LMFDB - Embedded newform 168.2.ba.c.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +O(q^{10})$	\(q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +(0.00458308 + 0.551736i) q^{10} +(0.748582 + 1.29658i) q^{11} +(1.13530 - 3.27278i) q^{12} +3.28768 q^{13} +(1.73911 - 3.31293i) q^{14} +(0.634670 + 0.232043i) q^{15} +(-2.11397 - 3.39575i) q^{16} +(1.68169 + 2.91278i) q^{17} +(-3.26476 - 2.70950i) q^{18} +(-2.56203 + 4.43756i) q^{19} +(0.669184 - 0.401321i) q^{20} +(-3.05110 - 3.41918i) q^{21} +(1.04339 - 1.84237i) q^{22} +(4.72764 + 2.72950i) q^{23} +(-4.80326 + 0.963690i) q^{24} +(-2.42389 - 4.19830i) q^{25} +(-2.35811 - 4.00712i) q^{26} +(-4.51125 + 2.57850i) q^{27} +(-5.28528 + 0.256545i) q^{28} +4.13801 q^{29} +(-0.172400 - 0.939988i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(-2.62258 + 5.01219i) q^{32} +(-1.66397 - 1.98889i) q^{33} +(2.34398 - 4.13891i) q^{34} +(-0.0329110 - 1.03171i) q^{35} +(-0.960750 + 5.92258i) q^{36} +(7.46581 + 4.31038i) q^{37} +(7.24625 - 0.0601921i) q^{38} +(-5.60934 + 0.980702i) q^{39} +(-0.969118 - 0.527771i) q^{40} -11.1607 q^{41} +(-1.97898 + 6.17120i) q^{42} -4.79323i q^{43} +(-2.99391 + 0.0497422i) q^{44} +(-1.15207 - 0.206585i) q^{45} +(-0.0641268 - 7.71993i) q^{46} +(2.51067 - 4.34861i) q^{47} +(4.61974 + 5.16314i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(-3.37846 + 5.96557i) q^{50} +(-3.73813 - 4.46806i) q^{51} +(-3.19263 + 5.74826i) q^{52} +(0.499243 + 0.864715i) q^{53} +(6.37846 + 3.64900i) q^{54} -0.584118i q^{55} +(4.10358 + 6.25784i) q^{56} +(3.04755 - 8.33548i) q^{57} +(-2.96801 - 5.04353i) q^{58} +(-1.36034 + 0.785391i) q^{59} +(-1.02203 + 0.884338i) q^{60} +(3.40889 - 5.90437i) q^{61} +(5.11878 + 2.89891i) q^{62} +(6.22563 + 4.92357i) q^{63} +(7.99007 - 0.398545i) q^{64} +(-1.11084 - 0.641343i) q^{65} +(-1.23062 + 3.45464i) q^{66} +(3.05467 - 1.76361i) q^{67} +(-6.72585 + 0.111746i) q^{68} +(-8.88036 - 3.24676i) q^{69} +(-1.23388 + 0.780115i) q^{70} -14.3360i q^{71} +(7.90772 - 3.07701i) q^{72} +(2.76107 - 1.59410i) q^{73} +(-0.101268 - 12.1912i) q^{74} +(5.38791 + 6.43999i) q^{75} +(-5.27078 - 8.78877i) q^{76} +(-1.87018 + 3.49184i) q^{77} +(5.21864 + 6.13342i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(0.0518426 + 1.55974i) q^{80} +(6.92781 - 5.74504i) q^{81} +(8.00508 + 13.6030i) q^{82} -17.4548i q^{83} +(8.94106 - 2.01429i) q^{84} -1.31222i q^{85} +(-5.84213 + 3.43797i) q^{86} +(-7.06016 + 1.23435i) q^{87} +(2.20803 + 3.61339i) q^{88} +(-2.54840 + 4.41396i) q^{89} +(0.574539 + 1.55235i) q^{90} +(4.58716 + 7.39053i) q^{91} +(-9.36328 + 5.61532i) q^{92} +(5.52586 - 4.62312i) q^{93} +(-7.10101 + 0.0589856i) q^{94} +(1.73131 - 0.999573i) q^{95} +(2.97945 - 9.33396i) q^{96} +9.00074i q^{97} +(9.87379 - 0.712973i) q^{98} +(3.43230 + 2.89703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.717256	−	1.21883i	−0.507176	−	0.861842i
$2$	−0.717256	−	1.21883i	−0.507176	−	0.861842i
$3$	−1.70617	+	0.298296i	−0.985058	+	0.172221i
$3$	−1.70617	+	0.298296i	−0.985058	+	0.172221i
$4$	−0.971089	+	1.74842i	−0.485544	+	0.874212i
$5$	−0.337879	−	0.195075i	−0.151104	−	0.0872401i	0.422542	−	0.906344i	$-0.361138\pi$
$5$	−0.337879	−	0.195075i	−0.151104	−	0.0872401i	−0.573646	+	0.819103i	$0.694471\pi$
$6$	1.58733	+	1.86558i	0.648026	+	0.761618i
$7$	1.39526	+	2.24795i	0.527357	+	0.849644i
$7$	1.39526	+	2.24795i	0.527357	+	0.849644i
$8$	2.82755	−	0.0704754i	0.999690	−	0.0249168i
$9$	2.82204	−	1.01789i	0.940680	−	0.339296i
$10$	0.00458308	+	0.551736i	0.00144930	+	0.174474i
$11$	0.748582	+	1.29658i	0.225706	+	0.390934i	0.956531	−	0.291631i	$-0.0941978\pi$
$11$	0.748582	+	1.29658i	0.225706	+	0.390934i	−0.730825	+	0.682565i	$0.760864\pi$
$12$	1.13530	−	3.27278i	0.327732	−	0.944771i
$13$	3.28768			0.911838			0.455919	−	0.890021i	$-0.349311\pi$
$13$	3.28768			0.911838			0.455919	+	0.890021i	$0.349311\pi$
$14$	1.73911	−	3.31293i	0.464796	−	0.885418i
$15$	0.634670	+	0.232043i	0.163871	+	0.0599132i
$16$	−2.11397	−	3.39575i	−0.528493	−	0.848938i
$17$	1.68169	+	2.91278i	0.407871	+	0.706453i	0.994651	−	0.103293i	$-0.0329381\pi$
$17$	1.68169	+	2.91278i	0.407871	+	0.706453i	−0.586780	+	0.809746i	$0.699605\pi$
$18$	−3.26476	−	2.70950i	−0.769510	−	0.638635i
$19$	−2.56203	+	4.43756i	−0.587769	+	1.01805i	0.406755	+	0.913537i	$0.366660\pi$
$19$	−2.56203	+	4.43756i	−0.587769	+	1.01805i	−0.994524	+	0.104509i	$0.966673\pi$
$20$	0.669184	−	0.401321i	0.149634	−	0.0897382i
$21$	−3.05110	−	3.41918i	−0.665805	−	0.746126i
$22$	1.04339	−	1.84237i	0.222451	−	0.392795i
$23$	4.72764	+	2.72950i	0.985780	+	0.569141i	0.904010	−	0.427511i	$-0.140609\pi$
$23$	4.72764	+	2.72950i	0.985780	+	0.569141i	0.0817700	+	0.996651i	$0.473943\pi$
$24$	−4.80326	+	0.963690i	−0.980461	+	0.196712i
$25$	−2.42389	−	4.19830i	−0.484778	−	0.839661i
$26$	−2.35811	−	4.00712i	−0.462463	−	0.785861i
$27$	−4.51125	+	2.57850i	−0.868190	+	0.496232i
$28$	−5.28528	+	0.256545i	−0.998824	+	0.0484825i
$29$	4.13801			0.768410			0.384205	−	0.923248i	$-0.374476\pi$
$29$	4.13801			0.768410			0.384205	+	0.923248i	$0.374476\pi$
$30$	−0.172400	−	0.939988i	−0.0314758	−	0.171618i
$31$	−3.60237	+	2.07983i	−0.647005	+	0.373549i	−0.787308	−	0.616560i	$-0.788526\pi$
$31$	−3.60237	+	2.07983i	−0.647005	+	0.373549i	0.140303	+	0.990109i	$0.455192\pi$
$32$	−2.62258	+	5.01219i	−0.463611	+	0.886039i
$33$	−1.66397	−	1.98889i	−0.289661	−	0.346222i
$34$	2.34398	−	4.13891i	0.401989	−	0.709816i
$35$	−0.0329110	−	1.03171i	−0.00556298	−	0.174391i
$36$	−0.960750	+	5.92258i	−0.160125	+	0.987097i
$37$	7.46581	+	4.31038i	1.22737	+	0.708623i	0.966479	−	0.256745i	$-0.0826501\pi$
$37$	7.46581	+	4.31038i	1.22737	+	0.708623i	0.260892	+	0.965368i	$0.415983\pi$
$38$	7.24625	−	0.0601921i	1.17550	−	0.00976445i
$39$	−5.60934	+	0.980702i	−0.898214	+	0.157038i
$40$	−0.969118	−	0.527771i	−0.153231	−	0.0834480i
$41$	−11.1607			−1.74301			−0.871505	−	0.490387i	$-0.836855\pi$
$41$	−11.1607			−1.74301			−0.871505	+	0.490387i	$0.836855\pi$
$42$	−1.97898	+	6.17120i	−0.305363	+	0.952236i
$43$		−	4.79323i		−	0.730961i	−0.930819	−	0.365480i	$-0.880905\pi$
$43$		−	4.79323i		−	0.730961i	0.930819	−	0.365480i	$-0.119095\pi$
$44$	−2.99391	+	0.0497422i	−0.451350	+	0.00749892i
$45$	−1.15207	−	0.206585i	−0.171741	−	0.0307959i
$46$	−0.0641268	−	7.71993i	−0.00945498	−	1.13824i
$47$	2.51067	−	4.34861i	0.366219	−	0.634310i	−0.622752	−	0.782419i	$-0.713985\pi$
$47$	2.51067	−	4.34861i	0.366219	−	0.634310i	0.988971	+	0.148109i	$0.0473187\pi$
$48$	4.61974	+	5.16314i	0.666802	+	0.745235i
$49$	−3.10652	+	6.27292i	−0.443788	+	0.896132i
$50$	−3.37846	+	5.96557i	−0.477787	+	0.843658i
$51$	−3.73813	−	4.46806i	−0.523443	−	0.625653i
$52$	−3.19263	+	5.74826i	−0.442738	+	0.797140i
$53$	0.499243	+	0.864715i	0.0685763	+	0.118778i	0.898275	−	0.439434i	$-0.144821\pi$
$53$	0.499243	+	0.864715i	0.0685763	+	0.118778i	−0.829699	+	0.558212i	$0.811488\pi$
$54$	6.37846	+	3.64900i	0.867999	+	0.496566i
$55$		−	0.584118i		−	0.0787624i
$56$	4.10358	+	6.25784i	0.548364	+	0.836240i
$57$	3.04755	−	8.33548i	0.403657	−	1.10406i
$58$	−2.96801	−	5.04353i	−0.389719	−	0.662248i
$59$	−1.36034	+	0.785391i	−0.177101	+	0.102249i	−0.585930	−	0.810362i	$-0.699271\pi$
$59$	−1.36034	+	0.785391i	−0.177101	+	0.102249i	0.408829	+	0.912611i	$0.365937\pi$
$60$	−1.02203	+	0.884338i	−0.131944	+	0.114168i
$61$	3.40889	−	5.90437i	0.436464	−	0.755977i	−0.560950	−	0.827850i	$-0.689564\pi$
$61$	3.40889	−	5.90437i	0.436464	−	0.755977i	0.997414	+	0.0718723i	$0.0228974\pi$
$62$	5.11878	+	2.89891i	0.650085	+	0.368161i
$63$	6.22563	+	4.92357i	0.784355	+	0.620312i
$64$	7.99007	−	0.398545i	0.998758	−	0.0498181i
$65$	−1.11084	−	0.641343i	−0.137783	−	0.0795488i
$66$	−1.23062	+	3.45464i	−0.151479	+	0.425237i
$67$	3.05467	−	1.76361i	0.373187	−	0.215460i	−0.301663	−	0.953415i	$-0.597542\pi$
$67$	3.05467	−	1.76361i	0.373187	−	0.215460i	0.674850	+	0.737955i	$0.264208\pi$
$68$	−6.72585	+	0.111746i	−0.815629	+	0.0135512i
$69$	−8.88036	−	3.24676i	−1.06907	−	0.390864i
$70$	−1.23388	+	0.780115i	−0.147477	+	0.0932416i
$71$		−	14.3360i		−	1.70137i	−0.525677	−	0.850684i	$-0.676188\pi$
$71$		−	14.3360i		−	1.70137i	0.525677	−	0.850684i	$-0.323812\pi$
$72$	7.90772	−	3.07701i	0.931933	−	0.362630i
$73$	2.76107	−	1.59410i	0.323159	−	0.186576i	−0.329641	−	0.944106i	$-0.606928\pi$
$73$	2.76107	−	1.59410i	0.323159	−	0.186576i	0.652800	+	0.757531i	$0.273594\pi$
$74$	−0.101268	−	12.1912i	−0.0117722	−	1.41720i
$75$	5.38791	+	6.43999i	0.622142	+	0.743626i
$76$	−5.27078	−	8.78877i	−0.604600	−	1.00814i
$77$	−1.87018	+	3.49184i	−0.213127	+	0.397932i
$78$	5.21864	+	6.13342i	0.590895	+	0.694473i
$79$	−0.239413	+	0.414676i	−0.0269361	+	0.0466547i	−0.879179	−	0.476491i	$-0.841908\pi$
$79$	−0.239413	+	0.414676i	−0.0269361	+	0.0466547i	0.852243	+	0.523146i	$0.175242\pi$
$80$	0.0518426	+	1.55974i	0.00579618	+	0.174384i
$81$	6.92781	−	5.74504i	0.769756	−	0.638338i
$82$	8.00508	+	13.6030i	0.884013	+	1.50220i
$83$		−	17.4548i		−	1.91591i	−0.286911	−	0.957957i	$-0.592628\pi$
$83$		−	17.4548i		−	1.91591i	0.286911	−	0.957957i	$-0.407372\pi$
$84$	8.94106	−	2.01429i	0.975550	−	0.219777i
$85$		−	1.31222i		−	0.142331i
$86$	−5.84213	+	3.43797i	−0.629973	+	0.370726i
$87$	−7.06016	+	1.23435i	−0.756928	+	0.132337i
$88$	2.20803	+	3.61339i	0.235377	+	0.385189i
$89$	−2.54840	+	4.41396i	−0.270130	+	0.467879i	−0.968895	−	0.247473i	$-0.920400\pi$
$89$	−2.54840	+	4.41396i	−0.270130	+	0.467879i	0.698765	+	0.715351i	$0.253733\pi$
$90$	0.574539	+	1.55235i	0.0605617	+	0.163633i
$91$	4.58716	+	7.39053i	0.480865	+	0.774738i
$92$	−9.36328	+	5.61532i	−0.976190	+	0.585438i
$93$	5.52586	−	4.62312i	0.573005	−	0.479395i
$94$	−7.10101	+	0.0589856i	−0.732413	+	0.00608390i
$95$	1.73131	−	0.999573i	0.177629	−	0.102554i
$96$	2.97945	−	9.33396i	0.304089	−	0.952644i
$97$			9.00074i			0.913887i	0.889496	+	0.456943i	$0.151056\pi$
$97$			9.00074i			0.913887i	−0.889496	+	0.456943i	$0.848944\pi$
$98$	9.87379	−	0.712973i	0.997403	−	0.0720212i
$99$	3.43230	+	2.89703i	0.344959	+	0.291163i
$100$	9.69423	−	0.161064i	0.969423	−	0.0161064i
$101$	4.63907	−	2.67837i	0.461605	−	0.266508i	−0.251114	−	0.967958i	$-0.580797\pi$
$101$	4.63907	−	2.67837i	0.461605	−	0.266508i	0.712719	+	0.701450i	$0.247464\pi$
$102$	−2.76460	+	7.76088i	−0.273737	+	0.768442i
$103$	7.70831	+	4.45039i	0.759522	+	0.438510i	0.829124	−	0.559065i	$-0.188840\pi$
$103$	7.70831	+	4.45039i	0.759522	+	0.438510i	−0.0696021	+	0.997575i	$0.522173\pi$
$104$	9.29608	−	0.231700i	0.911555	−	0.0227201i
$105$	0.363908	+	1.75046i	0.0355138	+	0.170828i
$106$	0.695854	−	1.22871i	0.0675874	−	0.119343i
$107$	−7.85256	+	13.6010i	−0.759135	+	1.31486i	0.184157	+	0.982897i	$0.441045\pi$
$107$	−7.85256	+	13.6010i	−0.759135	+	1.31486i	−0.943292	+	0.331964i	$0.892289\pi$
$108$	−0.127480	−	10.3915i	−0.0122668	−	0.999925i
$109$	−15.1582	+	8.75159i	−1.45189	+	0.838250i	−0.998589	−	0.0531069i	$-0.983088\pi$
$109$	−15.1582	+	8.75159i	−1.45189	+	0.838250i	−0.453303	+	0.891357i	$0.649754\pi$
$110$	−0.711940	+	0.418962i	−0.0678808	+	0.0399464i
$111$	−14.0237	−	5.12723i	−1.33107	−	0.486655i
$112$	4.68393	−	9.49004i	0.442590	−	0.896724i
$113$		−	0.0726142i		−	0.00683097i	−0.999994	−	0.00341549i	$-0.998913\pi$
$113$		−	0.0726142i		−	0.00683097i	0.999994	−	0.00341549i	$-0.00108718\pi$
$114$	−12.3454	+	2.26423i	−1.15625	+	0.212064i
$115$	−1.06491	−	1.84448i	−0.0993037	−	0.171999i
$116$	−4.01838	+	7.23500i	−0.373097	+	0.671753i
$117$	9.27796	−	3.34649i	0.857748	−	0.309383i
$118$	1.93297	+	1.09469i	0.177944	+	0.100775i
$119$	−4.20138	+	7.84443i	−0.385139	+	0.719098i
$120$	1.81091	+	0.611384i	0.165313	+	0.0558114i
$121$	4.37925	−	7.58508i	0.398114	−	0.689553i
$122$	−9.64147	+	0.0800883i	−0.872897	+	0.00725085i
$123$	19.0421	−	3.32920i	1.71697	−	0.300183i
$124$	−0.138202	−	8.31817i	−0.0124109	−	0.746994i
$125$			3.84211i			0.343649i
$126$	1.53563	−	11.1194i	0.136805	−	0.990598i
$127$	−8.81577			−0.782273			−0.391137	−	0.920333i	$-0.627918\pi$
$127$	−8.81577			−0.782273			−0.391137	+	0.920333i	$0.627918\pi$
$128$	−6.21668	−	9.45267i	−0.549482	−	0.835506i
$129$	1.42980	+	8.17807i	0.125887	+	0.720039i
$130$	0.0150677	+	1.81393i	0.00132152	+	0.159092i
$131$	−4.36183	−	2.51830i	−0.381095	−	0.220025i	0.297200	−	0.954815i	$-0.403947\pi$
$131$	−4.36183	−	2.51830i	−0.381095	−	0.220025i	−0.678294	+	0.734790i	$0.737281\pi$
$132$	5.09329	−	0.977942i	0.443314	−	0.0851189i
$133$	−13.5501	+	0.432239i	−1.17494	+	0.0374799i
$134$	−4.34052	−	2.45816i	−0.374964	−	0.212352i
$135$	2.02726	+	0.00881014i	0.174478	+	0.000758256i
$136$	4.96035	+	8.11751i	0.425347	+	0.696071i
$137$	6.34787	−	3.66494i	0.542335	−	0.313117i	−0.203690	−	0.979035i	$-0.565293\pi$
$137$	6.34787	−	3.66494i	0.542335	−	0.313117i	0.746025	+	0.665918i	$0.231960\pi$
$138$	2.41224	+	13.1524i	0.205343	+	1.11961i
$139$	15.7497			1.33587			0.667935	−	0.744220i	$-0.267178\pi$
$139$	15.7497			1.33587			0.667935	+	0.744220i	$0.267178\pi$
$140$	1.83583	+	0.944343i	0.155156	+	0.0798116i
$141$	−2.98646	+	8.16840i	−0.251505	+	0.687903i
$142$	−17.4731	+	10.2826i	−1.46631	+	0.862894i
$143$	2.46110	+	4.26275i	0.205807	+	0.356469i
$144$	−9.42221	−	7.43115i	−0.785184	−	0.619262i
$145$	−1.39815	−	0.807222i	−0.116110	−	0.0670361i
$146$	−3.92333	−	2.22189i	−0.324697	−	0.183885i
$147$	3.42906	−	11.6293i	0.282824	−	0.959172i
$148$	−14.7863	+	8.86763i	−1.21543	+	0.728914i
$149$	−8.98969	+	15.5706i	−0.736464	+	1.27559i	0.217613	+	0.976035i	$0.430173\pi$
$149$	−8.98969	+	15.5706i	−0.736464	+	1.27559i	−0.954078	+	0.299559i	$0.903161\pi$
$150$	3.98473	−	11.1861i	0.325352	−	0.913338i
$151$	−7.89149	−	13.6685i	−0.642201	−	1.11232i	−0.984940	−	0.172894i	$-0.944688\pi$
$151$	−7.89149	−	13.6685i	−0.642201	−	1.11232i	0.342740	−	0.939430i	$-0.388645\pi$
$152$	−6.93152	+	12.7280i	−0.562220	+	1.03238i
$153$	7.71069	+	6.50820i	0.623373	+	0.526157i
$154$	5.59735	−	0.225107i	0.451047	−	0.0181396i
$155$	1.62289			0.130354
$156$	3.73249	−	10.7599i	0.298838	−	0.861478i
$157$	−2.53274	−	4.38683i	−0.202134	−	0.350107i	0.747082	−	0.664732i	$-0.231454\pi$
$157$	−2.53274	−	4.38683i	−0.202134	−	0.350107i	−0.949216	+	0.314625i	$0.898121\pi$
$158$	0.677140	−	0.00562477i	0.0538704	−	0.000447482i
$159$	−1.10974	−	1.32643i	−0.0880077	−	0.105193i
$160$	1.86387	−	1.18192i	0.147352	−	0.0934387i
$161$	0.460494	+	14.4358i	0.0362920	+	1.13770i
$162$	−11.9712	−	4.32315i	−0.940549	−	0.339659i
$163$	−10.8745	−	6.27840i	−0.851757	−	0.491762i	0.00948597	−	0.999955i	$-0.496980\pi$
$163$	−10.8745	−	6.27840i	−0.851757	−	0.491762i	−0.861243	+	0.508193i	$0.830314\pi$
$164$	10.8380	−	19.5136i	0.846308	−	1.52376i
$165$	0.174240	+	0.996605i	0.0135646	+	0.0775856i
$166$	−21.2744	+	12.5196i	−1.65122	+	0.971706i
$167$	7.43145			0.575063			0.287531	−	0.957771i	$-0.407165\pi$
$167$	7.43145			0.575063			0.287531	+	0.957771i	$0.407165\pi$
$168$	−8.86810	−	9.45287i	−0.684189	−	0.729305i
$169$	−2.19116			−0.168551
$170$	−1.59938	+	0.941200i	−0.122667	+	0.0721868i
$171$	−2.71320	+	15.1308i	−0.207483	+	1.15708i
$172$	8.38060	+	4.65465i	0.639014	+	0.354914i
$173$	−15.2445	−	8.80144i	−1.15902	−	0.669161i	−0.207952	−	0.978139i	$-0.566680\pi$
$173$	−15.2445	−	8.80144i	−1.15902	−	0.669161i	−0.951069	+	0.308978i	$0.900013\pi$
$174$	6.56840	+	7.71978i	0.497949	+	0.585235i
$175$	6.05561	−	11.3065i	0.457761	−	0.854690i
$176$	2.82039	−	5.28294i	0.212595	−	0.398216i
$177$	2.08669	−	1.74579i	0.156845	−	0.131222i
$178$	7.20771	−	0.0598720i	0.540241	−	0.00448759i
$179$	−8.11784	−	14.0605i	−0.606756	−	1.05093i	−0.991771	−	0.128022i	$-0.959137\pi$
$179$	−8.11784	−	14.0605i	−0.606756	−	1.05093i	0.385016	−	0.922910i	$-0.374196\pi$
$180$	1.47996	−	1.81370i	0.110310	−	0.135185i
$181$	−6.19340			−0.460351			−0.230176	−	0.973149i	$-0.573930\pi$
$181$	−6.19340			−0.460351			−0.230176	+	0.973149i	$0.573930\pi$
$182$	5.71762	−	10.8919i	0.423818	−	0.807358i
$183$	−4.05490	+	11.0907i	−0.299747	+	0.819850i
$184$	13.5600	+	7.38462i	0.999655	+	0.544401i
$185$	−1.68169	−	2.91278i	−0.123641	−	0.214152i
$186$	−9.59824	−	3.41912i	−0.703777	−	0.250702i
$187$	−2.51777	+	4.36091i	−0.184118	+	0.318901i
$188$	5.16513	+	8.61261i	0.376706	+	0.628139i
$189$	−12.0907	−	6.54338i	−0.879467	−	0.475961i
$190$	−2.46010	−	1.39322i	−0.178475	−	0.101075i
$191$	7.28788	+	4.20766i	0.527333	+	0.304456i	0.739930	−	0.672684i	$-0.234859\pi$
$191$	7.28788	+	4.20766i	0.527333	+	0.304456i	−0.212597	+	0.977140i	$0.568192\pi$
$192$	−13.5135	+	3.06339i	−0.975255	+	0.221081i
$193$	6.57333	+	11.3853i	0.473158	+	0.819534i	0.999528	−	0.0307215i	$-0.00978048\pi$
$193$	6.57333	+	11.3853i	0.473158	+	0.819534i	−0.526370	+	0.850256i	$0.676447\pi$
$194$	10.9704	−	6.45583i	0.787626	−	0.463502i
$195$	2.08659	+	0.762882i	0.149424	+	0.0546311i
$196$	−7.95102	−	11.5231i	−0.567930	−	0.823077i
$197$	17.6119			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$197$	17.6119			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$198$	1.06915	−	6.26130i	0.0759810	−	0.444971i
$199$	17.2688	−	9.97017i	1.22416	−	0.706767i	0.258354	−	0.966050i	$-0.416820\pi$
$199$	17.2688	−	9.97017i	1.22416	−	0.706767i	0.965801	+	0.259284i	$0.0834864\pi$
$200$	−7.14955	−	11.7001i	−0.505549	−	0.827321i
$201$	−4.68570	+	3.92022i	−0.330504	+	0.276511i
$202$	−6.59187	−	3.73316i	−0.463803	−	0.262664i
$203$	5.77359	+	9.30203i	0.405227	+	0.652874i
$204$	11.4421	−	2.19695i	0.801108	−	0.153818i
$205$	3.77097	+	2.17717i	0.263376	+	0.152060i
$206$	−0.104557	−	12.5872i	−0.00728485	−	0.876990i
$207$	16.1199	+	2.89055i	1.12041	+	0.200907i
$208$	−6.95007	−	11.1641i	−0.481900	−	0.774094i
$209$	−7.67154			−0.530652
$210$	1.87250	−	1.69907i	0.129215	−	0.117247i
$211$		−	14.5159i		−	0.999314i	−0.866223	−	0.499657i	$-0.833459\pi$
$211$		−	14.5159i		−	0.999314i	0.866223	−	0.499657i	$-0.166541\pi$
$212$	−1.99670	+	0.0331740i	−0.137134	+	0.00227840i
$213$	4.27637	+	24.4596i	0.293012	+	1.67595i
$214$	22.2096	−	0.184488i	1.51822	−	0.0126113i
$215$	−0.935038	+	1.61953i	−0.0637691	+	0.110451i
$216$	−12.5741	+	7.60875i	−0.855556	+	0.517710i
$217$	−9.70158	−	5.19604i	−0.658586	−	0.352730i
$218$	21.5390	+	12.1981i	1.45880	+	0.826161i
$219$	−4.23534	+	3.54343i	−0.286198	+	0.239443i
$220$	1.02129	+	0.567230i	0.0688550	+	0.0382426i
$221$	5.52887	+	9.57629i	0.371912	+	0.644171i
$222$	3.80937	+	20.7700i	0.255668	+	1.39399i
$223$			2.77897i			0.186093i	0.995662	+	0.0930467i	$0.0296606\pi$
$223$			2.77897i			0.186093i	−0.995662	+	0.0930467i	$0.970339\pi$
$224$	−14.9263	+	1.09788i	−0.997306	+	0.0733549i
$225$	−11.1137	−	9.38052i	−0.740915	−	0.625368i
$226$	−0.0885043	+	0.0520830i	−0.00588722	+	0.00346451i
$227$	14.0438	−	8.10819i	0.932119	−	0.538159i	0.0446379	−	0.999003i	$-0.485787\pi$
$227$	14.0438	−	8.10819i	0.932119	−	0.538159i	0.887481	+	0.460844i	$0.152453\pi$
$228$	11.6145	+	13.4229i	0.769190	+	0.888953i
$229$	10.3150	−	17.8661i	0.681633	−	1.18062i	−0.292849	−	0.956159i	$-0.594603\pi$
$229$	10.3150	−	17.8661i	0.681633	−	1.18062i	0.974482	−	0.224464i	$-0.0720633\pi$
$230$	−1.48430	+	2.62091i	−0.0978716	+	0.172818i
$231$	2.14925	−	6.51554i	0.141410	−	0.428691i
$232$	11.7004	−	0.291628i	0.768171	−	0.0191463i
$233$	1.80462	+	1.04190i	0.118225	+	0.0682572i	0.557946	−	0.829877i	$-0.311589\pi$
$233$	1.80462	+	1.04190i	0.118225	+	0.0682572i	−0.439721	+	0.898134i	$0.644923\pi$
$234$	−10.7335	−	8.90796i	−0.701669	−	0.582331i
$235$	−1.69661	+	0.979538i	−0.110675	+	0.0638980i
$236$	−0.0521881	−	3.14113i	−0.00339716	−	0.204470i
$237$	0.284784	−	0.778925i	0.0184987	−	0.0505966i
$238$	12.5745	−	0.505704i	0.815083	−	0.0327799i
$239$			0.851762i			0.0550959i	0.999620	+	0.0275480i	$0.00876990\pi$
$239$			0.851762i			0.0550959i	−0.999620	+	0.0275480i	$0.991230\pi$
$240$	−0.553716	−	2.64571i	−0.0357422	−	0.170780i
$241$	13.0417	−	7.52961i	0.840087	−	0.485025i	−0.0172066	−	0.999852i	$-0.505477\pi$
$241$	13.0417	−	7.52961i	0.840087	−	0.485025i	0.857294	+	0.514827i	$0.172144\pi$
$242$	−12.3860	+	0.102886i	−0.796200	+	0.00661375i
$243$	−10.1063	+	11.8686i	−0.648319	+	0.761369i
$244$	7.01301	+	11.6939i	0.448962	+	0.748622i
$245$	2.27332	−	1.51349i	0.145237	−	0.0966932i
$246$	−17.7158	−	20.8211i	−1.12952	−	1.32751i
$247$	−8.42312	+	14.5893i	−0.535950	+	0.928293i
$248$	−10.0393	+	6.13470i	−0.637496	+	0.389554i
$249$	5.20670	+	29.7809i	0.329961	+	1.88729i
$250$	4.68287	−	2.75577i	0.296171	−	0.174290i
$251$			11.8022i			0.744948i	0.928043	+	0.372474i	$0.121490\pi$
$251$			11.8022i			0.744948i	−0.928043	+	0.372474i	$0.878510\pi$
$252$	−14.6541	+	6.10381i	−0.923123	+	0.384504i
$253$			8.17302i			0.513834i
$254$	6.32316	+	10.7449i	0.396750	+	0.674196i
$255$	0.391432	+	2.23888i	0.0245124	+	0.140204i
$256$	−7.06224	+	14.3570i	−0.441390	+	0.897315i
$257$	8.86901	−	15.3616i	0.553233	−	0.958228i	−0.444805	−	0.895627i	$-0.646727\pi$
$257$	8.86901	−	15.3616i	0.553233	−	0.958228i	0.998039	−	0.0626011i	$-0.0199396\pi$
$258$	8.94213	−	7.60845i	0.556713	−	0.473681i
$259$	0.727204	+	22.7968i	0.0451863	+	1.41653i
$260$	2.20006	−	1.31942i	0.136442	−	0.0818267i
$261$	11.6776	−	4.21204i	0.722827	−	0.260719i
$262$	0.0591649	+	7.12259i	0.00365522	+	0.440035i
$263$	−6.27815	+	3.62469i	−0.387128	+	0.223508i	−0.680915	−	0.732363i	$-0.738418\pi$
$263$	−6.27815	+	3.62469i	−0.387128	+	0.223508i	0.293787	+	0.955871i	$0.405084\pi$
$264$	−4.84514	−	5.50642i	−0.298198	−	0.338897i
$265$		−	0.389559i		−	0.0239304i
$266$	10.2457	+	16.2052i	0.628204	+	0.993605i
$267$	3.03134	−	8.29114i	0.185515	−	0.507410i
$268$	0.117190	+	7.05348i	0.00715850	+	0.430860i
$269$	2.95817	−	1.70790i	0.180363	−	0.104132i	−0.407100	−	0.913383i	$-0.633460\pi$
$269$	2.95817	−	1.70790i	0.180363	−	0.104132i	0.587463	+	0.809251i	$0.300127\pi$
$270$	−1.44332	−	2.47720i	−0.0878379	−	0.150758i
$271$	3.96989	+	2.29201i	0.241153	+	0.139230i	0.615707	−	0.787975i	$-0.288871\pi$
$271$	3.96989	+	2.29201i	0.241153	+	0.139230i	−0.374553	+	0.927205i	$0.622204\pi$
$272$	6.33602	−	11.8682i	0.384177	−	0.719612i
$273$	−10.0310	−	11.2412i	−0.607106	−	0.680346i
$274$	−9.01998	−	5.10826i	−0.544917	−	0.308601i
$275$	3.62896	−	6.28555i	0.218835	−	0.379033i
$276$	14.3003	−	12.3737i	0.860779	−	0.744811i
$277$	−10.6940	+	6.17421i	−0.642543	+	0.370972i	−0.785593	−	0.618743i	$-0.787642\pi$
$277$	−10.6940	+	6.17421i	−0.642543	+	0.370972i	0.143050	+	0.989715i	$0.454309\pi$
$278$	−11.2965	−	19.1962i	−0.677521	−	1.15131i
$279$	−8.04900	+	9.53617i	−0.481881	+	0.570916i
$280$	−0.165768	−	2.91490i	−0.00990653	−	0.174199i
$281$			7.91565i			0.472208i	0.971728	+	0.236104i	$0.0758706\pi$
$281$			7.91565i			0.472208i	−0.971728	+	0.236104i	$0.924129\pi$
$282$	12.0979	−	2.21884i	0.720422	−	0.132130i
$283$	−11.3552	−	19.6678i	−0.674999	−	1.16913i	−0.976469	−	0.215656i	$-0.930811\pi$
$283$	−11.3552	−	19.6678i	−0.674999	−	1.16913i	0.301471	−	0.953475i	$-0.402522\pi$
$284$	25.0654	+	13.9215i	1.48736	+	0.826090i
$285$	−2.65574	+	2.22189i	−0.157313	+	0.131613i
$286$	3.43032	−	6.05714i	0.202839	−	0.358166i
$287$	−15.5720	−	25.0887i	−0.919189	−	1.48094i
$288$	−2.29917	+	16.8141i	−0.135480	+	0.990780i
$289$	2.84381	−	4.92562i	0.167283	−	0.289742i
$290$	0.0189648	+	2.28309i	0.00111365	+	0.134068i
$291$	−2.68489	−	15.3568i	−0.157391	−	0.900232i
$292$	0.105926	+	6.37554i	0.00619885	+	0.373100i
$293$		−	12.8246i		−	0.749220i	−0.927183	−	0.374610i	$-0.877777\pi$
$293$		−	12.8246i		−	0.749220i	0.927183	−	0.374610i	$-0.122223\pi$
$294$	−16.6337	+	4.16177i	−0.970097	+	0.242719i
$295$	0.612840			0.0356809
$296$	21.4137	+	11.6617i	1.24465	+	0.677821i
$297$	−6.72027	−	3.91899i	−0.389950	−	0.227403i
$298$	25.4258	−	0.211203i	1.47288	−	0.0122347i
$299$	15.5430	+	8.97373i	0.898872	+	0.518964i
$300$	−16.4920	+	3.16655i	−0.952164	+	0.182821i
$301$	10.7749	−	6.68778i	0.621056	−	0.385477i
$302$	−10.9993	+	19.4222i	−0.632939	+	1.11762i
$303$	−7.11610	+	5.95357i	−0.408809	+	0.342024i
$304$	20.4849	−	0.680878i	1.17489	−	0.0390511i
$305$	−2.30359	+	1.32998i	−0.131903	+	0.0761542i
$306$	2.40185	−	14.0661i	0.137304	−	0.804103i
$307$	−12.3622			−0.705549			−0.352774	−	0.935708i	$-0.614762\pi$
$307$	−12.3622			−0.705549			−0.352774	+	0.935708i	$0.614762\pi$
$308$	−4.28910	−	6.66075i	−0.244394	−	0.379532i
$309$	−14.4792	−	5.29377i	−0.823694	−	0.301152i
$310$	−1.16403	−	1.97802i	−0.0661123	−	0.112344i
$311$	−0.720819	−	1.24850i	−0.0408739	−	0.0707957i	0.844865	−	0.534980i	$-0.179681\pi$
$311$	−0.720819	−	1.24850i	−0.0408739	−	0.0707957i	−0.885739	+	0.464184i	$0.846348\pi$
$312$	−15.7916	+	3.16830i	−0.894022	+	0.179370i
$313$	−20.8822	−	12.0564i	−1.18033	−	0.681466i	−0.224242	−	0.974533i	$-0.571991\pi$
$313$	−20.8822	−	12.0564i	−1.18033	−	0.681466i	−0.956092	+	0.293067i	$0.905324\pi$
$314$	−3.53017	+	6.23345i	−0.199219	+	0.351774i
$315$	−1.14305	−	2.87804i	−0.0644033	−	0.162159i
$316$	−0.492538	−	0.821284i	−0.0277074	−	0.0462008i
$317$	13.4686	−	23.3283i	0.756472	−	1.31025i	−0.188167	−	0.982137i	$-0.560255\pi$
$317$	13.4686	−	23.3283i	0.756472	−	1.31025i	0.944639	−	0.328111i	$-0.106412\pi$
$318$	−0.820726	+	2.30397i	−0.0460240	+	0.129200i
$319$	3.09764	+	5.36527i	0.173435	+	0.300398i
$320$	−2.77742	−	1.42400i	−0.155263	−	0.0796040i
$321$	9.34067	−	25.5481i	0.521345	−	1.42595i
$322$	17.2645	−	10.9154i	0.962114	−	0.608294i
$323$	−17.2342			−0.958935
$324$	3.31726	+	17.6917i	0.184292	+	0.982872i
$325$	−7.96898	−	13.8027i	−0.442039	−	0.765635i
$326$	0.147504	+	17.7574i	0.00816952	+	0.983491i
$327$	23.2519	−	19.4533i	1.28583	−	1.07577i
$328$	−31.5574	+	0.786555i	−1.74247	+	0.0434302i
$329$	13.2785	−	0.423575i	0.732066	−	0.0233524i
$330$	1.08972	−	0.927189i	0.0599869	−	0.0510401i
$331$	−15.2782	−	8.82087i	−0.839766	−	0.484839i	0.0174189	−	0.999848i	$-0.494455\pi$
$331$	−15.2782	−	8.82087i	−0.839766	−	0.484839i	−0.857185	+	0.515009i	$0.827788\pi$
$332$	30.5184	+	16.9502i	1.67492	+	0.930262i
$333$	25.4563	+	4.56471i	1.39500	+	0.250145i
$334$	−5.33025	−	9.05766i	−0.291658	−	0.495613i
$335$	−1.37615			−0.0751868
$336$	−5.16074	+	17.5888i	−0.281541	+	0.959549i
$337$	11.0396			0.601365			0.300682	−	0.953724i	$-0.402786\pi$
$337$	11.0396			0.601365			0.300682	+	0.953724i	$0.402786\pi$
$338$	1.57162	+	2.67065i	0.0854850	+	0.145264i
$339$	0.0216605	+	0.123892i	0.00117644	+	0.00672890i
$340$	2.29432	+	1.27429i	0.124427	+	0.0691079i
$341$	−5.39334	−	3.11385i	−0.292066	−	0.168624i
$342$	20.3879	−	7.54574i	1.10245	−	0.408027i
$343$	−18.4356	+	1.76905i	−0.995428	+	0.0955198i
$344$	−0.337805	−	13.5531i	−0.0182132	−	0.730734i
$345$	2.36713	+	2.82935i	0.127442	+	0.152327i
$346$	0.206781	+	24.8934i	0.0111166	+	1.33828i
$347$	10.8299	+	18.7579i	0.581377	+	1.00697i	0.995316	+	0.0966701i	$0.0308192\pi$
$347$	10.8299	+	18.7579i	0.581377	+	1.00697i	−0.413940	+	0.910304i	$0.635848\pi$
$348$	4.69787	−	13.5428i	0.251832	−	0.725971i
$349$	6.46130			0.345865			0.172933	−	0.984934i	$-0.444676\pi$
$349$	6.46130			0.345865			0.172933	+	0.984934i	$0.444676\pi$
$350$	−18.1241	+	0.728891i	−0.968774	+	0.0389609i
$351$	−14.8315	+	8.47727i	−0.791649	+	0.452483i
$352$	−8.46193	+	0.351646i	−0.451023	+	0.0187428i
$353$	−14.9846	−	25.9541i	−0.797549	−	1.38140i	−0.921208	−	0.389071i	$-0.872796\pi$
$353$	−14.9846	−	25.9541i	−0.797549	−	1.38140i	0.123659	−	0.992325i	$-0.460537\pi$
$354$	−3.62451	−	1.29114i	−0.192641	−	0.0686231i
$355$	−2.79659	+	4.84383i	−0.148428	+	0.257084i
$356$	−5.24275	−	8.74203i	−0.277865	−	0.463327i
$357$	4.82830	−	14.6372i	0.255541	−	0.774683i
$358$	−11.3148	+	19.9792i	−0.598005	+	1.05594i
$359$	−9.44412	−	5.45257i	−0.498442	−	0.287775i	0.229628	−	0.973278i	$-0.426249\pi$
$359$	−9.44412	−	5.45257i	−0.498442	−	0.287775i	−0.728070	+	0.685503i	$0.759582\pi$
$360$	−3.27210	−	0.502936i	−0.172455	−	0.0265071i
$361$	−3.62795	−	6.28380i	−0.190945	−	0.330726i
$362$	4.44225	+	7.54869i	0.233479	+	0.396750i
$363$	−5.20915	+	14.2478i	−0.273409	+	0.747814i
$364$	−17.3763	+	0.843438i	−0.910766	+	0.0442082i
$365$	−1.24388			−0.0651075
$366$	16.4261	−	3.01266i	0.858606	−	0.157474i
$367$	−2.43552	+	1.40615i	−0.127133	+	0.0734002i	−0.562218	−	0.826989i	$-0.690052\pi$
$367$	−2.43552	+	1.40615i	−0.127133	+	0.0734002i	0.435085	+	0.900389i	$0.356718\pi$
$368$	−0.725387	−	21.8240i	−0.0378134	−	1.13765i
$369$	−31.4959	+	11.3604i	−1.63961	+	0.591396i
$370$	−2.34398	+	4.13891i	−0.121858	+	0.215171i
$371$	−1.24726	+	2.32877i	−0.0647545	+	0.120904i
$372$	2.71708	+	14.1510i	0.140874	+	0.733695i
$373$	26.9266	+	15.5461i	1.39421	+	0.804947i	0.993778	−	0.111380i	$-0.0355271\pi$
$373$	26.9266	+	15.5461i	1.39421	+	0.804947i	0.400431	+	0.916327i	$0.368860\pi$
$374$	7.12109	−	0.0591524i	0.368223	−	0.00305870i
$375$	−1.14609	−	6.55529i	−0.0591836	−	0.338514i
$376$	6.79258	−	12.4729i	0.350301	−	0.643238i
$377$	13.6045			0.700665
$378$	0.696839	+	19.4297i	0.0358415	+	0.999357i
$379$			17.6950i			0.908931i	0.890764	+	0.454465i	$0.150170\pi$
$379$			17.6950i			0.908931i	−0.890764	+	0.454465i	$0.849830\pi$
$380$	0.0664203	+	3.99774i	0.00340729	+	0.205080i
$381$	15.0412	−	2.62971i	0.770585	−	0.134724i
$382$	−0.0988546	−	11.9007i	−0.00505784	−	0.608890i
$383$	−17.4953	+	30.3028i	−0.893968	+	1.54840i	−0.0588917	+	0.998264i	$0.518757\pi$
$383$	−17.4953	+	30.3028i	−0.893968	+	1.54840i	−0.835076	+	0.550134i	$0.814577\pi$
$384$	13.4264	+	14.2735i	0.685164	+	0.728389i
$385$	1.31306	−	0.814994i	0.0669200	−	0.0415359i
$386$	9.16202	−	16.1780i	0.466335	−	0.823436i
$387$	−4.87897	−	13.5267i	−0.248012	−	0.687600i
$388$	−15.7371	−	8.74052i	−0.798931	−	0.443733i
$389$	−10.4422	−	18.0864i	−0.529439	−	0.917015i	−0.999410	−	0.0343338i	$-0.989069\pi$
$389$	−10.4422	−	18.0864i	−0.529439	−	0.917015i	0.469971	−	0.882682i	$-0.344264\pi$
$390$	−0.566797	−	3.09038i	−0.0287009	−	0.156487i
$391$			18.3608i			0.928543i
$392$	−8.34175	+	17.9559i	−0.421322	+	0.906911i
$393$	8.19322	+	2.99554i	0.413293	+	0.151105i
$394$	−12.6322	−	21.4659i	−0.636402	−	1.08144i
$395$	0.161786	−	0.0934070i	0.00814032	−	0.00469982i
$396$	−8.39831	+	3.18785i	−0.422031	+	0.160195i
$397$	2.44443	−	4.23387i	0.122682	−	0.212492i	−0.798142	−	0.602469i	$-0.794184\pi$
$397$	2.44443	−	4.23387i	0.122682	−	0.212492i	0.920825	+	0.389977i	$0.127517\pi$
$398$	−24.5381	−	13.8966i	−1.22998	−	0.696574i
$399$	22.9898	−	4.77941i	1.15093	−	0.239270i
$400$	−9.13235	+	17.1060i	−0.456617	+	0.855301i
$401$	−6.62355	−	3.82411i	−0.330764	−	0.190967i	0.325416	−	0.945571i	$-0.394496\pi$
$401$	−6.62355	−	3.82411i	−0.330764	−	0.190967i	−0.656180	+	0.754604i	$0.727829\pi$
$402$	8.13893	+	2.89927i	0.405933	+	0.144603i
$403$	−11.8434	+	6.83782i	−0.589964	+	0.340616i
$404$	0.177974	+	10.7120i	0.00885453	+	0.532942i
$405$	−3.46148	+	0.589691i	−0.172002	+	0.0293020i
$406$	7.19644	−	13.7090i	0.357153	−	0.680364i
$407$			12.9067i			0.639762i
$408$	−10.8846	−	12.3702i	−0.538870	−	0.612416i
$409$	−6.66584	+	3.84852i	−0.329604	+	0.190297i	−0.655666	−	0.755051i	$-0.727612\pi$
$409$	−6.66584	+	3.84852i	−0.329604	+	0.190297i	0.326061	+	0.945349i	$0.394279\pi$
$410$	−0.0511504	−	6.15776i	−0.00252614	−	0.304110i
$411$	−9.73731	+	8.14656i	−0.480306	+	0.401840i
$412$	−15.2666	+	9.15566i	−0.752133	+	0.451067i
$413$	−3.66354	−	1.96214i	−0.180271	−	0.0965507i
$414$	−8.03900	−	21.7207i	−0.395095	−	1.06751i
$415$	−3.40499	+	5.89762i	−0.167145	+	0.289503i
$416$	−8.62221	+	16.4785i	−0.422738	+	0.807924i
$417$	−26.8716	+	4.69807i	−1.31591	+	0.230065i
$418$	5.50246	+	9.35030i	0.269134	+	0.457338i
$419$		−	4.38235i		−	0.214092i	−0.994254	−	0.107046i	$-0.965861\pi$
$419$		−	4.38235i		−	0.214092i	0.994254	−	0.107046i	$-0.0341392\pi$
$420$	−3.41394	−	1.06359i	−0.166583	−	0.0518978i
$421$			11.9400i			0.581921i	0.956735	+	0.290961i	$0.0939749\pi$
$421$			11.9400i			0.581921i	−0.956735	+	0.290961i	$0.906025\pi$
$422$	−17.6924	+	10.4116i	−0.861251	+	0.506829i
$423$	2.65881	−	14.8275i	0.129276	−	0.720940i
$424$	1.47258	+	2.40984i	0.0715146	+	0.117032i
$425$	8.15249	−	14.1205i	0.395454	−	0.684946i
$426$	26.7449	−	22.7560i	1.29579	−	1.10253i
$427$	18.0290	−	0.575113i	0.872484	−	0.0278317i
$428$	−16.1548	−	26.9374i	−0.780873	−	1.30207i
$429$	−5.47061	−	6.53884i	−0.264124	−	0.315698i
$430$	2.64460	−	0.0219677i	0.127534	−	0.00105938i
$431$	0.588922	−	0.340014i	0.0283674	−	0.0163779i	−0.485749	−	0.874098i	$-0.661453\pi$
$431$	0.588922	−	0.340014i	0.0283674	−	0.0163779i	0.514117	+	0.857720i	$0.328120\pi$
$432$	18.2926	+	9.86820i	0.880102	+	0.474784i
$433$			0.238499i			0.0114615i	0.999984	+	0.00573077i	$0.00182417\pi$
$433$			0.238499i			0.0114615i	−0.999984	+	0.00573077i	$0.998176\pi$
$434$	0.625428	+	15.5515i	0.0300215	+	0.746494i
$435$	2.62627	+	0.960196i	0.125920	+	0.0460379i
$436$	−0.581531	−	35.0015i	−0.0278503	−	1.67627i
$437$	−24.2247	+	13.9861i	−1.15882	+	0.669046i
$438$	7.35666	+	2.62061i	0.351515	+	0.125218i
$439$	3.29894	+	1.90465i	0.157450	+	0.0909038i	0.576655	−	0.816988i	$-0.304358\pi$
$439$	3.29894	+	1.90465i	0.157450	+	0.0909038i	−0.419205	+	0.907892i	$0.637691\pi$
$440$	−0.0411659	−	1.65162i	−0.00196251	−	0.0787380i
$441$	−2.38158	+	20.8645i	−0.113409	+	0.993548i
$442$	7.70624	−	13.6074i	0.366549	−	0.647238i
$443$	−3.02001	+	5.23080i	−0.143485	+	0.248523i	−0.928807	−	0.370565i	$-0.879164\pi$
$443$	−3.02001	+	5.23080i	−0.143485	+	0.248523i	0.785322	+	0.619088i	$0.212497\pi$
$444$	22.5828	−	19.5404i	1.07173	−	0.927346i
$445$	1.72210	−	0.994257i	0.0816355	−	0.0471323i
$446$	3.38709	−	1.99323i	0.160383	−	0.0943822i
$447$	10.6933	−	29.2477i	0.505776	−	1.38337i
$448$	12.0441	+	17.4052i	0.569030	+	0.822317i
$449$			28.1482i			1.32839i	0.747558	+	0.664197i	$0.231226\pi$
$449$			28.1482i			1.32839i	−0.747558	+	0.664197i	$0.768774\pi$
$450$	−3.46188	+	20.2740i	−0.163194	+	0.955724i
$451$	−8.35470	−	14.4708i	−0.393408	−	0.681402i
$452$	0.126960	+	0.0705149i	0.00597172	+	0.00331674i
$453$	17.5415	+	20.9667i	0.824171	+	0.985103i
$454$	−19.9555	−	11.3013i	−0.936557	−	0.530398i
$455$	−0.108201	−	3.39194i	−0.00507254	−	0.159017i
$456$	8.02964	−	23.7837i	0.376022	−	1.11378i
$457$	−6.23304	+	10.7959i	−0.291569	+	0.505013i	−0.974181	−	0.225768i	$-0.927511\pi$
$457$	−6.23304	+	10.7959i	−0.291569	+	0.505013i	0.682612	+	0.730781i	$0.260844\pi$
$458$	−29.1742	+	0.242340i	−1.36322	+	0.0113238i
$459$	−15.0971	−	8.80403i	−0.704674	−	0.410937i
$460$	4.25907	−	0.0707621i	0.198580	−	0.00329930i
$461$			31.6209i			1.47273i	0.676583	+	0.736367i	$0.263460\pi$
$461$			31.6209i			1.47273i	−0.676583	+	0.736367i	$0.736540\pi$
$462$	−9.48289	+	2.05374i	−0.441184	+	0.0955486i
$463$	23.5095			1.09258			0.546290	−	0.837596i	$-0.316040\pi$
$463$	23.5095			1.09258			0.546290	+	0.837596i	$0.316040\pi$
$464$	−8.74765	−	14.0517i	−0.406099	−	0.652332i
$465$	−2.76893	+	0.484102i	−0.128406	+	0.0224497i
$466$	−0.0244784	−	2.94684i	−0.00113394	−	0.136510i
$467$	12.7642	+	7.36942i	0.590657	+	0.341016i	0.765357	−	0.643606i	$-0.222562\pi$
$467$	12.7642	+	7.36942i	0.590657	+	0.341016i	−0.174700	+	0.984622i	$0.555896\pi$
$468$	−3.15864	+	19.4715i	−0.146008	+	0.900073i
$469$	8.22655	+	4.40603i	0.379867	+	0.203452i
$470$	2.41079	+	1.36530i	0.111201	+	0.0629765i
$471$	5.62985	+	6.72917i	0.259410	+	0.310064i
$472$	−3.79107	+	2.31660i	−0.174498	+	0.106630i
$473$	6.21481	−	3.58812i	0.285757	−	0.164982i
$474$	−1.15364	+	0.211585i	−0.0529884	+	0.00971843i
$475$	24.8403			1.13975
$476$	−9.63548	−	14.9634i	−0.441642	−	0.685848i
$477$	2.28907	+	1.93208i	0.104809	+	0.0884641i
$478$	1.03815	−	0.610931i	0.0474840	−	0.0279433i
$479$	17.3034	+	29.9703i	0.790611	+	1.36938i	0.925589	+	0.378529i	$0.123570\pi$
$479$	17.3034	+	29.9703i	0.790611	+	1.36938i	−0.134979	+	0.990848i	$0.543097\pi$
$480$	−2.82752	+	2.57254i	−0.129058	+	0.117420i
$481$	24.5452	+	14.1712i	1.11916	+	0.646150i
$482$	−18.5315	−	10.4949i	−0.844087	−	0.478030i
$483$	−5.09183	−	24.4926i	−0.231686	−	1.11445i
$484$	9.00930	+	15.0226i	0.409514	+	0.682844i
$485$	1.75582	−	3.04117i	0.0797276	−	0.138092i
$486$	21.7145	+	3.80506i	0.984992	+	0.172601i
$487$	−12.0284	−	20.8338i	−0.545058	−	0.944068i	−0.998603	−	0.0528351i	$-0.983174\pi$
$487$	−12.0284	−	20.8338i	−0.545058	−	0.944068i	0.453545	−	0.891233i	$-0.350159\pi$
$488$	9.22269	−	16.9351i	0.417492	−	0.766618i
$489$	20.4266	+	7.46820i	0.923723	+	0.337724i
$490$	−3.47523	−	1.68523i	−0.156995	−	0.0761308i
$491$	−15.3708			−0.693675			−0.346837	−	0.937925i	$-0.612744\pi$
$491$	−15.3708			−0.693675			−0.346837	+	0.937925i	$0.612744\pi$
$492$	−12.6707	+	36.5266i	−0.571239	+	1.64674i
$493$	6.95887	+	12.0531i	0.313412	+	0.542845i
$494$	23.8234	−	0.197892i	1.07186	−	0.00890360i
$495$	−0.594567	−	1.64840i	−0.0267238	−	0.0740902i
$496$	14.6779	+	7.83605i	0.659057	+	0.351849i
$497$	32.2265	−	20.0024i	1.44556	−	0.897229i
$498$	32.5633	−	27.7066i	1.45920	−	1.24156i
$499$	22.8684	+	13.2031i	1.02373	+	0.591051i	0.915182	−	0.403040i	$-0.132047\pi$
$499$	22.8684	+	13.2031i	1.02373	+	0.591051i	0.108548	+	0.994091i	$0.465380\pi$
$500$	−6.71763	−	3.73103i	−0.300422	−	0.166857i
$501$	−12.6793	+	2.21677i	−0.566470	+	0.0990381i
$502$	14.3849	−	8.46519i	0.642028	−	0.377820i
$503$	28.3616			1.26458			0.632291	−	0.774731i	$-0.282115\pi$
$503$	28.3616			1.26458			0.632291	+	0.774731i	$0.282115\pi$
$504$	17.9503	+	13.4829i	0.799568	+	0.600576i
$505$	−2.08993			−0.0930006
$506$	9.96152	−	5.86215i	0.442844	−	0.260604i
$507$	3.73850	−	0.653615i	0.166032	−	0.0290281i
$508$	8.56090	−	15.4137i	0.379828	−	0.683873i
$509$	−18.3731	−	10.6077i	−0.814373	−	0.470179i	0.0340991	−	0.999418i	$-0.489144\pi$
$509$	−18.3731	−	10.6077i	−0.814373	−	0.470179i	−0.848472	+	0.529240i	$0.822477\pi$
$510$	2.44805	−	2.08294i	0.108402	−	0.0922340i
$511$	7.43586	+	3.98255i	0.328943	+	0.176178i
$512$	22.5642	−	1.69001i	0.997207	−	0.0746885i
$513$	0.115709	−	26.6251i	0.00510866	−	1.17553i
$514$	−25.0845	+	0.208368i	−1.10643	+	0.00919072i
$515$	−1.73632	−	3.00739i	−0.0765113	−	0.132522i
$516$	−15.6872	−	5.44173i	−0.690590	−	0.239559i
$517$	7.51778			0.330631
$518$	27.2638	−	17.2375i	1.19790	−	0.757371i
$519$	28.6352	+	10.4694i	1.25695	+	0.459554i
$520$	−3.18615	−	1.73514i	−0.139722	−	0.0760910i
$521$	5.91179	+	10.2395i	0.259000	+	0.448601i	0.965974	−	0.258638i	$-0.0832737\pi$
$521$	5.91179	+	10.2395i	0.259000	+	0.448601i	−0.706974	+	0.707239i	$0.749940\pi$
$522$	−13.5096	−	11.2119i	−0.591299	−	0.490733i
$523$	3.37960	−	5.85364i	0.147780	−	0.255962i	−0.782627	−	0.622491i	$-0.786121\pi$
$523$	3.37960	−	5.85364i	0.147780	−	0.255962i	0.930407	+	0.366529i	$0.119454\pi$
$524$	8.63878	−	5.18083i	0.377387	−	0.226326i
$525$	−6.95922	+	21.0972i	−0.303725	+	0.920756i
$526$	8.92092	+	5.05217i	0.388971	+	0.220285i
$527$	−12.1162	−	6.99528i	−0.527789	−	0.304719i
$528$	−3.23618	+	9.85490i	−0.140837	+	0.428880i
$529$	3.40036	+	5.88960i	0.147842	+	0.256070i
$530$	−0.474806	+	0.279413i	−0.0206242	+	0.0121369i
$531$	−3.03948	+	3.60108i	−0.131902	+	0.156273i
$532$	12.4026	−	24.1110i	0.537720	−	1.04535i
$533$	−36.6928			−1.58934
$534$	−12.2797	+	2.25219i	−0.531396	+	0.0974616i
$535$	5.30643	−	3.06367i	0.229417	−	0.132454i
$536$	8.51293	−	5.20198i	0.367702	−	0.224691i
$537$	18.0446	+	21.5681i	0.778683	+	0.930733i
$538$	−4.20340	−	2.38050i	−0.181221	−	0.102631i
$539$	−10.4588	+	0.667940i	−0.450494	+	0.0287702i
$540$	−1.98405	+	3.53595i	−0.0853799	+	0.152163i
$541$	−15.3128	−	8.84087i	−0.658351	−	0.380099i	0.133298	−	0.991076i	$-0.457443\pi$
$541$	−15.3128	−	8.84087i	−0.658351	−	0.380099i	−0.791648	+	0.610977i	$0.790777\pi$
$542$	−0.0538485	−	6.48257i	−0.00231299	−	0.278450i
$543$	10.5670	−	1.84747i	0.453473	−	0.0792824i
$544$	−19.0098	+	0.789975i	−0.815038	+	0.0338699i
$545$	6.82885			0.292516
$546$	−6.50624	+	20.2889i	−0.278442	+	0.868285i
$547$			1.49834i			0.0640644i	0.999487	+	0.0320322i	$0.0101979\pi$
$547$			1.49834i			0.0640644i	−0.999487	+	0.0320322i	$0.989802\pi$
$548$	0.243530	+	14.6577i	0.0104031	+	0.626148i
$549$	3.61003	−	20.1322i	0.154072	−	0.859223i
$550$	−10.2639	+	0.0852587i	−0.437654	+	0.00363544i
$551$	−10.6017	+	18.3627i	−0.451647	+	0.782276i
$552$	−25.3385	−	8.55453i	−1.07848	−	0.364105i
$553$	−1.26621	+	0.0403914i	−0.0538448	+	0.00171762i
$554$	15.1957	+	8.60573i	0.645602	+	0.365622i
$555$	3.73813	+	4.46806i	0.158675	+	0.189658i
$556$	−15.2943	+	27.5371i	−0.648624	+	1.16783i
$557$	1.46808	+	2.54278i	0.0622044	+	0.107741i	0.895450	−	0.445161i	$-0.146854\pi$
$557$	1.46808	+	2.54278i	0.0622044	+	0.107741i	−0.833246	+	0.552902i	$0.813520\pi$
$558$	17.3962	+	2.97048i	0.736438	+	0.125750i
$559$		−	15.7586i		−	0.666518i
$560$	−3.43387	+	2.29277i	−0.145107	+	0.0968873i
$561$	2.99491	−	8.19150i	0.126445	−	0.345845i
$562$	9.64783	−	5.67755i	0.406969	−	0.239493i
$563$	−14.3950	+	8.31096i	−0.606677	+	0.350265i	−0.771664	−	0.636031i	$-0.780575\pi$
$563$	−14.3950	+	8.31096i	−0.606677	+	0.350265i	0.164987	+	0.986296i	$0.447242\pi$
$564$	−11.3817	−	13.1538i	−0.479256	−	0.553877i
$565$	−0.0141652	+	0.0245348i	−0.000595934	+	0.00103219i
$566$	−15.8271	+	27.9470i	−0.665264	+	1.17470i
$567$	22.5806	+	7.55752i	0.948296	+	0.317386i
$568$	−1.01033	−	40.5357i	−0.0423927	−	1.70084i
$569$	−19.2204	−	11.0969i	−0.805763	−	0.465207i	0.0397194	−	0.999211i	$-0.487354\pi$
$569$	−19.2204	−	11.0969i	−0.805763	−	0.465207i	−0.845482	+	0.534003i	$0.820687\pi$
$570$	4.61295	+	1.64324i	0.193215	+	0.0688277i
$571$	5.22532	−	3.01684i	0.218673	−	0.126251i	−0.386663	−	0.922221i	$-0.626372\pi$
$571$	5.22532	−	3.01684i	0.218673	−	0.126251i	0.605336	+	0.795970i	$0.293039\pi$
$572$	−9.84303	+	0.163537i	−0.411558	+	0.00683781i
$573$	−13.6895	−	5.00504i	−0.571887	−	0.209089i
$574$	−19.4096	+	36.9746i	−0.810143	+	1.54329i
$575$		−	26.4641i		−	1.10363i
$576$	22.1426	−	9.25771i	0.922608	−	0.385738i
$577$	−17.4549	+	10.0776i	−0.726659	+	0.419537i	−0.817199	−	0.576356i	$-0.804474\pi$
$577$	−17.4549	+	10.0776i	−0.726659	+	0.419537i	0.0905396	+	0.995893i	$0.471141\pi$
$578$	−8.04323	+	0.0668123i	−0.334554	+	0.00277902i
$579$	−14.6114	−	17.4645i	−0.607230	−	0.725801i
$580$	2.76909	−	1.66067i	0.114980	−	0.0689557i
$581$	39.2375	−	24.3539i	1.62784	−	1.01037i
$582$	−16.7916	+	14.2872i	−0.696033	+	0.592222i
$583$	−0.747449	+	1.29462i	−0.0309562	+	0.0536177i
$584$	7.69472	−	4.70200i	0.318410	−	0.194570i
$585$	−3.78765	−	0.679185i	−0.156600	−	0.0280808i
$586$	−15.6310	+	9.19850i	−0.645709	+	0.379986i
$587$		−	0.369829i		−	0.0152645i	−0.999971	−	0.00763224i	$-0.997571\pi$
$587$		−	0.369829i		−	0.0152645i	0.999971	−	0.00763224i	$-0.00242944\pi$
$588$	17.0031	+	17.2886i	0.701196	+	0.712969i
$589$		−	21.3143i		−	0.878241i
$590$	−0.439563	−	0.746947i	−0.0180965	−	0.0307513i
$591$	−30.0489	+	5.25356i	−1.23605	+	0.216103i
$592$	−1.14552	−	34.4640i	−0.0470805	−	1.41646i
$593$	−4.89233	+	8.47376i	−0.200904	+	0.347976i	−0.948820	−	0.315818i	$-0.897721\pi$
$593$	−4.89233	+	8.47376i	−0.200904	+	0.347976i	0.747916	+	0.663793i	$0.231055\pi$
$594$	0.0435743	+	11.0018i	0.00178788	+	0.451408i
$595$	2.94981	−	1.83089i	0.120930	−	0.0750592i
$596$	−18.4942	−	30.8382i	−0.757553	−	1.26318i
$597$	−26.4895	+	22.1620i	−1.08414	+	0.907032i
$598$	−0.210828	−	25.3807i	−0.00862141	−	1.03789i
$599$	−31.2524	+	18.0436i	−1.27694	+	0.737240i	−0.976284	−	0.216494i	$-0.930538\pi$
$599$	−31.2524	+	18.0436i	−1.27694	+	0.737240i	−0.300653	+	0.953734i	$0.597205\pi$
$600$	15.6884	+	17.8297i	0.640478	+	0.727893i
$601$		−	9.75944i		−	0.398096i	−0.979990	−	0.199048i	$-0.936215\pi$
$601$		−	9.75944i		−	0.398096i	0.979990	−	0.199048i	$-0.0637849\pi$
$602$	−15.8796	−	8.33593i	−0.647206	−	0.339747i
$603$	6.82523	−	8.08629i	0.277945	−	0.329299i
$604$	31.5616	−	0.524379i	1.28422	−	0.0213367i
$605$	−2.95932	+	1.70856i	−0.120313	+	0.0694629i
$606$	12.3605	+	4.40308i	0.502109	+	0.178863i
$607$	−7.33740	−	4.23625i	−0.297816	−	0.171944i	0.343645	−	0.939099i	$-0.388338\pi$
$607$	−7.33740	−	4.23625i	−0.297816	−	0.171944i	−0.641461	+	0.767155i	$0.721672\pi$
$608$	−15.5228	−	24.4792i	−0.629532	−	0.992764i
$609$	−12.6255	−	14.1486i	−0.511611	−	0.573331i
$610$	3.27328	+	1.85375i	0.132531	+	0.0750560i
$611$	8.25429	−	14.2968i	0.333933	−	0.578388i
$612$	−18.8669	+	7.16152i	−0.762648	+	0.289487i
$613$	−10.1968	+	5.88712i	−0.411844	+	0.237779i	−0.691582	−	0.722298i	$-0.743086\pi$
$613$	−10.1968	+	5.88712i	−0.411844	+	0.237779i	0.279737	+	0.960077i	$0.409753\pi$
$614$	8.86687	+	15.0674i	0.357838	+	0.608072i
$615$	−7.08336	−	2.58976i	−0.285629	−	0.104429i
$616$	−5.04194	+	10.0051i	−0.203146	+	0.403118i
$617$			17.5244i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$617$			17.5244i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$618$	3.93310	+	21.4447i	0.158212	+	0.862632i
$619$	12.8081	+	22.1843i	0.514801	+	0.891661i	0.999852	+	0.0171755i	$0.00546739\pi$
$619$	12.8081	+	22.1843i	0.514801	+	0.891661i	−0.485052	+	0.874485i	$0.661199\pi$
$620$	−1.57597	+	2.83750i	−0.0632925	+	0.113957i
$621$	−28.3655	−	0.123272i	−1.13827	−	0.00494674i
$622$	−1.00469	+	1.77405i	−0.0402844	+	0.0711328i
$623$	−13.4780	+	0.429940i	−0.539985	+	0.0172252i
$624$	15.1882	+	16.9748i	0.608015	+	0.679534i
$625$	−11.3700	+	19.6933i	−0.454798	+	0.787734i
$626$	0.283252	+	34.0994i	0.0113210	+	1.36289i
$627$	13.0890	−	2.28839i	0.522723	−	0.0913896i
$628$	10.1295	−	0.168297i	0.404213	−	0.00671577i
$629$			28.9950i			1.15611i
$630$	−2.68798	+	3.45747i	−0.107092	+	0.137749i
$631$	−7.24555			−0.288441			−0.144220	−	0.989546i	$-0.546067\pi$
$631$	−7.24555			−0.288441			−0.144220	+	0.989546i	$0.546067\pi$
$632$	−0.647729	+	1.18939i	−0.0257653	+	0.0473114i
$633$	4.33003	+	24.7666i	0.172103	+	0.984383i
$634$	−38.0937	+	0.316431i	−1.51289	+	0.0125671i
$635$	2.97867	+	1.71973i	0.118205	+	0.0682456i
$636$	3.39681	−	0.652208i	0.134692	−	0.0258617i
$637$	−10.2132	+	20.6234i	−0.404663	+	0.817127i
$638$	4.31755	−	7.62377i	0.170933	−	0.301828i
$639$	−14.5924	−	40.4567i	−0.577268	−	1.60044i
$640$	0.256511	+	4.40658i	0.0101395	+	0.174185i
$641$	11.9401	−	6.89362i	0.471606	−	0.272282i	−0.245306	−	0.969446i	$-0.578888\pi$
$641$	11.9401	−	6.89362i	0.471606	−	0.272282i	0.716912	+	0.697164i	$0.245555\pi$
$642$	−37.8384	+	6.93981i	−1.49336	+	0.273893i
$643$	20.7470			0.818184			0.409092	−	0.912493i	$-0.365846\pi$
$643$	20.7470			0.818184			0.409092	+	0.912493i	$0.365846\pi$
$644$	−25.6871	−	13.2133i	−1.01221	−	0.520678i
$645$	1.11223	−	3.04212i	0.0437942	−	0.119783i
$646$	12.3613	+	21.0055i	0.486349	+	0.826451i
$647$	−16.1242	−	27.9279i	−0.633907	−	1.09796i	−0.986746	−	0.162275i	$-0.948117\pi$
$647$	−16.1242	−	27.9279i	−0.633907	−	1.09796i	0.352838	−	0.935684i	$-0.385217\pi$
$648$	19.1838	−	16.7326i	0.753612	−	0.657320i
$649$	−2.03665	−	1.17586i	−0.0799454	−	0.0461565i
$650$	−11.1073	+	19.6129i	−0.435665	+	0.769280i
$651$	18.1025	+	5.97139i	0.709493	+	0.234037i
$652$	21.5374	−	12.9164i	0.843471	−	0.505844i
$653$	9.95455	−	17.2418i	0.389552	−	0.674723i	−0.602838	−	0.797864i	$-0.705963\pi$
$653$	9.95455	−	17.2418i	0.389552	−	0.674723i	0.992389	+	0.123141i	$0.0392966\pi$
$654$	−40.3878	−	14.3871i	−1.57929	−	0.562579i
$655$	0.982514	+	1.70176i	0.0383900	+	0.0664934i
$656$	23.5934	+	37.8990i	0.921168	+	1.47971i
$657$	6.16923	−	7.30909i	0.240684	−	0.285155i
$658$	−10.0403	−	15.8804i	−0.391413	−	0.619082i
$659$	11.4275			0.445153			0.222576	−	0.974915i	$-0.428553\pi$
$659$	11.4275			0.445153			0.222576	+	0.974915i	$0.428553\pi$
$660$	−1.91169	−	0.663146i	−0.0744124	−	0.0258129i
$661$	−2.31268	−	4.00568i	−0.0899529	−	0.155803i	0.817538	−	0.575875i	$-0.195338\pi$
$661$	−2.31268	−	4.00568i	−0.0899529	−	0.155803i	−0.907491	+	0.420071i	$0.862005\pi$
$662$	0.207237	+	24.9483i	0.00805450	+	0.969644i
$663$	−12.2898	−	14.6895i	−0.477295	−	0.570495i
$664$	−1.23013	−	49.3543i	−0.0477385	−	1.91532i
$665$	4.66261	+	2.49723i	0.180808	+	0.0968385i
$666$	−12.6951	−	34.3009i	−0.491923	−	1.32913i
$667$	19.5630	+	11.2947i	0.757483	+	0.437333i
$668$	−7.21660	+	12.9933i	−0.279218	+	0.502727i
$669$	−0.828955	−	4.74139i	−0.0320493	−	0.183313i
$670$	0.987048	+	1.67729i	0.0381330	+	0.0647992i
$671$	10.2073			0.394050
$672$	25.1393	−	6.32562i	0.969771	−	0.244016i
$673$	19.2606			0.742441			0.371220	−	0.928545i	$-0.378939\pi$
$673$	19.2606			0.742441			0.371220	+	0.928545i	$0.378939\pi$
$674$	−7.91821	−	13.4554i	−0.304998	−	0.518282i
$675$	21.7601	+	12.6896i	0.837546	+	0.488423i
$676$	2.12781	−	3.83108i	0.0818389	−	0.147349i
$677$	36.2236	+	20.9137i	1.39219	+	0.803780i	0.993557	−	0.113332i	$-0.0361524\pi$
$677$	36.2236	+	20.9137i	1.39219	+	0.803780i	0.398630	+	0.917112i	$0.369486\pi$
$678$	0.135467	−	0.115263i	0.00520259	−	0.00442665i
$679$	−20.2332	+	12.5583i	−0.776478	+	0.481945i
$680$	−0.0924795	−	3.71038i	−0.00354643	−	0.142287i
$681$	−21.5425	+	18.0232i	−0.825509	+	0.690649i
$682$	0.0731565	+	8.80698i	0.00280131	+	0.337237i
$683$	−6.73357	−	11.6629i	−0.257653	−	0.446268i	0.707960	−	0.706253i	$-0.249616\pi$
$683$	−6.73357	−	11.6629i	−0.257653	−	0.446268i	−0.965613	+	0.259985i	$0.916282\pi$
$684$	−23.8203	−	19.4372i	−0.910793	−	0.743199i
$685$	−2.85975			−0.109265
$686$	15.3792	+	21.2010i	0.587180	+	0.809456i
$687$	−12.2697	+	33.5595i	−0.468120	+	1.28037i
$688$	−16.2766	+	10.1328i	−0.620540	+	0.386308i
$689$	1.64135	+	2.84291i	0.0625305	+	0.108306i
$690$	1.75065	−	4.91449i	0.0666463	−	0.187091i
$691$	15.2232	−	26.3674i	0.579118	−	1.00306i	−0.416463	−	0.909153i	$-0.636730\pi$
$691$	15.2232	−	26.3674i	0.579118	−	1.00306i	0.995581	−	0.0939090i	$-0.0299363\pi$
$692$	30.1925	−	18.1069i	1.14774	−	0.688323i
$693$	−1.72342	+	11.7577i	−0.0654675	+	0.446639i
$694$	15.0948	−	26.6539i	0.572993	−	1.01177i
$695$	−5.32149	−	3.07236i	−0.201856	−	0.116541i
$696$	−19.8760	+	3.98776i	−0.753396	+	0.151156i
$697$	−18.7689	−	32.5087i	−0.710923	−	1.23135i
$698$	−4.63440	−	7.87522i	−0.175415	−	0.298081i
$699$	−3.38979	−	1.23935i	−0.128214	−	0.0468764i
$700$	13.8880	+	21.5674i	0.524917	+	0.815170i
$701$	37.2839			1.40819			0.704096	−	0.710105i	$-0.251353\pi$
$701$	37.2839			1.40819			0.704096	+	0.710105i	$0.251353\pi$
$702$	20.9703	+	11.9967i	0.791475	+	0.452788i
$703$	−38.2552	+	22.0866i	−1.44282	+	0.833013i
$704$	6.49797	+	10.0614i	0.244901	+	0.379204i
$705$	2.60251	−	2.17735i	0.0980163	−	0.0820038i
$706$	−20.8858	+	36.8793i	−0.786047	+	1.38797i
$707$	12.4935	+	6.69137i	0.469867	+	0.251655i
$708$	1.02603	+	5.34374i	0.0385605	+	0.200830i
$709$	−39.5076	−	22.8097i	−1.48374	−	0.856637i	−0.483910	−	0.875118i	$-0.660784\pi$
$709$	−39.5076	−	22.8097i	−1.48374	−	0.856637i	−0.999829	+	0.0184810i	$0.994117\pi$
$710$	7.90968	−	0.0657029i	0.296845	−	0.00246579i
$711$	−0.253540	+	1.41393i	−0.00950848	+	0.0530265i
$712$	−6.89465	+	12.6603i	−0.258388	+	0.474464i
$713$	−22.7076			−0.850406
$714$	−21.3034	+	4.61374i	−0.797259	+	0.172665i
$715$		−	1.92039i		−	0.0718186i
$716$	32.4669	−	0.539419i	1.21334	−	0.0201590i
$717$	−0.254077	−	1.45325i	−0.00948869	−	0.0542727i
$718$	0.128102	+	15.4217i	0.00478074	+	0.575531i
$719$	8.37315	−	14.5027i	0.312266	−	0.540860i	−0.666587	−	0.745428i	$-0.732245\pi$
$719$	8.37315	−	14.5027i	0.312266	−	0.540860i	0.978853	+	0.204567i	$0.0655787\pi$
$720$	1.73394	+	4.34887i	0.0646201	+	0.162073i
$721$	0.750825	+	23.5373i	0.0279622	+	0.876575i
$722$	−5.05671	+	8.92895i	−0.188191	+	0.332301i
$723$	−20.0053	+	16.7371i	−0.744003	+	0.622458i
$724$	6.01434	−	10.8287i	0.223521	−	0.402445i
$725$	−10.0301	−	17.3726i	−0.372508	−	0.645204i
$726$	21.1019	−	3.87023i	0.783164	−	0.143638i
$727$		−	14.7144i		−	0.545726i	−0.962053	−	0.272863i	$-0.912029\pi$
$727$		−	14.7144i		−	0.545726i	0.962053	−	0.272863i	$-0.0879705\pi$
$728$	13.4913	+	20.5738i	0.500019	+	0.762515i
$729$	13.7027	−	23.2645i	0.507508	−	0.861647i
$730$	0.892178	+	1.51607i	0.0330210	+	0.0561124i
$731$	13.9616	−	8.06075i	0.516389	−	0.298137i
$732$	−15.4536	−	17.8598i	−0.571182	−	0.660116i
$733$	−17.1186	+	29.6503i	−0.632290	+	1.09516i	0.354793	+	0.934945i	$0.384551\pi$
$733$	−17.1186	+	29.6503i	−0.632290	+	1.09516i	−0.987082	+	0.160213i	$0.948782\pi$
$734$	3.46074	+	1.95991i	0.127738	+	0.0723417i
$735$	−3.42720	+	3.26039i	−0.126414	+	0.120261i
$736$	−26.0794	+	16.5375i	−0.961299	+	0.609580i
$737$	4.57334	+	2.64042i	0.168461	+	0.0972610i
$738$	36.4370	+	30.2399i	1.34126	+	1.11315i
$739$	1.92964	−	1.11408i	0.0709829	−	0.0409820i	−0.464089	−	0.885789i	$-0.653618\pi$
$739$	1.92964	−	1.11408i	0.0709829	−	0.0409820i	0.535071	+	0.844807i	$0.320285\pi$
$740$	6.72585	−	0.111746i	0.247247	−	0.00410787i
$741$	10.0194	−	27.4044i	0.368070	−	1.00673i
$742$	3.73298	−	0.150128i	0.137042	−	0.00551137i
$743$		−	14.7964i		−	0.542829i	−0.962463	−	0.271414i	$-0.912509\pi$
$743$		−	14.7964i		−	0.542829i	0.962463	−	0.271414i	$-0.0874914\pi$
$744$	15.2988	−	13.4615i	0.560882	−	0.493524i
$745$	6.07486	−	3.50732i	0.222566	−	0.128498i
$746$	−0.365239	−	43.9695i	−0.0133724	−	1.60984i
$747$	−17.7671	−	49.2582i	−0.650063	−	1.80226i
$748$	−5.17974	−	8.63696i	−0.189390	−	0.315799i
$749$	−41.5307	+	1.32480i	−1.51750	+	0.0484073i
$750$	−7.16774	+	6.09870i	−0.261729	+	0.222693i
$751$	18.2439	−	31.5994i	0.665729	−	1.15308i	−0.313358	−	0.949635i	$-0.601454\pi$
$751$	18.2439	−	31.5994i	0.665729	−	1.15308i	0.979087	−	0.203442i	$-0.0652128\pi$
$752$	−20.0743	+	0.667231i	−0.732034	+	0.0243314i
$753$	−3.52055	−	20.1366i	−0.128296	−	0.733817i
$754$	−9.75788	−	16.5815i	−0.355361	−	0.603863i
$755$			6.15772i			0.224103i
$756$	23.1817	−	14.7854i	0.843111	−	0.537740i
$757$			19.9557i			0.725302i	0.931925	+	0.362651i	$0.118128\pi$
$757$			19.9557i			0.725302i	−0.931925	+	0.362651i	$0.881872\pi$
$758$	21.5672	−	12.6918i	0.783355	−	0.460988i
$759$	−2.43798	−	13.9446i	−0.0884931	−	0.506156i
$760$	4.82492	−	2.94836i	0.175018	−	0.106948i
$761$	18.2013	−	31.5257i	0.659798	−	1.14280i	−0.320869	−	0.947124i	$-0.603975\pi$
$761$	18.2013	−	31.5257i	0.659798	−	1.14280i	0.980668	−	0.195681i	$-0.0626917\pi$
$762$	−13.9936	−	16.4465i	−0.506933	−	0.595794i
$763$	−40.8227	−	21.8641i	−1.47788	−	0.791533i
$764$	−14.4340	+	8.65630i	−0.522202	+	0.313174i
$765$	−1.33570	−	3.70315i	−0.0482923	−	0.133888i
$766$	49.4825	−	0.411034i	1.78787	−	0.0148513i
$767$	−4.47235	+	2.58211i	−0.161487	+	0.0932347i
$768$	7.76673	−	26.6022i	0.280258	−	0.959925i
$769$			33.7570i			1.21731i	0.793436	+	0.608654i	$0.208290\pi$
$769$			33.7570i			1.21731i

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +O(q^{10})\)	\(q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +(0.00458308 + 0.551736i) q^{10} +(0.748582 + 1.29658i) q^{11} +(1.13530 - 3.27278i) q^{12} +3.28768 q^{13} +(1.73911 - 3.31293i) q^{14} +(0.634670 + 0.232043i) q^{15} +(-2.11397 - 3.39575i) q^{16} +(1.68169 + 2.91278i) q^{17} +(-3.26476 - 2.70950i) q^{18} +(-2.56203 + 4.43756i) q^{19} +(0.669184 - 0.401321i) q^{20} +(-3.05110 - 3.41918i) q^{21} +(1.04339 - 1.84237i) q^{22} +(4.72764 + 2.72950i) q^{23} +(-4.80326 + 0.963690i) q^{24} +(-2.42389 - 4.19830i) q^{25} +(-2.35811 - 4.00712i) q^{26} +(-4.51125 + 2.57850i) q^{27} +(-5.28528 + 0.256545i) q^{28} +4.13801 q^{29} +(-0.172400 - 0.939988i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(-2.62258 + 5.01219i) q^{32} +(-1.66397 - 1.98889i) q^{33} +(2.34398 - 4.13891i) q^{34} +(-0.0329110 - 1.03171i) q^{35} +(-0.960750 + 5.92258i) q^{36} +(7.46581 + 4.31038i) q^{37} +(7.24625 - 0.0601921i) q^{38} +(-5.60934 + 0.980702i) q^{39} +(-0.969118 - 0.527771i) q^{40} -11.1607 q^{41} +(-1.97898 + 6.17120i) q^{42} -4.79323i q^{43} +(-2.99391 + 0.0497422i) q^{44} +(-1.15207 - 0.206585i) q^{45} +(-0.0641268 - 7.71993i) q^{46} +(2.51067 - 4.34861i) q^{47} +(4.61974 + 5.16314i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(-3.37846 + 5.96557i) q^{50} +(-3.73813 - 4.46806i) q^{51} +(-3.19263 + 5.74826i) q^{52} +(0.499243 + 0.864715i) q^{53} +(6.37846 + 3.64900i) q^{54} -0.584118i q^{55} +(4.10358 + 6.25784i) q^{56} +(3.04755 - 8.33548i) q^{57} +(-2.96801 - 5.04353i) q^{58} +(-1.36034 + 0.785391i) q^{59} +(-1.02203 + 0.884338i) q^{60} +(3.40889 - 5.90437i) q^{61} +(5.11878 + 2.89891i) q^{62} +(6.22563 + 4.92357i) q^{63} +(7.99007 - 0.398545i) q^{64} +(-1.11084 - 0.641343i) q^{65} +(-1.23062 + 3.45464i) q^{66} +(3.05467 - 1.76361i) q^{67} +(-6.72585 + 0.111746i) q^{68} +(-8.88036 - 3.24676i) q^{69} +(-1.23388 + 0.780115i) q^{70} -14.3360i q^{71} +(7.90772 - 3.07701i) q^{72} +(2.76107 - 1.59410i) q^{73} +(-0.101268 - 12.1912i) q^{74} +(5.38791 + 6.43999i) q^{75} +(-5.27078 - 8.78877i) q^{76} +(-1.87018 + 3.49184i) q^{77} +(5.21864 + 6.13342i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(0.0518426 + 1.55974i) q^{80} +(6.92781 - 5.74504i) q^{81} +(8.00508 + 13.6030i) q^{82} -17.4548i q^{83} +(8.94106 - 2.01429i) q^{84} -1.31222i q^{85} +(-5.84213 + 3.43797i) q^{86} +(-7.06016 + 1.23435i) q^{87} +(2.20803 + 3.61339i) q^{88} +(-2.54840 + 4.41396i) q^{89} +(0.574539 + 1.55235i) q^{90} +(4.58716 + 7.39053i) q^{91} +(-9.36328 + 5.61532i) q^{92} +(5.52586 - 4.62312i) q^{93} +(-7.10101 + 0.0589856i) q^{94} +(1.73131 - 0.999573i) q^{95} +(2.97945 - 9.33396i) q^{96} +9.00074i q^{97} +(9.87379 - 0.712973i) q^{98} +(3.43230 + 2.89703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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