0.0381018	−	0.247079i
$113$	−8.30792	+	4.79658i	−0.781544	+	0.451224i	−0.836977	−	0.547238i	$-0.815679\pi$
$113$	−8.30792	+	4.79658i	−0.781544	+	0.451224i	0.0554335	+	0.998462i	$0.482346\pi$
$114$	−1.20333	+	2.71723i	−0.112702	+	0.254492i
$115$	−23.4690	−	6.28849i	−2.18849	−	0.586404i
$116$	−4.33877	+	7.51497i	−0.402845	+	0.697748i
$117$	9.45911	−	5.24645i	0.874495	−	0.485035i
$118$	5.06827			0.466572
$119$	−1.92296	+	12.4699i	−0.176278	+	1.14311i
$120$	−3.93023	−	5.38697i	−0.358780	−	0.491760i
$121$	−4.46966	−	2.58056i	−0.406333	−	0.234596i
$122$	−1.73608	−	6.47913i	−0.157177	−	0.586593i
$123$	0.867170	+	2.24571i	0.0781901	+	0.202489i
$124$	−0.191374	−	0.714216i	−0.0171859	−	0.0641385i
$125$	−13.1271	−	13.1271i	−1.17413	−	1.17413i
$126$	−5.94109	−	5.26341i	−0.529274	−	0.468902i
$127$	−14.7759	−	8.53085i	−1.31115	−	0.756991i	−0.328860	−	0.944379i	$-0.606664\pi$
$127$	−14.7759	−	8.53085i	−1.31115	−	0.756991i	−0.982286	+	0.187388i	$0.939998\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	5.80275	−	4.23358i	0.510903	−	0.372746i
$130$	9.50459	−	10.1168i	0.833607	−	0.887301i
$131$	−4.76748	+	2.75250i	−0.416536	+	0.240487i	−0.693594	−	0.720366i	$-0.743974\pi$
$131$	−4.76748	+	2.75250i	−0.416536	+	0.240487i	0.277058	+	0.960853i	$0.410641\pi$
$132$	−6.87942	−	1.07559i	−0.598777	−	0.0936179i
$133$	0.492898	+	4.51259i	0.0427396	+	0.391292i
$134$	4.84848	+	8.39782i	0.418845	+	0.725461i
$135$	−19.9709	+	1.16602i	−1.71882	+	0.100355i
$136$	3.37210	+	3.37210i	0.289155	+	0.289155i
$137$	7.15682	+	7.15682i	0.611448	+	0.611448i	0.943323	−	0.331875i	$-0.107681\pi$
$137$	7.15682	+	7.15682i	0.611448	+	0.611448i	−0.331875	+	0.943323i	$0.607681\pi$
$138$	−6.86216	+	8.50857i	−0.584146	+	0.724297i
$139$	−3.51840	−	6.09405i	−0.298427	−	0.516890i	0.677349	−	0.735661i	$-0.263129\pi$
$139$	−3.51840	−	6.09405i	−0.298427	−	0.516890i	−0.975776	+	0.218771i	$0.929795\pi$
$140$	−9.32217	−	4.10505i	−0.787867	−	0.346940i
$141$	−1.93545	+	12.3790i	−0.162994	+	1.04250i
$142$	−8.36194	+	4.82777i	−0.701718	+	0.405137i
$143$	−0.452023	−	14.4876i	−0.0378001	−	1.21151i
$144$	−2.93194	+	0.635390i	−0.244328	+	0.0529492i
$145$	23.6230	+	23.6230i	1.96179	+	1.96179i
$146$	8.58843	+	4.95853i	0.710784	+	0.410371i
$147$	−11.8844	−	2.40043i	−0.980205	−	0.197984i
$148$	−2.45903	−	2.45903i	−0.202131	−	0.202131i
$149$	−4.93128	−	18.4038i	−0.403986	−	1.50770i	−0.805918	−	0.592027i	$-0.798328\pi$
$149$	−4.93128	−	18.4038i	−0.403986	−	1.50770i	0.401932	−	0.915670i	$-0.368339\pi$
$150$	−15.8702	+	6.12820i	−1.29580	+	0.500365i
$151$	−1.68868	−	6.30222i	−0.137422	−	0.512868i	−0.999976	−	0.00690207i	$-0.997803\pi$
$151$	−1.68868	−	6.30222i	−0.137422	−	0.512868i	0.862554	−	0.505965i	$-0.168864\pi$
$152$	1.48588	+	0.857872i	0.120521	+	0.0695826i
$153$	13.9821	−	3.03009i	1.13038	−	0.244969i
$154$	−9.91409	+	3.85210i	−0.798900	+	0.310411i
$155$	−2.84669			−0.228652
$156$	−2.43017	−	5.75276i	−0.194569	−	0.460590i
$157$	6.02174	−	10.4300i	0.480588	−	0.832402i	−0.519164	−	0.854674i	$-0.673757\pi$
$157$	6.02174	−	10.4300i	0.480588	−	0.832402i	0.999752	+	0.0222723i	$0.00709009\pi$
$158$	−3.81158	−	1.02131i	−0.303233	−	0.0812511i
$159$	−8.97937	−	3.97652i	−0.712110	−	0.315358i
$160$	−3.33415	+	1.92497i	−0.263587	+	0.152182i
$161$	−2.54478	+	16.5022i	−0.200557	+	1.30055i
$162$	−3.15844	+	8.42759i	−0.248150	+	0.662134i
$163$	2.41820	+	9.02485i	0.189408	+	0.706881i	0.993644	+	0.112570i	$0.0359084\pi$
$163$	2.41820	+	9.02485i	0.189408	+	0.706881i	−0.804236	+	0.594311i	$0.797425\pi$
$164$	1.34251	−	0.359724i	0.104832	−	0.0280898i
$165$	−10.8548	+	24.5112i	−0.845043	+	1.90819i
$166$		−	10.6834i		−	0.829190i
$167$	1.42509	−	0.381851i	0.110277	−	0.0295485i	−0.203259	−	0.979125i	$-0.565153\pi$
$167$	1.42509	−	0.381851i	0.110277	−	0.0295485i	0.313535	+	0.949577i	$0.398487\pi$
$168$	−3.38686	+	3.08693i	−0.261302	+	0.238162i
$169$	10.8312	−	7.18921i	0.833171	−	0.553016i
$170$	15.9001	−	9.17994i	1.21948	−	0.704069i
$171$	4.57690	−	2.35500i	0.350004	−	0.180091i
$172$	−2.07355	−	3.59149i	−0.158106	−	0.273848i
$173$	−1.52894	+	2.64821i	−0.116243	+	0.201339i	−0.918276	−	0.395941i	$-0.870419\pi$
$173$	−1.52894	+	2.64821i	−0.116243	+	0.201339i	0.802033	+	0.597280i	$0.203752\pi$
$174$	14.0209	−	5.41412i	1.06292	−	0.410443i
$175$	−16.2715	+	20.2619i	−1.23001	+	1.53166i
$176$	−1.04048	+	3.88311i	−0.0784288	+	0.292700i
$177$	−6.83314	−	5.51092i	−0.513610	−	0.414226i
$178$	−11.1430			−0.835201
$179$	−11.0533	−	19.1449i	−0.826164	−	1.43096i	−0.901026	−	0.433765i	$-0.857185\pi$
$179$	−11.0533	−	19.1449i	−0.826164	−	1.43096i	0.0748617	−	0.997194i	$-0.476148\pi$
$180$	−0.558637	+	11.5363i	−0.0416383	+	0.859865i
$181$			8.17207i			0.607426i	0.952764	+	0.303713i	$0.0982263\pi$
$181$			8.17207i			0.607426i	−0.952764	+	0.303713i	$0.901774\pi$
$182$	−7.62056	−	5.73821i	−0.564874	−	0.425344i
$183$	−4.70440	+	10.6230i	−0.347759	+	0.785274i
$184$	4.46253	+	4.46253i	0.328982	+	0.328982i
$185$	−11.5948	+	6.69427i	−0.852467	+	0.492172i
$186$	−0.518581	+	1.17101i	−0.0380242	+	0.0858625i
$187$	4.96190	−	18.5181i	0.362850	−	1.35417i
$188$	6.98738	+	1.87226i	0.509607	+	0.136549i
$189$	2.28678	+	13.5562i	0.166339	+	0.986069i
$190$	4.67080	−	4.67080i	0.338856	−	0.338856i
$191$	−1.17188	−	0.676587i	−0.0847945	−	0.0489561i	0.457003	−	0.889465i	$-0.348923\pi$
$191$	−1.17188	−	0.676587i	−0.0847945	−	0.0489561i	−0.541798	+	0.840509i	$0.682256\pi$
$192$	0.184470	+	1.72220i	0.0133130	+	0.124289i
$193$	23.1604	+	6.20581i	1.66712	+	0.446704i	0.964332	−	0.264694i	$-0.0852711\pi$
$193$	23.1604	+	6.20581i	1.66712	+	0.446704i	0.702789	+	0.711398i	$0.251938\pi$
$194$	−2.19945	−	3.80956i	−0.157911	−	0.273510i
$195$	−23.8146	+	3.30494i	−1.70540	+	0.236672i
$196$	−2.10878	+	6.67481i	−0.150627	+	0.476772i
$197$	−2.18679	−	8.16122i	−0.155803	−	0.581463i	−0.999035	−	0.0439145i	$-0.986017\pi$
$197$	−2.18679	−	8.16122i	−0.155803	−	0.581463i	0.843233	−	0.537549i	$-0.180650\pi$
$198$	8.10544	+	8.93039i	0.576029	+	0.634655i
$199$			3.27977i			0.232497i	0.993220	+	0.116249i	$0.0370869\pi$
$199$			3.27977i			0.232497i	−0.993220	+	0.116249i	$0.962913\pi$
$200$	2.54213	+	9.48737i	0.179756	+	0.670858i
$201$	2.59445	−	16.5940i	0.182999	−	1.17045i
$202$	−17.5500	−	4.70250i	−1.23481	−	0.330867i
$203$	14.3755	−	17.9009i	1.00896	−	1.25640i
$204$	−0.879717	−	8.21295i	−0.0615925	−	0.575022i
$205$		−	5.35091i		−	0.373724i
$206$	−1.56373	+	5.83594i	−0.108951	+	0.406609i
$207$	18.5034	−	4.00992i	1.28607	−	0.278709i
$208$	−3.45190	+	1.04134i	−0.239346	+	0.0722040i
$209$		−	6.89745i		−	0.477106i
$210$	8.10475	+	15.6709i	0.559281	+	1.08139i
$211$	2.78527	−	4.82423i	0.191746	−	0.332113i	−0.754083	−	0.656779i	$-0.771918\pi$
$211$	2.78527	−	4.82423i	0.191746	−	0.332113i	0.945829	+	0.324666i	$0.105252\pi$
$212$	−2.83493	+	4.91024i	−0.194704	+	0.337237i
$213$	16.5231	+	2.58337i	1.13215	+	0.177009i
$214$	−2.13374	−	2.13374i	−0.145859	−	0.145859i
$215$	−15.4220	+	4.13232i	−1.05177	+	0.281822i
$216$	4.64378	+	2.33137i	0.315969	+	0.158629i
$217$	0.212417	+	1.94473i	0.0144198	+	0.132017i
$218$	7.50534	−	12.9996i	0.508326	−	0.880447i
$219$	−6.18748	−	16.0237i	−0.418111	−	1.08278i
$220$	13.4036	+	7.73855i	0.903668	+	0.521733i
$221$	16.4617	−	4.96602i	1.10733	−	0.334051i
$222$	0.641513	+	5.98911i	0.0430556	+	0.401963i
$223$	−16.0081	+	4.28935i	−1.07198	+	0.287236i	−0.751307	−	0.659953i	$-0.770576\pi$
$223$	−16.0081	+	4.28935i	−1.07198	+	0.287236i	−0.320674	+	0.947190i	$0.603909\pi$
$224$	1.56385	+	2.13410i	0.104489	+	0.142591i
$225$	28.0599	+	8.99411i	1.87066	+	0.599608i
$226$	2.48289	−	9.26628i	0.165160	−	0.616384i
$227$	−16.3435	+	16.3435i	−1.08475	+	1.08475i	−0.0886956	+	0.996059i	$0.528270\pi$
$227$	−16.3435	+	16.3435i	−1.08475	+	1.08475i	−0.996059	+	0.0886956i	$0.971730\pi$
$228$	−1.07049	−	2.77225i	−0.0708951	−	0.183597i
$229$	9.89167	+	2.65046i	0.653660	+	0.175148i	0.570383	−	0.821379i	$-0.306795\pi$
$229$	9.89167	+	2.65046i	0.653660	+	0.175148i	0.0832768	+	0.996526i	$0.473461\pi$
$230$	21.0417	−	12.1484i	1.38745	−	0.801043i
$231$	17.5549	+	5.58650i	1.15503	+	0.367564i
$232$	−2.24591	−	8.38186i	−0.147451	−	0.550296i
$233$	3.27880	+	5.67905i	0.214801	+	0.372047i	0.953211	−	0.302305i	$-0.0977562\pi$
$233$	3.27880	+	5.67905i	0.214801	+	0.372047i	−0.738410	+	0.674352i	$0.764423\pi$
$234$	−2.97880	+	10.3984i	−0.194730	+	0.679765i
$235$	13.9250	−	24.1188i	0.908366	−	1.57334i
$236$	−3.58381	+	3.58381i	−0.233286	+	0.233286i
$237$	4.02834	+	5.52143i	0.261669	+	0.358656i
$238$	−7.45778	−	10.1773i	−0.483416	−	0.659694i
$239$	13.1617	−	13.1617i	0.851359	−	0.851359i	−0.138942	−	0.990301i	$-0.544370\pi$
$239$	13.1617	−	13.1617i	0.851359	−	0.851359i	0.990301	+	0.138942i	$0.0443701\pi$
$240$	6.58826	+	1.03006i	0.425270	+	0.0664903i
$241$	−9.36335	+	9.36335i	−0.603147	+	0.603147i	−0.941146	−	0.338000i	$-0.890250\pi$
$241$	−9.36335	+	9.36335i	−0.603147	+	0.603147i	0.338000	+	0.941146i	$0.390250\pi$
$242$	4.98526	−	1.33580i	0.320465	−	0.0858683i
$243$	13.4219	−	7.92795i	0.861016	−	0.508578i
$244$	5.80903	+	3.35385i	0.371885	+	0.214708i
$245$	22.7207	+	14.4931i	1.45157	+	0.925928i
$246$	−2.20114	−	0.974775i	−0.140340	−	0.0621494i
$247$	5.25834	−	3.25867i	0.334580	−	0.207344i
$248$	0.640349	+	0.369706i	0.0406622	+	0.0234763i
$249$	−11.6164	+	14.4035i	−0.736162	+	0.912786i
$250$	18.5646			1.17413
$251$	9.38960	+	16.2633i	0.592666	+	1.02653i	0.993872	+	0.110540i	$0.0352580\pi$
$251$	9.38960	+	16.2633i	0.592666	+	1.02653i	−0.401206	+	0.915988i	$0.631409\pi$
$252$	7.92278	−	0.479193i	0.499088	−	0.0301863i
$253$	6.56641	−	24.5062i	0.412827	−	1.54069i
$254$	16.4803	−	4.41589i	1.03407	−	0.277078i
$255$	−31.4186	−	4.91225i	−1.96751	−	0.307617i
$256$	1.00000			0.0625000
$257$	−17.4808			−1.09042			−0.545210	−	0.838300i	$-0.683550\pi$
$257$	−17.4808			−1.09042			−0.545210	+	0.838300i	$0.683550\pi$
$258$	−1.10957	+	7.09676i	−0.0690786	+	0.441825i
$259$	5.43842	+	7.42154i	0.337927	+	0.461152i
$260$	0.432891	+	13.8744i	0.0268468	+	0.860454i
$261$	−24.7903	−	7.94608i	−1.53448	−	0.491850i
$262$	1.42480	−	5.31743i	0.0880245	−	0.328512i
$263$	−9.17666	+	5.29815i	−0.565857	+	0.326698i	−0.755493	−	0.655157i	$-0.772603\pi$
$263$	−9.17666	+	5.29815i	−0.565857	+	0.326698i	0.189636	+	0.981854i	$0.439269\pi$
$264$	5.62504	−	4.10393i	0.346197	−	0.252580i
$265$	15.4352	+	15.4352i	0.948174	+	0.948174i
$266$	−3.53942	−	2.84235i	−0.217016	−	0.174276i
$267$	15.0232	+	12.1162i	0.919403	+	0.741498i
$268$	−9.36655	−	2.50976i	−0.572153	−	0.153308i
$269$			1.15797i			0.0706028i	0.999377	+	0.0353014i	$0.0112391\pi$
$269$			1.15797i			0.0706028i	−0.999377	+	0.0353014i	$0.988761\pi$
$270$	13.2970	−	14.9460i	0.809232	−	0.909587i
$271$	0.379449	−	0.379449i	0.0230499	−	0.0230499i	−0.695488	−	0.718538i	$-0.744812\pi$
$271$	0.379449	−	0.379449i	0.0230499	−	0.0230499i	0.718538	+	0.695488i	$0.244812\pi$
$272$	−4.76887			−0.289155
$273$	4.03482	+	16.0225i	0.244198	+	0.969725i
$274$	−10.1213			−0.611448
$275$	27.9205	−	27.9205i	1.68367	−	1.68367i
$276$	−1.16419	−	10.8687i	−0.0700758	−	0.654221i
$277$			17.7605i			1.06713i	0.845760	+	0.533564i	$0.179147\pi$
$277$			17.7605i			1.06713i	−0.845760	+	0.533564i	$0.820853\pi$
$278$	6.79703	+	1.82126i	0.407658	+	0.109232i
$279$	1.97244	−	1.01490i	0.118087	−	0.0607606i
$280$	9.49448	−	3.68906i	0.567404	−	0.220464i
$281$	−8.89317	−	8.89317i	−0.530522	−	0.530522i	0.390206	−	0.920728i	$-0.372404\pi$
$281$	−8.89317	−	8.89317i	−0.530522	−	0.530522i	−0.920728	+	0.390206i	$0.872404\pi$
$282$	−7.38474	−	10.1219i	−0.439755	−	0.602749i
$283$	−15.4992	+	8.94845i	−0.921331	+	0.531930i	−0.884059	−	0.467375i	$-0.845200\pi$
$283$	−15.4992	+	8.94845i	−0.921331	+	0.531930i	−0.0372712	+	0.999305i	$0.511867\pi$
$284$	2.49904	−	9.32653i	0.148290	−	0.553428i
$285$	−11.3760	+	1.21852i	−0.673857	+	0.0721791i
$286$	10.5639	+	9.92464i	0.624657	+	0.586857i
$287$	−3.65550	+	0.399280i	−0.215778	+	0.0235688i
$288$	1.62391	−	2.52248i	0.0956896	−	0.148639i
$289$	5.74216			0.337774
$290$	−33.4080			−1.96179
$291$	−1.17694	+	7.52767i	−0.0689934	+	0.441280i
$292$	−9.57915	+	2.56673i	−0.560577	+	0.150206i
$293$	−6.18403	+	23.0791i	−0.361275	+	1.34830i	0.511126	+	0.859506i	$0.329228\pi$
$293$	−6.18403	+	23.0791i	−0.361275	+	1.34830i	−0.872401	+	0.488791i	$0.837438\pi$
$294$	10.1009	−	6.70615i	0.589095	−	0.391111i
$295$	9.75627	+	16.8984i	0.568032	+	0.983860i
$296$	3.47759			0.202131
$297$	−1.21756	−	20.8535i	−0.0706498	−	1.21004i
$298$	16.5004	+	9.52650i	0.955841	+	0.551855i
$299$	21.7848	−	6.57187i	1.25985	−	0.380061i
$300$	6.88863	−	15.5552i	0.397715	−	0.898080i
$301$	3.97379	+	10.2273i	0.229046	+	0.589491i
$302$	5.65042	+	3.26227i	0.325145	+	0.187723i
$303$	18.5480	+	25.4227i	1.06555	+	1.46050i
$304$	−1.65728	+	0.444067i	−0.0950516	+	0.0254690i
$305$	18.2605	−	18.2605i	1.04559	−	1.04559i
$306$	−7.74421	+	12.0294i	−0.442707	+	0.687676i
$307$	−1.18591	+	1.18591i	−0.0676832	+	0.0676832i	−0.740138	−	0.672455i	$-0.765240\pi$
$307$	−1.18591	+	1.18591i	−0.0676832	+	0.0676832i	0.672455	+	0.740138i	$0.265240\pi$
$308$	4.28647	−	9.73417i	0.244245	−	0.554656i
$309$	8.45389	−	6.16781i	0.480925	−	0.350875i
$310$	2.01291	−	2.01291i	0.114326	−	0.114326i
$311$	2.52872	−	4.37988i	0.143391	−	0.248360i	−0.785381	−	0.619013i	$-0.787533\pi$
$311$	2.52872	−	4.37988i	0.143391	−	0.248360i	0.928771	+	0.370653i	$0.120866\pi$
$312$	5.78621	+	2.34943i	0.327579	+	0.133010i
$313$	−8.23916	−	14.2706i	−0.465705	−	0.806624i	0.533528	−	0.845782i	$-0.320866\pi$
$313$	−8.23916	−	14.2706i	−0.465705	−	0.806624i	−0.999233	+	0.0391578i	$0.987532\pi$
$314$	3.11708	+	11.6331i	0.175907	+	0.656495i
$315$	6.11255	−	29.9404i	0.344403	−	1.68695i
$316$	3.41737	−	1.97302i	0.192242	−	0.110991i
$317$	20.1659	+	5.40345i	1.13263	+	0.303488i	0.775985	−	0.630751i	$-0.217253\pi$
$317$	20.1659	+	5.40345i	1.13263	+	0.303488i	0.356647	+	0.934239i	$0.383920\pi$
$318$	9.16119	−	3.53755i	0.513734	−	0.198376i
$319$	−24.6671	+	24.6671i	−1.38109	+	1.38109i
$320$	0.996438	−	3.71876i	0.0557026	−	0.207885i
$321$	0.556651	+	5.19684i	0.0310692	+	0.290060i
$322$	−9.86938	−	13.4682i	−0.549999	−	0.750556i
$323$	7.90337	−	2.11770i	0.439755	−	0.117832i
$324$	−3.72585	−	8.19256i	−0.206992	−	0.455142i
$325$	34.4764	+	8.09456i	1.91241	+	0.449005i
$326$	−8.09146	−	4.67161i	−0.448145	−	0.258736i
$327$	−24.2539	+	9.36551i	−1.34124	+	0.517914i
$328$	−0.694934	+	1.20366i	−0.0383713	+	0.0664611i
$329$	−17.5160	−	7.71321i	−0.965686	−	0.425243i
$330$	−9.65652	−	25.0075i	−0.531574	−	1.37662i
$331$	−4.39986	+	1.17894i	−0.241838	+	0.0648004i	−0.377702	−	0.925927i	$-0.623286\pi$
$331$	−4.39986	+	1.17894i	−0.241838	+	0.0648004i	0.135864	+	0.990728i	$0.456619\pi$
$332$	7.55428	+	7.55428i	0.414595	+	0.414595i
$333$	5.64729	−	8.77218i	0.309470	−	0.480712i
$334$	−0.737679	+	1.27770i	−0.0403640	+	0.0699125i
$335$	−18.6664	+	32.3311i	−1.01985	+	1.76644i
$336$	0.212084	−	4.57767i	0.0115701	−	0.249732i
$337$			20.9388i			1.14061i	0.821434	+	0.570304i	$0.193175\pi$
$337$			20.9388i			1.14061i	−0.821434	+	0.570304i	$0.806825\pi$
$338$	−2.57529	+	12.7424i	−0.140077	+	0.693093i
$339$	−13.4231	+	9.79323i	−0.729041	+	0.531895i
$340$	−4.75189	+	17.7343i	−0.257707	+	0.961777i
$341$		−	2.97250i		−	0.160970i
$342$	−1.57112	+	4.90159i	−0.0849564	+	0.265048i
$343$	8.20561	−	16.6033i	0.443061	−	0.896491i
$344$	4.00578	+	1.07335i	0.215977	+	0.0578709i
$345$	−41.5783	−	6.50070i	−2.23850	−	0.349986i
$346$	−0.791439	−	2.95369i	−0.0425480	−	0.158791i
$347$			4.28774i			0.230178i	0.993355	+	0.115089i	$0.0367153\pi$
$347$			4.28774i			0.230178i	−0.993355	+	0.115089i	$0.963285\pi$
$348$	−6.08594	+	13.7427i	−0.326240	+	0.736684i
$349$	0.480623	+	1.79371i	0.0257272	+	0.0960151i	0.977596	−	0.210492i	$-0.0675065\pi$
$349$	0.480623	+	1.79371i	0.0257272	+	0.0960151i	−0.951868	+	0.306507i	$0.900840\pi$
$350$	−2.82167	−	25.8330i	−0.150825	−	1.38083i
$351$	15.3227	−	10.7804i	0.817863	−	0.575413i
$352$	−2.01004	−	3.48150i	−0.107136	−	0.185565i
$353$	32.1884	+	8.62486i	1.71322	+	0.459055i	0.976210	−	0.216829i	$-0.0695714\pi$
$353$	32.1884	+	8.62486i	1.71322	+	0.459055i	0.737008	+	0.675884i	$0.236238\pi$
$354$	8.72857	−	0.934946i	0.463918	−	0.0496918i
$355$	−32.1930	−	18.5866i	−1.70862	−	0.986475i
$356$	7.87927	−	7.87927i	0.417601	−	0.417601i
$357$	−1.01140	+	21.8303i	−0.0535291	+	1.15538i
$358$	21.3534	+	5.72162i	1.12856	+	0.302397i
$359$	0.0244477	−	0.0912401i	0.00129030	−	0.00481547i	−0.965278	−	0.261226i	$-0.915873\pi$
$359$	0.0244477	−	0.0912401i	0.00129030	−	0.00481547i	0.966568	+	0.256411i	$0.0825399\pi$
$360$	−7.76238	−	8.55242i	−0.409114	−	0.450752i
$361$	−13.9051	+	8.02811i	−0.731847	+	0.422532i
$362$	−5.77853	−	5.77853i	−0.303713	−	0.303713i
$363$	−8.17369	−	3.61972i	−0.429007	−	0.189986i
$364$	9.44608	−	1.33103i	0.495109	−	0.0697648i
$365$			38.1801i			1.99844i
$366$	−4.18508	−	10.8381i	−0.218758	−	0.566517i
$367$	−0.434426	−	0.752448i	−0.0226769	−	0.0392775i	0.854464	−	0.519510i	$-0.173886\pi$
$367$	−0.434426	−	0.752448i	−0.0226769	−	0.0392775i	−0.877141	+	0.480233i	$0.840552\pi$
$368$	−6.31097			−0.328982
$369$	1.90771	+	3.70759i	0.0993113	+	0.193010i
$370$	3.46521	−	12.9323i	0.180148	−	0.672320i
$371$	9.39285	−	11.6964i	0.487653	−	0.607245i
$372$	−0.461335	−	1.19472i	−0.0239191	−	0.0619433i
$373$	−12.5306	+	21.7036i	−0.648809	+	1.12377i	0.334599	+	0.942361i	$0.391399\pi$
$373$	−12.5306	+	21.7036i	−0.648809	+	1.12377i	−0.983408	+	0.181409i	$0.941934\pi$
$374$	9.58565	+	16.6028i	0.495662	+	0.858512i
$375$	−25.0291	−	20.1860i	−1.29250	−	1.04240i
$376$	−6.26472	+	3.61694i	−0.323078	+	0.186529i
$377$	−30.4591	−	7.15135i	−1.56872	−	0.368313i
$378$	−11.2027	−	7.96868i	−0.576204	−	0.409865i
$379$	−19.8801	+	5.32687i	−1.02117	+	0.273623i	−0.730291	−	0.683136i	$-0.760616\pi$
$379$	−19.8801	+	5.32687i	−1.02117	+	0.273623i	−0.290883	+	0.956759i	$0.593949\pi$
$380$			6.60552i			0.338856i
$381$	−27.0207	−	11.9661i	−1.38431	−	0.613043i
$382$	1.30707	−	0.350227i	0.0668753	−	0.0179192i
$383$	−6.17738	−	23.0543i	−0.315650	−	1.17802i	−0.923383	−	0.383879i	$-0.874588\pi$
$383$	−6.17738	−	23.0543i	−0.315650	−	1.17802i	0.607734	−	0.794141i	$-0.292079\pi$
$384$	−1.34822	−	1.08734i	−0.0688010	−	0.0554880i
$385$	−31.9278	−	25.6399i	−1.62719	−	1.30673i
$386$	−20.7650	+	11.9887i	−1.05691	+	0.610209i
$387$	9.21252	−	8.36151i	0.468298	−	0.425039i
$388$	4.24901	+	1.13852i	0.215711	+	0.0577996i
$389$	7.04572	−	12.2036i	0.357232	−	0.618745i	−0.630265	−	0.776380i	$-0.717054\pi$
$389$	7.04572	−	12.2036i	0.357232	−	0.618745i	0.987497	+	0.157635i	$0.0503871\pi$
$390$	14.5025	−	19.1764i	0.734365	−	0.971037i
$391$	30.0962			1.52203
$392$	−3.22867	−	6.21093i	−0.163073	−	0.313699i
$393$	−7.70279	+	5.61982i	−0.388554	+	0.283482i
$394$	7.31715	+	4.22456i	0.368633	+	0.212830i
$395$	−3.93199	−	14.6744i	−0.197840	−	0.738348i
$396$	−12.0462	−	0.583326i	−0.605342	−	0.0293132i
$397$	−0.550842	−	2.05577i	−0.0276460	−	0.103176i	0.950724	−	0.310038i	$-0.100342\pi$
$397$	−0.550842	−	2.05577i	−0.0276460	−	0.103176i	−0.978370	+	0.206862i	$0.933675\pi$
$398$	−2.31915	−	2.31915i	−0.116249	−	0.116249i
$399$	1.68131	+	7.68066i	0.0841707	+	0.384514i
$400$	−8.50614	−	4.91102i	−0.425307	−	0.245551i
$401$	22.8723	+	22.8723i	1.14219	+	1.14219i	0.988049	+	0.154138i	$0.0492601\pi$
$401$	22.8723	+	22.8723i	1.14219	+	1.14219i	0.154138	+	0.988049i	$0.450740\pi$
$402$	9.89920	+	13.5683i	0.493727	+	0.676726i
$403$	2.26612	−	1.40435i	0.112883	−	0.0699554i
$404$	15.7349	−	9.08453i	0.782839	−	0.451972i
$405$	−34.1787	+	5.69216i	−1.69835	+	0.282846i
$406$	2.49288	+	22.8229i	0.123719	+	1.13268i
$407$	−6.99012	−	12.1072i	−0.346487	−	0.600134i
$408$	6.42949	+	5.18538i	0.318307	+	0.256715i
$409$	19.9577	+	19.9577i	0.986845	+	0.986845i	0.999915	−	0.0130695i	$-0.00416026\pi$
$409$	19.9577	+	19.9577i	0.986845	+	0.986845i	−0.0130695	+	0.999915i	$0.504160\pi$
$410$	3.78367	+	3.78367i	0.186862	+	0.186862i
$411$	13.6457	+	11.0052i	0.673092	+	0.542849i
$412$	−3.02090	−	5.23236i	−0.148829	−	0.257780i
$413$	10.8162	−	7.92599i	0.532230	−	0.390012i
$414$	−10.2484	+	15.9193i	−0.503683	+	0.782392i
$415$	35.6199	−	20.5652i	1.74851	−	1.00950i
$416$	1.70452	−	3.17720i	0.0835711	−	0.155775i
$417$	−7.18356	−	9.84612i	−0.351780	−	0.482167i
$418$	4.87723	+	4.87723i	0.238553	+	0.238553i
$419$	−16.2655	−	9.39087i	−0.794620	−	0.458774i	0.0469666	−	0.998896i	$-0.485045\pi$
$419$	−16.2655	−	9.39087i	−0.794620	−	0.458774i	−0.841586	+	0.540122i	$0.818378\pi$
$420$	−16.8119	−	5.35005i	−0.820337	−	0.261056i
$421$	6.36724	+	6.36724i	0.310320	+	0.310320i	0.845034	−	0.534713i	$-0.179580\pi$
$421$	6.36724	+	6.36724i	0.310320	+	0.310320i	−0.534713	+	0.845034i	$0.679580\pi$
$422$	1.44176	+	5.38072i	0.0701838	+	0.261930i
$423$	−1.04965	+	21.6762i	−0.0510359	+	1.05393i
$424$	−1.46747	−	5.47666i	−0.0712665	−	0.265970i
$425$	40.5647	+	23.4200i	1.96768	+	1.13604i
$426$	−13.5103	+	9.85691i	−0.654578	+	0.477569i
$427$	−13.8373	−	11.1122i	−0.669635	−	0.537755i
$428$	3.01756			0.145859
$429$	−3.45101	−	24.8671i	−0.166616	−	1.20060i
$430$	7.98303	−	13.8270i	0.384976	−	0.666798i
$431$	−22.7945	−	6.10776i	−1.09797	−	0.294201i	−0.336033	−	0.941850i	$-0.609085\pi$
$431$	−22.7945	−	6.10776i	−1.09797	−	0.294201i	−0.761938	+	0.647649i	$0.775752\pi$
$432$	−4.93218	+	1.63512i	−0.237299	+	0.0786700i
$433$	0.164373	−	0.0949005i	0.00789924	−	0.00456063i	−0.496045	−	0.868297i	$-0.665215\pi$
$433$	0.164373	−	0.0949005i	0.00789924	−	0.00456063i	0.503944	+	0.863736i	$0.331882\pi$
$434$	−1.52533	−	1.22493i	−0.0732184	−	0.0587986i
$435$	45.0413	+	36.3258i	2.15957	+	1.74169i
$436$	3.88505	+	14.4992i	0.186060	+	0.694386i
$437$	10.4591	−	2.80249i	0.500324	−	0.134061i
$438$	15.7057	+	6.95527i	0.750447	+	0.332336i
$439$			17.7985i			0.849476i	0.905316	+	0.424738i	$0.139634\pi$
$439$			17.7985i			0.849476i	−0.905316	+	0.424738i	$0.860366\pi$
$440$	−14.9497	+	4.00577i	−0.712701	+	0.190968i
$441$	−20.9100	−	1.94170i	−0.995716	−	0.0924619i
$442$	−8.12865	+	15.1517i	−0.386640	+	0.720691i
$443$	24.8326	−	14.3371i	1.17983	−	0.681176i	0.223855	−	0.974622i	$-0.428136\pi$
$443$	24.8326	−	14.3371i	1.17983	−	0.681176i	0.955975	+	0.293447i	$0.0948023\pi$
$444$	−4.68856	−	3.78132i	−0.222509	−	0.179454i
$445$	−21.4499	−	37.1523i	−1.01682	−	1.76119i
$446$	8.28640	−	14.3525i	0.392372	−	0.679609i
$447$	−11.8876	−	30.7853i	−0.562264	−	1.45610i
$448$	−2.61484	−	0.403232i	−0.123540	−	0.0190509i
$449$	4.61100	−	17.2085i	0.217606	−	0.812118i	−0.767626	−	0.640898i	$-0.778562\pi$
$449$	4.61100	−	17.2085i	0.217606	−	0.812118i	0.985233	−	0.171221i	$-0.0547711\pi$
$450$	−26.2012	+	13.4816i	−1.23513	+	0.635527i
$451$	5.58740			0.263100
$452$	4.79658	+	8.30792i	0.225612	+	0.390772i
$453$	−4.07081	−	10.5422i	−0.191263	−	0.495314i
$454$		−	23.1132i		−	1.08475i
$455$	4.46266	−	36.4540i	0.209213	−	1.70899i
$456$	2.71723	+	1.20333i	0.127246	+	0.0563509i
$457$	−18.7041	−	18.7041i	−0.874942	−	0.874942i	0.118064	−	0.993006i	$-0.462331\pi$
$457$	−18.7041	−	18.7041i	−0.874942	−	0.874942i	−0.993006	+	0.118064i	$0.962331\pi$
$458$	−8.86863	+	5.12030i	−0.414404	+	0.239256i
$459$	23.5209	−	7.79770i	1.09786	−	0.363966i
$460$	−6.28849	+	23.4690i	−0.293202	+	1.09425i
$461$	−1.17017	−	0.313547i	−0.0545004	−	0.0146033i	0.231466	−	0.972843i	$-0.425648\pi$
$461$	−1.17017	−	0.313547i	−0.0545004	−	0.0146033i	−0.285966	+	0.958240i	$0.592315\pi$
$462$	−16.3634	+	8.46294i	−0.761296	+	0.393732i
$463$	13.0245	−	13.0245i	0.605302	−	0.605302i	−0.336413	−	0.941715i	$-0.609214\pi$
$463$	13.0245	−	13.0245i	0.605302	−	0.605302i	0.941715	+	0.336413i	$0.109214\pi$
$464$	7.51497	+	4.33877i	0.348874	+	0.201422i
$465$	−4.90257	+	0.525130i	−0.227351	+	0.0243523i
$466$	−6.33416	−	1.69723i	−0.293424	−	0.0786228i
$467$	−9.52020	−	16.4895i	−0.440542	−	0.763042i	0.557187	−	0.830387i	$-0.311881\pi$
$467$	−9.52020	−	16.4895i	−0.440542	−	0.763042i	−0.997730	+	0.0673449i	$0.978547\pi$
$468$	−5.24645	−	9.45911i	−0.242517	−	0.437247i
$469$	23.4800	+	10.3395i	1.08421	+	0.477435i
$470$	7.20811	+	26.9010i	0.332485	+	1.24085i
$471$	8.44662	−	19.0733i	0.389200	−	0.878852i
$472$		−	5.06827i		−	0.233286i
$473$	−4.31495	−	16.1036i	−0.198401	−	0.740444i
$474$	−6.75271	−	1.05578i	−0.310162	−	0.0484934i
$475$	16.2779	+	4.36165i	0.746881	+	0.200126i
$476$	12.4699	+	1.92296i	0.571555	+	0.0881388i
$477$	−16.1978	−	5.19192i	−0.741647	−	0.237722i
$478$			18.6134i			0.851359i
$479$	−7.96410	+	29.7224i	−0.363889	+	1.35805i	0.505031	+	0.863101i	$0.331481\pi$
$479$	−7.96410	+	29.7224i	−0.363889	+	1.35805i	−0.868920	+	0.494952i	$0.835186\pi$
$480$	−5.38697	+	3.93023i	−0.245880	+	0.179390i
$481$	5.92764	−	11.0490i	0.270277	−	0.503792i
$482$		−	13.2418i		−	0.603147i
$483$	−1.33846	+	28.8895i	−0.0609019	+	1.31452i
$484$	−2.58056	+	4.46966i	−0.117298	+	0.203166i
$485$	8.46775	−	14.6666i	0.384501	−	0.665975i
$486$	−3.88482	+	15.0966i	−0.176219	+	0.684797i
$487$	−9.02402	−	9.02402i	−0.408917	−	0.408917i	0.472444	−	0.881361i	$-0.343372\pi$
$487$	−9.02402	−	9.02402i	−0.408917	−	0.408917i	−0.881361	+	0.472444i	$0.843372\pi$
$488$	−6.47913	+	1.73608i	−0.293297	+	0.0785886i
$489$	5.82945	+	15.0965i	0.263617	+	0.682688i
$490$	−26.3141	+	5.81784i	−1.18875	+	0.262823i
$491$	1.59689	−	2.76589i	0.0720664	−	0.124823i	−0.827740	−	0.561111i	$-0.810374\pi$
$491$	1.59689	−	2.76589i	0.0720664	−	0.124823i	0.899807	+	0.436289i	$0.143707\pi$
$492$	2.24571	−	0.867170i	0.101244	−	0.0390951i
$493$	−35.8380	−	20.6911i	−1.61406	−	0.931878i
$494$	−1.41398	+	6.02244i	−0.0636181	+	0.270962i
$495$	−14.1725	+	44.2155i	−0.637006	+	1.98734i
$496$	−0.714216	+	0.191374i	−0.0320693	+	0.00859293i
$497$	−10.2953	+	23.3797i	−0.461809	+	1.04872i
$498$	−1.97077	−	18.3989i	−0.0883121	−	0.824474i
$499$	−8.21553	+	30.6608i	−0.367777	+	1.37256i	0.495839	+	0.868415i	$0.334861\pi$
$499$	−8.21553	+	30.6608i	−0.367777	+	1.37256i	−0.863616	+	0.504150i	$0.831806\pi$
$500$	−13.1271	+	13.1271i	−0.587064	+	0.587064i
$501$	2.38384	−	0.920510i	0.106502	−	0.0411253i
$502$	−18.1393	−	4.86041i	−0.809597	−	0.216931i
$503$	−31.4519	+	18.1588i	−1.40237	+	0.809659i	−0.994636	−	0.103441i	$-0.967015\pi$
$503$	−31.4519	+	18.1588i	−1.40237	+	0.809659i	−0.407735	+	0.913100i	$0.633681\pi$
$504$	−5.26341	+	5.94109i	−0.234451	+	0.264637i
$505$	−18.1043	−	67.5663i	−0.805633	−	3.00666i
$506$	12.6853	+	21.9716i	0.563932	+	0.976758i
$507$	17.3273	−	14.3793i	0.769533	−	0.638607i
$508$	−8.53085	+	14.7759i	−0.378495	+	0.655573i
$509$	−26.1012	+	26.1012i	−1.15691	+	1.15691i	−0.171779	+	0.985135i	$0.554952\pi$
$509$	−26.1012	+	26.1012i	−1.15691	+	1.15691i	−0.985135	+	0.171779i	$0.945048\pi$
$510$	25.6898	−	18.7428i	1.13756	−	0.829945i
$511$	26.0830	−	2.84897i	1.15384	−	0.126031i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	7.44790	−	4.90008i	0.328833	−	0.216344i
$514$	12.3608	−	12.3608i	0.545210	−	0.545210i
$515$	−22.4680	+	6.02029i	−0.990059	+	0.265285i
$516$	−4.23358	−	5.80275i	−0.186373	−	0.255452i
$517$	25.1847	+	14.5404i	1.10762	+	0.639486i
$518$	−9.09336	−	1.40228i	−0.399539	−	0.0616125i
$519$	−2.14463	+	4.84279i	−0.0941387	+	0.212575i
$520$	−10.1168	−	9.50459i	−0.443651	−	0.416804i
$521$	1.64039	+	0.947080i	0.0718668	+	0.0414923i	0.535503	−	0.844533i	$-0.320122\pi$
$521$	1.64039	+	0.947080i	0.0718668	+	0.0414923i	−0.463636	+	0.886026i	$0.653455\pi$
$522$	23.1481	−	11.9106i	1.01316	−	0.521314i
$523$	−30.4876			−1.33313			−0.666565	−	0.745447i	$-0.732236\pi$
$523$	−30.4876			−1.33313			−0.666565	+	0.745447i	$0.732236\pi$
$524$	2.75250	+	4.76748i	0.120244	+	0.208268i
$525$	−24.2850	+	37.8967i	−1.05989	+	1.65395i
$526$	2.74252	−	10.2352i	0.119580	−	0.446277i
$527$	3.40601	−	0.912637i	0.148368	−	0.0397551i
$528$	−1.07559	+	6.87942i	−0.0468090	+	0.299389i
$529$	16.8283			0.731665
$530$	−21.8286			−0.948174
$531$	−12.7846	−	8.23040i	−0.554806	−	0.357169i
$532$	4.51259	−	0.492898i	0.195646	−	0.0213698i
$533$	2.63974	+	4.25961i	0.114340	+	0.184504i
$534$	−19.1904	+	2.05555i	−0.830451	+	0.0889523i
$535$	3.00681	−	11.2216i	0.129996	−	0.485151i
$536$	8.39782	−	4.84848i	0.362730	−	0.209423i
$537$	−22.5677	−	30.9324i	−0.973868	−	1.33483i
$538$	−0.818810	−	0.818810i	−0.0353014	−	0.0353014i
$539$	−15.1336	+	23.7249i	−0.651850	+	1.02190i
$540$	1.16602	+	19.9709i	0.0501777	+	0.859409i
$541$	29.0838	+	7.79299i	1.25041	+	0.335047i	0.822495	−	0.568772i	$-0.192581\pi$
$541$	29.0838	+	7.79299i	1.25041	+	0.335047i	0.427916	+	0.903819i	$0.359248\pi$
$542$			0.536622i			0.0230499i
$543$	1.50751	+	14.0739i	0.0646933	+	0.603971i
$544$	3.37210	−	3.37210i	0.144578	−	0.144578i
$545$	57.7903			2.47546
$546$	−14.1827	−	8.47657i	−0.606962	−	0.362764i
$547$	−25.1916			−1.07711			−0.538557	−	0.842589i	$-0.681030\pi$
$547$	−25.1916			−1.07711			−0.538557	+	0.842589i	$0.681030\pi$
$548$	7.15682	−	7.15682i	0.305724	−	0.305724i
$549$	−6.14228	+	19.1627i	−0.262146	+	0.817846i
$550$			39.4855i			1.68367i
$551$	−14.3811	−	3.85341i	−0.612657	−	0.164161i
$552$	8.50857	+	6.86216i	0.362149	+	0.292073i
$553$	−9.73148	+	3.78115i	−0.413825	+	0.160791i
$554$	−12.5586	−	12.5586i	−0.533564	−	0.533564i
$555$	−18.7337	+	13.6678i	−0.795200	+	0.580164i
$556$	−6.09405	+	3.51840i	−0.258445	+	0.149213i
$557$	8.65110	−	32.2863i	0.366559	−	1.36802i	−0.498737	−	0.866754i	$-0.666202\pi$
$557$	8.65110	−	32.2863i	0.366559	−	1.36802i	0.865295	−	0.501262i	$-0.167131\pi$
$558$	−0.677084	+	2.11237i	−0.0286632	+	0.0894238i
$559$	10.2382	−	10.8976i	0.433029	−	0.460921i
$560$	−4.10505	+	9.32217i	−0.173470	+	0.393934i
$561$	5.12934	−	32.8071i	0.216561	−	1.38512i
$562$	12.5768			0.530522
$563$	28.2366			1.19003			0.595016	−	0.803714i	$-0.297146\pi$
$563$	28.2366			1.19003			0.595016	+	0.803714i	$0.297146\pi$
$564$	12.3790	+	1.93545i	0.521252	+	0.0814970i
$565$	35.6746	−	9.55899i	1.50084	−	0.402150i
$566$	4.63206	−	17.2871i	0.194700	−	0.726630i
$567$	6.43902	+	22.9246i	0.270413	+	0.962744i
$568$	4.82777	+	8.36194i	0.202569	+	0.350859i
$569$	−26.0505			−1.09209			−0.546047	−	0.837755i	$-0.683868\pi$
$569$	−26.0505			−1.09209			−0.546047	+	0.837755i	$0.683868\pi$
$570$	7.18243	−	8.90568i	0.300839	−	0.373018i
$571$	26.2753	+	15.1701i	1.09959	+	0.634848i	0.936113	−	0.351700i	$-0.114396\pi$
$571$	26.2753	+	15.1701i	1.09959	+	0.634848i	0.163475	+	0.986547i	$0.447730\pi$
$572$	−14.4876	+	0.452023i	−0.605757	+	0.0189000i
$573$	−2.14303	−	0.949039i	−0.0895262	−	0.0396467i
$574$	2.30250	−	2.86717i	0.0961044	−	0.119673i
$575$	53.6820	+	30.9933i	2.23869	+	1.29251i
$576$	0.635390	+	2.93194i	0.0264746	+	0.122164i
$577$	15.3948	−	4.12503i	0.640895	−	0.171727i	0.0762863	−	0.997086i	$-0.475694\pi$
$577$	15.3948	−	4.12503i	0.640895	−	0.171727i	0.564609	+	0.825359i	$0.309027\pi$
$578$	−4.06032	+	4.06032i	−0.168887	+	0.168887i
$579$	41.0316	+	6.41523i	1.70522	+	0.266608i
$580$	23.6230	−	23.6230i	0.980893	−	0.980893i
$581$	−16.7071	−	22.7994i	−0.693129	−	0.945878i
$582$	−4.49064	−	6.15509i	−0.186143	−	0.255137i
$583$	−16.1173	+	16.1173i	−0.667511	+	0.667511i
$584$	4.95853	−	8.58843i	0.205186	−	0.355392i
$585$	−40.4039	+	10.0849i	−1.67050	+	0.416958i
$586$	−11.9466	−	20.6922i	−0.493511	−	0.854786i
$587$	−6.60185	−	24.6384i	−0.272487	−	1.01694i	−0.957506	−	0.288412i	$-0.906873\pi$
$587$	−6.60185	−	24.6384i	−0.272487	−	1.01694i	0.685019	−	0.728525i	$-0.259794\pi$
$588$	−2.40043	+	11.8844i	−0.0989919	+	0.490103i
$589$	1.09867	−	0.634320i	0.0452701	−	0.0261367i
$590$	−18.8477	−	5.05022i	−0.775946	−	0.207914i
$591$	−5.27160	−	13.6519i	−0.216845	−	0.561562i
$592$	−2.45903	+	2.45903i	−0.101066	+	0.101066i
$593$	6.17464	−	23.0441i	0.253562	−	0.946307i	−0.715322	−	0.698795i	$-0.753720\pi$
$593$	6.17464	−	23.0441i	0.253562	−	0.946307i	0.968885	−	0.247513i	$-0.0796132\pi$
$594$	15.6066	+	13.8847i	0.640346	+	0.569696i
$595$	19.5765	−	44.4563i	0.802557	−	1.82253i
$596$	−18.4038	+	4.93128i	−0.753848	+	0.201993i
$597$	0.605022	+	5.64843i	0.0247619	+	0.231175i
$598$	−10.7572	+	20.0512i	−0.439894	+	0.819955i
$599$	19.8526	+	11.4619i	0.811153	+	0.468320i	0.847356	−	0.531025i	$-0.178193\pi$
$599$	19.8526	+	11.4619i	0.811153	+	0.468320i	−0.0362029	+	0.999344i	$0.511526\pi$
$600$	6.12820	+	15.8702i	0.250183	+	0.647898i
$601$	12.1680	−	21.0756i	0.496343	−	0.859690i	−0.503649	−	0.863909i	$-0.668009\pi$
$601$	12.1680	−	21.0756i	0.496343	−	0.859690i	0.999991	+	0.00421817i	$0.00134269\pi$
$602$	−10.0417	−	4.42189i	−0.409268	−	0.180223i
$603$	1.40706	−	29.0568i	0.0572997	−	1.18329i
$604$	−6.30222	+	1.68868i	−0.256434	+	0.0687112i
$605$	14.0502	+	14.0502i	0.571223	+	0.571223i
$606$	−31.0920	−	4.86119i	−1.26303	−	0.197472i
$607$	−6.57272	+	11.3843i	−0.266779	+	0.462074i	−0.968028	−	0.250842i	$-0.919293\pi$
$607$	−6.57272	+	11.3843i	−0.266779	+	0.462074i	0.701249	+	0.712916i	$0.252626\pi$
$608$	0.857872	−	1.48588i	0.0347913	−	0.0602603i
$609$	21.4552	−	33.4808i	0.869410	−	1.35671i
$610$			25.8242i			1.04559i
$611$	0.813384	+	26.0694i	0.0329060	+	1.05466i
$612$	−3.03009	−	13.9821i	−0.122484	−	0.565191i
$613$	−1.92996	+	7.20269i	−0.0779502	+	0.290914i	−0.993886	−	0.110411i	$-0.964783\pi$
$613$	−1.92996	+	7.20269i	−0.0779502	+	0.290914i	0.915936	+	0.401325i	$0.131450\pi$
$614$		−	1.67712i		−	0.0676832i
$615$	−0.987085	−	9.21533i	−0.0398031	−	0.371598i
$616$	3.85210	+	9.91409i	0.155206	+	0.399450i
$617$	−19.6403	−	5.26260i	−0.790688	−	0.211864i	−0.159196	−	0.987247i	$-0.550890\pi$
$617$	−19.6403	−	5.26260i	−0.790688	−	0.211864i	−0.631492	+	0.775383i	$0.717557\pi$
$618$	−1.61650	+	10.3391i	−0.0650253	+	0.415900i
$619$	3.57282	+	13.3339i	0.143604	+	0.535936i	0.999814	+	0.0193082i	$0.00614638\pi$
$619$	3.57282	+	13.3339i	0.143604	+	0.535936i	−0.856210	+	0.516628i	$0.827187\pi$
$620$			2.84669i			0.114326i
$621$	31.1268	−	10.3192i	1.24908	−	0.414096i
$622$	1.30896	+	4.88512i	0.0524847	+	0.195875i
$623$	−23.7802	+	17.4259i	−0.952735	+	0.698153i
$624$	−5.75276	+	2.43017i	−0.230295	+	0.0972847i
$625$	11.1812	+	19.3664i	0.447247	+	0.774655i
$626$	15.9168	+	4.26490i	0.636165	+	0.170460i
$627$	−1.27238	−	11.8788i	−0.0508138	−	0.474393i
$628$	−10.4300	−	6.02174i	−0.416201	−	0.240294i
$629$	11.7268	−	11.7268i	0.467578	−	0.467578i
$630$	16.8488	+	25.4933i	0.671273	+	1.01568i
$631$	−41.0333	−	10.9948i	−1.63351	−	0.437697i	−0.678579	−	0.734528i	$-0.737404\pi$
$631$	−41.0333	−	10.9948i	−1.63351	−	0.437697i	−0.954930	+	0.296830i	$0.904070\pi$
$632$	−1.02131	+	3.81158i	−0.0406256	+	0.151617i
$633$	3.90686	−	8.82208i	0.155284	−	0.350646i
$634$	−18.0803	+	10.4387i	−0.718060	+	0.414572i
$635$	46.4474	+	46.4474i	1.84321	+	1.84321i
$636$	−3.97652	+	8.97937i	−0.157679	+	0.356055i
$637$	−25.2367	−	0.328529i	−0.999915	−	0.0130168i
$638$		−	34.8845i		−	1.38109i
$639$	28.9327	+	1.40104i	1.14456	+	0.0554244i
$640$	1.92497	+	3.33415i	0.0760911	+	0.131794i
$641$	−1.73578			−0.0685590			−0.0342795	−	0.999412i	$-0.510914\pi$
$641$	−1.73578			−0.0685590			−0.0342795	+	0.999412i	$0.510914\pi$
$642$	−4.06834	−	3.28111i	−0.160564	−	0.129495i
$643$	−3.79013	+	14.1449i	−0.149468	+	0.557822i	0.850048	+	0.526706i	$0.176573\pi$
$643$	−3.79013	+	14.1449i	−0.149468	+	0.557822i	−0.999516	+	0.0311165i	$0.990094\pi$
$644$	16.5022	+	2.54478i	0.650277	+	0.100278i
$645$	−25.7975	+	9.96158i	−1.01578	+	0.392237i
$646$	−4.09108	+	7.08597i	−0.160962	+	0.278794i
$647$	−6.17783	−	10.7003i	−0.242876	−	0.420673i	0.718657	−	0.695365i	$-0.244757\pi$
$647$	−6.17783	−	10.7003i	−0.242876	−	0.420673i	−0.961532	+	0.274692i	$0.911424\pi$
$648$	8.42759	+	3.15844i	0.331067	+	0.124075i
$649$	−17.6452	+	10.1874i	−0.692634	+	0.399892i
$650$	−30.1022	+	18.6548i	−1.18071	+	0.731700i
$651$	0.724571	+	3.31003i	0.0283982	+	0.129730i
$652$	9.02485	−	2.41820i	0.353441	−	0.0947041i
$653$			30.0923i			1.17760i	0.808278	+	0.588801i	$0.200400\pi$
$653$			30.0923i			1.17760i	−0.808278	+	0.588801i	$0.799600\pi$
$654$	10.5276	−	23.7725i	0.411664	−	0.929578i
$655$	20.4718	−	5.48540i	0.799899	−	0.214332i
$656$	−0.359724	−	1.34251i	−0.0140449	−	0.0524162i
$657$	−13.6120	−	26.4546i	−0.531054	−	1.03209i
$658$	17.8397	−	6.93159i	0.695464	−	0.270221i
$659$	−29.0006	+	16.7435i	−1.12970	+	0.652235i	−0.943861	−	0.330344i	$-0.892835\pi$
$659$	−29.0006	+	16.7435i	−1.12970	+	0.652235i	−0.185844	+	0.982579i	$0.559502\pi$
$660$	24.5112	+	10.8548i	0.954095	+	0.422521i
$661$	−12.2326	−	3.27771i	−0.475792	−	0.127488i	0.0129504	−	0.999916i	$-0.495878\pi$
$661$	−12.2326	−	3.27771i	−0.475792	−	0.127488i	−0.488743	+	0.872428i	$0.662544\pi$
$662$	2.27754	−	3.94481i	0.0885190	−	0.153319i
$663$	27.4342	−	11.5892i	1.06546	−	0.450086i
$664$	−10.6834			−0.414595
$665$	2.66355	−	17.2724i	0.103288	−	0.669794i
$666$	2.20963	+	10.1961i	0.0856214	+	0.395091i
$667$	−47.4267	−	27.3818i	−1.83637	−	1.06023i
$668$	−0.381851	−	1.42509i	−0.0147743	−	0.0551383i
$669$	−26.7779	+	10.3401i	−1.03529	+	0.399773i
$670$	−9.66242	−	36.0607i	−0.373292	−	1.39314i
$671$	19.0675	+	19.0675i	0.736093	+	0.736093i
$672$	3.08693	+	3.38686i	0.119081	+	0.130651i
$673$	14.9509	+	8.63190i	0.576315	+	0.332735i	0.759667	−	0.650312i	$-0.225362\pi$
$673$	14.9509	+	8.63190i	0.576315	+	0.332735i	−0.183353	+	0.983047i	$0.558695\pi$
$674$	−14.8060	−	14.8060i	−0.570304	−	0.570304i
$675$	49.9839	+	10.3134i	1.92388	+	0.396964i
$676$	−7.18921	−	10.8312i	−0.276508	−	0.416585i
$677$	−2.21973	+	1.28156i	−0.0853113	+	0.0492545i	−0.542049	−	0.840347i	$-0.682351\pi$
$677$	−2.21973	+	1.28156i	−0.0853113	+	0.0492545i	0.456738	+	0.889602i	$0.349018\pi$
$678$	2.56668	−	16.4164i	0.0985728	−	0.630468i
$679$	−10.6514	−	4.69039i	−0.408764	−	0.180000i
$680$	−9.17994	−	15.9001i	−0.352035	−	0.609742i
$681$	−25.1318	+	31.1616i	−0.963054	+	1.19412i
$682$	2.10187	+	2.10187i	0.0804849	+	0.0804849i
$683$	27.0444	+	27.0444i	1.03483	+	1.03483i	0.999371	+	0.0354547i	$0.0112879\pi$
$683$	27.0444	+	27.0444i	1.03483	+	1.03483i	0.0354547	+	0.999371i	$0.488712\pi$
$684$	−2.35500	−	4.57690i	−0.0900457	−	0.175002i
$685$	−19.4831	−	33.7458i	−0.744413	−	1.28936i
$686$	5.93803	+	17.5425i	0.226715	+	0.669776i
$687$	17.5244	+	2.73991i	0.668596	+	0.104534i
$688$	−3.59149	+	2.07355i	−0.136924	+	0.0790532i
$689$	−19.9018	−	4.67265i	−0.758197	−	0.178014i
$690$	33.9970	−	24.8036i	1.29424	−	0.944256i
$691$	−16.2080	−	16.2080i	−0.616581	−	0.616581i	0.328072	−	0.944653i	$-0.393601\pi$
$691$	−16.2080	−	16.2080i	−0.616581	−	0.616581i	−0.944653	+	0.328072i	$0.893601\pi$
$692$	2.64821	+	1.52894i	0.100670	+	0.0581217i
$693$	31.2636	+	6.38270i	1.18761	+	0.242459i
$694$	−3.03189	−	3.03189i	−0.115089	−	0.115089i
$695$	7.01173	+	26.1681i	0.265970	+	0.992614i
$696$	−5.41412	−	14.0209i	−0.205222	−	0.531462i
$697$	1.71548	+	6.40226i	0.0649784	+	0.242503i
$698$	−1.60820	−	0.928493i	−0.0608711	−	0.0351440i
$699$	6.69437	+	9.17562i	0.253204	+	0.347054i
$700$	20.2619	+	16.2715i	0.765829	+	0.615005i
$701$	24.3586			0.920011			0.460006	−	0.887916i	$-0.347847\pi$
$701$	24.3586			0.920011			0.460006	+	0.887916i	$0.347847\pi$
$702$	−3.21188	+	18.4576i	−0.121225	+	0.696638i
$703$	2.98333	−	5.16728i	0.112518	−	0.194888i
$704$	3.88311	+	1.04048i	0.146350	+	0.0392144i
$705$	19.5324	−	44.1061i	0.735633	−	1.66113i
$706$	−28.8594	+	16.6620i	−1.08614	+	0.627081i
$707$	−44.8074	+	17.4098i	−1.68515	+	0.654764i
$708$	−5.51092	+	6.83314i	−0.207113	+	0.256805i
$709$	8.29691	+	30.9645i	0.311597	+	1.16290i	0.927116	+	0.374774i	$0.122280\pi$
$709$	8.29691	+	30.9645i	0.311597	+	1.16290i	−0.615519	+	0.788122i	$0.711054\pi$
$710$	35.9066	−	9.62114i	1.34755	−	0.361075i
$711$	7.95615	+	8.76590i	0.298379	+	0.328747i
$712$			11.1430i			0.417601i
$713$	4.50739	−	1.20775i	0.168803	−	0.0452307i
$714$	−14.7212	−	16.1515i	−0.550927	−	0.604456i
$715$	−12.7550	+	54.3262i	−0.477011	+	2.03169i
$716$	−19.1449	+	11.0533i	−0.715479	+	0.413082i
$717$	20.2391	−	25.0950i	0.755843	−	0.937190i
$718$	0.0472294	+	0.0818037i	0.00176258	+	0.00305289i
$719$	8.91238	−	15.4367i	0.332376	−	0.575691i	−0.650602	−	0.759419i	$-0.725483\pi$
$719$	8.91238	−	15.4367i	0.332376	−	0.575691i	0.982977	+	0.183728i	$0.0588165\pi$
$720$	11.5363	+	0.558637i	0.429933	+	0.0208192i
$721$	5.78933	+	14.8999i	0.215606	+	0.554902i
$722$	4.15566	−	15.5091i	0.154657	−	0.577190i
$723$	−14.3983	+	17.8528i	−0.535479	+	0.663954i
$724$	8.17207			0.303713
$725$	−42.6156	−	73.8124i	−1.58270	−	2.74132i
$726$	8.33920	−	3.22014i	0.309497	−	0.119511i
$727$		−	35.4327i		−	1.31413i	−0.753835	−	0.657064i	$-0.771798\pi$
$727$		−	35.4327i		−	1.31413i	0.753835	−	0.657064i	$-0.228202\pi$
$728$	−5.73821	+	7.62056i	−0.212672	+	0.282437i
$729$	21.6527	−	16.1294i	0.801953	−	0.597387i
$730$	−26.9974	−	26.9974i	−0.999219	−	0.999219i
$731$	17.1273	−	9.88848i	0.633478	−	0.365738i
$732$	10.6230	+	4.70440i	0.392637	+	0.173879i
$733$	−8.96990	+	33.4761i	−0.331311	+	1.23647i	0.576503	+	0.817095i	$0.304417\pi$
$733$	−8.96990	+	33.4761i	−0.331311	+	1.23647i	−0.907814	+	0.419374i	$0.862250\pi$
$734$	0.839247	+	0.224876i	0.0309772	+	0.00830031i
$735$	41.8032	+	20.7686i	1.54193	+	0.766063i
$736$	4.46253	−	4.46253i	0.164491	−	0.164491i
$737$	−33.7600	−	19.4913i	−1.24356	−	0.717973i
$738$	−3.97062	−	1.27271i	−0.146160	−	0.0468492i
$739$	3.44920	+	0.924211i	0.126881	+	0.0339977i	0.321701	−	0.946841i	$-0.395746\pi$
$739$	3.44920	+	0.924211i	0.126881	+	0.0339977i	−0.194820	+	0.980839i	$0.562412\pi$
$740$	6.69427	+	11.5948i	0.246086	+	0.426234i
$741$	8.45479	−	6.58209i	0.310594	−	0.241799i
$742$	1.62883	+	14.9123i	0.0597963	+	0.547449i
$743$	−10.7093	−	39.9675i	−0.392884	−	1.46626i	−0.825354	−	0.564616i	$-0.809024\pi$
$743$	−10.7093	−	39.9675i	−0.392884	−	1.46626i	0.432469	−	0.901649i	$-0.357642\pi$
$744$	1.17101	+	0.518581i	0.0429312	+	0.0190121i
$745$			73.3529i			2.68744i
$746$	−6.48630	−	24.2072i	−0.237480	−	0.886289i
$747$	−17.3488	+	26.9486i	−0.634759	+	0.985998i
$748$	−18.5181	−	4.96190i	−0.677087	−	0.181425i
$749$	−7.89045	−	1.21678i	−0.288311	−	0.0444601i
$750$	31.9719	−	3.42462i	1.16745	−	0.125049i
$751$		−	15.0621i		−	0.549624i	−0.961498	−	0.274812i	$-0.911384\pi$
$751$		−	15.0621i		−	0.549624i	0.961498	−	0.274812i	$-0.0886156\pi$
$752$	1.87226	−	6.98738i	0.0682744	−	0.254804i
$753$	19.1709	+	26.2765i	0.698625	+	0.957568i
$754$	26.5946	−	16.4810i	0.968517	−	0.600204i
$755$			25.1191i			0.914177i
$756$	13.5562	−	2.28678i	0.493034	−	0.0831695i
$757$	−23.3536	+	40.4496i	−0.848802	+	1.47017i	0.0334769	+	0.999439i	$0.489342\pi$
$757$	−23.3536	+	40.4496i	−0.848802	+	1.47017i	−0.882278	+	0.470728i	$0.843991\pi$
$758$	10.2907	−	17.8241i	0.373776	−	0.647399i
$759$	6.78800	−	43.4158i	0.246389	−	1.57589i
$760$	−4.67080	−	4.67080i	−0.169428	−	0.169428i
$761$	23.9510	−	6.41764i	0.868222	−	0.232639i	0.202903	−	0.979199i	$-0.434962\pi$
$761$	23.9510	−	6.41764i	0.868222	−	0.232639i	0.665319	+	0.746559i	$0.268296\pi$
$762$	27.5678	−	10.6452i	0.998677	−	0.385634i
$763$	−4.31226	−	39.4797i	−0.156114	−	1.42926i
$764$	−0.676587	+	1.17188i	−0.0244780	+	0.0423972i
$765$	−55.0152	−	2.66407i	−1.98908	−	0.0963196i
$766$	20.6699	+	11.9338i	0.746835	+	0.431185i
$767$	−16.1029	−	8.63898i	−0.581442	−	0.311935i
$768$	1.72220	−	0.184470i	0.0621445	−	0.00665651i
$769$	−22.1205	+	5.92717i	−0.797686	+	0.213739i	−0.634568	−	0.772867i	$-0.718822\pi$
$769$	−22.1205	+	5.92717i	−0.797686	+	0.213739i	−0.163118	+	0.986607i	$0.552155\pi$
$770$	40.7065	−	4.44625i	1.46696	−	0.160232i
$771$	−30.1054	+	3.22468i	−1.08422	+	0.116134i
$772$	6.20581	−	23.1604i	0.223352	−	0.833561i
$773$	10.0452	−	10.0452i	0.361299	−	0.361299i	−0.502992	−	0.864291i	$-0.667767\pi$
$773$	10.0452	−	10.0452i	0.361299	−	0.361299i	0.864291	+	0.502992i	$0.167767\pi$
$774$	−0.601754	+	12.4267i	−0.0216296	+	0.446669i
$775$	7.01506	+	1.87968i	0.251989	+	0.0675201i
$776$	−3.80956	+	2.19945i	−0.136755	+	0.0789557i
$777$	10.7351	+	11.7781i	0.385119	+	0.422538i
$778$	3.64714	+	13.6113i	0.130756	+	0.487989i
$779$	1.19233	+	2.06518i	0.0427196	+	0.0739926i
$780$	3.30494	+	23.8146i	0.118336	+	0.852701i
$781$	19.4081	−	33.6157i	0.694475	−	1.20287i
$782$	−21.2812	+	21.2812i	−0.761015	+	0.761015i
$783$	−44.1596	−	9.11167i	−1.57814	−	0.325624i
$784$	6.67481	+	2.10878i	0.238386	+	0.0753134i
$785$	−32.7862	+	32.7862i	−1.17019	+	1.17019i
$786$	1.47288	−	9.42050i	0.0525360	−	0.336018i
$787$	27.0874	−	27.0874i	0.965562	−	0.965562i	−0.0338644	−	0.999426i	$-0.510781\pi$
$787$	27.0874	−	27.0874i	0.965562	−	0.965562i	0.999426	+	0.0338644i	$0.0107814\pi$
$788$	−8.16122	+	2.18679i	−0.290732	+	0.0779013i
$789$	−14.8267	+	10.8173i	−0.527844	+	0.385106i
$790$	13.1567	+	7.59602i	0.468094	+	0.270254i
$791$	−9.19229	−	23.6580i	−0.326840	−	0.841183i
$792$	8.93039	−	8.10544i	0.317328	−	0.288014i
$793$	−5.52795	+	23.5447i	−0.196303	+	0.836096i
$794$	1.84315	+	1.06414i	0.0654110	+	0.0377651i
$795$	29.4297	+	23.7351i	1.04377	+	0.841797i
$796$	3.27977			0.116249
$797$	5.71829	+	9.90437i	0.202552	+	0.350831i	0.949350	−	0.314220i	$-0.101743\pi$
$797$	5.71829	+	9.90437i	0.202552	+	0.350831i	−0.746798	+	0.665051i	$0.768410\pi$
$798$	−6.61991	−	4.24218i	−0.234342	−	0.150172i
$799$	−8.92859	+	33.3220i	−0.315871	+	1.17885i
$800$	9.48737	−	2.54213i	0.335429	−	0.0898780i
$801$	28.1080	+	18.0952i	0.993146	+	0.639361i
$802$	−32.3463			−1.14219
$803$	−39.8675			−1.40689
$804$	−16.5940	−	2.59445i	−0.585227	−	0.0914993i
$805$	25.9068	−	58.8319i	0.913096	−	2.07355i
$806$	−0.609365	+	2.59541i	−0.0214640	+	0.0914194i
$807$	0.213612	+	1.99426i	0.00751949	+	0.0702012i
$808$	−4.70250	+	17.5500i	−0.165433	+	0.617405i
$809$	−19.4886	+	11.2518i	−0.685184	+	0.395591i	−0.801805	−	0.597585i	$-0.796127\pi$
$809$	−19.4886	+	11.2518i	−0.685184	+	0.395591i	0.116621	+	0.993176i	$0.462794\pi$
$810$	20.1430	−	28.1930i	0.707754	−	0.990600i
$811$	−13.3542	−	13.3542i	−0.468928	−	0.468928i	0.432639	−	0.901567i	$-0.357582\pi$
$811$	−13.3542	−	13.3542i	−0.468928	−	0.468928i	−0.901567	+	0.432639i	$0.857582\pi$
$812$	−17.9009	−	14.3755i	−0.628200	−	0.504480i
$813$	0.583489	−	0.723483i	0.0204639	−	0.0253737i
$814$	13.5039	+	3.61835i	0.473311	+	0.126823i
$815$		−	35.9708i		−	1.26000i
$816$	−8.21295	+	0.879717i	−0.287511	+	0.0307962i
$817$	5.03131	−	5.03131i	0.176023	−	0.176023i
$818$	−28.2245			−0.986845
$819$	9.90444	+	26.8496i	0.346089	+	0.938202i
$820$	−5.35091			−0.186862
$821$	1.48596	−	1.48596i	0.0518605	−	0.0518605i	−0.680701	−	0.732561i	$-0.738325\pi$
$821$	1.48596	−	1.48596i	0.0518605	−	0.0518605i	0.732561	+	0.680701i	$0.238325\pi$
$822$	−17.4308	+	1.86708i	−0.607970	+	0.0651217i
$823$		−	44.3573i		−	1.54620i	−0.634285	−	0.773099i	$-0.718705\pi$
$823$		−	44.3573i		−	1.54620i	0.634285	−	0.773099i	$-0.281295\pi$
$824$	5.83594	+	1.56373i	0.203304	+	0.0544753i
$825$	42.9341	−	53.2351i	1.49477	−	1.85341i
$826$	−2.04369	+	13.2527i	−0.0711090	+	0.461121i
$827$	−8.95024	−	8.95024i	−0.311231	−	0.311231i	0.534156	−	0.845386i	$-0.320630\pi$
$827$	−8.95024	−	8.95024i	−0.311231	−	0.311231i	−0.845386	+	0.534156i	$0.820630\pi$
$828$	−4.00992	−	18.5034i	−0.139355	−	0.643037i
$829$	28.3747	−	16.3822i	0.985495	−	0.568976i	0.0815707	−	0.996668i	$-0.474006\pi$
$829$	28.3747	−	16.3822i	0.985495	−	0.568976i	0.903925	+	0.427691i	$0.140673\pi$
$830$	−10.6453	+	39.7288i	−0.369504	+	1.37901i
$831$	3.27629	+	30.5872i	0.113653	+	1.06106i
$832$	1.04134	+	3.45190i	0.0361020	+	0.119673i
$833$	−31.8313	−	10.0565i	−1.10289	−	0.348437i
$834$	12.0418	+	1.88272i	0.416973	+	0.0651932i
$835$	−5.68004			−0.196566
$836$	−6.89745			−0.238553
$837$	3.20972	−	2.11172i	0.110944	−	0.0729918i
$838$	18.1418	−	4.86107i	0.626697	−	0.167923i
$839$	0.880405	−	3.28572i	0.0303950	−	0.113436i	−0.949062	−	0.315090i	$-0.897965\pi$
$839$	0.880405	−	3.28572i	0.0303950	−	0.113436i	0.979457	+	0.201655i	$0.0646319\pi$
$840$	15.6709	−	8.10475i	0.540696	−	0.279640i
$841$	23.1499	+	40.0967i	0.798271	+	1.38265i
$842$	−9.00463			−0.310320
$843$	−16.9563	−	13.6753i	−0.584007	−	0.471002i
$844$	−4.82423	−	2.78527i	−0.166057	−	0.0958729i
$845$	−47.4423	+	15.9423i	−1.63206	+	0.548431i
$846$	−14.5852	−	16.0696i	−0.501449	−	0.552485i
$847$	8.55007	−	10.6469i	0.293784	−	0.365832i
$848$	4.91024	+	2.83493i	0.168618	+	0.0973518i
$849$	−25.0419	+	18.2702i	−0.859437	+	0.627030i
$850$	−45.2441	+	12.1231i	−1.55186	+	0.415819i
$851$	15.5189	−	15.5189i	0.531980	−	0.531980i
$852$	2.58337	−	16.5231i	0.0885047	−	0.566073i
$853$	20.9347	−	20.9347i	0.716791	−	0.716791i	−0.251156	−	0.967947i	$-0.580811\pi$
$853$	20.9347	−	20.9347i	0.716791	−	0.716791i	0.967947	+	0.251156i	$0.0808106\pi$
$854$	17.6420	−	1.92698i	0.603695	−	0.0659399i
$855$	−19.3670	+	4.19708i	−0.662337	+	0.143537i
$856$	−2.13374	+	2.13374i	−0.0729297	+	0.0729297i
$857$	−3.66436	+	6.34685i	−0.125172	+	0.216804i	−0.921800	−	0.387665i	$-0.873282\pi$
$857$	−3.66436	+	6.34685i	−0.125172	+	0.216804i	0.796628	+	0.604470i	$0.206615\pi$
$858$	20.0239	+	15.1435i	0.683606	+	0.516990i
$859$	22.8218	+	39.5285i	0.778670	+	1.34870i	0.932708	+	0.360632i	$0.117439\pi$
$859$	22.8218	+	39.5285i	0.778670	+	1.34870i	−0.154038	+	0.988065i	$0.549228\pi$
$860$	4.13232	+	15.4220i	0.140911	+	0.525887i
$861$	−6.22185	+	1.36197i	−0.212040	+	0.0464159i
$862$	20.4370	−	11.7993i	0.696086	−	0.401886i
$863$	−14.2956	−	3.83050i	−0.486628	−	0.130392i	0.00715898	−	0.999974i	$-0.497721\pi$
$863$	−14.2956	−	3.83050i	−0.486628	−	0.130392i	−0.493787	+	0.869583i	$0.664388\pi$
$864$	2.33137	−	4.64378i	0.0793147	−	0.157985i
$865$	8.32454	−	8.32454i	0.283043	−	0.283043i
$866$	−0.0491241	+	0.183334i	−0.00166931	+	0.00622993i
$867$	9.88914	−	1.05926i	0.335853	−	0.0359743i
$868$	1.94473	−	0.212417i	0.0660085	−	0.00720992i
$869$	15.3229	−	4.10576i	0.519794	−	0.139278i
$870$	−57.5353	+	6.16279i	−1.95063	+	0.208938i
$871$	−1.09034	−	34.9459i	−0.0369447	−	1.18410i
$872$	−12.9996	−	7.50534i	−0.440223	−	0.254163i
$873$	−0.638292	+	13.1813i	−0.0216029	+	0.446118i
$874$	−5.41400	+	9.37733i	−0.183131	+	0.317193i
$875$	39.6187	−	29.0321i	1.33936	−	0.981466i
$876$	−16.0237	+	6.18748i	−0.541391	+	0.209056i
$877$	32.7433	−	8.77354i	1.10566	−	0.296261i	0.340594	−	0.940211i	$-0.389372\pi$
$877$	32.7433	−	8.77354i	1.10566	−	0.296261i	0.765068	+	0.643949i	$0.222705\pi$
$878$	−12.5854	−	12.5854i	−0.424738	−	0.424738i
$879$	−6.39272	+	40.8876i	−0.215621	+	1.37910i
$880$	7.73855	−	13.4036i	0.260867	−	0.451834i
$881$	−17.4587	+	30.2394i	−0.588199	+	1.01879i	0.406270	+	0.913753i	$0.366829\pi$
$881$	−17.4587	+	30.2394i	−0.588199	+	1.01879i	−0.994468	+	0.105037i	$0.966504\pi$
$882$	16.1586	−	13.4126i	0.544089	−	0.451627i
$883$		−	56.9398i		−	1.91618i	−0.286475	−	0.958088i	$-0.592483\pi$
$883$		−	56.9398i		−	1.91618i	0.286475	−	0.958088i	$-0.407517\pi$
$884$	−4.96602	−	16.4617i	−0.167025	−	0.553666i
$885$	19.9195	+	27.3026i	0.669586	+	0.917767i
$886$	−7.42142	+	27.6971i	−0.249328	+	0.930503i
$887$		−	15.8909i		−	0.533565i	−0.963757	−	0.266782i	$-0.914039\pi$
$887$		−	15.8909i		−	0.533565i	0.963757	−	0.266782i	$-0.0859605\pi$
$888$	5.98911	−	0.641513i	0.200981	−	0.0215278i
$889$	28.2649	−	35.1967i	0.947976	−	1.18046i
$890$	41.4380	+	11.1033i	1.38901	+	0.372183i
$891$	−5.94373	−	35.6893i	−0.199122	−	1.19564i
$892$	4.28935	+	16.0081i	0.143618	+	0.535990i
$893$			12.4115i			0.415334i
$894$	30.1743	+	13.3627i	1.00918	+	0.446915i
$895$	22.0279	+	82.2093i	0.736312	+	2.74795i
$896$	2.13410	−	1.56385i	0.0712953	−	0.0522444i
$897$	36.3055	−	15.3367i	1.21221	−	0.512078i
$898$	8.90777	+	15.4287i	0.297256	+	0.514862i
$899$	−6.19764	−	1.66065i	−0.206703	−	0.0553859i
$900$	8.99411	−	28.0599i	0.299804	−	0.935331i
$901$	−23.4163	−	13.5194i	−0.780110	−	0.450397i
$902$	−3.95088	+	3.95088i	−0.131550	+	0.131550i
$903$	8.73030	+	16.8804i	0.290526	+	0.561744i
$904$	−9.26628	−	2.48289i	−0.308192	−	0.0825798i
$905$	8.14297	−	30.3900i	0.270681	−	1.01020i
$906$	10.3329	+	4.57594i	0.343289	+	0.152026i
$907$	9.47624	−	5.47111i	0.314653	−	0.181665i	−0.334354	−	0.942448i	$-0.608518\pi$
$907$	9.47624	−	5.47111i	0.314653	−	0.181665i	0.649007	+	0.760783i	$0.275185\pi$
$908$	16.3435	+	16.3435i	0.542377	+	0.542377i
$909$	36.6331	+	40.3615i	1.21504	+	1.33871i
$910$	22.6213	+	28.9324i	0.749888	+	0.959100i
$911$			22.4731i			0.744568i	0.928119	+	0.372284i	$0.121425\pi$
$911$			22.4731i			0.744568i	−0.928119	+	0.372284i	$0.878575\pi$
$912$	−2.77225	+	1.07049i	−0.0917985	+	0.0354475i
$913$	21.4740	+	37.1941i	0.710687	+	1.23095i
$914$	26.4516			0.874942
$915$	28.0797	−	34.8167i	0.928285	−	1.15100i
$916$	2.65046	−	9.89167i	0.0875738	−	0.326830i
$917$	−5.27497	−	13.5761i	−0.174195	−	0.448322i
$918$	−11.1180	+	22.1456i	−0.366949	+	0.730914i
$919$	17.0614	−	29.5513i	0.562804	−	0.974806i	−0.434446	−	0.900698i	$-0.643056\pi$
$919$	17.0614	−	29.5513i	0.562804	−	0.974806i	0.997250	−	0.0741079i	$-0.0236109\pi$
$920$	−12.1484	−	21.0417i	−0.400522	−	0.693724i
$921$	−1.82360	+	2.26113i	−0.0600897	+	0.0745068i
$922$	1.04915	−	0.605726i	0.0345519	−	0.0199485i
$923$	34.7966	−	1.08568i	1.14534	−	0.0357355i
$924$	5.58650	−	17.5549i	0.183782	−	0.577514i
$925$	32.9932	−	8.84050i	1.08481	−	0.290674i
$926$			18.4195i			0.605302i
$927$	13.4215	−	12.1817i	0.440820	−	0.400099i
$928$	−8.38186	+	2.24591i	−0.275148	+	0.0737257i
$929$	−2.32091	−	8.66174i	−0.0761465	−	0.284183i	0.917344	−	0.398095i	$-0.130328\pi$
$929$	−2.32091	−	8.66174i	−0.0761465	−	0.284183i	−0.993491	+	0.113912i	$0.963662\pi$
$930$	3.09531	−	3.83796i	0.101499	−	0.125852i
$931$	−11.9985	−	0.530772i	−0.393234	−	0.0173953i
$932$	5.67905	−	3.27880i	0.186024	−	0.107401i
$933$	3.54701	−	8.00950i	0.116124	−	0.262219i
$934$	18.3916	+	4.92802i	0.601792	+	0.161250i
$935$	−36.9042	+	63.9199i	−1.20690	+	2.09041i
$936$	10.3984	+	2.97880i	0.339882	+	0.0973650i
$937$	−25.3471			−0.828053			−0.414027	−	0.910265i	$-0.635878\pi$
$937$	−25.3471			−0.828053			−0.414027	+	0.910265i	$0.635878\pi$
$938$	−23.9140	+	9.29175i	−0.780821	+	0.303386i
$939$	−16.8220	−	23.0570i	−0.548965	−	0.752437i
$940$	−24.1188	−	13.9250i	−0.786668	−	0.454183i
$941$	0.996574	+	3.71927i	0.0324874	+	0.121245i	0.980265	−	0.197687i	$-0.0633428\pi$
$941$	0.996574	+	3.71927i	0.0324874	+	0.121245i	−0.947778	+	0.318931i	$0.896676\pi$
$942$	7.51421	+	19.4595i	0.244826	+	0.634026i
$943$	2.27021	+	8.47253i	0.0739282	+	0.275904i
$944$	3.58381	+	3.58381i	0.116643	+	0.116643i
$945$	5.00392	−	52.6909i	0.162778	−	1.71403i
$946$	14.4381	+	8.33584i	0.469423	+	0.271021i
$947$	7.30273	+	7.30273i	0.237307	+	0.237307i	0.815734	−	0.578427i	$-0.196333\pi$
$947$	7.30273	+	7.30273i	0.237307	+	0.237307i	−0.578427	+	0.815734i	$0.696333\pi$
$948$	5.52143	−	4.02834i	0.179328	−	0.130834i
$949$	−18.8352	−	30.3934i	−0.611418	−	0.986612i
$950$	−14.5944	+	8.42606i	−0.473504	+	0.273378i
$951$	35.7266	+	5.58579i	1.15851	+	0.181132i
$952$	−10.1773	+	7.45778i	−0.329847	+	0.241708i
$953$	5.03077	+	8.71354i	0.162962	+	0.282259i	0.935930	−	0.352186i	$-0.114562\pi$
$953$	5.03077	+	8.71354i	0.162962	+	0.282259i	−0.772967	+	0.634446i	$0.781228\pi$
$954$	15.1248	−	7.78234i	0.489684	−	0.251963i
$955$	3.68377	+	3.68377i	0.119204	+	0.119204i
$956$	−13.1617	−	13.1617i	−0.425679	−	0.425679i
$957$	−37.9313	+	47.0319i	−1.22614	+	1.52033i
$958$	−15.3855	−	26.6484i	−0.497082	−	0.860971i
$959$	−21.5998	+	15.8281i	−0.697494	+	0.511116i
$960$	1.03006	−	6.58826i	0.0332452	−	0.212635i
$961$	−26.3733	+	15.2266i	−0.850752	+	0.491182i
$962$	3.62136	+	12.0043i	0.116757	+	0.387034i
$963$	1.91733	+	8.84732i	0.0617851	+	0.285101i
$964$	9.36335	+	9.36335i	0.301573	+	0.301573i
$965$	−79.9442	−	46.1558i	−2.57349	−	1.48581i
$966$	−19.4815	−	21.3744i	−0.626808	−	0.687710i
$967$	32.9135	+	32.9135i	1.05843	+	1.05843i	0.998184	+	0.0602436i	$0.0191878\pi$
$967$	32.9135	+	32.9135i	1.05843	+	1.05843i	0.0602436	+	0.998184i	$0.480812\pi$
$968$	−1.33580	−	4.98526i	−0.0429341	−	0.160232i
$969$	13.2205	−	5.10504i	0.424704	−	0.163998i
$970$	4.38323	+	16.3584i	0.140737	+	0.525238i
$971$	26.8738	+	15.5156i	0.862422	+	0.497920i	0.864823	−	0.502078i	$-0.167431\pi$
$971$	26.8738	+	15.5156i	0.862422	+	0.497920i	−0.00240063	+	0.999997i	$0.500764\pi$
$972$	−7.92795	−	13.4219i	−0.254289	−	0.430508i
$973$	17.3537	−	6.74275i	0.556334	−	0.216163i
$974$	12.7619			0.408917
$975$	60.8684	+	7.58057i	1.94935	+	0.242773i
$976$	3.35385	−	5.80903i	0.107354	−	0.185943i
$977$	47.1099	+	12.6231i	1.50718	+	0.403847i	0.915497	−	0.402324i	$-0.131797\pi$
$977$	47.1099	+	12.6231i	1.50718	+	0.403847i	0.591682	+	0.806171i	$0.298464\pi$
$978$	−14.7969	−	6.55280i	−0.473152	−	0.209536i
$979$	38.7943	−	22.3979i	1.23987	−	0.715839i
$980$	14.4931	−	22.7207i	0.462964	−	0.725787i
$981$	−40.0423	+	20.6034i	−1.27845	+	0.657816i
$982$	0.826609	+	3.08495i	0.0263781	+	0.0984446i
$983$	−24.5330	+	6.57359i	−0.782481	+	0.209665i	−0.627878	−	0.778312i	$-0.716076\pi$
$983$	−24.5330	+	6.57359i	−0.782481	+	0.209665i	−0.154602	+	0.987977i	$0.549410\pi$
$984$	−0.974775	+	2.20114i	−0.0310747	+	0.0701698i
$985$			32.5286i			1.03645i
$986$	39.9720	−	10.7105i	1.27297	−	0.341091i
$987$	−31.5888	−	10.0525i	−1.00548	−	0.319975i
$988$	−3.25867	−	5.25834i	−0.103672	−	0.167290i
$989$	22.6657	−	13.0861i	0.720729	−	0.416113i
$990$	−21.2436	−	41.2865i	−0.675166	−	1.31217i
$991$	0.945747	+	1.63808i	0.0300426	+	0.0520354i	0.880656	−	0.473757i	$-0.157102\pi$
$991$	0.945747	+	1.63808i	0.0300426	+	0.0520354i	−0.850613	+	0.525792i	$0.823769\pi$
$992$	0.369706	−	0.640349i	0.0117382	−	0.0203311i
$993$	−7.35996	+	2.84201i	−0.233561	+	0.0901886i
$994$	−9.25205	−	23.8119i	−0.293457	−	0.755266i
$995$	3.26809	−	12.1967i	0.103605	−	0.386661i
$996$	14.4035	+	11.6164i	0.456393	+	0.368081i
$997$	20.9061			0.662104			0.331052	−	0.943613i	$-0.392597\pi$
$997$	20.9061			0.662104			0.331052	+	0.943613i	$0.392597\pi$
$998$	−15.8712	−	27.4897i	−0.502393	−	0.870171i
$999$	8.10755	−	16.1492i	0.256512	−	0.510938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.19	yes	152
3.2	odd	2	inner	546.2.ch.a.137.25	yes	152
7.2	even	3		546.2.bw.a.527.27	yes	152
13.2	odd	12		546.2.bw.a.431.8	✓	152
21.2	odd	6		546.2.bw.a.527.8	yes	152
39.2	even	12		546.2.bw.a.431.27	yes	152
91.2	odd	12	inner	546.2.ch.a.275.25	yes	152
273.2	even	12	inner	546.2.ch.a.275.19	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.8	✓	152	13.2	odd	12
546.2.bw.a.431.27	yes	152	39.2	even	12
546.2.bw.a.527.8	yes	152	21.2	odd	6
546.2.bw.a.527.27	yes	152	7.2	even	3
546.2.ch.a.137.19	yes	152	1.1	even	1	trivial
546.2.ch.a.137.25	yes	152	3.2	odd	2	inner
546.2.ch.a.275.19	yes	152	273.2	even	12	inner
546.2.ch.a.275.25	yes	152	91.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.72220 - 0.184470i) q^{3} -1.00000i q^{4} +(-3.71876 - 0.996438i) q^{5} +(-1.08734 + 1.34822i) q^{6} +(-0.403232 + 2.61484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.93194 - 0.635390i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.72220 - 0.184470i) q^{3} -1.00000i q^{4} +(-3.71876 - 0.996438i) q^{5} +(-1.08734 + 1.34822i) q^{6} +(-0.403232 + 2.61484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.93194 - 0.635390i) q^{9} +(3.33415 - 1.92497i) q^{10} +(1.04048 - 3.88311i) q^{11} +(-0.184470 - 1.72220i) q^{12} +(3.45190 - 1.04134i) q^{13} +(-1.56385 - 2.13410i) q^{14} +(-6.58826 - 1.03006i) q^{15} -1.00000 q^{16} +4.76887 q^{17} +(-1.62391 + 2.52248i) q^{18} +(1.65728 - 0.444067i) q^{19} +(-0.996438 + 3.71876i) q^{20} +(-0.212084 + 4.57767i) q^{21} +(2.01004 + 3.48150i) q^{22} +6.31097 q^{23} +(1.34822 + 1.08734i) q^{24} +(8.50614 + 4.91102i) q^{25} +(-1.70452 + 3.17720i) q^{26} +(4.93218 - 1.63512i) q^{27} +(2.61484 + 0.403232i) q^{28} +(-7.51497 - 4.33877i) q^{29} +(5.38697 - 3.93023i) q^{30} +(0.714216 - 0.191374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.07559 - 6.87942i) q^{33} +(-3.37210 + 3.37210i) q^{34} +(4.10505 - 9.32217i) q^{35} +(-0.635390 - 2.93194i) q^{36} +(2.45903 - 2.45903i) q^{37} +(-0.857872 + 1.48588i) q^{38} +(5.75276 - 2.43017i) q^{39} +(-1.92497 - 3.33415i) q^{40} +(0.359724 + 1.34251i) q^{41} +(-3.08693 - 3.38686i) q^{42} +(3.59149 - 2.07355i) q^{43} +(-3.88311 - 1.04048i) q^{44} +(-11.5363 - 0.558637i) q^{45} +(-4.46253 + 4.46253i) q^{46} +(-1.87226 + 6.98738i) q^{47} +(-1.72220 + 0.184470i) q^{48} +(-6.67481 - 2.10878i) q^{49} +(-9.48737 + 2.54213i) q^{50} +(8.21295 - 0.879717i) q^{51} +(-1.04134 - 3.45190i) q^{52} +(-4.91024 - 2.83493i) q^{53} +(-2.33137 + 4.64378i) q^{54} +(-7.73855 + 13.4036i) q^{55} +(-2.13410 + 1.56385i) q^{56} +(2.77225 - 1.07049i) q^{57} +(8.38186 - 2.24591i) q^{58} +(-3.58381 - 3.58381i) q^{59} +(-1.03006 + 6.58826i) q^{60} +(-3.35385 + 5.80903i) q^{61} +(-0.369706 + 0.640349i) q^{62} +(0.479193 + 7.92278i) q^{63} +1.00000i q^{64} +(-13.8744 + 0.432891i) q^{65} +(4.10393 + 5.62504i) q^{66} +(2.50976 - 9.36655i) q^{67} -4.76887i q^{68} +(10.8687 - 1.16419i) q^{69} +(3.68906 + 9.49448i) q^{70} +(9.32653 + 2.49904i) q^{71} +(2.52248 + 1.62391i) q^{72} +(-2.56673 - 9.57915i) q^{73} +3.47759i q^{74} +(15.5552 + 6.88863i) q^{75} +(-0.444067 - 1.65728i) q^{76} +(9.73417 + 4.28647i) q^{77} +(-2.34943 + 5.78621i) q^{78} +(1.97302 + 3.41737i) q^{79} +(3.71876 + 0.996438i) q^{80} +(8.19256 - 3.72585i) q^{81} +(-1.20366 - 0.694934i) q^{82} +(-7.55428 + 7.55428i) q^{83} +(4.57767 + 0.212084i) q^{84} +(-17.7343 - 4.75189i) q^{85} +(-1.07335 + 4.00578i) q^{86} +(-13.7427 - 6.08594i) q^{87} +(3.48150 - 2.01004i) q^{88} +(7.87927 + 7.87927i) q^{89} +(8.55242 - 7.76238i) q^{90} +(1.33103 + 9.44608i) q^{91} -6.31097i q^{92} +(1.19472 - 0.461335i) q^{93} +(-3.61694 - 6.26472i) q^{94} -6.60552 q^{95} +(1.08734 - 1.34822i) q^{96} +(-1.13852 + 4.24901i) q^{97} +(6.21093 - 3.22867i) q^{98} +(0.583326 - 12.0462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

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