LMFDB - Embedded newform 770.2.l.c.727.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.3
Character	$\chi$	$=$	770.727
Dual form			770.2.l.c.573.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.903547 - 0.903547i) q^{3} +1.00000i q^{4} +(-1.41673 + 1.72999i) q^{5} +1.27781i q^{6} +(1.36406 - 2.26701i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.36720i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.903547 - 0.903547i) q^{3} +1.00000i q^{4} +(-1.41673 + 1.72999i) q^{5} +1.27781i q^{6} +(1.36406 - 2.26701i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.36720i q^{9} +(2.22507 - 0.221508i) q^{10} -1.00000 q^{11} +(0.903547 - 0.903547i) q^{12} +(4.51196 + 4.51196i) q^{13} +(-2.56755 + 0.638484i) q^{14} +(2.84321 - 0.283045i) q^{15} -1.00000 q^{16} +(-4.77930 + 4.77930i) q^{17} +(-0.966759 + 0.966759i) q^{18} +6.06268 q^{19} +(-1.72999 - 1.41673i) q^{20} +(-3.28084 + 0.815861i) q^{21} +(0.707107 + 0.707107i) q^{22} +(1.28935 - 1.28935i) q^{23} -1.27781 q^{24} +(-0.985742 - 4.90187i) q^{25} -6.38087i q^{26} +(-3.94598 + 3.94598i) q^{27} +(2.26701 + 1.36406i) q^{28} -7.55147i q^{29} +(-2.21060 - 1.81031i) q^{30} -7.78472i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.903547 + 0.903547i) q^{33} +6.75895 q^{34} +(1.98941 + 5.57156i) q^{35} +1.36720 q^{36} +(4.82324 + 4.82324i) q^{37} +(-4.28696 - 4.28696i) q^{38} -8.15354i q^{39} +(0.221508 + 2.22507i) q^{40} -5.27619i q^{41} +(2.89681 + 1.74301i) q^{42} +(6.22344 - 6.22344i) q^{43} -1.00000i q^{44} +(2.36525 + 1.93696i) q^{45} -1.82342 q^{46} +(4.65334 - 4.65334i) q^{47} +(0.903547 + 0.903547i) q^{48} +(-3.27869 - 6.18468i) q^{49} +(-2.76912 + 4.16317i) q^{50} +8.63665 q^{51} +(-4.51196 + 4.51196i) q^{52} +(4.24814 - 4.24814i) q^{53} +5.58045 q^{54} +(1.41673 - 1.72999i) q^{55} +(-0.638484 - 2.56755i) q^{56} +(-5.47792 - 5.47792i) q^{57} +(-5.33970 + 5.33970i) q^{58} +1.55180 q^{59} +(0.283045 + 2.84321i) q^{60} +0.913067i q^{61} +(-5.50463 + 5.50463i) q^{62} +(-3.09947 - 1.86495i) q^{63} -1.00000i q^{64} +(-14.1979 + 1.41342i) q^{65} -1.27781i q^{66} +(-8.57879 - 8.57879i) q^{67} +(-4.77930 - 4.77930i) q^{68} -2.32998 q^{69} +(2.53296 - 5.34641i) q^{70} +6.02338 q^{71} +(-0.966759 - 0.966759i) q^{72} +(-2.79071 - 2.79071i) q^{73} -6.82109i q^{74} +(-3.53841 + 5.31974i) q^{75} +6.06268i q^{76} +(-1.36406 + 2.26701i) q^{77} +(-5.76542 + 5.76542i) q^{78} +6.11533i q^{79} +(1.41673 - 1.72999i) q^{80} +3.02914 q^{81} +(-3.73083 + 3.73083i) q^{82} +(5.04120 + 5.04120i) q^{83} +(-0.815861 - 3.28084i) q^{84} +(-1.49716 - 15.0391i) q^{85} -8.80128 q^{86} +(-6.82312 + 6.82312i) q^{87} +(-0.707107 + 0.707107i) q^{88} +7.76249 q^{89} +(-0.302847 - 3.04212i) q^{90} +(16.3832 - 4.07409i) q^{91} +(1.28935 + 1.28935i) q^{92} +(-7.03386 + 7.03386i) q^{93} -6.58082 q^{94} +(-8.58919 + 10.4884i) q^{95} -1.27781i q^{96} +(-6.01682 + 6.01682i) q^{97} +(-2.05484 + 6.69161i) q^{98} +1.36720i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.903547	−	0.903547i	−0.521663	−	0.521663i	0.396410	−	0.918074i	$-0.370256\pi$
$3$	−0.903547	−	0.903547i	−0.521663	−	0.521663i	−0.918074	+	0.396410i	$0.870256\pi$
$4$			1.00000i			0.500000i
$5$	−1.41673	+	1.72999i	−0.633582	+	0.773676i
$5$	−1.41673	+	1.72999i	−0.633582	+	0.773676i
$6$			1.27781i			0.521663i
$7$	1.36406	−	2.26701i	0.515566	−	0.856850i
$7$	1.36406	−	2.26701i	0.515566	−	0.856850i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.36720i		−	0.455735i
$10$	2.22507	−	0.221508i	0.703629	−	0.0700470i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.903547	−	0.903547i	0.260832	−	0.260832i
$13$	4.51196	+	4.51196i	1.25139	+	1.25139i	0.955096	+	0.296296i	$0.0957514\pi$
$13$	4.51196	+	4.51196i	1.25139	+	1.25139i	0.296296	+	0.955096i	$0.404249\pi$
$14$	−2.56755	+	0.638484i	−0.686208	+	0.170642i
$15$	2.84321	−	0.283045i	0.734115	−	0.0730820i
$16$	−1.00000			−0.250000
$17$	−4.77930	+	4.77930i	−1.15915	+	1.15915i	−0.174492	+	0.984659i	$0.555828\pi$
$17$	−4.77930	+	4.77930i	−1.15915	+	1.15915i	−0.984659	+	0.174492i	$0.944172\pi$
$18$	−0.966759	+	0.966759i	−0.227867	+	0.227867i
$19$	6.06268			1.39087			0.695437	−	0.718587i	$-0.255211\pi$
$19$	6.06268			1.39087			0.695437	+	0.718587i	$0.255211\pi$
$20$	−1.72999	−	1.41673i	−0.386838	−	0.316791i
$21$	−3.28084	+	0.815861i	−0.715939	+	0.178035i
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	1.28935	−	1.28935i	0.268848	−	0.268848i	−0.559788	−	0.828636i	$-0.689117\pi$
$23$	1.28935	−	1.28935i	0.268848	−	0.268848i	0.828636	+	0.559788i	$0.189117\pi$
$24$	−1.27781			−0.260832
$25$	−0.985742	−	4.90187i	−0.197148	−	0.980374i
$26$		−	6.38087i		−	1.25139i
$27$	−3.94598	+	3.94598i	−0.759403	+	0.759403i
$28$	2.26701	+	1.36406i	0.428425	+	0.257783i
$29$		−	7.55147i		−	1.40227i	−0.713027	−	0.701137i	$-0.752676\pi$
$29$		−	7.55147i		−	1.40227i	0.713027	−	0.701137i	$-0.247324\pi$
$30$	−2.21060	−	1.81031i	−0.403598	−	0.330516i
$31$		−	7.78472i		−	1.39818i	−0.715036	−	0.699088i	$-0.753589\pi$
$31$		−	7.78472i		−	1.39818i	0.715036	−	0.699088i	$-0.246411\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.903547	+	0.903547i	0.157287	+	0.157287i
$34$	6.75895			1.15915
$35$	1.98941	+	5.57156i	0.336271	+	0.941765i
$36$	1.36720			0.227867
$37$	4.82324	+	4.82324i	0.792935	+	0.792935i	0.981970	−	0.189035i	$-0.0605360\pi$
$37$	4.82324	+	4.82324i	0.792935	+	0.792935i	−0.189035	+	0.981970i	$0.560536\pi$
$38$	−4.28696	−	4.28696i	−0.695437	−	0.695437i
$39$		−	8.15354i		−	1.30561i
$40$	0.221508	+	2.22507i	0.0350235	+	0.351814i
$41$		−	5.27619i		−	0.824003i	−0.911183	−	0.412001i	$-0.864830\pi$
$41$		−	5.27619i		−	0.824003i	0.911183	−	0.412001i	$-0.135170\pi$
$42$	2.89681	+	1.74301i	0.446987	+	0.268952i
$43$	6.22344	−	6.22344i	0.949066	−	0.949066i	−0.0496984	−	0.998764i	$-0.515826\pi$
$43$	6.22344	−	6.22344i	0.949066	−	0.949066i	0.998764	+	0.0496984i	$0.0158260\pi$
$44$		−	1.00000i		−	0.150756i
$45$	2.36525	+	1.93696i	0.352591	+	0.288745i
$46$	−1.82342			−0.268848
$47$	4.65334	−	4.65334i	0.678760	−	0.678760i	−0.280960	−	0.959720i	$-0.590653\pi$
$47$	4.65334	−	4.65334i	0.678760	−	0.678760i	0.959720	+	0.280960i	$0.0906527\pi$
$48$	0.903547	+	0.903547i	0.130416	+	0.130416i
$49$	−3.27869	−	6.18468i	−0.468384	−	0.883525i
$50$	−2.76912	+	4.16317i	−0.391613	+	0.588761i
$51$	8.63665			1.20937
$52$	−4.51196	+	4.51196i	−0.625696	+	0.625696i
$53$	4.24814	−	4.24814i	0.583527	−	0.583527i	−0.352344	−	0.935871i	$-0.614615\pi$
$53$	4.24814	−	4.24814i	0.583527	−	0.583527i	0.935871	+	0.352344i	$0.114615\pi$
$54$	5.58045			0.759403
$55$	1.41673	−	1.72999i	0.191032	−	0.233272i
$56$	−0.638484	−	2.56755i	−0.0853211	−	0.343104i
$57$	−5.47792	−	5.47792i	−0.725568	−	0.725568i
$58$	−5.33970	+	5.33970i	−0.701137	+	0.701137i
$59$	1.55180			0.202027			0.101013	−	0.994885i	$-0.467792\pi$
$59$	1.55180			0.202027			0.101013	+	0.994885i	$0.467792\pi$
$60$	0.283045	+	2.84321i	0.0365410	+	0.367057i
$61$			0.913067i			0.116906i	0.998290	+	0.0584531i	$0.0186168\pi$
$61$			0.913067i			0.116906i	−0.998290	+	0.0584531i	$0.981383\pi$
$62$	−5.50463	+	5.50463i	−0.699088	+	0.699088i
$63$	−3.09947	−	1.86495i	−0.390496	−	0.234961i
$64$		−	1.00000i		−	0.125000i
$65$	−14.1979	+	1.41342i	−1.76103	+	0.175313i
$66$		−	1.27781i		−	0.157287i
$67$	−8.57879	−	8.57879i	−1.04807	−	1.04807i	−0.998785	−	0.0492814i	$-0.984307\pi$
$67$	−8.57879	−	8.57879i	−1.04807	−	1.04807i	−0.0492814	−	0.998785i	$-0.515693\pi$
$68$	−4.77930	−	4.77930i	−0.579575	−	0.579575i
$69$	−2.32998			−0.280496
$70$	2.53296	−	5.34641i	0.302747	−	0.639018i
$71$	6.02338			0.714843			0.357422	−	0.933943i	$-0.383656\pi$
$71$	6.02338			0.714843			0.357422	+	0.933943i	$0.383656\pi$
$72$	−0.966759	−	0.966759i	−0.113934	−	0.113934i
$73$	−2.79071	−	2.79071i	−0.326627	−	0.326627i	0.524675	−	0.851303i	$-0.324187\pi$
$73$	−2.79071	−	2.79071i	−0.326627	−	0.326627i	−0.851303	+	0.524675i	$0.824187\pi$
$74$		−	6.82109i		−	0.792935i
$75$	−3.53841	+	5.31974i	−0.408580	+	0.614270i
$76$			6.06268i			0.695437i
$77$	−1.36406	+	2.26701i	−0.155449	+	0.258350i
$78$	−5.76542	+	5.76542i	−0.652805	+	0.652805i
$79$			6.11533i			0.688029i	0.938964	+	0.344014i	$0.111787\pi$
$79$			6.11533i			0.688029i	−0.938964	+	0.344014i	$0.888213\pi$
$80$	1.41673	−	1.72999i	0.158395	−	0.193419i
$81$	3.02914			0.336571
$82$	−3.73083	+	3.73083i	−0.412001	+	0.412001i
$83$	5.04120	+	5.04120i	0.553344	+	0.553344i	0.927404	−	0.374060i	$-0.122035\pi$
$83$	5.04120	+	5.04120i	0.553344	+	0.553344i	−0.374060	+	0.927404i	$0.622035\pi$
$84$	−0.815861	−	3.28084i	−0.0890177	−	0.357970i
$85$	−1.49716	−	15.0391i	−0.162390	−	1.63122i
$86$	−8.80128			−0.949066
$87$	−6.82312	+	6.82312i	−0.731515	+	0.731515i
$88$	−0.707107	+	0.707107i	−0.0753778	+	0.0753778i
$89$	7.76249			0.822822			0.411411	−	0.911450i	$-0.365036\pi$
$89$	7.76249			0.822822			0.411411	+	0.911450i	$0.365036\pi$
$90$	−0.302847	−	3.04212i	−0.0319229	−	0.320668i
$91$	16.3832	−	4.07409i	1.71743	−	0.427080i
$92$	1.28935	+	1.28935i	0.134424	+	0.134424i
$93$	−7.03386	+	7.03386i	−0.729377	+	0.729377i
$94$	−6.58082			−0.678760
$95$	−8.58919	+	10.4884i	−0.881233	+	1.07609i
$96$		−	1.27781i		−	0.130416i
$97$	−6.01682	+	6.01682i	−0.610916	+	0.610916i	−0.943185	−	0.332269i	$-0.892186\pi$
$97$	−6.01682	+	6.01682i	−0.610916	+	0.610916i	0.332269	+	0.943185i	$0.392186\pi$
$98$	−2.05484	+	6.69161i	−0.207571	+	0.675954i
$99$			1.36720i			0.137409i
$100$	4.90187	−	0.985742i	0.490187	−	0.0985742i
$101$		−	11.9147i		−	1.18555i	−0.805367	−	0.592777i	$-0.798032\pi$
$101$		−	11.9147i		−	1.18555i	0.805367	−	0.592777i	$-0.201968\pi$
$102$	−6.10703	−	6.10703i	−0.604686	−	0.604686i
$103$	4.70655	+	4.70655i	0.463750	+	0.463750i	0.899882	−	0.436133i	$-0.143652\pi$
$103$	4.70655	+	4.70655i	0.463750	+	0.463750i	−0.436133	+	0.899882i	$0.643652\pi$
$104$	6.38087			0.625696
$105$	3.23664	−	6.83169i	0.315864	−	0.666705i
$106$	−6.00777			−0.583527
$107$	−6.67198	−	6.67198i	−0.645005	−	0.645005i	0.306777	−	0.951782i	$-0.400750\pi$
$107$	−6.67198	−	6.67198i	−0.645005	−	0.645005i	−0.951782	+	0.306777i	$0.900750\pi$
$108$	−3.94598	−	3.94598i	−0.379702	−	0.379702i
$109$			4.01592i			0.384655i	0.981331	+	0.192328i	$0.0616037\pi$
$109$			4.01592i			0.384655i	−0.981331	+	0.192328i	$0.938396\pi$
$110$	−2.22507	+	0.221508i	−0.212152	+	0.0211200i
$111$		−	8.71604i		−	0.827290i
$112$	−1.36406	+	2.26701i	−0.128891	+	0.214213i
$113$	−2.80703	+	2.80703i	−0.264064	+	0.264064i	−0.826703	−	0.562639i	$-0.809786\pi$
$113$	−2.80703	+	2.80703i	−0.264064	+	0.264064i	0.562639	+	0.826703i	$0.309786\pi$
$114$			7.74695i			0.725568i
$115$	0.403902	+	4.05723i	0.0376640	+	0.378339i
$116$	7.55147			0.701137
$117$	6.16877	−	6.16877i	0.570303	−	0.570303i
$118$	−1.09729	−	1.09729i	−0.101013	−	0.101013i
$119$	4.31548	+	17.3540i	0.395600	+	1.59084i
$120$	1.81031	−	2.21060i	0.165258	−	0.201799i
$121$	1.00000			0.0909091
$122$	0.645636	−	0.645636i	0.0584531	−	0.0584531i
$123$	−4.76729	+	4.76729i	−0.429852	+	0.429852i
$124$	7.78472			0.699088
$125$	9.87672	+	5.23931i	0.883401	+	0.468618i
$126$	0.872938	+	3.51037i	0.0777675	+	0.312729i
$127$	6.14002	+	6.14002i	0.544839	+	0.544839i	0.924943	−	0.380105i	$-0.124112\pi$
$127$	6.14002	+	6.14002i	0.544839	+	0.544839i	−0.380105	+	0.924943i	$0.624112\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−11.2463			−0.990186
$130$	11.0389	+	9.03998i	0.968172	+	0.792859i
$131$			3.78268i			0.330495i	0.986252	+	0.165247i	$0.0528422\pi$
$131$			3.78268i			0.330495i	−0.986252	+	0.165247i	$0.947158\pi$
$132$	−0.903547	+	0.903547i	−0.0786437	+	0.0786437i
$133$	8.26985	−	13.7442i	0.717087	−	1.19177i
$134$			12.1322i			1.04807i
$135$	−1.23612	−	12.4169i	−0.106388	−	1.06868i
$136$			6.75895i			0.579575i
$137$	12.1143	+	12.1143i	1.03500	+	1.03500i	0.999365	+	0.0356308i	$0.0113440\pi$
$137$	12.1143	+	12.1143i	1.03500	+	1.03500i	0.0356308	+	0.999365i	$0.488656\pi$
$138$	1.64754	+	1.64754i	0.140248	+	0.140248i
$139$	11.2832			0.957027			0.478513	−	0.878080i	$-0.341176\pi$
$139$	11.2832			0.957027			0.478513	+	0.878080i	$0.341176\pi$
$140$	−5.57156	+	1.98941i	−0.470883	+	0.168136i
$141$	−8.40904			−0.708169
$142$	−4.25917	−	4.25917i	−0.357422	−	0.357422i
$143$	−4.51196	−	4.51196i	−0.377309	−	0.377309i
$144$			1.36720i			0.113934i
$145$	13.0640	+	10.6984i	1.08491	+	0.888455i
$146$			3.94665i			0.326627i
$147$	−2.62570	+	8.55060i	−0.216564	+	0.705241i
$148$	−4.82324	+	4.82324i	−0.396468	+	0.396468i
$149$		−	12.3218i		−	1.00944i	−0.863282	−	0.504721i	$-0.831595\pi$
$149$		−	12.3218i		−	1.00944i	0.863282	−	0.504721i	$-0.168405\pi$
$150$	6.26365	−	1.25959i	0.511425	−	0.102845i
$151$	−1.30380			−0.106101			−0.0530507	−	0.998592i	$-0.516894\pi$
$151$	−1.30380			−0.106101			−0.0530507	+	0.998592i	$0.516894\pi$
$152$	4.28696	−	4.28696i	0.347719	−	0.347719i
$153$	6.53428	+	6.53428i	0.528265	+	0.528265i
$154$	2.56755	−	0.638484i	0.206899	−	0.0514505i
$155$	13.4675	+	11.0289i	1.08174	+	0.885859i
$156$	8.15354			0.652805
$157$	−4.57812	+	4.57812i	−0.365374	+	0.365374i	−0.865787	−	0.500413i	$-0.833181\pi$
$157$	−4.57812	+	4.57812i	−0.365374	+	0.365374i	0.500413	+	0.865787i	$0.333181\pi$
$158$	4.32419	−	4.32419i	0.344014	−	0.344014i
$159$	−7.67679			−0.608809
$160$	−2.22507	+	0.221508i	−0.175907	+	0.0175118i
$161$	−1.16422	−	4.68172i	−0.0917536	−	0.368971i
$162$	−2.14193	−	2.14193i	−0.168286	−	0.168286i
$163$	7.74337	−	7.74337i	0.606508	−	0.606508i	−0.335524	−	0.942032i	$-0.608913\pi$
$163$	7.74337	−	7.74337i	0.606508	−	0.606508i	0.942032	+	0.335524i	$0.108913\pi$
$164$	5.27619			0.412001
$165$	−2.84321	+	0.283045i	−0.221344	+	0.0220350i
$166$		−	7.12934i		−	0.553344i
$167$	−2.03274	+	2.03274i	−0.157298	+	0.157298i	−0.781368	−	0.624070i	$-0.785478\pi$
$167$	−2.03274	+	2.03274i	−0.157298	+	0.157298i	0.624070	+	0.781368i	$0.285478\pi$
$168$	−1.74301	+	2.89681i	−0.134476	+	0.223494i
$169$			27.7155i			2.13196i
$170$	−9.57562	+	11.6929i	−0.734417	+	0.896807i
$171$		−	8.28892i		−	0.633870i
$172$	6.22344	+	6.22344i	0.474533	+	0.474533i
$173$	−12.5579	−	12.5579i	−0.954759	−	0.954759i	0.0442614	−	0.999020i	$-0.485907\pi$
$173$	−12.5579	−	12.5579i	−0.954759	−	0.954759i	−0.999020	+	0.0442614i	$0.985907\pi$
$174$	9.64934			0.731515
$175$	−12.4572	−	4.45175i	−0.941676	−	0.336520i
$176$	1.00000			0.0753778
$177$	−1.40212	−	1.40212i	−0.105390	−	0.105390i
$178$	−5.48891	−	5.48891i	−0.411411	−	0.411411i
$179$			15.0363i			1.12387i	0.827182	+	0.561934i	$0.189942\pi$
$179$			15.0363i			1.12387i	−0.827182	+	0.561934i	$0.810058\pi$
$180$	−1.93696	+	2.36525i	−0.144373	+	0.176295i
$181$		−	13.8733i		−	1.03119i	−0.856832	−	0.515596i	$-0.827570\pi$
$181$		−	13.8733i		−	1.03119i	0.856832	−	0.515596i	$-0.172430\pi$
$182$	−14.4655	−	8.70389i	−1.07226	−	0.645175i
$183$	0.824999	−	0.824999i	0.0609857	−	0.0609857i
$184$		−	1.82342i		−	0.134424i
$185$	−15.1774	+	1.51093i	−1.11586	+	0.111086i
$186$	9.94738			0.729377
$187$	4.77930	−	4.77930i	0.349497	−	0.349497i
$188$	4.65334	+	4.65334i	0.339380	+	0.339380i
$189$	3.56303	+	14.3281i	0.259172	+	1.04222i
$190$	13.4899	−	1.34293i	0.978659	−	0.0974267i
$191$	2.93911			0.212666			0.106333	−	0.994331i	$-0.466089\pi$
$191$	2.93911			0.212666			0.106333	+	0.994331i	$0.466089\pi$
$192$	−0.903547	+	0.903547i	−0.0652079	+	0.0652079i
$193$	11.5176	−	11.5176i	0.829053	−	0.829053i	−0.158333	−	0.987386i	$-0.550612\pi$
$193$	11.5176	−	11.5176i	0.829053	−	0.829053i	0.987386	+	0.158333i	$0.0506118\pi$
$194$	8.50907			0.610916
$195$	14.1056	+	11.5514i	1.01012	+	0.827211i
$196$	6.18468	−	3.27869i	0.441763	−	0.234192i
$197$	16.3524	+	16.3524i	1.16506	+	1.16506i	0.983352	+	0.181711i	$0.0581636\pi$
$197$	16.3524	+	16.3524i	1.16506	+	1.16506i	0.181711	+	0.983352i	$0.441836\pi$
$198$	0.966759	−	0.966759i	0.0687046	−	0.0687046i
$199$	−15.7021			−1.11309			−0.556547	−	0.830816i	$-0.687874\pi$
$199$	−15.7021			−1.11309			−0.556547	+	0.830816i	$0.687874\pi$
$200$	−4.16317	−	2.76912i	−0.294381	−	0.195806i
$201$			15.5027i			1.09348i
$202$	−8.42494	+	8.42494i	−0.592777	+	0.592777i
$203$	−17.1193	−	10.3007i	−1.20154	−	0.722964i
$204$			8.63665i			0.604686i
$205$	9.12777	+	7.47495i	0.637511	+	0.522073i
$206$		−	6.65606i		−	0.463750i
$207$	−1.76280	−	1.76280i	−0.122523	−	0.122523i
$208$	−4.51196	−	4.51196i	−0.312848	−	0.312848i
$209$	−6.06268			−0.419364
$210$	−7.11939	+	2.54208i	−0.491284	+	0.175420i
$211$	6.03962			0.415784			0.207892	−	0.978152i	$-0.433340\pi$
$211$	6.03962			0.415784			0.207892	+	0.978152i	$0.433340\pi$
$212$	4.24814	+	4.24814i	0.291763	+	0.291763i
$213$	−5.44241	−	5.44241i	−0.372908	−	0.372908i
$214$			9.43561i			0.645005i
$215$	1.94955	+	19.5834i	0.132959	+	1.33558i
$216$			5.58045i			0.379702i
$217$	−17.6480	−	10.6188i	−1.19803	−	0.720852i
$218$	2.83969	−	2.83969i	0.192328	−	0.192328i
$219$			5.04307i			0.340779i
$220$	1.72999	+	1.41673i	0.116636	+	0.0955160i
$221$	−43.1280			−2.90110
$222$	−6.16317	+	6.16317i	−0.413645	+	0.413645i
$223$	5.52624	+	5.52624i	0.370064	+	0.370064i	0.867501	−	0.497436i	$-0.165725\pi$
$223$	5.52624	+	5.52624i	0.370064	+	0.370064i	−0.497436	+	0.867501i	$0.665725\pi$
$224$	2.56755	−	0.638484i	0.171552	−	0.0426605i
$225$	−6.70185	+	1.34771i	−0.446790	+	0.0898474i
$226$	3.96975			0.264064
$227$	−8.48532	+	8.48532i	−0.563190	+	0.563190i	−0.930212	−	0.367022i	$-0.880377\pi$
$227$	−8.48532	+	8.48532i	−0.563190	+	0.563190i	0.367022	+	0.930212i	$0.380377\pi$
$228$	5.47792	−	5.47792i	0.362784	−	0.362784i
$229$	−15.3666			−1.01545			−0.507727	−	0.861518i	$-0.669514\pi$
$229$	−15.3666			−1.01545			−0.507727	+	0.861518i	$0.669514\pi$
$230$	2.58329	−	3.15450i	0.170337	−	0.208001i
$231$	3.28084	−	0.815861i	0.215864	−	0.0536797i
$232$	−5.33970	−	5.33970i	−0.350568	−	0.350568i
$233$	−8.25655	+	8.25655i	−0.540905	+	0.540905i	−0.923794	−	0.382889i	$-0.874929\pi$
$233$	−8.25655	+	8.25655i	−0.540905	+	0.540905i	0.382889	+	0.923794i	$0.374929\pi$
$234$	−8.72395			−0.570303
$235$	1.45771	+	14.6428i	0.0950903	+	0.955190i
$236$			1.55180i			0.101013i
$237$	5.52549	−	5.52549i	0.358919	−	0.358919i
$238$	9.21961	−	15.3226i	0.597618	−	0.993218i
$239$		−	16.8327i		−	1.08881i	−0.838821	−	0.544407i	$-0.816755\pi$
$239$		−	16.8327i		−	1.08881i	0.838821	−	0.544407i	$-0.183245\pi$
$240$	−2.84321	+	0.283045i	−0.183529	+	0.0182705i
$241$		−	18.0615i		−	1.16344i	−0.813388	−	0.581721i	$-0.802379\pi$
$241$		−	18.0615i		−	1.16344i	0.813388	−	0.581721i	$-0.197621\pi$
$242$	−0.707107	−	0.707107i	−0.0454545	−	0.0454545i
$243$	9.10095	+	9.10095i	0.583827	+	0.583827i
$244$	−0.913067			−0.0584531
$245$	15.3445	+	3.08992i	0.980321	+	0.197408i
$246$	6.74196			0.429852
$247$	27.3546	+	27.3546i	1.74053	+	1.74053i
$248$	−5.50463	−	5.50463i	−0.349544	−	0.349544i
$249$		−	9.10993i		−	0.577319i
$250$	−3.27915	−	10.6886i	−0.207392	−	0.676009i
$251$			8.99865i			0.567990i	0.958826	+	0.283995i	$0.0916599\pi$
$251$			8.99865i			0.567990i	−0.958826	+	0.283995i	$0.908340\pi$
$252$	1.86495	−	3.09947i	0.117481	−	0.195248i
$253$	−1.28935	+	1.28935i	−0.0810608	+	0.0810608i
$254$		−	8.68330i		−	0.544839i
$255$	−12.2358	+	14.9413i	−0.766237	+	0.935662i
$256$	1.00000			0.0625000
$257$	−6.62646	+	6.62646i	−0.413347	+	0.413347i	−0.882903	−	0.469556i	$-0.844414\pi$
$257$	−6.62646	+	6.62646i	−0.413347	+	0.413347i	0.469556	+	0.882903i	$0.344414\pi$
$258$	7.95237	+	7.95237i	0.495093	+	0.495093i
$259$	17.5135	−	4.35516i	1.08824	−	0.270616i
$260$	−1.41342	−	14.1979i	−0.0876563	−	0.880515i
$261$	−10.3244			−0.639065
$262$	2.67476	−	2.67476i	0.165247	−	0.165247i
$263$	−3.70702	+	3.70702i	−0.228585	+	0.228585i	−0.812101	−	0.583517i	$-0.801676\pi$
$263$	−3.70702	+	3.70702i	−0.228585	+	0.228585i	0.583517	+	0.812101i	$0.301676\pi$
$264$	1.27781			0.0786437
$265$	1.33077	+	13.3677i	0.0817486	+	0.821172i
$266$	−15.5663	+	3.87093i	−0.954429	+	0.237342i
$267$	−7.01378	−	7.01378i	−0.429236	−	0.429236i
$268$	8.57879	−	8.57879i	0.524033	−	0.524033i
$269$	0.172624			0.0105251			0.00526255	−	0.999986i	$-0.498325\pi$
$269$	0.172624			0.0105251			0.00526255	+	0.999986i	$0.498325\pi$
$270$	−7.90600	+	9.65414i	−0.481144	+	0.587532i
$271$			1.31360i			0.0797953i	0.999204	+	0.0398976i	$0.0127032\pi$
$271$			1.31360i			0.0797953i	−0.999204	+	0.0398976i	$0.987297\pi$
$272$	4.77930	−	4.77930i	0.289788	−	0.289788i
$273$	−18.4842	−	11.1219i	−1.11871	−	0.673128i
$274$		−	17.1322i		−	1.03500i
$275$	0.985742	+	4.90187i	0.0594425	+	0.295594i
$276$		−	2.32998i		−	0.140248i
$277$	6.74454	+	6.74454i	0.405240	+	0.405240i	0.880075	−	0.474835i	$-0.157492\pi$
$277$	6.74454	+	6.74454i	0.405240	+	0.405240i	−0.474835	+	0.880075i	$0.657492\pi$
$278$	−7.97841	−	7.97841i	−0.478513	−	0.478513i
$279$	−10.6433			−0.637197
$280$	5.34641	+	2.53296i	0.319509	+	0.151374i
$281$	0.293644			0.0175173			0.00875867	−	0.999962i	$-0.497212\pi$
$281$	0.293644			0.0175173			0.00875867	+	0.999962i	$0.497212\pi$
$282$	5.94609	+	5.94609i	0.354084	+	0.354084i
$283$	12.1941	+	12.1941i	0.724866	+	0.724866i	0.969592	−	0.244726i	$-0.0786980\pi$
$283$	12.1941	+	12.1941i	0.724866	+	0.724866i	−0.244726	+	0.969592i	$0.578698\pi$
$284$			6.02338i			0.357422i
$285$	17.2375	−	1.71601i	1.02106	−	0.101648i
$286$			6.38087i			0.377309i
$287$	−11.9612	−	7.19703i	−0.706047	−	0.424828i
$288$	0.966759	−	0.966759i	0.0569668	−	0.0569668i
$289$		−	28.6834i		−	1.68726i
$290$	−1.67271	−	16.8026i	−0.0982251	−	0.986680i
$291$	10.8730			0.637385
$292$	2.79071	−	2.79071i	0.163314	−	0.163314i
$293$	−16.5925	−	16.5925i	−0.969342	−	0.969342i	0.0302022	−	0.999544i	$-0.490385\pi$
$293$	−16.5925	−	16.5925i	−0.969342	−	0.969342i	−0.999544	+	0.0302022i	$0.990385\pi$
$294$	7.90283	−	4.18954i	0.460903	−	0.244339i
$295$	−2.19848	+	2.68460i	−0.128000	+	0.156303i
$296$	6.82109			0.396468
$297$	3.94598	−	3.94598i	0.228969	−	0.228969i
$298$	−8.71284	+	8.71284i	−0.504721	+	0.504721i
$299$	11.6350			0.672869
$300$	−5.31974	−	3.53841i	−0.307135	−	0.204290i
$301$	−5.61948	−	22.5978i	−0.323901	−	1.30251i
$302$	0.921922	+	0.921922i	0.0530507	+	0.0530507i
$303$	−10.7655	+	10.7655i	−0.618460	+	0.618460i
$304$	−6.06268			−0.347719
$305$	−1.57960	−	1.29357i	−0.0904475	−	0.0740696i
$306$		−	9.24086i		−	0.528265i
$307$	11.9789	−	11.9789i	0.683670	−	0.683670i	−0.277155	−	0.960825i	$-0.589392\pi$
$307$	11.9789	−	11.9789i	0.683670	−	0.683670i	0.960825	+	0.277155i	$0.0893915\pi$
$308$	−2.26701	−	1.36406i	−0.129175	−	0.0777245i
$309$		−	8.50517i		−	0.483842i
$310$	−1.72438	−	17.3215i	−0.0979381	−	0.983797i
$311$		−	2.03050i		−	0.115139i	−0.998342	−	0.0575695i	$-0.981665\pi$
$311$		−	2.03050i		−	0.115139i	0.998342	−	0.0575695i	$-0.0183351\pi$
$312$	−5.76542	−	5.76542i	−0.326403	−	0.326403i
$313$	−1.38288	−	1.38288i	−0.0781648	−	0.0781648i	0.666944	−	0.745108i	$-0.267602\pi$
$313$	−1.38288	−	1.38288i	−0.0781648	−	0.0781648i	−0.745108	+	0.666944i	$0.767602\pi$
$314$	6.47444			0.365374
$315$	7.61746	−	2.71992i	0.429195	−	0.153250i
$316$	−6.11533			−0.344014
$317$	−0.758491	−	0.758491i	−0.0426011	−	0.0426011i	0.685485	−	0.728086i	$-0.259590\pi$
$317$	−0.758491	−	0.758491i	−0.0426011	−	0.0426011i	−0.728086	+	0.685485i	$0.759590\pi$
$318$	5.42831	+	5.42831i	0.304404	+	0.304404i
$319$			7.55147i			0.422801i
$320$	1.72999	+	1.41673i	0.0967095	+	0.0791977i
$321$			12.0569i			0.672951i
$322$	−2.48725	+	4.13371i	−0.138609	+	0.230363i
$323$	−28.9754	+	28.9754i	−1.61223	+	1.61223i
$324$			3.02914i			0.168286i
$325$	17.6694	−	26.5647i	0.980122	−	1.47354i
$326$	−10.9508			−0.606508
$327$	3.62858	−	3.62858i	0.200661	−	0.200661i
$328$	−3.73083	−	3.73083i	−0.206001	−	0.206001i
$329$	−4.20175	−	16.8966i	−0.231650	−	0.931541i
$330$	2.21060	+	1.81031i	0.121689	+	0.0996544i
$331$	21.9453			1.20622			0.603111	−	0.797657i	$-0.293927\pi$
$331$	21.9453			1.20622			0.603111	+	0.797657i	$0.293927\pi$
$332$	−5.04120	+	5.04120i	−0.276672	+	0.276672i
$333$	6.59435	−	6.59435i	0.361368	−	0.361368i
$334$	2.87473			0.157298
$335$	26.9951	−	2.68739i	1.47490	−	0.146828i
$336$	3.28084	−	0.815861i	0.178985	−	0.0445089i
$337$	−24.9600	−	24.9600i	−1.35966	−	1.35966i	−0.874337	−	0.485320i	$-0.838703\pi$
$337$	−24.9600	−	24.9600i	−1.35966	−	1.35966i	−0.485320	−	0.874337i	$-0.661297\pi$
$338$	19.5978	−	19.5978i	1.06598	−	1.06598i
$339$	5.07258			0.275505
$340$	15.0391	−	1.49716i	0.815612	−	0.0811951i
$341$			7.78472i			0.421566i
$342$	−5.86115	+	5.86115i	−0.316935	+	0.316935i
$343$	−18.4931	−	1.00344i	−0.998531	−	0.0541806i
$344$		−	8.80128i		−	0.474533i
$345$	3.30095	−	4.03084i	0.177717	−	0.217013i
$346$			17.7595i			0.954759i
$347$	−2.67023	−	2.67023i	−0.143345	−	0.143345i	0.631792	−	0.775138i	$-0.282320\pi$
$347$	−2.67023	−	2.67023i	−0.143345	−	0.143345i	−0.775138	+	0.631792i	$0.782320\pi$
$348$	−6.82312	−	6.82312i	−0.365757	−	0.365757i
$349$	30.6454			1.64041			0.820205	−	0.572069i	$-0.193859\pi$
$349$	30.6454			1.64041			0.820205	+	0.572069i	$0.193859\pi$
$350$	5.66071	+	11.9564i	0.302578	+	0.639098i
$351$	−35.6082			−1.90062
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	23.8875	+	23.8875i	1.27140	+	1.27140i	0.945352	+	0.326051i	$0.105718\pi$
$353$	23.8875	+	23.8875i	1.27140	+	1.27140i	0.326051	+	0.945352i	$0.394282\pi$
$354$			1.98290i			0.105390i
$355$	−8.53351	+	10.4204i	−0.452912	+	0.553057i
$356$			7.76249i			0.411411i
$357$	11.7809	−	19.5794i	0.623511	−	1.03625i
$358$	10.6323	−	10.6323i	0.561934	−	0.561934i
$359$			13.4959i			0.712286i	0.934432	+	0.356143i	$0.115908\pi$
$359$			13.4959i			0.712286i	−0.934432	+	0.356143i	$0.884092\pi$
$360$	3.04212	−	0.302847i	0.160334	−	0.0159614i
$361$	17.7561			0.934532
$362$	−9.80989	+	9.80989i	−0.515596	+	0.515596i
$363$	−0.903547	−	0.903547i	−0.0474239	−	0.0474239i
$364$	4.07409	+	16.3832i	0.213540	+	0.858715i
$365$	8.78158	−	0.874216i	0.459649	−	0.0457586i
$366$	−1.16672			−0.0609857
$367$	−20.1156	+	20.1156i	−1.05003	+	1.05003i	−0.0513475	+	0.998681i	$0.516352\pi$
$367$	−20.1156	+	20.1156i	−1.05003	+	1.05003i	−0.998681	+	0.0513475i	$0.983648\pi$
$368$	−1.28935	+	1.28935i	−0.0672120	+	0.0672120i
$369$	−7.21363			−0.375526
$370$	11.8004	+	9.66365i	0.613475	+	0.502389i
$371$	−3.83587	−	15.4253i	−0.199148	−	0.800841i
$372$	−7.03386	−	7.03386i	−0.364689	−	0.364689i
$373$	−13.8116	+	13.8116i	−0.715137	+	0.715137i	−0.967605	−	0.252468i	$-0.918758\pi$
$373$	−13.8116	+	13.8116i	−0.715137	+	0.715137i	0.252468	+	0.967605i	$0.418758\pi$
$374$	−6.75895			−0.349497
$375$	−4.19013	−	13.6581i	−0.216377	−	0.705299i
$376$		−	6.58082i		−	0.339380i
$377$	34.0719	−	34.0719i	1.75479	−	1.75479i
$378$	7.61207	−	12.6510i	0.391522	−	0.650695i
$379$			5.38208i			0.276459i	0.990400	+	0.138229i	$0.0441411\pi$
$379$			5.38208i			0.276459i	−0.990400	+	0.138229i	$0.955859\pi$
$380$	−10.4884	−	8.58919i	−0.538043	−	0.440616i
$381$		−	11.0956i		−	0.568445i
$382$	−2.07826	−	2.07826i	−0.106333	−	0.106333i
$383$	15.2507	+	15.2507i	0.779273	+	0.779273i	0.979707	−	0.200434i	$-0.0642354\pi$
$383$	15.2507	+	15.2507i	0.779273	+	0.779273i	−0.200434	+	0.979707i	$0.564235\pi$
$384$	1.27781			0.0652079
$385$	−1.98941	−	5.57156i	−0.101390	−	0.283953i
$386$	−16.2883			−0.829053
$387$	−8.50871	−	8.50871i	−0.432522	−	0.432522i
$388$	−6.01682	−	6.01682i	−0.305458	−	0.305458i
$389$		−	0.769292i		−	0.0390047i	−0.999810	−	0.0195023i	$-0.993792\pi$
$389$		−	0.769292i		−	0.0390047i	0.999810	−	0.0195023i	$-0.00620818\pi$
$390$	−1.80608	−	18.1422i	−0.0914542	−	0.918665i
$391$			12.3244i			0.623271i
$392$	−6.69161	−	2.05484i	−0.337977	−	0.103785i
$393$	3.41783	−	3.41783i	0.172407	−	0.172407i
$394$		−	23.1258i		−	1.16506i
$395$	−10.5795	−	8.66379i	−0.532311	−	0.435922i
$396$	−1.36720			−0.0687046
$397$	−22.4072	+	22.4072i	−1.12459	+	1.12459i	−0.133543	+	0.991043i	$0.542636\pi$
$397$	−22.4072	+	22.4072i	−1.12459	+	1.12459i	−0.991043	+	0.133543i	$0.957364\pi$
$398$	11.1031	+	11.1031i	0.556547	+	0.556547i
$399$	−19.8907	+	4.94631i	−0.995781	+	0.247625i
$400$	0.985742	+	4.90187i	0.0492871	+	0.245093i
$401$	−4.50377			−0.224908			−0.112454	−	0.993657i	$-0.535871\pi$
$401$	−4.50377			−0.224908			−0.112454	+	0.993657i	$0.535871\pi$
$402$	10.9621	−	10.9621i	0.546738	−	0.546738i
$403$	35.1243	−	35.1243i	1.74967	−	1.74967i
$404$	11.9147			0.592777
$405$	−4.29148	+	5.24039i	−0.213245	+	0.260397i
$406$	4.82150	+	19.3888i	0.239287	+	0.962251i
$407$	−4.82324	−	4.82324i	−0.239079	−	0.239079i
$408$	6.10703	−	6.10703i	0.302343	−	0.302343i
$409$	−12.9747			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$409$	−12.9747			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$410$	−1.16872	−	11.7399i	−0.0577189	−	0.579792i
$411$		−	21.8917i		−	1.07984i
$412$	−4.70655	+	4.70655i	−0.231875	+	0.231875i
$413$	2.11674	−	3.51794i	0.104158	−	0.173107i
$414$			2.49298i			0.122523i
$415$	−15.8633	+	1.57921i	−0.778697	+	0.0775202i
$416$			6.38087i			0.312848i
$417$	−10.1949	−	10.1949i	−0.499246	−	0.499246i
$418$	4.28696	+	4.28696i	0.209682	+	0.209682i
$419$	−13.6879			−0.668696			−0.334348	−	0.942450i	$-0.608516\pi$
$419$	−13.6879			−0.668696			−0.334348	+	0.942450i	$0.608516\pi$
$420$	6.83169	+	3.23664i	0.333352	+	0.157932i
$421$	−28.2277			−1.37573			−0.687866	−	0.725838i	$-0.741452\pi$
$421$	−28.2277			−1.37573			−0.687866	+	0.725838i	$0.741452\pi$
$422$	−4.27065	−	4.27065i	−0.207892	−	0.207892i
$423$	−6.36207	−	6.36207i	−0.309334	−	0.309334i
$424$		−	6.00777i		−	0.291763i
$425$	28.1387	+	18.7163i	1.36493	+	0.907876i
$426$			7.69673i			0.372908i
$427$	2.06993	+	1.24548i	0.100171	+	0.0602728i
$428$	6.67198	−	6.67198i	0.322502	−	0.322502i
$429$			8.15354i			0.393656i
$430$	12.4690	−	15.2261i	0.601311	−	0.734269i
$431$	22.9860			1.10720			0.553598	−	0.832784i	$-0.313255\pi$
$431$	22.9860			1.10720			0.553598	+	0.832784i	$0.313255\pi$
$432$	3.94598	−	3.94598i	0.189851	−	0.189851i
$433$	−3.58733	−	3.58733i	−0.172396	−	0.172396i	0.615635	−	0.788031i	$-0.288899\pi$
$433$	−3.58733	−	3.58733i	−0.172396	−	0.172396i	−0.788031	+	0.615635i	$0.788899\pi$
$434$	4.97042	+	19.9877i	0.238588	+	0.959440i
$435$	−2.13741	−	21.4705i	−0.102481	−	1.02943i
$436$	−4.01592			−0.192328
$437$	7.81692	−	7.81692i	0.373934	−	0.373934i
$438$	3.56599	−	3.56599i	0.170390	−	0.170390i
$439$	−29.7935			−1.42197			−0.710984	−	0.703208i	$-0.751750\pi$
$439$	−29.7935			−1.42197			−0.710984	+	0.703208i	$0.751750\pi$
$440$	−0.221508	−	2.22507i	−0.0105600	−	0.106076i
$441$	−8.45571	+	4.48263i	−0.402653	+	0.213459i
$442$	30.4961	+	30.4961i	1.45055	+	1.45055i
$443$	20.7036	−	20.7036i	0.983659	−	0.983659i	−0.0162100	−	0.999869i	$-0.505160\pi$
$443$	20.7036	−	20.7036i	0.983659	−	0.983659i	0.999869	+	0.0162100i	$0.00516002\pi$
$444$	8.71604			0.413645
$445$	−10.9974	+	13.4290i	−0.521325	+	0.636598i
$446$		−	7.81528i		−	0.370064i
$447$	−11.1333	+	11.1333i	−0.526589	+	0.526589i
$448$	−2.26701	−	1.36406i	−0.107106	−	0.0644457i
$449$			22.6538i			1.06910i	0.845137	+	0.534550i	$0.179519\pi$
$449$			22.6538i			1.06910i	−0.845137	+	0.534550i	$0.820481\pi$
$450$	5.69190	+	3.78595i	0.268319	+	0.178471i
$451$			5.27619i			0.248446i
$452$	−2.80703	−	2.80703i	−0.132032	−	0.132032i
$453$	1.17804	+	1.17804i	0.0553492	+	0.0553492i
$454$	12.0001			0.563190
$455$	−16.1625	+	34.1148i	−0.757711	+	1.59932i
$456$	−7.74695			−0.362784
$457$	−13.4113	−	13.4113i	−0.627353	−	0.627353i	0.320048	−	0.947401i	$-0.396301\pi$
$457$	−13.4113	−	13.4113i	−0.627353	−	0.627353i	−0.947401	+	0.320048i	$0.896301\pi$
$458$	10.8658	+	10.8658i	0.507727	+	0.507727i
$459$		−	37.7180i		−	1.76053i
$460$	−4.05723	+	0.403902i	−0.189169	+	0.0188320i
$461$			21.3588i			0.994780i	0.867527	+	0.497390i	$0.165708\pi$
$461$			21.3588i			0.994780i	−0.867527	+	0.497390i	$0.834292\pi$
$462$	−2.89681	−	1.74301i	−0.134772	−	0.0810920i
$463$	17.8048	−	17.8048i	0.827459	−	0.827459i	−0.159705	−	0.987165i	$-0.551054\pi$
$463$	17.8048	−	17.8048i	0.827459	−	0.827459i	0.987165	+	0.159705i	$0.0510544\pi$
$464$			7.55147i			0.350568i
$465$	−2.20343	−	22.1336i	−0.102181	−	1.02642i
$466$	11.6765			0.540905
$467$	−5.93179	+	5.93179i	−0.274491	+	0.274491i	−0.830905	−	0.556414i	$-0.812177\pi$
$467$	−5.93179	+	5.93179i	−0.274491	+	0.274491i	0.556414	+	0.830905i	$0.312177\pi$
$468$	6.16877	+	6.16877i	0.285151	+	0.285151i
$469$	−31.1502	+	7.74625i	−1.43838	+	0.357689i
$470$	9.32326	−	11.3848i	0.430050	−	0.525140i
$471$	8.27309			0.381204
$472$	1.09729	−	1.09729i	0.0505067	−	0.0505067i
$473$	−6.22344	+	6.22344i	−0.286154	+	0.286154i
$474$	−7.81423			−0.358919
$475$	−5.97624	−	29.7185i	−0.274209	−	1.36358i
$476$	−17.3540	+	4.31548i	−0.795418	+	0.197800i
$477$	−5.80807	−	5.80807i	−0.265933	−	0.265933i
$478$	−11.9025	+	11.9025i	−0.544407	+	0.544407i
$479$	−20.3027			−0.927655			−0.463827	−	0.885926i	$-0.653524\pi$
$479$	−20.3027			−0.927655			−0.463827	+	0.885926i	$0.653524\pi$
$480$	2.21060	+	1.81031i	0.100900	+	0.0826291i
$481$			43.5245i			1.98455i
$482$	−12.7714	+	12.7714i	−0.581721	+	0.581721i
$483$	−3.17823	+	5.28209i	−0.144614	+	0.240343i
$484$			1.00000i			0.0454545i
$485$	−1.88483	−	18.9333i	−0.0855857	−	0.859716i
$486$		−	12.8707i		−	0.583827i
$487$	1.93767	+	1.93767i	0.0878042	+	0.0878042i	0.749645	−	0.661840i	$-0.230224\pi$
$487$	1.93767	+	1.93767i	0.0878042	+	0.0878042i	−0.661840	+	0.749645i	$0.730224\pi$
$488$	0.645636	+	0.645636i	0.0292265	+	0.0292265i
$489$	−13.9930			−0.632786
$490$	−8.66526	−	13.0351i	−0.391457	−	0.588865i
$491$	3.28230			0.148128			0.0740641	−	0.997253i	$-0.476403\pi$
$491$	3.28230			0.148128			0.0740641	+	0.997253i	$0.476403\pi$
$492$	−4.76729	−	4.76729i	−0.214926	−	0.214926i
$493$	36.0908	+	36.0908i	1.62545	+	1.62545i
$494$		−	38.6852i		−	1.74053i
$495$	−2.36525	−	1.93696i	−0.106310	−	0.0870599i
$496$			7.78472i			0.349544i
$497$	8.21624	−	13.6551i	0.368549	−	0.612514i
$498$	−6.44170	+	6.44170i	−0.288659	+	0.288659i
$499$		−	34.2199i		−	1.53189i	−0.642904	−	0.765946i	$-0.722271\pi$
$499$		−	34.2199i		−	1.53189i	0.642904	−	0.765946i	$-0.277729\pi$
$500$	−5.23931	+	9.87672i	−0.234309	+	0.441701i
$501$	3.67336			0.164114
$502$	6.36301	−	6.36301i	0.283995	−	0.283995i
$503$	−24.1925	−	24.1925i	−1.07869	−	1.07869i	−0.996627	−	0.0820631i	$-0.973849\pi$
$503$	−24.1925	−	24.1925i	−1.07869	−	1.07869i	−0.0820631	−	0.996627i	$-0.526151\pi$
$504$	−3.51037	+	0.872938i	−0.156364	+	0.0388838i
$505$	20.6123	+	16.8799i	0.917234	+	0.751145i
$506$	1.82342			0.0810608
$507$	25.0423	−	25.0423i	1.11217	−	1.11217i
$508$	−6.14002	+	6.14002i	−0.272419	+	0.272419i
$509$	15.1097			0.669726			0.334863	−	0.942267i	$-0.391310\pi$
$509$	15.1097			0.669726			0.334863	+	0.942267i	$0.391310\pi$
$510$	19.2171	−	1.91309i	0.850950	−	0.0847130i
$511$	−10.1333	+	2.51988i	−0.448269	+	0.111473i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−23.9232	+	23.9232i	−1.05623	+	1.05623i
$514$	9.37123			0.413347
$515$	−14.8102	+	1.47437i	−0.652615	+	0.0649686i
$516$		−	11.2463i		−	0.495093i
$517$	−4.65334	+	4.65334i	−0.204654	+	0.204654i
$518$	−15.4635	−	9.30436i	−0.679426	−	0.408810i
$519$			22.6933i			0.996125i
$520$	−9.03998	+	11.0389i	−0.396430	+	0.484086i
$521$			12.1371i			0.531734i	0.964010	+	0.265867i	$0.0856582\pi$
$521$			12.1371i			0.531734i	−0.964010	+	0.265867i	$0.914342\pi$
$522$	7.30046	+	7.30046i	0.319532	+	0.319532i
$523$	−0.478912	−	0.478912i	−0.0209414	−	0.0209414i	0.696559	−	0.717500i	$-0.254714\pi$
$523$	−0.478912	−	0.478912i	−0.0209414	−	0.0209414i	−0.717500	+	0.696559i	$0.754714\pi$
$524$	−3.78268			−0.165247
$525$	7.23331	+	15.2780i	0.315688	+	0.666788i
$526$	5.24252			0.228585
$527$	37.2055	+	37.2055i	1.62070	+	1.62070i
$528$	−0.903547	−	0.903547i	−0.0393219	−	0.0393219i
$529$			19.6752i			0.855441i
$530$	8.51140	−	10.3934i	0.369712	−	0.451460i
$531$		−	2.12162i		−	0.0920706i
$532$	13.7442	+	8.26985i	0.595885	+	0.358544i
$533$	23.8060	−	23.8060i	1.03115	−	1.03115i
$534$			9.91898i			0.429236i
$535$	20.9949	−	2.09006i	0.907688	−	0.0903614i
$536$	−12.1322			−0.524033
$537$	13.5860	−	13.5860i	0.586280	−	0.586280i
$538$	−0.122064	−	0.122064i	−0.00526255	−	0.00526255i
$539$	3.27869	+	6.18468i	0.141223	+	0.266393i
$540$	12.4169	−	1.23612i	0.534338	−	0.0531940i
$541$	29.2796			1.25883			0.629414	−	0.777070i	$-0.283295\pi$
$541$	29.2796			1.25883			0.629414	+	0.777070i	$0.283295\pi$
$542$	0.928853	−	0.928853i	0.0398976	−	0.0398976i
$543$	−12.5352	+	12.5352i	−0.537935	+	0.537935i
$544$	−6.75895			−0.289788
$545$	−6.94751	−	5.68948i	−0.297599	−	0.243711i
$546$	5.20591	+	20.9347i	0.222792	+	0.895920i
$547$	14.0735	+	14.0735i	0.601741	+	0.601741i	0.940774	−	0.339034i	$-0.110100\pi$
$547$	14.0735	+	14.0735i	0.601741	+	0.601741i	−0.339034	+	0.940774i	$0.610100\pi$
$548$	−12.1143	+	12.1143i	−0.517498	+	0.517498i
$549$	1.24835			0.0532782
$550$	2.76912	−	4.16317i	0.118076	−	0.177518i
$551$		−	45.7822i		−	1.95039i
$552$	−1.64754	+	1.64754i	−0.0701241	+	0.0701241i
$553$	13.8635	+	8.34168i	0.589538	+	0.354724i
$554$		−	9.53822i		−	0.405240i
$555$	15.0787	+	12.3483i	0.640055	+	0.524156i
$556$			11.2832i			0.478513i
$557$	−19.4265	−	19.4265i	−0.823129	−	0.823129i	0.163426	−	0.986556i	$-0.447745\pi$
$557$	−19.4265	−	19.4265i	−0.823129	−	0.823129i	−0.986556	+	0.163426i	$0.947745\pi$
$558$	7.52595	+	7.52595i	0.318599	+	0.318599i
$559$	56.1598			2.37531
$560$	−1.98941	−	5.57156i	−0.0840678	−	0.235441i
$561$	−8.63665			−0.364640
$562$	−0.207638	−	0.207638i	−0.00875867	−	0.00875867i
$563$	−19.1451	−	19.1451i	−0.806868	−	0.806868i	0.177291	−	0.984159i	$-0.443267\pi$
$563$	−19.1451	−	19.1451i	−0.806868	−	0.806868i	−0.984159	+	0.177291i	$0.943267\pi$
$564$		−	8.40904i		−	0.354084i
$565$	−0.879331	−	8.83296i	−0.0369938	−	0.371606i
$566$		−	17.2451i		−	0.724866i
$567$	4.13193	−	6.86710i	0.173525	−	0.288391i
$568$	4.25917	−	4.25917i	0.178711	−	0.178711i
$569$		−	42.5991i		−	1.78585i	−0.450209	−	0.892923i	$-0.648651\pi$
$569$		−	42.5991i		−	1.78585i	0.450209	−	0.892923i	$-0.351349\pi$
$570$	−13.4022	−	10.9754i	−0.561355	−	0.459707i
$571$	1.34853			0.0564343			0.0282172	−	0.999602i	$-0.491017\pi$
$571$	1.34853			0.0564343			0.0282172	+	0.999602i	$0.491017\pi$
$572$	4.51196	−	4.51196i	0.188654	−	0.188654i
$573$	−2.65562	−	2.65562i	−0.110940	−	0.110940i
$574$	3.36877	+	13.5469i	0.140610	+	0.565437i
$575$	−7.59119	−	5.04926i	−0.316575	−	0.210569i
$576$	−1.36720			−0.0569668
$577$	7.01450	−	7.01450i	0.292018	−	0.292018i	−0.545859	−	0.837877i	$-0.683797\pi$
$577$	7.01450	−	7.01450i	0.292018	−	0.292018i	0.837877	+	0.545859i	$0.183797\pi$
$578$	−20.2822	+	20.2822i	−0.843630	+	0.843630i
$579$	−20.8134			−0.864973
$580$	−10.6984	+	13.0640i	−0.444227	+	0.542453i
$581$	18.3050	−	4.55197i	0.759418	−	0.188848i
$582$	−7.68835	−	7.68835i	−0.318692	−	0.318692i
$583$	−4.24814	+	4.24814i	−0.175940	+	0.175940i
$584$	−3.94665			−0.163314
$585$	1.93243	+	19.4114i	0.0798960	+	0.802563i
$586$			23.4653i			0.969342i
$587$	13.2305	−	13.2305i	0.546080	−	0.546080i	−0.379225	−	0.925305i	$-0.623809\pi$
$587$	13.2305	−	13.2305i	0.546080	−	0.546080i	0.925305	+	0.379225i	$0.123809\pi$
$588$	−8.55060	−	2.62570i	−0.352621	−	0.108282i
$589$		−	47.1963i		−	1.94469i
$590$	3.45286	−	0.343736i	0.142152	−	0.0141514i
$591$		−	29.5504i		−	1.21554i
$592$	−4.82324	−	4.82324i	−0.198234	−	0.198234i
$593$	−25.2664	−	25.2664i	−1.03757	−	1.03757i	−0.999266	−	0.0382996i	$-0.987806\pi$
$593$	−25.2664	−	25.2664i	−1.03757	−	1.03757i	−0.0382996	−	0.999266i	$-0.512194\pi$
$594$	−5.58045			−0.228969
$595$	−36.1361	−	17.1202i	−1.48144	−	0.701859i
$596$	12.3218			0.504721
$597$	14.1876	+	14.1876i	0.580660	+	0.580660i
$598$	−8.22718	−	8.22718i	−0.336434	−	0.336434i
$599$			13.9693i			0.570770i	0.958413	+	0.285385i	$0.0921214\pi$
$599$			13.9693i			0.570770i	−0.958413	+	0.285385i	$0.907879\pi$
$600$	1.25959	+	6.26365i	0.0514226	+	0.255713i
$601$			29.7532i			1.21366i	0.794832	+	0.606830i	$0.207559\pi$
$601$			29.7532i			1.21366i	−0.794832	+	0.606830i	$0.792441\pi$
$602$	−12.0055	+	19.9526i	−0.489306	+	0.813207i
$603$	−11.7290	+	11.7290i	−0.477640	+	0.477640i
$604$		−	1.30380i		−	0.0530507i
$605$	−1.41673	+	1.72999i	−0.0575983	+	0.0703342i
$606$	15.2247			0.618460
$607$	−20.3342	+	20.3342i	−0.825339	+	0.825339i	−0.986868	−	0.161529i	$-0.948357\pi$
$607$	−20.3342	+	20.3342i	−0.825339	+	0.825339i	0.161529	+	0.986868i	$0.448357\pi$
$608$	4.28696	+	4.28696i	0.173859	+	0.173859i
$609$	6.16095	+	24.7752i	0.249654	+	1.00394i
$610$	0.202252	+	2.03164i	0.00818893	+	0.0822586i
$611$	41.9914			1.69879
$612$	−6.53428	+	6.53428i	−0.264133	+	0.264133i
$613$	−24.6878	+	24.6878i	−0.997132	+	0.997132i	−0.999996	−	0.00286351i	$-0.999089\pi$
$613$	−24.6878	+	24.6878i	−0.997132	+	0.997132i	0.00286351	+	0.999996i	$0.499089\pi$
$614$	−16.9407			−0.683670
$615$	−1.49340	−	15.0013i	−0.0602197	−	0.604912i
$616$	0.638484	+	2.56755i	0.0257253	+	0.103450i
$617$	27.4111	+	27.4111i	1.10353	+	1.10353i	0.993981	+	0.109550i	$0.0349409\pi$
$617$	27.4111	+	27.4111i	1.10353	+	1.10353i	0.109550	+	0.993981i	$0.465059\pi$
$618$	−6.01407	+	6.01407i	−0.241921	+	0.241921i
$619$	−24.9497			−1.00281			−0.501407	−	0.865211i	$-0.667184\pi$
$619$	−24.9497			−1.00281			−0.501407	+	0.865211i	$0.667184\pi$
$620$	−11.0289	+	13.4675i	−0.442929	+	0.540868i
$621$			10.1755i			0.408328i
$622$	−1.43578	+	1.43578i	−0.0575695	+	0.0575695i
$623$	10.5885	−	17.5977i	0.424219	−	0.705035i
$624$			8.15354i			0.326403i
$625$	−23.0566	+	9.66396i	−0.922265	+	0.386558i
$626$			1.95568i			0.0781648i
$627$	5.47792	+	5.47792i	0.218767	+	0.218767i
$628$	−4.57812	−	4.57812i	−0.182687	−	0.182687i
$629$	−46.1034			−1.83826
$630$	−7.30963	−	3.46308i	−0.291223	−	0.137972i
$631$	−36.9175			−1.46966			−0.734832	−	0.678249i	$-0.762739\pi$
$631$	−36.9175			−1.46966			−0.734832	+	0.678249i	$0.762739\pi$
$632$	4.32419	+	4.32419i	0.172007	+	0.172007i
$633$	−5.45708	−	5.45708i	−0.216899	−	0.216899i
$634$			1.07267i			0.0426011i
$635$	−19.3209	+	1.92342i	−0.766728	+	0.0763287i
$636$		−	7.67679i		−	0.304404i
$637$	13.1117	−	42.6983i	0.519504	−	1.69177i
$638$	5.33970	−	5.33970i	0.211401	−	0.211401i
$639$		−	8.23519i		−	0.325779i
$640$	−0.221508	−	2.22507i	−0.00875588	−	0.0879536i
$641$	22.1299			0.874078			0.437039	−	0.899443i	$-0.356027\pi$
$641$	22.1299			0.874078			0.437039	+	0.899443i	$0.356027\pi$
$642$	8.52552	−	8.52552i	0.336475	−	0.336475i
$643$	21.3104	+	21.3104i	0.840400	+	0.840400i	0.988911	−	0.148511i	$-0.0474481\pi$
$643$	21.3104	+	21.3104i	0.840400	+	0.840400i	−0.148511	+	0.988911i	$0.547448\pi$
$644$	4.68172	−	1.16422i	0.184486	−	0.0458768i
$645$	15.9331	−	19.4561i	0.627364	−	0.766083i
$646$	40.9774			1.61223
$647$	30.0056	−	30.0056i	1.17964	−	1.17964i	0.199806	−	0.979835i	$-0.435969\pi$
$647$	30.0056	−	30.0056i	1.17964	−	1.17964i	0.979835	−	0.199806i	$-0.0640312\pi$
$648$	2.14193	−	2.14193i	0.0841428	−	0.0841428i
$649$	−1.55180			−0.0609134
$650$	−31.2782	+	6.28990i	−1.22683	+	0.246710i
$651$	6.35125	+	25.5404i	0.248925	+	1.00101i
$652$	7.74337	+	7.74337i	0.303254	+	0.303254i
$653$	−19.0791	+	19.0791i	−0.746621	+	0.746621i	−0.973843	−	0.227222i	$-0.927036\pi$
$653$	−19.0791	+	19.0791i	−0.746621	+	0.746621i	0.227222	+	0.973843i	$0.427036\pi$
$654$	−5.13158			−0.200661
$655$	−6.54401	−	5.35905i	−0.255696	−	0.209395i
$656$			5.27619i			0.206001i
$657$	−3.81546	+	3.81546i	−0.148855	+	0.148855i
$658$	−8.97663	+	14.9188i	−0.349945	+	0.581596i
$659$			17.5265i			0.682737i	0.939930	+	0.341368i	$0.110890\pi$
$659$			17.5265i			0.682737i	−0.939930	+	0.341368i	$0.889110\pi$
$660$	−0.283045	−	2.84321i	−0.0110175	−	0.110672i
$661$			28.8634i			1.12265i	0.827594	+	0.561327i	$0.189709\pi$
$661$			28.8634i			1.12265i	−0.827594	+	0.561327i	$0.810291\pi$
$662$	−15.5177	−	15.5177i	−0.603111	−	0.603111i
$663$	38.9682	+	38.9682i	1.51340	+	1.51340i
$664$	7.12934			0.276672
$665$	12.0611	+	33.7786i	0.467711	+	1.30988i
$666$	−9.32581			−0.361368
$667$	−9.73650	−	9.73650i	−0.376999	−	0.376999i
$668$	−2.03274	−	2.03274i	−0.0786492	−	0.0786492i
$669$		−	9.98644i		−	0.386098i
$670$	−20.9887	−	17.1881i	−0.810864	−	0.664036i
$671$		−	0.913067i		−	0.0352485i
$672$	−2.89681	−	1.74301i	−0.111747	−	0.0672379i
$673$	−14.1089	+	14.1089i	−0.543860	+	0.543860i	−0.924658	−	0.380798i	$-0.875649\pi$
$673$	−14.1089	+	14.1089i	−0.543860	+	0.543860i	0.380798	+	0.924658i	$0.375649\pi$
$674$			35.2987i			1.35966i
$675$	23.2324	+	15.4529i	0.894214	+	0.594784i
$676$	−27.7155			−1.06598
$677$	−20.5043	+	20.5043i	−0.788044	+	0.788044i	−0.981173	−	0.193130i	$-0.938136\pi$
$677$	−20.5043	+	20.5043i	−0.788044	+	0.788044i	0.193130	+	0.981173i	$0.438136\pi$
$678$	−3.58685	−	3.58685i	−0.137752	−	0.137752i
$679$	5.43291	+	21.8475i	0.208496	+	0.838431i
$680$	−11.6929	−	9.57562i	−0.448403	−	0.367208i
$681$	15.3338			0.587592
$682$	5.50463	−	5.50463i	0.210783	−	0.210783i
$683$	21.7027	−	21.7027i	0.830432	−	0.830432i	−0.157144	−	0.987576i	$-0.550229\pi$
$683$	21.7027	−	21.7027i	0.830432	−	0.830432i	0.987576	+	0.157144i	$0.0502286\pi$
$684$	8.28892			0.316935
$685$	−38.1204	+	3.79493i	−1.45651	+	0.144997i
$686$	12.3670	+	13.7861i	0.472175	+	0.526356i
$687$	13.8845	+	13.8845i	0.529725	+	0.529725i
$688$	−6.22344	+	6.22344i	−0.237266	+	0.237266i
$689$	38.3348			1.46044
$690$	−5.18436	+	0.516109i	−0.197365	+	0.0196479i
$691$			32.1941i			1.22472i	0.790578	+	0.612361i	$0.209780\pi$
$691$			32.1941i			1.22472i	−0.790578	+	0.612361i	$0.790220\pi$
$692$	12.5579	−	12.5579i	0.477379	−	0.477379i
$693$	3.09947	+	1.86495i	0.117739	+	0.0708435i
$694$			3.77627i			0.143345i
$695$	−15.9852	+	19.5198i	−0.606355	+	0.740428i
$696$			9.64934i			0.365757i
$697$	25.2165	+	25.2165i	0.955143	+	0.955143i
$698$	−21.6696	−	21.6696i	−0.820205	−	0.820205i
$699$	14.9204			0.564341
$700$	4.45175	−	12.4572i	0.168260	−	0.470838i
$701$	39.8618			1.50556			0.752780	−	0.658272i	$-0.228712\pi$
$701$	39.8618			1.50556			0.752780	+	0.658272i	$0.228712\pi$
$702$	25.1788	+	25.1788i	0.950311	+	0.950311i
$703$	29.2417	+	29.2417i	1.10287	+	1.10287i
$704$			1.00000i			0.0376889i
$705$	11.9133	−	14.5476i	0.448683	−	0.547893i
$706$		−	33.7820i		−	1.27140i
$707$	−27.0107	−	16.2523i	−1.01584	−	0.611231i
$708$	1.40212	−	1.40212i	0.0526950	−	0.0526950i
$709$			4.80833i			0.180580i	0.995915	+	0.0902902i	$0.0287795\pi$
$709$			4.80833i			0.180580i	−0.995915	+	0.0902902i	$0.971221\pi$
$710$	13.4024	−	1.33423i	0.502984	−	0.0500727i
$711$	8.36091			0.313559
$712$	5.48891	−	5.48891i	0.205706	−	0.205706i
$713$	−10.0372	−	10.0372i	−0.375897	−	0.375897i
$714$	−22.1751	+	5.51437i	−0.829881	+	0.206370i
$715$	14.1979	−	1.41342i	0.530971	−	0.0528587i
$716$	−15.0363			−0.561934
$717$	−15.2091	+	15.2091i	−0.567994	+	0.567994i
$718$	9.54303	−	9.54303i	0.356143	−	0.356143i
$719$	27.6376			1.03071			0.515354	−	0.856977i	$-0.327660\pi$
$719$	27.6376			1.03071			0.515354	+	0.856977i	$0.327660\pi$
$720$	−2.36525	−	1.93696i	−0.0881477	−	0.0721863i
$721$	17.0898	−	4.24979i	0.636457	−	0.158270i
$722$	−12.5555	−	12.5555i	−0.467266	−	0.467266i
$723$	−16.3194	+	16.3194i	−0.606925	+	0.606925i
$724$	13.8733			0.515596
$725$	−37.0163	+	7.44381i	−1.37475	+	0.276456i
$726$			1.27781i			0.0474239i
$727$	15.6166	−	15.6166i	0.579186	−	0.579186i	−0.355493	−	0.934679i	$-0.615687\pi$
$727$	15.6166	−	15.6166i	0.579186	−	0.579186i	0.934679	+	0.355493i	$0.115687\pi$
$728$	8.70389	−	14.4655i	0.322587	−	0.536128i
$729$		−	25.5337i		−	0.945693i
$730$	−6.82768	−	5.59135i	−0.252704	−	0.206945i
$731$			59.4874i			2.20022i
$732$	0.824999	+	0.824999i	0.0304928	+	0.0304928i
$733$	−14.1369	−	14.1369i	−0.522157	−	0.522157i	0.396065	−	0.918222i	$-0.370375\pi$
$733$	−14.1369	−	14.1369i	−0.522157	−	0.522157i	−0.918222	+	0.396065i	$0.870375\pi$
$734$	28.4478			1.05003
$735$	−11.0726	−	16.6563i	−0.408417	−	0.614378i
$736$	1.82342			0.0672120
$737$	8.57879	+	8.57879i	0.316004	+	0.316004i
$738$	5.10081	+	5.10081i	0.187763	+	0.187763i
$739$		−	24.8828i		−	0.915329i	−0.889125	−	0.457665i	$-0.848686\pi$
$739$		−	24.8828i		−	0.915329i	0.889125	−	0.457665i	$-0.151314\pi$
$740$	−1.51093	−	15.1774i	−0.0555428	−	0.557932i
$741$		−	49.4323i		−	1.81594i
$742$	−8.19496	+	13.6197i	−0.300846	+	0.499995i
$743$	−14.7790	+	14.7790i	−0.542190	+	0.542190i	−0.924171	−	0.381980i	$-0.875242\pi$
$743$	−14.7790	+	14.7790i	−0.542190	+	0.542190i	0.381980	+	0.924171i	$0.375242\pi$
$744$			9.94738i			0.364689i
$745$	21.3166	+	17.4567i	0.780981	+	0.639564i
$746$	19.5325			0.715137
$747$	6.89235	−	6.89235i	0.252178	−	0.252178i
$748$	4.77930	+	4.77930i	0.174749	+	0.174749i
$749$	−24.2264	+	6.02449i	−0.885215	+	0.220130i
$750$	−6.69483	+	12.6206i	−0.244461	+	0.460838i
$751$	−43.4872			−1.58687			−0.793435	−	0.608655i	$-0.791709\pi$
$751$	−43.4872			−1.58687			−0.793435	+	0.608655i	$0.791709\pi$
$752$	−4.65334	+	4.65334i	−0.169690	+	0.169690i
$753$	8.13071	−	8.13071i	0.296299	−	0.296299i
$754$	−48.1850			−1.75479
$755$	1.84713	−	2.25555i	0.0672239	−	0.0820880i
$756$	−14.3281	+	3.56303i	−0.521109	+	0.129586i
$757$	24.1126	+	24.1126i	0.876386	+	0.876386i	0.993159	−	0.116773i	$-0.0372549\pi$
$757$	24.1126	+	24.1126i	0.876386	+	0.876386i	−0.116773	+	0.993159i	$0.537255\pi$
$758$	3.80570	−	3.80570i	0.138229	−	0.138229i
$759$	2.32998			0.0845729
$760$	1.34293	+	13.4899i	0.0487133	+	0.489330i
$761$			11.5097i			0.417226i	0.977998	+	0.208613i	$0.0668950\pi$
$761$			11.5097i			0.417226i	−0.977998	+	0.208613i	$0.933105\pi$
$762$	−7.84577	+	7.84577i	−0.284222	+	0.284222i
$763$	9.10414	+	5.47795i	0.329592	+	0.198315i
$764$			2.93911i			0.106333i
$765$	−20.5616	+	2.04693i	−0.743405	+	0.0740068i
$766$		−	21.5677i		−	0.779273i
$767$	7.00164	+	7.00164i	0.252815	+	0.252815i
$768$	−0.903547	−	0.903547i	−0.0326040	−	0.0326040i
$769$	−37.8720			−1.36570			−0.682849	−	0.730560i	$-0.739259\pi$
$769$	−37.8720			−1.36570			−0.682849	+	0.730560i	$0.739259\pi$
$770$	−2.53296	+	5.34641i	−0.0912817	+	0.192671i
$771$	11.9746			0.431256
$772$	11.5176	+	11.5176i	0.414527	+	0.414527i
$773$	2.36055	+	2.36055i	0.0849030	+	0.0849030i	0.748283	−	0.663380i	$-0.230879\pi$
$773$	2.36055	+	2.36055i	0.0849030	+	0.0849030i	−0.663380	+	0.748283i	$0.730879\pi$
$774$			12.0331i			0.432522i
$775$	−38.1597	+	7.67372i	−1.37074	+	0.275648i
$776$			8.50907i			0.305458i
$777$	−19.7594	−	11.8892i	−0.708864	−	0.426523i
$778$	−0.543972	+	0.543972i	−0.0195023	+	0.0195023i
$779$		−	31.9879i		−	1.14608i
$780$	−11.5514	+	14.1056i	−0.413606	+	0.505060i
$781$	−6.02338			−0.215533
$782$	8.71466	−	8.71466i	0.311635	−	0.311635i
$783$	29.7979	+	29.7979i	1.06489	+	1.06489i
$784$	3.27869	+	6.18468i	0.117096	+	0.220881i
$785$	−1.43414	−	14.4061i	−0.0511867	−	0.514175i
$786$	−4.83355			−0.172407
$787$	−13.6315	+	13.6315i	−0.485909	+	0.485909i	−0.907013	−	0.421104i	$-0.861643\pi$
$787$	−13.6315	+	13.6315i	−0.485909	+	0.485909i	0.421104	+	0.907013i	$0.361643\pi$
$788$	−16.3524	+	16.3524i	−0.582532	+	0.582532i
$789$	6.69894			0.238489
$790$	1.35460	+	13.6070i	0.0481944	+	0.484117i
$791$	2.53462	+	10.1925i	0.0901208	+	0.362405i
$792$	0.966759	+	0.966759i	0.0343523	+	0.0343523i
$793$	−4.11972	+	4.11972i	−0.146295	+	0.146295i
$794$	31.6886			1.12459
$795$	10.8759	−	13.2808i	0.385730	−	0.471021i
$796$		−	15.7021i		−	0.556547i
$797$	−1.99769	+	1.99769i	−0.0707619	+	0.0707619i	−0.741602	−	0.670840i	$-0.765934\pi$
$797$	−1.99769	+	1.99769i	−0.0707619	+	0.0707619i	0.670840	+	0.741602i	$0.265934\pi$
$798$	17.5624	+	10.5673i	0.621703	+	0.374078i
$799$			44.4795i			1.57357i
$800$	2.76912	−	4.16317i	0.0979031	−	0.147190i
$801$		−	10.6129i		−	0.374989i
$802$	3.18465	+	3.18465i	0.112454	+	0.112454i
$803$	2.79071	+	2.79071i	0.0984819	+	0.0984819i
$804$	−15.5027			−0.546738
$805$	9.74873	+	4.61865i	0.343598	+	0.162786i
$806$	−49.6733			−1.74967
$807$	−0.155974	−	0.155974i	−0.00549056	−	0.00549056i
$808$	−8.42494	−	8.42494i	−0.296388	−	0.296388i
$809$			15.6494i			0.550202i	0.961415	+	0.275101i	$0.0887114\pi$
$809$			15.6494i			0.550202i	−0.961415	+	0.275101i	$0.911289\pi$
$810$	6.74005	−	0.670980i	0.236821	−	0.0235758i
$811$		−	14.4469i		−	0.507300i	−0.967296	−	0.253650i	$-0.918369\pi$
$811$		−	14.4469i		−	0.507300i	0.967296	−	0.253650i	$-0.0816311\pi$
$812$	10.3007	−	17.1193i	0.361482	−	0.600769i
$813$	1.18690	−	1.18690i	0.0416263	−	0.0416263i
$814$			6.82109i			0.239079i
$815$	2.42569	+	24.3663i	0.0849682	+	0.853513i
$816$	−8.63665			−0.302343
$817$	37.7307	−	37.7307i	1.32003	−	1.32003i
$818$	9.17448	+	9.17448i	0.320778	+	0.320778i
$819$	−5.57011	−	22.3992i	−0.194635	−	0.782692i
$820$	−7.47495	+	9.12777i	−0.261036	+	0.318755i
$821$	−50.3895			−1.75861			−0.879303	−	0.476263i	$-0.841991\pi$
$821$	−50.3895			−1.75861			−0.879303	+	0.476263i	$0.841991\pi$
$822$	−15.4798	+	15.4798i	−0.539919	+	0.539919i
$823$	12.2979	−	12.2979i	0.428679	−	0.428679i	−0.459499	−	0.888178i	$-0.651971\pi$
$823$	12.2979	−	12.2979i	0.428679	−	0.428679i	0.888178	+	0.459499i	$0.151971\pi$
$824$	6.65606			0.231875
$825$	3.53841	−	5.31974i	0.123191	−	0.185209i
$826$	−3.98432	+	0.990798i	−0.138632	+	0.0344743i
$827$	7.54816	+	7.54816i	0.262475	+	0.262475i	0.826059	−	0.563584i	$-0.190578\pi$
$827$	7.54816	+	7.54816i	0.262475	+	0.262475i	−0.563584	+	0.826059i	$0.690578\pi$
$828$	1.76280	−	1.76280i	0.0612617	−	0.0612617i
$829$	13.1758			0.457616			0.228808	−	0.973472i	$-0.426517\pi$
$829$	13.1758			0.457616			0.228808	+	0.973472i	$0.426517\pi$
$830$	12.3337	+	10.1004i	0.428109	+	0.350589i
$831$		−	12.1880i		−	0.422798i
$832$	4.51196	−	4.51196i	0.156424	−	0.156424i
$833$	45.2283	+	13.8886i	1.56707	+	0.481211i
$834$			14.4177i			0.499246i
$835$	−0.636777	−	6.39648i	−0.0220366	−	0.221359i
$836$		−	6.06268i		−	0.209682i
$837$	30.7183	+	30.7183i	1.06178	+	1.06178i
$838$	9.67878	+	9.67878i	0.334348	+	0.334348i
$839$	−33.3835			−1.15253			−0.576263	−	0.817264i	$-0.695490\pi$
$839$	−33.3835			−1.15253			−0.576263	+	0.817264i	$0.695490\pi$
$840$	−2.54208	−	7.11939i	−0.0877102	−	0.245642i
$841$	−28.0248			−0.966371
$842$	19.9600	+	19.9600i	0.687866	+	0.687866i
$843$	−0.265322	−	0.265322i	−0.00913816	−	0.00913816i
$844$			6.03962i			0.207892i
$845$	−47.9476	−	39.2655i	−1.64945	−	1.35077i
$846$			8.99733i			0.309334i
$847$	1.36406	−	2.26701i	0.0468696	−	0.0778955i
$848$	−4.24814	+	4.24814i	−0.145882	+	0.145882i
$849$		−	22.0360i		−	0.756272i
$850$	−6.66258	−	33.1315i	−0.228525	−	1.13640i
$851$	12.4377			0.426358
$852$	5.44241	−	5.44241i	0.186454	−	0.186454i
$853$	−26.6354	−	26.6354i	−0.911979	−	0.911979i	0.0844490	−	0.996428i	$-0.473087\pi$
$853$	−26.6354	−	26.6354i	−0.911979	−	0.911979i	−0.996428	+	0.0844490i	$0.973087\pi$
$854$	−0.582979	−	2.34435i	−0.0199491	−	0.0802220i
$855$	14.3398	+	11.7432i	0.490410	+	0.401608i
$856$	−9.43561			−0.322502
$857$	11.3454	−	11.3454i	0.387552	−	0.387552i	−0.486261	−	0.873813i	$-0.661640\pi$
$857$	11.3454	−	11.3454i	0.387552	−	0.387552i	0.873813	+	0.486261i	$0.161640\pi$
$858$	5.76542	−	5.76542i	0.196828	−	0.196828i
$859$	46.6811			1.59274			0.796369	−	0.604811i	$-0.206752\pi$
$859$	46.6811			1.59274			0.796369	+	0.604811i	$0.206752\pi$
$860$	−19.5834	+	1.94955i	−0.667790	+	0.0664793i
$861$	4.30464	+	17.3104i	0.146702	+	0.589936i
$862$	−16.2535	−	16.2535i	−0.553598	−	0.553598i
$863$	−9.00736	+	9.00736i	−0.306614	+	0.306614i	−0.843595	−	0.536981i	$-0.819565\pi$
$863$	−9.00736	+	9.00736i	−0.306614	+	0.306614i	0.536981	+	0.843595i	$0.319565\pi$
$864$	−5.58045			−0.189851
$865$	39.5162	−	3.93388i	1.34359	−	0.133756i
$866$			5.07325i			0.172396i
$867$	−25.9168	+	25.9168i	−0.880182	+	0.880182i
$868$	10.6188	−	17.6480i	0.360426	−	0.599014i
$869$		−	6.11533i		−	0.207449i
$870$	−13.6705	+	16.6933i	−0.463474	+	0.565955i
$871$		−	77.4143i		−	2.62308i
$872$	2.83969	+	2.83969i	0.0961639	+	0.0961639i
$873$	8.22622	+	8.22622i	0.278416	+	0.278416i
$874$	−11.0548			−0.373934
$875$	25.3500	−	15.2439i	0.856987	−	0.515339i
$876$	−5.04307			−0.170390
$877$	7.42300	+	7.42300i	0.250657	+	0.250657i	0.821240	−	0.570583i	$-0.193283\pi$
$877$	7.42300	+	7.42300i	0.250657	+	0.250657i	−0.570583	+	0.821240i	$0.693283\pi$
$878$	21.0672	+	21.0672i	0.710984	+	0.710984i
$879$			29.9841i			1.01134i
$880$	−1.41673	+	1.72999i	−0.0477580	+	0.0583180i
$881$		−	10.2086i		−	0.343938i	−0.985102	−	0.171969i	$-0.944987\pi$
$881$		−	10.2086i		−	0.343938i	0.985102	−	0.171969i	$-0.0550129\pi$
$882$	9.14879	+	2.80939i	0.308056	+	0.0945971i
$883$	9.26344	−	9.26344i	0.311740	−	0.311740i	−0.533844	−	0.845583i	$-0.679253\pi$
$883$	9.26344	−	9.26344i	0.311740	−	0.311740i	0.845583	+	0.533844i	$0.179253\pi$
$884$		−	43.1280i		−	1.45055i
$885$	4.41209	−	0.439229i	0.148311	−	0.0147645i
$886$	−29.2793			−0.983659
$887$	32.3206	−	32.3206i	1.08522	−	1.08522i	0.0892072	−	0.996013i	$-0.471567\pi$
$887$	32.3206	−	32.3206i	1.08522	−	1.08522i	0.996013	−	0.0892072i	$-0.0284333\pi$
$888$	−6.16317	−	6.16317i	−0.206823	−	0.206823i
$889$	22.2949	−	5.54415i	0.747745	−	0.185945i
$890$	17.2721	−	1.71946i	0.578962	−	0.0576363i
$891$	−3.02914			−0.101480
$892$	−5.52624	+	5.52624i	−0.185032	+	0.185032i
$893$	28.2117	−	28.2117i	0.944070	−	0.944070i
$894$	15.7449			0.526589
$895$	−26.0127	−	21.3024i	−0.869509	−	0.712062i
$896$	0.638484	+	2.56755i	0.0213303	+	0.0857760i
$897$	−10.5128	−	10.5128i	−0.351011	−	0.351011i
$898$	16.0187	−	16.0187i	0.534550	−	0.534550i
$899$	−58.7861			−1.96063
$900$	−1.34771	−	6.70185i	−0.0449237	−	0.223395i
$901$			40.6063i			1.35279i
$902$	3.73083	−	3.73083i	0.124223	−	0.124223i
$903$	−15.3407	+	25.4956i	−0.510506	+	0.848441i
$904$			3.96975i			0.132032i
$905$	24.0007	+	19.6547i	0.797809	+	0.653345i
$906$		−	1.66600i		−	0.0553492i
$907$	−29.4475	−	29.4475i	−0.977789	−	0.977789i	0.0219699	−	0.999759i	$-0.493006\pi$
$907$	−29.4475	−	29.4475i	−0.977789	−	0.977789i	−0.999759	+	0.0219699i	$0.993006\pi$
$908$	−8.48532	−	8.48532i	−0.281595	−	0.281595i
$909$	−16.2898			−0.540298
$910$	35.5514	−	12.6941i	1.17852	−	0.420807i
$911$	−39.7846			−1.31812			−0.659062	−	0.752089i	$-0.729046\pi$
$911$	−39.7846			−1.31812			−0.659062	+	0.752089i	$0.729046\pi$
$912$	5.47792	+	5.47792i	0.181392	+	0.181392i
$913$	−5.04120	−	5.04120i	−0.166839	−	0.166839i
$914$			18.9664i			0.627353i
$915$	0.258439	+	2.59604i	0.00854373	+	0.0858226i
$916$		−	15.3666i		−	0.507727i
$917$	8.57539	+	5.15980i	0.283184	+	0.170392i
$918$	−26.6707	+	26.6707i	−0.880263	+	0.880263i
$919$		−	46.3097i		−	1.52762i	−0.645443	−	0.763808i	$-0.723327\pi$
$919$		−	46.3097i		−	1.52762i	0.645443	−	0.763808i	$-0.276673\pi$
$920$	3.15450	+	2.58329i	0.104001	+	0.0851686i
$921$	−21.6470			−0.713292
$922$	15.1030	−	15.1030i	0.497390	−	0.497390i
$923$	27.1772	+	27.1772i	0.894549	+	0.894549i
$924$	0.815861	+	3.28084i	0.0268399	+	0.107932i
$925$	18.8884	−	28.3973i	0.621047	−	0.933699i
$926$	−25.1798			−0.827459
$927$	6.43481	−	6.43481i	0.211347	−	0.211347i
$928$	5.33970	−	5.33970i	0.175284	−	0.175284i
$929$	−0.956653			−0.0313868			−0.0156934	−	0.999877i	$-0.504996\pi$
$929$	−0.956653			−0.0313868			−0.0156934	+	0.999877i	$0.504996\pi$
$930$	−14.0928	+	17.2089i	−0.462120	+	0.564302i
$931$	−19.8776	−	37.4957i	−0.651463	−	1.22887i
$932$	−8.25655	−	8.25655i	−0.270452	−	0.270452i
$933$	−1.83465	+	1.83465i	−0.0600638	+	0.0600638i
$934$	8.38882			0.274491
$935$	1.49716	+	15.0391i	0.0489625	+	0.491832i
$936$		−	8.72395i		−	0.285151i
$937$	−17.9858	+	17.9858i	−0.587571	+	0.587571i	−0.936973	−	0.349402i	$-0.886385\pi$
$937$	−17.9858	+	17.9858i	−0.587571	+	0.587571i	0.349402	+	0.936973i	$0.386385\pi$
$938$	27.5039	+	16.5491i	0.898036	+	0.540347i
$939$			2.49899i			0.0815514i
$940$	−14.6428	+	1.45771i	−0.477595	+	0.0475451i
$941$			43.0392i			1.40304i	0.712652	+	0.701518i	$0.247494\pi$
$941$			43.0392i			1.40304i	−0.712652	+	0.701518i	$0.752506\pi$
$942$	−5.84996	−	5.84996i	−0.190602	−	0.190602i
$943$	−6.80286	−	6.80286i	−0.221532	−	0.221532i
$944$	−1.55180			−0.0505067
$945$	−29.8354	−	14.1351i	−0.970545	−	0.459814i
$946$	8.80128			0.286154
$947$	−26.4283	−	26.4283i	−0.858806	−	0.858806i	0.132392	−	0.991197i	$-0.457734\pi$
$947$	−26.4283	−	26.4283i	−0.858806	−	0.858806i	−0.991197	+	0.132392i	$0.957734\pi$
$948$	5.52549	+	5.52549i	0.179460	+	0.179460i
$949$		−	25.1831i		−	0.817478i
$950$	−16.7883	+	25.2400i	−0.544684	+	0.818893i
$951$			1.37067i			0.0444469i
$952$	15.3226	+	9.21961i	0.496609	+	0.298809i
$953$	8.40083	−	8.40083i	0.272129	−	0.272129i	−0.557827	−	0.829957i	$-0.688365\pi$
$953$	8.40083	−	8.40083i	0.272129	−	0.272129i	0.829957	+	0.557827i	$0.188365\pi$
$954$			8.21385i			0.265933i
$955$	−4.16393	+	5.08463i	−0.134742	+	0.164535i
$956$	16.8327			0.544407
$957$	6.82312	−	6.82312i	0.220560	−	0.220560i
$958$	14.3562	+	14.3562i	0.463827	+	0.463827i
$959$	43.9879	−	10.9387i	1.42044	−	0.353228i
$960$	−0.283045	−	2.84321i	−0.00913524	−	0.0917643i
$961$	−29.6018			−0.954897
$962$	30.7765	−	30.7765i	0.992273	−	0.992273i
$963$	−9.12196	+	9.12196i	−0.293951	+	0.293951i
$964$	18.0615			0.581721
$965$	3.60799	+	36.2426i	0.116145	+	1.16669i
$966$	5.98235	−	1.48765i	0.192479	−	0.0478645i
$967$	−33.1683	−	33.1683i	−1.06662	−	1.06662i	−0.997616	−	0.0690054i	$-0.978017\pi$
$967$	−33.1683	−	33.1683i	−1.06662	−	1.06662i	−0.0690054	−	0.997616i	$-0.521983\pi$
$968$	0.707107	−	0.707107i	0.0227273	−	0.0227273i
$969$	52.3613			1.68209
$970$	−12.0551	+	14.7206i	−0.387065	+	0.472651i
$971$			13.3889i			0.429671i	0.976650	+	0.214836i	$0.0689216\pi$
$971$			13.3889i			0.429671i	−0.976650	+	0.214836i	$0.931078\pi$
$972$	−9.10095	+	9.10095i	−0.291913	+	0.291913i
$973$	15.3909	−	25.5791i	0.493410	−	0.820028i
$974$		−	2.74028i		−	0.0878042i
$975$	−39.9676	+	8.03729i	−1.27999	+	0.257399i
$976$		−	0.913067i		−	0.0292265i
$977$	11.4580	+	11.4580i	0.366574	+	0.366574i	0.866226	−	0.499652i	$-0.166539\pi$
$977$	11.4580	+	11.4580i	0.366574	+	0.366574i	−0.499652	+	0.866226i	$0.666539\pi$
$978$	9.89456	+	9.89456i	0.316393	+	0.316393i
$979$	−7.76249			−0.248090
$980$	−3.08992	+	15.3445i	−0.0987040	+	0.490161i
$981$	5.49058			0.175301
$982$	−2.32094	−	2.32094i	−0.0740641	−	0.0740641i
$983$	−24.6936	−	24.6936i	−0.787603	−	0.787603i	0.193498	−	0.981101i	$-0.438017\pi$
$983$	−24.6936	−	24.6936i	−0.787603	−	0.787603i	−0.981101	+	0.193498i	$0.938017\pi$
$984$			6.74196i			0.214926i
$985$	−51.4566	+	5.12256i	−1.63954	+	0.163218i
$986$		−	51.0400i		−	1.62545i
$987$	−11.4704	+	19.0634i	−0.365107	+	0.606794i
$988$	−27.3546	+	27.3546i	−0.870265	+	0.870265i
$989$		−	16.0484i		−	0.510309i
$990$	0.302847	+	3.04212i	0.00962510	+	0.0966850i
$991$	45.0226			1.43019			0.715096	−	0.699026i	$-0.246383\pi$
$991$	45.0226			1.43019			0.715096	+	0.699026i	$0.246383\pi$
$992$	5.50463	−	5.50463i	0.174772	−	0.174772i
$993$	−19.8286	−	19.8286i	−0.629242	−	0.629242i
$994$	−15.4654	+	3.84583i	−0.490531	+	0.121982i
$995$	22.2457	−	27.1645i	0.705236	−	0.861173i
$996$	9.10993			0.288659
$997$	−6.59782	+	6.59782i	−0.208955	+	0.208955i	−0.803823	−	0.594868i	$-0.797204\pi$
$997$	−6.59782	+	6.59782i	−0.208955	+	0.208955i	0.594868	+	0.803823i	$0.297204\pi$
$998$	−24.1971	+	24.1971i	−0.765946	+	0.765946i
$999$	−38.0647			−1.20432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.727.3	yes	40
5.3	odd	4	inner	770.2.l.c.573.8	yes	40
7.6	odd	2	inner	770.2.l.c.727.8	yes	40
35.13	even	4	inner	770.2.l.c.573.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.3	✓	40	35.13	even	4	inner
770.2.l.c.573.8	yes	40	5.3	odd	4	inner
770.2.l.c.727.3	yes	40	1.1	even	1	trivial
770.2.l.c.727.8	yes	40	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.903547 - 0.903547i) q^{3} +1.00000i q^{4} +(-1.41673 + 1.72999i) q^{5} +1.27781i q^{6} +(1.36406 - 2.26701i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.36720i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.903547 - 0.903547i) q^{3} +1.00000i q^{4} +(-1.41673 + 1.72999i) q^{5} +1.27781i q^{6} +(1.36406 - 2.26701i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.36720i q^{9} +(2.22507 - 0.221508i) q^{10} -1.00000 q^{11} +(0.903547 - 0.903547i) q^{12} +(4.51196 + 4.51196i) q^{13} +(-2.56755 + 0.638484i) q^{14} +(2.84321 - 0.283045i) q^{15} -1.00000 q^{16} +(-4.77930 + 4.77930i) q^{17} +(-0.966759 + 0.966759i) q^{18} +6.06268 q^{19} +(-1.72999 - 1.41673i) q^{20} +(-3.28084 + 0.815861i) q^{21} +(0.707107 + 0.707107i) q^{22} +(1.28935 - 1.28935i) q^{23} -1.27781 q^{24} +(-0.985742 - 4.90187i) q^{25} -6.38087i q^{26} +(-3.94598 + 3.94598i) q^{27} +(2.26701 + 1.36406i) q^{28} -7.55147i q^{29} +(-2.21060 - 1.81031i) q^{30} -7.78472i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.903547 + 0.903547i) q^{33} +6.75895 q^{34} +(1.98941 + 5.57156i) q^{35} +1.36720 q^{36} +(4.82324 + 4.82324i) q^{37} +(-4.28696 - 4.28696i) q^{38} -8.15354i q^{39} +(0.221508 + 2.22507i) q^{40} -5.27619i q^{41} +(2.89681 + 1.74301i) q^{42} +(6.22344 - 6.22344i) q^{43} -1.00000i q^{44} +(2.36525 + 1.93696i) q^{45} -1.82342 q^{46} +(4.65334 - 4.65334i) q^{47} +(0.903547 + 0.903547i) q^{48} +(-3.27869 - 6.18468i) q^{49} +(-2.76912 + 4.16317i) q^{50} +8.63665 q^{51} +(-4.51196 + 4.51196i) q^{52} +(4.24814 - 4.24814i) q^{53} +5.58045 q^{54} +(1.41673 - 1.72999i) q^{55} +(-0.638484 - 2.56755i) q^{56} +(-5.47792 - 5.47792i) q^{57} +(-5.33970 + 5.33970i) q^{58} +1.55180 q^{59} +(0.283045 + 2.84321i) q^{60} +0.913067i q^{61} +(-5.50463 + 5.50463i) q^{62} +(-3.09947 - 1.86495i) q^{63} -1.00000i q^{64} +(-14.1979 + 1.41342i) q^{65} -1.27781i q^{66} +(-8.57879 - 8.57879i) q^{67} +(-4.77930 - 4.77930i) q^{68} -2.32998 q^{69} +(2.53296 - 5.34641i) q^{70} +6.02338 q^{71} +(-0.966759 - 0.966759i) q^{72} +(-2.79071 - 2.79071i) q^{73} -6.82109i q^{74} +(-3.53841 + 5.31974i) q^{75} +6.06268i q^{76} +(-1.36406 + 2.26701i) q^{77} +(-5.76542 + 5.76542i) q^{78} +6.11533i q^{79} +(1.41673 - 1.72999i) q^{80} +3.02914 q^{81} +(-3.73083 + 3.73083i) q^{82} +(5.04120 + 5.04120i) q^{83} +(-0.815861 - 3.28084i) q^{84} +(-1.49716 - 15.0391i) q^{85} -8.80128 q^{86} +(-6.82312 + 6.82312i) q^{87} +(-0.707107 + 0.707107i) q^{88} +7.76249 q^{89} +(-0.302847 - 3.04212i) q^{90} +(16.3832 - 4.07409i) q^{91} +(1.28935 + 1.28935i) q^{92} +(-7.03386 + 7.03386i) q^{93} -6.58082 q^{94} +(-8.58919 + 10.4884i) q^{95} -1.27781i q^{96} +(-6.01682 + 6.01682i) q^{97} +(-2.05484 + 6.69161i) q^{98} +1.36720i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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