LMFDB - Embedded newform 168.2.ba.c.5.16

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			5.16
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.717256 + 1.21883i) q^{2} +(1.11142 - 1.32844i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(0.337879 + 0.195075i) q^{5} +(2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 + 0.0704754i) q^{8} +(-0.529502 - 2.95290i) q^{9} +O(q^{10})$	\(q+(0.717256 + 1.21883i) q^{2} +(1.11142 - 1.32844i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(0.337879 + 0.195075i) q^{5} +(2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 + 0.0704754i) q^{8} +(-0.529502 - 2.95290i) q^{9} +(0.00458308 + 0.551736i) q^{10} +(-0.748582 - 1.29658i) q^{11} +(1.24339 + 3.23326i) 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} +(3.21929 - 2.76336i) q^{18} +(-2.56203 + 4.43756i) q^{19} +(-0.669184 + 0.401321i) q^{20} +(4.53697 + 0.644892i) q^{21} +(1.04339 - 1.84237i) q^{22} +(-4.72764 - 2.72950i) q^{23} +(-3.04897 + 3.83455i) 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} +(0.738041 + 0.607120i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(2.62258 - 5.01219i) q^{32} +(-2.55442 - 0.446598i) q^{33} +(2.34398 - 4.13891i) q^{34} +(0.0329110 + 1.03171i) q^{35} +(5.67712 + 1.94174i) q^{36} +(7.46581 + 4.31038i) q^{37} +(-7.24625 + 0.0601921i) q^{38} +(3.65399 - 4.36748i) q^{39} +(-0.969118 - 0.527771i) q^{40} +11.1607 q^{41} +(2.46815 + 5.99235i) q^{42} -4.79323i q^{43} +(2.99391 - 0.0497422i) q^{44} +(0.397129 - 1.10102i) q^{45} +(-0.0641268 - 7.71993i) q^{46} +(-2.51067 + 4.34861i) q^{47} +(-6.86055 - 0.965812i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(3.37846 - 5.96557i) q^{50} +(-5.73852 - 1.00329i) q^{51} +(-3.19263 + 5.74826i) q^{52} +(-0.499243 - 0.864715i) q^{53} +(-0.0929724 - 7.34788i) 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} +(-0.210612 + 1.33501i) q^{60} +(3.40889 - 5.90437i) q^{61} +(-5.11878 - 2.89891i) q^{62} +(5.89917 - 5.31035i) q^{63} +(7.99007 - 0.398545i) q^{64} +(1.11084 + 0.641343i) q^{65} +(-1.28784 - 3.43372i) 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} +(1.70530 + 8.31216i) q^{72} +(2.76107 - 1.59410i) q^{73} +(0.101268 + 12.1912i) q^{74} +(-8.27115 - 1.44608i) q^{75} +(-5.27078 - 8.78877i) q^{76} +(1.87018 - 3.49184i) q^{77} +(7.94406 + 1.32098i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(-0.0518426 - 1.55974i) q^{80} +(-8.43926 + 3.12713i) q^{81} +(8.00508 + 13.6030i) q^{82} +17.4548i q^{83} +(-5.53335 + 7.30630i) q^{84} -1.31222i q^{85} +(5.84213 - 3.43797i) q^{86} +(-4.59906 + 5.49710i) q^{87} +(2.20803 + 3.61339i) q^{88} +(2.54840 - 4.41396i) q^{89} +(1.62679 - 0.305678i) q^{90} +(4.58716 + 7.39053i) q^{91} +(9.36328 - 5.61532i) q^{92} +(-1.24081 + 7.09709i) q^{93} +(-7.10101 + 0.0589856i) q^{94} +(-1.73131 + 0.999573i) q^{95} +(-3.74361 - 9.05458i) 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
$3$	1.11142	−	1.32844i	0.641677	−	0.766975i
$3$	1.11142	−	1.32844i	0.641677	−	0.766975i
$4$	−0.971089	+	1.74842i	−0.485544	+	0.874212i
$5$	0.337879	+	0.195075i	0.151104	+	0.0872401i	0.573646	−	0.819103i	$-0.305529\pi$
$5$	0.337879	+	0.195075i	0.151104	+	0.0872401i	−0.422542	+	0.906344i	$0.638862\pi$
$6$	2.41631	+	0.401798i	0.986455	+	0.164033i
$7$	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
$9$	−0.529502	−	2.95290i	−0.176501	−	0.984301i
$10$	0.00458308	+	0.551736i	0.00144930	+	0.174474i
$11$	−0.748582	−	1.29658i	−0.225706	−	0.390934i	0.730825	−	0.682565i	$-0.239136\pi$
$11$	−0.748582	−	1.29658i	−0.225706	−	0.390934i	−0.956531	+	0.291631i	$0.905802\pi$
$12$	1.24339	+	3.23326i	0.358936	+	0.933362i
$13$	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	0.586780	−	0.809746i	$-0.300395\pi$
$17$	−1.68169	−	2.91278i	−0.407871	−	0.706453i	−0.994651	+	0.103293i	$0.967062\pi$
$18$	3.21929	−	2.76336i	0.758795	−	0.651330i
$19$	−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
$21$	4.53697	+	0.644892i	0.990048	+	0.140727i
$22$	1.04339	−	1.84237i	0.222451	−	0.392795i
$23$	−4.72764	−	2.72950i	−0.985780	−	0.569141i	−0.0817700	−	0.996651i	$-0.526057\pi$
$23$	−4.72764	−	2.72950i	−0.985780	−	0.569141i	−0.904010	+	0.427511i	$0.859391\pi$
$24$	−3.04897	+	3.83455i	−0.622367	+	0.782725i
$25$	−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	$-0.625524\pi$
$29$	−4.13801			−0.768410			−0.384205	+	0.923248i	$0.625524\pi$
$30$	0.738041	+	0.607120i	0.134747	+	0.110845i
$31$	−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
$33$	−2.55442	−	0.446598i	−0.444667	−	0.0777428i
$34$	2.34398	−	4.13891i	0.401989	−	0.709816i
$35$	0.0329110	+	1.03171i	0.00556298	+	0.174391i
$36$	5.67712	+	1.94174i	0.946186	+	0.323623i
$37$	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
$39$	3.65399	−	4.36748i	0.585106	−	0.699357i
$40$	−0.969118	−	0.527771i	−0.153231	−	0.0834480i
$41$	11.1607			1.74301			0.871505	−	0.490387i	$-0.163145\pi$
$41$	11.1607			1.74301			0.871505	+	0.490387i	$0.163145\pi$
$42$	2.46815	+	5.99235i	0.380845	+	0.924639i
$43$		−	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
$45$	0.397129	−	1.10102i	0.0592005	−	0.164130i
$46$	−0.0641268	−	7.71993i	−0.00945498	−	1.13824i
$47$	−2.51067	+	4.34861i	−0.366219	+	0.634310i	−0.988971	−	0.148109i	$-0.952681\pi$
$47$	−2.51067	+	4.34861i	−0.366219	+	0.634310i	0.622752	+	0.782419i	$0.286015\pi$
$48$	−6.86055	−	0.965812i	−0.990236	−	0.139403i
$49$	−3.10652	+	6.27292i	−0.443788	+	0.896132i
$50$	3.37846	−	5.96557i	0.477787	−	0.843658i
$51$	−5.73852	−	1.00329i	−0.803553	−	0.140488i
$52$	−3.19263	+	5.74826i	−0.442738	+	0.797140i
$53$	−0.499243	−	0.864715i	−0.0685763	−	0.118778i	0.829699	−	0.558212i	$-0.188512\pi$
$53$	−0.499243	−	0.864715i	−0.0685763	−	0.118778i	−0.898275	+	0.439434i	$0.855179\pi$
$54$	−0.0929724	−	7.34788i	−0.0126519	−	0.999920i
$55$		−	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	−0.408829	−	0.912611i	$-0.634063\pi$
$59$	1.36034	−	0.785391i	0.177101	−	0.102249i	0.585930	+	0.810362i	$0.300729\pi$
$60$	−0.210612	+	1.33501i	−0.0271899	+	0.172349i
$61$	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
$63$	5.89917	−	5.31035i	0.743226	−	0.669041i
$64$	7.99007	−	0.398545i	0.998758	−	0.0498181i
$65$	1.11084	+	0.641343i	0.137783	+	0.0795488i
$66$	−1.28784	−	3.43372i	−0.158523	−	0.422662i
$67$	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	$0.323812\pi$
$71$			14.3360i			1.70137i	−0.525677	+	0.850684i	$0.676188\pi$
$72$	1.70530	+	8.31216i	0.200971	+	0.979597i
$73$	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
$75$	−8.27115	−	1.44608i	−0.955070	−	0.166978i
$76$	−5.27078	−	8.78877i	−0.604600	−	1.00814i
$77$	1.87018	−	3.49184i	0.213127	−	0.397932i
$78$	7.94406	+	1.32098i	0.899487	+	0.149572i
$79$	−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
$81$	−8.43926	+	3.12713i	−0.937695	+	0.347459i
$82$	8.00508	+	13.6030i	0.884013	+	1.50220i
$83$			17.4548i			1.91591i	0.286911	+	0.957957i	$0.407372\pi$
$83$			17.4548i			1.91591i	−0.286911	+	0.957957i	$0.592628\pi$
$84$	−5.53335	+	7.30630i	−0.603738	+	0.797183i
$85$		−	1.31222i		−	0.142331i
$86$	5.84213	−	3.43797i	0.629973	−	0.370726i
$87$	−4.59906	+	5.49710i	−0.493071	+	0.589351i
$88$	2.20803	+	3.61339i	0.235377	+	0.385189i
$89$	2.54840	−	4.41396i	0.270130	−	0.467879i	−0.698765	−	0.715351i	$-0.746267\pi$
$89$	2.54840	−	4.41396i	0.270130	−	0.467879i	0.968895	+	0.247473i	$0.0796000\pi$
$90$	1.62679	−	0.305678i	0.171479	−	0.0322213i
$91$	4.58716	+	7.39053i	0.480865	+	0.774738i
$92$	9.36328	−	5.61532i	0.976190	−	0.585438i
$93$	−1.24081	+	7.09709i	−0.128666	+	0.735934i
$94$	−7.10101	+	0.0589856i	−0.732413	+	0.00608390i
$95$	−1.73131	+	0.999573i	−0.177629	+	0.102554i
$96$	−3.74361	−	9.05458i	−0.382081	−	0.924129i
$97$			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	−0.712719	−	0.701450i	$-0.752536\pi$
$101$	−4.63907	+	2.67837i	−0.461605	+	0.266508i	0.251114	+	0.967958i	$0.419203\pi$
$102$	−2.89315	−	7.71388i	−0.286464	−	0.763788i
$103$	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
$105$	1.40715	+	1.10294i	0.137323	+	0.107636i
$106$	0.695854	−	1.22871i	0.0675874	−	0.119343i
$107$	7.85256	−	13.6010i	0.759135	−	1.31486i	−0.184157	−	0.982897i	$-0.558955\pi$
$107$	7.85256	−	13.6010i	0.759135	−	1.31486i	0.943292	−	0.331964i	$-0.107711\pi$
$108$	8.88913	−	5.38363i	0.855357	−	0.518040i
$109$	−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	$0.00108718\pi$
$113$			0.0726142i			0.00683097i	−0.999994	+	0.00341549i	$0.998913\pi$
$114$	−7.97365	+	9.69311i	−0.746801	+	0.907843i
$115$	−1.06491	−	1.84448i	−0.0993037	−	0.171999i
$116$	4.01838	−	7.23500i	0.373097	−	0.671753i
$117$	−1.74083	−	9.70819i	−0.160940	−	0.897523i
$118$	1.93297	+	1.09469i	0.177944	+	0.100775i
$119$	4.20138	−	7.84443i	0.385139	−	0.719098i
$120$	−1.77821	+	0.700841i	−0.162327	+	0.0639777i
$121$	4.37925	−	7.58508i	0.398114	−	0.689553i
$122$	9.64147	−	0.0800883i	0.872897	−	0.00725085i
$123$	12.4042	−	14.8263i	1.11845	−	1.33684i
$124$	−0.138202	−	8.31817i	−0.0124109	−	0.746994i
$125$		−	3.84211i		−	0.343649i
$126$	10.7036	+	3.38121i	0.953554	+	0.301222i
$127$	−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
$129$	−6.36751	−	5.32728i	−0.560628	−	0.469041i
$130$	0.0150677	+	1.81393i	0.00132152	+	0.159092i
$131$	4.36183	+	2.51830i	0.381095	+	0.220025i	0.678294	−	0.734790i	$-0.262719\pi$
$131$	4.36183	+	2.51830i	0.381095	+	0.220025i	−0.297200	+	0.954815i	$0.596053\pi$
$132$	3.26141	−	4.03252i	0.283869	−	0.350986i
$133$	−13.5501	+	0.432239i	−1.17494	+	0.0374799i
$134$	4.34052	+	2.45816i	0.374964	+	0.212352i
$135$	−1.02126	−	1.75125i	−0.0878959	−	0.150724i
$136$	4.96035	+	8.11751i	0.425347	+	0.696071i
$137$	−6.34787	+	3.66494i	−0.542335	+	0.313117i	−0.746025	−	0.665918i	$-0.768040\pi$
$137$	−6.34787	+	3.66494i	−0.542335	+	0.313117i	0.203690	+	0.979035i	$0.434707\pi$
$138$	−10.3267	−	8.49488i	−0.879070	−	0.723132i
$139$	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
$144$	−8.90796	+	8.04041i	−0.742330	+	0.670034i
$145$	−1.39815	−	0.807222i	−0.116110	−	0.0670361i
$146$	3.92333	+	2.22189i	0.324697	+	0.183885i
$147$	4.88056	+	11.0987i	0.402542	+	0.915402i
$148$	−14.7863	+	8.86763i	−1.21543	+	0.728914i
$149$	8.98969	−	15.5706i	0.736464	−	1.27559i	−0.217613	−	0.976035i	$-0.569827\pi$
$149$	8.98969	−	15.5706i	0.736464	−	1.27559i	0.954078	−	0.299559i	$-0.0968395\pi$
$150$	−4.17001	−	11.1183i	−0.340480	−	0.907807i
$151$	−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
$156$	4.08787	+	10.6299i	0.327291	+	0.851075i
$157$	−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
$159$	−1.70359	−	0.297845i	−0.135103	−	0.0236206i
$160$	1.86387	−	1.18192i	0.147352	−	0.0934387i
$161$	−0.460494	−	14.4358i	−0.0362920	−	1.13770i
$162$	−9.86455	−	8.04306i	−0.775032	−	0.631922i
$163$	−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
$165$	−0.775965	−	0.649199i	−0.0604088	−	0.0505400i
$166$	−21.2744	+	12.5196i	−1.65122	+	0.971706i
$167$	−7.43145			−0.575063			−0.287531	−	0.957771i	$-0.592835\pi$
$167$	−7.43145			−0.575063			−0.287531	+	0.957771i	$0.592835\pi$
$168$	−12.8740	−	1.50372i	−0.993248	−	0.116015i
$169$	−2.19116			−0.168551
$170$	1.59938	−	0.941200i	0.122667	−	0.0721868i
$171$	14.4603	+	5.21571i	1.10580	+	0.398856i
$172$	8.38060	+	4.65465i	0.639014	+	0.354914i
$173$	15.2445	+	8.80144i	1.15902	+	0.669161i	0.951069	−	0.308978i	$-0.0999870\pi$
$173$	15.2445	+	8.80144i	1.15902	+	0.669161i	0.207952	+	0.978139i	$0.433320\pi$
$174$	−9.99873	−	1.66264i	−0.758002	−	0.126045i
$175$	6.05561	−	11.3065i	0.457761	−	0.854690i
$176$	−2.82039	+	5.28294i	−0.212595	+	0.398216i
$177$	0.468558	−	2.68002i	0.0352190	−	0.201443i
$178$	7.20771	−	0.0598720i	0.540241	−	0.00448759i
$179$	8.11784	+	14.0605i	0.606756	+	1.05093i	0.991771	+	0.128022i	$0.0408627\pi$
$179$	8.11784	+	14.0605i	0.606756	+	1.05093i	−0.385016	+	0.922910i	$0.625804\pi$
$180$	1.53940	+	1.76353i	0.114740	+	0.131446i
$181$	−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
$186$	−9.54012	+	3.57809i	−0.699516	+	0.262358i
$187$	−2.51777	+	4.36091i	−0.184118	+	0.318901i
$188$	−5.16513	−	8.61261i	−0.376706	−	0.628139i
$189$	−0.498031	−	13.7387i	−0.0362264	−	0.999344i
$190$	−2.46010	−	1.39322i	−0.178475	−	0.101075i
$191$	−7.28788	−	4.20766i	−0.527333	−	0.304456i	0.212597	−	0.977140i	$-0.431808\pi$
$191$	−7.28788	−	4.20766i	−0.527333	−	0.304456i	−0.739930	+	0.672684i	$0.765141\pi$
$192$	8.35086	−	11.0573i	0.602671	−	0.797990i
$193$	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	$-0.715880\pi$
$197$	−17.6119			−1.25480			−0.627398	+	0.778699i	$0.715880\pi$
$198$	−5.99282	−	2.10548i	−0.425891	−	0.149630i
$199$	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
$201$	1.05216	−	6.01805i	0.0742135	−	0.424480i
$202$	−6.59187	−	3.73316i	−0.463803	−	0.262664i
$203$	−5.77359	−	9.30203i	−0.405227	−	0.652874i
$204$	7.32678	−	9.05908i	0.512977	−	0.634262i
$205$	3.77097	+	2.17717i	0.263376	+	0.152060i
$206$	0.104557	+	12.5872i	0.00728485	+	0.876990i
$207$	−5.55666	+	15.4055i	−0.386214	+	1.07076i
$208$	−6.95007	−	11.1641i	−0.481900	−	0.774094i
$209$	7.67154			0.530652
$210$	−0.335017	+	2.50616i	−0.0231184	+	0.172942i
$211$		−	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
$213$	19.0445	+	15.9333i	1.30491	+	1.09173i
$214$	22.2096	−	0.184488i	1.51822	−	0.0126113i
$215$	0.935038	−	1.61953i	0.0637691	−	0.110451i
$216$	12.9375	+	6.97289i	0.880285	+	0.474445i
$217$	−9.70158	−	5.19604i	−0.658586	−	0.352730i
$218$	−21.5390	−	12.1981i	−1.45880	−	0.826161i
$219$	0.951031	−	5.43963i	0.0642647	−	0.367576i
$220$	1.02129	+	0.567230i	0.0688550	+	0.0382426i
$221$	−5.52887	−	9.57629i	−0.371912	−	0.644171i
$222$	16.3078	+	13.4150i	1.09451	+	0.900354i
$223$			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	−0.887481	−	0.460844i	$-0.847547\pi$
$227$	−14.0438	+	8.10819i	−0.932119	+	0.538159i	−0.0446379	+	0.999003i	$0.514213\pi$
$228$	−17.5334	−	2.76608i	−1.16118	−	0.183188i
$229$	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
$231$	−2.56014	−	6.36531i	−0.168445	−	0.418807i
$232$	11.7004	−	0.291628i	0.768171	−	0.0191463i
$233$	−1.80462	−	1.04190i	−0.118225	−	0.0682572i	0.439721	−	0.898134i	$-0.355077\pi$
$233$	−1.80462	−	1.04190i	−0.118225	−	0.0682572i	−0.557946	+	0.829877i	$0.688411\pi$
$234$	10.5840	−	9.08503i	0.691898	−	0.593907i
$235$	−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	$-0.991230\pi$
$239$		−	0.851762i		−	0.0550959i	0.999620	−	0.0275480i	$-0.00876990\pi$
$240$	−2.12963	−	1.66465i	−0.137467	−	0.107453i
$241$	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
$243$	−5.22533	+	14.6866i	−0.335205	+	0.942145i
$244$	7.01301	+	11.6939i	0.448962	+	0.748622i
$245$	−2.27332	+	1.51349i	−0.145237	+	0.0966932i
$246$	26.9677	+	4.48434i	1.71940	+	0.285911i
$247$	−8.42312	+	14.5893i	−0.535950	+	0.928293i
$248$	10.0393	−	6.13470i	0.637496	−	0.389554i
$249$	23.1877	+	19.3996i	1.46946	+	1.22940i
$250$	4.68287	−	2.75577i	0.296171	−	0.174290i
$251$		−	11.8022i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$251$		−	11.8022i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$252$	3.55612	+	15.4711i	0.224014	+	0.974586i
$253$			8.17302i			0.513834i
$254$	−6.32316	−	10.7449i	−0.396750	−	0.674196i
$255$	−1.74321	−	1.45843i	−0.109164	−	0.0913304i
$256$	−7.06224	+	14.3570i	−0.441390	+	0.897315i
$257$	−8.86901	+	15.3616i	−0.553233	+	0.958228i	0.444805	+	0.895627i	$0.353273\pi$
$257$	−8.86901	+	15.3616i	−0.553233	+	0.958228i	−0.998039	+	0.0626011i	$0.980060\pi$
$258$	1.92591	−	11.5819i	0.119902	−	0.721060i
$259$	0.727204	+	22.7968i	0.0451863	+	1.41653i
$260$	−2.20006	+	1.31942i	−0.136442	+	0.0818267i
$261$	2.19109	+	12.2191i	0.135625	+	0.756346i
$262$	0.0591649	+	7.12259i	0.00365522	+	0.440035i
$263$	6.27815	−	3.62469i	0.387128	−	0.223508i	−0.293787	−	0.955871i	$-0.594916\pi$
$263$	6.27815	−	3.62469i	0.387128	−	0.223508i	0.680915	+	0.732363i	$0.261582\pi$
$264$	7.25421	+	1.08275i	0.446466	+	0.0666390i
$265$		−	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	−0.587463	−	0.809251i	$-0.699873\pi$
$269$	−2.95817	+	1.70790i	−0.180363	+	0.104132i	0.407100	+	0.913383i	$0.366540\pi$
$270$	1.40197	−	2.50083i	0.0853213	−	0.152196i
$271$	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
$273$	14.9161	+	2.12020i	0.902764	+	0.128320i
$274$	−9.01998	−	5.10826i	−0.544917	−	0.308601i
$275$	−3.62896	+	6.28555i	−0.218835	+	0.379033i
$276$	2.94690	−	18.6795i	0.177383	−	1.12438i
$277$	−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	$-0.924129\pi$
$281$		−	7.91565i		−	0.472208i	0.971728	−	0.236104i	$-0.0758706\pi$
$282$	−7.81383	+	9.49882i	−0.465307	+	0.565646i
$283$	−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
$285$	−0.596338	+	3.41089i	−0.0353240	+	0.202043i
$286$	3.43032	−	6.05714i	0.202839	−	0.358166i
$287$	15.5720	+	25.0887i	0.919189	+	1.48094i
$288$	−16.1892	−	5.09026i	−0.953956	−	0.299946i
$289$	2.84381	−	4.92562i	0.167283	−	0.289742i
$290$	−0.0189648	−	2.28309i	−0.00111365	−	0.134068i
$291$	11.9569	+	10.0036i	0.700928	+	0.586420i
$292$	0.105926	+	6.37554i	0.00619885	+	0.373100i
$293$			12.8246i			0.749220i	0.927183	+	0.374610i	$0.122223\pi$
$293$			12.8246i			0.749220i	−0.927183	+	0.374610i	$0.877777\pi$
$294$	−10.0268	+	13.9091i	−0.584772	+	0.811197i
$295$	0.612840			0.0356809
$296$	−21.4137	−	11.6617i	−1.24465	−	0.677821i
$297$	0.0338081	+	7.77942i	0.00196175	+	0.451408i
$298$	25.4258	−	0.211203i	1.47288	−	0.0122347i
$299$	−15.5430	−	8.97373i	−0.898872	−	0.518964i
$300$	10.5604	−	13.0572i	0.609703	−	0.753858i
$301$	10.7749	−	6.68778i	0.621056	−	0.385477i
$302$	10.9993	−	19.4222i	0.632939	−	1.11762i
$303$	−1.59789	+	9.13951i	−0.0917966	+	0.525051i
$304$	20.4849	−	0.680878i	1.17489	−	0.0390511i
$305$	2.30359	−	1.32998i	0.131903	−	0.0761542i
$306$	−13.4629	−	4.72997i	−0.769624	−	0.270395i
$307$	−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	0.885739	−	0.464184i	$-0.153652\pi$
$311$	0.720819	+	1.24850i	0.0408739	+	0.0707957i	−0.844865	+	0.534980i	$0.820319\pi$
$312$	−10.0240	+	12.6068i	−0.567498	+	0.713719i
$313$	−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
$315$	3.02912	−	0.643477i	0.170672	−	0.0362558i
$316$	−0.492538	−	0.821284i	−0.0277074	−	0.0462008i
$317$	−13.4686	+	23.3283i	−0.756472	+	1.31025i	0.188167	+	0.982137i	$0.439745\pi$
$317$	−13.4686	+	23.3283i	−0.756472	+	1.31025i	−0.944639	+	0.328111i	$0.893588\pi$
$318$	−0.858887	−	2.29001i	−0.0481640	−	0.128418i
$319$	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
$324$	2.72771	−	17.7921i	0.151540	−	0.988451i
$325$	−7.96898	−	13.8027i	−0.442039	−	0.765635i
$326$	−0.147504	−	17.7574i	−0.00816952	−	0.983491i
$327$	−5.22113	+	29.8634i	−0.288729	+	1.65145i
$328$	−31.5574	+	0.786555i	−1.74247	+	0.0434302i
$329$	−13.2785	+	0.423575i	−0.732066	+	0.0233524i
$330$	0.234697	−	1.41141i	0.0129196	−	0.0776956i
$331$	−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
$333$	8.77498	−	24.3281i	0.480866	−	1.33317i
$334$	−5.33025	−	9.05766i	−0.291658	−	0.495613i
$335$	1.37615			0.0751868
$336$	−7.40114	−	16.7697i	−0.403765	−	0.914863i
$337$	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
$339$	0.0964636	+	0.0807047i	0.00523918	+	0.00438328i
$340$	2.29432	+	1.27429i	0.124427	+	0.0691079i
$341$	5.39334	+	3.11385i	0.292066	+	0.168624i
$342$	4.01465	+	21.3656i	0.217087	+	1.15532i
$343$	−18.4356	+	1.76905i	−0.995428	+	0.0955198i
$344$	0.337805	+	13.5531i	0.0182132	+	0.730734i
$345$	−3.63385	−	0.635319i	−0.195640	−	0.0342045i
$346$	0.206781	+	24.8934i	0.0111166	+	1.33828i
$347$	−10.8299	−	18.7579i	−0.581377	−	1.00697i	−0.995316	−	0.0966701i	$-0.969181\pi$
$347$	−10.8299	−	18.7579i	−0.581377	−	1.00697i	0.413940	−	0.910304i	$-0.364152\pi$
$348$	−5.14516	−	13.3793i	−0.275810	−	0.717205i
$349$	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	$0.127204\pi$
$353$	14.9846	+	25.9541i	0.797549	+	1.38140i	−0.123659	+	0.992325i	$0.539463\pi$
$354$	3.60257	−	1.35117i	0.191474	−	0.0718138i
$355$	−2.79659	+	4.84383i	−0.148428	+	0.257084i
$356$	5.24275	+	8.74203i	0.277865	+	0.463327i
$357$	−5.75137	−	14.2997i	−0.304395	−	0.756821i
$358$	−11.3148	+	19.9792i	−0.598005	+	1.05594i
$359$	9.44412	+	5.45257i	0.498442	+	0.287775i	0.728070	−	0.685503i	$-0.240418\pi$
$359$	9.44412	+	5.45257i	0.498442	+	0.287775i	−0.229628	+	0.973278i	$0.573751\pi$
$360$	−1.04531	+	3.14117i	−0.0550925	+	0.165554i
$361$	−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
$366$	10.6093	−	12.8971i	0.554557	−	0.674143i
$367$	−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
$369$	−5.90961	−	32.9565i	−0.307642	−	1.71564i
$370$	−2.34398	+	4.13891i	−0.121858	+	0.215171i
$371$	1.24726	−	2.32877i	0.0647545	−	0.120904i
$372$	−11.2038	−	9.06137i	−0.580889	−	0.469810i
$373$	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
$375$	−5.10401	−	4.27019i	−0.263570	−	0.220511i
$376$	6.79258	−	12.4729i	0.350301	−	0.643238i
$377$	−13.6045			−0.700665
$378$	16.3879	−	10.4612i	0.842903	−	0.538065i
$379$			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
$381$	−9.79800	+	11.7112i	−0.501967	+	0.599984i
$382$	−0.0988546	−	11.9007i	−0.00505784	−	0.608890i
$383$	17.4953	−	30.3028i	0.893968	−	1.54840i	0.0588917	−	0.998264i	$-0.481243\pi$
$383$	17.4953	−	30.3028i	0.893968	−	1.54840i	0.835076	−	0.550134i	$-0.185423\pi$
$384$	19.4666	+	2.24738i	0.993402	+	0.114686i
$385$	1.31306	−	0.814994i	0.0669200	−	0.0415359i
$386$	−9.16202	+	16.1780i	−0.466335	+	0.823436i
$387$	−14.1539	+	2.53802i	−0.719485	+	0.129015i
$388$	−15.7371	−	8.74052i	−0.798931	−	0.443733i
$389$	10.4422	+	18.0864i	0.529439	+	0.917015i	0.999410	+	0.0343338i	$0.0109309\pi$
$389$	10.4422	+	18.0864i	0.529439	+	0.917015i	−0.469971	+	0.882682i	$0.655736\pi$
$390$	2.42644	+	1.99602i	0.122868	+	0.101072i
$391$			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
$396$	−1.73217	−	8.81440i	−0.0870447	−	0.442940i
$397$	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
$399$	−14.4856	+	18.4808i	−0.725186	+	0.925200i
$400$	−9.13235	+	17.1060i	−0.456617	+	0.855301i
$401$	6.62355	+	3.82411i	0.330764	+	0.190967i	0.656180	−	0.754604i	$-0.272171\pi$
$401$	6.62355	+	3.82411i	0.330764	+	0.190967i	−0.325416	+	0.945571i	$0.605504\pi$
$402$	8.08964	−	3.03408i	0.403475	−	0.151326i
$403$	−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
$408$	16.2966	+	2.43242i	0.806804	+	0.120423i
$409$	−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
$411$	−2.18648	+	12.5060i	−0.107851	+	0.616877i
$412$	−15.2666	+	9.15566i	−0.752133	+	0.451067i
$413$	3.66354	+	1.96214i	0.180271	+	0.0965507i
$414$	−22.7622	+	4.27708i	−1.11870	+	0.210207i
$415$	−3.40499	+	5.89762i	−0.167145	+	0.289503i
$416$	8.62221	−	16.4785i	0.422738	−	0.807924i
$417$	17.5045	−	20.9225i	0.857197	−	1.02458i
$418$	5.50246	+	9.35030i	0.269134	+	0.457338i
$419$			4.38235i			0.214092i	0.994254	+	0.107046i	$0.0341392\pi$
$419$			4.38235i			0.214092i	−0.994254	+	0.107046i	$0.965861\pi$
$420$	−3.29488	+	1.38923i	−0.160774	+	0.0677876i
$421$			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
$423$	14.1704	+	5.11117i	0.688990	+	0.248514i
$424$	1.47258	+	2.40984i	0.0715146	+	0.117032i
$425$	−8.15249	+	14.1205i	−0.395454	+	0.684946i
$426$	−5.76017	+	34.6402i	−0.279081	+	1.67832i
$427$	18.0290	−	0.575113i	0.872484	−	0.0278317i
$428$	16.1548	+	26.9374i	0.780873	+	1.30207i
$429$	−8.39811	−	1.46827i	−0.405464	−	0.0708888i
$430$	2.64460	−	0.0219677i	0.127534	−	0.00105938i
$431$	−0.588922	+	0.340014i	−0.0283674	+	0.0163779i	−0.514117	−	0.857720i	$-0.671880\pi$
$431$	−0.588922	+	0.340014i	−0.0283674	+	0.0163779i	0.485749	+	0.874098i	$0.338547\pi$
$432$	0.780729	+	20.7699i	0.0375628	+	0.999294i
$433$			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
$438$	7.31211	−	2.74246i	0.349386	−	0.131040i
$439$	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
$441$	20.1682	+	5.85172i	0.960392	+	0.278653i
$442$	7.70624	−	13.6074i	0.366549	−	0.647238i
$443$	3.02001	−	5.23080i	0.143485	−	0.248523i	−0.785322	−	0.619088i	$-0.787503\pi$
$443$	3.02001	−	5.23080i	0.143485	−	0.248523i	0.928807	+	0.370565i	$0.120836\pi$
$444$	−4.65370	+	29.4984i	−0.220855	+	1.39993i
$445$	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	$-0.768774\pi$
$449$		−	28.1482i		−	1.32839i	0.747558	−	0.664197i	$-0.231226\pi$
$450$	−19.4046	−	6.81750i	−0.914743	−	0.321380i
$451$	−8.35470	−	14.4708i	−0.393408	−	0.681402i
$452$	−0.126960	−	0.0705149i	−0.00597172	−	0.00331674i
$453$	−26.9285	−	4.70801i	−1.26521	−	0.221201i
$454$	−19.9555	−	11.3013i	−0.936557	−	0.530398i
$455$	0.108201	+	3.39194i	0.00507254	+	0.159017i
$456$	−9.20453	−	23.3542i	−0.431042	−	1.09366i
$457$	−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
$459$	0.0759502	+	17.4765i	0.00354505	+	0.815734i
$460$	4.25907	−	0.0707621i	0.198580	−	0.00329930i
$461$		−	31.6209i		−	1.47273i	−0.676583	−	0.736367i	$-0.736540\pi$
$461$		−	31.6209i		−	1.47273i	0.676583	−	0.736367i	$-0.263460\pi$
$462$	5.92195	−	7.68593i	0.275514	−	0.357582i
$463$	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
$465$	−1.80371	+	2.15591i	−0.0836449	+	0.0999779i
$466$	−0.0244784	−	2.94684i	−0.00113394	−	0.136510i
$467$	−12.7642	−	7.36942i	−0.590657	−	0.341016i	0.174700	−	0.984622i	$-0.444104\pi$
$467$	−12.7642	−	7.36942i	−0.590657	−	0.341016i	−0.765357	+	0.643606i	$0.777438\pi$
$468$	18.6645	+	6.38381i	0.862769	+	0.295092i
$469$	8.22655	+	4.40603i	0.379867	+	0.203452i
$470$	−2.41079	−	1.36530i	−0.111201	−	0.0629765i
$471$	−8.64256	−	1.51101i	−0.398228	−	0.0696237i
$472$	−3.79107	+	2.31660i	−0.174498	+	0.106630i
$473$	−6.21481	+	3.58812i	−0.285757	+	0.164982i
$474$	−0.745113	+	0.905791i	−0.0342242	+	0.0416044i
$475$	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	$-0.876430\pi$
$479$	−17.3034	−	29.9703i	−0.790611	−	1.36938i	0.134979	−	0.990848i	$-0.456903\pi$
$480$	0.501431	−	3.78964i	0.0228871	−	0.172973i
$481$	24.5452	+	14.1712i	1.11916	+	0.646150i
$482$	18.5315	+	10.4949i	0.844087	+	0.478030i
$483$	−19.6889	−	15.4325i	−0.895877	−	0.702203i
$484$	9.00930	+	15.0226i	0.409514	+	0.682844i
$485$	−1.75582	+	3.04117i	−0.0797276	+	0.138092i
$486$	−21.6483	+	4.16526i	−0.981989	+	0.188940i
$487$	−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	$-0.387256\pi$
$491$	15.3708			0.693675			0.346837	+	0.937925i	$0.387256\pi$
$492$	13.8771	+	36.0855i	0.625628	+	1.62686i
$493$	6.95887	+	12.0531i	0.313412	+	0.542845i
$494$	−23.8234	+	0.197892i	−1.07186	+	0.00890360i
$495$	−1.72484	+	0.309291i	−0.0775259	+	0.0139016i
$496$	14.6779	+	7.83605i	0.659057	+	0.351849i
$497$	−32.2265	+	20.0024i	−1.44556	+	0.897229i
$498$	−7.01330	+	42.1763i	−0.314274	+	1.88996i
$499$	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
$501$	−8.25944	+	9.87223i	−0.369005	+	0.441059i
$502$	14.3849	−	8.46519i	0.642028	−	0.377820i
$503$	−28.3616			−1.26458			−0.632291	−	0.774731i	$-0.717885\pi$
$503$	−28.3616			−1.26458			−0.632291	+	0.774731i	$0.717885\pi$
$504$	−16.3059	+	15.4310i	−0.726325	+	0.687352i
$505$	−2.08993			−0.0930006
$506$	−9.96152	+	5.86215i	−0.442844	+	0.260604i
$507$	−2.43530	+	2.91083i	−0.108155	+	0.129274i
$508$	8.56090	−	15.4137i	0.379828	−	0.683873i
$509$	18.3731	+	10.6077i	0.814373	+	0.470179i	0.848472	−	0.529240i	$-0.177523\pi$
$509$	18.3731	+	10.6077i	0.814373	+	0.470179i	−0.0340991	+	0.999418i	$0.510856\pi$
$510$	0.527249	−	3.17074i	0.0233470	−	0.140403i
$511$	7.43586	+	3.98255i	0.328943	+	0.176178i
$512$	−22.5642	+	1.69001i	−0.997207	+	0.0746885i
$513$	23.0002	−	13.4128i	1.01548	−	0.592188i
$514$	−25.0845	+	0.208368i	−1.10643	+	0.00919072i
$515$	1.73632	+	3.00739i	0.0765113	+	0.132522i
$516$	15.4978	−	5.95985i	0.682251	−	0.262368i
$517$	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	0.706974	−	0.707239i	$-0.250060\pi$
$521$	−5.91179	−	10.2395i	−0.259000	−	0.448601i	−0.965974	+	0.258638i	$0.916726\pi$
$522$	−13.3215	+	11.4348i	−0.583065	+	0.500488i
$523$	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
$525$	−8.28967	−	20.6107i	−0.361791	−	0.899526i
$526$	8.92092	+	5.05217i	0.388971	+	0.220285i
$527$	12.1162	+	6.99528i	0.527789	+	0.304719i
$528$	3.88343	+	9.61826i	0.169005	+	0.418581i
$529$	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
$534$	7.93124	−	9.64155i	0.343218	−	0.417231i
$535$	5.30643	−	3.06367i	0.229417	−	0.132454i
$536$	−8.51293	+	5.20198i	−0.367702	+	0.224691i
$537$	27.7008	+	4.84304i	1.19538	+	0.208993i
$538$	−4.20340	−	2.38050i	−0.181221	−	0.102631i
$539$	10.4588	−	0.667940i	0.450494	−	0.0287702i
$540$	4.05366	−	0.0849721i	0.174442	−	0.00365662i
$541$	−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
$543$	−6.88345	+	8.22755i	−0.295397	+	0.353078i
$544$	−19.0098	+	0.789975i	−0.815038	+	0.0338699i
$545$	−6.82885			−0.292516
$546$	8.11450	+	19.7009i	0.347269	+	0.843121i
$547$			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
$549$	−19.2400	−	6.93974i	−0.821145	−	0.296181i
$550$	−10.2639	+	0.0852587i	−0.437654	+	0.00363544i
$551$	10.6017	−	18.3627i	0.451647	−	0.782276i
$552$	24.8808	−	9.80622i	1.05900	−	0.417381i
$553$	−1.26621	+	0.0403914i	−0.0538448	+	0.00171762i
$554$	−15.1957	−	8.60573i	−0.645602	−	0.365622i
$555$	5.73852	+	1.00329i	0.243586	+	0.0425871i
$556$	−15.2943	+	27.5371i	−0.648624	+	1.16783i
$557$	−1.46808	−	2.54278i	−0.0622044	−	0.107741i	0.833246	−	0.552902i	$-0.186480\pi$
$557$	−1.46808	−	2.54278i	−0.0622044	−	0.107741i	−0.895450	+	0.445161i	$0.853146\pi$
$558$	−5.84978	+	16.6502i	−0.247641	+	0.704860i
$559$		−	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	−0.164987	−	0.986296i	$-0.552758\pi$
$563$	14.3950	−	8.31096i	0.606677	−	0.350265i	0.771664	+	0.636031i	$0.219425\pi$
$564$	−17.1819	−	2.71064i	−0.723490	−	0.114139i
$565$	−0.0141652	+	0.0245348i	−0.000595934	+	0.00103219i
$566$	15.8271	−	27.9470i	0.665264	−	1.17470i
$567$	−18.8046	−	14.6078i	−0.789717	−	0.613471i
$568$	−1.01033	−	40.5357i	−0.0423927	−	1.70084i
$569$	19.2204	+	11.0969i	0.805763	+	0.465207i	0.845482	−	0.534003i	$-0.179313\pi$
$569$	19.2204	+	11.0969i	0.805763	+	0.465207i	−0.0397194	+	0.999211i	$0.512646\pi$
$570$	−4.58501	+	1.71964i	−0.192045	+	0.0720279i
$571$	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
$576$	−5.40762	−	23.3828i	−0.225317	−	0.974285i
$577$	−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
$579$	22.4304	+	3.92160i	0.932177	+	0.162976i
$580$	2.76909	−	1.66067i	0.114980	−	0.0689557i
$581$	−39.2375	+	24.3539i	−1.62784	+	1.01037i
$582$	−3.61648	+	21.7486i	−0.149908	+	0.901508i
$583$	−0.747449	+	1.29462i	−0.0309562	+	0.0536177i
$584$	−7.69472	+	4.70200i	−0.318410	+	0.194570i
$585$	1.30563	−	3.61979i	0.0539812	−	0.149660i
$586$	−15.6310	+	9.19850i	−0.645709	+	0.379986i
$587$			0.369829i			0.0152645i	0.999971	+	0.00763224i	$0.00242944\pi$
$587$			0.369829i			0.0152645i	−0.999971	+	0.00763224i	$0.997571\pi$
$588$	−24.1446	−	2.24450i	−0.995707	−	0.0925616i
$589$		−	21.3143i		−	0.878241i
$590$	0.439563	+	0.746947i	0.0180965	+	0.0307513i
$591$	−19.5742	+	23.3963i	−0.805174	+	0.962396i
$592$	−1.14552	−	34.4640i	−0.0470805	−	1.41646i
$593$	4.89233	−	8.47376i	0.200904	−	0.347976i	−0.747916	−	0.663793i	$-0.768945\pi$
$593$	4.89233	−	8.47376i	0.200904	−	0.347976i	0.948820	+	0.315818i	$0.102279\pi$
$594$	−9.45753	+	5.62104i	−0.388047	+	0.230634i
$595$	2.94981	−	1.83089i	0.120930	−	0.0750592i
$596$	18.4942	+	30.8382i	0.757553	+	1.26318i
$597$	5.94813	−	34.0216i	0.243441	−	1.39241i
$598$	−0.210828	−	25.3807i	−0.00862141	−	1.03789i
$599$	31.2524	−	18.0436i	1.27694	−	0.737240i	0.300653	−	0.953734i	$-0.402795\pi$
$599$	31.2524	−	18.0436i	1.27694	−	0.737240i	0.976284	+	0.216494i	$0.0694621\pi$
$600$	23.4890	+	3.50594i	0.958934	+	0.143129i
$601$		−	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
$606$	−12.2856	+	4.60780i	−0.499068	+	0.187179i
$607$	−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
$609$	−18.7741	−	2.66857i	−0.760763	−	0.108136i
$610$	3.27328	+	1.85375i	0.132531	+	0.0750560i
$611$	−8.25429	+	14.2968i	−0.333933	+	0.578388i
$612$	−3.89133	−	19.8016i	−0.157298	−	0.800432i
$613$	−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	$-0.885246\pi$
$617$		−	17.5244i		−	0.705506i	0.935717	−	0.352753i	$-0.114754\pi$
$618$	16.8375	+	13.8507i	0.677304	+	0.557157i
$619$	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
$621$	14.2895	+	24.5037i	0.573419	+	0.983298i
$622$	−1.00469	+	1.77405i	−0.0402844	+	0.0711328i
$623$	13.4780	−	0.429940i	0.539985	−	0.0172252i
$624$	−22.5553	−	3.17528i	−0.902935	−	0.127113i
$625$	−11.3700	+	19.6933i	−0.454798	+	0.787734i
$626$	−0.283252	−	34.0994i	−0.0113210	−	1.36289i
$627$	8.52629	−	10.1912i	0.340507	−	0.406997i
$628$	10.1295	−	0.168297i	0.404213	−	0.00671577i
$629$		−	28.9950i		−	1.15611i
$630$	2.95694	+	3.23045i	0.117807	+	0.128704i
$631$	−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
$633$	−19.2835	−	16.1332i	−0.766449	−	0.641237i
$634$	−38.0937	+	0.316431i	−1.51289	+	0.0125671i
$635$	−2.97867	−	1.71973i	−0.118205	−	0.0682456i
$636$	2.17509	−	2.68936i	0.0862481	−	0.106640i
$637$	−10.2132	+	20.6234i	−0.404663	+	0.817127i
$638$	−4.31755	+	7.62377i	−0.170933	+	0.301828i
$639$	42.3328	−	7.59093i	1.67466	−	0.300293i
$640$	0.256511	+	4.40658i	0.0101395	+	0.174185i
$641$	−11.9401	+	6.89362i	−0.471606	+	0.272282i	−0.716912	−	0.697164i	$-0.754445\pi$
$641$	−11.9401	+	6.89362i	−0.471606	+	0.272282i	0.245306	+	0.969446i	$0.421112\pi$
$642$	24.4391	−	29.7092i	0.964534	−	1.17253i
$643$	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	$0.0518832\pi$
$647$	16.1242	+	27.9279i	0.633907	+	1.09796i	−0.352838	+	0.935684i	$0.614783\pi$
$648$	23.6420	−	9.43688i	0.928746	−	0.370716i
$649$	−2.03665	−	1.17586i	−0.0799454	−	0.0461565i
$650$	11.1073	−	19.6129i	0.435665	−	0.769280i
$651$	−17.6851	+	7.11299i	−0.693135	+	0.278780i
$652$	21.5374	−	12.9164i	0.843471	−	0.505844i
$653$	−9.95455	+	17.2418i	−0.389552	+	0.674723i	−0.992389	−	0.123141i	$-0.960703\pi$
$653$	−9.95455	+	17.2418i	−0.389552	+	0.674723i	0.602838	+	0.797864i	$0.294037\pi$
$654$	−40.1433	+	15.0560i	−1.56973	+	0.588737i
$655$	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	$-0.571447\pi$
$659$	−11.4275			−0.445153			−0.222576	+	0.974915i	$0.571447\pi$
$660$	1.88861	−	0.726286i	0.0735139	−	0.0282706i
$661$	−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
$663$	−18.8664	−	3.29848i	−0.732710	−	0.128102i
$664$	−1.23013	−	49.3543i	−0.0477385	−	1.91532i
$665$	−4.66261	−	2.49723i	−0.180808	−	0.0968385i
$666$	35.9458	−	6.75429i	1.39287	−	0.261724i
$667$	19.5630	+	11.2947i	0.757483	+	0.437333i
$668$	7.21660	−	12.9933i	0.279218	−	0.502727i
$669$	3.69169	+	3.08859i	0.142729	+	0.119412i
$670$	0.987048	+	1.67729i	0.0381330	+	0.0647992i
$671$	−10.2073			−0.394050
$672$	15.1309	−	21.0489i	0.583687	−	0.811979i
$673$	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
$675$	0.109470	+	25.1896i	0.00421350	+	0.969548i
$676$	2.12781	−	3.83108i	0.0818389	−	0.147349i
$677$	−36.2236	−	20.9137i	−1.39219	−	0.803780i	−0.398630	−	0.917112i	$-0.630514\pi$
$677$	−36.2236	−	20.9137i	−1.39219	−	0.803780i	−0.993557	+	0.113332i	$0.963848\pi$
$678$	−0.0291762	+	0.175459i	−0.00112051	+	0.00673844i
$679$	−20.2332	+	12.5583i	−0.776478	+	0.481945i
$680$	0.0924795	+	3.71038i	0.00354643	+	0.142287i
$681$	−4.83728	+	27.6679i	−0.185365	+	1.06024i
$682$	0.0731565	+	8.80698i	0.00280131	+	0.337237i
$683$	6.73357	+	11.6629i	0.257653	+	0.446268i	0.965613	−	0.259985i	$-0.0837176\pi$
$683$	6.73357	+	11.6629i	0.257653	+	0.446268i	−0.707960	+	0.706253i	$0.750384\pi$
$684$	−23.1615	+	20.2178i	−0.885602	+	0.773046i
$685$	−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
$690$	−1.83205	−	4.88473i	−0.0697451	−	0.185958i
$691$	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
$693$	−11.3013	−	3.67353i	−0.429301	−	0.139546i
$694$	15.0948	−	26.6539i	0.572993	−	1.01177i
$695$	5.32149	+	3.07236i	0.201856	+	0.116541i
$696$	12.6167	−	15.8674i	0.478233	−	0.601454i
$697$	−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	$-0.748647\pi$
$701$	−37.2839			−1.40819			−0.704096	+	0.710105i	$0.748647\pi$
$702$	−0.305663	−	24.1575i	−0.0115365	−	0.911765i
$703$	−38.2552	+	22.0866i	−1.44282	+	0.833013i
$704$	−6.49797	−	10.0614i	−0.244901	−	0.379204i
$705$	−0.584385	+	3.34252i	−0.0220092	+	0.125886i
$706$	−20.8858	+	36.8793i	−0.786047	+	1.38797i
$707$	−12.4935	−	6.69137i	−0.469867	−	0.251655i
$708$	4.23080	+	3.42178i	0.159003	+	0.128598i
$709$	−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
$711$	1.35127	+	0.487392i	0.0506765	+	0.0182786i
$712$	−6.89465	+	12.6603i	−0.258388	+	0.474464i
$713$	22.7076			0.850406
$714$	13.3037	−	17.2665i	0.497879	−	0.646182i
$715$		−	1.92039i		−	0.0718186i
$716$	−32.4669	+	0.539419i	−1.21334	+	0.0201590i
$717$	−1.13151	−	0.946663i	−0.0422572	−	0.0353538i
$718$	0.128102	+	15.4217i	0.00478074	+	0.575531i
$719$	−8.37315	+	14.5027i	−0.312266	+	0.540860i	−0.978853	−	0.204567i	$-0.934421\pi$
$719$	−8.37315	+	14.5027i	−0.312266	+	0.540860i	0.666587	+	0.745428i	$0.267755\pi$
$720$	−4.57830	+	0.978970i	−0.170623	+	0.0364840i
$721$	0.750825	+	23.5373i	0.0279622	+	0.876575i
$722$	5.05671	−	8.92895i	0.188191	−	0.332301i
$723$	4.49211	−	25.6936i	0.167063	−	0.955555i
$724$	6.01434	−	10.8287i	0.223521	−	0.402445i
$725$	10.0301	+	17.3726i	0.372508	+	0.645204i
$726$	13.6293	−	16.5683i	0.505831	−	0.614909i
$727$		−	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
$732$	23.3290	+	3.68040i	0.862263	+	0.136031i
$733$	−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
$735$	−0.516028	+	4.70208i	−0.0190340	+	0.173439i
$736$	−26.0794	+	16.5375i	−0.961299	+	0.609580i
$737$	−4.57334	−	2.64042i	−0.168461	−	0.0972610i
$738$	35.9296	−	30.8410i	1.32259	−	1.13527i
$739$	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	$0.0874914\pi$
$743$			14.7964i			0.542829i	−0.962463	+	0.271414i	$0.912509\pi$
$744$	3.00828	−	20.1548i	0.110289	−	0.738912i
$745$	6.07486	−	3.50732i	0.222566	−	0.128498i
$746$	0.365239	+	43.9695i	0.0133724	+	1.60984i
$747$	51.5423	−	9.24236i	1.88584	−	0.338160i
$748$	−5.17974	−	8.63696i	−0.189390	−	0.315799i
$749$	41.5307	−	1.32480i	1.51750	−	0.0484073i
$750$	1.54375	−	9.28373i	0.0563698	−	0.338994i
$751$	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
$753$	−15.6785	−	13.1172i	−0.571356	−	0.478016i
$754$	−9.75788	−	16.5815i	−0.355361	−	0.603863i
$755$		−	6.15772i		−	0.224103i
$756$	24.5047	+	12.4707i	0.891228	+	0.453556i
$757$			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
$759$	10.8574	+	9.08364i	0.394097	+	0.329715i
$760$	4.82492	−	2.94836i	0.175018	−	0.106948i
$761$	−18.2013	+	31.5257i	−0.659798	+	1.14280i	0.320869	+	0.947124i	$0.396025\pi$
$761$	−18.2013	+	31.5257i	−0.659798	+	1.14280i	−0.980668	+	0.195681i	$0.937308\pi$
$762$	−21.3016	−	3.54216i	−0.771677	−	0.128319i
$763$	−40.8227	−	21.8641i	−1.47788	−	0.791533i
$764$	14.4340	−	8.65630i	0.522202	−	0.313174i
$765$	−3.87487	+	0.694825i	−0.140096	+	0.0251215i
$766$	49.4825	−	0.411034i	1.78787	−	0.0148513i
$767$	4.47235	−	2.58211i	0.161487	−	0.0932347i
$768$	11.2234	+	25.3384i	0.404988	+	0.914322i
$769$			33.7570i			1.21731i	0.793436	+	0.608654i	$0.208290\pi$

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)

\(f(q)\)	\(=\)	\(q+(0.717256 + 1.21883i) q^{2} +(1.11142 - 1.32844i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(0.337879 + 0.195075i) q^{5} +(2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 + 0.0704754i) q^{8} +(-0.529502 - 2.95290i) q^{9} +O(q^{10})\)	\(q+(0.717256 + 1.21883i) q^{2} +(1.11142 - 1.32844i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(0.337879 + 0.195075i) q^{5} +(2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 + 0.0704754i) q^{8} +(-0.529502 - 2.95290i) q^{9} +(0.00458308 + 0.551736i) q^{10} +(-0.748582 - 1.29658i) q^{11} +(1.24339 + 3.23326i) 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} +(3.21929 - 2.76336i) q^{18} +(-2.56203 + 4.43756i) q^{19} +(-0.669184 + 0.401321i) q^{20} +(4.53697 + 0.644892i) q^{21} +(1.04339 - 1.84237i) q^{22} +(-4.72764 - 2.72950i) q^{23} +(-3.04897 + 3.83455i) 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} +(0.738041 + 0.607120i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(2.62258 - 5.01219i) q^{32} +(-2.55442 - 0.446598i) q^{33} +(2.34398 - 4.13891i) q^{34} +(0.0329110 + 1.03171i) q^{35} +(5.67712 + 1.94174i) q^{36} +(7.46581 + 4.31038i) q^{37} +(-7.24625 + 0.0601921i) q^{38} +(3.65399 - 4.36748i) q^{39} +(-0.969118 - 0.527771i) q^{40} +11.1607 q^{41} +(2.46815 + 5.99235i) q^{42} -4.79323i q^{43} +(2.99391 - 0.0497422i) q^{44} +(0.397129 - 1.10102i) q^{45} +(-0.0641268 - 7.71993i) q^{46} +(-2.51067 + 4.34861i) q^{47} +(-6.86055 - 0.965812i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(3.37846 - 5.96557i) q^{50} +(-5.73852 - 1.00329i) q^{51} +(-3.19263 + 5.74826i) q^{52} +(-0.499243 - 0.864715i) q^{53} +(-0.0929724 - 7.34788i) 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} +(-0.210612 + 1.33501i) q^{60} +(3.40889 - 5.90437i) q^{61} +(-5.11878 - 2.89891i) q^{62} +(5.89917 - 5.31035i) q^{63} +(7.99007 - 0.398545i) q^{64} +(1.11084 + 0.641343i) q^{65} +(-1.28784 - 3.43372i) 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} +(1.70530 + 8.31216i) q^{72} +(2.76107 - 1.59410i) q^{73} +(0.101268 + 12.1912i) q^{74} +(-8.27115 - 1.44608i) q^{75} +(-5.27078 - 8.78877i) q^{76} +(1.87018 - 3.49184i) q^{77} +(7.94406 + 1.32098i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(-0.0518426 - 1.55974i) q^{80} +(-8.43926 + 3.12713i) q^{81} +(8.00508 + 13.6030i) q^{82} +17.4548i q^{83} +(-5.53335 + 7.30630i) q^{84} -1.31222i q^{85} +(5.84213 - 3.43797i) q^{86} +(-4.59906 + 5.49710i) q^{87} +(2.20803 + 3.61339i) q^{88} +(2.54840 - 4.41396i) q^{89} +(1.62679 - 0.305678i) q^{90} +(4.58716 + 7.39053i) q^{91} +(9.36328 - 5.61532i) q^{92} +(-1.24081 + 7.09709i) q^{93} +(-7.10101 + 0.0589856i) q^{94} +(-1.73131 + 0.999573i) q^{95} +(-3.74361 - 9.05458i) 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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