LMFDB - Embedded newform 168.2.ba.c.101.16

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			101.16
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.16

$q$-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} +(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} - 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}+ \cdots + 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

Character values

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

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

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	−0.422542	−	0.906344i	$-0.638862\pi$
$5$	0.337879	−	0.195075i	0.151104	−	0.0872401i	0.573646	+	0.819103i	$0.305529\pi$
$6$	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	−0.956531	−	0.291631i	$-0.905802\pi$
$11$	−0.748582	+	1.29658i	−0.225706	+	0.390934i	0.730825	+	0.682565i	$0.239136\pi$
$12$	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	−0.994651	−	0.103293i	$-0.967062\pi$
$17$	−1.68169	+	2.91278i	−0.407871	+	0.706453i	0.586780	+	0.809746i	$0.300395\pi$
$18$	3.21929	+	2.76336i	0.758795	+	0.651330i
$19$	−2.56203	−	4.43756i	−0.587769	−	1.01805i	−0.994524	−	0.104509i	$-0.966673\pi$
$19$	−2.56203	−	4.43756i	−0.587769	−	1.01805i	0.406755	−	0.913537i	$-0.366660\pi$
$20$	−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	−0.904010	−	0.427511i	$-0.859391\pi$
$23$	−4.72764	+	2.72950i	−0.985780	+	0.569141i	−0.0817700	+	0.996651i	$0.526057\pi$
$24$	−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	0.140303	−	0.990109i	$-0.455192\pi$
$31$	−3.60237	−	2.07983i	−0.647005	−	0.373549i	−0.787308	+	0.616560i	$0.788526\pi$
$32$	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	0.260892	−	0.965368i	$-0.415983\pi$
$37$	7.46581	−	4.31038i	1.22737	−	0.708623i	0.966479	+	0.256745i	$0.0826501\pi$
$38$	−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	$0.119095\pi$
$43$			4.79323i			0.730961i	−0.930819	+	0.365480i	$0.880905\pi$
$44$	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	0.622752	−	0.782419i	$-0.286015\pi$
$47$	−2.51067	−	4.34861i	−0.366219	−	0.634310i	−0.988971	+	0.148109i	$0.952681\pi$
$48$	−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	−0.898275	−	0.439434i	$-0.855179\pi$
$53$	−0.499243	+	0.864715i	−0.0685763	+	0.118778i	0.829699	+	0.558212i	$0.188512\pi$
$54$	−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	0.585930	−	0.810362i	$-0.300729\pi$
$59$	1.36034	+	0.785391i	0.177101	+	0.102249i	−0.408829	+	0.912611i	$0.634063\pi$
$60$	−0.210612	−	1.33501i	−0.0271899	−	0.172349i
$61$	3.40889	+	5.90437i	0.436464	+	0.755977i	0.997414	−	0.0718723i	$-0.0228974\pi$
$61$	3.40889	+	5.90437i	0.436464	+	0.755977i	−0.560950	+	0.827850i	$0.689564\pi$
$62$	−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	0.674850	−	0.737955i	$-0.264208\pi$
$67$	3.05467	+	1.76361i	0.373187	+	0.215460i	−0.301663	+	0.953415i	$0.597542\pi$
$68$	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	$-0.323812\pi$
$72$	1.70530	−	8.31216i	0.200971	−	0.979597i
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	0.652800	−	0.757531i	$-0.273594\pi$
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	−0.329641	+	0.944106i	$0.606928\pi$
$74$	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	0.852243	−	0.523146i	$-0.175242\pi$
$79$	−0.239413	−	0.414676i	−0.0269361	−	0.0466547i	−0.879179	+	0.476491i	$0.841908\pi$
$80$	−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	$-0.592628\pi$
$83$		−	17.4548i		−	1.91591i	0.286911	−	0.957957i	$-0.407372\pi$
$84$	−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	0.968895	−	0.247473i	$-0.0796000\pi$
$89$	2.54840	+	4.41396i	0.270130	+	0.467879i	−0.698765	+	0.715351i	$0.746267\pi$
$90$	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	$-0.848944\pi$
$97$		−	9.00074i		−	0.913887i	0.889496	−	0.456943i	$-0.151056\pi$
$98$	−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	$-0.419203\pi$
$101$	−4.63907	−	2.67837i	−0.461605	−	0.266508i	−0.712719	+	0.701450i	$0.752536\pi$
$102$	−2.89315	+	7.71388i	−0.286464	+	0.763788i
$103$	7.70831	−	4.45039i	0.759522	−	0.438510i	−0.0696021	−	0.997575i	$-0.522173\pi$
$103$	7.70831	−	4.45039i	0.759522	−	0.438510i	0.829124	+	0.559065i	$0.188840\pi$
$104$	−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	0.943292	+	0.331964i	$0.107711\pi$
$107$	7.85256	+	13.6010i	0.759135	+	1.31486i	−0.184157	+	0.982897i	$0.558955\pi$
$108$	8.88913	+	5.38363i	0.855357	+	0.518040i
$109$	−15.1582	−	8.75159i	−1.45189	−	0.838250i	−0.453303	−	0.891357i	$-0.649754\pi$
$109$	−15.1582	−	8.75159i	−1.45189	−	0.838250i	−0.998589	+	0.0531069i	$0.983088\pi$
$110$	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	$-0.00108718\pi$
$114$	−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	−0.297200	−	0.954815i	$-0.596053\pi$
$131$	4.36183	−	2.51830i	0.381095	−	0.220025i	0.678294	+	0.734790i	$0.262719\pi$
$132$	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	0.203690	−	0.979035i	$-0.434707\pi$
$137$	−6.34787	−	3.66494i	−0.542335	−	0.313117i	−0.746025	+	0.665918i	$0.768040\pi$
$138$	−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	0.954078	+	0.299559i	$0.0968395\pi$
$149$	8.98969	+	15.5706i	0.736464	+	1.27559i	−0.217613	+	0.976035i	$0.569827\pi$
$150$	−4.17001	+	11.1183i	−0.340480	+	0.907807i
$151$	−7.89149	+	13.6685i	−0.642201	+	1.11232i	0.342740	+	0.939430i	$0.388645\pi$
$151$	−7.89149	+	13.6685i	−0.642201	+	1.11232i	−0.984940	+	0.172894i	$0.944688\pi$
$152$	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	−0.949216	−	0.314625i	$-0.898121\pi$
$157$	−2.53274	+	4.38683i	−0.202134	+	0.350107i	0.747082	+	0.664732i	$0.231454\pi$
$158$	−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	−0.861243	−	0.508193i	$-0.830314\pi$
$163$	−10.8745	+	6.27840i	−0.851757	+	0.491762i	0.00948597	+	0.999955i	$0.496980\pi$
$164$	−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	0.207952	−	0.978139i	$-0.433320\pi$
$173$	15.2445	−	8.80144i	1.15902	−	0.669161i	0.951069	+	0.308978i	$0.0999870\pi$
$174$	−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	−0.385016	−	0.922910i	$-0.625804\pi$
$179$	8.11784	−	14.0605i	0.606756	−	1.05093i	0.991771	−	0.128022i	$-0.0408627\pi$
$180$	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	−0.739930	−	0.672684i	$-0.765141\pi$
$191$	−7.28788	+	4.20766i	−0.527333	+	0.304456i	0.212597	+	0.977140i	$0.431808\pi$
$192$	8.35086	+	11.0573i	0.602671	+	0.797990i
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	−0.526370	−	0.850256i	$-0.676447\pi$
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	0.999528	+	0.0307215i	$0.00978048\pi$
$194$	−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	0.965801	−	0.259284i	$-0.0834864\pi$
$199$	17.2688	+	9.97017i	1.22416	+	0.706767i	0.258354	+	0.966050i	$0.416820\pi$
$200$	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	$0.166541\pi$
$211$			14.5159i			0.999314i	−0.866223	+	0.499657i	$0.833459\pi$
$212$	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	$-0.970339\pi$
$223$		−	2.77897i		−	0.186093i	0.995662	−	0.0930467i	$-0.0296606\pi$
$224$	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	$-0.514213\pi$
$227$	−14.0438	−	8.10819i	−0.932119	−	0.538159i	−0.887481	+	0.460844i	$0.847547\pi$
$228$	−17.5334	+	2.76608i	−1.16118	+	0.183188i
$229$	10.3150	+	17.8661i	0.681633	+	1.18062i	0.974482	+	0.224464i	$0.0720633\pi$
$229$	10.3150	+	17.8661i	0.681633	+	1.18062i	−0.292849	+	0.956159i	$0.594603\pi$
$230$	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	−0.557946	−	0.829877i	$-0.688411\pi$
$233$	−1.80462	+	1.04190i	−0.118225	+	0.0682572i	0.439721	+	0.898134i	$0.355077\pi$
$234$	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	$0.00876990\pi$
$239$			0.851762i			0.0550959i	−0.999620	+	0.0275480i	$0.991230\pi$
$240$	−2.12963	+	1.66465i	−0.137467	+	0.107453i
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	0.857294	−	0.514827i	$-0.172144\pi$
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	−0.0172066	+	0.999852i	$0.505477\pi$
$242$	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	$0.121490\pi$
$251$			11.8022i			0.744948i	−0.928043	+	0.372474i	$0.878510\pi$
$252$	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	−0.998039	−	0.0626011i	$-0.980060\pi$
$257$	−8.86901	−	15.3616i	−0.553233	−	0.958228i	0.444805	−	0.895627i	$-0.353273\pi$
$258$	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	0.680915	−	0.732363i	$-0.261582\pi$
$263$	6.27815	+	3.62469i	0.387128	+	0.223508i	−0.293787	+	0.955871i	$0.594916\pi$
$264$	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	0.407100	−	0.913383i	$-0.366540\pi$
$269$	−2.95817	−	1.70790i	−0.180363	−	0.104132i	−0.587463	+	0.809251i	$0.699873\pi$
$270$	1.40197	+	2.50083i	0.0853213	+	0.152196i
$271$	3.96989	−	2.29201i	0.241153	−	0.139230i	−0.374553	−	0.927205i	$-0.622204\pi$
$271$	3.96989	−	2.29201i	0.241153	−	0.139230i	0.615707	+	0.787975i	$0.288871\pi$
$272$	−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	0.143050	−	0.989715i	$-0.454309\pi$
$277$	−10.6940	−	6.17421i	−0.642543	−	0.370972i	−0.785593	+	0.618743i	$0.787642\pi$
$278$	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	$0.924129\pi$
$282$	−7.81383	−	9.49882i	−0.465307	−	0.565646i
$283$	−11.3552	+	19.6678i	−0.674999	+	1.16913i	0.301471	+	0.953475i	$0.402522\pi$
$283$	−11.3552	+	19.6678i	−0.674999	+	1.16913i	−0.976469	+	0.215656i	$0.930811\pi$
$284$	−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	$-0.877777\pi$
$293$		−	12.8246i		−	0.749220i	0.927183	−	0.374610i	$-0.122223\pi$
$294$	−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	−0.844865	−	0.534980i	$-0.820319\pi$
$311$	0.720819	−	1.24850i	0.0408739	−	0.0707957i	0.885739	+	0.464184i	$0.153652\pi$
$312$	−10.0240	−	12.6068i	−0.567498	−	0.713719i
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.956092	−	0.293067i	$-0.905324\pi$
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.224242	+	0.974533i	$0.571991\pi$
$314$	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	−0.944639	−	0.328111i	$-0.893588\pi$
$317$	−13.4686	−	23.3283i	−0.756472	−	1.31025i	0.188167	−	0.982137i	$-0.439745\pi$
$318$	−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	−0.857185	−	0.515009i	$-0.827788\pi$
$331$	−15.2782	+	8.82087i	−0.839766	+	0.484839i	0.0174189	+	0.999848i	$0.494455\pi$
$332$	−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	0.413940	+	0.910304i	$0.364152\pi$
$347$	−10.8299	+	18.7579i	−0.581377	+	1.00697i	−0.995316	+	0.0966701i	$0.969181\pi$
$348$	−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	−0.123659	−	0.992325i	$-0.539463\pi$
$353$	14.9846	−	25.9541i	0.797549	−	1.38140i	0.921208	−	0.389071i	$-0.127204\pi$
$354$	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	−0.229628	−	0.973278i	$-0.573751\pi$
$359$	9.44412	−	5.45257i	0.498442	−	0.287775i	0.728070	+	0.685503i	$0.240418\pi$
$360$	−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	0.435085	−	0.900389i	$-0.356718\pi$
$367$	−2.43552	−	1.40615i	−0.127133	−	0.0734002i	−0.562218	+	0.826989i	$0.690052\pi$
$368$	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	0.400431	−	0.916327i	$-0.368860\pi$
$373$	26.9266	−	15.5461i	1.39421	−	0.804947i	0.993778	+	0.111380i	$0.0355271\pi$
$374$	−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	$-0.849830\pi$
$379$		−	17.6950i		−	0.908931i	0.890764	−	0.454465i	$-0.150170\pi$
$380$	−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	0.835076	+	0.550134i	$0.185423\pi$
$383$	17.4953	+	30.3028i	0.893968	+	1.54840i	0.0588917	+	0.998264i	$0.481243\pi$
$384$	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	−0.469971	−	0.882682i	$-0.655736\pi$
$389$	10.4422	−	18.0864i	0.529439	−	0.917015i	0.999410	−	0.0343338i	$-0.0109309\pi$
$390$	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	0.920825	−	0.389977i	$-0.127517\pi$
$397$	2.44443	+	4.23387i	0.122682	+	0.212492i	−0.798142	+	0.602469i	$0.794184\pi$
$398$	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	−0.325416	−	0.945571i	$-0.605504\pi$
$401$	6.62355	−	3.82411i	0.330764	−	0.190967i	0.656180	+	0.754604i	$0.272171\pi$
$402$	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	0.326061	−	0.945349i	$-0.394279\pi$
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	−0.655666	+	0.755051i	$0.727612\pi$
$410$	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	$-0.965861\pi$
$419$		−	4.38235i		−	0.214092i	0.994254	−	0.107046i	$-0.0341392\pi$
$420$	−3.29488	−	1.38923i	−0.160774	−	0.0677876i
$421$		−	11.9400i		−	0.581921i	−0.956735	−	0.290961i	$-0.906025\pi$
$421$		−	11.9400i		−	0.581921i	0.956735	−	0.290961i	$-0.0939749\pi$
$422$	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	0.485749	−	0.874098i	$-0.338547\pi$
$431$	−0.588922	−	0.340014i	−0.0283674	−	0.0163779i	−0.514117	+	0.857720i	$0.671880\pi$
$432$	0.780729	−	20.7699i	0.0375628	−	0.999294i
$433$		−	0.238499i		−	0.0114615i	−0.999984	−	0.00573077i	$-0.998176\pi$
$433$		−	0.238499i		−	0.0114615i	0.999984	−	0.00573077i	$-0.00182417\pi$
$434$	−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	−0.419205	−	0.907892i	$-0.637691\pi$
$439$	3.29894	−	1.90465i	0.157450	−	0.0909038i	0.576655	+	0.816988i	$0.304358\pi$
$440$	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	0.928807	−	0.370565i	$-0.120836\pi$
$443$	3.02001	+	5.23080i	0.143485	+	0.248523i	−0.785322	+	0.619088i	$0.787503\pi$
$444$	−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	$0.231226\pi$
$449$			28.1482i			1.32839i	−0.747558	+	0.664197i	$0.768774\pi$
$450$	−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	0.682612	−	0.730781i	$-0.260844\pi$
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	−0.974181	+	0.225768i	$0.927511\pi$
$458$	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	$0.263460\pi$
$461$			31.6209i			1.47273i	−0.676583	+	0.736367i	$0.736540\pi$
$462$	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	−0.765357	−	0.643606i	$-0.777438\pi$
$467$	−12.7642	+	7.36942i	−0.590657	+	0.341016i	0.174700	+	0.984622i	$0.444104\pi$
$468$	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	0.134979	+	0.990848i	$0.456903\pi$
$479$	−17.3034	+	29.9703i	−0.790611	+	1.36938i	−0.925589	+	0.378529i	$0.876430\pi$
$480$	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	0.453545	+	0.891233i	$0.350159\pi$
$487$	−12.0284	+	20.8338i	−0.545058	+	0.944068i	−0.998603	+	0.0528351i	$0.983174\pi$
$488$	−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	0.108548	−	0.994091i	$-0.465380\pi$
$499$	22.8684	−	13.2031i	1.02373	−	0.591051i	0.915182	+	0.403040i	$0.132047\pi$
$500$	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	−0.0340991	−	0.999418i	$-0.510856\pi$
$509$	18.3731	−	10.6077i	0.814373	−	0.470179i	0.848472	+	0.529240i	$0.177523\pi$
$510$	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	−0.965974	−	0.258638i	$-0.916726\pi$
$521$	−5.91179	+	10.2395i	−0.259000	+	0.448601i	0.706974	+	0.707239i	$0.250060\pi$
$522$	−13.3215	−	11.4348i	−0.583065	−	0.500488i
$523$	3.37960	+	5.85364i	0.147780	+	0.255962i	0.930407	−	0.366529i	$-0.119454\pi$
$523$	3.37960	+	5.85364i	0.147780	+	0.255962i	−0.782627	+	0.622491i	$0.786121\pi$
$524$	−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	−0.791648	−	0.610977i	$-0.790777\pi$
$541$	−15.3128	+	8.84087i	−0.658351	+	0.380099i	0.133298	+	0.991076i	$0.457443\pi$
$542$	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	$-0.989802\pi$
$547$		−	1.49834i		−	0.0640644i	0.999487	−	0.0320322i	$-0.0101979\pi$
$548$	−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	−0.895450	−	0.445161i	$-0.853146\pi$
$557$	−1.46808	+	2.54278i	−0.0622044	+	0.107741i	0.833246	+	0.552902i	$0.186480\pi$
$558$	−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	0.771664	−	0.636031i	$-0.219425\pi$
$563$	14.3950	+	8.31096i	0.606677	+	0.350265i	−0.164987	+	0.986296i	$0.552758\pi$
$564$	−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	−0.0397194	−	0.999211i	$-0.512646\pi$
$569$	19.2204	−	11.0969i	0.805763	−	0.465207i	0.845482	+	0.534003i	$0.179313\pi$
$570$	−4.58501	−	1.71964i	−0.192045	−	0.0720279i
$571$	5.22532	+	3.01684i	0.218673	+	0.126251i	0.605336	−	0.795970i	$-0.293039\pi$
$571$	5.22532	+	3.01684i	0.218673	+	0.126251i	−0.386663	+	0.922221i	$0.626372\pi$
$572$	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	0.0905396	−	0.995893i	$-0.471141\pi$
$577$	−17.4549	−	10.0776i	−0.726659	−	0.419537i	−0.817199	+	0.576356i	$0.804474\pi$
$578$	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	$-0.997571\pi$
$587$		−	0.369829i		−	0.0152645i	0.999971	−	0.00763224i	$-0.00242944\pi$
$588$	−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	0.948820	−	0.315818i	$-0.102279\pi$
$593$	4.89233	+	8.47376i	0.200904	+	0.347976i	−0.747916	+	0.663793i	$0.768945\pi$
$594$	−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	0.976284	−	0.216494i	$-0.0694621\pi$
$599$	31.2524	+	18.0436i	1.27694	+	0.737240i	0.300653	+	0.953734i	$0.402795\pi$
$600$	23.4890	−	3.50594i	0.958934	−	0.143129i
$601$			9.75944i			0.398096i	0.979990	+	0.199048i	$0.0637849\pi$
$601$			9.75944i			0.398096i	−0.979990	+	0.199048i	$0.936215\pi$
$602$	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	−0.641461	−	0.767155i	$-0.721672\pi$
$607$	−7.33740	+	4.23625i	−0.297816	+	0.171944i	0.343645	+	0.939099i	$0.388338\pi$
$608$	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	0.279737	−	0.960077i	$-0.409753\pi$
$613$	−10.1968	−	5.88712i	−0.411844	−	0.237779i	−0.691582	+	0.722298i	$0.743086\pi$
$614$	−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	$0.885246\pi$
$618$	16.8375	−	13.8507i	0.677304	−	0.557157i
$619$	12.8081	−	22.1843i	0.514801	−	0.891661i	−0.485052	−	0.874485i	$-0.661199\pi$
$619$	12.8081	−	22.1843i	0.514801	−	0.891661i	0.999852	−	0.0171755i	$-0.00546739\pi$
$620$	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	0.245306	−	0.969446i	$-0.421112\pi$
$641$	−11.9401	−	6.89362i	−0.471606	−	0.272282i	−0.716912	+	0.697164i	$0.754445\pi$
$642$	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	−0.352838	−	0.935684i	$-0.614783\pi$
$647$	16.1242	−	27.9279i	0.633907	−	1.09796i	0.986746	−	0.162275i	$-0.0518832\pi$
$648$	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	0.602838	−	0.797864i	$-0.294037\pi$
$653$	−9.95455	−	17.2418i	−0.389552	−	0.674723i	−0.992389	+	0.123141i	$0.960703\pi$
$654$	−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	−0.907491	−	0.420071i	$-0.862005\pi$
$661$	−2.31268	+	4.00568i	−0.0899529	+	0.155803i	0.817538	+	0.575875i	$0.195338\pi$
$662$	−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	−0.993557	−	0.113332i	$-0.963848\pi$
$677$	−36.2236	+	20.9137i	−1.39219	+	0.803780i	−0.398630	+	0.917112i	$0.630514\pi$
$678$	−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	−0.707960	−	0.706253i	$-0.750384\pi$
$683$	6.73357	−	11.6629i	0.257653	−	0.446268i	0.965613	+	0.259985i	$0.0837176\pi$
$684$	−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	0.995581	+	0.0939090i	$0.0299363\pi$
$691$	15.2232	+	26.3674i	0.579118	+	1.00306i	−0.416463	+	0.909153i	$0.636730\pi$
$692$	−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	−0.999829	−	0.0184810i	$-0.994117\pi$
$709$	−39.5076	+	22.8097i	−1.48374	+	0.856637i	−0.483910	+	0.875118i	$0.660784\pi$
$710$	−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	0.666587	−	0.745428i	$-0.267755\pi$
$719$	−8.37315	−	14.5027i	−0.312266	−	0.540860i	−0.978853	+	0.204567i	$0.934421\pi$
$720$	−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	$0.0879705\pi$
$727$			14.7144i			0.545726i	−0.962053	+	0.272863i	$0.912029\pi$
$728$	−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	−0.987082	−	0.160213i	$-0.948782\pi$
$733$	−17.1186	−	29.6503i	−0.632290	−	1.09516i	0.354793	−	0.934945i	$-0.384551\pi$
$734$	−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	0.535071	−	0.844807i	$-0.320285\pi$
$739$	1.92964	+	1.11408i	0.0709829	+	0.0409820i	−0.464089	+	0.885789i	$0.653618\pi$
$740$	−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	$-0.0874914\pi$
$744$	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	0.979087	+	0.203442i	$0.0652128\pi$
$751$	18.2439	+	31.5994i	0.665729	+	1.15308i	−0.313358	+	0.949635i	$0.601454\pi$
$752$	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	$-0.881872\pi$
$757$		−	19.9557i		−	0.725302i	0.931925	−	0.362651i	$-0.118128\pi$
$758$	−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	−0.980668	−	0.195681i	$-0.937308\pi$
$761$	−18.2013	−	31.5257i	−0.659798	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$762$	−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	$-0.791710\pi$
$769$		−	33.7570i		−	1.21731i	0.793436	−	0.608654i	$-0.208290\pi$
$770$	1.93514	−	1.01584i	0.0697377	−	0.0366084i
$771$	10.5497	−	28.8551i	0.379940	−	1.03919i
$772$	−26.2897	−	0.436789i	−0.946186	−	0.0157204i
$773$	−35.3297	−	20.3976i	−1.27072	−	0.733651i	−0.295597	−	0.955313i	$-0.595519\pi$
$773$	−35.3297	−	20.3976i	−1.27072	−	0.733651i	−0.975124	+	0.221662i	$0.928852\pi$
$774$	−13.2454	+	15.4308i	−0.476096	+	0.554649i
$775$	17.4635	−	10.0826i	0.627308	−	0.362176i
$776$	−0.634331	+	25.4500i	−0.0227711	+	0.913603i
$777$	31.0924	−	24.3707i	1.11543	−	0.874295i
$778$	−14.5545	−	25.6998i	−0.521804	−	0.921382i
$779$	−28.5940	−	49.5263i	−1.02449	−	1.77446i
$780$	−0.692425	−	4.38907i	−0.0247928	−	0.157154i
$781$	18.5878	+	10.7317i	0.665123	+	0.384009i
$782$	−22.3786	−	13.1694i	−0.800258	−	0.470935i
$783$	18.6676	−	10.6698i	0.667126	−	0.381309i
$784$	27.8684	+	2.71183i	0.995299	+	0.0968509i
$785$			1.97629i			0.0705368i
$786$	9.52768	−	7.83757i	0.339841	−	0.279557i
$787$	5.80545	−	10.0553i	0.206942	−	0.358434i	−0.743808	−	0.668394i	$-0.766982\pi$
$787$	5.80545	−	10.0553i	0.206942	−	0.358434i	0.950750	+	0.309960i	$0.100316\pi$
$788$	17.1027	+	30.7931i	0.609259	+	1.09696i
$789$	2.16246	+	12.3687i	0.0769858	+	0.440337i
$790$	−0.229889	+	0.130192i	−0.00817908	+	0.00463204i
$791$	−0.163233	−	0.101315i	−0.00580389	−	0.00360236i
$792$	9.50084	+	8.43339i	0.337597	+	0.299667i
$793$	11.2073	+	19.4117i	0.397984	+	0.689329i
$794$	6.91365	+	0.0574292i	0.245356	+	0.00203809i
$795$	−0.517505	+	0.432963i	−0.0183540	+	0.0153556i
$796$	0.662504	−	39.8752i	0.0234818	−	1.41334i
$797$		−	9.90792i		−	0.350956i	−0.984483	−	0.175478i	$-0.943853\pi$
$797$		−	9.90792i		−	0.350956i	0.984483	−	0.175478i	$-0.0561472\pi$
$798$	−32.9149	+	4.39996i	−1.16517	+	0.155757i
$799$	16.8887			0.597481
$800$	−27.3996	−	1.13862i	−0.968721	−	0.0402563i
$801$	−14.3834	+	5.18797i	−0.508211	+	0.183308i
$802$	0.0898434	−	10.8158i	0.00317248	−	0.381920i
$803$	−4.13377	+	2.38664i	−0.145878	+	0.0842225i
$804$	9.50036	−	7.68368i	0.335052	−	0.270982i
$805$	2.66047	+	4.96740i	0.0937694	+	0.175078i
$806$	−16.8289	+	9.53067i	−0.592773	+	0.335704i
$807$	−1.01892	−	5.82793i	−0.0358677	−	0.205153i
$808$	12.9284	+	7.90016i	0.454821	+	0.277927i
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	0.730708	−	0.682690i	$-0.239190\pi$
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	−0.225873	+	0.974157i	$0.572523\pi$
$810$	−1.76403	+	4.64191i	−0.0619817	+	0.163100i
$811$	−49.5706			−1.74066			−0.870330	−	0.492470i	$-0.836094\pi$
$811$	−49.5706			−1.74066			−0.870330	+	0.492470i	$0.836094\pi$
$812$	21.8706	+	1.06159i	0.767506	+	0.0372544i
$813$	7.45700	+	2.72637i	0.261528	+	0.0956179i
$814$	15.7311	+	9.25740i	0.551374	+	0.324472i
$815$	−2.44952	+	4.24268i	−0.0858028	+	0.148615i
$816$	8.72416	−	21.6075i	0.305407	−	0.756413i
$817$	21.2702	−	12.2804i	0.744151	−	0.429636i
$818$	−9.47180	+	5.36414i	−0.331174	+	0.187553i
$819$	19.3946	+	17.4587i	0.677702	+	0.610057i
$820$	−7.46857	−	4.47903i	−0.260814	−	0.156415i
$821$	26.4055	+	45.7357i	0.921559	+	1.59619i	0.797004	+	0.603973i	$0.206417\pi$
$821$	26.4055	+	45.7357i	0.921559	+	1.59619i	0.124554	+	0.992213i	$0.460250\pi$
$822$	−16.8110	−	6.30508i	−0.586350	−	0.219915i
$823$	12.3351	−	21.3650i	0.429975	−	0.744739i	−0.566896	−	0.823790i	$-0.691856\pi$
$823$	12.3351	−	21.3650i	0.429975	−	0.744739i	0.996871	+	0.0790510i	$0.0251890\pi$
$824$	−22.1093	+	12.0405i	−0.770212	+	0.419449i
$825$	4.31668	−	11.8067i	0.150287	−	0.411057i
$826$	0.236176	−	5.87258i	0.00821760	−	0.204333i
$827$	23.0662			0.802091			0.401045	−	0.916058i	$-0.368647\pi$
$827$	23.0662			0.802091			0.401045	+	0.916058i	$0.368647\pi$
$828$	−21.5394	+	24.6755i	−0.748545	+	0.857534i
$829$	−12.2068	+	21.1429i	−0.423961	+	0.734322i	−0.996323	−	0.0856795i	$-0.972694\pi$
$829$	−12.2068	+	21.1429i	−0.423961	+	0.734322i	0.572362	+	0.820001i	$0.306027\pi$
$830$	−9.63044	−	0.0799967i	−0.334278	−	0.00277673i
$831$	−3.68349	−	21.0685i	−0.127779	−	0.730859i
$832$	26.2688	+	1.31029i	0.910706	+	0.0454261i
$833$	23.4959	+	1.50053i	0.814083	+	0.0519904i
$834$	38.0561	−	6.32818i	1.31778	−	0.219127i
$835$	−2.51093	+	1.44969i	−0.0868944	+	0.0501685i
$836$	−7.44975	−	13.4131i	−0.257655	−	0.463902i
$837$	21.6140	+	0.0939312i	0.747090	+	0.00324674i
$838$	−5.34133	−	3.14326i	−0.184513	−	0.108582i
$839$	−48.3464			−1.66910			−0.834551	−	0.550931i	$-0.814273\pi$
$839$	−48.3464			−1.66910			−0.834551	+	0.550931i	$0.814273\pi$
$840$	−4.05651	+	3.01946i	−0.139963	+	0.104181i
$841$	−11.8768			−0.409546
$842$	−14.5529	−	8.56405i	−0.501525	−	0.295137i
$843$	−10.5155	+	8.79760i	−0.362172	+	0.303005i
$844$	25.3799	−	14.0962i	0.873613	−	0.485212i
$845$	−0.740348	+	0.427440i	−0.0254688	+	0.0147044i
$846$	3.93418	−	20.9373i	0.135260	−	0.719841i
$847$	23.1610	+	0.738822i	0.795823	+	0.0253862i
$848$	−1.88097	−	3.52329i	−0.0645927	−	0.120990i
$849$	−38.7479	+	6.77445i	−1.32983	+	0.232498i
$850$	−23.0579	−	0.191534i	−0.790880	−	0.00656957i
$851$	−23.5304	+	40.7559i	−0.806612	+	1.39709i
$852$	−46.3520	−	17.8252i	−1.58799	−	0.610682i
$853$	34.6867			1.18765			0.593825	−	0.804595i	$-0.297617\pi$
$853$	34.6867			1.18765			0.593825	+	0.804595i	$0.297617\pi$
$854$	13.6324	−	21.5617i	0.466489	−	0.737828i
$855$	3.86837	−	4.58312i	0.132296	−	0.156739i
$856$	−21.2450	−	39.0110i	−0.726138	−	1.33337i
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	−0.621786	−	0.783187i	$-0.713593\pi$
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	0.989153	+	0.146889i	$0.0469262\pi$
$858$	−4.23402	+	11.2890i	−0.144547	+	0.385400i
$859$	−0.332259	−	0.575490i	−0.0113365	−	0.0196355i	0.860301	−	0.509786i	$-0.170275\pi$
$859$	−0.332259	−	0.575490i	−0.0113365	−	0.0196355i	−0.871638	+	0.490150i	$0.836942\pi$
$860$	1.92363	−	3.20755i	0.0655951	−	0.109377i
$861$	50.6358	−	7.19745i	1.72566	−	0.245289i
$862$	−0.836827	+	0.473918i	−0.0285025	+	0.0161417i
$863$	−14.2150	+	8.20702i	−0.483883	+	0.279370i	−0.722033	−	0.691858i	$-0.756792\pi$
$863$	−14.2150	+	8.20702i	−0.483883	+	0.279370i	0.238150	+	0.971228i	$0.423459\pi$
$864$	−24.7550	−	15.8489i	−0.842183	−	0.539192i
$865$	3.43388	−	5.94765i	0.116755	−	0.202226i
$866$	−0.290690	−	0.171065i	−0.00987805	−	0.00581303i
$867$	−3.38273	+	9.25225i	−0.114884	+	0.314223i
$868$	18.5060	+	11.9167i	0.628134	+	0.404478i
$869$	0.716882			0.0243186
$870$	−3.05402	+	2.51227i	−0.103541	+	0.0851740i
$871$	10.0428	+	5.79819i	0.340286	+	0.196464i
$872$	42.2438	+	25.8138i	1.43055	+	0.874166i
$873$	26.5783	+	4.76591i	0.899539	+	0.161302i
$874$	34.4219	−	19.4941i	1.16434	−	0.659398i
$875$	8.63685	+	5.36073i	0.291979	+	0.181226i
$876$	8.58724	−	6.94517i	0.290136	−	0.234655i
$877$	−11.1473	+	6.43591i	−0.376419	+	0.217325i	−0.676259	−	0.736664i	$-0.736400\pi$
$877$	−11.1473	+	6.43591i	−0.376419	+	0.217325i	0.299840	+	0.953989i	$0.403067\pi$
$878$	0.0447477	−	5.38697i	0.00151016	−	0.181801i
$879$	17.0367	−	14.2535i	0.574633	−	0.480757i
$880$	−1.98352	−	1.23481i	−0.0668644	−	0.0416254i
$881$	42.1373			1.41964			0.709821	−	0.704382i	$-0.248776\pi$
$881$	42.1373			1.41964			0.709821	+	0.704382i	$0.248776\pi$
$882$	7.33353	−	28.7788i	0.246933	−	0.969033i
$883$		−	14.3108i		−	0.481596i	−0.970575	−	0.240798i	$-0.922591\pi$
$883$		−	14.3108i		−	0.481596i	0.970575	−	0.240798i	$-0.0774091\pi$
$884$	22.1124	+	0.367386i	0.743722	+	0.0123565i
$885$	0.681121	+	0.814120i	0.0228956	+	0.0273664i
$886$	8.54157	+	0.0709519i	0.286960	+	0.00238367i
$887$	−3.93855	−	6.82176i	−0.132243	−	0.229052i	0.792298	−	0.610135i	$-0.208885\pi$
$887$	−3.93855	−	6.82176i	−0.132243	−	0.229052i	−0.924541	+	0.381082i	$0.875551\pi$
$888$	−39.2914	−	15.4858i	−1.31853	−	0.519670i
$889$	−12.3003	+	19.8174i	−0.412538	+	0.664653i
$890$	2.44702	−	1.38581i	0.0820242	−	0.0464526i
$891$	10.3721	−	8.60127i	0.347477	−	0.288153i
$892$	−4.85881	+	2.69862i	−0.162685	+	0.0903566i
$893$	−12.8648	+	22.2825i	−0.430505	+	0.745656i
$894$	27.9781	+	34.0114i	0.935729	+	1.13751i
$895$		−	6.33434i		−	0.211734i
$896$	−12.5752	−	27.1636i	−0.420109	−	0.907474i
$897$	−29.1958	−	10.6743i	−0.974818	−	0.356405i
$898$	34.3078	+	20.1894i	1.14487	+	0.673730i
$899$	14.9067	+	8.60636i	0.497165	+	0.287038i
$900$	−5.60872	+	28.5408i	−0.186957	+	0.951361i
$901$	−1.67915	−	2.90837i	−0.0559406	−	0.0968919i
$902$	11.6449	+	20.5622i	0.387734	+	0.684646i
$903$	3.09112	+	21.7467i	0.102866	+	0.723686i
$904$	−0.00511751	+	0.205320i	−0.000170206	+	0.00682885i
$905$	−2.09262	+	1.20818i	−0.0695611	+	0.0401611i
$906$	−13.5763	+	36.1981i	−0.451044	+	1.20260i
$907$	−24.8886	−	14.3694i	−0.826413	−	0.477130i	0.0262101	−	0.999656i	$-0.491656\pi$
$907$	−24.8886	−	14.3694i	−0.826413	−	0.477130i	−0.852623	+	0.522527i	$0.824989\pi$
$908$	−0.538778	+	32.4283i	−0.0178800	+	1.07617i
$909$	10.3654	−	12.2805i	0.343797	−	0.407319i
$910$	−4.05659	−	2.56477i	−0.134475	−	0.0850213i
$911$			4.32207i			0.143197i	0.997434	+	0.0715983i	$0.0228100\pi$
$911$			4.32207i			0.143197i	−0.997434	+	0.0715983i	$0.977190\pi$
$912$	21.8628	+	27.9697i	0.723949	+	0.926169i
$913$	22.6316	+	13.0664i	0.748996	+	0.432433i
$914$	−17.6291	−	0.146439i	−0.583119	−	0.00484377i
$915$	0.793454	+	4.53834i	0.0262308	+	0.150033i
$916$	21.2207	−	35.3845i	0.701152	−	1.16914i
$917$	0.424862	−	13.3188i	0.0140302	−	0.439826i
$918$	−21.2464	−	12.6277i	−0.701236	−	0.416776i
$919$	18.1008	+	31.3515i	0.597089	+	1.03419i	0.993248	+	0.116007i	$0.0370095\pi$
$919$	18.1008	+	31.3515i	0.597089	+	1.03419i	−0.396159	+	0.918182i	$0.629657\pi$
$920$	3.14109	−	5.14032i	0.103559	−	0.169471i
$921$	−13.7396	−	16.4225i	−0.452735	−	0.541138i
$922$	38.5405	+	22.6803i	1.26926	+	0.746935i
$923$		−	47.1321i		−	1.55137i
$924$	13.6154	−	1.70507i	0.447913	−	0.0560928i
$925$			41.7916i			1.37410i
$926$	16.8623	−	28.6541i	0.554131	−	0.941632i
$927$	9.06001	+	25.1184i	0.297570	+	0.824995i
$928$	−10.8523	−	20.7405i	−0.356243	−	0.680841i
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	0.859881	−	0.510494i	$-0.170537\pi$
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	−0.872041	+	0.489432i	$0.837204\pi$
$930$	−3.92140	+	0.652073i	−0.128588	+	0.0213823i
$931$	−19.8775	+	29.8567i	−0.651458	+	0.978515i
$932$	3.57413	+	2.14347i	0.117075	+	0.0702117i
$933$	2.45968	−	0.430035i	0.0805264	−	0.0140787i
$934$	−0.173137	+	20.8431i	−0.00566521	+	0.682008i
$935$	−1.70141	−	0.982307i	−0.0556419	−	0.0321249i
$936$	5.60648	−	27.3277i	0.183253	−	0.893234i
$937$			49.0746i			1.60320i	0.597863	+	0.801598i	$0.296017\pi$
$937$			49.0746i			1.60320i	−0.597863	+	0.801598i	$0.703983\pi$
$938$	0.530338	−	13.1870i	0.0173161	−	0.430571i
$939$	−39.2250	−	14.3411i	−1.28006	−	0.468005i
$940$	−0.0650889	+	3.91761i	−0.00212297	+	0.127778i
$941$	26.9660	+	15.5688i	0.879065	+	0.507529i	0.870350	−	0.492433i	$-0.163892\pi$
$941$	26.9660	+	15.5688i	0.879065	+	0.507529i	0.00871528	+	0.999962i	$0.497226\pi$
$942$	−4.35726	+	11.6176i	−0.141967	+	0.378521i
$943$	−52.7638	+	30.4632i	−1.71822	+	0.992017i
$944$	−5.54271	+	2.95907i	−0.180400	+	0.0963095i
$945$	2.51180	+	4.73918i	0.0817088	+	0.154165i
$946$	−8.83092	+	5.00119i	−0.287118	+	0.162603i
$947$	11.6780	+	20.2270i	0.379485	+	0.657288i	0.990987	−	0.133955i	$-0.0427678\pi$
$947$	11.6780	+	20.2270i	0.379485	+	0.657288i	−0.611502	+	0.791243i	$0.709434\pi$
$948$	−1.63844	+	0.258482i	−0.0532141	+	0.00839511i
$949$	9.07751	+	5.24090i	0.294669	+	0.170127i
$950$	17.8168	−	30.2761i	0.578055	−	0.982286i
$951$	16.0210	−	43.8197i	0.519517	−	1.42095i
$952$	−11.3268	−	22.4766i	−0.367102	−	0.728471i
$953$			37.3593i			1.21019i	0.796155	+	0.605093i	$0.206864\pi$
$953$			37.3593i			1.21019i	−0.796155	+	0.605093i	$0.793136\pi$
$954$	−3.99673	+	1.40418i	−0.129399	+	0.0454621i
$955$	−1.64162	+	2.84336i	−0.0531215	+	0.0920091i
$956$	1.48924	−	0.827137i	0.0481655	−	0.0267515i
$957$	10.5702	−	1.84803i	0.341686	−	0.0597383i
$958$	24.1177	+	42.5862i	0.779209	+	1.37590i
$959$	−17.0955	+	9.15612i	−0.552042	+	0.295667i
$960$	4.97858	+	2.10698i	0.160683	+	0.0680025i
$961$	−6.84861	−	11.8621i	−0.220923	−	0.382650i
$962$	0.332937	−	40.0807i	0.0107343	−	1.29225i
$963$	−44.3204	+	15.9861i	−1.42821	+	0.515144i
$964$	0.500332	−	30.1143i	0.0161146	−	0.969915i
$965$		−	5.12916i		−	0.165114i
$966$	4.68758	+	35.0665i	0.150821	+	1.12825i
$967$	−32.9761			−1.06044			−0.530220	−	0.847860i	$-0.677891\pi$
$967$	−32.9761			−1.06044			−0.530220	+	0.847860i	$0.677891\pi$
$968$	−11.8480	−	21.7558i	−0.380809	−	0.699259i
$969$	19.1544	+	22.8946i	0.615327	+	0.735479i
$970$	−4.96603	−	0.0412511i	−0.159450	−	0.00132449i
$971$	14.3859	−	8.30570i	0.461665	−	0.266543i	−0.251079	−	0.967967i	$-0.580785\pi$
$971$	14.3859	−	8.30570i	0.461665	−	0.266543i	0.712744	+	0.701424i	$0.247452\pi$
$972$	−20.6041	+	23.3981i	−0.660878	+	0.750494i
$973$	21.9748	−	35.4044i	0.704481	−	1.13501i
$974$	16.7654	+	29.6037i	0.537198	+	0.948563i
$975$	−27.1929	+	4.75423i	−0.870869	+	0.152257i
$976$	−27.2561	−	0.905939i	−0.872446	−	0.0289984i
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	0.489702	−	0.871890i	$-0.337106\pi$
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	−0.510228	+	0.860039i	$0.670439\pi$
$978$	−23.7536	+	19.5399i	−0.759555	+	0.624818i
$979$	−7.63074			−0.243880
$980$	−0.438625	+	5.44445i	−0.0140114	+	0.173917i
$981$	33.8689	−	40.1267i	1.08135	−	1.28115i
$982$	11.0248	−	18.7344i	0.351815	−	0.597838i
$983$	−5.11340	+	8.85666i	−0.163092	+	0.282484i	−0.935976	−	0.352064i	$-0.885480\pi$
$983$	−5.11340	+	8.85666i	−0.163092	+	0.282484i	0.772884	+	0.634547i	$0.218813\pi$
$984$	−34.0286	−	42.7963i	−1.08479	−	1.36430i
$985$	−5.95069	+	3.43563i	−0.189605	+	0.109468i
$986$	−9.69941	−	17.1268i	−0.308892	−	0.545430i
$987$	−14.1952	−	18.1104i	−0.451839	−	0.576461i
$988$	−17.3286	+	28.8947i	−0.551297	+	0.919262i
$989$	−13.0831	−	22.6606i	−0.416019	−	0.720567i
$990$	−1.61413	+	1.88045i	−0.0513003	+	0.0597645i
$991$	22.7297	−	39.3690i	0.722032	−	1.25060i	−0.238152	−	0.971228i	$-0.576541\pi$
$991$	22.7297	−	39.3690i	0.722032	−	1.25060i	0.960184	−	0.279369i	$-0.0901252\pi$
$992$	0.976999	−	23.5103i	0.0310197	−	0.746453i
$993$	−28.6984	−	10.4925i	−0.910718	−	0.332969i
$994$	−47.4941	+	24.9318i	−1.50642	+	0.790789i
$995$	7.77971			0.246633
$996$	−56.4360	−	21.7031i	−1.78824	−	0.687690i
$997$	13.6051	−	23.5647i	0.430877	−	0.746300i	−0.566072	−	0.824356i	$-0.691538\pi$
$997$	13.6051	−	23.5647i	0.430877	−	0.746300i	0.996949	+	0.0780552i	$0.0248710\pi$
$998$	0.310192	−	37.3426i	0.00981897	−	1.18206i
$999$	−22.5658	+	38.6958i	−0.713950	+	1.22428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.16	yes	48
3.2	odd	2	inner	168.2.ba.c.101.9	yes	48
4.3	odd	2		672.2.bi.c.17.6		48
7.5	odd	6	inner	168.2.ba.c.5.1	✓	48
8.3	odd	2		672.2.bi.c.17.19		48
8.5	even	2	inner	168.2.ba.c.101.24	yes	48
12.11	even	2		672.2.bi.c.17.23		48
21.5	even	6	inner	168.2.ba.c.5.24	yes	48
24.5	odd	2	inner	168.2.ba.c.101.1	yes	48
24.11	even	2		672.2.bi.c.17.2		48
28.19	even	6		672.2.bi.c.593.2		48
56.5	odd	6	inner	168.2.ba.c.5.9	yes	48
56.19	even	6		672.2.bi.c.593.23		48
84.47	odd	6		672.2.bi.c.593.19		48
168.5	even	6	inner	168.2.ba.c.5.16	yes	48
168.131	odd	6		672.2.bi.c.593.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.1	✓	48	7.5	odd	6	inner
168.2.ba.c.5.9	yes	48	56.5	odd	6	inner
168.2.ba.c.5.16	yes	48	168.5	even	6	inner
168.2.ba.c.5.24	yes	48	21.5	even	6	inner
168.2.ba.c.101.1	yes	48	24.5	odd	2	inner
168.2.ba.c.101.9	yes	48	3.2	odd	2	inner
168.2.ba.c.101.16	yes	48	1.1	even	1	trivial
168.2.ba.c.101.24	yes	48	8.5	even	2	inner
672.2.bi.c.17.2		48	24.11	even	2
672.2.bi.c.17.6		48	4.3	odd	2
672.2.bi.c.17.19		48	8.3	odd	2
672.2.bi.c.17.23		48	12.11	even	2
672.2.bi.c.593.2		48	28.19	even	6
672.2.bi.c.593.6		48	168.131	odd	6
672.2.bi.c.593.19		48	84.47	odd	6
672.2.bi.c.593.23		48	56.19	even	6

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 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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