LMFDB - Embedded newform 168.2.ba.c.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.717256 + 1.21883i) q^{2} +(-1.70617 - 0.298296i) q^{3} +(-0.971089 - 1.74842i) q^{4} +(-0.337879 + 0.195075i) q^{5} +(1.58733 - 1.86558i) q^{6} +(1.39526 - 2.24795i) q^{7} +(2.82755 + 0.0704754i) q^{8} +(2.82204 + 1.01789i) q^{9} +(0.00458308 - 0.551736i) q^{10} +(0.748582 - 1.29658i) q^{11} +(1.13530 + 3.27278i) q^{12} +3.28768 q^{13} +(1.73911 + 3.31293i) q^{14} +(0.634670 - 0.232043i) q^{15} +(-2.11397 + 3.39575i) q^{16} +(1.68169 - 2.91278i) q^{17} +(-3.26476 + 2.70950i) q^{18} +(-2.56203 - 4.43756i) q^{19} +(0.669184 + 0.401321i) q^{20} +(-3.05110 + 3.41918i) q^{21} +(1.04339 + 1.84237i) q^{22} +(4.72764 - 2.72950i) q^{23} +(-4.80326 - 0.963690i) q^{24} +(-2.42389 + 4.19830i) q^{25} +(-2.35811 + 4.00712i) q^{26} +(-4.51125 - 2.57850i) q^{27} +(-5.28528 - 0.256545i) q^{28} +4.13801 q^{29} +(-0.172400 + 0.939988i) q^{30} +(-3.60237 - 2.07983i) q^{31} +(-2.62258 - 5.01219i) q^{32} +(-1.66397 + 1.98889i) q^{33} +(2.34398 + 4.13891i) q^{34} +(-0.0329110 + 1.03171i) q^{35} +(-0.960750 - 5.92258i) q^{36} +(7.46581 - 4.31038i) q^{37} +(7.24625 + 0.0601921i) q^{38} +(-5.60934 - 0.980702i) q^{39} +(-0.969118 + 0.527771i) q^{40} -11.1607 q^{41} +(-1.97898 - 6.17120i) q^{42} +4.79323i q^{43} +(-2.99391 - 0.0497422i) q^{44} +(-1.15207 + 0.206585i) q^{45} +(-0.0641268 + 7.71993i) q^{46} +(2.51067 + 4.34861i) q^{47} +(4.61974 - 5.16314i) q^{48} +(-3.10652 - 6.27292i) q^{49} +(-3.37846 - 5.96557i) q^{50} +(-3.73813 + 4.46806i) q^{51} +(-3.19263 - 5.74826i) q^{52} +(0.499243 - 0.864715i) q^{53} +(6.37846 - 3.64900i) q^{54} +0.584118i q^{55} +(4.10358 - 6.25784i) q^{56} +(3.04755 + 8.33548i) q^{57} +(-2.96801 + 5.04353i) q^{58} +(-1.36034 - 0.785391i) q^{59} +(-1.02203 - 0.884338i) q^{60} +(3.40889 + 5.90437i) q^{61} +(5.11878 - 2.89891i) q^{62} +(6.22563 - 4.92357i) q^{63} +(7.99007 + 0.398545i) q^{64} +(-1.11084 + 0.641343i) q^{65} +(-1.23062 - 3.45464i) q^{66} +(3.05467 + 1.76361i) q^{67} +(-6.72585 - 0.111746i) q^{68} +(-8.88036 + 3.24676i) q^{69} +(-1.23388 - 0.780115i) q^{70} +14.3360i q^{71} +(7.90772 + 3.07701i) q^{72} +(2.76107 + 1.59410i) q^{73} +(-0.101268 + 12.1912i) q^{74} +(5.38791 - 6.43999i) q^{75} +(-5.27078 + 8.78877i) q^{76} +(-1.87018 - 3.49184i) q^{77} +(5.21864 - 6.13342i) q^{78} +(-0.239413 - 0.414676i) q^{79} +(0.0518426 - 1.55974i) q^{80} +(6.92781 + 5.74504i) q^{81} +(8.00508 - 13.6030i) q^{82} +17.4548i q^{83} +(8.94106 + 2.01429i) q^{84} +1.31222i q^{85} +(-5.84213 - 3.43797i) q^{86} +(-7.06016 - 1.23435i) q^{87} +(2.20803 - 3.61339i) q^{88} +(-2.54840 - 4.41396i) q^{89} +(0.574539 - 1.55235i) q^{90} +(4.58716 - 7.39053i) q^{91} +(-9.36328 - 5.61532i) q^{92} +(5.52586 + 4.62312i) q^{93} +(-7.10101 - 0.0589856i) q^{94} +(1.73131 + 0.999573i) q^{95} +(2.97945 + 9.33396i) q^{96} -9.00074i q^{97} +(9.87379 + 0.712973i) q^{98} +(3.43230 - 2.89703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 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
$3$	−1.70617	−	0.298296i	−0.985058	−	0.172221i
$3$	−1.70617	−	0.298296i	−0.985058	−	0.172221i
$4$	−0.971089	−	1.74842i	−0.485544	−	0.874212i
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	−0.573646	−	0.819103i	$-0.694471\pi$
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	0.422542	+	0.906344i	$0.361138\pi$
$6$	1.58733	−	1.86558i	0.648026	−	0.761618i
$7$	1.39526	−	2.24795i	0.527357	−	0.849644i
$7$	1.39526	−	2.24795i	0.527357	−	0.849644i
$8$	2.82755	+	0.0704754i	0.999690	+	0.0249168i
$9$	2.82204	+	1.01789i	0.940680	+	0.339296i
$10$	0.00458308	−	0.551736i	0.00144930	−	0.174474i
$11$	0.748582	−	1.29658i	0.225706	−	0.390934i	−0.730825	−	0.682565i	$-0.760864\pi$
$11$	0.748582	−	1.29658i	0.225706	−	0.390934i	0.956531	+	0.291631i	$0.0941978\pi$
$12$	1.13530	+	3.27278i	0.327732	+	0.944771i
$13$	3.28768			0.911838			0.455919	−	0.890021i	$-0.349311\pi$
$13$	3.28768			0.911838			0.455919	+	0.890021i	$0.349311\pi$
$14$	1.73911	+	3.31293i	0.464796	+	0.885418i
$15$	0.634670	−	0.232043i	0.163871	−	0.0599132i
$16$	−2.11397	+	3.39575i	−0.528493	+	0.848938i
$17$	1.68169	−	2.91278i	0.407871	−	0.706453i	−0.586780	−	0.809746i	$-0.699605\pi$
$17$	1.68169	−	2.91278i	0.407871	−	0.706453i	0.994651	+	0.103293i	$0.0329381\pi$
$18$	−3.26476	+	2.70950i	−0.769510	+	0.638635i
$19$	−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
$21$	−3.05110	+	3.41918i	−0.665805	+	0.746126i
$22$	1.04339	+	1.84237i	0.222451	+	0.392795i
$23$	4.72764	−	2.72950i	0.985780	−	0.569141i	0.0817700	−	0.996651i	$-0.473943\pi$
$23$	4.72764	−	2.72950i	0.985780	−	0.569141i	0.904010	+	0.427511i	$0.140609\pi$
$24$	−4.80326	−	0.963690i	−0.980461	−	0.196712i
$25$	−2.42389	+	4.19830i	−0.484778	+	0.839661i
$26$	−2.35811	+	4.00712i	−0.462463	+	0.785861i
$27$	−4.51125	−	2.57850i	−0.868190	−	0.496232i
$28$	−5.28528	−	0.256545i	−0.998824	−	0.0484825i
$29$	4.13801			0.768410			0.384205	−	0.923248i	$-0.374476\pi$
$29$	4.13801			0.768410			0.384205	+	0.923248i	$0.374476\pi$
$30$	−0.172400	+	0.939988i	−0.0314758	+	0.171618i
$31$	−3.60237	−	2.07983i	−0.647005	−	0.373549i	0.140303	−	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
$33$	−1.66397	+	1.98889i	−0.289661	+	0.346222i
$34$	2.34398	+	4.13891i	0.401989	+	0.709816i
$35$	−0.0329110	+	1.03171i	−0.00556298	+	0.174391i
$36$	−0.960750	−	5.92258i	−0.160125	−	0.987097i
$37$	7.46581	−	4.31038i	1.22737	−	0.708623i	0.260892	−	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
$39$	−5.60934	−	0.980702i	−0.898214	−	0.157038i
$40$	−0.969118	+	0.527771i	−0.153231	+	0.0834480i
$41$	−11.1607			−1.74301			−0.871505	−	0.490387i	$-0.836855\pi$
$41$	−11.1607			−1.74301			−0.871505	+	0.490387i	$0.836855\pi$
$42$	−1.97898	−	6.17120i	−0.305363	−	0.952236i
$43$			4.79323i			0.730961i	0.930819	+	0.365480i	$0.119095\pi$
$43$			4.79323i			0.730961i	−0.930819	+	0.365480i	$0.880905\pi$
$44$	−2.99391	−	0.0497422i	−0.451350	−	0.00749892i
$45$	−1.15207	+	0.206585i	−0.171741	+	0.0307959i
$46$	−0.0641268	+	7.71993i	−0.00945498	+	1.13824i
$47$	2.51067	+	4.34861i	0.366219	+	0.634310i	0.988971	−	0.148109i	$-0.0473187\pi$
$47$	2.51067	+	4.34861i	0.366219	+	0.634310i	−0.622752	+	0.782419i	$0.713985\pi$
$48$	4.61974	−	5.16314i	0.666802	−	0.745235i
$49$	−3.10652	−	6.27292i	−0.443788	−	0.896132i
$50$	−3.37846	−	5.96557i	−0.477787	−	0.843658i
$51$	−3.73813	+	4.46806i	−0.523443	+	0.625653i
$52$	−3.19263	−	5.74826i	−0.442738	−	0.797140i
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	−0.829699	−	0.558212i	$-0.811488\pi$
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	0.898275	+	0.439434i	$0.144821\pi$
$54$	6.37846	−	3.64900i	0.867999	−	0.496566i
$55$			0.584118i			0.0787624i
$56$	4.10358	−	6.25784i	0.548364	−	0.836240i
$57$	3.04755	+	8.33548i	0.403657	+	1.10406i
$58$	−2.96801	+	5.04353i	−0.389719	+	0.662248i
$59$	−1.36034	−	0.785391i	−0.177101	−	0.102249i	0.408829	−	0.912611i	$-0.365937\pi$
$59$	−1.36034	−	0.785391i	−0.177101	−	0.102249i	−0.585930	+	0.810362i	$0.699271\pi$
$60$	−1.02203	−	0.884338i	−0.131944	−	0.114168i
$61$	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
$63$	6.22563	−	4.92357i	0.784355	−	0.620312i
$64$	7.99007	+	0.398545i	0.998758	+	0.0498181i
$65$	−1.11084	+	0.641343i	−0.137783	+	0.0795488i
$66$	−1.23062	−	3.45464i	−0.151479	−	0.425237i
$67$	3.05467	+	1.76361i	0.373187	+	0.215460i	0.674850	−	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	$0.323812\pi$
$71$			14.3360i			1.70137i	−0.525677	+	0.850684i	$0.676188\pi$
$72$	7.90772	+	3.07701i	0.931933	+	0.362630i
$73$	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
$75$	5.38791	−	6.43999i	0.622142	−	0.743626i
$76$	−5.27078	+	8.78877i	−0.604600	+	1.00814i
$77$	−1.87018	−	3.49184i	−0.213127	−	0.397932i
$78$	5.21864	−	6.13342i	0.590895	−	0.694473i
$79$	−0.239413	−	0.414676i	−0.0269361	−	0.0466547i	0.852243	−	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
$81$	6.92781	+	5.74504i	0.769756	+	0.638338i
$82$	8.00508	−	13.6030i	0.884013	−	1.50220i
$83$			17.4548i			1.91591i	0.286911	+	0.957957i	$0.407372\pi$
$83$			17.4548i			1.91591i	−0.286911	+	0.957957i	$0.592628\pi$
$84$	8.94106	+	2.01429i	0.975550	+	0.219777i
$85$			1.31222i			0.142331i
$86$	−5.84213	−	3.43797i	−0.629973	−	0.370726i
$87$	−7.06016	−	1.23435i	−0.756928	−	0.132337i
$88$	2.20803	−	3.61339i	0.235377	−	0.385189i
$89$	−2.54840	−	4.41396i	−0.270130	−	0.467879i	0.698765	−	0.715351i	$-0.253733\pi$
$89$	−2.54840	−	4.41396i	−0.270130	−	0.467879i	−0.968895	+	0.247473i	$0.920400\pi$
$90$	0.574539	−	1.55235i	0.0605617	−	0.163633i
$91$	4.58716	−	7.39053i	0.480865	−	0.774738i
$92$	−9.36328	−	5.61532i	−0.976190	−	0.585438i
$93$	5.52586	+	4.62312i	0.573005	+	0.479395i
$94$	−7.10101	−	0.0589856i	−0.732413	−	0.00608390i
$95$	1.73131	+	0.999573i	0.177629	+	0.102554i
$96$	2.97945	+	9.33396i	0.304089	+	0.952644i
$97$		−	9.00074i		−	0.913887i	−0.889496	−	0.456943i	$-0.848944\pi$
$97$		−	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	0.712719	−	0.701450i	$-0.247464\pi$
$101$	4.63907	+	2.67837i	0.461605	+	0.266508i	−0.251114	+	0.967958i	$0.580797\pi$
$102$	−2.76460	−	7.76088i	−0.273737	−	0.768442i
$103$	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
$105$	0.363908	−	1.75046i	0.0355138	−	0.170828i
$106$	0.695854	+	1.22871i	0.0675874	+	0.119343i
$107$	−7.85256	−	13.6010i	−0.759135	−	1.31486i	−0.943292	−	0.331964i	$-0.892289\pi$
$107$	−7.85256	−	13.6010i	−0.759135	−	1.31486i	0.184157	−	0.982897i	$-0.441045\pi$
$108$	−0.127480	+	10.3915i	−0.0122668	+	0.999925i
$109$	−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	$0.00108718\pi$
$113$			0.0726142i			0.00683097i	−0.999994	+	0.00341549i	$0.998913\pi$
$114$	−12.3454	−	2.26423i	−1.15625	−	0.212064i
$115$	−1.06491	+	1.84448i	−0.0993037	+	0.171999i
$116$	−4.01838	−	7.23500i	−0.373097	−	0.671753i
$117$	9.27796	+	3.34649i	0.857748	+	0.309383i
$118$	1.93297	−	1.09469i	0.177944	−	0.100775i
$119$	−4.20138	−	7.84443i	−0.385139	−	0.719098i
$120$	1.81091	−	0.611384i	0.165313	−	0.0558114i
$121$	4.37925	+	7.58508i	0.398114	+	0.689553i
$122$	−9.64147	−	0.0800883i	−0.872897	−	0.00725085i
$123$	19.0421	+	3.32920i	1.71697	+	0.300183i
$124$	−0.138202	+	8.31817i	−0.0124109	+	0.746994i
$125$		−	3.84211i		−	0.343649i
$126$	1.53563	+	11.1194i	0.136805	+	0.990598i
$127$	−8.81577			−0.782273			−0.391137	−	0.920333i	$-0.627918\pi$
$127$	−8.81577			−0.782273			−0.391137	+	0.920333i	$0.627918\pi$
$128$	−6.21668	+	9.45267i	−0.549482	+	0.835506i
$129$	1.42980	−	8.17807i	0.125887	−	0.720039i
$130$	0.0150677	−	1.81393i	0.00132152	−	0.159092i
$131$	−4.36183	+	2.51830i	−0.381095	+	0.220025i	−0.678294	−	0.734790i	$-0.737281\pi$
$131$	−4.36183	+	2.51830i	−0.381095	+	0.220025i	0.297200	+	0.954815i	$0.403947\pi$
$132$	5.09329	+	0.977942i	0.443314	+	0.0851189i
$133$	−13.5501	−	0.432239i	−1.17494	−	0.0374799i
$134$	−4.34052	+	2.45816i	−0.374964	+	0.212352i
$135$	2.02726	−	0.00881014i	0.174478	−	0.000758256i
$136$	4.96035	−	8.11751i	0.425347	−	0.696071i
$137$	6.34787	+	3.66494i	0.542335	+	0.313117i	0.746025	−	0.665918i	$-0.231960\pi$
$137$	6.34787	+	3.66494i	0.542335	+	0.313117i	−0.203690	+	0.979035i	$0.565293\pi$
$138$	2.41224	−	13.1524i	0.205343	−	1.11961i
$139$	15.7497			1.33587			0.667935	−	0.744220i	$-0.267178\pi$
$139$	15.7497			1.33587			0.667935	+	0.744220i	$0.267178\pi$
$140$	1.83583	−	0.944343i	0.155156	−	0.0798116i
$141$	−2.98646	−	8.16840i	−0.251505	−	0.687903i
$142$	−17.4731	−	10.2826i	−1.46631	−	0.862894i
$143$	2.46110	−	4.26275i	0.205807	−	0.356469i
$144$	−9.42221	+	7.43115i	−0.785184	+	0.619262i
$145$	−1.39815	+	0.807222i	−0.116110	+	0.0670361i
$146$	−3.92333	+	2.22189i	−0.324697	+	0.183885i
$147$	3.42906	+	11.6293i	0.282824	+	0.959172i
$148$	−14.7863	−	8.86763i	−1.21543	−	0.728914i
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	−0.954078	−	0.299559i	$-0.903161\pi$
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	0.217613	−	0.976035i	$-0.430173\pi$
$150$	3.98473	+	11.1861i	0.325352	+	0.913338i
$151$	−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
$156$	3.73249	+	10.7599i	0.298838	+	0.861478i
$157$	−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
$159$	−1.10974	+	1.32643i	−0.0880077	+	0.105193i
$160$	1.86387	+	1.18192i	0.147352	+	0.0934387i
$161$	0.460494	−	14.4358i	0.0362920	−	1.13770i
$162$	−11.9712	+	4.32315i	−0.940549	+	0.339659i
$163$	−10.8745	+	6.27840i	−0.851757	+	0.491762i	−0.861243	−	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
$165$	0.174240	−	0.996605i	0.0135646	−	0.0775856i
$166$	−21.2744	−	12.5196i	−1.65122	−	0.971706i
$167$	7.43145			0.575063			0.287531	−	0.957771i	$-0.407165\pi$
$167$	7.43145			0.575063			0.287531	+	0.957771i	$0.407165\pi$
$168$	−8.86810	+	9.45287i	−0.684189	+	0.729305i
$169$	−2.19116			−0.168551
$170$	−1.59938	−	0.941200i	−0.122667	−	0.0721868i
$171$	−2.71320	−	15.1308i	−0.207483	−	1.15708i
$172$	8.38060	−	4.65465i	0.639014	−	0.354914i
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.951069	−	0.308978i	$-0.900013\pi$
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.207952	+	0.978139i	$0.566680\pi$
$174$	6.56840	−	7.71978i	0.497949	−	0.585235i
$175$	6.05561	+	11.3065i	0.457761	+	0.854690i
$176$	2.82039	+	5.28294i	0.212595	+	0.398216i
$177$	2.08669	+	1.74579i	0.156845	+	0.131222i
$178$	7.20771	+	0.0598720i	0.540241	+	0.00448759i
$179$	−8.11784	+	14.0605i	−0.606756	+	1.05093i	0.385016	+	0.922910i	$0.374196\pi$
$179$	−8.11784	+	14.0605i	−0.606756	+	1.05093i	−0.991771	+	0.128022i	$0.959137\pi$
$180$	1.47996	+	1.81370i	0.110310	+	0.135185i
$181$	−6.19340			−0.460351			−0.230176	−	0.973149i	$-0.573930\pi$
$181$	−6.19340			−0.460351			−0.230176	+	0.973149i	$0.573930\pi$
$182$	5.71762	+	10.8919i	0.423818	+	0.807358i
$183$	−4.05490	−	11.0907i	−0.299747	−	0.819850i
$184$	13.5600	−	7.38462i	0.999655	−	0.544401i
$185$	−1.68169	+	2.91278i	−0.123641	+	0.214152i
$186$	−9.59824	+	3.41912i	−0.703777	+	0.250702i
$187$	−2.51777	−	4.36091i	−0.184118	−	0.318901i
$188$	5.16513	−	8.61261i	0.376706	−	0.628139i
$189$	−12.0907	+	6.54338i	−0.879467	+	0.475961i
$190$	−2.46010	+	1.39322i	−0.178475	+	0.101075i
$191$	7.28788	−	4.20766i	0.527333	−	0.304456i	−0.212597	−	0.977140i	$-0.568192\pi$
$191$	7.28788	−	4.20766i	0.527333	−	0.304456i	0.739930	+	0.672684i	$0.234859\pi$
$192$	−13.5135	−	3.06339i	−0.975255	−	0.221081i
$193$	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	$-0.284120\pi$
$197$	17.6119			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$198$	1.06915	+	6.26130i	0.0759810	+	0.444971i
$199$	17.2688	+	9.97017i	1.22416	+	0.706767i	0.965801	−	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
$201$	−4.68570	−	3.92022i	−0.330504	−	0.276511i
$202$	−6.59187	+	3.73316i	−0.463803	+	0.262664i
$203$	5.77359	−	9.30203i	0.405227	−	0.652874i
$204$	11.4421	+	2.19695i	0.801108	+	0.153818i
$205$	3.77097	−	2.17717i	0.263376	−	0.152060i
$206$	−0.104557	+	12.5872i	−0.00728485	+	0.876990i
$207$	16.1199	−	2.89055i	1.12041	−	0.200907i
$208$	−6.95007	+	11.1641i	−0.481900	+	0.774094i
$209$	−7.67154			−0.530652
$210$	1.87250	+	1.69907i	0.129215	+	0.117247i
$211$			14.5159i			0.999314i	0.866223	+	0.499657i	$0.166541\pi$
$211$			14.5159i			0.999314i	−0.866223	+	0.499657i	$0.833459\pi$
$212$	−1.99670	−	0.0331740i	−0.137134	−	0.00227840i
$213$	4.27637	−	24.4596i	0.293012	−	1.67595i
$214$	22.2096	+	0.184488i	1.51822	+	0.0126113i
$215$	−0.935038	−	1.61953i	−0.0637691	−	0.110451i
$216$	−12.5741	−	7.60875i	−0.855556	−	0.517710i
$217$	−9.70158	+	5.19604i	−0.658586	+	0.352730i
$218$	21.5390	−	12.1981i	1.45880	−	0.826161i
$219$	−4.23534	−	3.54343i	−0.286198	−	0.239443i
$220$	1.02129	−	0.567230i	0.0688550	−	0.0382426i
$221$	5.52887	−	9.57629i	0.371912	−	0.644171i
$222$	3.80937	−	20.7700i	0.255668	−	1.39399i
$223$		−	2.77897i		−	0.186093i	−0.995662	−	0.0930467i	$-0.970339\pi$
$223$		−	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	0.887481	−	0.460844i	$-0.152453\pi$
$227$	14.0438	+	8.10819i	0.932119	+	0.538159i	0.0446379	+	0.999003i	$0.485787\pi$
$228$	11.6145	−	13.4229i	0.769190	−	0.888953i
$229$	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
$231$	2.14925	+	6.51554i	0.141410	+	0.428691i
$232$	11.7004	+	0.291628i	0.768171	+	0.0191463i
$233$	1.80462	−	1.04190i	0.118225	−	0.0682572i	−0.439721	−	0.898134i	$-0.644923\pi$
$233$	1.80462	−	1.04190i	0.118225	−	0.0682572i	0.557946	+	0.829877i	$0.311589\pi$
$234$	−10.7335	+	8.90796i	−0.701669	+	0.582331i
$235$	−1.69661	−	0.979538i	−0.110675	−	0.0638980i
$236$	−0.0521881	+	3.14113i	−0.00339716	+	0.204470i
$237$	0.284784	+	0.778925i	0.0184987	+	0.0505966i
$238$	12.5745	+	0.505704i	0.815083	+	0.0327799i
$239$		−	0.851762i		−	0.0550959i	−0.999620	−	0.0275480i	$-0.991230\pi$
$239$		−	0.851762i		−	0.0550959i	0.999620	−	0.0275480i	$-0.00876990\pi$
$240$	−0.553716	+	2.64571i	−0.0357422	+	0.170780i
$241$	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
$243$	−10.1063	−	11.8686i	−0.648319	−	0.761369i
$244$	7.01301	−	11.6939i	0.448962	−	0.748622i
$245$	2.27332	+	1.51349i	0.145237	+	0.0966932i
$246$	−17.7158	+	20.8211i	−1.12952	+	1.32751i
$247$	−8.42312	−	14.5893i	−0.535950	−	0.928293i
$248$	−10.0393	−	6.13470i	−0.637496	−	0.389554i
$249$	5.20670	−	29.7809i	0.329961	−	1.88729i
$250$	4.68287	+	2.75577i	0.296171	+	0.174290i
$251$		−	11.8022i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$251$		−	11.8022i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$252$	−14.6541	−	6.10381i	−0.923123	−	0.384504i
$253$		−	8.17302i		−	0.513834i
$254$	6.32316	−	10.7449i	0.396750	−	0.674196i
$255$	0.391432	−	2.23888i	0.0245124	−	0.140204i
$256$	−7.06224	−	14.3570i	−0.441390	−	0.897315i
$257$	8.86901	+	15.3616i	0.553233	+	0.958228i	0.998039	+	0.0626011i	$0.0199396\pi$
$257$	8.86901	+	15.3616i	0.553233	+	0.958228i	−0.444805	+	0.895627i	$0.646727\pi$
$258$	8.94213	+	7.60845i	0.556713	+	0.473681i
$259$	0.727204	−	22.7968i	0.0451863	−	1.41653i
$260$	2.20006	+	1.31942i	0.136442	+	0.0818267i
$261$	11.6776	+	4.21204i	0.722827	+	0.260719i
$262$	0.0591649	−	7.12259i	0.00365522	−	0.440035i
$263$	−6.27815	−	3.62469i	−0.387128	−	0.223508i	0.293787	−	0.955871i	$-0.405084\pi$
$263$	−6.27815	−	3.62469i	−0.387128	−	0.223508i	−0.680915	+	0.732363i	$0.738418\pi$
$264$	−4.84514	+	5.50642i	−0.298198	+	0.338897i
$265$			0.389559i			0.0239304i
$266$	10.2457	−	16.2052i	0.628204	−	0.993605i
$267$	3.03134	+	8.29114i	0.185515	+	0.507410i
$268$	0.117190	−	7.05348i	0.00715850	−	0.430860i
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	0.587463	−	0.809251i	$-0.300127\pi$
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	−0.407100	+	0.913383i	$0.633460\pi$
$270$	−1.44332	+	2.47720i	−0.0878379	+	0.150758i
$271$	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
$273$	−10.0310	+	11.2412i	−0.607106	+	0.680346i
$274$	−9.01998	+	5.10826i	−0.544917	+	0.308601i
$275$	3.62896	+	6.28555i	0.218835	+	0.379033i
$276$	14.3003	+	12.3737i	0.860779	+	0.744811i
$277$	−10.6940	−	6.17421i	−0.642543	−	0.370972i	0.143050	−	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	$-0.924129\pi$
$281$		−	7.91565i		−	0.472208i	0.971728	−	0.236104i	$-0.0758706\pi$
$282$	12.0979	+	2.21884i	0.720422	+	0.132130i
$283$	−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
$285$	−2.65574	−	2.22189i	−0.157313	−	0.131613i
$286$	3.43032	+	6.05714i	0.202839	+	0.358166i
$287$	−15.5720	+	25.0887i	−0.919189	+	1.48094i
$288$	−2.29917	−	16.8141i	−0.135480	−	0.990780i
$289$	2.84381	+	4.92562i	0.167283	+	0.289742i
$290$	0.0189648	−	2.28309i	0.00111365	−	0.134068i
$291$	−2.68489	+	15.3568i	−0.157391	+	0.900232i
$292$	0.105926	−	6.37554i	0.00619885	−	0.373100i
$293$			12.8246i			0.749220i	0.927183	+	0.374610i	$0.122223\pi$
$293$			12.8246i			0.749220i	−0.927183	+	0.374610i	$0.877777\pi$
$294$	−16.6337	−	4.16177i	−0.970097	−	0.242719i
$295$	0.612840			0.0356809
$296$	21.4137	−	11.6617i	1.24465	−	0.677821i
$297$	−6.72027	+	3.91899i	−0.389950	+	0.227403i
$298$	25.4258	+	0.211203i	1.47288	+	0.0122347i
$299$	15.5430	−	8.97373i	0.898872	−	0.518964i
$300$	−16.4920	−	3.16655i	−0.952164	−	0.182821i
$301$	10.7749	+	6.68778i	0.621056	+	0.385477i
$302$	−10.9993	−	19.4222i	−0.632939	−	1.11762i
$303$	−7.11610	−	5.95357i	−0.408809	−	0.342024i
$304$	20.4849	+	0.680878i	1.17489	+	0.0390511i
$305$	−2.30359	−	1.32998i	−0.131903	−	0.0761542i
$306$	2.40185	+	14.0661i	0.137304	+	0.804103i
$307$	−12.3622			−0.705549			−0.352774	−	0.935708i	$-0.614762\pi$
$307$	−12.3622			−0.705549			−0.352774	+	0.935708i	$0.614762\pi$
$308$	−4.28910	+	6.66075i	−0.244394	+	0.379532i
$309$	−14.4792	+	5.29377i	−0.823694	+	0.301152i
$310$	−1.16403	+	1.97802i	−0.0661123	+	0.112344i
$311$	−0.720819	+	1.24850i	−0.0408739	+	0.0707957i	−0.885739	−	0.464184i	$-0.846348\pi$
$311$	−0.720819	+	1.24850i	−0.0408739	+	0.0707957i	0.844865	+	0.534980i	$0.179681\pi$
$312$	−15.7916	−	3.16830i	−0.894022	−	0.179370i
$313$	−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
$315$	−1.14305	+	2.87804i	−0.0644033	+	0.162159i
$316$	−0.492538	+	0.821284i	−0.0277074	+	0.0462008i
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	0.944639	+	0.328111i	$0.106412\pi$
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	−0.188167	+	0.982137i	$0.560255\pi$
$318$	−0.820726	−	2.30397i	−0.0460240	−	0.129200i
$319$	3.09764	−	5.36527i	0.173435	−	0.300398i
$320$	−2.77742	+	1.42400i	−0.155263	+	0.0796040i
$321$	9.34067	+	25.5481i	0.521345	+	1.42595i
$322$	17.2645	+	10.9154i	0.962114	+	0.608294i
$323$	−17.2342			−0.958935
$324$	3.31726	−	17.6917i	0.184292	−	0.982872i
$325$	−7.96898	+	13.8027i	−0.442039	+	0.765635i
$326$	0.147504	−	17.7574i	0.00816952	−	0.983491i
$327$	23.2519	+	19.4533i	1.28583	+	1.07577i
$328$	−31.5574	−	0.786555i	−1.74247	−	0.0434302i
$329$	13.2785	+	0.423575i	0.732066	+	0.0233524i
$330$	1.08972	+	0.927189i	0.0599869	+	0.0510401i
$331$	−15.2782	+	8.82087i	−0.839766	+	0.484839i	−0.857185	−	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
$333$	25.4563	−	4.56471i	1.39500	−	0.250145i
$334$	−5.33025	+	9.05766i	−0.291658	+	0.495613i
$335$	−1.37615			−0.0751868
$336$	−5.16074	−	17.5888i	−0.281541	−	0.959549i
$337$	11.0396			0.601365			0.300682	−	0.953724i	$-0.402786\pi$
$337$	11.0396			0.601365			0.300682	+	0.953724i	$0.402786\pi$
$338$	1.57162	−	2.67065i	0.0854850	−	0.145264i
$339$	0.0216605	−	0.123892i	0.00117644	−	0.00672890i
$340$	2.29432	−	1.27429i	0.124427	−	0.0691079i
$341$	−5.39334	+	3.11385i	−0.292066	+	0.168624i
$342$	20.3879	+	7.54574i	1.10245	+	0.408027i
$343$	−18.4356	−	1.76905i	−0.995428	−	0.0955198i
$344$	−0.337805	+	13.5531i	−0.0182132	+	0.730734i
$345$	2.36713	−	2.82935i	0.127442	−	0.152327i
$346$	0.206781	−	24.8934i	0.0111166	−	1.33828i
$347$	10.8299	−	18.7579i	0.581377	−	1.00697i	−0.413940	−	0.910304i	$-0.635848\pi$
$347$	10.8299	−	18.7579i	0.581377	−	1.00697i	0.995316	−	0.0966701i	$-0.0308192\pi$
$348$	4.69787	+	13.5428i	0.251832	+	0.725971i
$349$	6.46130			0.345865			0.172933	−	0.984934i	$-0.444676\pi$
$349$	6.46130			0.345865			0.172933	+	0.984934i	$0.444676\pi$
$350$	−18.1241	−	0.728891i	−0.968774	−	0.0389609i
$351$	−14.8315	−	8.47727i	−0.791649	−	0.452483i
$352$	−8.46193	−	0.351646i	−0.451023	−	0.0187428i
$353$	−14.9846	+	25.9541i	−0.797549	+	1.38140i	0.123659	+	0.992325i	$0.460537\pi$
$353$	−14.9846	+	25.9541i	−0.797549	+	1.38140i	−0.921208	+	0.389071i	$0.872796\pi$
$354$	−3.62451	+	1.29114i	−0.192641	+	0.0686231i
$355$	−2.79659	−	4.84383i	−0.148428	−	0.257084i
$356$	−5.24275	+	8.74203i	−0.277865	+	0.463327i
$357$	4.82830	+	14.6372i	0.255541	+	0.774683i
$358$	−11.3148	−	19.9792i	−0.598005	−	1.05594i
$359$	−9.44412	+	5.45257i	−0.498442	+	0.287775i	−0.728070	−	0.685503i	$-0.759582\pi$
$359$	−9.44412	+	5.45257i	−0.498442	+	0.287775i	0.229628	+	0.973278i	$0.426249\pi$
$360$	−3.27210	+	0.502936i	−0.172455	+	0.0265071i
$361$	−3.62795	+	6.28380i	−0.190945	+	0.330726i
$362$	4.44225	−	7.54869i	0.233479	−	0.396750i
$363$	−5.20915	−	14.2478i	−0.273409	−	0.747814i
$364$	−17.3763	−	0.843438i	−0.910766	−	0.0442082i
$365$	−1.24388			−0.0651075
$366$	16.4261	+	3.01266i	0.858606	+	0.157474i
$367$	−2.43552	−	1.40615i	−0.127133	−	0.0734002i	0.435085	−	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
$369$	−31.4959	−	11.3604i	−1.63961	−	0.591396i
$370$	−2.34398	−	4.13891i	−0.121858	−	0.215171i
$371$	−1.24726	−	2.32877i	−0.0647545	−	0.120904i
$372$	2.71708	−	14.1510i	0.140874	−	0.733695i
$373$	26.9266	−	15.5461i	1.39421	−	0.804947i	0.400431	−	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
$375$	−1.14609	+	6.55529i	−0.0591836	+	0.338514i
$376$	6.79258	+	12.4729i	0.350301	+	0.643238i
$377$	13.6045			0.700665
$378$	0.696839	−	19.4297i	0.0358415	−	0.999357i
$379$		−	17.6950i		−	0.908931i	−0.890764	−	0.454465i	$-0.849830\pi$
$379$		−	17.6950i		−	0.908931i	0.890764	−	0.454465i	$-0.150170\pi$
$380$	0.0664203	−	3.99774i	0.00340729	−	0.205080i
$381$	15.0412	+	2.62971i	0.770585	+	0.134724i
$382$	−0.0988546	+	11.9007i	−0.00505784	+	0.608890i
$383$	−17.4953	−	30.3028i	−0.893968	−	1.54840i	−0.835076	−	0.550134i	$-0.814577\pi$
$383$	−17.4953	−	30.3028i	−0.893968	−	1.54840i	−0.0588917	−	0.998264i	$-0.518757\pi$
$384$	13.4264	−	14.2735i	0.685164	−	0.728389i
$385$	1.31306	+	0.814994i	0.0669200	+	0.0415359i
$386$	9.16202	+	16.1780i	0.466335	+	0.823436i
$387$	−4.87897	+	13.5267i	−0.248012	+	0.687600i
$388$	−15.7371	+	8.74052i	−0.798931	+	0.443733i
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	0.469971	+	0.882682i	$0.344264\pi$
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	−0.999410	+	0.0343338i	$0.989069\pi$
$390$	−0.566797	+	3.09038i	−0.0287009	+	0.156487i
$391$		−	18.3608i		−	0.928543i
$392$	−8.34175	−	17.9559i	−0.421322	−	0.906911i
$393$	8.19322	−	2.99554i	0.413293	−	0.151105i
$394$	−12.6322	+	21.4659i	−0.636402	+	1.08144i
$395$	0.161786	+	0.0934070i	0.00814032	+	0.00469982i
$396$	−8.39831	−	3.18785i	−0.422031	−	0.160195i
$397$	2.44443	+	4.23387i	0.122682	+	0.212492i	0.920825	−	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
$399$	22.9898	+	4.77941i	1.15093	+	0.239270i
$400$	−9.13235	−	17.1060i	−0.456617	−	0.855301i
$401$	−6.62355	+	3.82411i	−0.330764	+	0.190967i	−0.656180	−	0.754604i	$-0.727829\pi$
$401$	−6.62355	+	3.82411i	−0.330764	+	0.190967i	0.325416	+	0.945571i	$0.394496\pi$
$402$	8.13893	−	2.89927i	0.405933	−	0.144603i
$403$	−11.8434	−	6.83782i	−0.589964	−	0.340616i
$404$	0.177974	−	10.7120i	0.00885453	−	0.532942i
$405$	−3.46148	−	0.589691i	−0.172002	−	0.0293020i
$406$	7.19644	+	13.7090i	0.357153	+	0.680364i
$407$		−	12.9067i		−	0.639762i
$408$	−10.8846	+	12.3702i	−0.538870	+	0.612416i
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	0.326061	−	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
$411$	−9.73731	−	8.14656i	−0.480306	−	0.401840i
$412$	−15.2666	−	9.15566i	−0.752133	−	0.451067i
$413$	−3.66354	+	1.96214i	−0.180271	+	0.0965507i
$414$	−8.03900	+	21.7207i	−0.395095	+	1.06751i
$415$	−3.40499	−	5.89762i	−0.167145	−	0.289503i
$416$	−8.62221	−	16.4785i	−0.422738	−	0.807924i
$417$	−26.8716	−	4.69807i	−1.31591	−	0.230065i
$418$	5.50246	−	9.35030i	0.269134	−	0.457338i
$419$			4.38235i			0.214092i	0.994254	+	0.107046i	$0.0341392\pi$
$419$			4.38235i			0.214092i	−0.994254	+	0.107046i	$0.965861\pi$
$420$	−3.41394	+	1.06359i	−0.166583	+	0.0518978i
$421$		−	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
$423$	2.65881	+	14.8275i	0.129276	+	0.720940i
$424$	1.47258	−	2.40984i	0.0715146	−	0.117032i
$425$	8.15249	+	14.1205i	0.395454	+	0.684946i
$426$	26.7449	+	22.7560i	1.29579	+	1.10253i
$427$	18.0290	+	0.575113i	0.872484	+	0.0278317i
$428$	−16.1548	+	26.9374i	−0.780873	+	1.30207i
$429$	−5.47061	+	6.53884i	−0.264124	+	0.315698i
$430$	2.64460	+	0.0219677i	0.127534	+	0.00105938i
$431$	0.588922	+	0.340014i	0.0283674	+	0.0163779i	0.514117	−	0.857720i	$-0.328120\pi$
$431$	0.588922	+	0.340014i	0.0283674	+	0.0163779i	−0.485749	+	0.874098i	$0.661453\pi$
$432$	18.2926	−	9.86820i	0.880102	−	0.474784i
$433$		−	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
$438$	7.35666	−	2.62061i	0.351515	−	0.125218i
$439$	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
$441$	−2.38158	−	20.8645i	−0.113409	−	0.993548i
$442$	7.70624	+	13.6074i	0.366549	+	0.647238i
$443$	−3.02001	−	5.23080i	−0.143485	−	0.248523i	0.785322	−	0.619088i	$-0.212497\pi$
$443$	−3.02001	−	5.23080i	−0.143485	−	0.248523i	−0.928807	+	0.370565i	$0.879164\pi$
$444$	22.5828	+	19.5404i	1.07173	+	0.927346i
$445$	1.72210	+	0.994257i	0.0816355	+	0.0471323i
$446$	3.38709	+	1.99323i	0.160383	+	0.0943822i
$447$	10.6933	+	29.2477i	0.505776	+	1.38337i
$448$	12.0441	−	17.4052i	0.569030	−	0.822317i
$449$		−	28.1482i		−	1.32839i	−0.747558	−	0.664197i	$-0.768774\pi$
$449$		−	28.1482i		−	1.32839i	0.747558	−	0.664197i	$-0.231226\pi$
$450$	−3.46188	−	20.2740i	−0.163194	−	0.955724i
$451$	−8.35470	+	14.4708i	−0.393408	+	0.681402i
$452$	0.126960	−	0.0705149i	0.00597172	−	0.00331674i
$453$	17.5415	−	20.9667i	0.824171	−	0.985103i
$454$	−19.9555	+	11.3013i	−0.936557	+	0.530398i
$455$	−0.108201	+	3.39194i	−0.00507254	+	0.159017i
$456$	8.02964	+	23.7837i	0.376022	+	1.11378i
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	0.682612	−	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
$459$	−15.0971	+	8.80403i	−0.704674	+	0.410937i
$460$	4.25907	+	0.0707621i	0.198580	+	0.00329930i
$461$		−	31.6209i		−	1.47273i	−0.676583	−	0.736367i	$-0.736540\pi$
$461$		−	31.6209i		−	1.47273i	0.676583	−	0.736367i	$-0.263460\pi$
$462$	−9.48289	−	2.05374i	−0.441184	−	0.0955486i
$463$	23.5095			1.09258			0.546290	−	0.837596i	$-0.316040\pi$
$463$	23.5095			1.09258			0.546290	+	0.837596i	$0.316040\pi$
$464$	−8.74765	+	14.0517i	−0.406099	+	0.652332i
$465$	−2.76893	−	0.484102i	−0.128406	−	0.0224497i
$466$	−0.0244784	+	2.94684i	−0.00113394	+	0.136510i
$467$	12.7642	−	7.36942i	0.590657	−	0.341016i	−0.174700	−	0.984622i	$-0.555896\pi$
$467$	12.7642	−	7.36942i	0.590657	−	0.341016i	0.765357	+	0.643606i	$0.222562\pi$
$468$	−3.15864	−	19.4715i	−0.146008	−	0.900073i
$469$	8.22655	−	4.40603i	0.379867	−	0.203452i
$470$	2.41079	−	1.36530i	0.111201	−	0.0629765i
$471$	5.62985	−	6.72917i	0.259410	−	0.310064i
$472$	−3.79107	−	2.31660i	−0.174498	−	0.106630i
$473$	6.21481	+	3.58812i	0.285757	+	0.164982i
$474$	−1.15364	−	0.211585i	−0.0529884	−	0.00971843i
$475$	24.8403			1.13975
$476$	−9.63548	+	14.9634i	−0.441642	+	0.685848i
$477$	2.28907	−	1.93208i	0.104809	−	0.0884641i
$478$	1.03815	+	0.610931i	0.0474840	+	0.0279433i
$479$	17.3034	−	29.9703i	0.790611	−	1.36938i	−0.134979	−	0.990848i	$-0.543097\pi$
$479$	17.3034	−	29.9703i	0.790611	−	1.36938i	0.925589	−	0.378529i	$-0.123570\pi$
$480$	−2.82752	−	2.57254i	−0.129058	−	0.117420i
$481$	24.5452	−	14.1712i	1.11916	−	0.646150i
$482$	−18.5315	+	10.4949i	−0.844087	+	0.478030i
$483$	−5.09183	+	24.4926i	−0.231686	+	1.11445i
$484$	9.00930	−	15.0226i	0.409514	−	0.682844i
$485$	1.75582	+	3.04117i	0.0797276	+	0.138092i
$486$	21.7145	−	3.80506i	0.984992	−	0.172601i
$487$	−12.0284	+	20.8338i	−0.545058	+	0.944068i	0.453545	+	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	$-0.612744\pi$
$491$	−15.3708			−0.693675			−0.346837	+	0.937925i	$0.612744\pi$
$492$	−12.6707	−	36.5266i	−0.571239	−	1.64674i
$493$	6.95887	−	12.0531i	0.313412	−	0.542845i
$494$	23.8234	+	0.197892i	1.07186	+	0.00890360i
$495$	−0.594567	+	1.64840i	−0.0267238	+	0.0740902i
$496$	14.6779	−	7.83605i	0.659057	−	0.351849i
$497$	32.2265	+	20.0024i	1.44556	+	0.897229i
$498$	32.5633	+	27.7066i	1.45920	+	1.24156i
$499$	22.8684	−	13.2031i	1.02373	−	0.591051i	0.108548	−	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
$501$	−12.6793	−	2.21677i	−0.566470	−	0.0990381i
$502$	14.3849	+	8.46519i	0.642028	+	0.377820i
$503$	28.3616			1.26458			0.632291	−	0.774731i	$-0.282115\pi$
$503$	28.3616			1.26458			0.632291	+	0.774731i	$0.282115\pi$
$504$	17.9503	−	13.4829i	0.799568	−	0.600576i
$505$	−2.08993			−0.0930006
$506$	9.96152	+	5.86215i	0.442844	+	0.260604i
$507$	3.73850	+	0.653615i	0.166032	+	0.0290281i
$508$	8.56090	+	15.4137i	0.379828	+	0.683873i
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	−0.848472	−	0.529240i	$-0.822477\pi$
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	0.0340991	+	0.999418i	$0.489144\pi$
$510$	2.44805	+	2.08294i	0.108402	+	0.0922340i
$511$	7.43586	−	3.98255i	0.328943	−	0.176178i
$512$	22.5642	+	1.69001i	0.997207	+	0.0746885i
$513$	0.115709	+	26.6251i	0.00510866	+	1.17553i
$514$	−25.0845	−	0.208368i	−1.10643	−	0.00919072i
$515$	−1.73632	+	3.00739i	−0.0765113	+	0.132522i
$516$	−15.6872	+	5.44173i	−0.690590	+	0.239559i
$517$	7.51778			0.330631
$518$	27.2638	+	17.2375i	1.19790	+	0.757371i
$519$	28.6352	−	10.4694i	1.25695	−	0.459554i
$520$	−3.18615	+	1.73514i	−0.139722	+	0.0760910i
$521$	5.91179	−	10.2395i	0.259000	−	0.448601i	−0.706974	−	0.707239i	$-0.749940\pi$
$521$	5.91179	−	10.2395i	0.259000	−	0.448601i	0.965974	+	0.258638i	$0.0832737\pi$
$522$	−13.5096	+	11.2119i	−0.591299	+	0.490733i
$523$	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
$525$	−6.95922	−	21.0972i	−0.303725	−	0.920756i
$526$	8.92092	−	5.05217i	0.388971	−	0.220285i
$527$	−12.1162	+	6.99528i	−0.527789	+	0.304719i
$528$	−3.23618	−	9.85490i	−0.140837	−	0.428880i
$529$	3.40036	−	5.88960i	0.147842	−	0.256070i
$530$	−0.474806	−	0.279413i	−0.0206242	−	0.0121369i
$531$	−3.03948	−	3.60108i	−0.131902	−	0.156273i
$532$	12.4026	+	24.1110i	0.537720	+	1.04535i
$533$	−36.6928			−1.58934
$534$	−12.2797	−	2.25219i	−0.531396	−	0.0974616i
$535$	5.30643	+	3.06367i	0.229417	+	0.132454i
$536$	8.51293	+	5.20198i	0.367702	+	0.224691i
$537$	18.0446	−	21.5681i	0.778683	−	0.930733i
$538$	−4.20340	+	2.38050i	−0.181221	+	0.102631i
$539$	−10.4588	−	0.667940i	−0.450494	−	0.0287702i
$540$	−1.98405	−	3.53595i	−0.0853799	−	0.152163i
$541$	−15.3128	+	8.84087i	−0.658351	+	0.380099i	−0.791648	−	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
$543$	10.5670	+	1.84747i	0.453473	+	0.0792824i
$544$	−19.0098	−	0.789975i	−0.815038	−	0.0338699i
$545$	6.82885			0.292516
$546$	−6.50624	−	20.2889i	−0.278442	−	0.868285i
$547$		−	1.49834i		−	0.0640644i	−0.999487	−	0.0320322i	$-0.989802\pi$
$547$		−	1.49834i		−	0.0640644i	0.999487	−	0.0320322i	$-0.0101979\pi$
$548$	0.243530	−	14.6577i	0.0104031	−	0.626148i
$549$	3.61003	+	20.1322i	0.154072	+	0.859223i
$550$	−10.2639	−	0.0852587i	−0.437654	−	0.00363544i
$551$	−10.6017	−	18.3627i	−0.451647	−	0.782276i
$552$	−25.3385	+	8.55453i	−1.07848	+	0.364105i
$553$	−1.26621	−	0.0403914i	−0.0538448	−	0.00171762i
$554$	15.1957	−	8.60573i	0.645602	−	0.365622i
$555$	3.73813	−	4.46806i	0.158675	−	0.189658i
$556$	−15.2943	−	27.5371i	−0.648624	−	1.16783i
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	−0.833246	−	0.552902i	$-0.813520\pi$
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	0.895450	+	0.445161i	$0.146854\pi$
$558$	17.3962	−	2.97048i	0.736438	−	0.125750i
$559$			15.7586i			0.666518i
$560$	−3.43387	−	2.29277i	−0.145107	−	0.0968873i
$561$	2.99491	+	8.19150i	0.126445	+	0.345845i
$562$	9.64783	+	5.67755i	0.406969	+	0.239493i
$563$	−14.3950	−	8.31096i	−0.606677	−	0.350265i	0.164987	−	0.986296i	$-0.447242\pi$
$563$	−14.3950	−	8.31096i	−0.606677	−	0.350265i	−0.771664	+	0.636031i	$0.780575\pi$
$564$	−11.3817	+	13.1538i	−0.479256	+	0.553877i
$565$	−0.0141652	−	0.0245348i	−0.000595934	−	0.00103219i
$566$	−15.8271	−	27.9470i	−0.665264	−	1.17470i
$567$	22.5806	−	7.55752i	0.948296	−	0.317386i
$568$	−1.01033	+	40.5357i	−0.0423927	+	1.70084i
$569$	−19.2204	+	11.0969i	−0.805763	+	0.465207i	−0.845482	−	0.534003i	$-0.820687\pi$
$569$	−19.2204	+	11.0969i	−0.805763	+	0.465207i	0.0397194	+	0.999211i	$0.487354\pi$
$570$	4.61295	−	1.64324i	0.193215	−	0.0688277i
$571$	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
$576$	22.1426	+	9.25771i	0.922608	+	0.385738i
$577$	−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
$579$	−14.6114	+	17.4645i	−0.607230	+	0.725801i
$580$	2.76909	+	1.66067i	0.114980	+	0.0689557i
$581$	39.2375	+	24.3539i	1.62784	+	1.01037i
$582$	−16.7916	−	14.2872i	−0.696033	−	0.592222i
$583$	−0.747449	−	1.29462i	−0.0309562	−	0.0536177i
$584$	7.69472	+	4.70200i	0.318410	+	0.194570i
$585$	−3.78765	+	0.679185i	−0.156600	+	0.0280808i
$586$	−15.6310	−	9.19850i	−0.645709	−	0.379986i
$587$			0.369829i			0.0152645i	0.999971	+	0.00763224i	$0.00242944\pi$
$587$			0.369829i			0.0152645i	−0.999971	+	0.00763224i	$0.997571\pi$
$588$	17.0031	−	17.2886i	0.701196	−	0.712969i
$589$			21.3143i			0.878241i
$590$	−0.439563	+	0.746947i	−0.0180965	+	0.0307513i
$591$	−30.0489	−	5.25356i	−1.23605	−	0.216103i
$592$	−1.14552	+	34.4640i	−0.0470805	+	1.41646i
$593$	−4.89233	−	8.47376i	−0.200904	−	0.347976i	0.747916	−	0.663793i	$-0.231055\pi$
$593$	−4.89233	−	8.47376i	−0.200904	−	0.347976i	−0.948820	+	0.315818i	$0.897721\pi$
$594$	0.0435743	−	11.0018i	0.00178788	−	0.451408i
$595$	2.94981	+	1.83089i	0.120930	+	0.0750592i
$596$	−18.4942	+	30.8382i	−0.757553	+	1.26318i
$597$	−26.4895	−	22.1620i	−1.08414	−	0.907032i
$598$	−0.210828	+	25.3807i	−0.00862141	+	1.03789i
$599$	−31.2524	−	18.0436i	−1.27694	−	0.737240i	−0.300653	−	0.953734i	$-0.597205\pi$
$599$	−31.2524	−	18.0436i	−1.27694	−	0.737240i	−0.976284	+	0.216494i	$0.930538\pi$
$600$	15.6884	−	17.8297i	0.640478	−	0.727893i
$601$			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
$606$	12.3605	−	4.40308i	0.502109	−	0.178863i
$607$	−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
$609$	−12.6255	+	14.1486i	−0.511611	+	0.573331i
$610$	3.27328	−	1.85375i	0.132531	−	0.0750560i
$611$	8.25429	+	14.2968i	0.333933	+	0.578388i
$612$	−18.8669	−	7.16152i	−0.762648	−	0.289487i
$613$	−10.1968	−	5.88712i	−0.411844	−	0.237779i	0.279737	−	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	$-0.885246\pi$
$617$		−	17.5244i		−	0.705506i	0.935717	−	0.352753i	$-0.114754\pi$
$618$	3.93310	−	21.4447i	0.158212	−	0.862632i
$619$	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
$621$	−28.3655	+	0.123272i	−1.13827	+	0.00494674i
$622$	−1.00469	−	1.77405i	−0.0402844	−	0.0711328i
$623$	−13.4780	−	0.429940i	−0.539985	−	0.0172252i
$624$	15.1882	−	16.9748i	0.608015	−	0.679534i
$625$	−11.3700	−	19.6933i	−0.454798	−	0.787734i
$626$	0.283252	−	34.0994i	0.0113210	−	1.36289i
$627$	13.0890	+	2.28839i	0.522723	+	0.0913896i
$628$	10.1295	+	0.168297i	0.404213	+	0.00671577i
$629$		−	28.9950i		−	1.15611i
$630$	−2.68798	−	3.45747i	−0.107092	−	0.137749i
$631$	−7.24555			−0.288441			−0.144220	−	0.989546i	$-0.546067\pi$
$631$	−7.24555			−0.288441			−0.144220	+	0.989546i	$0.546067\pi$
$632$	−0.647729	−	1.18939i	−0.0257653	−	0.0473114i
$633$	4.33003	−	24.7666i	0.172103	−	0.984383i
$634$	−38.0937	−	0.316431i	−1.51289	−	0.0125671i
$635$	2.97867	−	1.71973i	0.118205	−	0.0682456i
$636$	3.39681	+	0.652208i	0.134692	+	0.0258617i
$637$	−10.2132	−	20.6234i	−0.404663	−	0.817127i
$638$	4.31755	+	7.62377i	0.170933	+	0.301828i
$639$	−14.5924	+	40.4567i	−0.577268	+	1.60044i
$640$	0.256511	−	4.40658i	0.0101395	−	0.174185i
$641$	11.9401	+	6.89362i	0.471606	+	0.272282i	0.716912	−	0.697164i	$-0.245555\pi$
$641$	11.9401	+	6.89362i	0.471606	+	0.272282i	−0.245306	+	0.969446i	$0.578888\pi$
$642$	−37.8384	−	6.93981i	−1.49336	−	0.273893i
$643$	20.7470			0.818184			0.409092	−	0.912493i	$-0.365846\pi$
$643$	20.7470			0.818184			0.409092	+	0.912493i	$0.365846\pi$
$644$	−25.6871	+	13.2133i	−1.01221	+	0.520678i
$645$	1.11223	+	3.04212i	0.0437942	+	0.119783i
$646$	12.3613	−	21.0055i	0.486349	−	0.826451i
$647$	−16.1242	+	27.9279i	−0.633907	+	1.09796i	0.352838	+	0.935684i	$0.385217\pi$
$647$	−16.1242	+	27.9279i	−0.633907	+	1.09796i	−0.986746	+	0.162275i	$0.948117\pi$
$648$	19.1838	+	16.7326i	0.753612	+	0.657320i
$649$	−2.03665	+	1.17586i	−0.0799454	+	0.0461565i
$650$	−11.1073	−	19.6129i	−0.435665	−	0.769280i
$651$	18.1025	−	5.97139i	0.709493	−	0.234037i
$652$	21.5374	+	12.9164i	0.843471	+	0.505844i
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	0.992389	−	0.123141i	$-0.0392966\pi$
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	−0.602838	+	0.797864i	$0.705963\pi$
$654$	−40.3878	+	14.3871i	−1.57929	+	0.562579i
$655$	0.982514	−	1.70176i	0.0383900	−	0.0664934i
$656$	23.5934	−	37.8990i	0.921168	−	1.47971i
$657$	6.16923	+	7.30909i	0.240684	+	0.285155i
$658$	−10.0403	+	15.8804i	−0.391413	+	0.619082i
$659$	11.4275			0.445153			0.222576	−	0.974915i	$-0.428553\pi$
$659$	11.4275			0.445153			0.222576	+	0.974915i	$0.428553\pi$
$660$	−1.91169	+	0.663146i	−0.0744124	+	0.0258129i
$661$	−2.31268	+	4.00568i	−0.0899529	+	0.155803i	−0.907491	−	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
$663$	−12.2898	+	14.6895i	−0.477295	+	0.570495i
$664$	−1.23013	+	49.3543i	−0.0477385	+	1.91532i
$665$	4.66261	−	2.49723i	0.180808	−	0.0968385i
$666$	−12.6951	+	34.3009i	−0.491923	+	1.32913i
$667$	19.5630	−	11.2947i	0.757483	−	0.437333i
$668$	−7.21660	−	12.9933i	−0.279218	−	0.502727i
$669$	−0.828955	+	4.74139i	−0.0320493	+	0.183313i
$670$	0.987048	−	1.67729i	0.0381330	−	0.0647992i
$671$	10.2073			0.394050
$672$	25.1393	+	6.32562i	0.969771	+	0.244016i
$673$	19.2606			0.742441			0.371220	−	0.928545i	$-0.378939\pi$
$673$	19.2606			0.742441			0.371220	+	0.928545i	$0.378939\pi$
$674$	−7.91821	+	13.4554i	−0.304998	+	0.518282i
$675$	21.7601	−	12.6896i	0.837546	−	0.488423i
$676$	2.12781	+	3.83108i	0.0818389	+	0.147349i
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.398630	−	0.917112i	$-0.369486\pi$
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.993557	+	0.113332i	$0.0361524\pi$
$678$	0.135467	+	0.115263i	0.00520259	+	0.00442665i
$679$	−20.2332	−	12.5583i	−0.776478	−	0.481945i
$680$	−0.0924795	+	3.71038i	−0.00354643	+	0.142287i
$681$	−21.5425	−	18.0232i	−0.825509	−	0.690649i
$682$	0.0731565	−	8.80698i	0.00280131	−	0.337237i
$683$	−6.73357	+	11.6629i	−0.257653	+	0.446268i	−0.965613	−	0.259985i	$-0.916282\pi$
$683$	−6.73357	+	11.6629i	−0.257653	+	0.446268i	0.707960	+	0.706253i	$0.249616\pi$
$684$	−23.8203	+	19.4372i	−0.910793	+	0.743199i
$685$	−2.85975			−0.109265
$686$	15.3792	−	21.2010i	0.587180	−	0.809456i
$687$	−12.2697	−	33.5595i	−0.468120	−	1.28037i
$688$	−16.2766	−	10.1328i	−0.620540	−	0.386308i
$689$	1.64135	−	2.84291i	0.0625305	−	0.108306i
$690$	1.75065	+	4.91449i	0.0666463	+	0.187091i
$691$	15.2232	+	26.3674i	0.579118	+	1.00306i	0.995581	+	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
$693$	−1.72342	−	11.7577i	−0.0654675	−	0.446639i
$694$	15.0948	+	26.6539i	0.572993	+	1.01177i
$695$	−5.32149	+	3.07236i	−0.201856	+	0.116541i
$696$	−19.8760	−	3.98776i	−0.753396	−	0.151156i
$697$	−18.7689	+	32.5087i	−0.710923	+	1.23135i
$698$	−4.63440	+	7.87522i	−0.175415	+	0.298081i
$699$	−3.38979	+	1.23935i	−0.128214	+	0.0468764i
$700$	13.8880	−	21.5674i	0.524917	−	0.815170i
$701$	37.2839			1.40819			0.704096	−	0.710105i	$-0.251353\pi$
$701$	37.2839			1.40819			0.704096	+	0.710105i	$0.251353\pi$
$702$	20.9703	−	11.9967i	0.791475	−	0.452788i
$703$	−38.2552	−	22.0866i	−1.44282	−	0.833013i
$704$	6.49797	−	10.0614i	0.244901	−	0.379204i
$705$	2.60251	+	2.17735i	0.0980163	+	0.0820038i
$706$	−20.8858	−	36.8793i	−0.786047	−	1.38797i
$707$	12.4935	−	6.69137i	0.469867	−	0.251655i
$708$	1.02603	−	5.34374i	0.0385605	−	0.200830i
$709$	−39.5076	+	22.8097i	−1.48374	+	0.856637i	−0.999829	−	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
$711$	−0.253540	−	1.41393i	−0.00950848	−	0.0530265i
$712$	−6.89465	−	12.6603i	−0.258388	−	0.474464i
$713$	−22.7076			−0.850406
$714$	−21.3034	−	4.61374i	−0.797259	−	0.172665i
$715$			1.92039i			0.0718186i
$716$	32.4669	+	0.539419i	1.21334	+	0.0201590i
$717$	−0.254077	+	1.45325i	−0.00948869	+	0.0542727i
$718$	0.128102	−	15.4217i	0.00478074	−	0.575531i
$719$	8.37315	+	14.5027i	0.312266	+	0.540860i	0.978853	−	0.204567i	$-0.0655787\pi$
$719$	8.37315	+	14.5027i	0.312266	+	0.540860i	−0.666587	+	0.745428i	$0.732245\pi$
$720$	1.73394	−	4.34887i	0.0646201	−	0.162073i
$721$	0.750825	−	23.5373i	0.0279622	−	0.876575i
$722$	−5.05671	−	8.92895i	−0.188191	−	0.332301i
$723$	−20.0053	−	16.7371i	−0.744003	−	0.622458i
$724$	6.01434	+	10.8287i	0.223521	+	0.402445i
$725$	−10.0301	+	17.3726i	−0.372508	+	0.645204i
$726$	21.1019	+	3.87023i	0.783164	+	0.143638i
$727$			14.7144i			0.545726i	0.962053	+	0.272863i	$0.0879705\pi$
$727$			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
$732$	−15.4536	+	17.8598i	−0.571182	+	0.660116i
$733$	−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
$735$	−3.42720	−	3.26039i	−0.126414	−	0.120261i
$736$	−26.0794	−	16.5375i	−0.961299	−	0.609580i
$737$	4.57334	−	2.64042i	0.168461	−	0.0972610i
$738$	36.4370	−	30.2399i	1.34126	−	1.11315i
$739$	1.92964	+	1.11408i	0.0709829	+	0.0409820i	0.535071	−	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	$0.0874914\pi$
$743$			14.7964i			0.542829i	−0.962463	+	0.271414i	$0.912509\pi$
$744$	15.2988	+	13.4615i	0.560882	+	0.493524i
$745$	6.07486	+	3.50732i	0.222566	+	0.128498i
$746$	−0.365239	+	43.9695i	−0.0133724	+	1.60984i
$747$	−17.7671	+	49.2582i	−0.650063	+	1.80226i
$748$	−5.17974	+	8.63696i	−0.189390	+	0.315799i
$749$	−41.5307	−	1.32480i	−1.51750	−	0.0484073i
$750$	−7.16774	−	6.09870i	−0.261729	−	0.222693i
$751$	18.2439	+	31.5994i	0.665729	+	1.15308i	0.979087	+	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
$753$	−3.52055	+	20.1366i	−0.128296	+	0.733817i
$754$	−9.75788	+	16.5815i	−0.355361	+	0.603863i
$755$		−	6.15772i		−	0.224103i
$756$	23.1817	+	14.7854i	0.843111	+	0.537740i
$757$		−	19.9557i		−	0.725302i	−0.931925	−	0.362651i	$-0.881872\pi$
$757$		−	19.9557i		−	0.725302i	0.931925	−	0.362651i	$-0.118128\pi$
$758$	21.5672	+	12.6918i	0.783355	+	0.460988i
$759$	−2.43798	+	13.9446i	−0.0884931	+	0.506156i
$760$	4.82492	+	2.94836i	0.175018	+	0.106948i
$761$	18.2013	+	31.5257i	0.659798	+	1.14280i	0.980668	+	0.195681i	$0.0626917\pi$
$761$	18.2013	+	31.5257i	0.659798	+	1.14280i	−0.320869	+	0.947124i	$0.603975\pi$
$762$	−13.9936	+	16.4465i	−0.506933	+	0.595794i
$763$	−40.8227	+	21.8641i	−1.47788	+	0.791533i
$764$	−14.4340	−	8.65630i	−0.522202	−	0.313174i
$765$	−1.33570	+	3.70315i	−0.0482923	+	0.133888i
$766$	49.4825	+	0.411034i	1.78787	+	0.0148513i
$767$	−4.47235	−	2.58211i	−0.161487	−	0.0932347i
$768$	7.76673	+	26.6022i	0.280258	+	0.959925i
$769$		−	33.7570i		−	1.21731i	−0.793436	−	0.608654i	$-0.791710\pi$
$769$		−	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	0.975124	−	0.221662i	$-0.0711481\pi$
$773$	35.3297	+	20.3976i	1.27072	+	0.733651i	0.295597	+	0.955313i	$0.404481\pi$
$774$	−12.9872	−	15.6487i	−0.466817	−	0.562482i
$775$	17.4635	−	10.0826i	0.627308	−	0.362176i
$776$	0.634331	−	25.4500i	0.0227711	−	0.913603i
$777$	−8.04094	+	38.6783i	−0.288467	+	1.38758i
$778$	−14.5545	−	25.6998i	−0.521804	−	0.921382i
$779$	28.5940	+	49.5263i	1.02449	+	1.77446i
$780$	−3.36011	−	2.90742i	−0.120311	−	0.104102i
$781$	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
$786$	−2.22559	+	12.1347i	−0.0793840	+	0.432831i
$787$	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
$789$	9.63037	+	8.05710i	0.342850	+	0.286840i
$790$	−0.229889	+	0.130192i	−0.00817908	+	0.00463204i
$791$	0.163233	+	0.101315i	0.00580389	+	0.00360236i
$792$	9.90917	−	7.94960i	0.352107	−	0.282477i
$793$	11.2073	+	19.4117i	0.397984	+	0.689329i
$794$	−6.91365	−	0.0574292i	−0.245356	−	0.00203809i
$795$	0.116204	−	0.664654i	0.00412133	−	0.0235729i
$796$	0.662504	−	39.8752i	0.0234818	−	1.41334i
$797$			9.90792i			0.350956i	0.984483	+	0.175478i	$0.0561472\pi$
$797$			9.90792i			0.350956i	−0.984483	+	0.175478i	$0.943853\pi$
$798$	−22.3149	+	24.5926i	−0.789937	+	0.870568i
$799$	16.8887			0.597481
$800$	27.3996	+	1.13862i	0.968721	+	0.0402563i
$801$	−2.69877	−	15.0503i	−0.0953562	−	0.531778i
$802$	0.0898434	−	10.8158i	0.00317248	−	0.381920i
$803$	4.13377	−	2.38664i	0.145878	−	0.0842225i
$804$	−2.30397	+	11.9995i	−0.0812548	+	0.423189i
$805$	2.66047	+	4.96740i	0.0937694	+	0.175078i
$806$	16.8289	−	9.53067i	0.592773	−	0.335704i
$807$	−4.53768	−	3.79638i	−0.159734	−	0.133639i
$808$	12.9284	+	7.90016i	0.454821	+	0.277927i
$809$	−14.3590	−	8.29016i	−0.504835	−	0.291466i	0.225873	−	0.974157i	$-0.427477\pi$
$809$	−14.3590	−	8.29016i	−0.504835	−	0.291466i	−0.730708	+	0.682690i	$0.760810\pi$
$810$	3.20150	−	3.79599i	0.112489	−	0.133377i
$811$	−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
$816$	−7.27010	−	22.1391i	−0.254505	−	0.775024i
$817$	21.2702	−	12.2804i	0.744151	−	0.429636i
$818$	9.47180	−	5.36414i	0.331174	−	0.187553i
$819$	20.4679	−	16.1871i	0.715205	−	0.565624i
$820$	−7.46857	−	4.47903i	−0.260814	−	0.156415i
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.797004	−	0.603973i	$-0.793583\pi$
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.124554	−	0.992213i	$-0.539750\pi$
$822$	16.9134	−	6.02495i	0.589923	−	0.210144i
$823$	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	$-0.631353\pi$
$827$	−23.0662			−0.802091			−0.401045	+	0.916058i	$0.631353\pi$
$828$	−20.7078	−	25.3774i	−0.719645	−	0.881927i
$829$	−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
$831$	16.4041	+	13.7243i	0.569053	+	0.476089i
$832$	26.2688	+	1.31029i	0.910706	+	0.0454261i
$833$	−23.4959	−	1.50053i	−0.814083	−	0.0519904i
$834$	25.0000	−	29.3822i	0.865678	−	1.01742i
$835$	−2.51093	+	1.44969i	−0.0868944	+	0.0501685i
$836$	7.44975	+	13.4131i	0.257655	+	0.463902i
$837$	10.8884	+	18.6713i	0.376357	+	0.645376i
$838$	−5.34133	−	3.14326i	−0.184513	−	0.108582i
$839$	48.3464			1.66910			0.834551	−	0.550931i	$-0.185727\pi$
$839$	48.3464			1.66910			0.834551	+	0.550931i	$0.185727\pi$
$840$	1.15233	−	4.92387i	0.0397592	−	0.169890i
$841$	−11.8768			−0.409546
$842$	14.5529	+	8.56405i	0.501525	+	0.295137i
$843$	−2.36121	+	13.5055i	−0.0813244	+	0.465153i
$844$	25.3799	−	14.0962i	0.873613	−	0.485212i
$845$	0.740348	−	0.427440i	0.0254688	−	0.0147044i
$846$	−19.9793	−	7.39450i	−0.686902	−	0.254228i
$847$	23.1610	+	0.738822i	0.795823	+	0.0253862i
$848$	1.88097	+	3.52329i	0.0645927	+	0.120990i
$849$	25.2408	−	30.1695i	0.866262	−	1.03541i
$850$	−23.0579	−	0.191534i	−0.790880	−	0.00656957i
$851$	23.5304	−	40.7559i	0.806612	−	1.39709i
$852$	−46.9186	+	16.2756i	−1.60740	+	0.557592i
$853$	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	−0.989153	−	0.146889i	$-0.953074\pi$
$857$	−10.7545	+	18.6273i	−0.367366	+	0.636297i	0.621786	+	0.783187i	$0.286407\pi$
$858$	−4.04590	−	11.3578i	−0.138125	−	0.387748i
$859$	−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
$861$	34.0524	−	38.1605i	1.16050	−	1.30050i
$862$	−0.836827	+	0.473918i	−0.0285025	+	0.0161417i
$863$	14.2150	−	8.20702i	0.483883	−	0.279370i	−0.238150	−	0.971228i	$-0.576541\pi$
$863$	14.2150	−	8.20702i	0.483883	−	0.279370i	0.722033	+	0.691858i	$0.243208\pi$
$864$	−1.09280	+	29.3736i	−0.0371779	+	0.999309i
$865$	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
$870$	−0.713394	+	3.88968i	−0.0241863	+	0.131873i
$871$	10.0428	+	5.79819i	0.340286	+	0.196464i
$872$	−42.2438	−	25.8138i	−1.43055	−	0.874166i
$873$	9.16175	−	25.4004i	0.310078	−	0.859675i
$874$	34.4219	−	19.4941i	1.16434	−	0.659398i
$875$	−8.63685	−	5.36073i	−0.291979	−	0.181226i
$876$	−2.08253	+	10.8462i	−0.0703621	+	0.366458i
$877$	−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
$879$	3.82552	−	21.8809i	0.129032	−	0.738025i
$880$	−1.98352	−	1.23481i	−0.0668644	−	0.0416254i
$881$	−42.1373			−1.41964			−0.709821	−	0.704382i	$-0.751224\pi$
$881$	−42.1373			−1.41964			−0.709821	+	0.704382i	$0.751224\pi$
$882$	27.1385	+	12.0625i	0.913800	+	0.406164i
$883$		−	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
$885$	−1.04561	−	0.182808i	−0.0351478	−	0.00614502i
$886$	8.54157	+	0.0709519i	0.286960	+	0.00238367i
$887$	3.93855	+	6.82176i	0.132243	+	0.229052i	0.924541	−	0.381082i	$-0.124449\pi$
$887$	3.93855	+	6.82176i	0.132243	+	0.229052i	−0.792298	+	0.610135i	$0.791115\pi$
$888$	−40.0141	+	13.5092i	−1.34278	+	0.453338i
$889$	−12.3003	+	19.8174i	−0.412538	+	0.664653i
$890$	−2.44702	+	1.38581i	−0.0820242	+	0.0464526i
$891$	12.6349	−	4.68183i	0.423287	−	0.156847i
$892$	−4.85881	+	2.69862i	−0.162685	+	0.0903566i
$893$	12.8648	−	22.2825i	0.430505	−	0.745656i
$894$	−43.3178	−	7.94477i	−1.44876	−	0.265713i
$895$		−	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
$900$	27.1935	+	10.3222i	0.906451	+	0.344073i
$901$	−1.67915	−	2.90837i	−0.0559406	−	0.0968919i
$902$	−11.6449	−	20.5622i	−0.387734	−	0.684646i
$903$	−16.3889	−	14.6246i	−0.545389	−	0.486677i
$904$	−0.00511751	+	0.205320i	−0.000170206	+	0.00682885i
$905$	2.09262	−	1.20818i	0.0695611	−	0.0401611i
$906$	12.9731	+	36.4186i	0.431004	+	1.20993i
$907$	−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	$-0.977190\pi$
$911$		−	4.32207i		−	0.143197i	0.997434	−	0.0715983i	$-0.0228100\pi$
$912$	−34.7476	−	7.27226i	−1.15061	−	0.240809i
$913$	22.6316	+	13.0664i	0.748996	+	0.432433i
$914$	17.6291	+	0.146439i	0.583119	+	0.00484377i
$915$	3.53359	+	2.95632i	0.116817	+	0.0977329i
$916$	21.2207	−	35.3845i	0.701152	−	1.16914i
$917$	−0.424862	+	13.3188i	−0.0140302	+	0.439826i
$918$	0.0978901	−	24.7156i	0.00323085	−	0.815735i
$919$	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
$921$	21.0921	+	3.68760i	0.695007	+	0.121511i
$922$	38.5405	+	22.6803i	1.26926	+	0.746935i
$923$			47.1321i			1.55137i
$924$	9.30481	−	10.0850i	0.306106	−	0.331771i
$925$			41.7916i			1.37410i
$926$	−16.8623	+	28.6541i	−0.554131	+	0.941632i
$927$	26.2831	−	4.71298i	0.863252	−	0.154795i
$928$	−10.8523	−	20.7405i	−0.356243	−	0.680841i
$929$	0.370626	+	0.641943i	0.0121598	+	0.0210615i	0.872041	−	0.489432i	$-0.162796\pi$
$929$	0.370626	+	0.641943i	0.0121598	+	0.0210615i	−0.859881	+	0.510494i	$0.829463\pi$
$930$	2.57607	−	3.02762i	0.0844725	−	0.0992797i
$931$	−19.8775	+	29.8567i	−0.651458	+	0.978515i
$932$	−3.57413	−	2.14347i	−0.117075	−	0.0702117i
$933$	1.60226	−	1.91513i	0.0524557	−	0.0626985i
$934$	−0.173137	+	20.8431i	−0.00566521	+	0.682008i
$935$	1.70141	+	0.982307i	0.0556419	+	0.0321249i
$936$	25.9980	+	10.1162i	0.849773	+	0.330660i
$937$			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	−0.00871528	−	0.999962i	$-0.502774\pi$
$941$	−26.9660	−	15.5688i	−0.879065	−	0.507529i	−0.870350	+	0.492433i	$0.836108\pi$
$942$	4.16367	+	11.6884i	0.135660	+	0.380828i
$943$	−52.7638	+	30.4632i	−1.71822	+	0.992017i
$944$	5.54271	−	2.95907i	0.180400	−	0.0963095i
$945$	2.80874	−	4.56946i	0.0913683	−	0.148644i
$946$	−8.83092	+	5.00119i	−0.287118	+	0.162603i
$947$	−11.6780	−	20.2270i	−0.379485	−	0.657288i	0.611502	−	0.791243i	$-0.290566\pi$
$947$	−11.6780	−	20.2270i	−0.379485	−	0.657288i	−0.990987	+	0.133955i	$0.957232\pi$
$948$	1.08534	−	1.25433i	0.0352502	−	0.0407387i
$949$	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	$-0.793136\pi$
$953$		−	37.3593i		−	1.21019i	0.796155	−	0.605093i	$-0.206864\pi$
$954$	0.713035	+	4.17578i	0.0230853	+	0.135196i
$955$	−1.64162	+	2.84336i	−0.0531215	+	0.0920091i
$956$	−1.48924	+	0.827137i	−0.0481655	+	0.0267515i
$957$	−6.88555	+	8.23006i	−0.222578	+	0.266040i
$958$	24.1177	+	42.5862i	0.779209	+	1.37590i
$959$	17.0955	−	9.15612i	0.552042	−	0.295667i
$960$	5.16353	−	1.60109i	0.166652	−	0.0516750i
$961$	−6.84861	−	11.8621i	−0.220923	−	0.382650i
$962$	−0.332937	+	40.0807i	−0.0107343	+	1.29225i
$963$	−8.31589	−	46.3757i	−0.267976	−	1.49443i
$964$	0.500332	−	30.1143i	0.0161146	−	0.969915i
$965$			5.12916i			0.165114i
$966$	−26.2002	−	23.7735i	−0.842977	−	0.764901i
$967$	−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
$969$	29.4045	+	5.14089i	0.944607	+	0.165149i
$970$	−4.96603	−	0.0412511i	−0.159450	−	0.00132449i
$971$	−14.3859	+	8.30570i	−0.461665	+	0.266543i	−0.712744	−	0.701424i	$-0.752548\pi$
$971$	−14.3859	+	8.30570i	−0.461665	+	0.266543i	0.251079	+	0.967967i	$0.419215\pi$
$972$	−10.9372	+	29.1955i	−0.350810	+	0.936447i
$973$	21.9748	−	35.4044i	0.704481	−	1.13501i
$974$	−16.7654	−	29.6037i	−0.537198	−	0.948563i
$975$	17.7137	−	21.1726i	0.567293	−	0.678066i
$976$	−27.2561	−	0.905939i	−0.872446	−	0.0289984i
$977$	0.641595	+	0.370425i	0.0205264	+	0.0118509i	0.510228	−	0.860039i	$-0.329561\pi$
$977$	0.641595	+	0.370425i	0.0205264	+	0.0118509i	−0.489702	+	0.871890i	$0.662894\pi$
$978$	−5.54863	+	30.2531i	−0.177426	+	0.967389i
$979$	−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	−0.772884	−	0.634547i	$-0.781187\pi$
$983$	5.11340	−	8.85666i	0.163092	−	0.282484i	0.935976	+	0.352064i	$0.114520\pi$
$984$	53.6078	+	10.7555i	1.70895	+	0.342872i
$985$	−5.95069	+	3.43563i	−0.189605	+	0.109468i
$986$	9.69941	+	17.1268i	0.308892	+	0.545430i
$987$	−22.5290	−	4.68361i	−0.717106	−	0.149081i
$988$	−17.3286	+	28.8947i	−0.551297	+	0.919262i
$989$	13.0831	+	22.6606i	0.416019	+	0.720567i
$990$	−1.58266	−	1.90700i	−0.0503004	−	0.0606085i
$991$	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
$996$	−57.1258	+	19.8164i	−1.81010	+	0.627906i
$997$	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
$999$	−44.7944	+	0.194670i	−1.41723	+	0.00615907i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.1	✓	48	21.5	even	6	inner
168.2.ba.c.5.9	yes	48	168.5	even	6	inner
168.2.ba.c.5.16	yes	48	56.5	odd	6	inner
168.2.ba.c.5.24	yes	48	7.5	odd	6	inner
168.2.ba.c.101.1	yes	48	8.5	even	2	inner
168.2.ba.c.101.9	yes	48	1.1	even	1	trivial
168.2.ba.c.101.16	yes	48	3.2	odd	2	inner
168.2.ba.c.101.24	yes	48	24.5	odd	2	inner
672.2.bi.c.17.2		48	8.3	odd	2
672.2.bi.c.17.6		48	12.11	even	2
672.2.bi.c.17.19		48	24.11	even	2
672.2.bi.c.17.23		48	4.3	odd	2
672.2.bi.c.593.2		48	84.47	odd	6
672.2.bi.c.593.6		48	56.19	even	6
672.2.bi.c.593.19		48	28.19	even	6
672.2.bi.c.593.23		48	168.131	odd	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} +(-1.70617 - 0.298296i) q^{3} +(-0.971089 - 1.74842i) q^{4} +(-0.337879 + 0.195075i) q^{5} +(1.58733 - 1.86558i) q^{6} +(1.39526 - 2.24795i) q^{7} +(2.82755 + 0.0704754i) q^{8} +(2.82204 + 1.01789i) q^{9} +(0.00458308 - 0.551736i) q^{10} +(0.748582 - 1.29658i) q^{11} +(1.13530 + 3.27278i) q^{12} +3.28768 q^{13} +(1.73911 + 3.31293i) q^{14} +(0.634670 - 0.232043i) q^{15} +(-2.11397 + 3.39575i) q^{16} +(1.68169 - 2.91278i) q^{17} +(-3.26476 + 2.70950i) q^{18} +(-2.56203 - 4.43756i) q^{19} +(0.669184 + 0.401321i) q^{20} +(-3.05110 + 3.41918i) q^{21} +(1.04339 + 1.84237i) q^{22} +(4.72764 - 2.72950i) q^{23} +(-4.80326 - 0.963690i) q^{24} +(-2.42389 + 4.19830i) q^{25} +(-2.35811 + 4.00712i) q^{26} +(-4.51125 - 2.57850i) q^{27} +(-5.28528 - 0.256545i) q^{28} +4.13801 q^{29} +(-0.172400 + 0.939988i) q^{30} +(-3.60237 - 2.07983i) q^{31} +(-2.62258 - 5.01219i) q^{32} +(-1.66397 + 1.98889i) q^{33} +(2.34398 + 4.13891i) q^{34} +(-0.0329110 + 1.03171i) q^{35} +(-0.960750 - 5.92258i) q^{36} +(7.46581 - 4.31038i) q^{37} +(7.24625 + 0.0601921i) q^{38} +(-5.60934 - 0.980702i) q^{39} +(-0.969118 + 0.527771i) q^{40} -11.1607 q^{41} +(-1.97898 - 6.17120i) q^{42} +4.79323i q^{43} +(-2.99391 - 0.0497422i) q^{44} +(-1.15207 + 0.206585i) q^{45} +(-0.0641268 + 7.71993i) q^{46} +(2.51067 + 4.34861i) q^{47} +(4.61974 - 5.16314i) q^{48} +(-3.10652 - 6.27292i) q^{49} +(-3.37846 - 5.96557i) q^{50} +(-3.73813 + 4.46806i) q^{51} +(-3.19263 - 5.74826i) q^{52} +(0.499243 - 0.864715i) q^{53} +(6.37846 - 3.64900i) q^{54} +0.584118i q^{55} +(4.10358 - 6.25784i) q^{56} +(3.04755 + 8.33548i) q^{57} +(-2.96801 + 5.04353i) q^{58} +(-1.36034 - 0.785391i) q^{59} +(-1.02203 - 0.884338i) q^{60} +(3.40889 + 5.90437i) q^{61} +(5.11878 - 2.89891i) q^{62} +(6.22563 - 4.92357i) q^{63} +(7.99007 + 0.398545i) q^{64} +(-1.11084 + 0.641343i) q^{65} +(-1.23062 - 3.45464i) q^{66} +(3.05467 + 1.76361i) q^{67} +(-6.72585 - 0.111746i) q^{68} +(-8.88036 + 3.24676i) q^{69} +(-1.23388 - 0.780115i) q^{70} +14.3360i q^{71} +(7.90772 + 3.07701i) q^{72} +(2.76107 + 1.59410i) q^{73} +(-0.101268 + 12.1912i) q^{74} +(5.38791 - 6.43999i) q^{75} +(-5.27078 + 8.78877i) q^{76} +(-1.87018 - 3.49184i) q^{77} +(5.21864 - 6.13342i) q^{78} +(-0.239413 - 0.414676i) q^{79} +(0.0518426 - 1.55974i) q^{80} +(6.92781 + 5.74504i) q^{81} +(8.00508 - 13.6030i) q^{82} +17.4548i q^{83} +(8.94106 + 2.01429i) q^{84} +1.31222i q^{85} +(-5.84213 - 3.43797i) q^{86} +(-7.06016 - 1.23435i) q^{87} +(2.20803 - 3.61339i) q^{88} +(-2.54840 - 4.41396i) q^{89} +(0.574539 - 1.55235i) q^{90} +(4.58716 - 7.39053i) q^{91} +(-9.36328 - 5.61532i) q^{92} +(5.52586 + 4.62312i) q^{93} +(-7.10101 - 0.0589856i) q^{94} +(1.73131 + 0.999573i) q^{95} +(2.97945 + 9.33396i) q^{96} -9.00074i q^{97} +(9.87379 + 0.712973i) q^{98} +(3.43230 - 2.89703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 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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